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+%------------------------------------------------------------------------------
+% File : SYN000_2 : TPTP v5.5.0. Bugfixed v5.5.1.
+% Domain : Syntactic
+% Problem : Advanced TPTP TF0 syntax without arithmetic
+% Version : Biased.
+% English : Advanced TPTP TF0 syntax that you will encounter some time.
+
+% Refs :
+% Source : [TPTP]
+% Names :
+
+% Status : Satisfiable
+% Rating : ? v5.5.1
+% Syntax : Number of formulae : 26 ( 18 unit; 7 type)
+% Number of atoms : 42 ( 2 equality)
+% Maximal formula depth : 5 ( 2 average)
+% Number of connectives : 6 ( 2 ~; 0 |; 1 &)
+% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
+% ( 1 ~|; 1 ~&)
+% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
+% Number of predicates : 14 ( 11 propositional; 0-2 arity)
+% Number of functors : 6 ( 4 constant; 0-2 arity)
+% Number of variables : 18 ( 0 sgn; 13 !; 1 ?)
+% Maximal term depth : 2 ( 1 average)
+% SPC : TF0_SAT_EQU_NAR
+
+% Comments :
+% Bugfixes : v5.5.1 - Fixed let_binders.
+%------------------------------------------------------------------------------
+%----Quoted symbols
+tff(distinct_object,axiom,(
+ "An Apple" != "A \"Microsoft \\ escape\"" )).
+
+%----Types for stuff below
+tff(a_type,type,(
+ a: $i )).
+
+tff(b_type,type,(
+ b: $i )).
+
+tff(f_type,type,(
+ f: $i > $i )).
+
+tff(g_type,type,(
+ g: ( $i * $i ) > $i )).
+
+tff(h_type,type,(
+ h: ( $i * $i * $i ) > $i )).
+
+tff(p_type,type,(
+ p: $i > $o )).
+
+tff(q_type,type,(
+ q: ( $i * $i ) > $o )).
+
+%----Conditional constructs
+tff(conditionals,axiom,(
+ ! [Z: $i] :
+ $ite_f(
+ ? [X: $i] : p(X)
+ , ! [X: $i] : q(X,X)
+ , q(Z,$ite_t(! [X: $i] : p(X), f(a), f(Z))) ) )).
+
+%----Let binders
+tff(let_binders,axiom,(
+ ! [X: $i] :
+ $let_ff(
+ ! [Y1: $i,Y2: $i] :
+ ( q(Y1,Y2)
+ <=> p(Y1) )
+ , ( q($let_tt(! [Z1: $i] : f(Z1) = g(Z1,b), f(a)),X)
+ & p($let_ft(! [Y3: $i] : ! [Y4: $i] : ( q(Y3,Y4) <=> $ite_f(Y3 = Y4, q(a,a), q(Y3,Y4) ) ), $ite_t(q(b,b), f(a), f(X)))) ) ) )).
+
+%----Rare connectives
+tff(never_used_connectives,axiom,(
+ ! [X: $i] :
+ ( ( p(X)
+ ~| ~ q(X,a) )
+ ~& p(X) ) )).
+
+%----Roles
+tff(role_definition,definition,(
+ ! [X: $i] : f(a) = f(X) )).
+
+tff(role_assumption,assumption,(
+ p(a) )).
+
+tff(role_lemma,lemma,(
+ p(a) )).
+
+tff(role_theorem,theorem,(
+ p(a) )).
+
+tff(role_unknown,unknown,(
+ p(a) )).
+
+%----Selective include directive
+include('Axioms/SYN000_0.ax',[ia1,ia3]).
+
+%----Source
+tff(source_unknown,axiom,(
+ ! [X: $i] : p(X) ),
+ unknown).
+
+tff(source,axiom,(
+ ! [X: $i] : p(X) ),
+ file('SYN000-1.p')).
+
+tff(source_name,axiom,(
+ ! [X: $i] : p(X) ),
+ file('SYN000-1.p',source_unknown)).
+
+tff(source_copy,axiom,(
+ ! [X: $i] : p(X) ),
+ source_unknown).
+
+tff(source_introduced_assumption,axiom,(
+ ! [X: $i] : p(X) ),
+ introduced(assumption,[from,the,world])).
+
+tff(source_inference,plain,(
+ p(a) ),
+ inference(magic,[status(thm),assumptions([source_introduced_assumption])],[theory(equality),source_unknown])).
+
+tff(source_inference_with_bind,plain,(
+ p(a) ),
+ inference(magic,[status(thm)],[theory(equality),source_unknown:[bind(X,$fot(a))]])).
+
+%----Useful info
+tff(useful_info,axiom,(
+ ! [X: $i] : p(X) ),
+ unknown,
+ [simple,prolog(like,Data,[nested,12.2]),AVariable,12.2,"A distinct object",$tff(p(X) | ~ q(X,a)),data(name):[colon,list,2],[simple,prolog(like,Data,[nested,12.2]),AVariable,12.2]]).
+
+%------------------------------------------------------------------------------
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