%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP209_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:11:59 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 51 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 158 ( 78 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 177 ( 76 ~; 72 |; 0 &)
% ( 20 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 187 ( 165 !; 0 ?; 187 :)
% Comments :
%------------------------------------------------------------------------------
tff(aa_a_a_type,type,
aa_a_a: ( fun_a_a * a ) > a ).
tff(b_type,type,
b: a ).
tff(aa_a_fun_a_a_type,type,
aa_a_fun_a_a: ( fun_a_fun_a_a * a ) > fun_a_a ).
tff(c_type,type,
c: a ).
tff(a2_type,type,
a2: a ).
tff(f_type,type,
f: fun_a_fun_a_a ).
tff(syntax_ac_operator_a_type,type,
syntax_ac_operator_a: fun_a_fun_a_a > $o ).
tff(1,plain,
^ [F: fun_a_fun_a_a,A: a,B: a] :
refl(( ( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) )
<=> ( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [F: fun_a_fun_a_a,A: a,B: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) )
<=> ! [F: fun_a_fun_a_a,A: a,B: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [F: fun_a_fun_a_a,A: a,B: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) )
<=> ! [F: fun_a_fun_a_a,A: a,B: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [F: fun_a_fun_a_a,A: a,B: a] :
rewrite(( ( syntax_ac_operator_a(F)
=> ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) )
<=> ( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [F: fun_a_fun_a_a,A: a,B: a] :
( syntax_ac_operator_a(F)
=> ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) )
<=> ! [F: fun_a_fun_a_a,A: a,B: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [F: fun_a_fun_a_a,A: a,B: a] :
( syntax_ac_operator_a(F)
=> ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_ac__operator_Ocommute) ).
tff(7,plain,
! [F: fun_a_fun_a_a,A: a,B: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [F: fun_a_fun_a_a,A: a,B: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [F: fun_a_fun_a_a,A: a,B: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [F: fun_a_fun_a_a,A: a,B: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( syntax_ac_operator_a(f)
<=> syntax_ac_operator_a(f) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
syntax_ac_operator_a(f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_ac__operator__axioms) ).
tff(13,plain,
syntax_ac_operator_a(f),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [F: fun_a_fun_a_a,A: a,B: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) )
| ~ syntax_ac_operator_a(f)
| ( aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b) ) )
<=> ( ~ ! [F: fun_a_fun_a_a,A: a,B: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) )
| ~ syntax_ac_operator_a(f)
| ( aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [F: fun_a_fun_a_a,A: a,B: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) )
| ~ syntax_ac_operator_a(f)
| ( aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [F: fun_a_fun_a_a,A: a,B: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),B) = aa_a_a(aa_a_fun_a_a(F,B),A) ) )
| ~ syntax_ac_operator_a(f)
| ( aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [F: fun_a_fun_a_a,A: a,B: a,C: a] :
refl(( ( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) )
<=> ( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) )
<=> ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) )
<=> ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [F: fun_a_fun_a_a,A: a,B: a,C: a] :
rewrite(( ( syntax_ac_operator_a(F)
=> ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) )
<=> ( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( syntax_ac_operator_a(F)
=> ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) )
<=> ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( syntax_ac_operator_a(F)
=> ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_ac__operator_Oleft__commute) ).
tff(24,plain,
! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) )
| ~ syntax_ac_operator_a(f)
| ( aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)) = aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)) ) )
<=> ( ~ ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) )
| ~ syntax_ac_operator_a(f)
| ( aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)) = aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) )
| ~ syntax_ac_operator_a(f)
| ( aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)) = aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,B),aa_a_a(aa_a_fun_a_a(F,A),C)) ) )
| ~ syntax_ac_operator_a(f)
| ( aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)) = aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)) = aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)),
inference(unit_resolution,[status(thm)],[30,13,27]) ).
tff(32,plain,
^ [F: fun_a_fun_a_a,A: a,B: a,C: a] :
refl(( ( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) )
<=> ( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) )
<=> ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) )
<=> ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [F: fun_a_fun_a_a,A: a,B: a,C: a] :
rewrite(( ( syntax_ac_operator_a(F)
=> ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) )
<=> ( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( syntax_ac_operator_a(F)
=> ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) )
<=> ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( syntax_ac_operator_a(F)
=> ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_ac__operator_Oleft__assoc) ).
tff(38,plain,
! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) )
| ~ syntax_ac_operator_a(f)
| ( aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) ) )
<=> ( ~ ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) )
| ~ syntax_ac_operator_a(f)
| ( aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) )
| ~ syntax_ac_operator_a(f)
| ( aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [F: fun_a_fun_a_a,A: a,B: a,C: a] :
( ~ syntax_ac_operator_a(F)
| ( aa_a_a(aa_a_fun_a_a(F,A),aa_a_a(aa_a_fun_a_a(F,B),C)) = aa_a_a(aa_a_fun_a_a(F,aa_a_a(aa_a_fun_a_a(F,A),B)),C) ) )
| ~ syntax_ac_operator_a(f)
| ( aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c),
inference(unit_resolution,[status(thm)],[44,13,41]) ).
tff(46,plain,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) = aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
inference(transitivity,[status(thm)],[46,31,17]) ).
tff(48,plain,
( ( aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b) )
<=> ( aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(50,plain,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
$false,
inference(unit_resolution,[status(thm)],[50,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP209_1 : TPTP v9.0.0. Released v8.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 18:30:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------