%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ITP004+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:44:02 PM UTC 2026
% Result : Theorem 96.17s 13.84s
% Output : Proof 96.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 12
% Syntax : Number of formulae : 95 ( 72 unt; 0 def)
% Number of atoms : 153 ( 70 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 105 ( 47 ~; 34 |; 17 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 8 con; 0-4 aty)
% Number of variables : 127 ( 6 sgn 46 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
! [A_27a,V0s_2E0,V1t_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))
<=> ! [V2x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__DEF) ).
fof(f27_nnf,plain,
! [A_27a,V0s_2E0,V1t_2E0] :
( ( ? [V2x_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) )
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) )
& ( ! [V2x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A_27a,V0s_2E0,V1t_2E0,V2x_2E0] :
( ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,sk3(A_27a,V0s_2E0,V1t_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,sk3(A_27a,V0s_2E0,V1t_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) )
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f27_nnf]) ).
cnf(c50,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,sk3(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(t139,plain,
ifeq(p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X1,sk3(X1,X2,X3)),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))),true,p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))),true) = true,
inference(equality_encoding,[status(esa)],[c50]) ).
cnf(t4251,plain,
ifeq(p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X1,sk3(X1,X2,X3)),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))),true,p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))),true) = true,
inference(orient,[status(thm)],[t139]) ).
fof(f28,axiom,
! [A_27a,V0s_2E0,V1x_2E0,V2y_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2y_2E0))))))
<=> ( s(A_27a,V1x_2E0) != s(A_27a,V2y_2E0)
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__DELETE) ).
fof(f28_nnf,plain,
! [A_27a,V0s_2E0,V1x_2E0,V2y_2E0] :
( ( s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2y_2E0)))))) )
& ( ( s(A_27a,V1x_2E0) != s(A_27a,V2y_2E0)
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2y_2E0)))))) ) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [A_27a,V1x_2E0,V0s_2E0,V2y_2E0] :
( ( s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2y_2E0)))))) )
& ( ( s(A_27a,V1x_2E0) != s(A_27a,V2y_2E0)
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2y_2E0)))))) ) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c51,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3)))))) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(t149,plain,
ifeq(p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X1,X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4)))))),true,p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X1,X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))),true) = true,
inference(equality_encoding,[status(esa)],[c51]) ).
cnf(t4143,plain,
ifeq(p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X1,X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4)))))),true,p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X1,X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))),true) = true,
inference(orient,[status(thm)],[t149]) ).
fof(f29,axiom,
! [A_27a,V0s_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__DEF) ).
fof(f29_nnf,plain,
! [A_27a,V0s_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [A_27a,V0s_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c54,plain,
s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(t96,plain,
s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2),s(X1,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2))))) = s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2))),
inference(equality_encoding,[status(esa)],[c54]) ).
cnf(t676,plain,
s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2),s(X1,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2))))) = s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2))),
inference(orient,[status(thm)],[t96]) ).
cnf(t4159,plain,
true = ifeq(p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X1,X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))))),true,p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X1,X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))),true),
inference(cp,[status(thm)],[t4143,t676]) ).
cnf(t8946,plain,
ifeq(p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X1,X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))))),true,p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X1,X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))),true) = true,
inference(orient,[status(thm)],[t4159]) ).
fof(f1,axiom,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
=> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
fof(f1_nnf,plain,
! [V0_2E0,V1_2E0] :
( s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0)
| ( p(s(tyop_2Emin_2Ebool,V1_2E0))
& ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) )
| ( ~ p(s(tyop_2Emin_2Ebool,V1_2E0))
& p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V0_2E0,V1_2E0] :
( s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0)
| ( p(s(tyop_2Emin_2Ebool,V1_2E0))
& ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) )
| ( ~ p(s(tyop_2Emin_2Ebool,V1_2E0))
& p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1)
| ~ p(s(tyop_2Emin_2Ebool,X0))
| ~ p(s(tyop_2Emin_2Ebool,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t54,plain,
ifeq(p(s(tyop_2Emin_2Ebool,X1)),true,ifeq(p(s(tyop_2Emin_2Ebool,X2)),true,s(tyop_2Emin_2Ebool,X2),s(tyop_2Emin_2Ebool,X1)),s(tyop_2Emin_2Ebool,X1)) = s(tyop_2Emin_2Ebool,X1),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t353,plain,
ifeq(p(s(tyop_2Emin_2Ebool,X1)),true,ifeq(p(s(tyop_2Emin_2Ebool,X2)),true,s(tyop_2Emin_2Ebool,X2),s(tyop_2Emin_2Ebool,X1)),s(tyop_2Emin_2Ebool,X1)) = s(tyop_2Emin_2Ebool,X1),
inference(orient,[status(thm)],[t54]) ).
fof(f2,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
fof(f2_nnf,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c5,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(t8,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t715,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t716,plain,
s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = ifeq(true,true,ifeq(p(s(tyop_2Emin_2Ebool,X1)),true,s(tyop_2Emin_2Ebool,X1),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(cp,[status(thm)],[t353,t715]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t9103,plain,
s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = ifeq(p(s(tyop_2Emin_2Ebool,X1)),true,s(tyop_2Emin_2Ebool,X1),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(step,[status(thm)],[t716,t258]) ).
cnf(t4995,plain,
ifeq(p(s(tyop_2Emin_2Ebool,X1)),true,s(tyop_2Emin_2Ebool,X1),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
inference(orient,[status(thm)],[t9103]) ).
cnf(c49,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,sk3(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))
| p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(t136,plain,
or(p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))),p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X1,sk3(X1,X2,X3)),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2))))) = true,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(t2010,plain,
or(p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))),p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X1,sk3(X1,X2,X3)),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2))))) = true,
inference(orient,[status(thm)],[t136]) ).
cnf(t11,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t259,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(c2,plain,
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1)
| p(s(tyop_2Emin_2Ebool,X1))
| p(s(tyop_2Emin_2Ebool,X0)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t34,plain,
or(p(s(tyop_2Emin_2Ebool,X1)),or(p(s(tyop_2Emin_2Ebool,X2)),eq(s(tyop_2Emin_2Ebool,X1),s(tyop_2Emin_2Ebool,X2)))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t1877,plain,
or(p(s(tyop_2Emin_2Ebool,X1)),or(p(s(tyop_2Emin_2Ebool,X2)),eq(s(tyop_2Emin_2Ebool,X1),s(tyop_2Emin_2Ebool,X2)))) = true,
inference(orient,[status(thm)],[t34]) ).
fof(f3,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
fof(f3_nnf,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c6,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t7,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) = false,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t4403,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t4404,plain,
true = or(false,or(p(s(tyop_2Emin_2Ebool,X1)),eq(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,X1)))),
inference(cp,[status(thm)],[t1877,t4403]) ).
cnf(t5,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t257,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t9097,plain,
true = or(p(s(tyop_2Emin_2Ebool,X1)),eq(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,X1))),
inference(step,[status(thm)],[t4404,t257]) ).
cnf(t4894,plain,
or(p(s(tyop_2Emin_2Ebool,X1)),eq(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,X1))) = true,
inference(orient,[status(thm)],[t9097]) ).
fof(f30,conjecture,
! [A_27a,V0s_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__SUBSET) ).
fof(f30_neg,negated_conjecture,
~ ! [A_27a,V0s_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f30_nnf,plain,
? [A_27a,V0s_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))),
inference(nnf_transformation,[status(thm)],[f30_neg]) ).
fof(f30_sk,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5])],[f30_nnf]) ).
cnf(c55,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(t41,plain,
p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))) = false,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(t4348,plain,
p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))) = false,
inference(orient,[status(thm)],[t41]) ).
cnf(t4897,plain,
true = or(false,eq(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))))),
inference(cp,[status(thm)],[t4894,t4348]) ).
cnf(t9160,plain,
true = eq(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))),
inference(step,[status(thm)],[t4897,t257]) ).
cnf(t6788,plain,
eq(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))) = true,
inference(orient,[status(thm)],[t9160]) ).
cnf(t6789,plain,
s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))) = ifeq(true,true,s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))),
inference(cp,[status(thm)],[t259,t6788]) ).
cnf(t9161,plain,
s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
inference(step,[status(thm)],[t6789,t258]) ).
cnf(t6792,plain,
s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
inference(orient,[status(thm)],[t9161]) ).
cnf(t6802,plain,
true = or(p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sk4,sk3(sk4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)),sk5)),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))))))),
inference(cp,[status(thm)],[t2010,t6792]) ).
cnf(t9190,plain,
true = or(false,p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sk4,sk3(sk4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)),sk5)),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))))))),
inference(step,[status(thm)],[t6802,t4403]) ).
cnf(t9191,plain,
true = p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sk4,sk3(sk4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)),sk5)),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))))),
inference(step,[status(thm)],[t9190,t257]) ).
cnf(t8076,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sk4,sk3(sk4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)),sk5)),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))))) = true,
inference(orient,[status(thm)],[t9191]) ).
cnf(t8079,plain,
s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = ifeq(true,true,s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sk4,sk3(sk4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)),sk5)),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(cp,[status(thm)],[t4995,t8076]) ).
cnf(t9192,plain,
s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sk4,sk3(sk4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)),sk5)),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))))),
inference(step,[status(thm)],[t8079,t258]) ).
cnf(t8107,plain,
s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sk4,sk3(sk4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)),sk5)),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
inference(orient,[status(thm)],[t9192]) ).
cnf(t8947,plain,
true = ifeq(p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),true,p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sk4,sk3(sk4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)),sk5)),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))),true),
inference(cp,[status(thm)],[t8946,t8107]) ).
cnf(t9221,plain,
true = ifeq(true,true,p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sk4,sk3(sk4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)),sk5)),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))),true),
inference(step,[status(thm)],[t8947,t715]) ).
cnf(t9222,plain,
true = p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sk4,sk3(sk4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)),sk5)),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))),
inference(step,[status(thm)],[t9221,t258]) ).
cnf(t9020,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sk4,sk3(sk4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)),sk5)),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))) = true,
inference(orient,[status(thm)],[t9222]) ).
cnf(t9035,plain,
true = ifeq(true,true,p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))),true),
inference(cp,[status(thm)],[t4251,t9020]) ).
cnf(t9225,plain,
true = p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5))),s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk5)))),
inference(step,[status(thm)],[t9035,t258]) ).
cnf(t9226,plain,
true = false,
inference(step,[status(thm)],[t9225,t4348]) ).
cnf(t9055,plain,
false = true,
inference(orient,[status(thm)],[t9226]) ).
fof(f10,axiom,
! [V0_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).
fof(f10_nnf,plain,
! [V0_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,V0_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [V0_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,V0_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) ) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c17,plain,
( ~ p(s(tyop_2Emin_2Ebool,X0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,X0)))) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f17,axiom,
! [X0_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
fof(f17_nnf,plain,
! [X0_2E0] :
( ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,X0_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))
| p(s(tyop_2Emin_2Ebool,X0_2E0)) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X0_2E0] :
( ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,X0_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))
| p(s(tyop_2Emin_2Ebool,X0_2E0)) ) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c35,plain,
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0))))
| ~ p(s(tyop_2Emin_2Ebool,X0)) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(c52,plain,
( s(X0,X2) != s(X0,X3)
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3)))))) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c6,c17,c35,c52,c55]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t9055]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP004+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 17:28:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 96.17/13.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 96.17/13.84 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------