%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP013+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 : Thu Sep 24 12:53:39 PM UTC 2026
% Result : Theorem 0.17s 15.54s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 15 unt; 0 def)
% Number of atoms : 93 ( 55 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 83 ( 27 ~; 25 |; 19 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 69 ( 2 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm_2Ebool_2EEQ__CLAUSES,axiom,
! [X8] :
( ( s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
<=> ~ p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X8)
<=> ~ p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
<=> p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X8)
<=> p(s(tyop_2Emin_2Ebool,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
fof(thm_2Ewords_2EWORD__LITERAL__ADD,axiom,
! [X1,X2] :
( ! [X33,X34] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X33))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X34))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X34),s(tyop_2Enum_2Enum,X33))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X33),s(tyop_2Enum_2Enum,X34))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X2),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X34),s(tyop_2Enum_2Enum,X33)))))))))
& ! [X31,X32] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X31))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X32))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X31),s(tyop_2Enum_2Enum,X32))))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LITERAL__ADD) ).
fof(thm_2Ewords_2Eword__sub__def,axiom,
! [X1,X29,X30] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X29),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X30))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X29),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X30))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__def) ).
fof(reserved_2Eho_2Eboolext,axiom,
! [X6,X7] :
( ( p(s(tyop_2Emin_2Ebool,X6))
<=> p(s(tyop_2Emin_2Ebool,X7)) )
=> s(tyop_2Emin_2Ebool,X6) = s(tyop_2Emin_2Ebool,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
fof(thm_2Ewords_2En2w__sub,conjecture,
! [X1,X35,X36] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X36),s(tyop_2Enum_2Enum,X35))))
=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X35),s(tyop_2Enum_2Enum,X36))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X35))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X36))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub) ).
fof(reserved_2Eho_2Enotfalse,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
fof(thm_2Ebool_2Ebool__case__thm,axiom,
! [X1] :
( ! [X27,X28] : s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X1,X27),s(X1,X28))) = s(X1,X28)
& ! [X16,X17] : s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X1,X16),s(X1,X17))) = s(X1,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
fof(reserved_2Eho_2Ebool__cases__ax,axiom,
! [X8] :
( s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
fof(c_0_8,plain,
! [X8] :
( ( s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
<=> ~ p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X8)
<=> ~ p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
<=> p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X8)
<=> p(s(tyop_2Emin_2Ebool,X8)) ) ),
inference(fof_simplification,[status(thm)],[thm_2Ebool_2EEQ__CLAUSES]) ).
fof(c_0_9,plain,
! [X46,X47,X48,X49,X50,X51] :
( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X47),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X47),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X50))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X47),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X47),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X51))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X47),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X51),s(tyop_2Enum_2Enum,X50))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X47),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X50),s(tyop_2Enum_2Enum,X51))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X47),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X47),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X51),s(tyop_2Enum_2Enum,X50)))))))))
& s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X46),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X46),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X46),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X48))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X46),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X46),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X49))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X46),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X46),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X48),s(tyop_2Enum_2Enum,X49))))))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[thm_2Ewords_2EWORD__LITERAL__ADD])]) ).
fof(c_0_10,plain,
! [X43,X44,X45] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X43),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X43),X44),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X43),X45))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X43),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X43),X44),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X43),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X43),X45))))),
inference(variable_rename,[status(thm)],[thm_2Ewords_2Eword__sub__def]) ).
fof(c_0_11,plain,
! [X75] :
( ( s(tyop_2Emin_2Ebool,X75) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| p(s(tyop_2Emin_2Ebool,X75)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X75))
| s(tyop_2Emin_2Ebool,X75) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X75)
| p(s(tyop_2Emin_2Ebool,X75)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X75))
| s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,X75) )
& ( s(tyop_2Emin_2Ebool,X75) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X75)) )
& ( p(s(tyop_2Emin_2Ebool,X75))
| s(tyop_2Emin_2Ebool,X75) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X75)
| ~ p(s(tyop_2Emin_2Ebool,X75)) )
& ( p(s(tyop_2Emin_2Ebool,X75))
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,X75) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X52,X53] :
( ( s(tyop_2Emin_2Ebool,X52) = s(tyop_2Emin_2Ebool,X53)
| p(s(tyop_2Emin_2Ebool,X53))
| p(s(tyop_2Emin_2Ebool,X52)) )
& ( s(tyop_2Emin_2Ebool,X52) = s(tyop_2Emin_2Ebool,X53)
| ~ p(s(tyop_2Emin_2Ebool,X53))
| ~ p(s(tyop_2Emin_2Ebool,X52)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reserved_2Eho_2Eboolext])])])]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X35,X36] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X36),s(tyop_2Enum_2Enum,X35))))
=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X35),s(tyop_2Enum_2Enum,X36))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X35))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X36))))) ),
inference(assume_negation,[status(cth)],[thm_2Ewords_2En2w__sub]) ).
fof(c_0_14,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(fof_simplification,[status(thm)],[reserved_2Eho_2Enotfalse]) ).
cnf(c_0_15,plain,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X2))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X3))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X3),s(tyop_2Enum_2Enum,X2))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X3))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X3),s(tyop_2Enum_2Enum,X2))))))))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X2),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X3))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X2),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),X3))))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( ~ p(s(tyop_2Emin_2Ebool,X1))
| s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X2)
| p(s(tyop_2Emin_2Ebool,X2))
| p(s(tyop_2Emin_2Ebool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_19,plain,
! [X68,X69,X70,X71,X72] :
( s(X68,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X68,X71),s(X68,X72))) = s(X68,X72)
& s(X68,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X68,X69),s(X68,X70))) = s(X68,X69) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[thm_2Ebool_2Ebool__case__thm])]) ).
fof(c_0_20,negated_conjecture,
( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,esk2_0),s(tyop_2Enum_2Enum,esk3_0))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,esk2_0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,esk3_0)))))
& p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,esk3_0),s(tyop_2Enum_2Enum,esk2_0)))) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_21,plain,
! [X73] :
( s(tyop_2Emin_2Ebool,X73) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,X73) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(variable_rename,[status(thm)],[reserved_2Eho_2Ebool__cases__ax]) ).
fof(c_0_22,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X3))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X3),s(tyop_2Enum_2Enum,X2))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X3))))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X3))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X2))))),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,plain,
( p(s(tyop_2Emin_2Ebool,X2))
| s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,X1)
| s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,plain,
s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X1,X2),s(X1,X3))) = s(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,esk3_0),s(tyop_2Enum_2Enum,esk2_0)))),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( ~ p(s(tyop_2Emin_2Ebool,X1))
| s(tyop_2Emin_2Ebool,X1) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,plain,
( s(tyop_2Emin_2Ebool,X1) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| p(s(tyop_2Emin_2Ebool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_31,negated_conjecture,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,esk2_0),s(tyop_2Enum_2Enum,esk3_0))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,esk2_0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,esk3_0))))),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,plain,
( p(s(tyop_2Emin_2Ebool,X4))
| s(tyop_2Emin_2Ebool,X4) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X3),s(tyop_2Enum_2Enum,X2)))
| s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X2))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X3))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X3))))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_33,negated_conjecture,
s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,esk3_0),s(tyop_2Enum_2Enum,esk2_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_34,plain,
( s(tyop_2Emin_2Ebool,X1) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,X1) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_17]) ).
cnf(c_0_36,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP013+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/15.40 % Computer : n010.cluster.edu
% 0.13/15.40 % Model : x86_64 x86_64
% 0.13/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/15.40 % Memory : 8046.5625MB
% 0.13/15.40 % OS : Linux 6.8.0-71-generic
% 0.13/15.40 % CPULimit : 300
% 0.13/15.40 % WCLimit : 300
% 0.13/15.40 % DateTime : Sun Sep 20 21:47:26 UTC 2026
% 0.13/15.40 % CPUTime :
% 0.13/15.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/15.45 Running first-order theorem proving
% 0.13/15.45 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/15.54 % Version: 3.5.1
% 0.17/15.54 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/15.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/15.54 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/15.54 % Starting new_bool_3 with 300s (1) cores
% 0.17/15.54 % Starting new_bool_1 with 300s (1) cores
% 0.17/15.54 % Starting sh5l with 300s (1) cores
% 0.17/15.54 % new_bool_1 with pid 3550721 completed with status 0
% 0.17/15.54 % Result found by new_bool_1
% 0.17/15.54 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/15.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/15.54 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/15.54 % Starting new_bool_3 with 300s (1) cores
% 0.17/15.54 % Starting new_bool_1 with 300s (1) cores
% 0.17/15.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/15.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/15.54 % Search class: FGHSM-FFMM31-DFFFFFNN
% 0.17/15.54 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/15.54 % Starting SubtermCWHack with 31s (1) cores
% 0.17/15.54 % SubtermCWHack with pid 3550727 completed with status 0
% 0.17/15.54 % Result found by SubtermCWHack
% 0.17/15.54 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.17/15.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/15.54 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.17/15.54 % Starting new_bool_3 with 300s (1) cores
% 0.17/15.54 % Starting new_bool_1 with 300s (1) cores
% 0.17/15.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/15.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/15.54 % Search class: FGHSM-FFMM31-DFFFFFNN
% 0.17/15.54 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/15.54 % Starting SubtermCWHack with 31s (1) cores
% 0.17/15.54 % Preprocessing time : 0.001 s
% 0.17/15.54
% 0.17/15.54 % Proof found!
% 0.17/15.54 % SZS status Theorem
% 0.17/15.54 % SZS output start CNFRefutation
% See solution above
% 0.17/15.54 % Parsed axioms : 46
% 0.17/15.54 % Removed by relevancy pruning/SinE : 30
% 0.17/15.54 % Initial clauses : 56
% 0.17/15.54 % Removed in clause preprocessing : 25
% 0.17/15.54 % Initial clauses in saturation : 31
% 0.17/15.54 % Processed clauses : 881
% 0.17/15.54 % ...of these trivial : 15
% 0.17/15.54 % ...subsumed : 799
% 0.17/15.54 % ...remaining for further processing : 67
% 0.17/15.54 % Other redundant clauses eliminated : 0
% 0.17/15.54 % Clauses deleted for lack of memory : 0
% 0.17/15.54 % Backward-subsumed : 15
% 0.17/15.54 % Backward-rewritten : 27
% 0.17/15.54 % Generated clauses : 8059
% 0.17/15.54 % ...of the previous two non-redundant : 6912
% 0.17/15.54 % ...aggressively subsumed : 0
% 0.17/15.54 % Contextual simplify-reflections : 4
% 0.17/15.54 % Paramodulations : 7818
% 0.17/15.54 % Factorizations : 213
% 0.17/15.54 % NegExts : 0
% 0.17/15.54 % Equation resolutions : 23
% 0.17/15.54 % Disequality decompositions : 0
% 0.17/15.54 % Total rewrite steps : 1072
% 0.17/15.54 % ...of those cached : 931
% 0.17/15.54 % Propositional unsat checks : 0
% 0.17/15.54 % Propositional check models : 0
% 0.17/15.54 % Propositional check unsatisfiable : 0
% 0.17/15.54 % Propositional clauses : 0
% 0.17/15.54 % Propositional clauses after purity: 0
% 0.17/15.54 % Propositional unsat core size : 0
% 0.17/15.54 % Propositional preprocessing time : 0.000
% 0.17/15.54 % Propositional encoding time : 0.000
% 0.17/15.54 % Propositional solver time : 0.000
% 0.17/15.54 % Success case prop preproc time : 0.000
% 0.17/15.54 % Success case prop encoding time : 0.000
% 0.17/15.54 % Success case prop solver time : 0.000
% 0.17/15.54 % Current number of processed clauses : 20
% 0.17/15.54 % Positive orientable unit clauses : 6
% 0.17/15.54 % Positive unorientable unit clauses: 1
% 0.17/15.54 % Negative unit clauses : 1
% 0.17/15.54 % Non-unit-clauses : 12
% 0.17/15.54 % Current number of unprocessed clauses: 5991
% 0.17/15.54 % ...number of literals in the above : 33710
% 0.17/15.54 % Current number of archived formulas : 0
% 0.17/15.54 % Current number of archived clauses : 47
% 0.17/15.54 % Clause-clause subsumption calls (NU) : 4188
% 0.17/15.54 % Rec. Clause-clause subsumption calls : 1876
% 0.17/15.54 % Non-unit clause-clause subsumptions : 744
% 0.17/15.54 % Unit Clause-clause subsumption calls : 28
% 0.17/15.54 % Rewrite failures with RHS unbound : 3
% 0.17/15.54 % BW rewrite match attempts : 17
% 0.17/15.54 % BW rewrite match successes : 14
% 0.17/15.54 % Condensation attempts : 0
% 0.17/15.54 % Condensation successes : 0
% 0.17/15.54 % Termbank termtop insertions : 179952
% 0.17/15.54 % Search garbage collected termcells : 919
% 0.17/15.54
% 0.17/15.54 % -------------------------------------------------
% 0.17/15.54 % User time : 0.068 s
% 0.17/15.54 % System time : 0.007 s
% 0.17/15.54 % Total time : 0.074 s
% 0.17/15.54 % Maximum resident set size: 3740 pages
% 0.17/15.54
% 0.17/15.54 % -------------------------------------------------
% 0.17/15.54 % User time : 0.070 s
% 0.17/15.54 % System time : 0.012 s
% 0.17/15.54 % Total time : 0.082 s
% 0.17/15.54 % Maximum resident set size: 4864 pages
% 0.17/15.54 % E exiting
%------------------------------------------------------------------------------