%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP015+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 : n026.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 12:53:41 PM UTC 2026
% Result : Theorem 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 28 unt; 0 def)
% Number of atoms : 68 ( 45 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 51 ( 20 ~; 13 |; 14 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 48 ( 3 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_2Eprim__rec_2ENOT__LESS__0,axiom,
! [X26] : ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X26),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eprim__rec_2ENOT__LESS__0) ).
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_2Einteger_2EINT__LT__CALCULATE,axiom,
! [X26,X27] :
( s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X26))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X27))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& ( p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X26))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X27))))))
<=> ( s(tyop_2Enum_2Enum,X27) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
| s(tyop_2Enum_2Enum,X26) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ) )
& s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X26))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X27))))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X27),s(tyop_2Enum_2Enum,X26)))
& s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X26))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X27))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X26),s(tyop_2Enum_2Enum,X27))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__CALCULATE) ).
fof(thm_2Einteger__word_2Ei2w__0,conjecture,
! [X1] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__0) ).
fof(thm_2Einteger__word_2Ei2w__def,axiom,
! [X1,X28] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,X28))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,X28),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),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_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,X28))))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,X28))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__def) ).
fof(thm_2Einteger_2ENUM__OF__INT,axiom,
! [X26] : s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X26))))) = s(tyop_2Enum_2Enum,X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__OF__INT) ).
fof(thm_2Ewords_2EWORD__NEG__0,axiom,
! [X1] : 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_2Enum_2E0_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__0) ).
fof(thm_2Ebool_2Ebool__case__thm,axiom,
! [X1] :
( ! [X24,X25] : s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X1,X24),s(X1,X25))) = s(X1,X25)
& ! [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(thm_2Einteger_2EINT__NEG__0,axiom,
s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__0) ).
fof(c_0_10,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(fof_simplification,[status(thm)],[reserved_2Eho_2Enotfalse]) ).
fof(c_0_11,plain,
! [X26] : ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X26),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))),
inference(fof_simplification,[status(thm)],[thm_2Eprim__rec_2ENOT__LESS__0]) ).
fof(c_0_12,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(fof_nnf,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X55,X56] :
( ( s(tyop_2Emin_2Ebool,X55) = s(tyop_2Emin_2Ebool,X56)
| p(s(tyop_2Emin_2Ebool,X56))
| p(s(tyop_2Emin_2Ebool,X55)) )
& ( s(tyop_2Emin_2Ebool,X55) = s(tyop_2Emin_2Ebool,X56)
| ~ p(s(tyop_2Emin_2Ebool,X56))
| ~ p(s(tyop_2Emin_2Ebool,X55)) ) ),
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_14,plain,
! [X26,X27] :
( s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X26))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X27))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& ( p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X26))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X27))))))
<=> ( s(tyop_2Enum_2Enum,X27) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
| s(tyop_2Enum_2Enum,X26) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ) )
& s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X26))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X27))))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X27),s(tyop_2Enum_2Enum,X26)))
& s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X26))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X27))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X26),s(tyop_2Enum_2Enum,X27))) ),
inference(fof_simplification,[status(thm)],[thm_2Einteger_2EINT__LT__CALCULATE]) ).
fof(c_0_15,plain,
! [X62] : ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X62),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_11])]) ).
cnf(c_0_16,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,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_13]) ).
fof(c_0_18,negated_conjecture,
~ ! [X1] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
inference(assume_negation,[status(cth)],[thm_2Einteger__word_2Ei2w__0]) ).
fof(c_0_19,plain,
! [X35,X36] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X35),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,X36))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X35),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,X36),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X35),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X35),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,X36))))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X35),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,X36))))))),
inference(variable_rename,[status(thm)],[thm_2Einteger__word_2Ei2w__def]) ).
fof(c_0_20,plain,
! [X37,X38] :
( s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X37))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X38))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& ( p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X37))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X38))))))
| s(tyop_2Enum_2Enum,X38) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) )
& ( p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X37))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X38))))))
| s(tyop_2Enum_2Enum,X37) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) )
& ( s(tyop_2Enum_2Enum,X38) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
| s(tyop_2Enum_2Enum,X37) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X37))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X38)))))) )
& s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X37))))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X38))))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X38),s(tyop_2Enum_2Enum,X37)))
& s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X37))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X38))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X37),s(tyop_2Enum_2Enum,X38))) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
cnf(c_0_21,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( p(s(tyop_2Emin_2Ebool,X1))
| s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_23,plain,
! [X51] : s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X51))))) = s(tyop_2Enum_2Enum,X51),
inference(variable_rename,[status(thm)],[thm_2Einteger_2ENUM__OF__INT]) ).
fof(c_0_24,plain,
! [X52] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X52),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X52),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X52),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
inference(variable_rename,[status(thm)],[thm_2Ewords_2EWORD__NEG__0]) ).
fof(c_0_25,plain,
! [X46,X47,X48,X49,X50] :
( s(X46,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X46,X49),s(X46,X50))) = s(X46,X50)
& s(X46,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X46,X47),s(X46,X48))) = s(X46,X47) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[thm_2Ebool_2Ebool__case__thm])]) ).
fof(c_0_26,negated_conjecture,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
cnf(c_0_27,plain,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,X2))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,X2),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),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_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,X2))))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,X2))))))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
inference(split_conjunct,[status(thm)],[thm_2Einteger_2EINT__NEG__0]) ).
cnf(c_0_29,plain,
s(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X1))),s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X2))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_31,plain,
s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,X1))))) = s(tyop_2Enum_2Enum,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
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_2Enum_2E0_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X1,X2),s(X1,X3))) = s(X1,X3),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,negated_conjecture,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,esk1_0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]),c_0_28]),c_0_31]),c_0_32]),c_0_31]),c_0_33]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP015+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 21:51:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.46 % Version: 3.5.1
% 0.14/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.46 % Starting sh5l with 300s (1) cores
% 0.14/0.46 % new_bool_3 with pid 632502 completed with status 0
% 0.14/0.46 % Result found by new_bool_3
% 0.14/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.46 % Search class: FGHSM-FFMS31-DFFFFFNN
% 0.14/0.46 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.46 % SubtermCWHack with pid 632507 completed with status 0
% 0.14/0.46 % Result found by SubtermCWHack
% 0.14/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.46 % Search class: FGHSM-FFMS31-DFFFFFNN
% 0.14/0.46 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.46 % Preprocessing time : 0.002 s
% 0.14/0.46
% 0.14/0.46 % Proof found!
% 0.14/0.46 % SZS status Theorem
% 0.14/0.46 % SZS output start CNFRefutation
% See solution above
% 0.14/0.46 % Parsed axioms : 50
% 0.14/0.46 % Removed by relevancy pruning/SinE : 31
% 0.14/0.46 % Initial clauses : 39
% 0.14/0.46 % Removed in clause preprocessing : 13
% 0.14/0.46 % Initial clauses in saturation : 26
% 0.14/0.46 % Processed clauses : 170
% 0.14/0.46 % ...of these trivial : 2
% 0.14/0.46 % ...subsumed : 131
% 0.14/0.46 % ...remaining for further processing : 37
% 0.14/0.46 % Other redundant clauses eliminated : 0
% 0.14/0.46 % Clauses deleted for lack of memory : 0
% 0.14/0.46 % Backward-subsumed : 0
% 0.14/0.46 % Backward-rewritten : 2
% 0.14/0.46 % Generated clauses : 941
% 0.14/0.46 % ...of the previous two non-redundant : 632
% 0.14/0.46 % ...aggressively subsumed : 0
% 0.14/0.46 % Contextual simplify-reflections : 0
% 0.14/0.46 % Paramodulations : 881
% 0.14/0.46 % Factorizations : 56
% 0.14/0.46 % NegExts : 0
% 0.14/0.46 % Equation resolutions : 4
% 0.14/0.46 % Disequality decompositions : 0
% 0.14/0.46 % Total rewrite steps : 354
% 0.14/0.46 % ...of those cached : 272
% 0.14/0.46 % Propositional unsat checks : 0
% 0.14/0.46 % Propositional check models : 0
% 0.14/0.46 % Propositional check unsatisfiable : 0
% 0.14/0.46 % Propositional clauses : 0
% 0.14/0.46 % Propositional clauses after purity: 0
% 0.14/0.46 % Propositional unsat core size : 0
% 0.14/0.46 % Propositional preprocessing time : 0.000
% 0.14/0.46 % Propositional encoding time : 0.000
% 0.14/0.46 % Propositional solver time : 0.000
% 0.14/0.46 % Success case prop preproc time : 0.000
% 0.14/0.46 % Success case prop encoding time : 0.000
% 0.14/0.46 % Success case prop solver time : 0.000
% 0.14/0.46 % Current number of processed clauses : 35
% 0.14/0.46 % Positive orientable unit clauses : 12
% 0.14/0.46 % Positive unorientable unit clauses: 0
% 0.14/0.46 % Negative unit clauses : 1
% 0.14/0.46 % Non-unit-clauses : 22
% 0.14/0.46 % Current number of unprocessed clauses: 485
% 0.14/0.46 % ...number of literals in the above : 2006
% 0.14/0.46 % Current number of archived formulas : 0
% 0.14/0.46 % Current number of archived clauses : 2
% 0.14/0.46 % Clause-clause subsumption calls (NU) : 334
% 0.14/0.46 % Rec. Clause-clause subsumption calls : 236
% 0.14/0.46 % Non-unit clause-clause subsumptions : 113
% 0.14/0.46 % Unit Clause-clause subsumption calls : 0
% 0.14/0.46 % Rewrite failures with RHS unbound : 0
% 0.14/0.46 % BW rewrite match attempts : 7
% 0.14/0.46 % BW rewrite match successes : 2
% 0.14/0.46 % Condensation attempts : 0
% 0.14/0.46 % Condensation successes : 0
% 0.14/0.46 % Termbank termtop insertions : 20066
% 0.14/0.46 % Search garbage collected termcells : 721
% 0.14/0.46
% 0.14/0.46 % -------------------------------------------------
% 0.14/0.46 % User time : 0.016 s
% 0.14/0.46 % System time : 0.005 s
% 0.14/0.46 % Total time : 0.021 s
% 0.14/0.46 % Maximum resident set size: 3740 pages
% 0.14/0.46
% 0.14/0.46 % -------------------------------------------------
% 0.14/0.46 % User time : 0.020 s
% 0.14/0.46 % System time : 0.010 s
% 0.14/0.46 % Total time : 0.030 s
% 0.14/0.46 % Maximum resident set size: 4608 pages
% 0.14/0.46 % E exiting
%------------------------------------------------------------------------------