%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ITP013+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 : Sun Sep 27 07:38:04 AM UTC 2026
% Result : Theorem 34.00s 4.90s
% Output : CNFRefutation 34.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 17
% Syntax : Number of formulae : 101 ( 21 unt; 0 def)
% Number of atoms : 405 ( 44 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 587 ( 283 ~; 269 |; 2 &)
% ( 1 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-2 aty)
% Number of variables : 177 ( 65 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mem_c_2Ebool_2EF,axiom,
mem('c$u2Ebool$u2EF',bool) ).
fof(ax_false_p,axiom,
~ p('c$u2Ebool$u2EF') ).
fof(mem_c_2Ebool_2ET,axiom,
mem('c$u2Ebool$u2ET',bool) ).
fof(ax_true_p,axiom,
p('c$u2Ebool$u2ET') ).
fof(ne_ty_2Efcp_2Ecart,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ne('ty$u2Efcp$u2Ecart'(X0,X1)) ) ) ).
fof(mem_c_2Earithmetic_2E_2D,axiom,
mem('c$u2Earithmetic$u2E$u2D',arr('ty$u2Enum$u2Enum',arr('ty$u2Enum$u2Enum','ty$u2Enum$u2Enum'))) ).
fof(mem_c_2Earithmetic_2E_3C_3D,axiom,
mem('c$u2Earithmetic$u2E$u3C$u3D',arr('ty$u2Enum$u2Enum',arr('ty$u2Enum$u2Enum',bool))) ).
fof(mem_c_2Ebool_2ECOND,axiom,
! [X0] :
( ne(X0)
=> mem('c$u2Ebool$u2ECOND'(X0),arr(bool,arr(X0,arr(X0,X0)))) ) ).
fof(mem_c_2Ewords_2En2w,axiom,
! [X0] :
( ne(X0)
=> mem('c$u2Ewords$u2En2w'(X0),arr('ty$u2Enum$u2Enum','ty$u2Efcp$u2Ecart'(bool,X0))) ) ).
fof(mem_c_2Ewords_2Eword__2comp,axiom,
! [X0] :
( ne(X0)
=> mem('c$u2Ewords$u2Eword$u$u2comp'(X0),arr('ty$u2Efcp$u2Ecart'(bool,X0),'ty$u2Efcp$u2Ecart'(bool,X0))) ) ).
fof(conj_thm_2Ebool_2Ebool__case__thm,axiom,
! [X0] :
( ne(X0)
=> ( ! [X3] :
( mem(X3,X0)
=> ! [X4] :
( mem(X4,X0)
=> ap(ap(ap('c$u2Ebool$u2ECOND'(X0),'c$u2Ebool$u2EF'),X3),X4) = X4 ) )
& ! [X1] :
( mem(X1,X0)
=> ! [X2] :
( mem(X2,X0)
=> ap(ap(ap('c$u2Ebool$u2ECOND'(X0),'c$u2Ebool$u2ET'),X1),X2) = X1 ) ) ) ) ).
fof(ax_thm_2Ewords_2Eword__sub__def,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,'ty$u2Efcp$u2Ecart'(bool,X0))
=> ! [X2] :
( mem(X2,'ty$u2Efcp$u2Ecart'(bool,X0))
=> ap(ap('c$u2Ewords$u2Eword$u$usub'(X0),X1),X2) = ap(ap('c$u2Ewords$u2Eword$u$uadd'(X0),X1),ap('c$u2Ewords$u2Eword$u$u2comp'(X0),X2)) ) ) ) ).
fof(conj_thm_2Ewords_2EWORD__LITERAL__ADD,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ( ! [X4] :
( mem(X4,'ty$u2Enum$u2Enum')
=> ! [X5] :
( mem(X5,'ty$u2Enum$u2Enum')
=> ap(ap('c$u2Ewords$u2Eword$u$uadd'(X1),ap('c$u2Ewords$u2En2w'(X1),X4)),ap('c$u2Ewords$u2Eword$u$u2comp'(X1),ap('c$u2Ewords$u2En2w'(X1),X5))) = ap(ap(ap('c$u2Ebool$u2ECOND'('ty$u2Efcp$u2Ecart'(bool,X1)),ap(ap('c$u2Earithmetic$u2E$u3C$u3D',X5),X4)),ap('c$u2Ewords$u2En2w'(X1),ap(ap('c$u2Earithmetic$u2E$u2D',X4),X5))),ap('c$u2Ewords$u2Eword$u$u2comp'(X1),ap('c$u2Ewords$u2En2w'(X1),ap(ap('c$u2Earithmetic$u2E$u2D',X5),X4)))) ) )
& ! [X2] :
( mem(X2,'ty$u2Enum$u2Enum')
=> ! [X3] :
( mem(X3,'ty$u2Enum$u2Enum')
=> ap(ap('c$u2Ewords$u2Eword$u$uadd'(X0),ap('c$u2Ewords$u2Eword$u$u2comp'(X0),ap('c$u2Ewords$u2En2w'(X0),X2))),ap('c$u2Ewords$u2Eword$u$u2comp'(X0),ap('c$u2Ewords$u2En2w'(X0),X3))) = ap('c$u2Ewords$u2Eword$u$u2comp'(X0),ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2B',X2),X3))) ) ) ) ) ) ).
fof(bool_ne,axiom,
ne(bool) ).
fof(ap_tp,axiom,
! [X0,X1,X2] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ) ).
fof(boolext,axiom,
! [X0] :
( mem(X0,bool)
=> ! [X1] :
( mem(X1,bool)
=> ( ( p(X0)
<=> p(X1) )
=> X0 = X1 ) ) ) ).
fof(conj_thm_2Ewords_2En2w__sub,conjecture,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,'ty$u2Enum$u2Enum')
=> ! [X2] :
( mem(X2,'ty$u2Enum$u2Enum')
=> ( p(ap(ap('c$u2Earithmetic$u2E$u3C$u3D',X2),X1))
=> ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',X1),X2)) = ap(ap('c$u2Ewords$u2Eword$u$usub'(X0),ap('c$u2Ewords$u2En2w'(X0),X1)),ap('c$u2Ewords$u2En2w'(X0),X2)) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,'ty$u2Enum$u2Enum')
=> ! [X2] :
( mem(X2,'ty$u2Enum$u2Enum')
=> ( p(ap(ap('c$u2Earithmetic$u2E$u3C$u3D',X2),X1))
=> ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',X1),X2)) = ap(ap('c$u2Ewords$u2Eword$u$usub'(X0),ap('c$u2Ewords$u2En2w'(X0),X1)),ap('c$u2Ewords$u2En2w'(X0),X2)) ) ) ) ),
inference(negate_conjecture,[status(cth)],[conj_thm_2Ewords_2En2w__sub]) ).
cnf(c7,plain,
mem('c$u2Ebool$u2EF',bool),
inference(clausification,[status(esa)],[mem_c_2Ebool_2EF]) ).
cnf(c8,plain,
~ p('c$u2Ebool$u2EF'),
inference(clausification,[status(esa)],[ax_false_p]) ).
cnf(c9,plain,
mem('c$u2Ebool$u2ET',bool),
inference(clausification,[status(esa)],[mem_c_2Ebool_2ET]) ).
cnf(c10,plain,
p('c$u2Ebool$u2ET'),
inference(clausification,[status(esa)],[ax_true_p]) ).
cnf(c11,plain,
( ne('ty$u2Efcp$u2Ecart'(X0,X1))
| ~ ne(X1)
| ~ ne(X0) ),
inference(clausification,[status(esa)],[ne_ty_2Efcp_2Ecart]) ).
cnf(c14,plain,
mem('c$u2Earithmetic$u2E$u2D',arr('ty$u2Enum$u2Enum',arr('ty$u2Enum$u2Enum','ty$u2Enum$u2Enum'))),
inference(clausification,[status(esa)],[mem_c_2Earithmetic_2E_2D]) ).
cnf(c15,plain,
mem('c$u2Earithmetic$u2E$u3C$u3D',arr('ty$u2Enum$u2Enum',arr('ty$u2Enum$u2Enum',bool))),
inference(clausification,[status(esa)],[mem_c_2Earithmetic_2E_3C_3D]) ).
cnf(c16,plain,
( mem('c$u2Ebool$u2ECOND'(X0),arr(bool,arr(X0,arr(X0,X0))))
| ~ ne(X0) ),
inference(clausification,[status(esa)],[mem_c_2Ebool_2ECOND]) ).
cnf(c18,plain,
( mem('c$u2Ewords$u2En2w'(X0),arr('ty$u2Enum$u2Enum','ty$u2Efcp$u2Ecart'(bool,X0)))
| ~ ne(X0) ),
inference(clausification,[status(esa)],[mem_c_2Ewords_2En2w]) ).
cnf(c19,plain,
( mem('c$u2Ewords$u2Eword$u$u2comp'(X0),arr('ty$u2Efcp$u2Ecart'(bool,X0),'ty$u2Efcp$u2Ecart'(bool,X0)))
| ~ ne(X0) ),
inference(clausification,[status(esa)],[mem_c_2Ewords_2Eword__2comp]) ).
cnf(c79,plain,
( ap(ap(ap('c$u2Ebool$u2ECOND'(X0),'c$u2Ebool$u2ET'),X1),X2) = X1
| ~ mem(X2,X0)
| ~ mem(X1,X0)
| ~ ne(X0) ),
inference(clausification,[status(esa)],[conj_thm_2Ebool_2Ebool__case__thm]) ).
cnf(c80,plain,
( ap(ap(ap('c$u2Ebool$u2ECOND'(X0),'c$u2Ebool$u2EF'),X1),X2) = X2
| ~ mem(X2,X0)
| ~ mem(X1,X0)
| ~ ne(X0) ),
inference(clausification,[status(esa)],[conj_thm_2Ebool_2Ebool__case__thm]) ).
cnf(c81,plain,
( ap(ap('c$u2Ewords$u2Eword$u$usub'(X0),X1),X2) = ap(ap('c$u2Ewords$u2Eword$u$uadd'(X0),X1),ap('c$u2Ewords$u2Eword$u$u2comp'(X0),X2))
| ~ mem(X2,'ty$u2Efcp$u2Ecart'(bool,X0))
| ~ mem(X1,'ty$u2Efcp$u2Ecart'(bool,X0))
| ~ ne(X0) ),
inference(clausification,[status(esa)],[ax_thm_2Ewords_2Eword__sub__def]) ).
cnf(c83,plain,
( ~ ne(X3)
| ~ mem(X1,'ty$u2Enum$u2Enum')
| ~ ne(X0)
| ~ mem(X2,'ty$u2Enum$u2Enum')
| ap(ap('c$u2Ewords$u2Eword$u$uadd'(X0),ap('c$u2Ewords$u2En2w'(X0),X1)),ap('c$u2Ewords$u2Eword$u$u2comp'(X0),ap('c$u2Ewords$u2En2w'(X0),X2))) = ap(ap(ap('c$u2Ebool$u2ECOND'('ty$u2Efcp$u2Ecart'(bool,X0)),ap(ap('c$u2Earithmetic$u2E$u3C$u3D',X2),X1)),ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',X1),X2))),ap('c$u2Ewords$u2Eword$u$u2comp'(X0),ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',X2),X1)))) ),
inference(clausification,[status(esa)],[conj_thm_2Ewords_2EWORD__LITERAL__ADD]) ).
cnf(c84,plain,
ne(bool),
inference(clausification,[status(esa)],[bool_ne]) ).
cnf(c87,plain,
( mem(ap(X0,X3),X2)
| ~ mem(X3,X1)
| ~ mem(X0,arr(X1,X2)) ),
inference(clausification,[status(esa)],[ap_tp]) ).
cnf(c89,plain,
( ~ mem(X0,bool)
| ~ mem(X1,bool)
| X1 = X0
| p(X1)
| p(X0) ),
inference(clausification,[status(esa)],[boolext]) ).
cnf(c90,plain,
( ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ p(X1)
| ~ p(X0)
| X0 = X1 ),
inference(clausification,[status(esa)],[boolext]) ).
cnf(c96,plain,
ne(sK80),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c97,plain,
mem(sK81,'ty$u2Enum$u2Enum'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c98,plain,
mem(sK82,'ty$u2Enum$u2Enum'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c99,plain,
p(ap(ap('c$u2Earithmetic$u2E$u3C$u3D',sK82),sK81)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c100,plain,
ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)) != ap(ap('c$u2Ewords$u2Eword$u$usub'(sK80),ap('c$u2Ewords$u2En2w'(sK80),sK81)),ap('c$u2Ewords$u2En2w'(sK80),sK82)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( mem(ap('c$u2Earithmetic$u2E$u2D',X0),arr('ty$u2Enum$u2Enum','ty$u2Enum$u2Enum'))
| ~ mem(X0,'ty$u2Enum$u2Enum') ),
inference(resolution,[status(thm)],[c87,c14]) ).
cnf(d1,plain,
( mem(ap(ap('c$u2Earithmetic$u2E$u2D',X0),X1),'ty$u2Enum$u2Enum')
| ~ mem(X1,'ty$u2Enum$u2Enum')
| ~ mem(X0,'ty$u2Enum$u2Enum') ),
inference(resolution,[status(thm)],[d0,c87]) ).
cnf(d2,plain,
( ~ ne(X1)
| mem(ap('c$u2Ewords$u2En2w'(X1),X0),'ty$u2Efcp$u2Ecart'(bool,X1))
| ~ mem(X0,'ty$u2Enum$u2Enum') ),
inference(resolution,[status(thm)],[c87,c18]) ).
cnf(d3,plain,
( ~ ne(X1)
| mem(ap('c$u2Ewords$u2Eword$u$u2comp'(X1),X0),'ty$u2Efcp$u2Ecart'(bool,X1))
| ~ mem(X0,'ty$u2Efcp$u2Ecart'(bool,X1)) ),
inference(resolution,[status(thm)],[c87,c19]) ).
cnf(d4,plain,
( mem(ap('c$u2Earithmetic$u2E$u3C$u3D',X0),arr('ty$u2Enum$u2Enum',bool))
| ~ mem(X0,'ty$u2Enum$u2Enum') ),
inference(resolution,[status(thm)],[c87,c15]) ).
cnf(d5,plain,
( mem(ap(ap('c$u2Earithmetic$u2E$u3C$u3D',X0),X1),bool)
| ~ mem(X1,'ty$u2Enum$u2Enum')
| ~ mem(X0,'ty$u2Enum$u2Enum') ),
inference(resolution,[status(thm)],[d4,c87]) ).
cnf(d6,plain,
( ~ p('c$u2Ebool$u2ET')
| ~ p(X0)
| ~ mem(X0,bool)
| X0 = 'c$u2Ebool$u2ET' ),
inference(resolution,[status(thm)],[c90,c9]) ).
cnf(d7,plain,
( ~ p(X0)
| ~ mem(X0,bool)
| X0 = 'c$u2Ebool$u2ET' ),
inference(resolution,[status(thm)],[c10,d6]) ).
cnf(d8,plain,
( ~ ne(X1)
| mem(ap('c$u2Ebool$u2ECOND'(X1),X0),arr(X1,arr(X1,X1)))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[c87,c16]) ).
cnf(d9,plain,
( mem(ap(ap('c$u2Ebool$u2ECOND'(X1),X0),X2),arr(X1,X1))
| ~ mem(X2,X1)
| ~ ne(X1)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[d8,c87]) ).
cnf(d10,plain,
( mem(ap(ap(ap('c$u2Ebool$u2ECOND'(X1),X2),X0),X3),X1)
| ~ mem(X3,X1)
| ~ ne(X1)
| ~ mem(X2,bool)
| ~ mem(X0,X1) ),
inference(resolution,[status(thm)],[d9,c87]) ).
cnf(d11,plain,
( ~ p(ap(ap(ap('c$u2Ebool$u2ECOND'(bool),X1),X2),X0))
| ap(ap(ap('c$u2Ebool$u2ECOND'(bool),X1),X2),X0) = 'c$u2Ebool$u2ET'
| ~ ne(bool)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
( ~ p(ap(ap(ap('c$u2Ebool$u2ECOND'(bool),X0),X1),X2))
| ~ mem(X2,bool)
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| ap(ap(ap('c$u2Ebool$u2ECOND'(bool),X0),X1),X2) = 'c$u2Ebool$u2ET' ),
inference(resolution,[status(thm)],[c84,d11]) ).
cnf(d13,plain,
( ~ ne(bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ p(ap(ap(ap('c$u2Ebool$u2ECOND'(bool),'c$u2Ebool$u2EF'),X0),X1))
| ~ mem('c$u2Ebool$u2EF',bool)
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| X1 = 'c$u2Ebool$u2ET' ),
inference(superposition,[status(thm)],[c80,d12]) ).
cnf(d14,plain,
( ~ p(ap(ap(ap('c$u2Ebool$u2ECOND'(bool),'c$u2Ebool$u2EF'),X1),X0))
| ~ mem('c$u2Ebool$u2EF',bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| X0 = 'c$u2Ebool$u2ET' ),
inference(resolution,[status(thm)],[c84,d13]) ).
cnf(d15,plain,
( ~ p(ap(ap(ap('c$u2Ebool$u2ECOND'(bool),'c$u2Ebool$u2EF'),X1),X0))
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| X0 = 'c$u2Ebool$u2ET' ),
inference(resolution,[status(thm)],[c7,d14]) ).
cnf(d16,plain,
( p('c$u2Ebool$u2EF')
| p(X0)
| ~ mem(X0,bool)
| X0 = 'c$u2Ebool$u2EF' ),
inference(resolution,[status(thm)],[c89,c7]) ).
cnf(d17,plain,
( p(X0)
| ~ mem(X0,bool)
| X0 = 'c$u2Ebool$u2EF' ),
inference(resolution,[status(thm)],[c8,d16]) ).
cnf(d18,plain,
( p(ap(ap(ap('c$u2Ebool$u2ECOND'(bool),X1),X2),X0))
| ap(ap(ap('c$u2Ebool$u2ECOND'(bool),X1),X2),X0) = 'c$u2Ebool$u2EF'
| ~ ne(bool)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[d10,d17]) ).
cnf(d19,plain,
( p(ap(ap(ap('c$u2Ebool$u2ECOND'(bool),X0),X1),X2))
| ~ mem(X2,bool)
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| ap(ap(ap('c$u2Ebool$u2ECOND'(bool),X0),X1),X2) = 'c$u2Ebool$u2EF' ),
inference(resolution,[status(thm)],[c84,d18]) ).
cnf(d20,plain,
( p(ap(ap(ap('c$u2Ebool$u2ECOND'(bool),'c$u2Ebool$u2EF'),X0),X1))
| ~ mem('c$u2Ebool$u2EF',bool)
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| ~ ne(bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| 'c$u2Ebool$u2EF' = X1 ),
inference(superposition,[status(thm)],[d19,c80]) ).
cnf(d21,plain,
( p(ap(ap(ap('c$u2Ebool$u2ECOND'(bool),'c$u2Ebool$u2EF'),X1),X0))
| ~ mem('c$u2Ebool$u2EF',bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| 'c$u2Ebool$u2EF' = X0 ),
inference(resolution,[status(thm)],[c84,d20]) ).
cnf(d22,plain,
( p(ap(ap(ap('c$u2Ebool$u2ECOND'(bool),'c$u2Ebool$u2EF'),X1),X0))
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| 'c$u2Ebool$u2EF' = X0 ),
inference(resolution,[status(thm)],[c7,d21]) ).
cnf(d23,plain,
( ~ mem(X0,bool)
| ~ mem(X1,bool)
| X0 = 'c$u2Ebool$u2ET'
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| 'c$u2Ebool$u2EF' = X0 ),
inference(resolution,[status(thm)],[d22,d15]) ).
cnf(d24,plain,
( ~ mem(X0,'ty$u2Enum$u2Enum')
| ~ mem(X1,'ty$u2Enum$u2Enum')
| ~ mem(X2,bool)
| 'c$u2Ebool$u2EF' = ap(ap('c$u2Earithmetic$u2E$u3C$u3D',X0),X1)
| ap(ap('c$u2Earithmetic$u2E$u3C$u3D',X0),X1) = 'c$u2Ebool$u2ET' ),
inference(resolution,[status(thm)],[d23,d5]) ).
cnf(d25,plain,
( ~ mem(sK82,'ty$u2Enum$u2Enum')
| ~ mem(sK81,'ty$u2Enum$u2Enum')
| ~ mem(X0,bool)
| ap(ap('c$u2Earithmetic$u2E$u3C$u3D',sK82),sK81) = 'c$u2Ebool$u2ET'
| p('c$u2Ebool$u2EF') ),
inference(superposition,[status(thm)],[d24,c99]) ).
cnf(d26,plain,
( p('c$u2Ebool$u2EF')
| ~ mem(sK82,'ty$u2Enum$u2Enum')
| ~ mem(X0,bool)
| ap(ap('c$u2Earithmetic$u2E$u3C$u3D',sK82),sK81) = 'c$u2Ebool$u2ET' ),
inference(resolution,[status(thm)],[c97,d25]) ).
cnf(d27,plain,
( p('c$u2Ebool$u2EF')
| ~ mem(X0,bool)
| ap(ap('c$u2Earithmetic$u2E$u3C$u3D',sK82),sK81) = 'c$u2Ebool$u2ET' ),
inference(resolution,[status(thm)],[c98,d26]) ).
cnf(d28,plain,
( ~ mem(X0,bool)
| ap(ap('c$u2Earithmetic$u2E$u3C$u3D',sK82),sK81) = 'c$u2Ebool$u2ET' ),
inference(resolution,[status(thm)],[c8,d27]) ).
cnf(d29,plain,
( ~ mem(X2,bool)
| ~ ne(X0)
| ~ ne(X1)
| ~ mem(sK82,'ty$u2Enum$u2Enum')
| ~ mem(sK81,'ty$u2Enum$u2Enum')
| ap(ap('c$u2Ewords$u2Eword$u$uadd'(X0),ap('c$u2Ewords$u2En2w'(X0),sK81)),ap('c$u2Ewords$u2Eword$u$u2comp'(X0),ap('c$u2Ewords$u2En2w'(X0),sK82))) = ap(ap(ap('c$u2Ebool$u2ECOND'('ty$u2Efcp$u2Ecart'(bool,X0)),'c$u2Ebool$u2ET'),ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82))),ap('c$u2Ewords$u2Eword$u$u2comp'(X0),ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81)))) ),
inference(superposition,[status(thm)],[d28,c83]) ).
cnf(d30,plain,
( ~ ne(X0)
| ~ ne(X2)
| ~ mem(sK82,'ty$u2Enum$u2Enum')
| ~ mem(X1,bool)
| ap(ap('c$u2Ewords$u2Eword$u$uadd'(X0),ap('c$u2Ewords$u2En2w'(X0),sK81)),ap('c$u2Ewords$u2Eword$u$u2comp'(X0),ap('c$u2Ewords$u2En2w'(X0),sK82))) = ap(ap(ap('c$u2Ebool$u2ECOND'('ty$u2Efcp$u2Ecart'(bool,X0)),'c$u2Ebool$u2ET'),ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82))),ap('c$u2Ewords$u2Eword$u$u2comp'(X0),ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81)))) ),
inference(resolution,[status(thm)],[c97,d29]) ).
cnf(d31,plain,
( ~ ne(X0)
| ~ ne(X2)
| ~ mem(X1,bool)
| ap(ap('c$u2Ewords$u2Eword$u$uadd'(X0),ap('c$u2Ewords$u2En2w'(X0),sK81)),ap('c$u2Ewords$u2Eword$u$u2comp'(X0),ap('c$u2Ewords$u2En2w'(X0),sK82))) = ap(ap(ap('c$u2Ebool$u2ECOND'('ty$u2Efcp$u2Ecart'(bool,X0)),'c$u2Ebool$u2ET'),ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82))),ap('c$u2Ewords$u2Eword$u$u2comp'(X0),ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81)))) ),
inference(resolution,[status(thm)],[c98,d30]) ).
cnf(d32,plain,
( ~ ne(X0)
| ~ ne(X2)
| ~ mem(X1,bool)
| ~ ne('ty$u2Efcp$u2Ecart'(bool,X0))
| ~ mem(ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)),'ty$u2Efcp$u2Ecart'(bool,X0))
| ~ mem(ap('c$u2Ewords$u2Eword$u$u2comp'(X0),ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81))),'ty$u2Efcp$u2Ecart'(bool,X0))
| ap(ap('c$u2Ewords$u2Eword$u$uadd'(X0),ap('c$u2Ewords$u2En2w'(X0),sK81)),ap('c$u2Ewords$u2Eword$u$u2comp'(X0),ap('c$u2Ewords$u2En2w'(X0),sK82))) = ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)) ),
inference(superposition,[status(thm)],[d31,c79]) ).
cnf(d33,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,X0))
| ~ ne(X0)
| ~ ne(X2)
| ~ mem(ap('c$u2Ewords$u2Eword$u$u2comp'(X0),ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81))),'ty$u2Efcp$u2Ecart'(bool,X0))
| ~ mem(ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)),'ty$u2Efcp$u2Ecart'(bool,X0))
| ~ mem(X1,bool)
| ~ ne(X0)
| ~ mem(ap('c$u2Ewords$u2En2w'(X0),sK81),'ty$u2Efcp$u2Ecart'(bool,X0))
| ~ mem(ap('c$u2Ewords$u2En2w'(X0),sK82),'ty$u2Efcp$u2Ecart'(bool,X0))
| ap(ap('c$u2Ewords$u2Eword$u$usub'(X0),ap('c$u2Ewords$u2En2w'(X0),sK81)),ap('c$u2Ewords$u2En2w'(X0),sK82)) = ap('c$u2Ewords$u2En2w'(X0),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)) ),
inference(superposition,[status(thm)],[d32,c81]) ).
cnf(d34,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(sK80)
| ~ ne(X1)
| ~ mem(ap('c$u2Ewords$u2Eword$u$u2comp'(sK80),ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81))),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK82),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK81),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(X0,bool)
| ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)) != ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)) ),
inference(superposition,[status(thm)],[d33,c100]) ).
cnf(d35,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(ap('c$u2Ewords$u2Eword$u$u2comp'(sK80),ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81))),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK82),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK81),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(X0,bool)
| ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)) != ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)) ),
inference(resolution,[status(thm)],[c96,d34]) ).
cnf(d36,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(ap('c$u2Ewords$u2Eword$u$u2comp'(sK80),ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81))),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK82),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK81),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(X0,bool) ),
inference(equality_resolution,[status(thm)],[d35]) ).
cnf(d37,plain,
( ~ ne(sK80)
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81)),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK82),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK81),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[d36,d3]) ).
cnf(d38,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK82),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK81),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81)),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[c96,d37]) ).
cnf(d39,plain,
( ~ ne(sK80)
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81),'ty$u2Enum$u2Enum')
| ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK82),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK81),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[d38,d2]) ).
cnf(d40,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK82),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK81),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82)),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81),'ty$u2Enum$u2Enum')
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[c96,d39]) ).
cnf(d41,plain,
( ~ ne(sK80)
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82),'ty$u2Enum$u2Enum')
| ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK82),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK81),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81),'ty$u2Enum$u2Enum')
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[d40,d2]) ).
cnf(d42,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK82),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK81),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81),'ty$u2Enum$u2Enum')
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82),'ty$u2Enum$u2Enum')
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[c96,d41]) ).
cnf(d43,plain,
( ~ ne(sK80)
| ~ mem(sK82,'ty$u2Enum$u2Enum')
| ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK81),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81),'ty$u2Enum$u2Enum')
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82),'ty$u2Enum$u2Enum')
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[d42,d2]) ).
cnf(d44,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(sK82,'ty$u2Enum$u2Enum')
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK81),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81),'ty$u2Enum$u2Enum')
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82),'ty$u2Enum$u2Enum')
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[c96,d43]) ).
cnf(d45,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(ap('c$u2Ewords$u2En2w'(sK80),sK81),'ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81),'ty$u2Enum$u2Enum')
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82),'ty$u2Enum$u2Enum')
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[c98,d44]) ).
cnf(d46,plain,
( ~ ne(sK80)
| ~ mem(sK81,'ty$u2Enum$u2Enum')
| ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81),'ty$u2Enum$u2Enum')
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82),'ty$u2Enum$u2Enum')
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[d45,d2]) ).
cnf(d47,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(sK81,'ty$u2Enum$u2Enum')
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81),'ty$u2Enum$u2Enum')
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82),'ty$u2Enum$u2Enum')
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[c96,d46]) ).
cnf(d48,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK82),sK81),'ty$u2Enum$u2Enum')
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82),'ty$u2Enum$u2Enum')
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[c97,d47]) ).
cnf(d49,plain,
( ~ mem(sK82,'ty$u2Enum$u2Enum')
| ~ mem(sK81,'ty$u2Enum$u2Enum')
| ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82),'ty$u2Enum$u2Enum')
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[d48,d1]) ).
cnf(d50,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(sK82,'ty$u2Enum$u2Enum')
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82),'ty$u2Enum$u2Enum')
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[c97,d49]) ).
cnf(d51,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(ap(ap('c$u2Earithmetic$u2E$u2D',sK81),sK82),'ty$u2Enum$u2Enum')
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[c98,d50]) ).
cnf(d52,plain,
( ~ mem(sK81,'ty$u2Enum$u2Enum')
| ~ mem(sK82,'ty$u2Enum$u2Enum')
| ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[d51,d1]) ).
cnf(d53,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(sK82,'ty$u2Enum$u2Enum')
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[c97,d52]) ).
cnf(d54,plain,
( ~ ne('ty$u2Efcp$u2Ecart'(bool,sK80))
| ~ ne(X1)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[c98,d53]) ).
cnf(d55,plain,
( ~ ne(bool)
| ~ ne(sK80)
| ~ ne(X1)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[d54,c11]) ).
cnf(d56,plain,
( ~ ne(bool)
| ~ ne(X1)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[c96,d55]) ).
cnf(d57,plain,
( ~ ne(X1)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[c84,d56]) ).
cnf(d58,plain,
~ ne(X0),
inference(resolution,[status(thm)],[d57,c7]) ).
cnf(d59,plain,
$false,
inference(resolution,[status(thm)],[d58,c96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP013+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.54 % Computer : n016.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Fri Sep 25 17:22:15 UTC 2026
% 0.09/0.55 % CPUTime :
% 0.09/0.55 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.00/4.90 % SZS status Theorem for theBenchmark.p
% 34.00/4.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------