TSTP Solution File: ITP015^3 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : ITP015^3 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 10:35:51 EDT 2024
% Result : Theorem 8.70s 2.85s
% Output : Refutation 8.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 25
% Syntax : Number of formulae : 68 ( 37 unt; 16 typ; 0 def)
% Number of atoms : 145 ( 74 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 531 ( 33 ~; 16 |; 15 &; 458 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 113 ( 0 ^ 108 !; 1 ?; 113 :)
% ( 4 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Einteger_2Eint_type,type,
tyop_2Einteger_2Eint: $tType ).
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $tType ).
thf(c_2Enum_2E0_type,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(c_2Eprim__rec_2E_3C_type,type,
c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2ECOND_type,type,
c_2Ebool_2ECOND:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(c_2Ebool_2EF_type,type,
c_2Ebool_2EF: $o ).
thf(c_2Einteger_2ENum_type,type,
c_2Einteger_2ENum: tyop_2Einteger_2Eint > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ET_type,type,
c_2Ebool_2ET: $o ).
thf(c_2Einteger__word_2Ei2w_type,type,
c_2Einteger__word_2Ei2w:
!>[TA: $tType] : ( tyop_2Einteger_2Eint > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Einteger_2Eint__lt_type,type,
c_2Einteger_2Eint__lt: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).
thf(c_2Einteger_2Eint__neg_type,type,
c_2Einteger_2Eint__neg: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__of__num_type,type,
c_2Einteger_2Eint__of__num: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).
thf(c_2Ewords_2En2w_type,type,
c_2Ewords_2En2w:
!>[TA: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__2comp_type,type,
c_2Ewords_2Eword__2comp:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(6,axiom,
! [TA: $tType] :
( ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
thf(25,plain,
! [TA: $tType] :
( ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(26,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(cnf,[status(esa)],[25]) ).
thf(28,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(lifteq,[status(thm)],[26]) ).
thf(29,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(simp,[status(thm)],[28]) ).
thf(5,axiom,
! [A: $o] :
( c_2Ebool_2EF
=> A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).
thf(20,plain,
! [A: $o] :
( c_2Ebool_2EF
=> A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,plain,
( c_2Ebool_2EF
=> $false ),
inference(instance,[status(thm)],[20]) ).
thf(24,plain,
~ c_2Ebool_2EF,
inference(simp,[status(thm)],[23]) ).
thf(108,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ $false @ A @ B )
= B ),
inference(rewrite,[status(thm)],[29,24]) ).
thf(7,axiom,
! [TA: $tType,A: $o,B: $o,C: TA,D: TA,E: TA,F: TA] :
( ( ( A = B )
& ( B
=> ( C = D ) )
& ( ~ B
=> ( E = F ) ) )
=> ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).
thf(31,plain,
! [TA: $tType,A: $o,B: $o,C: TA,D: TA,E: TA,F: TA] :
( ( ( A = B )
& ( B
=> ( C = D ) )
& ( ~ B
=> ( E = F ) ) )
=> ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(33,plain,
! [TA: $tType,F: TA,E: TA,D: TA,C: TA,B: $o,A: $o] :
( ( A != B )
| B
| ( E != F )
| ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(38,plain,
! [TA: $tType,F: TA,E: TA,D: TA,C: TA,B: $o,A: $o] :
( ( A != B )
| ( E != F )
| ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) )
| B ),
inference(lifteq,[status(thm)],[33]) ).
thf(39,plain,
! [TA: $tType,D: TA,C: TA,B: TA,A: $o] :
( ( ( c_2Ebool_2ECOND @ TA @ A @ B @ D )
= ( c_2Ebool_2ECOND @ TA @ A @ C @ D ) )
| A ),
inference(simp,[status(thm)],[38]) ).
thf(256,plain,
! [TB: $tType,F: TB,E: TB,D: TB,C: $o,B: TB,A: TB] :
( ( B
= ( c_2Ebool_2ECOND @ TB @ C @ E @ F ) )
| C
| ( ( c_2Ebool_2ECOND @ TB @ $false @ A @ B )
!= ( c_2Ebool_2ECOND @ TB @ C @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[108,39]) ).
thf(257,plain,
! [TB: $tType,B: TB,A: TB] :
( ( ( c_2Ebool_2ECOND @ TB @ $false @ B @ A )
= A )
| $false ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( $false )),bind(D,$thf( A )),bind(E,$thf( E )),bind(F,$thf( B ))]]) ).
thf(300,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ $false @ B @ A )
= A ),
inference(simp,[status(thm)],[257]) ).
thf(9,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__of__num @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__OF__INT) ).
thf(47,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__of__num @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(48,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__of__num @ A ) )
= A ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__of__num @ A ) )
= A ),
inference(lifteq,[status(thm)],[48]) ).
thf(13,axiom,
! [TA: $tType,A: tyop_2Einteger_2Eint] :
( ( c_2Einteger__word_2Ei2w @ TA @ A )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) ) ) @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__def) ).
thf(58,plain,
! [TA: $tType,A: tyop_2Einteger_2Eint] :
( ( c_2Einteger__word_2Ei2w @ TA @ A )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) ) ) @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(59,plain,
! [TA: $tType,A: tyop_2Einteger_2Eint] :
( ( c_2Einteger__word_2Ei2w @ TA @ A )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) ) ) @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ A ) ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(60,plain,
! [TA: $tType,A: tyop_2Einteger_2Eint] :
( ( c_2Einteger__word_2Ei2w @ TA @ A )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) ) ) @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ A ) ) ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(1,conjecture,
! [TA: $tType] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__0) ).
thf(2,negated_conjecture,
~ ! [TA: $tType] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ! [TA: $tType] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
( ( c_2Einteger__word_2Ei2w @ skt1 @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
!= ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
( ( c_2Einteger__word_2Ei2w @ skt1 @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
!= ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(849,plain,
! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ skt1 ) @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) ) ) @ ( c_2Ewords_2En2w @ skt1 @ ( c_2Einteger_2ENum @ A ) ) )
!= ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) )
| ( ( c_2Einteger__word_2Ei2w @ skt1 @ A )
!= ( c_2Einteger__word_2Ei2w @ skt1 @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,17]) ).
thf(850,plain,
( ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ skt1 ) @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ) @ ( c_2Ewords_2En2w @ skt1 @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) )
!= ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ),
inference(pattern_uni,[status(thm)],[849:[bind(A,$thf( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ))]]) ).
thf(11,axiom,
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__0) ).
thf(53,plain,
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(54,plain,
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(14,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= ( c_2Eprim__rec_2E_3C @ B @ A ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( ( A != c_2Enum_2E0 )
| ( B != c_2Enum_2E0 ) ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= c_2Ebool_2EF ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__CALCULATE) ).
thf(61,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= ( c_2Eprim__rec_2E_3C @ B @ A ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( ( A != c_2Enum_2E0 )
| ( B != c_2Enum_2E0 ) ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(62,plain,
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= ( c_2Eprim__rec_2E_3C @ B @ A ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( ( A != c_2Enum_2E0 )
| ( B != c_2Enum_2E0 ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= c_2Ebool_2EF ) ),
inference(miniscope,[status(thm)],[61]) ).
thf(66,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) ),
inference(cnf,[status(esa)],[62]) ).
thf(73,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) ),
inference(lifteq,[status(thm)],[66]) ).
thf(918,plain,
( ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ skt1 ) @ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__2comp @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) @ ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) )
!= ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ),
inference(rewrite,[status(thm)],[850,49,54,73]) ).
thf(942,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ skt1 ) @ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__2comp @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ A ) ) @ ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) )
!= ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) )
| ( ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__of__num @ A ) )
!= ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,918]) ).
thf(943,plain,
( ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ skt1 ) @ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__2comp @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) )
!= ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ),
inference(pattern_uni,[status(thm)],[942:[bind(A,$thf( c_2Enum_2E0 ))]]) ).
thf(10,axiom,
! [A: tyop_2Enum_2Enum] :
~ ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eprim__rec_2ENOT__LESS__0) ).
thf(50,plain,
! [A: tyop_2Enum_2Enum] :
~ ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(51,plain,
~ ? [A: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ),
inference(miniscope,[status(thm)],[50]) ).
thf(52,plain,
! [A: tyop_2Enum_2Enum] :
~ ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ),
inference(cnf,[status(esa)],[51]) ).
thf(979,plain,
( ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ skt1 ) @ $false @ ( c_2Ewords_2Eword__2comp @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) )
!= ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ),
inference(rewrite,[status(thm)],[943,52]) ).
thf(995,plain,
! [B: tyop_2Efcp_2Ecart @ $o @ skt1,A: tyop_2Efcp_2Ecart @ $o @ skt1] :
( ( A
!= ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) )
| ( ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ skt1 ) @ $false @ B @ A )
!= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ skt1 ) @ $false @ ( c_2Ewords_2Eword__2comp @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[300,979]) ).
thf(996,plain,
( ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 )
!= ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ),
inference(pattern_uni,[status(thm)],[995:[bind(A,$thf( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 )),bind(B,$thf( c_2Ewords_2Eword__2comp @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ))]]) ).
thf(1018,plain,
$false,
inference(simp,[status(thm)],[996]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : ITP015^3 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n004.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 22:19:09 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.88/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.06 % [INFO] Parsing done (203ms).
% 1.40/1.08 % [INFO] Running in sequential loop mode.
% 1.79/1.34 % [INFO] nitpick registered as external prover.
% 1.79/1.35 % [INFO] Scanning for conjecture ...
% 1.92/1.40 % [INFO] Found a conjecture and 22 axioms. Running axiom selection ...
% 1.92/1.44 % [INFO] Axiom selection finished. Selected 12 axioms (removed 10 axioms).
% 2.16/1.47 % [INFO] Problem is higher-order (TPTP THF).
% 2.16/1.47 % [INFO] Type checking passed.
% 2.16/1.47 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 8.70/2.85 % [INFO] Killing All external provers ...
% 8.70/2.85 % Time passed: 2343ms (effective reasoning time: 1763ms)
% 8.70/2.85 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.70/2.85 % Axioms used in derivation (8): thm_2Ebool_2EFALSITY, thm_2Ebool_2ECOND__CONG, thm_2Einteger_2EINT__NEG__0, thm_2Eprim__rec_2ENOT__LESS__0, thm_2Einteger_2EINT__LT__CALCULATE, thm_2Einteger__word_2Ei2w__def, thm_2Einteger_2ENUM__OF__INT, thm_2Ebool_2Ebool__case__thm
% 8.70/2.85 % No. of inferences in proof: 52
% 8.70/2.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2343 ms resp. 1763 ms w/o parsing
% 8.70/2.90 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.70/2.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------