TSTP Solution File: REL045+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : REL045+2 : TPTP v8.1.2. Released v4.0.0.
% 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 : Fri May 19 11:48:41 EDT 2023
% Result : Theorem 24.14s 4.77s
% Output : Refutation 24.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 26
% Syntax : Number of formulae : 121 ( 75 unt; 9 typ; 0 def)
% Number of atoms : 181 ( 180 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1056 ( 104 ~; 69 |; 0 &; 883 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 153 ( 0 ^; 153 !; 0 ?; 153 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_type,type,
join: $i > $i > $i ).
thf(composition_type,type,
composition: $i > $i > $i ).
thf(converse_type,type,
converse: $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(top_type,type,
top: $i ).
thf(one_type,type,
one: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(18,axiom,
! [A: $i] :
( ( composition @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).
thf(67,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(68,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(cnf,[status(esa)],[67]) ).
thf(69,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(lifteq,[status(thm)],[68]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
thf(61,plain,
! [A: $i,B: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
thf(28,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(lifteq,[status(thm)],[29]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
inference(lifteq,[status(thm)],[56]) ).
thf(620,plain,
! [C: $i,B: $i,A: $i] :
( ( ( converse @ A )
= ( composition @ ( converse @ C ) @ ( converse @ B ) ) )
| ( ( composition @ A @ one )
!= ( composition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[69,57]) ).
thf(621,plain,
! [A: $i] :
( ( composition @ ( converse @ one ) @ ( converse @ A ) )
= ( converse @ A ) ),
inference(pattern_uni,[status(thm)],[620:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( one ))]]) ).
thf(865,plain,
! [B: $i,A: $i] :
( ( ( composition @ ( converse @ one ) @ A )
= ( converse @ B ) )
| ( ( converse @ ( converse @ A ) )
!= ( converse @ B ) ) ),
inference(paramod_ordered,[status(thm)],[30,621]) ).
thf(866,plain,
! [A: $i] :
( ( composition @ ( converse @ one ) @ A )
= ( converse @ ( converse @ A ) ) ),
inference(pattern_uni,[status(thm)],[865:[bind(A,$thf( C )),bind(B,$thf( converse @ C ))]]) ).
thf(896,plain,
! [A: $i] :
( ( composition @ ( converse @ one ) @ A )
= ( converse @ ( converse @ A ) ) ),
inference(simp,[status(thm)],[866]) ).
thf(910,plain,
! [A: $i] :
( ( composition @ ( converse @ one ) @ A )
= A ),
inference(rewrite,[status(thm)],[896,30]) ).
thf(3,axiom,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).
thf(22,plain,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,plain,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [A: $i] :
( ( meet @ A @ ( complement @ A ) )
= zero ),
inference(lifteq,[status(thm)],[23]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
thf(46,plain,
! [A: $i,B: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(cnf,[status(esa)],[46]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(184,plain,
! [A: $i] :
( ( complement @ ( join @ ( complement @ A ) @ ( complement @ ( complement @ A ) ) ) )
= zero ),
inference(rewrite,[status(thm)],[24,48]) ).
thf(15,axiom,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top) ).
thf(58,plain,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(59,plain,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(60,plain,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= top ),
inference(lifteq,[status(thm)],[59]) ).
thf(185,plain,
( ( complement @ top )
= zero ),
inference(rewrite,[status(thm)],[184,60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ C @ B )
= top )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[60,63]) ).
thf(97,plain,
! [A: $i] :
( ( join @ ( complement @ A ) @ A )
= top ),
inference(pattern_uni,[status(thm)],[96:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( complement @ D ))]]) ).
thf(102,plain,
! [A: $i] :
( ( join @ ( complement @ A ) @ A )
= top ),
inference(simp,[status(thm)],[97]) ).
thf(188,plain,
! [A: $i] :
( ( ( join @ zero @ A )
= top )
| ( ( complement @ top )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[185,102]) ).
thf(189,plain,
( ( join @ zero @ top )
= top ),
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( top ))]]) ).
thf(1,conjecture,
! [A: $i] :
( ( join @ A @ ( composition @ ( composition @ A @ ( converse @ A ) ) @ A ) )
= ( composition @ ( composition @ A @ ( converse @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( join @ A @ ( composition @ ( composition @ A @ ( converse @ A ) ) @ A ) )
= ( composition @ ( composition @ A @ ( converse @ A ) ) @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i] :
( ( join @ A @ ( composition @ ( composition @ A @ ( converse @ A ) ) @ A ) )
= ( composition @ ( composition @ A @ ( converse @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
( ( join @ sk1 @ ( composition @ ( composition @ sk1 @ ( converse @ sk1 ) ) @ sk1 ) )
!= ( composition @ ( composition @ sk1 @ ( converse @ sk1 ) ) @ sk1 ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
( ( join @ sk1 @ ( composition @ ( composition @ sk1 @ ( converse @ sk1 ) ) @ sk1 ) )
!= ( composition @ ( composition @ sk1 @ ( converse @ sk1 ) ) @ sk1 ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(72,plain,
! [A: $i] :
( ( ( join @ sk1 @ ( composition @ A @ sk1 ) )
!= ( composition @ ( composition @ sk1 @ ( converse @ sk1 ) ) @ sk1 ) )
| ( ( composition @ A @ one )
!= ( composition @ sk1 @ ( converse @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[69,21]) ).
thf(76,plain,
! [A: $i] :
( ( ( join @ sk1 @ ( composition @ A @ sk1 ) )
!= ( composition @ ( composition @ sk1 @ ( converse @ sk1 ) ) @ sk1 ) )
| ( A != sk1 )
| ( ( converse @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[72]) ).
thf(80,plain,
( ( ( composition @ ( composition @ sk1 @ ( converse @ sk1 ) ) @ sk1 )
!= ( join @ sk1 @ ( composition @ sk1 @ sk1 ) ) )
| ( ( converse @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[76]) ).
thf(84,plain,
! [A: $i] :
( ( ( composition @ A @ sk1 )
!= ( join @ sk1 @ ( composition @ sk1 @ sk1 ) ) )
| ( ( converse @ sk1 )
!= one )
| ( ( composition @ A @ one )
!= ( composition @ sk1 @ ( converse @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[69,80]) ).
thf(89,plain,
! [A: $i] :
( ( ( composition @ A @ sk1 )
!= ( join @ sk1 @ ( composition @ sk1 @ sk1 ) ) )
| ( ( converse @ sk1 )
!= one )
| ( A != sk1 )
| ( ( converse @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[84]) ).
thf(93,plain,
( ( ( join @ sk1 @ ( composition @ sk1 @ sk1 ) )
!= ( composition @ sk1 @ sk1 ) )
| ( ( converse @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[89]) ).
thf(108,plain,
! [A: $i] :
( ( ( join @ sk1 @ ( composition @ sk1 @ sk1 ) )
!= ( composition @ sk1 @ sk1 ) )
| ( A != one )
| ( ( converse @ ( converse @ A ) )
!= ( converse @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[30,93]) ).
thf(112,plain,
( ( ( join @ sk1 @ ( composition @ sk1 @ sk1 ) )
!= ( composition @ sk1 @ sk1 ) )
| ( ( converse @ one )
!= sk1 ) ),
inference(simp,[status(thm)],[108]) ).
thf(404,plain,
( ( ( composition @ sk1 @ sk1 )
!= top )
| ( ( converse @ one )
!= sk1 )
| ( ( join @ sk1 @ ( composition @ sk1 @ sk1 ) )
!= ( join @ zero @ top ) ) ),
inference(paramod_ordered,[status(thm)],[189,112]) ).
thf(425,plain,
( ( ( composition @ sk1 @ sk1 )
!= top )
| ( ( converse @ one )
!= sk1 )
| ( sk1 != zero )
| ( ( composition @ sk1 @ sk1 )
!= top ) ),
inference(simp,[status(thm)],[404]) ).
thf(436,plain,
( ( ( composition @ sk1 @ sk1 )
!= top )
| ( ( converse @ one )
!= sk1 )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[425]) ).
thf(926,plain,
! [A: $i] :
( ( A != top )
| ( ( converse @ one )
!= sk1 )
| ( sk1 != zero )
| ( ( composition @ ( converse @ one ) @ A )
!= ( composition @ sk1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[910,436]) ).
thf(953,plain,
( ( ( converse @ one )
!= sk1 )
| ( sk1 != zero )
| ( ( converse @ one )
!= sk1 )
| ( sk1 != top ) ),
inference(simp,[status(thm)],[926]) ).
thf(984,plain,
( ( ( converse @ one )
!= sk1 )
| ( sk1 != zero )
| ( sk1 != top ) ),
inference(simp,[status(thm)],[953]) ).
thf(913,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( composition @ ( converse @ one ) @ A )
!= ( composition @ B @ one ) ) ),
inference(paramod_ordered,[status(thm)],[910,69]) ).
thf(914,plain,
( ( converse @ one )
= one ),
inference(pattern_uni,[status(thm)],[913:[bind(A,$thf( one )),bind(B,$thf( converse @ one ))]]) ).
thf(997,plain,
( ( sk1 != one )
| ( sk1 != zero )
| ( sk1 != top ) ),
inference(rewrite,[status(thm)],[984,914]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( meet @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ B ) @ C ) )
= ( meet @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modular_law_2) ).
thf(49,plain,
! [A: $i,B: $i,C: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( meet @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ B ) @ C ) )
= ( meet @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(411,plain,
( ( ( composition @ sk1 @ sk1 )
!= top )
| ( ( converse @ sk1 )
!= one )
| ( ( join @ sk1 @ ( composition @ sk1 @ sk1 ) )
!= ( join @ zero @ top ) ) ),
inference(paramod_ordered,[status(thm)],[189,93]) ).
thf(426,plain,
( ( ( composition @ sk1 @ sk1 )
!= top )
| ( ( converse @ sk1 )
!= one )
| ( sk1 != zero )
| ( ( composition @ sk1 @ sk1 )
!= top ) ),
inference(simp,[status(thm)],[411]) ).
thf(437,plain,
( ( ( composition @ sk1 @ sk1 )
!= top )
| ( ( converse @ sk1 )
!= one )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[426]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).
thf(37,plain,
! [A: $i,B: $i,C: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( meet @ ( composition @ A @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) @ C ) )
= ( meet @ ( composition @ A @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modular_law_1) ).
thf(52,plain,
! [A: $i,B: $i,C: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( meet @ ( composition @ A @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) @ C ) )
= ( meet @ ( composition @ A @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(104,plain,
! [A: $i] :
( ( ( join @ sk1 @ A )
!= ( composition @ sk1 @ sk1 ) )
| ( ( converse @ sk1 )
!= one )
| ( ( composition @ A @ one )
!= ( composition @ sk1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[69,93]) ).
thf(109,plain,
! [A: $i] :
( ( ( join @ sk1 @ A )
!= ( composition @ sk1 @ sk1 ) )
| ( ( converse @ sk1 )
!= one )
| ( A != sk1 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[104]) ).
thf(113,plain,
( ( ( composition @ sk1 @ sk1 )
!= ( join @ sk1 @ sk1 ) )
| ( ( converse @ sk1 )
!= one )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[109]) ).
thf(190,plain,
! [A: $i] :
( ( A
!= ( join @ sk1 @ sk1 ) )
| ( ( converse @ sk1 )
!= one )
| ( sk1 != one )
| ( ( composition @ A @ one )
!= ( composition @ sk1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[69,113]) ).
thf(193,plain,
( ( ( converse @ sk1 )
!= one )
| ( sk1 != one )
| ( ( join @ sk1 @ sk1 )
!= sk1 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[190]) ).
thf(196,plain,
( ( ( converse @ sk1 )
!= one )
| ( sk1 != one )
| ( ( join @ sk1 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[193]) ).
thf(401,plain,
( ( ( composition @ ( composition @ sk1 @ ( converse @ sk1 ) ) @ sk1 )
!= top )
| ( ( join @ sk1 @ ( composition @ ( composition @ sk1 @ ( converse @ sk1 ) ) @ sk1 ) )
!= ( join @ zero @ top ) ) ),
inference(paramod_ordered,[status(thm)],[189,21]) ).
thf(431,plain,
( ( ( composition @ ( composition @ sk1 @ ( converse @ sk1 ) ) @ sk1 )
!= top )
| ( sk1 != zero )
| ( ( composition @ ( composition @ sk1 @ ( converse @ sk1 ) ) @ sk1 )
!= top ) ),
inference(simp,[status(thm)],[401]) ).
thf(438,plain,
( ( ( composition @ ( composition @ sk1 @ ( converse @ sk1 ) ) @ sk1 )
!= top )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[431]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity) ).
thf(34,plain,
! [A: $i,B: $i,C: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( composition @ A @ B ) @ C )
= ( composition @ A @ ( composition @ B @ C ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(598,plain,
( ( ( composition @ sk1 @ ( composition @ ( converse @ sk1 ) @ sk1 ) )
!= top )
| ( sk1 != zero ) ),
inference(rewrite,[status(thm)],[438,36]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( join @ ( composition @ ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @ ( complement @ B ) )
= ( complement @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( join @ ( composition @ ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @ ( complement @ B ) )
= ( complement @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( join @ ( converse @ A ) @ ( converse @ B ) )
= ( converse @ ( join @ A @ B ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(186,plain,
! [A: $i] :
( ( ( join @ A @ zero )
= top )
| ( ( complement @ top )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[185,60]) ).
thf(187,plain,
( ( join @ top @ zero )
= top ),
inference(pattern_uni,[status(thm)],[186:[bind(A,$thf( top ))]]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) )
= ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dedekind_law) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) )
= ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( A
= ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
thf(43,plain,
! [A: $i,B: $i] :
( A
= ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(988,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk1 != zero )
| ( sk1 != top )
| ( ( converse @ ( converse @ A ) )
!= ( converse @ one ) ) ),
inference(paramod_ordered,[status(thm)],[30,984]) ).
thf(991,plain,
( ( sk1 != zero )
| ( sk1 != top )
| ( ( converse @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[988]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity) ).
thf(40,plain,
! [A: $i,B: $i,C: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) )
= ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) )
= ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( complement @ ( join @ ( complement @ ( composition @ A @ B ) ) @ ( complement @ C ) ) ) @ ( composition @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ ( composition @ C @ ( converse @ B ) ) ) ) ) @ ( complement @ ( join @ ( complement @ B ) @ ( complement @ ( composition @ ( converse @ A ) @ C ) ) ) ) ) )
= ( composition @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ ( composition @ C @ ( converse @ B ) ) ) ) ) @ ( complement @ ( join @ ( complement @ B ) @ ( complement @ ( composition @ ( converse @ A ) @ C ) ) ) ) ) ),
inference(rewrite,[status(thm)],[33,48]) ).
thf(464,plain,
( ( join @ sk1 @ ( composition @ sk1 @ ( composition @ ( converse @ sk1 ) @ sk1 ) ) )
!= ( composition @ sk1 @ ( composition @ ( converse @ sk1 ) @ sk1 ) ) ),
inference(rewrite,[status(thm)],[21,36]) ).
thf(468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( composition @ A @ D )
= ( composition @ B @ ( composition @ C @ D ) ) )
| ( ( composition @ A @ one )
!= ( composition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[69,36]) ).
thf(469,plain,
! [B: $i,A: $i] :
( ( composition @ A @ ( composition @ one @ B ) )
= ( composition @ A @ B ) ),
inference(pattern_uni,[status(thm)],[468:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( one ))]]) ).
thf(501,plain,
! [B: $i,A: $i] :
( ( composition @ A @ ( composition @ one @ B ) )
= ( composition @ A @ B ) ),
inference(simp,[status(thm)],[469]) ).
thf(6144,plain,
$false,
inference(e,[status(thm)],[69,61,997,49,437,185,37,25,52,196,189,46,93,57,60,102,28,598,34,64,22,27,187,113,39,48,63,67,31,43,991,40,258,55,58,914,36,30,19,464,501]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL045+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 17:53:55 EDT 2023
% 0.14/0.36 % CPUTime :
% 1.00/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.03 % [INFO] Parsing done (136ms).
% 1.29/1.04 % [INFO] Running in sequential loop mode.
% 1.80/1.24 % [INFO] eprover registered as external prover.
% 1.80/1.25 % [INFO] cvc4 registered as external prover.
% 1.80/1.25 % [INFO] Scanning for conjecture ...
% 1.80/1.30 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 2.03/1.34 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.03/1.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.03/1.37 % [INFO] Type checking passed.
% 2.03/1.38 % [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 ...
% 24.14/4.75 % External prover 'e' found a proof!
% 24.14/4.76 % [INFO] Killing All external provers ...
% 24.14/4.77 % Time passed: 4253ms (effective reasoning time: 3723ms)
% 24.14/4.77 % 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)>
% 24.14/4.77 % Axioms used in derivation (16): modular_law_1, converse_cancellativity, dedekind_law, composition_identity, converse_idempotence, composition_associativity, maddux3_a_kind_of_de_Morgan, maddux2_join_associativity, maddux1_join_commutativity, modular_law_2, converse_multiplicativity, converse_additivity, def_top, def_zero, composition_distributivity, maddux4_definiton_of_meet
% 24.14/4.77 % No. of inferences in proof: 112
% 24.14/4.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4253 ms resp. 3723 ms w/o parsing
% 24.14/4.81 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.14/4.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------