TSTP Solution File: REL031+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : REL031+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 11:48:35 EDT 2023
% Result : Theorem 11.16s 3.02s
% Output : Refutation 11.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 24
% Syntax : Number of formulae : 118 ( 75 unt; 10 typ; 0 def)
% Number of atoms : 151 ( 150 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 863 ( 63 ~; 37 |; 3 &; 757 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 134 ( 0 ^; 134 !; 0 ?; 134 :)
% 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(one_type,type,
one: $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(top_type,type,
top: $i ).
thf(zero_type,type,
zero: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(8,axiom,
! [A: $i] :
( ( composition @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
thf(38,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(39,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(lifteq,[status(thm)],[39]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( ( join @ ( composition @ ( converse @ A ) @ A ) @ one )
= one )
& ( ( join @ ( composition @ ( converse @ B ) @ B ) @ one )
= one ) )
=> ( ( join @ ( composition @ ( converse @ ( composition @ A @ B ) ) @ ( composition @ A @ B ) ) @ one )
= one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( ( join @ ( composition @ ( converse @ A ) @ A ) @ one )
= one )
& ( ( join @ ( composition @ ( converse @ B ) @ B ) @ one )
= one ) )
=> ( ( join @ ( composition @ ( converse @ ( composition @ A @ B ) ) @ ( composition @ A @ B ) ) @ one )
= one ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i,B: $i] :
( ( ( ( join @ ( composition @ ( converse @ A ) @ A ) @ one )
= one )
& ( ( join @ ( composition @ ( converse @ B ) @ B ) @ one )
= one ) )
=> ( ( join @ ( composition @ ( converse @ ( composition @ A @ B ) ) @ ( composition @ A @ B ) ) @ one )
= one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,plain,
( ( join @ ( composition @ ( converse @ sk1 ) @ sk1 ) @ one )
= one ),
inference(cnf,[status(esa)],[16]) ).
thf(22,plain,
( ( join @ ( composition @ ( converse @ sk1 ) @ sk1 ) @ one )
= one ),
inference(lifteq,[status(thm)],[19]) ).
thf(65,plain,
! [A: $i] :
( ( ( join @ A @ one )
= one )
| ( ( composition @ A @ one )
!= ( composition @ ( converse @ sk1 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[40,22]) ).
thf(67,plain,
! [A: $i] :
( ( ( join @ A @ one )
= one )
| ( A
!= ( converse @ sk1 ) )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[65]) ).
thf(69,plain,
( ( ( join @ ( converse @ sk1 ) @ one )
= one )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[67]) ).
thf(17,plain,
( ( join @ ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) @ one )
!= one ),
inference(cnf,[status(esa)],[16]) ).
thf(20,plain,
( ( join @ ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) @ one )
!= one ),
inference(lifteq,[status(thm)],[17]) ).
thf(78,plain,
! [A: $i] :
( ( ( join @ ( composition @ ( converse @ A ) @ ( composition @ sk1 @ sk2 ) ) @ one )
!= one )
| ( ( composition @ A @ one )
!= ( composition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[40,20]) ).
thf(82,plain,
! [A: $i] :
( ( ( join @ ( composition @ ( converse @ A ) @ ( composition @ sk1 @ sk2 ) ) @ one )
!= one )
| ( A != sk1 )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[78]) ).
thf(88,plain,
( ( ( join @ ( composition @ ( converse @ sk1 ) @ ( composition @ sk1 @ sk2 ) ) @ one )
!= one )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[82]) ).
thf(95,plain,
! [A: $i] :
( ( ( join @ ( composition @ ( converse @ sk1 ) @ A ) @ one )
!= one )
| ( sk2 != one )
| ( ( composition @ A @ one )
!= ( composition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[40,88]) ).
thf(101,plain,
! [A: $i] :
( ( ( join @ ( composition @ ( converse @ sk1 ) @ A ) @ one )
!= one )
| ( sk2 != one )
| ( A != sk1 )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[95]) ).
thf(105,plain,
( ( ( join @ ( composition @ ( converse @ sk1 ) @ sk1 ) @ one )
!= one )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[101]) ).
thf(246,plain,
( ( one != one )
| ( sk2 != one ) ),
inference(rewrite,[status(thm)],[105,22]) ).
thf(247,plain,
sk2 != one,
inference(simp,[status(thm)],[246]) ).
thf(14,axiom,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
thf(56,plain,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(18,plain,
( ( join @ ( composition @ ( converse @ sk2 ) @ sk2 ) @ one )
= one ),
inference(cnf,[status(esa)],[16]) ).
thf(21,plain,
( ( join @ ( composition @ ( converse @ sk2 ) @ sk2 ) @ one )
= one ),
inference(lifteq,[status(thm)],[18]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
= one )
| ( ( join @ A @ B )
!= ( join @ ( composition @ ( converse @ sk2 ) @ sk2 ) @ one ) ) ),
inference(paramod_ordered,[status(thm)],[25,21]) ).
thf(164,plain,
( ( join @ one @ ( composition @ ( converse @ sk2 ) @ sk2 ) )
= one ),
inference(pattern_uni,[status(thm)],[163:[bind(A,$thf( composition @ ( converse @ sk2 ) @ sk2 )),bind(B,$thf( one ))]]) ).
thf(57,plain,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= top ),
inference(lifteq,[status(thm)],[57]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
thf(26,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)],[4]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(297,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ one @ C )
= ( join @ A @ ( join @ B @ C ) ) )
| ( ( join @ one @ ( composition @ ( converse @ sk2 ) @ sk2 ) )
!= ( join @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[164,28]) ).
thf(298,plain,
! [A: $i] :
( ( join @ one @ ( join @ ( composition @ ( converse @ sk2 ) @ sk2 ) @ A ) )
= ( join @ one @ A ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( one )),bind(B,$thf( composition @ ( converse @ sk2 ) @ sk2 )),bind(C,$thf( C ))]]) ).
thf(349,plain,
! [A: $i] :
( ( join @ one @ ( join @ ( composition @ ( converse @ sk2 ) @ sk2 ) @ A ) )
= ( join @ one @ A ) ),
inference(simp,[status(thm)],[298]) ).
thf(475,plain,
! [B: $i,A: $i] :
( ( ( join @ one @ top )
= ( join @ one @ B ) )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ ( composition @ ( converse @ sk2 ) @ sk2 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[58,349]) ).
thf(476,plain,
( ( join @ one @ ( complement @ ( composition @ ( converse @ sk2 ) @ sk2 ) ) )
= ( join @ one @ top ) ),
inference(pattern_uni,[status(thm)],[475:[bind(A,$thf( composition @ ( converse @ sk2 ) @ sk2 )),bind(B,$thf( complement @ ( composition @ ( converse @ sk2 ) @ sk2 ) ))]]) ).
thf(677,plain,
! [B: $i,A: $i] :
( ( ( join @ one @ top )
= ( join @ B @ A ) )
| ( ( join @ one @ ( complement @ ( composition @ ( converse @ sk2 ) @ sk2 ) ) )
!= ( join @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[476,25]) ).
thf(678,plain,
( ( join @ ( complement @ ( composition @ ( converse @ sk2 ) @ sk2 ) ) @ one )
= ( join @ one @ top ) ),
inference(pattern_uni,[status(thm)],[677:[bind(A,$thf( one )),bind(B,$thf( complement @ ( composition @ ( converse @ sk2 ) @ sk2 ) ))]]) ).
thf(76,plain,
( ( join @ ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) @ one )
!= ( join @ ( composition @ ( converse @ sk2 ) @ sk2 ) @ one ) ),
inference(paramod_ordered,[status(thm)],[21,20]) ).
thf(87,plain,
( ( ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) )
!= ( composition @ ( converse @ sk2 ) @ sk2 ) )
| ( one != one ) ),
inference(simp,[status(thm)],[76]) ).
thf(92,plain,
( ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) )
!= ( composition @ ( converse @ sk2 ) @ sk2 ) ),
inference(simp,[status(thm)],[87]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( join @ ( composition @ ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @ ( complement @ B ) )
= ( complement @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
thf(53,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)],[13]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
thf(41,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(15,axiom,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
thf(59,plain,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(60,plain,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
inference(cnf,[status(esa)],[59]) ).
thf(61,plain,
! [A: $i] :
( ( meet @ A @ ( complement @ A ) )
= zero ),
inference(lifteq,[status(thm)],[60]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(1037,plain,
! [A: $i] :
( ( complement @ ( join @ ( complement @ A ) @ ( complement @ ( complement @ A ) ) ) )
= zero ),
inference(rewrite,[status(thm)],[61,34]) ).
thf(1103,plain,
( ( complement @ top )
= zero ),
inference(rewrite,[status(thm)],[1037,58]) ).
thf(181,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ C @ B )
= top )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[58,25]) ).
thf(182,plain,
! [A: $i] :
( ( join @ ( complement @ A ) @ A )
= top ),
inference(pattern_uni,[status(thm)],[181:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( complement @ D ))]]) ).
thf(209,plain,
! [A: $i] :
( ( join @ ( complement @ A ) @ A )
= top ),
inference(simp,[status(thm)],[182]) ).
thf(1106,plain,
! [A: $i] :
( ( ( join @ zero @ A )
= top )
| ( ( complement @ top )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1103,209]) ).
thf(1107,plain,
( ( join @ zero @ top )
= top ),
inference(pattern_uni,[status(thm)],[1106:[bind(A,$thf( top ))]]) ).
thf(1276,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ top @ C )
= ( join @ A @ ( join @ B @ C ) ) )
| ( ( join @ zero @ top )
!= ( join @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1107,28]) ).
thf(1277,plain,
! [A: $i] :
( ( join @ zero @ ( join @ top @ A ) )
= ( join @ top @ A ) ),
inference(pattern_uni,[status(thm)],[1276:[bind(A,$thf( zero )),bind(B,$thf( top ))]]) ).
thf(1318,plain,
! [A: $i] :
( ( join @ zero @ ( join @ top @ A ) )
= ( join @ top @ A ) ),
inference(simp,[status(thm)],[1277]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
= one )
| ( ( join @ A @ B )
!= ( join @ ( composition @ ( converse @ sk1 ) @ sk1 ) @ one ) ) ),
inference(paramod_ordered,[status(thm)],[25,22]) ).
thf(172,plain,
( ( join @ one @ ( composition @ ( converse @ sk1 ) @ sk1 ) )
= one ),
inference(pattern_uni,[status(thm)],[171:[bind(A,$thf( composition @ ( converse @ sk1 ) @ sk1 )),bind(B,$thf( one ))]]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( A
= ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
thf(29,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)],[5]) ).
thf(30,plain,
! [B: $i,A: $i] :
( A
= ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) )
= A ),
inference(lifteq,[status(thm)],[30]) ).
thf(775,plain,
! [B: $i,A: $i] :
( ( ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ one @ top ) ) )
= A )
| ( ( join @ ( complement @ ( composition @ ( converse @ sk2 ) @ sk2 ) ) @ one )
!= ( join @ ( complement @ A ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[678,31]) ).
thf(776,plain,
( ( join @ ( complement @ ( join @ ( complement @ ( composition @ ( converse @ sk2 ) @ sk2 ) ) @ ( complement @ one ) ) ) @ ( complement @ ( join @ one @ top ) ) )
= ( composition @ ( converse @ sk2 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[775:[bind(A,$thf( composition @ ( converse @ sk2 ) @ sk2 )),bind(B,$thf( one ))]]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
thf(47,plain,
! [A: $i,B: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(80,plain,
! [A: $i] :
( ( ( join @ A @ one )
!= one )
| ( ( composition @ A @ one )
!= ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,20]) ).
thf(84,plain,
! [A: $i] :
( ( ( join @ A @ one )
!= one )
| ( A
!= ( converse @ ( composition @ sk1 @ sk2 ) ) )
| ( ( composition @ sk1 @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[80]) ).
thf(90,plain,
( ( ( join @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ one )
!= one )
| ( ( composition @ sk1 @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[84]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
thf(35,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(36,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( composition @ A @ B ) @ C )
= ( composition @ A @ ( composition @ B @ C ) ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(10,axiom,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
thf(44,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(45,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(lifteq,[status(thm)],[45]) ).
thf(77,plain,
( ( join @ ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) @ one )
!= ( join @ ( composition @ ( converse @ sk1 ) @ sk1 ) @ one ) ),
inference(paramod_ordered,[status(thm)],[22,20]) ).
thf(83,plain,
( ( ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) )
!= ( composition @ ( converse @ sk1 ) @ sk1 ) )
| ( one != one ) ),
inference(simp,[status(thm)],[77]) ).
thf(89,plain,
( ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) )
!= ( composition @ ( converse @ sk1 ) @ sk1 ) ),
inference(simp,[status(thm)],[83]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
!= one )
| ( ( join @ A @ B )
!= ( join @ ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) @ one ) ) ),
inference(paramod_ordered,[status(thm)],[25,20]) ).
thf(206,plain,
( ( join @ one @ ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) )
!= one ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) )),bind(B,$thf( one ))]]) ).
thf(1112,plain,
! [A: $i] :
( ( ( join @ A @ zero )
= top )
| ( ( complement @ top )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1103,58]) ).
thf(1113,plain,
( ( join @ top @ zero )
= top ),
inference(pattern_uni,[status(thm)],[1112:[bind(A,$thf( top ))]]) ).
thf(1038,plain,
( ( ( converse @ ( composition @ sk1 @ sk2 ) )
!= ( converse @ sk1 ) )
| ( ( composition @ sk1 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[89]) ).
thf(1084,plain,
( ( ( composition @ sk1 @ sk2 )
!= sk1 )
| ( ( composition @ sk1 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[1038]) ).
thf(1102,plain,
( ( composition @ sk1 @ sk2 )
!= sk1 ),
inference(simp,[status(thm)],[1084]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
= one )
| ( sk1 != one )
| ( ( join @ A @ B )
!= ( join @ ( converse @ sk1 ) @ one ) ) ),
inference(paramod_ordered,[status(thm)],[25,69]) ).
thf(194,plain,
( ( ( join @ one @ ( converse @ sk1 ) )
= one )
| ( sk1 != one ) ),
inference(pattern_uni,[status(thm)],[193:[bind(A,$thf( converse @ sk1 )),bind(B,$thf( one ))]]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
thf(50,plain,
! [A: $i,B: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2104,plain,
$false,
inference(e,[status(thm)],[69,247,56,164,678,92,53,476,41,1318,1107,172,776,43,58,47,90,37,25,20,46,29,89,206,349,21,28,38,1103,32,34,22,44,59,1113,1102,35,209,194,50,16,31,40,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : REL031+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 18:30:42 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.83/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/0.95 % [INFO] Parsing done (124ms).
% 1.29/0.96 % [INFO] Running in sequential loop mode.
% 1.69/1.16 % [INFO] eprover registered as external prover.
% 1.69/1.16 % [INFO] cvc4 registered as external prover.
% 1.69/1.17 % [INFO] Scanning for conjecture ...
% 1.76/1.22 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 1.88/1.25 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.88/1.27 % [INFO] Problem is first-order (TPTP FOF).
% 1.88/1.27 % [INFO] Type checking passed.
% 1.88/1.27 % [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 ...
% 11.16/3.01 % External prover 'e' found a proof!
% 11.16/3.01 % [INFO] Killing All external provers ...
% 11.16/3.01 % Time passed: 2505ms (effective reasoning time: 2048ms)
% 11.16/3.01 % 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)>
% 11.16/3.02 % Axioms used in derivation (13): converse_cancellativity, composition_identity, converse_idempotence, composition_associativity, maddux3_a_kind_of_de_Morgan, maddux2_join_associativity, maddux1_join_commutativity, converse_multiplicativity, converse_additivity, def_top, def_zero, composition_distributivity, maddux4_definiton_of_meet
% 11.16/3.02 % No. of inferences in proof: 108
% 11.16/3.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2505 ms resp. 2048 ms w/o parsing
% 11.16/3.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.16/3.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------