TSTP Solution File: REL044+1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : REL044+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 08:04:17 EDT 2024
% Result : Theorem 66.82s 11.62s
% Output : Refutation 66.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 25
% Syntax : Number of formulae : 122 ( 67 unt; 11 typ; 0 def)
% Number of atoms : 178 ( 177 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 877 ( 97 ~; 64 |; 0 &; 713 @)
% ( 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 : 13 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 146 ( 0 ^ 146 !; 0 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_type,type,
join: $i > $i > $i ).
thf(composition_type,type,
composition: $i > $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(converse_type,type,
converse: $i > $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(one_type,type,
one: $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(sk3_type,type,
sk3: $i ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( join @ ( composition @ ( complement @ A ) @ B ) @ ( complement @ C ) )
= ( complement @ C ) )
=> ( ( join @ ( composition @ C @ ( converse @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( join @ ( composition @ ( complement @ A ) @ B ) @ ( complement @ C ) )
= ( complement @ C ) )
=> ( ( join @ ( composition @ C @ ( converse @ B ) ) @ A )
= A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( join @ ( composition @ ( complement @ A ) @ B ) @ ( complement @ C ) )
= ( complement @ C ) )
=> ( ( join @ ( composition @ C @ ( converse @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
( ( join @ ( composition @ ( complement @ sk1 ) @ sk2 ) @ ( complement @ sk3 ) )
= ( complement @ sk3 ) ),
inference(cnf,[status(esa)],[16]) ).
thf(20,plain,
( ( join @ ( composition @ ( complement @ sk1 ) @ sk2 ) @ ( complement @ sk3 ) )
= ( complement @ sk3 ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
= ( complement @ sk3 ) )
| ( ( join @ A @ B )
!= ( join @ ( composition @ ( complement @ sk1 ) @ sk2 ) @ ( complement @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,20]) ).
thf(115,plain,
( ( join @ ( complement @ sk3 ) @ ( composition @ ( complement @ sk1 ) @ sk2 ) )
= ( complement @ sk3 ) ),
inference(pattern_uni,[status(thm)],[114:[bind(A,$thf( composition @ ( complement @ sk1 ) @ sk2 )),bind(B,$thf( complement @ sk3 ))]]) ).
thf(14,axiom,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
thf(54,plain,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(55,plain,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(56,plain,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= top ),
inference(lifteq,[status(thm)],[55]) ).
thf(17,plain,
( ( join @ ( composition @ sk3 @ ( converse @ sk2 ) ) @ sk1 )
!= sk1 ),
inference(cnf,[status(esa)],[16]) ).
thf(19,plain,
( ( join @ ( composition @ sk3 @ ( converse @ sk2 ) ) @ sk1 )
!= sk1 ),
inference(lifteq,[status(thm)],[17]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
!= sk1 )
| ( ( join @ A @ B )
!= ( join @ ( composition @ sk3 @ ( converse @ sk2 ) ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[23,19]) ).
thf(123,plain,
( ( join @ sk1 @ ( composition @ sk3 @ ( converse @ sk2 ) ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( composition @ sk3 @ ( converse @ sk2 ) )),bind(B,$thf( sk1 ))]]) ).
thf(136,plain,
! [A: $i] :
( ( sk1 != top )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ sk1 @ ( composition @ sk3 @ ( converse @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[56,123]) ).
thf(142,plain,
! [A: $i] :
( ( sk1 != top )
| ( A != sk1 )
| ( ( complement @ A )
!= ( composition @ sk3 @ ( converse @ sk2 ) ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(147,plain,
( ( sk1 != top )
| ( ( composition @ sk3 @ ( converse @ sk2 ) )
!= ( complement @ sk1 ) ) ),
inference(simp,[status(thm)],[142]) ).
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(24,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(25,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(206,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ ( complement @ sk3 ) @ C )
= ( join @ A @ ( join @ B @ C ) ) )
| ( ( join @ ( complement @ sk3 ) @ ( composition @ ( complement @ sk1 ) @ sk2 ) )
!= ( join @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[115,26]) ).
thf(207,plain,
! [A: $i] :
( ( join @ ( complement @ sk3 ) @ ( join @ ( composition @ ( complement @ sk1 ) @ sk2 ) @ A ) )
= ( join @ ( complement @ sk3 ) @ A ) ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( complement @ sk3 )),bind(B,$thf( composition @ ( complement @ sk1 ) @ sk2 )),bind(C,$thf( C ))]]) ).
thf(255,plain,
! [A: $i] :
( ( join @ ( complement @ sk3 ) @ ( join @ ( composition @ ( complement @ sk1 ) @ sk2 ) @ A ) )
= ( join @ ( complement @ sk3 ) @ A ) ),
inference(simp,[status(thm)],[207]) ).
thf(328,plain,
! [B: $i,A: $i] :
( ( ( join @ ( complement @ sk3 ) @ top )
= ( join @ ( complement @ sk3 ) @ B ) )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ ( composition @ ( complement @ sk1 ) @ sk2 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56,255]) ).
thf(329,plain,
( ( join @ ( complement @ sk3 ) @ ( complement @ ( composition @ ( complement @ sk1 ) @ sk2 ) ) )
= ( join @ ( complement @ sk3 ) @ top ) ),
inference(pattern_uni,[status(thm)],[328:[bind(A,$thf( composition @ ( complement @ sk1 ) @ sk2 )),bind(B,$thf( complement @ ( composition @ ( complement @ sk1 ) @ sk2 ) ))]]) ).
thf(8,axiom,
! [A: $i] :
( ( composition @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
thf(36,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(37,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(lifteq,[status(thm)],[37]) ).
thf(60,plain,
! [A: $i] :
( ( ( join @ A @ sk1 )
!= sk1 )
| ( ( composition @ A @ one )
!= ( composition @ sk3 @ ( converse @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[38,19]) ).
thf(61,plain,
! [A: $i] :
( ( ( join @ A @ sk1 )
!= sk1 )
| ( A != sk3 )
| ( ( converse @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[60]) ).
thf(62,plain,
( ( ( join @ sk3 @ sk1 )
!= sk1 )
| ( ( converse @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[61]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
!= sk1 )
| ( ( converse @ sk2 )
!= one )
| ( ( join @ A @ B )
!= ( join @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[23,62]) ).
thf(127,plain,
( ( ( join @ sk1 @ sk3 )
!= sk1 )
| ( ( converse @ sk2 )
!= one ) ),
inference(pattern_uni,[status(thm)],[126:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(177,plain,
! [A: $i] :
( ( sk1 != top )
| ( ( converse @ sk2 )
!= one )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[56,127]) ).
thf(183,plain,
! [A: $i] :
( ( sk1 != top )
| ( ( converse @ sk2 )
!= one )
| ( A != sk1 )
| ( ( complement @ A )
!= sk3 ) ),
inference(simp,[status(thm)],[177]) ).
thf(188,plain,
( ( sk1 != top )
| ( ( converse @ sk2 )
!= one )
| ( ( complement @ sk1 )
!= sk3 ) ),
inference(simp,[status(thm)],[183]) ).
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(39,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(40,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
inference(lifteq,[status(thm)],[40]) ).
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(33,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(34,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( composition @ A @ B ) @ C )
= ( composition @ A @ ( composition @ B @ C ) ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(68,plain,
! [A: $i] :
( ( ( join @ A @ ( complement @ sk3 ) )
= ( complement @ sk3 ) )
| ( ( composition @ A @ one )
!= ( composition @ ( complement @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[38,20]) ).
thf(70,plain,
! [A: $i] :
( ( ( join @ A @ ( complement @ sk3 ) )
= ( complement @ sk3 ) )
| ( A
!= ( complement @ sk1 ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[68]) ).
thf(72,plain,
( ( ( join @ ( complement @ sk1 ) @ ( complement @ sk3 ) )
= ( complement @ sk3 ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[70]) ).
thf(15,axiom,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
thf(57,plain,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(58,plain,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(59,plain,
! [A: $i] :
( ( meet @ A @ ( complement @ A ) )
= zero ),
inference(lifteq,[status(thm)],[58]) ).
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(30,plain,
! [A: $i,B: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(891,plain,
! [A: $i] :
( ( complement @ ( join @ ( complement @ A ) @ ( complement @ ( complement @ A ) ) ) )
= zero ),
inference(rewrite,[status(thm)],[59,32]) ).
thf(1363,plain,
( ( complement @ top )
= zero ),
inference(rewrite,[status(thm)],[891,56]) ).
thf(1366,plain,
! [A: $i] :
( ( ( join @ A @ zero )
= top )
| ( ( complement @ top )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1363,56]) ).
thf(1367,plain,
( ( join @ top @ zero )
= top ),
inference(pattern_uni,[status(thm)],[1366:[bind(A,$thf( top ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
thf(42,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
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(27,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(28,plain,
! [B: $i,A: $i] :
( A
= ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) )
= A ),
inference(lifteq,[status(thm)],[28]) ).
thf(43,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(cnf,[status(esa)],[42]) ).
thf(44,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(lifteq,[status(thm)],[43]) ).
thf(74,plain,
! [A: $i] :
( ( ( join @ sk3 @ sk1 )
!= sk1 )
| ( A != one )
| ( ( converse @ ( converse @ A ) )
!= ( converse @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[44,62]) ).
thf(77,plain,
( ( ( join @ sk3 @ sk1 )
!= sk1 )
| ( ( converse @ one )
!= sk2 ) ),
inference(simp,[status(thm)],[74]) ).
thf(89,plain,
! [A: $i] :
( ( sk1 != top )
| ( ( converse @ sk2 )
!= one )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[56,62]) ).
thf(91,plain,
! [A: $i] :
( ( sk1 != top )
| ( ( converse @ sk2 )
!= one )
| ( A != sk3 )
| ( ( complement @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[89]) ).
thf(96,plain,
( ( sk1 != top )
| ( ( converse @ sk2 )
!= one )
| ( ( complement @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[91]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ C @ B )
= top )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[56,23]) ).
thf(111,plain,
! [A: $i] :
( ( join @ ( complement @ A ) @ A )
= top ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( complement @ D ))]]) ).
thf(134,plain,
! [A: $i] :
( ( join @ ( complement @ A ) @ A )
= top ),
inference(simp,[status(thm)],[111]) ).
thf(403,plain,
! [B: $i,A: $i] :
( ( ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( complement @ sk3 ) ) )
= A )
| ( ( join @ ( complement @ sk3 ) @ ( composition @ ( complement @ sk1 ) @ sk2 ) )
!= ( join @ ( complement @ A ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[115,29]) ).
thf(404,plain,
( ( join @ ( complement @ ( join @ ( complement @ sk3 ) @ ( complement @ ( composition @ ( complement @ sk1 ) @ sk2 ) ) ) ) @ ( complement @ ( complement @ sk3 ) ) )
= sk3 ),
inference(pattern_uni,[status(thm)],[403:[bind(A,$thf( sk3 )),bind(B,$thf( composition @ ( complement @ sk1 ) @ sk2 ))]]) ).
thf(671,plain,
( ( join @ ( complement @ ( join @ ( complement @ sk3 ) @ top ) ) @ ( complement @ ( complement @ sk3 ) ) )
= sk3 ),
inference(rewrite,[status(thm)],[404,329]) ).
thf(717,plain,
! [B: $i,A: $i] :
( ( ( join @ ( complement @ ( join @ B @ A ) ) @ ( complement @ ( complement @ sk3 ) ) )
= sk3 )
| ( ( join @ A @ B )
!= ( join @ ( complement @ sk3 ) @ top ) ) ),
inference(paramod_ordered,[status(thm)],[23,671]) ).
thf(718,plain,
( ( join @ ( complement @ ( join @ top @ ( complement @ sk3 ) ) ) @ ( complement @ ( complement @ sk3 ) ) )
= sk3 ),
inference(pattern_uni,[status(thm)],[717:[bind(A,$thf( complement @ sk3 )),bind(B,$thf( top ))]]) ).
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(45,plain,
! [A: $i,B: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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(48,plain,
! [A: $i,B: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(711,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
= sk3 )
| ( ( join @ ( complement @ ( join @ ( complement @ sk3 ) @ top ) ) @ ( complement @ ( complement @ sk3 ) ) )
!= ( join @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[671,23]) ).
thf(712,plain,
( ( join @ ( complement @ ( complement @ sk3 ) ) @ ( complement @ ( join @ ( complement @ sk3 ) @ top ) ) )
= sk3 ),
inference(pattern_uni,[status(thm)],[711:[bind(A,$thf( complement @ ( join @ ( complement @ sk3 ) @ top ) )),bind(B,$thf( complement @ ( complement @ sk3 ) ))]]) ).
thf(88,plain,
! [A: $i] :
( ( sk1 != top )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ ( composition @ sk3 @ ( converse @ sk2 ) ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[56,19]) ).
thf(90,plain,
! [A: $i] :
( ( sk1 != top )
| ( A
!= ( composition @ sk3 @ ( converse @ sk2 ) ) )
| ( ( complement @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[88]) ).
thf(95,plain,
( ( sk1 != top )
| ( ( complement @ ( composition @ sk3 @ ( converse @ sk2 ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[90]) ).
thf(87,plain,
! [A: $i] :
( ( sk1 != top )
| ( ( converse @ one )
!= sk2 )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[56,77]) ).
thf(94,plain,
! [A: $i] :
( ( sk1 != top )
| ( ( converse @ one )
!= sk2 )
| ( A != sk3 )
| ( ( complement @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[87]) ).
thf(99,plain,
( ( sk1 != top )
| ( ( converse @ one )
!= sk2 )
| ( ( complement @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[94]) ).
thf(555,plain,
! [B: $i,A: $i] :
( ( ( join @ ( complement @ sk3 ) @ top )
= ( join @ B @ A ) )
| ( ( join @ ( complement @ sk3 ) @ ( complement @ ( composition @ ( complement @ sk1 ) @ sk2 ) ) )
!= ( join @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[329,23]) ).
thf(556,plain,
( ( join @ ( complement @ ( composition @ ( complement @ sk1 ) @ sk2 ) ) @ ( complement @ sk3 ) )
= ( join @ ( complement @ sk3 ) @ top ) ),
inference(pattern_uni,[status(thm)],[555:[bind(A,$thf( complement @ sk3 )),bind(B,$thf( complement @ ( composition @ ( complement @ sk1 ) @ sk2 ) ))]]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
!= sk1 )
| ( ( converse @ one )
!= sk2 )
| ( ( join @ A @ B )
!= ( join @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[23,77]) ).
thf(131,plain,
( ( ( join @ sk1 @ sk3 )
!= sk1 )
| ( ( converse @ one )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(192,plain,
! [A: $i] :
( ( sk1 != top )
| ( ( converse @ one )
!= sk2 )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[56,131]) ).
thf(198,plain,
! [A: $i] :
( ( sk1 != top )
| ( ( converse @ one )
!= sk2 )
| ( A != sk1 )
| ( ( complement @ A )
!= sk3 ) ),
inference(simp,[status(thm)],[192]) ).
thf(203,plain,
( ( sk1 != top )
| ( ( converse @ one )
!= sk2 )
| ( ( complement @ sk1 )
!= sk3 ) ),
inference(simp,[status(thm)],[198]) ).
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(51,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(827,plain,
! [B: $i,A: $i] :
( ( ( join @ ( complement @ ( complement @ sk3 ) ) @ ( complement @ ( join @ B @ A ) ) )
= sk3 )
| ( ( join @ A @ B )
!= ( join @ ( complement @ sk3 ) @ top ) ) ),
inference(paramod_ordered,[status(thm)],[23,712]) ).
thf(828,plain,
( ( join @ ( complement @ ( complement @ sk3 ) ) @ ( complement @ ( join @ top @ ( complement @ sk3 ) ) ) )
= sk3 ),
inference(pattern_uni,[status(thm)],[827:[bind(A,$thf( complement @ sk3 )),bind(B,$thf( top ))]]) ).
thf(26330,plain,
$false,
inference(e,[status(thm)],[115,56,147,329,188,41,54,39,35,72,1367,42,24,20,57,29,38,21,33,77,96,134,718,32,45,44,27,255,123,48,712,95,16,127,99,556,203,671,26,23,36,30,51,19,1363,828,131,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : REL044+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n025.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 12:47:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.06/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.37/1.15 % [INFO] Parsing done (162ms).
% 1.37/1.15 % [INFO] Running in sequential loop mode.
% 2.03/1.41 % [INFO] eprover registered as external prover.
% 2.03/1.42 % [INFO] cvc4 registered as external prover.
% 2.03/1.42 % [INFO] Scanning for conjecture ...
% 2.20/1.50 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 2.34/1.53 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.34/1.56 % [INFO] Problem is first-order (TPTP FOF).
% 2.34/1.57 % [INFO] Type checking passed.
% 2.34/1.57 % [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 ...
% 66.82/11.62 % External prover 'e' found a proof!
% 66.82/11.62 % [INFO] Killing All external provers ...
% 66.82/11.62 % Time passed: 11077ms (effective reasoning time: 10461ms)
% 66.82/11.62 % 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)>
% 66.82/11.62 % 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
% 66.82/11.62 % No. of inferences in proof: 111
% 66.82/11.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11077 ms resp. 10461 ms w/o parsing
% 66.82/11.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 66.82/11.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------