TSTP Solution File: REL012-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : REL012-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 11:48:23 EDT 2023
% Result : Unsatisfiable 48.98s 8.27s
% Output : Refutation 48.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 24
% Syntax : Number of formulae : 109 ( 57 unt; 10 typ; 0 def)
% Number of atoms : 181 ( 180 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 851 ( 120 ~; 82 |; 0 &; 649 @)
% ( 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 : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 107 ( 0 ^; 107 !; 0 ?; 107 :)
% 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(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $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(14,axiom,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
thf(42,plain,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(43,plain,
! [A: $i] :
( ( meet @ A @ ( complement @ A ) )
= zero ),
inference(lifteq,[status(thm)],[42]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(215,plain,
! [A: $i] :
( ( complement @ ( join @ ( complement @ A ) @ ( complement @ ( complement @ A ) ) ) )
= zero ),
inference(rewrite,[status(thm)],[43,25]) ).
thf(13,axiom,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
thf(40,plain,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(41,plain,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= top ),
inference(lifteq,[status(thm)],[40]) ).
thf(336,plain,
( ( complement @ top )
= zero ),
inference(rewrite,[status(thm)],[215,41]) ).
thf(339,plain,
! [A: $i] :
( ( ( join @ A @ zero )
= top )
| ( ( complement @ top )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[336,41]) ).
thf(340,plain,
( ( join @ top @ zero )
= top ),
inference(pattern_uni,[status(thm)],[339:[bind(A,$thf( top ))]]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(397,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ top @ C )
= ( join @ A @ ( join @ B @ C ) ) )
| ( ( join @ top @ zero )
!= ( join @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[340,21]) ).
thf(398,plain,
! [A: $i] :
( ( join @ top @ ( join @ zero @ A ) )
= ( join @ top @ A ) ),
inference(pattern_uni,[status(thm)],[397:[bind(A,$thf( top )),bind(B,$thf( zero ))]]) ).
thf(420,plain,
! [A: $i] :
( ( join @ top @ ( join @ zero @ A ) )
= ( join @ top @ A ) ),
inference(simp,[status(thm)],[398]) ).
thf(571,plain,
! [B: $i,A: $i] :
( ( ( join @ top @ top )
= ( join @ top @ B ) )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ zero @ B ) ) ),
inference(paramod_ordered,[status(thm)],[41,420]) ).
thf(572,plain,
( ( join @ top @ ( complement @ zero ) )
= ( join @ top @ top ) ),
inference(pattern_uni,[status(thm)],[571:[bind(A,$thf( zero )),bind(B,$thf( complement @ zero ))]]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(678,plain,
! [B: $i,A: $i] :
( ( ( join @ top @ top )
= ( join @ B @ A ) )
| ( ( join @ top @ ( complement @ zero ) )
!= ( join @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[572,19]) ).
thf(679,plain,
( ( join @ ( complement @ zero ) @ top )
= ( join @ top @ top ) ),
inference(pattern_uni,[status(thm)],[678:[bind(A,$thf( top )),bind(B,$thf( complement @ zero ))]]) ).
thf(4,axiom,
! [B: $i,A: $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_3) ).
thf(22,plain,
! [B: $i,A: $i] :
( A
= ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) )
= A ),
inference(lifteq,[status(thm)],[22]) ).
thf(747,plain,
! [B: $i,A: $i] :
( ( ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ top @ top ) ) )
= A )
| ( ( join @ ( complement @ zero ) @ top )
!= ( join @ ( complement @ A ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[679,23]) ).
thf(748,plain,
( ( join @ ( complement @ ( join @ ( complement @ zero ) @ ( complement @ top ) ) ) @ ( complement @ ( join @ top @ top ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[747:[bind(A,$thf( zero )),bind(B,$thf( top ))]]) ).
thf(802,plain,
( ( join @ ( complement @ ( join @ ( complement @ zero ) @ zero ) ) @ ( complement @ ( join @ top @ top ) ) )
= zero ),
inference(rewrite,[status(thm)],[748,336]) ).
thf(9,axiom,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
thf(32,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(33,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(lifteq,[status(thm)],[32]) ).
thf(7,axiom,
! [A: $i] :
( ( composition @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
thf(28,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(lifteq,[status(thm)],[28]) ).
thf(1,negated_conjecture,
( ( join @ ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
thf(15,plain,
( ( join @ ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(16,plain,
( ( join @ ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(17,plain,
( ( join @ ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(47,plain,
! [A: $i] :
( ( ( join @ A @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( ( composition @ A @ one )
!= ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,17]) ).
thf(51,plain,
! [A: $i] :
( ( ( join @ A @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( A
!= ( complement @ ( composition @ sk1 @ sk2 ) ) )
| ( ( converse @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[47]) ).
thf(55,plain,
( ( ( join @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( ( converse @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[51]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
!= ( complement @ sk1 ) )
| ( ( converse @ sk2 )
!= one )
| ( ( join @ A @ B )
!= ( join @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( complement @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,55]) ).
thf(85,plain,
( ( ( join @ ( complement @ sk1 ) @ ( complement @ ( composition @ sk1 @ sk2 ) ) )
!= ( complement @ sk1 ) )
| ( ( converse @ sk2 )
!= one ) ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( complement @ ( composition @ sk1 @ sk2 ) )),bind(B,$thf( complement @ sk1 ))]]) ).
thf(381,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( converse @ sk2 )
!= one )
| ( ( join @ ( complement @ sk1 ) @ ( complement @ ( composition @ sk1 @ sk2 ) ) )
!= ( join @ top @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[340,85]) ).
thf(408,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( converse @ sk2 )
!= one )
| ( ( complement @ sk1 )
!= top )
| ( ( complement @ ( composition @ sk1 @ sk2 ) )
!= zero ) ),
inference(simp,[status(thm)],[381]) ).
thf(422,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( converse @ sk2 )
!= one )
| ( ( complement @ ( composition @ sk1 @ sk2 ) )
!= zero ) ),
inference(simp,[status(thm)],[408]) ).
thf(494,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( converse @ sk2 )
!= one )
| ( ( complement @ ( composition @ sk1 @ sk2 ) )
!= ( complement @ top ) ) ),
inference(paramod_ordered,[status(thm)],[336,422]) ).
thf(499,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( converse @ sk2 )
!= one )
| ( ( composition @ sk1 @ sk2 )
!= top ) ),
inference(simp,[status(thm)],[494]) ).
thf(503,plain,
! [A: $i] :
( ( ( complement @ sk1 )
!= top )
| ( ( converse @ sk2 )
!= one )
| ( A != top )
| ( ( composition @ A @ one )
!= ( composition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[29,499]) ).
thf(507,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( converse @ sk2 )
!= one )
| ( top != sk1 )
| ( one != sk2 ) ),
inference(simp,[status(thm)],[503]) ).
thf(511,plain,
! [A: $i] :
( ( ( complement @ sk1 )
!= top )
| ( A != one )
| ( top != sk1 )
| ( one != sk2 )
| ( ( converse @ ( converse @ A ) )
!= ( converse @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[33,507]) ).
thf(514,plain,
( ( ( complement @ sk1 )
!= top )
| ( top != sk1 )
| ( one != sk2 )
| ( ( converse @ one )
!= sk2 ) ),
inference(simp,[status(thm)],[511]) ).
thf(512,plain,
( ( zero != top )
| ( ( converse @ sk2 )
!= one )
| ( top != sk1 )
| ( one != sk2 )
| ( ( complement @ top )
!= ( complement @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[336,507]) ).
thf(515,plain,
( ( zero != top )
| ( ( converse @ sk2 )
!= one )
| ( top != sk1 )
| ( one != sk2 )
| ( top != sk1 ) ),
inference(simp,[status(thm)],[512]) ).
thf(516,plain,
( ( zero != top )
| ( ( converse @ sk2 )
!= one )
| ( top != sk1 )
| ( one != sk2 ) ),
inference(simp,[status(thm)],[515]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ C @ B )
= top )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[41,19]) ).
thf(68,plain,
! [A: $i] :
( ( join @ ( complement @ A ) @ A )
= top ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( complement @ D ))]]) ).
thf(79,plain,
! [A: $i] :
( ( join @ ( complement @ A ) @ A )
= top ),
inference(simp,[status(thm)],[68]) ).
thf(796,plain,
! [A: $i] :
( ( zero != top )
| ( A != one )
| ( top != sk1 )
| ( one != sk2 )
| ( ( converse @ ( converse @ A ) )
!= ( converse @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[33,516]) ).
thf(798,plain,
( ( zero != top )
| ( top != sk1 )
| ( one != sk2 )
| ( ( converse @ one )
!= sk2 ) ),
inference(simp,[status(thm)],[796]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( join @ ( composition @ ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @ ( complement @ B ) )
= ( complement @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity_11) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( join @ ( composition @ ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @ ( complement @ B ) )
= ( complement @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(820,plain,
! [A: $i] :
( ( ( join @ ( complement @ top ) @ ( complement @ ( join @ top @ top ) ) )
= zero )
| ( ( join @ ( complement @ A ) @ A )
!= ( join @ ( complement @ zero ) @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[79,802]) ).
thf(821,plain,
( ( join @ ( complement @ top ) @ ( complement @ ( join @ top @ top ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[820:[bind(A,$thf( zero ))]]) ).
thf(1050,plain,
( ( join @ zero @ ( complement @ ( join @ top @ top ) ) )
= zero ),
inference(rewrite,[status(thm)],[821,336]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity_5) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( composition @ A @ B ) @ C )
= ( composition @ A @ ( composition @ B @ C ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(46,plain,
! [A: $i] :
( ( ( join @ ( composition @ ( complement @ A ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( ( composition @ A @ one )
!= ( composition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[29,17]) ).
thf(50,plain,
! [A: $i] :
( ( ( join @ ( composition @ ( complement @ A ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( A != sk1 )
| ( one != sk2 ) ),
inference(simp,[status(thm)],[46]) ).
thf(54,plain,
( ( ( join @ ( composition @ ( complement @ sk1 ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( one != sk2 ) ),
inference(simp,[status(thm)],[50]) ).
thf(349,plain,
! [A: $i] :
( ( ( join @ zero @ A )
= top )
| ( ( complement @ top )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[336,79]) ).
thf(350,plain,
( ( join @ zero @ top )
= top ),
inference(pattern_uni,[status(thm)],[349:[bind(A,$thf( top ))]]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
!= ( complement @ sk1 ) )
| ( ( join @ A @ B )
!= ( join @ ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,17]) ).
thf(72,plain,
( ( join @ ( complement @ sk1 ) @ ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) ) )
!= ( complement @ sk1 ) ),
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) )),bind(B,$thf( complement @ sk1 ))]]) ).
thf(400,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( join @ ( complement @ sk1 ) @ ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) ) )
!= ( join @ top @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[340,72]) ).
thf(416,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( complement @ sk1 )
!= top )
| ( ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) )
!= zero ) ),
inference(simp,[status(thm)],[400]) ).
thf(419,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) )
!= zero ) ),
inference(simp,[status(thm)],[416]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
!= ( complement @ sk1 ) )
| ( one != sk2 )
| ( ( join @ A @ B )
!= ( join @ ( composition @ ( complement @ sk1 ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,54]) ).
thf(76,plain,
( ( ( join @ ( complement @ sk1 ) @ ( composition @ ( complement @ sk1 ) @ ( converse @ sk2 ) ) )
!= ( complement @ sk1 ) )
| ( one != sk2 ) ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( composition @ ( complement @ sk1 ) @ ( converse @ sk2 ) )),bind(B,$thf( complement @ sk1 ))]]) ).
thf(504,plain,
! [A: $i] :
( ( ( complement @ sk1 )
!= top )
| ( A != one )
| ( ( composition @ sk1 @ sk2 )
!= top )
| ( ( converse @ ( converse @ A ) )
!= ( converse @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[33,499]) ).
thf(509,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( composition @ sk1 @ sk2 )
!= top )
| ( ( converse @ one )
!= sk2 ) ),
inference(simp,[status(thm)],[504]) ).
thf(57,plain,
! [A: $i] :
( ( ( join @ A @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( one != sk2 )
| ( ( composition @ A @ one )
!= ( composition @ ( complement @ sk1 ) @ ( converse @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,54]) ).
thf(60,plain,
! [A: $i] :
( ( ( join @ A @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( one != sk2 )
| ( A
!= ( complement @ sk1 ) )
| ( ( converse @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[57]) ).
thf(63,plain,
( ( ( join @ ( complement @ sk1 ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( one != sk2 )
| ( ( converse @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[60]) ).
thf(1100,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
= zero )
| ( ( join @ zero @ ( complement @ ( join @ top @ top ) ) )
!= ( join @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1050,19]) ).
thf(1101,plain,
( ( join @ ( complement @ ( join @ top @ top ) ) @ zero )
= zero ),
inference(pattern_uni,[status(thm)],[1100:[bind(A,$thf( zero )),bind(B,$thf( complement @ ( join @ top @ top ) ))]]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(23534,plain,
$false,
inference(e,[status(thm)],[340,802,514,507,679,516,31,79,15,42,24,25,20,29,85,798,21,33,28,38,420,499,1050,41,17,32,34,22,27,54,572,350,419,76,509,63,18,336,72,40,26,1101,55,23,36,30,19,422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL012-1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 18:04:13 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.91/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.96 % [INFO] Parsing done (124ms).
% 1.21/0.97 % [INFO] Running in sequential loop mode.
% 1.69/1.16 % [INFO] eprover registered as external prover.
% 1.69/1.17 % [INFO] cvc4 registered as external prover.
% 1.69/1.17 % [INFO] Scanning for conjecture ...
% 1.69/1.22 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 1.89/1.24 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.89/1.26 % [INFO] Problem is propositional (TPTP CNF).
% 1.89/1.26 % [INFO] Type checking passed.
% 1.89/1.27 % [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 ...
% 48.32/8.26 % External prover 'e' found a proof!
% 48.32/8.26 % [INFO] Killing All external provers ...
% 48.32/8.26 % Time passed: 7750ms (effective reasoning time: 7294ms)
% 48.32/8.26 % 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)>
% 48.98/8.27 % Axioms used in derivation (13): maddux3_a_kind_of_de_Morgan_3, converse_idempotence_8, maddux1_join_commutativity_1, def_top_12, converse_cancellativity_11, composition_associativity_5, maddux2_join_associativity_2, composition_distributivity_7, composition_identity_6, maddux4_definiton_of_meet_4, converse_additivity_9, def_zero_13, converse_multiplicativity_10
% 48.98/8.27 % No. of inferences in proof: 99
% 48.98/8.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7750 ms resp. 7294 ms w/o parsing
% 48.98/8.31 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 48.98/8.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------