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 : n011.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 11:48:24 EDT 2023
% Result : Theorem 55.77s 9.59s
% Output : Refutation 55.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 24
% Syntax : Number of formulae : 121 ( 65 unt; 10 typ; 0 def)
% Number of atoms : 208 ( 207 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 939 ( 141 ~; 97 |; 0 &; 701 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 131 ( 0 ^; 131 !; 0 ?; 131 :)
% 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(8,axiom,
! [A: $i] :
( ( composition @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).
thf(34,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(35,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(lifteq,[status(thm)],[35]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( join @ ( composition @ ( complement @ ( composition @ A @ B ) ) @ ( converse @ B ) ) @ ( complement @ A ) )
= ( complement @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( join @ ( composition @ ( complement @ ( composition @ A @ B ) ) @ ( converse @ B ) ) @ ( complement @ A ) )
= ( complement @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i,B: $i] :
( ( join @ ( composition @ ( complement @ ( composition @ A @ B ) ) @ ( converse @ B ) ) @ ( complement @ A ) )
= ( complement @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
( ( join @ ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
( ( join @ ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(62,plain,
! [A: $i] :
( ( ( join @ ( composition @ ( complement @ A ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( ( composition @ A @ one )
!= ( composition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[36,18]) ).
thf(66,plain,
! [A: $i] :
( ( ( join @ ( composition @ ( complement @ A ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( A != sk1 )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[62]) ).
thf(69,plain,
( ( ( join @ ( composition @ ( complement @ sk1 ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[66]) ).
thf(14,axiom,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top) ).
thf(52,plain,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15,axiom,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).
thf(55,plain,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(56,plain,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [A: $i] :
( ( meet @ A @ ( complement @ A ) )
= zero ),
inference(lifteq,[status(thm)],[56]) ).
thf(6,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(28,plain,
! [A: $i,B: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(229,plain,
! [A: $i] :
( ( complement @ ( join @ ( complement @ A ) @ ( complement @ ( complement @ A ) ) ) )
= zero ),
inference(rewrite,[status(thm)],[57,30]) ).
thf(53,plain,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= top ),
inference(lifteq,[status(thm)],[53]) ).
thf(350,plain,
( ( complement @ top )
= zero ),
inference(rewrite,[status(thm)],[229,54]) ).
thf(375,plain,
! [A: $i] :
( ( ( join @ A @ zero )
= top )
| ( ( complement @ top )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[350,54]) ).
thf(376,plain,
( ( join @ top @ zero )
= top ),
inference(pattern_uni,[status(thm)],[375:[bind(A,$thf( top ))]]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ C @ B )
= top )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[54,21]) ).
thf(86,plain,
! [A: $i] :
( ( join @ ( complement @ A ) @ A )
= top ),
inference(pattern_uni,[status(thm)],[85:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( complement @ D ))]]) ).
thf(93,plain,
! [A: $i] :
( ( join @ ( complement @ A ) @ A )
= top ),
inference(simp,[status(thm)],[86]) ).
thf(369,plain,
! [A: $i] :
( ( ( join @ zero @ A )
= top )
| ( ( complement @ top )
!= ( complement @ A ) ) ),
inference(paramod_ordered,[status(thm)],[350,93]) ).
thf(370,plain,
( ( join @ zero @ top )
= top ),
inference(pattern_uni,[status(thm)],[369:[bind(A,$thf( top ))]]) ).
thf(73,plain,
! [A: $i] :
( ( ( join @ A @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( sk2 != one )
| ( ( composition @ A @ one )
!= ( composition @ ( complement @ sk1 ) @ ( converse @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,69]) ).
thf(76,plain,
! [A: $i] :
( ( ( join @ A @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( sk2 != one )
| ( A
!= ( complement @ sk1 ) )
| ( ( converse @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[73]) ).
thf(78,plain,
( ( ( join @ ( complement @ sk1 ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( sk2 != one )
| ( ( converse @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[76]) ).
thf(410,plain,
( ( ( complement @ sk1 )
!= top )
| ( sk2 != one )
| ( ( converse @ sk2 )
!= one )
| ( ( join @ ( complement @ sk1 ) @ ( complement @ sk1 ) )
!= ( join @ zero @ top ) ) ),
inference(paramod_ordered,[status(thm)],[370,78]) ).
thf(427,plain,
( ( ( complement @ sk1 )
!= top )
| ( sk2 != one )
| ( ( converse @ sk2 )
!= one )
| ( ( complement @ sk1 )
!= zero )
| ( ( complement @ sk1 )
!= top ) ),
inference(simp,[status(thm)],[410]) ).
thf(437,plain,
( ( ( complement @ sk1 )
!= top )
| ( sk2 != one )
| ( ( converse @ sk2 )
!= one )
| ( ( complement @ sk1 )
!= zero ) ),
inference(simp,[status(thm)],[427]) ).
thf(507,plain,
( ( ( complement @ sk1 )
!= top )
| ( sk2 != one )
| ( ( converse @ sk2 )
!= one )
| ( ( complement @ sk1 )
!= ( complement @ top ) ) ),
inference(paramod_ordered,[status(thm)],[350,437]) ).
thf(511,plain,
( ( ( complement @ sk1 )
!= top )
| ( sk2 != one )
| ( ( converse @ sk2 )
!= one )
| ( sk1 != top ) ),
inference(simp,[status(thm)],[507]) ).
thf(515,plain,
( ( zero != top )
| ( sk2 != one )
| ( ( converse @ sk2 )
!= one )
| ( sk1 != top )
| ( ( complement @ sk1 )
!= ( complement @ top ) ) ),
inference(paramod_ordered,[status(thm)],[350,511]) ).
thf(518,plain,
( ( zero != top )
| ( sk2 != one )
| ( ( converse @ sk2 )
!= one )
| ( sk1 != top )
| ( sk1 != top ) ),
inference(simp,[status(thm)],[515]) ).
thf(519,plain,
( ( zero != top )
| ( sk2 != one )
| ( ( converse @ sk2 )
!= one )
| ( sk1 != top ) ),
inference(simp,[status(thm)],[518]) ).
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(37,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(38,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(63,plain,
! [A: $i] :
( ( ( join @ A @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( ( composition @ A @ one )
!= ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,18]) ).
thf(67,plain,
! [A: $i] :
( ( ( join @ A @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( A
!= ( complement @ ( composition @ sk1 @ sk2 ) ) )
| ( ( converse @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[63]) ).
thf(70,plain,
( ( ( join @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( complement @ sk1 ) )
| ( ( converse @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[67]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
!= ( complement @ sk1 ) )
| ( ( converse @ sk2 )
!= one )
| ( ( join @ A @ B )
!= ( join @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( complement @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,70]) ).
thf(99,plain,
( ( ( join @ ( complement @ sk1 ) @ ( complement @ ( composition @ sk1 @ sk2 ) ) )
!= ( complement @ sk1 ) )
| ( ( converse @ sk2 )
!= one ) ),
inference(pattern_uni,[status(thm)],[98:[bind(A,$thf( complement @ ( composition @ sk1 @ sk2 ) )),bind(B,$thf( complement @ sk1 ))]]) ).
thf(4,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(22,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(23,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(405,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)],[370,24]) ).
thf(406,plain,
! [A: $i] :
( ( join @ zero @ ( join @ top @ A ) )
= ( join @ top @ A ) ),
inference(pattern_uni,[status(thm)],[405:[bind(A,$thf( zero )),bind(B,$thf( top ))]]) ).
thf(442,plain,
! [A: $i] :
( ( join @ zero @ ( join @ top @ A ) )
= ( join @ top @ A ) ),
inference(simp,[status(thm)],[406]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
!= ( complement @ sk1 ) )
| ( ( join @ A @ B )
!= ( join @ ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,18]) ).
thf(90,plain,
( ( join @ ( complement @ sk1 ) @ ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) ) )
!= ( complement @ sk1 ) ),
inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) )),bind(B,$thf( complement @ sk1 ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
thf(40,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(41,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(cnf,[status(esa)],[40]) ).
thf(42,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(lifteq,[status(thm)],[41]) ).
thf(411,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( converse @ sk2 )
!= one )
| ( ( join @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( join @ zero @ top ) ) ),
inference(paramod_ordered,[status(thm)],[370,70]) ).
thf(432,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( converse @ sk2 )
!= one )
| ( ( complement @ ( composition @ sk1 @ sk2 ) )
!= zero )
| ( ( complement @ sk1 )
!= top ) ),
inference(simp,[status(thm)],[411]) ).
thf(441,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( converse @ sk2 )
!= one )
| ( ( complement @ ( composition @ sk1 @ sk2 ) )
!= zero ) ),
inference(simp,[status(thm)],[432]) ).
thf(683,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( converse @ sk2 )
!= one )
| ( ( complement @ ( composition @ sk1 @ sk2 ) )
!= ( complement @ top ) ) ),
inference(paramod_ordered,[status(thm)],[350,441]) ).
thf(685,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( converse @ sk2 )
!= one )
| ( ( composition @ sk1 @ sk2 )
!= top ) ),
inference(simp,[status(thm)],[683]) ).
thf(1034,plain,
! [A: $i] :
( ( ( complement @ sk1 )
!= top )
| ( A != one )
| ( ( composition @ sk1 @ sk2 )
!= top )
| ( ( converse @ ( converse @ A ) )
!= ( converse @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[42,685]) ).
thf(1041,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( composition @ sk1 @ sk2 )
!= top )
| ( ( converse @ one )
!= sk2 ) ),
inference(simp,[status(thm)],[1034]) ).
thf(401,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( join @ ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( join @ zero @ top ) ) ),
inference(paramod_ordered,[status(thm)],[370,18]) ).
thf(426,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) )
!= zero )
| ( ( complement @ sk1 )
!= top ) ),
inference(simp,[status(thm)],[401]) ).
thf(436,plain,
( ( ( complement @ sk1 )
!= top )
| ( ( composition @ ( complement @ ( composition @ sk1 @ sk2 ) ) @ ( converse @ sk2 ) )
!= zero ) ),
inference(simp,[status(thm)],[426]) ).
thf(5,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(25,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(12,axiom,
! [A: $i,B: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).
thf(46,plain,
! [A: $i,B: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(455,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)],[376,24]) ).
thf(456,plain,
! [A: $i] :
( ( join @ top @ ( join @ zero @ A ) )
= ( join @ top @ A ) ),
inference(pattern_uni,[status(thm)],[455:[bind(A,$thf( top )),bind(B,$thf( zero ))]]) ).
thf(484,plain,
! [A: $i] :
( ( join @ top @ ( join @ zero @ A ) )
= ( join @ top @ A ) ),
inference(simp,[status(thm)],[456]) ).
thf(814,plain,
! [B: $i,A: $i] :
( ( ( join @ top @ top )
= ( join @ top @ B ) )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ zero @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54,484]) ).
thf(815,plain,
( ( join @ top @ ( complement @ zero ) )
= ( join @ top @ top ) ),
inference(pattern_uni,[status(thm)],[814:[bind(A,$thf( zero )),bind(B,$thf( complement @ zero ))]]) ).
thf(893,plain,
! [B: $i,A: $i] :
( ( ( join @ top @ top )
= ( join @ B @ A ) )
| ( ( join @ top @ ( complement @ zero ) )
!= ( join @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[815,21]) ).
thf(894,plain,
( ( join @ ( complement @ zero ) @ top )
= ( join @ top @ top ) ),
inference(pattern_uni,[status(thm)],[893:[bind(A,$thf( top )),bind(B,$thf( complement @ zero ))]]) ).
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(31,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(32,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( composition @ A @ B ) @ C )
= ( composition @ A @ ( composition @ B @ C ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(520,plain,
! [A: $i] :
( ( zero != top )
| ( sk2 != one )
| ( A != one )
| ( sk1 != top )
| ( ( converse @ ( converse @ A ) )
!= ( converse @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[42,519]) ).
thf(522,plain,
( ( zero != top )
| ( sk2 != one )
| ( sk1 != top )
| ( ( converse @ one )
!= sk2 ) ),
inference(simp,[status(thm)],[520]) ).
thf(26,plain,
! [B: $i,A: $i] :
( A
= ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) )
= A ),
inference(lifteq,[status(thm)],[26]) ).
thf(13,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(49,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(395,plain,
( ( ( complement @ sk1 )
!= top )
| ( sk2 != one )
| ( ( join @ ( composition @ ( complement @ sk1 ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) )
!= ( join @ zero @ top ) ) ),
inference(paramod_ordered,[status(thm)],[370,69]) ).
thf(428,plain,
( ( ( complement @ sk1 )
!= top )
| ( sk2 != one )
| ( ( composition @ ( complement @ sk1 ) @ ( converse @ sk2 ) )
!= zero )
| ( ( complement @ sk1 )
!= top ) ),
inference(simp,[status(thm)],[395]) ).
thf(438,plain,
( ( ( complement @ sk1 )
!= top )
| ( sk2 != one )
| ( ( composition @ ( complement @ sk1 ) @ ( converse @ sk2 ) )
!= zero ) ),
inference(simp,[status(thm)],[428]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
!= ( complement @ sk1 ) )
| ( sk2 != one )
| ( ( join @ A @ B )
!= ( join @ ( composition @ ( complement @ sk1 ) @ ( converse @ sk2 ) ) @ ( complement @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,69]) ).
thf(80,plain,
( ( ( join @ ( complement @ sk1 ) @ ( composition @ ( complement @ sk1 ) @ ( converse @ sk2 ) ) )
!= ( complement @ sk1 ) )
| ( sk2 != one ) ),
inference(pattern_uni,[status(thm)],[79:[bind(A,$thf( composition @ ( complement @ sk1 ) @ ( converse @ sk2 ) )),bind(B,$thf( complement @ sk1 ))]]) ).
thf(514,plain,
! [A: $i] :
( ( ( complement @ sk1 )
!= top )
| ( sk2 != one )
| ( A != one )
| ( sk1 != top )
| ( ( converse @ ( converse @ A ) )
!= ( converse @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[42,511]) ).
thf(517,plain,
( ( ( complement @ sk1 )
!= top )
| ( sk2 != one )
| ( sk1 != top )
| ( ( converse @ one )
!= sk2 ) ),
inference(simp,[status(thm)],[514]) ).
thf(33264,plain,
$false,
inference(e,[status(thm)],[69,52,376,519,34,39,18,43,99,437,442,90,511,1041,42,24,436,37,25,46,93,78,894,28,70,21,815,33,484,522,22,27,54,49,350,685,438,80,370,31,441,16,517,40,55,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL012+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n011.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 17:58:04 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.99 % [INFO] Parsing done (116ms).
% 1.24/0.99 % [INFO] Running in sequential loop mode.
% 1.59/1.18 % [INFO] eprover registered as external prover.
% 1.59/1.18 % [INFO] cvc4 registered as external prover.
% 1.59/1.18 % [INFO] Scanning for conjecture ...
% 1.78/1.23 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 1.78/1.25 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.78/1.28 % [INFO] Problem is first-order (TPTP FOF).
% 2.03/1.28 % [INFO] Type checking passed.
% 2.03/1.28 % [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 ...
% 55.77/9.58 % External prover 'e' found a proof!
% 55.77/9.59 % [INFO] Killing All external provers ...
% 55.77/9.59 % Time passed: 9048ms (effective reasoning time: 8594ms)
% 55.77/9.59 % 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)>
% 55.77/9.59 % 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
% 55.77/9.59 % No. of inferences in proof: 111
% 55.77/9.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9048 ms resp. 8594 ms w/o parsing
% 55.77/9.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 55.77/9.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------