%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : REL028-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:24:02 AM UTC 2026
% Result : Unsatisfiable 31.72s 7.41s
% Output : Refutation 31.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 101 ( 69 unt; 0 typ; 0 def)
% Number of atoms : 150 ( 149 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 724 ( 67 ~; 49 |; 0 &; 608 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 136 ( 0 ^; 136 !; 0 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_decl,type,
join: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(one_decl,type,
one: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(composition_decl,type,
composition: $i > $i > $i ).
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(converse_decl,type,
converse: $i > $i ).
thf(complement_decl,type,
complement: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(top_decl,type,
top: $i ).
thf(6,axiom,
! [A: $i] :
( ( one @ ( A @ composition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
thf(31,plain,
! [A: $i] :
( ( one @ ( A @ composition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,plain,
! [A: $i] :
( ( one @ ( A @ composition ) )
= A ),
inference(lifteq,[status(thm)],[31]) ).
thf(13,axiom,
! [A: $i] :
( zero
= ( A @ complement @ ( A @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
thf(45,plain,
! [A: $i] :
( zero
= ( A @ complement @ ( A @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(46,plain,
! [A: $i] :
( ( A @ complement @ ( A @ meet ) )
= zero ),
inference(lifteq,[status(thm)],[45]) ).
thf(3,negated_conjecture,
( ( sk2 @ ( sk1 @ composition ) )
!= ( sk2 @ ( sk1 @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_19) ).
thf(22,plain,
( ( sk2 @ ( sk1 @ composition ) )
!= ( sk2 @ ( sk1 @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,plain,
( ( sk2 @ ( sk1 @ composition ) )
!= ( sk2 @ ( sk1 @ meet ) ) ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(26,plain,
( ( sk2 @ ( sk1 @ meet ) )
!= ( sk2 @ ( sk1 @ composition ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(65,plain,
! [A: $i] :
( ( ( A @ complement @ ( A @ meet ) )
!= ( sk2 @ ( sk1 @ meet ) ) )
| ( ( sk2 @ ( sk1 @ composition ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[46,26]) ).
thf(66,plain,
! [A: $i] :
( ( ( A @ complement )
!= sk2 )
| ( A != sk1 )
| ( ( sk2 @ ( sk1 @ composition ) )
!= zero ) ),
inference(simp,[status(thm)],[65]) ).
thf(67,plain,
( ( ( sk1 @ complement )
!= sk2 )
| ( ( sk2 @ ( sk1 @ composition ) )
!= zero ) ),
inference(simp,[status(thm)],[66]) ).
thf(150,plain,
! [A: $i] :
( ( ( one @ ( A @ composition ) )
!= ( sk2 @ ( sk1 @ composition ) ) )
| ( ( sk1 @ complement )
!= sk2 )
| ( A != zero ) ),
inference(paramod_ordered,[status(thm)],[32,67]) ).
thf(153,plain,
( ( sk2 != one )
| ( zero != sk1 )
| ( ( sk1 @ complement )
!= sk2 ) ),
inference(simp,[status(thm)],[150]) ).
thf(1,negated_conjecture,
( ( one @ ( sk1 @ join ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
thf(20,plain,
( ( one @ ( sk1 @ join ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(23,plain,
( ( one @ ( sk1 @ join ) )
= one ),
inference(lifteq,[status(thm)],[20]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( ( one @ ( sk1 @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[23,38]) ).
thf(116,plain,
( ( sk1 @ ( one @ join ) )
= one ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( sk1 )),bind(B,$thf( one ))]]) ).
thf(15,axiom,
! [A: $i] :
( top
= ( A @ complement @ ( A @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
thf(49,plain,
! [A: $i] :
( top
= ( A @ complement @ ( A @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(50,plain,
! [A: $i] :
( ( A @ complement @ ( A @ join ) )
= top ),
inference(lifteq,[status(thm)],[49]) ).
thf(176,plain,
! [A: $i] :
( ( ( sk1 @ ( one @ join ) )
!= ( A @ complement @ ( A @ join ) ) )
| ( top = one ) ),
inference(paramod_ordered,[status(thm)],[116,50]) ).
thf(182,plain,
! [A: $i] :
( ( ( A @ complement )
!= sk1 )
| ( one != A )
| ( top = one ) ),
inference(simp,[status(thm)],[176]) ).
thf(184,plain,
( ( ( one @ complement )
!= sk1 )
| ( top = one ) ),
inference(simp,[status(thm)],[182]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ converse @ composition ) @ ( B @ meet ) @ ( A @ composition ) @ meet ) @ ( C @ ( B @ ( A @ composition ) @ meet ) @ join ) )
= ( C @ ( C @ ( A @ converse @ composition ) @ ( B @ meet ) @ ( A @ composition ) @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law_1_15) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ converse @ composition ) @ ( B @ meet ) @ ( A @ composition ) @ meet ) @ ( C @ ( B @ ( A @ composition ) @ meet ) @ join ) )
= ( C @ ( C @ ( A @ converse @ composition ) @ ( B @ meet ) @ ( A @ composition ) @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2,negated_conjecture,
( ( one @ ( sk2 @ join ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
thf(21,plain,
( ( one @ ( sk2 @ join ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
( ( one @ ( sk2 @ join ) )
= one ),
inference(lifteq,[status(thm)],[21]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( one @ ( sk2 @ join ) ) )
| ( ( A @ ( B @ join ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[38,24]) ).
thf(96,plain,
( ( sk2 @ ( one @ join ) )
= one ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( sk2 )),bind(B,$thf( one ))]]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( B @ complement @ ( A @ complement @ join ) @ complement ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( B @ complement @ ( A @ complement @ join ) @ complement ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ composition ) @ converse )
= ( A @ converse @ ( B @ converse @ composition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ composition ) @ converse )
= ( A @ converse @ ( B @ converse @ composition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ converse @ converse )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
thf(27,plain,
! [A: $i] :
( ( A @ converse @ converse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
! [A: $i] :
( ( A @ converse @ converse )
= A ),
inference(lifteq,[status(thm)],[27]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ composition ) @ converse )
= ( A @ converse @ ( B @ converse @ composition ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ( ( one @ ( A @ composition ) )
!= ( C @ ( B @ composition ) ) )
| ( ( A @ converse )
= ( B @ converse @ ( C @ converse @ composition ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,36]) ).
thf(465,plain,
! [A: $i] :
( ( A @ converse @ ( one @ converse @ composition ) )
= ( A @ converse ) ),
inference(pattern_uni,[status(thm)],[464:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( one ))]]) ).
thf(508,plain,
! [B: $i,A: $i] :
( ( ( A @ converse @ converse )
!= ( B @ converse ) )
| ( ( A @ ( one @ converse @ composition ) )
= ( B @ converse ) ) ),
inference(paramod_ordered,[status(thm)],[28,465]) ).
thf(509,plain,
! [A: $i] :
( ( A @ ( one @ converse @ composition ) )
= ( A @ converse @ converse ) ),
inference(pattern_uni,[status(thm)],[508:[bind(A,$thf( C )),bind(B,$thf( C @ converse ))]]) ).
thf(546,plain,
! [A: $i] :
( ( A @ ( one @ converse @ composition ) )
= ( A @ converse @ converse ) ),
inference(simp,[status(thm)],[509]) ).
thf(551,plain,
! [A: $i] :
( ( A @ ( one @ converse @ composition ) )
= A ),
inference(rewrite,[status(thm)],[546,28]) ).
thf(561,plain,
! [B: $i,A: $i] :
( ( ( A @ ( one @ converse @ composition ) )
!= ( one @ ( B @ composition ) ) )
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[551,32]) ).
thf(562,plain,
( ( one @ converse )
= one ),
inference(pattern_uni,[status(thm)],[561:[bind(A,$thf( one )),bind(B,$thf( one @ converse ))]]) ).
thf(601,plain,
! [A: $i] :
( ( A @ ( one @ composition ) )
= A ),
inference(rewrite,[status(thm)],[551,562]) ).
thf(685,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( one @ composition ) )
!= ( C @ ( B @ composition ) ) )
| ( ( A @ converse )
= ( B @ converse @ ( C @ converse @ composition ) ) ) ),
inference(paramod_ordered,[status(thm)],[601,36]) ).
thf(686,plain,
! [A: $i] :
( ( one @ converse @ ( A @ converse @ composition ) )
= ( A @ converse ) ),
inference(pattern_uni,[status(thm)],[685:[bind(A,$thf( A )),bind(B,$thf( one )),bind(C,$thf( A ))]]) ).
thf(712,plain,
! [A: $i] :
( ( one @ ( A @ converse @ composition ) )
= ( A @ converse ) ),
inference(rewrite,[status(thm)],[686,562]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ converse )
= ( B @ converse @ ( A @ converse @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ converse )
= ( B @ converse @ ( A @ converse @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ converse @ composition ) @ ( B @ meet ) @ ( B @ converse @ ( C @ composition ) @ ( A @ meet ) @ composition ) @ ( C @ ( B @ ( A @ composition ) @ meet ) @ join ) )
= ( C @ ( A @ converse @ composition ) @ ( B @ meet ) @ ( B @ converse @ ( C @ composition ) @ ( A @ meet ) @ composition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dedekind_law_14) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ converse @ composition ) @ ( B @ meet ) @ ( B @ converse @ ( C @ composition ) @ ( A @ meet ) @ composition ) @ ( C @ ( B @ ( A @ composition ) @ meet ) @ join ) )
= ( C @ ( A @ converse @ composition ) @ ( B @ meet ) @ ( B @ converse @ ( C @ composition ) @ ( A @ meet ) @ composition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( B @ complement @ ( A @ complement @ join ) @ complement ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(762,plain,
( ( sk2 @ ( sk1 @ composition ) )
!= ( sk2 @ complement @ ( sk1 @ complement @ join ) @ complement ) ),
inference(rewrite,[status(thm)],[26,42]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ complement @ ( A @ join ) )
!= ( C @ ( B @ join ) ) )
| ( ( B @ ( C @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[50,38]) ).
thf(106,plain,
! [A: $i] :
( ( A @ ( A @ complement @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[105:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ complement ))]]) ).
thf(120,plain,
! [A: $i] :
( ( A @ ( A @ complement @ join ) )
= top ),
inference(simp,[status(thm)],[106]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ converse @ ( C @ composition ) @ ( A @ meet ) @ composition ) @ meet ) @ ( C @ ( B @ ( A @ composition ) @ meet ) @ join ) )
= ( C @ ( B @ ( B @ converse @ ( C @ composition ) @ ( A @ meet ) @ composition ) @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law_2_16) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ converse @ ( C @ composition ) @ ( A @ meet ) @ composition ) @ meet ) @ ( C @ ( B @ ( A @ composition ) @ meet ) @ join ) )
= ( C @ ( B @ ( B @ converse @ ( C @ composition ) @ ( A @ meet ) @ composition ) @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(70,plain,
! [A: $i] :
( ( ( A @ complement @ ( A @ join ) )
!= ( one @ ( sk1 @ join ) ) )
| ( top = one ) ),
inference(paramod_ordered,[status(thm)],[50,23]) ).
thf(74,plain,
! [A: $i] :
( ( ( A @ complement )
!= one )
| ( A != sk1 )
| ( top = one ) ),
inference(simp,[status(thm)],[70]) ).
thf(78,plain,
( ( ( sk1 @ complement )
!= one )
| ( top = one ) ),
inference(simp,[status(thm)],[74]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ composition ) )
= ( C @ ( B @ composition ) @ ( C @ ( A @ composition ) @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ composition ) )
= ( C @ ( B @ composition ) @ ( C @ ( A @ composition ) @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(565,plain,
! [A: $i] :
( ( ( A @ ( one @ converse @ composition ) )
!= ( sk2 @ ( sk1 @ composition ) ) )
| ( ( sk1 @ complement )
!= sk2 )
| ( A != zero ) ),
inference(paramod_ordered,[status(thm)],[551,67]) ).
thf(576,plain,
( ( zero != sk2 )
| ( ( one @ converse )
!= sk1 )
| ( ( sk1 @ complement )
!= sk2 ) ),
inference(simp,[status(thm)],[565]) ).
thf(602,plain,
( ( zero != sk2 )
| ( one != sk1 )
| ( ( sk1 @ complement )
!= sk2 ) ),
inference(rewrite,[status(thm)],[576,562]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ complement @ join ) @ complement @ ( B @ complement @ ( A @ complement @ join ) @ complement @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
thf(33,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ complement @ join ) @ complement @ ( B @ complement @ ( A @ complement @ join ) @ complement @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement @ join ) @ complement @ ( B @ complement @ ( A @ complement @ join ) @ complement @ join ) )
= A ),
inference(lifteq,[status(thm)],[33]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ converse @ ( A @ converse @ join ) )
= ( B @ ( A @ join ) @ converse ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(127,plain,
! [A: $i] :
( ( ( sk2 @ ( one @ join ) )
!= ( A @ complement @ ( A @ join ) ) )
| ( top = one ) ),
inference(paramod_ordered,[status(thm)],[96,50]) ).
thf(141,plain,
! [A: $i] :
( ( ( A @ complement )
!= sk2 )
| ( one != A )
| ( top = one ) ),
inference(simp,[status(thm)],[127]) ).
thf(144,plain,
( ( ( one @ complement )
!= sk2 )
| ( top = one ) ),
inference(simp,[status(thm)],[141]) ).
thf(68,plain,
! [A: $i] :
( ( ( A @ complement @ ( A @ join ) )
!= ( one @ ( sk2 @ join ) ) )
| ( top = one ) ),
inference(paramod_ordered,[status(thm)],[50,24]) ).
thf(72,plain,
! [A: $i] :
( ( ( A @ complement )
!= one )
| ( A != sk2 )
| ( top = one ) ),
inference(simp,[status(thm)],[68]) ).
thf(76,plain,
( ( ( sk2 @ complement )
!= one )
| ( top = one ) ),
inference(simp,[status(thm)],[72]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ composition ) @ ( A @ composition ) )
= ( C @ ( B @ ( A @ composition ) @ composition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity_5) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ composition ) @ ( A @ composition ) )
= ( C @ ( B @ ( A @ composition ) @ composition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(591,plain,
! [A: $i] :
( ( ( A @ converse @ converse )
!= ( one @ converse ) )
| ( zero != sk2 )
| ( A != sk1 )
| ( ( sk1 @ complement )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[28,576]) ).
thf(594,plain,
( ( ( sk1 @ converse )
!= one )
| ( zero != sk2 )
| ( ( sk1 @ complement )
!= sk2 ) ),
inference(simp,[status(thm)],[591]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ composition ) )
= ( C @ ( B @ composition ) @ ( C @ ( A @ composition ) @ join ) ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ join ) @ composition ) )
!= ( sk2 @ ( sk1 @ composition ) ) )
| ( ( sk1 @ complement )
!= sk2 )
| ( ( C @ ( B @ composition ) @ ( C @ ( A @ composition ) @ join ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[30,67]) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ( C != sk2 )
| ( ( B @ ( A @ join ) )
!= sk1 )
| ( ( sk1 @ complement )
!= sk2 )
| ( ( C @ ( B @ composition ) @ ( C @ ( A @ composition ) @ join ) )
!= zero ) ),
inference(simp,[status(thm)],[151]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= sk1 )
| ( ( sk1 @ complement )
!= sk2 )
| ( ( sk2 @ ( B @ composition ) @ ( sk2 @ ( A @ composition ) @ join ) )
!= zero ) ),
inference(simp,[status(thm)],[154]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ composition ) @ composition ) )
= ( C @ ( B @ composition ) @ ( A @ composition ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ join ) @ ( A @ join ) )
= ( C @ ( B @ ( A @ join ) @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ join ) @ ( A @ join ) )
= ( C @ ( B @ ( A @ join ) @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( B @ complement @ ( B @ ( A @ composition ) @ complement @ ( A @ converse @ composition ) @ join ) )
= ( B @ complement ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( B @ complement @ ( B @ ( A @ composition ) @ complement @ ( A @ converse @ composition ) @ join ) )
= ( B @ complement ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(761,plain,
! [A: $i] :
( ( A @ complement @ complement @ ( A @ complement @ join ) @ complement )
= zero ),
inference(rewrite,[status(thm)],[46,42]) ).
thf(865,plain,
( ( top @ complement )
= zero ),
inference(rewrite,[status(thm)],[761,50]) ).
thf(3914,plain,
$false,
inference(e,[status(thm)],[153,184,53,96,41,35,712,43,47,762,120,42,24,37,20,57,78,29,602,116,21,33,28,38,45,601,32,34,562,22,44,27,144,49,76,39,594,155,50,67,31,40,55,23,36,30,51,865]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL028-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.40 % Computer : n013.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sat Sep 26 05:32:51 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.19 % [INFO] Parsing done (206ms).
% 1.46/1.20 % [INFO] Running in sequential loop mode.
% 2.20/1.60 % [INFO] eprover registered as external prover.
% 2.20/1.61 % [INFO] Scanning for conjecture ...
% 2.39/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.39/1.76 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.60/1.80 % [INFO] Problem is propositional (TPTP CNF).
% 2.60/1.80 % [INFO] Type checking passed.
% 2.60/1.81 % [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 ...
% 31.72/7.40 % External prover 'e' found a proof!
% 31.72/7.40 % [INFO] Killing All external provers ...
% 31.72/7.41 % Time passed: 6864ms (effective reasoning time: 6197ms)
% 31.72/7.41 % Axioms used in derivation (16): maddux3_a_kind_of_de_Morgan_3, converse_idempotence_8, def_top_12, converse_cancellativity_11, composition_associativity_5, maddux2_join_associativity_2, composition_distributivity_7, maddux1_join_commutativity_1, modular_law_1_15, composition_identity_6, maddux4_definiton_of_meet_4, converse_additivity_9, dedekind_law_14, modular_law_2_16, def_zero_13, converse_multiplicativity_10
% 31.72/7.41 % No. of inferences in proof: 101
% 31.72/7.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6864 ms resp. 6197 ms w/o parsing
% 31.72/7.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 31.72/7.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------