%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT026-1 : TPTP v9.3.1. Released v2.2.0.
% 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 : n001.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 07:46:30 AM UTC 2026
% Result : Unsatisfiable 15.91s 4.18s
% Output : Refutation 13.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 94 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 175 ( 174 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 674 ( 129 ~; 81 |; 0 &; 464 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 156 ( 0 ^; 156 !; 0 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(join_decl,type,
join: $i > $i > $i ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(12,plain,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
inference(lifteq,[status(thm)],[12]) ).
thf(1,negated_conjecture,
( ( c @ ( b @ ( a @ meet ) @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_meet) ).
thf(9,plain,
( ( c @ ( b @ ( a @ meet ) @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,plain,
( ( c @ ( b @ ( a @ meet ) @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ meet ) ) ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( c @ ( b @ ( a @ meet ) @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ meet ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(27,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( b @ ( a @ meet ) @ meet ) ) )
| ( A
!= ( c @ ( b @ meet ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,11]) ).
thf(30,plain,
( ( ( c @ ( b @ meet ) @ ( a @ meet ) )
!= c )
| ( ( c @ ( b @ meet ) @ ( a @ meet ) )
!= ( b @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(1256,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( b @ meet ) ) )
| ( ( c @ ( b @ meet ) @ ( a @ meet ) )
!= c )
| ( ( A @ ( a @ meet ) )
!= ( b @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,30]) ).
thf(1303,plain,
! [A: $i] :
( ( A != c )
| ( A != b )
| ( ( c @ ( b @ meet ) @ ( a @ meet ) )
!= c )
| ( A != b )
| ( a != a ) ),
inference(simp,[status(thm)],[1256]) ).
thf(1411,plain,
( ( c != b )
| ( ( c @ ( b @ meet ) @ ( a @ meet ) )
!= c ) ),
inference(simp,[status(thm)],[1303]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ join ) @ ( B @ ( A @ join ) @ meet ) @ meet ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wal_1) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ join ) @ ( B @ ( A @ join ) @ meet ) @ meet ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ join ) @ ( B @ ( A @ join ) @ meet ) @ meet ) )
= B ),
inference(lifteq,[status(thm)],[20]) ).
thf(88,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( C @ ( D @ join ) @ ( C @ ( B @ join ) @ meet ) ) )
| ( ( C @ ( A @ meet ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[13,21]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ join ) @ meet ) )
= B ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( F @ ( E @ join ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ join ) @ meet ) )
= B ),
inference(simp,[status(thm)],[89]) ).
thf(204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( D @ ( C @ join ) ) )
| ( ( D @ ( A @ ( B @ join ) @ meet ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[19,144]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ join ) @ meet ) )
= B ),
inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( C @ ( D @ join ) ) )
| ( ( D @ ( A @ ( B @ join ) @ meet ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[19,205]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ join ) @ meet ) )
= A ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(14,plain,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1505,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( b @ meet ) ) )
| ( c != b )
| ( ( A @ ( a @ meet ) )
!= c ) ),
inference(paramod_ordered,[status(thm)],[13,1411]) ).
thf(1548,plain,
! [A: $i] :
( ( A != c )
| ( A != b )
| ( c != b )
| ( ( A @ ( a @ meet ) )
!= c ) ),
inference(simp,[status(thm)],[1505]) ).
thf(1555,plain,
( ( c != b )
| ( ( b @ ( a @ meet ) )
!= c ) ),
inference(simp,[status(thm)],[1548]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ meet ) @ ( B @ ( A @ meet ) @ join ) @ join ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wal_2) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ meet ) @ ( B @ ( A @ meet ) @ join ) @ join ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ join ) @ meet ) )
!= ( D @ ( C @ meet ) ) )
| ( B
= ( C @ ( D @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[144,17]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( B @ meet ) )
= B ),
inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ join ) )),bind(D,$thf( F ))]]) ).
thf(239,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( B @ meet ) )
= B ),
inference(simp,[status(thm)],[192]) ).
thf(26,plain,
( ( ( c @ ( b @ meet ) )
!= c )
| ( ( b @ ( a @ meet ) )
!= a ) ),
inference(simp,[status(thm)],[11]) ).
thf(68,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( b @ meet ) ) )
| ( A != c )
| ( ( b @ ( a @ meet ) )
!= a ) ),
inference(paramod_ordered,[status(thm)],[13,26]) ).
thf(76,plain,
( ( c != c )
| ( c != b )
| ( ( b @ ( a @ meet ) )
!= a ) ),
inference(simp,[status(thm)],[68]) ).
thf(78,plain,
( ( c != b )
| ( ( b @ ( a @ meet ) )
!= a ) ),
inference(simp,[status(thm)],[76]) ).
thf(542,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) @ ( B @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( c != b )
| ( B != a ) ),
inference(paramod_ordered,[status(thm)],[239,78]) ).
thf(560,plain,
! [A: $i] :
( ( ( a @ ( A @ join ) )
!= b )
| ( a != a )
| ( c != b ) ),
inference(simp,[status(thm)],[542]) ).
thf(599,plain,
! [A: $i] :
( ( ( a @ ( A @ join ) )
!= b )
| ( c != b ) ),
inference(simp,[status(thm)],[560]) ).
thf(107,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( D @ ( E @ join ) ) )
| ( ( D @ ( A @ ( B @ join ) @ ( D @ ( C @ join ) @ meet ) @ meet ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[19,21]) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ join ) @ ( B @ ( C @ join ) @ meet ) @ meet ) )
= B ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(28,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( ( c @ ( A @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,11]) ).
thf(33,plain,
! [A: $i] :
( ( A != b )
| ( A != a )
| ( ( c @ ( b @ meet ) )
!= c )
| ( A != a ) ),
inference(simp,[status(thm)],[28]) ).
thf(35,plain,
( ( b != a )
| ( ( c @ ( b @ meet ) )
!= c ) ),
inference(simp,[status(thm)],[33]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= ( c @ ( b @ ( a @ meet ) @ meet ) ) )
| ( ( A @ ( B @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,11]) ).
thf(38,plain,
( ( b @ ( a @ meet ) @ ( c @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ meet ) ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( b @ ( a @ meet ) )),bind(B,$thf( c ))]]) ).
thf(162,plain,
( ( ( c @ ( b @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( c != a ) ),
inference(simp,[status(thm)],[38]) ).
thf(206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ join ) )
!= ( D @ ( C @ join ) ) )
| ( ( D @ ( B @ ( A @ join ) @ meet ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[19,144]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ join ) @ meet ) )
= A ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ join ) @ ( B @ join ) @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ join ) @ ( B @ join ) @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1570,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( c != b )
| ( A != c ) ),
inference(paramod_ordered,[status(thm)],[13,1555]) ).
thf(1584,plain,
( ( c != b )
| ( c != a )
| ( c != b ) ),
inference(simp,[status(thm)],[1570]) ).
thf(1601,plain,
( ( c != a )
| ( c != b ) ),
inference(simp,[status(thm)],[1584]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ join ) @ ( B @ join ) @ ( A @ meet ) )
= A ),
inference(lifteq,[status(thm)],[24]) ).
thf(52,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( b @ meet ) ) )
| ( b != a )
| ( A != c ) ),
inference(paramod_ordered,[status(thm)],[13,35]) ).
thf(56,plain,
( ( c != c )
| ( c != b )
| ( b != a ) ),
inference(simp,[status(thm)],[52]) ).
thf(57,plain,
( ( c != b )
| ( b != a ) ),
inference(simp,[status(thm)],[56]) ).
thf(270,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ join ) @ meet ) )
!= ( c @ ( b @ meet ) ) )
| ( b != a )
| ( B != c ) ),
inference(paramod_ordered,[status(thm)],[205,35]) ).
thf(290,plain,
! [A: $i] :
( ( c != c )
| ( ( A @ ( c @ join ) )
!= b )
| ( b != a ) ),
inference(simp,[status(thm)],[270]) ).
thf(316,plain,
! [A: $i] :
( ( ( A @ ( c @ join ) )
!= b )
| ( b != a ) ),
inference(simp,[status(thm)],[290]) ).
thf(15,plain,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
inference(lifteq,[status(thm)],[14]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ meet ) @ ( B @ ( A @ meet ) @ join ) @ join ) )
= B ),
inference(lifteq,[status(thm)],[22]) ).
thf(474,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ join ) )
!= ( C @ ( D @ meet ) @ ( C @ ( B @ meet ) @ join ) ) )
| ( ( C @ ( A @ join ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[15,23]) ).
thf(475,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ meet ) @ join ) )
= B ),
inference(pattern_uni,[status(thm)],[474:[bind(A,$thf( F @ ( E @ meet ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(502,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ meet ) @ join ) )
= B ),
inference(simp,[status(thm)],[475]) ).
thf(1186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= ( D @ ( C @ meet ) ) )
| ( ( D @ ( A @ ( B @ meet ) @ join ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[17,502]) ).
thf(1187,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ meet ) @ join ) )
= B ),
inference(pattern_uni,[status(thm)],[1186:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(32,plain,
! [A: $i] :
( ( A != b )
| ( A != a )
| ( ( c @ ( A @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(34,plain,
( ( b != a )
| ( ( c @ ( b @ meet ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ join ) @ meet ) )
!= ( D @ ( C @ meet ) ) )
| ( B
= ( C @ ( D @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[205,17]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ join ) )),bind(D,$thf( E ))]]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
inference(simp,[status(thm)],[259]) ).
thf(1179,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ meet ) @ join ) )
!= ( C @ ( c @ join ) ) )
| ( B != b )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[502,316]) ).
thf(1197,plain,
! [B: $i,A: $i] :
( ( b != B )
| ( ( b @ ( A @ meet ) )
!= c )
| ( b != a ) ),
inference(simp,[status(thm)],[1179]) ).
thf(1218,plain,
! [A: $i] :
( ( ( b @ ( A @ meet ) )
!= c )
| ( b != a ) ),
inference(simp,[status(thm)],[1197]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ join ) @ meet ) )
!= ( c @ ( b @ meet ) ) )
| ( b != a )
| ( B != c ) ),
inference(paramod_ordered,[status(thm)],[144,35]) ).
thf(228,plain,
! [A: $i] :
( ( c != c )
| ( ( c @ ( A @ join ) )
!= b )
| ( b != a ) ),
inference(simp,[status(thm)],[199]) ).
thf(250,plain,
! [A: $i] :
( ( ( c @ ( A @ join ) )
!= b )
| ( b != a ) ),
inference(simp,[status(thm)],[228]) ).
thf(1188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ meet ) )
!= ( D @ ( C @ meet ) ) )
| ( ( D @ ( B @ ( A @ meet ) @ join ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[17,502]) ).
thf(1189,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ meet ) @ join ) )
= A ),
inference(pattern_uni,[status(thm)],[1188:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(915,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) @ ( A @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( c != b )
| ( A != a ) ),
inference(paramod_ordered,[status(thm)],[310,78]) ).
thf(954,plain,
! [A: $i] :
( ( ( A @ ( a @ join ) )
!= b )
| ( a != a )
| ( c != b ) ),
inference(simp,[status(thm)],[915]) ).
thf(992,plain,
! [A: $i] :
( ( ( A @ ( a @ join ) )
!= b )
| ( c != b ) ),
inference(simp,[status(thm)],[954]) ).
thf(1229,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ meet ) @ join ) )
!= ( C @ ( a @ join ) ) )
| ( B != b )
| ( c != b ) ),
inference(paramod_ordered,[status(thm)],[502,992]) ).
thf(1240,plain,
! [B: $i,A: $i] :
( ( b != B )
| ( ( b @ ( A @ meet ) )
!= a )
| ( c != b ) ),
inference(simp,[status(thm)],[1229]) ).
thf(1244,plain,
! [A: $i] :
( ( ( b @ ( A @ meet ) )
!= a )
| ( c != b ) ),
inference(simp,[status(thm)],[1240]) ).
thf(2835,plain,
$false,
inference(e,[status(thm)],[1411,276,14,1555,9,13,22,599,108,35,162,11,207,239,24,1601,25,20,57,316,78,38,21,205,1187,34,17,12,144,18,310,16,502,1218,250,1189,26,1244,23,30,19,992,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT026-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % 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
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 20:03:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 0.75/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.98/0.88 % [INFO] Parsing done (163ms).
% 1.18/0.90 % [INFO] Running in sequential loop mode.
% 1.64/1.16 % [INFO] eprover registered as external prover.
% 1.64/1.16 % [INFO] Scanning for conjecture ...
% 1.83/1.21 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 1.83/1.23 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.83/1.23 % [INFO] Problem is propositional (TPTP CNF).
% 1.83/1.24 % [INFO] Type checking passed.
% 1.83/1.24 % [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 ...
% 15.91/4.17 % External prover 'e' found a proof!
% 15.91/4.17 % [INFO] Killing All external provers ...
% 15.91/4.18 % Time passed: 3693ms (effective reasoning time: 3271ms)
% 15.91/4.18 % Axioms used in derivation (7): commutativity_of_join, wal_2, idempotence_of_join, commutativity_of_meet, idempotence_of_meet, absorbtion, wal_1
% 15.91/4.18 % No. of inferences in proof: 94
% 15.91/4.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3693 ms resp. 3271 ms w/o parsing
% 13.43/4.24 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.43/4.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------