%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT009-1 : 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 : n002.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 07:46:28 AM UTC 2026
% Result : Unsatisfiable 27.35s 6.88s
% Output : Refutation 24.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 98 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 182 ( 181 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 725 ( 131 ~; 84 |; 0 &; 510 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 163 ( 0 ^; 163 !; 0 ?; 163 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_decl,type,
join: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(14,plain,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
inference(lifteq,[status(thm)],[20]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ meet ) @ ( A @ join ) )
!= ( D @ ( C @ join ) ) )
| ( A
= ( C @ ( D @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,25]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ meet ) @ join ) )
= A ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ meet ) ))]]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ meet ) @ join ) )
= A ),
inference(simp,[status(thm)],[147]) ).
thf(484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= ( D @ ( C @ meet ) ) )
| ( ( C @ ( A @ ( B @ meet ) @ join ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[23,170]) ).
thf(485,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ meet ) @ join ) )
= A ),
inference(pattern_uni,[status(thm)],[484:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
inference(lifteq,[status(thm)],[18]) ).
thf(129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ join ) @ ( A @ meet ) )
!= ( D @ ( C @ meet ) ) )
| ( A
= ( C @ ( D @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,23]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ join ) @ meet ) )
= A ),
inference(pattern_uni,[status(thm)],[129:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ join ) ))]]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ join ) @ meet ) )
= A ),
inference(simp,[status(thm)],[130]) ).
thf(220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( D @ ( C @ join ) ) )
| ( ( C @ ( A @ ( B @ join ) @ meet ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[25,141]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ join ) @ meet ) )
= A ),
inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(16,plain,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
inference(lifteq,[status(thm)],[16]) ).
thf(1,negated_conjecture,
( ( c @ ( b @ meet ) @ ( a @ join ) )
!= ( c @ ( a @ join ) @ ( b @ ( a @ join ) @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
thf(11,plain,
( ( c @ ( b @ meet ) @ ( a @ join ) )
!= ( c @ ( a @ join ) @ ( b @ ( a @ join ) @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ( c @ ( b @ meet ) @ ( a @ join ) )
!= ( c @ ( a @ join ) @ ( b @ ( a @ join ) @ meet ) ) ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( c @ ( a @ join ) @ ( b @ ( a @ join ) @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ join ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(33,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( b @ ( a @ join ) ) )
| ( ( c @ ( a @ join ) @ ( A @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,13]) ).
thf(36,plain,
! [A: $i] :
( ( A != b )
| ( A != a )
| ( ( c @ ( a @ join ) @ ( A @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ join ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(40,plain,
( ( b != a )
| ( ( c @ ( a @ join ) @ ( a @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ join ) ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(65,plain,
( ( b != a )
| ( ( c @ ( b @ meet ) @ ( a @ join ) )
!= a ) ),
inference(rewrite,[status(thm)],[40,19]) ).
thf(32,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( c @ ( a @ join ) ) )
| ( ( A @ ( b @ ( a @ join ) @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,13]) ).
thf(35,plain,
! [A: $i] :
( ( A != c )
| ( A != a )
| ( ( A @ ( b @ ( a @ join ) @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ join ) ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(39,plain,
( ( c != a )
| ( ( a @ ( b @ ( a @ join ) @ meet ) )
!= ( c @ ( b @ meet ) @ ( a @ join ) ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(219,plain,
( ( c != a )
| ( ( c @ ( b @ meet ) @ ( a @ join ) )
!= a ) ),
inference(rewrite,[status(thm)],[39,141]) ).
thf(533,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( c @ ( b @ meet ) @ ( a @ join ) ) )
| ( c != a )
| ( A != a ) ),
inference(paramod_ordered,[status(thm)],[17,219]) ).
thf(538,plain,
( ( ( c @ ( b @ meet ) )
!= a )
| ( a != a )
| ( c != a ) ),
inference(simp,[status(thm)],[533]) ).
thf(556,plain,
( ( ( c @ ( b @ meet ) )
!= a )
| ( c != a ) ),
inference(simp,[status(thm)],[538]) ).
thf(113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= ( D @ ( C @ meet ) ) )
| ( ( A @ ( B @ meet ) @ ( C @ join ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[23,21]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ meet ) @ ( A @ join ) )
= A ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ meet ) @ ( A @ join ) )
!= ( D @ ( C @ join ) ) )
| ( A
= ( C @ ( D @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[114,25]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ meet ) @ join ) )
= B ),
inference(pattern_uni,[status(thm)],[173:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ meet ) ))]]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ meet ) @ join ) )
= B ),
inference(simp,[status(thm)],[174]) ).
thf(15,plain,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
inference(lifteq,[status(thm)],[14]) ).
thf(66,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( c @ ( b @ meet ) @ ( a @ join ) ) )
| ( b != a )
| ( A != a ) ),
inference(paramod_ordered,[status(thm)],[17,65]) ).
thf(70,plain,
( ( ( c @ ( b @ meet ) )
!= a )
| ( a != a )
| ( b != a ) ),
inference(simp,[status(thm)],[66]) ).
thf(73,plain,
( ( ( c @ ( b @ meet ) )
!= a )
| ( b != a ) ),
inference(simp,[status(thm)],[70]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) @ ( A @ meet ) )
!= ( c @ ( b @ meet ) ) )
| ( A != a )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[19,73]) ).
thf(107,plain,
! [A: $i] :
( ( ( A @ ( a @ join ) )
!= c )
| ( b != a )
| ( b != a ) ),
inference(simp,[status(thm)],[104]) ).
thf(111,plain,
! [A: $i] :
( ( ( A @ ( a @ join ) )
!= c )
| ( b != a ) ),
inference(simp,[status(thm)],[107]) ).
thf(564,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ join ) @ meet ) )
!= ( c @ ( b @ meet ) ) )
| ( A != a )
| ( c != a ) ),
inference(paramod_ordered,[status(thm)],[141,556]) ).
thf(579,plain,
! [A: $i] :
( ( c != a )
| ( ( A @ ( a @ join ) )
!= b )
| ( c != a ) ),
inference(simp,[status(thm)],[564]) ).
thf(582,plain,
! [A: $i] :
( ( ( A @ ( a @ join ) )
!= b )
| ( c != a ) ),
inference(simp,[status(thm)],[579]) ).
thf(68,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( b @ meet ) ) )
| ( b != a )
| ( ( A @ ( a @ join ) )
!= a ) ),
inference(paramod_ordered,[status(thm)],[15,65]) ).
thf(72,plain,
! [A: $i] :
( ( A != c )
| ( A != b )
| ( b != a )
| ( ( A @ ( a @ join ) )
!= a ) ),
inference(simp,[status(thm)],[68]) ).
thf(75,plain,
( ( c != b )
| ( b != a )
| ( ( b @ ( a @ join ) )
!= a ) ),
inference(simp,[status(thm)],[72]) ).
thf(278,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( b @ ( a @ join ) ) )
| ( c != b )
| ( b != a )
| ( A != a ) ),
inference(paramod_ordered,[status(thm)],[17,75]) ).
thf(283,plain,
( ( b != a )
| ( a != a )
| ( c != b )
| ( b != a ) ),
inference(simp,[status(thm)],[278]) ).
thf(288,plain,
( ( c != b )
| ( b != a ) ),
inference(simp,[status(thm)],[283]) ).
thf(785,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ join ) @ meet ) )
!= ( c @ ( b @ meet ) ) )
| ( A != a )
| ( c != a ) ),
inference(paramod_ordered,[status(thm)],[221,556]) ).
thf(814,plain,
! [A: $i] :
( ( c != a )
| ( ( a @ ( A @ join ) )
!= b )
| ( c != a ) ),
inference(simp,[status(thm)],[785]) ).
thf(841,plain,
! [A: $i] :
( ( ( a @ ( A @ join ) )
!= b )
| ( c != a ) ),
inference(simp,[status(thm)],[814]) ).
thf(530,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( b @ meet ) ) )
| ( c != a )
| ( ( A @ ( a @ join ) )
!= a ) ),
inference(paramod_ordered,[status(thm)],[15,219]) ).
thf(541,plain,
! [A: $i] :
( ( A != c )
| ( A != b )
| ( c != a )
| ( ( A @ ( a @ join ) )
!= a ) ),
inference(simp,[status(thm)],[530]) ).
thf(559,plain,
( ( c != b )
| ( c != a )
| ( ( b @ ( a @ join ) )
!= a ) ),
inference(simp,[status(thm)],[541]) ).
thf(297,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ join ) )
!= ( C @ ( a @ join ) ) )
| ( ( B @ ( A @ join ) )
!= c )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[25,111]) ).
thf(298,plain,
! [A: $i] :
( ( ( a @ ( A @ join ) )
!= c )
| ( b != a ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( A )),bind(B,$thf( a )),bind(C,$thf( A ))]]) ).
thf(302,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ meet ) @ ( A @ join ) )
!= ( a @ ( C @ join ) ) )
| ( A != c )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[21,298]) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c @ meet ) )
!= a )
| ( c != B )
| ( b != a ) ),
inference(simp,[status(thm)],[302]) ).
thf(316,plain,
! [A: $i] :
( ( ( A @ ( c @ meet ) )
!= a )
| ( b != a ) ),
inference(simp,[status(thm)],[311]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ join ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(717,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)],[23,214]) ).
thf(718,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ meet ) @ join ) )
= B ),
inference(pattern_uni,[status(thm)],[717:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) @ meet ) )
= ( C @ ( B @ meet ) @ ( A @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) @ meet ) )
= ( C @ ( B @ meet ) @ ( A @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) @ meet ) )
= ( C @ ( B @ meet ) @ ( A @ meet ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(309,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ meet ) @ ( A @ join ) )
!= ( a @ ( C @ join ) ) )
| ( A != c )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[114,298]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( ( c @ ( A @ meet ) )
!= a )
| ( c != B )
| ( b != a ) ),
inference(simp,[status(thm)],[309]) ).
thf(318,plain,
! [A: $i] :
( ( ( c @ ( A @ meet ) )
!= a )
| ( b != a ) ),
inference(simp,[status(thm)],[313]) ).
thf(222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ join ) )
!= ( D @ ( C @ join ) ) )
| ( ( C @ ( B @ ( A @ join ) @ meet ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[25,141]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ join ) @ meet ) )
= B ),
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( D @ ( C @ join ) ) )
| ( ( A @ ( B @ join ) @ ( C @ meet ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[25,19]) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ join ) @ ( A @ meet ) )
= A ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(794,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( C @ ( D @ join ) ) )
| ( ( C @ ( A @ ( B @ join ) @ meet ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[25,221]) ).
thf(795,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ join ) @ meet ) )
= B ),
inference(pattern_uni,[status(thm)],[794:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(105,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( b @ meet ) ) )
| ( A != a )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[15,73]) ).
thf(109,plain,
( ( c != a )
| ( b != a )
| ( b != a ) ),
inference(simp,[status(thm)],[105]) ).
thf(112,plain,
( ( c != a )
| ( b != a ) ),
inference(simp,[status(thm)],[109]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ meet ) @ ( B @ ( C @ ( B @ ( A @ meet ) @ join ) @ meet ) @ join ) )
= ( A @ ( C @ join ) @ ( B @ ( C @ ( B @ ( A @ join ) @ meet ) @ join ) @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_dual) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ meet ) @ ( B @ ( C @ ( B @ ( A @ meet ) @ join ) @ meet ) @ join ) )
= ( A @ ( C @ join ) @ ( B @ ( C @ ( B @ ( A @ join ) @ meet ) @ join ) @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ join ) @ ( B @ ( C @ ( B @ ( A @ join ) @ meet ) @ join ) @ meet ) )
= ( A @ ( C @ meet ) @ ( B @ ( C @ ( B @ ( A @ meet ) @ join ) @ meet ) @ join ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(3703,plain,
$false,
inference(e,[status(thm)],[14,485,221,65,141,13,18,11,556,214,15,111,170,582,288,25,841,24,559,20,316,29,28,21,73,718,298,17,22,27,219,318,223,167,795,112,16,31,26,114,23,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT009-1 : 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
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 19:59:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 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
% 0.70/0.75 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.15/0.91 % [INFO] Parsing done (158ms).
% 1.15/0.92 % [INFO] Running in sequential loop mode.
% 1.80/1.26 % [INFO] eprover registered as external prover.
% 1.80/1.27 % [INFO] Scanning for conjecture ...
% 2.08/1.35 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 2.29/1.40 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 2.29/1.43 % [INFO] Problem is propositional (TPTP CNF).
% 2.29/1.44 % [INFO] Type checking passed.
% 2.29/1.45 % [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 ...
% 27.35/6.87 % External prover 'e' found a proof!
% 27.35/6.87 % [INFO] Killing All external provers ...
% 27.35/6.88 % Time passed: 6402ms (effective reasoning time: 5947ms)
% 27.35/6.88 % Axioms used in derivation (9): commutativity_of_join, absorption1, associativity_of_meet, commutativity_of_meet, associativity_of_join, idempotence_of_join, absorption2, distributivity_dual, idempotence_of_meet
% 27.35/6.88 % No. of inferences in proof: 98
% 27.35/6.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6402 ms resp. 5947 ms w/o parsing
% 24.48/6.97 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.48/6.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------