%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT168-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 07:46:42 AM UTC 2026
% Result : Unsatisfiable 29.69s 8.90s
% Output : Refutation 26.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 96 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 189 ( 188 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 887 ( 138 ~; 93 |; 0 &; 656 @)
% ( 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 : 152 ( 0 ^; 152 !; 0 ?; 152 :)
% Comments :
%------------------------------------------------------------------------------
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(join_decl,type,
join: $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/sandbox2/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(15,plain,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
inference(lifteq,[status(thm)],[14]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/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 @ join ) @ ( a @ meet ) )
!= ( b @ ( a @ meet ) @ ( c @ join ) @ ( b @ ( a @ join ) @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_H58) ).
thf(11,plain,
( ( c @ ( b @ join ) @ ( a @ meet ) )
!= ( b @ ( a @ meet ) @ ( c @ join ) @ ( b @ ( a @ join ) @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ( c @ ( b @ join ) @ ( a @ meet ) )
!= ( b @ ( a @ meet ) @ ( c @ join ) @ ( b @ ( a @ join ) @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( b @ ( a @ meet ) @ ( c @ join ) @ ( b @ ( a @ join ) @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( b @ join ) @ ( a @ meet ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(60,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( b @ ( a @ meet ) @ ( c @ join ) ) )
| ( ( A @ ( b @ ( a @ join ) @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,13]) ).
thf(77,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ meet ) ) )
| ( A != c )
| ( ( A @ ( b @ ( a @ join ) @ meet ) @ ( b @ join ) )
!= ( c @ ( b @ join ) ) )
| ( a != a ) ),
inference(simp,[status(thm)],[60]) ).
thf(111,plain,
( ( ( b @ ( a @ meet ) )
!= c )
| ( ( c @ ( b @ ( a @ join ) @ meet ) @ ( b @ join ) )
!= ( c @ ( b @ join ) ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(141,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( b @ ( a @ join ) @ meet ) ) )
| ( ( b @ ( a @ meet ) )
!= c )
| ( ( A @ ( b @ join ) )
!= ( c @ ( b @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,111]) ).
thf(154,plain,
! [A: $i] :
( ( A != c )
| ( A
!= ( b @ ( a @ join ) ) )
| ( ( b @ ( a @ meet ) )
!= c )
| ( A != c )
| ( b != b ) ),
inference(simp,[status(thm)],[141]) ).
thf(175,plain,
( ( ( b @ ( a @ join ) )
!= c )
| ( ( b @ ( a @ meet ) )
!= c ) ),
inference(simp,[status(thm)],[154]) ).
thf(222,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( b @ ( a @ join ) ) )
| ( A != c )
| ( ( b @ ( a @ meet ) )
!= c ) ),
inference(paramod_ordered,[status(thm)],[17,175]) ).
thf(230,plain,
( ( c != b )
| ( c != a )
| ( ( b @ ( a @ meet ) )
!= c ) ),
inference(simp,[status(thm)],[222]) ).
thf(242,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( c != b )
| ( c != a )
| ( A != c ) ),
inference(paramod_ordered,[status(thm)],[15,230]) ).
thf(246,plain,
( ( c != b )
| ( c != a )
| ( c != b )
| ( c != a ) ),
inference(simp,[status(thm)],[242]) ).
thf(249,plain,
( ( c != b )
| ( c != a ) ),
inference(simp,[status(thm)],[246]) ).
thf(138,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( b @ ( a @ join ) ) )
| ( ( b @ ( a @ meet ) )
!= c )
| ( ( c @ ( A @ meet ) @ ( b @ join ) )
!= ( c @ ( b @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,111]) ).
thf(145,plain,
! [A: $i] :
( ( A != b )
| ( A != a )
| ( ( b @ ( a @ meet ) )
!= c )
| ( ( c @ ( A @ meet ) )
!= c )
| ( b != b ) ),
inference(simp,[status(thm)],[138]) ).
thf(170,plain,
( ( b != a )
| ( ( b @ ( a @ meet ) )
!= c )
| ( ( c @ ( a @ meet ) )
!= c ) ),
inference(simp,[status(thm)],[145]) ).
thf(890,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( b != a )
| ( ( b @ ( a @ meet ) )
!= c )
| ( A != c ) ),
inference(paramod_ordered,[status(thm)],[15,170]) ).
thf(914,plain,
( ( c != c )
| ( c != a )
| ( b != a )
| ( ( b @ ( a @ meet ) )
!= c ) ),
inference(simp,[status(thm)],[890]) ).
thf(930,plain,
( ( c != a )
| ( b != a )
| ( ( b @ ( a @ meet ) )
!= c ) ),
inference(simp,[status(thm)],[914]) ).
thf(896,plain,
( ( c != c )
| ( ( c @ ( a @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( b != a )
| ( ( b @ ( a @ meet ) )
!= c ) ),
inference(eqfactor_ordered,[status(thm)],[170]) ).
thf(907,plain,
( ( c != b )
| ( a != a )
| ( b != a )
| ( ( b @ ( a @ meet ) )
!= c ) ),
inference(simp,[status(thm)],[896]) ).
thf(924,plain,
( ( c != b )
| ( b != a )
| ( ( b @ ( a @ meet ) )
!= c ) ),
inference(simp,[status(thm)],[907]) ).
thf(54,plain,
( ( ( b @ ( a @ meet ) @ ( c @ join ) @ ( b @ ( a @ join ) @ meet ) @ ( b @ join ) )
!= ( c @ ( b @ join ) ) )
| ( a != a ) ),
inference(simp,[status(thm)],[13]) ).
thf(133,plain,
( ( b @ ( a @ meet ) @ ( c @ join ) @ ( b @ ( a @ join ) @ meet ) @ ( b @ join ) )
!= ( c @ ( b @ join ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/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(56,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) @ ( A @ join ) )
!= ( b @ ( a @ join ) ) )
| ( ( b @ ( a @ meet ) @ ( c @ join ) @ ( A @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,13]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) @ ( A @ join ) )
!= ( b @ ( a @ join ) ) )
| ( ( b @ ( a @ meet ) @ ( c @ join ) @ ( A @ meet ) @ ( b @ join ) )
!= ( c @ ( b @ join ) ) )
| ( a != a ) ),
inference(simp,[status(thm)],[56]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) @ ( A @ join ) )
!= ( b @ ( a @ join ) ) )
| ( ( b @ ( a @ meet ) @ ( c @ join ) @ ( A @ meet ) @ ( b @ join ) )
!= ( c @ ( b @ join ) ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(2826,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ join ) ) )
| ( ( b @ ( a @ meet ) @ ( c @ join ) @ ( A @ meet ) @ ( b @ join ) )
!= ( c @ ( b @ join ) ) ) ),
inference(rewrite,[status(thm)],[101,21]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox2/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(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox2/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(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
file('/export/starexec/sandbox2/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(200,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(201,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ join ) @ meet ) )
= A ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ join ) ))]]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ join ) @ meet ) )
= A ),
inference(simp,[status(thm)],[201]) ).
thf(636,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)],[25,218]) ).
thf(637,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ join ) @ meet ) )
= A ),
inference(pattern_uni,[status(thm)],[636:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(134,plain,
( ( ( b @ ( a @ meet ) )
!= c )
| ( ( c @ ( b @ ( a @ join ) @ meet ) )
!= c )
| ( b != b ) ),
inference(simp,[status(thm)],[111]) ).
thf(167,plain,
( ( ( b @ ( a @ meet ) )
!= c )
| ( ( c @ ( b @ ( a @ join ) @ meet ) )
!= c ) ),
inference(simp,[status(thm)],[134]) ).
thf(934,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ join ) @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( c != b )
| ( b != a )
| ( A != c ) ),
inference(paramod_ordered,[status(thm)],[218,924]) ).
thf(941,plain,
! [A: $i] :
( ( c != b )
| ( ( A @ ( c @ join ) )
!= a )
| ( c != b )
| ( b != a ) ),
inference(simp,[status(thm)],[934]) ).
thf(955,plain,
! [A: $i] :
( ( ( A @ ( c @ join ) )
!= a )
| ( c != b )
| ( b != a ) ),
inference(simp,[status(thm)],[941]) ).
thf(188,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(189,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ meet ) @ ( A @ join ) )
= A ),
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(395,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)],[189,25]) ).
thf(396,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ meet ) @ join ) )
= B ),
inference(pattern_uni,[status(thm)],[395:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ meet ) ))]]) ).
thf(464,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ meet ) @ join ) )
= B ),
inference(simp,[status(thm)],[396]) ).
thf(1268,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)],[23,464]) ).
thf(1269,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ meet ) @ join ) )
= B ),
inference(pattern_uni,[status(thm)],[1268:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(283,plain,
( ( ( b @ ( a @ meet ) @ ( c @ join ) @ ( b @ ( a @ join ) @ meet ) )
!= c )
| ( b != b ) ),
inference(simp,[status(thm)],[133]) ).
thf(344,plain,
( ( b @ ( a @ meet ) @ ( c @ join ) @ ( b @ ( a @ join ) @ meet ) )
!= c ),
inference(simp,[status(thm)],[283]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ join ) ) ),
file('/export/starexec/sandbox2/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(252,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(253,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ meet ) @ join ) )
= A ),
inference(pattern_uni,[status(thm)],[252:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ meet ) ))]]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ meet ) @ join ) )
= A ),
inference(simp,[status(thm)],[253]) ).
thf(1134,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)],[23,281]) ).
thf(1135,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ meet ) @ join ) )
= A ),
inference(pattern_uni,[status(thm)],[1134:[bind(A,$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/sandbox2/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(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ join ) @ ( B @ ( A @ join ) @ meet ) )
= ( C @ ( A @ meet ) @ ( B @ join ) @ ( C @ ( A @ join ) @ meet ) @ ( B @ ( A @ join ) @ meet ) @ ( A @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H18_dual) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ join ) @ ( B @ ( A @ join ) @ meet ) )
= ( C @ ( A @ meet ) @ ( B @ join ) @ ( C @ ( A @ join ) @ meet ) @ ( B @ ( A @ join ) @ meet ) @ ( A @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ meet ) @ ( B @ join ) @ ( C @ ( A @ join ) @ meet ) @ ( B @ ( A @ join ) @ meet ) @ ( A @ join ) )
= ( C @ ( A @ join ) @ ( B @ ( A @ join ) @ meet ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(964,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) @ ( A @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( c != a )
| ( b != a )
| ( A != c ) ),
inference(paramod_ordered,[status(thm)],[19,930]) ).
thf(969,plain,
! [A: $i] :
( ( ( A @ ( c @ join ) )
!= b )
| ( c != a )
| ( c != a )
| ( b != a ) ),
inference(simp,[status(thm)],[964]) ).
thf(978,plain,
! [A: $i] :
( ( ( A @ ( c @ join ) )
!= b )
| ( c != a )
| ( b != a ) ),
inference(simp,[status(thm)],[969]) ).
thf(272,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(273,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ join ) @ ( A @ meet ) )
= A ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(965,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ join ) @ ( A @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( c != a )
| ( b != a )
| ( A != c ) ),
inference(paramod_ordered,[status(thm)],[273,930]) ).
thf(967,plain,
! [A: $i] :
( ( ( c @ ( A @ join ) )
!= b )
| ( c != a )
| ( c != a )
| ( b != a ) ),
inference(simp,[status(thm)],[965]) ).
thf(976,plain,
! [A: $i] :
( ( ( c @ ( A @ join ) )
!= b )
| ( c != a )
| ( b != a ) ),
inference(simp,[status(thm)],[967]) ).
thf(1660,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)],[25,637]) ).
thf(1661,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ join ) @ meet ) )
= B ),
inference(pattern_uni,[status(thm)],[1660:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(64,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( b @ ( a @ meet ) @ ( c @ join ) @ ( b @ ( a @ join ) @ meet ) @ ( b @ join ) @ ( a @ meet ) ) )
| ( A
!= ( c @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,13]) ).
thf(82,plain,
( ( ( b @ ( a @ meet ) @ ( c @ join ) @ ( b @ ( a @ join ) @ meet ) @ ( b @ join ) )
!= ( c @ ( b @ join ) @ ( a @ meet ) ) )
| ( ( c @ ( b @ join ) @ ( a @ meet ) )
!= a ) ),
inference(simp,[status(thm)],[64]) ).
thf(638,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)],[25,218]) ).
thf(639,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ join ) @ meet ) )
= B ),
inference(pattern_uni,[status(thm)],[638:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(6980,plain,
$false,
inference(e,[status(thm)],[249,930,924,133,2826,637,13,167,18,955,170,1269,24,25,14,344,189,20,29,28,21,1135,17,22,281,27,16,31,11,175,978,976,218,26,23,1661,82,30,19,273,464,15,111,639]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT168-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/0.70 % Computer : n020.cluster.edu
% 0.23/0.70 % Model : x86_64 x86_64
% 0.23/0.70 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.70 % Memory : 8046.5625MB
% 0.23/0.70 % OS : Linux 6.8.0-71-generic
% 0.23/0.70 % CPULimit : 300
% 0.23/0.70 % WCLimit : 300
% 0.23/0.70 % DateTime : Fri Sep 25 20:11:34 UTC 2026
% 0.27/0.70 % CPUTime :
% 0.27/0.70 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.35/1.57 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.83/1.85 % [INFO] Parsing done (276ms).
% 1.83/1.88 % [INFO] Running in sequential loop mode.
% 2.77/2.44 % [INFO] eprover registered as external prover.
% 2.77/2.45 % [INFO] Scanning for conjecture ...
% 2.93/2.59 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 3.08/2.64 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 3.08/2.66 % [INFO] Problem is propositional (TPTP CNF).
% 3.08/2.67 % [INFO] Type checking passed.
% 3.08/2.68 % [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 ...
% 29.69/8.89 % External prover 'e' found a proof!
% 29.69/8.89 % [INFO] Killing All external provers ...
% 29.69/8.89 % Time passed: 7984ms (effective reasoning time: 7006ms)
% 29.69/8.90 % Axioms used in derivation (9): equation_H18_dual, commutativity_of_join, absorption1, associativity_of_meet, commutativity_of_meet, associativity_of_join, idempotence_of_meet, idempotence_of_join, absorption2
% 29.69/8.90 % No. of inferences in proof: 96
% 29.69/8.90 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7984 ms resp. 7006 ms w/o parsing
% 26.28/8.93 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 26.28/8.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------