%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT023-1 : TPTP v9.3.1. Released v2.2.0.
% 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 : 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 07:46:29 AM UTC 2026
% Result : Unsatisfiable 98.37s 24.45s
% Output : Refutation 92.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 202 ( 79 unt; 0 typ; 0 def)
% Number of atoms : 445 ( 444 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2258 ( 349 ~; 243 |; 0 &;1666 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 327 ( 0 ^; 327 !; 0 ?; 327 :)
% 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(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(lifteq,[status(thm)],[20]) ).
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(7,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(24,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)],[7]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ join ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(351,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ join ) )
!= ( C @ ( B @ join ) ) )
| ( ( D @ ( A @ join ) )
= ( D @ ( C @ join ) @ ( B @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,25]) ).
thf(352,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ join ) )
= ( B @ ( A @ join ) ) ),
inference(pattern_uni,[status(thm)],[351:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(362,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ join ) )
= ( B @ ( A @ join ) ) ),
inference(simp,[status(thm)],[352]) ).
thf(512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( D @ ( C @ join ) ) )
| ( ( A @ ( B @ join ) @ ( C @ join ) )
= ( D @ ( C @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,362]) ).
thf(513,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ join ) @ ( A @ join ) )
= ( B @ ( A @ join ) ) ),
inference(pattern_uni,[status(thm)],[512:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1771,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ join ) @ ( A @ join ) )
!= ( D @ ( C @ join ) ) )
| ( ( B @ ( A @ join ) )
= ( C @ ( D @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[513,21]) ).
thf(1772,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ join ) @ join ) )
= ( A @ ( B @ join ) ) ),
inference(pattern_uni,[status(thm)],[1771:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ join ) ))]]) ).
thf(1859,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ join ) @ join ) )
= ( A @ ( B @ join ) ) ),
inference(simp,[status(thm)],[1772]) ).
thf(4494,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ join ) @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(rewrite,[status(thm)],[1859,25]) ).
thf(4531,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( C @ ( D @ join ) ) )
| ( ( A @ ( B @ join ) )
= ( D @ ( D @ join ) @ ( C @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,4494]) ).
thf(4532,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ join ) @ ( B @ join ) )
= ( A @ ( B @ join ) ) ),
inference(pattern_uni,[status(thm)],[4531:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(lifteq,[status(thm)],[18]) ).
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(6,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(22,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)],[6]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) @ meet ) )
= ( C @ ( B @ meet ) @ ( A @ meet ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( C @ ( B @ meet ) ) )
| ( ( D @ ( A @ meet ) )
= ( D @ ( C @ meet ) @ ( B @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,23]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ meet ) )
= ( B @ ( A @ meet ) ) ),
inference(pattern_uni,[status(thm)],[151:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ meet ) )
= ( B @ ( A @ meet ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= ( D @ ( C @ meet ) ) )
| ( ( A @ ( B @ meet ) @ ( C @ meet ) )
= ( D @ ( C @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,188]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ meet ) @ ( A @ meet ) )
= ( B @ ( A @ meet ) ) ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(261,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ meet ) @ ( A @ meet ) )
!= ( D @ ( C @ meet ) ) )
| ( ( B @ ( A @ meet ) )
= ( C @ ( D @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[200,19]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ meet ) @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ meet ) ))]]) ).
thf(307,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ meet ) @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(simp,[status(thm)],[262]) ).
thf(378,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ meet ) @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(rewrite,[status(thm)],[307,23]) ).
thf(404,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ meet ) )
!= ( D @ ( C @ meet ) ) )
| ( ( B @ ( B @ meet ) @ ( A @ meet ) )
= ( C @ ( D @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[378,19]) ).
thf(405,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ meet ) @ ( A @ meet ) )
= ( B @ ( A @ meet ) ) ),
inference(pattern_uni,[status(thm)],[404:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(715,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ meet ) @ ( A @ meet ) )
!= ( C @ ( C @ meet ) ) )
| ( ( B @ ( A @ meet ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[405,15]) ).
thf(716,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ meet ) @ meet ) )
= ( A @ ( A @ meet ) ) ),
inference(pattern_uni,[status(thm)],[715:[bind(A,$thf( E @ ( E @ meet ) )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ meet ) ))]]) ).
thf(743,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ meet ) @ meet ) )
= ( A @ ( A @ meet ) ) ),
inference(simp,[status(thm)],[716]) ).
thf(3387,plain,
! [A: $i] :
( ( A @ ( A @ meet ) @ ( A @ meet ) )
= ( A @ ( A @ meet ) ) ),
inference(rewrite,[status(thm)],[743,23]) ).
thf(3480,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ meet ) @ ( A @ meet ) )
!= ( C @ ( B @ meet ) ) )
| ( ( A @ ( A @ meet ) )
= ( B @ ( C @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[3387,19]) ).
thf(3481,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ meet ) @ meet ) )
= ( A @ ( A @ meet ) ) ),
inference(pattern_uni,[status(thm)],[3480:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ meet ) ))]]) ).
thf(3567,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ meet ) @ meet ) )
= ( A @ ( A @ meet ) ) ),
inference(simp,[status(thm)],[3481]) ).
thf(5663,plain,
! [A: $i] :
( ( A @ ( A @ meet ) @ ( A @ meet ) )
= ( A @ ( A @ meet ) ) ),
inference(rewrite,[status(thm)],[3567,23]) ).
thf(400,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ meet ) @ ( A @ meet ) )
!= ( D @ ( C @ meet ) ) )
| ( ( A @ ( B @ meet ) )
= ( C @ ( D @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[378,19]) ).
thf(401,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ meet ) @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(pattern_uni,[status(thm)],[400:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ ( F @ meet ) ))]]) ).
thf(477,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ meet ) @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(simp,[status(thm)],[401]) ).
thf(879,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ meet ) @ ( B @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(rewrite,[status(thm)],[477,23]) ).
thf(1,negated_conjecture,
( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) @ ( b @ ( a @ meet ) @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_modularity) ).
thf(11,plain,
( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) @ ( b @ ( a @ meet ) @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) @ ( b @ ( a @ meet ) @ join ) ) ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( c @ ( a @ meet ) @ ( b @ ( a @ meet ) @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(32,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ ( a @ meet ) @ join ) ) )
| ( A
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,13]) ).
thf(36,plain,
( ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( b @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(2548,plain,
( ( ( c @ ( a @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) )
| ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( b @ ( a @ meet ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[36]) ).
thf(2638,plain,
( ( ( c @ ( a @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= b )
| ( a != a ) ),
inference(simp,[status(thm)],[2548]) ).
thf(2999,plain,
( ( ( c @ ( a @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= b ) ),
inference(simp,[status(thm)],[2638]) ).
thf(10108,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ meet ) @ ( B @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( ( A @ ( B @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[879,2999]) ).
thf(10217,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ meet ) )
!= c )
| ( B != a )
| ( A != b )
| ( B != a )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= b ) ),
inference(simp,[status(thm)],[10108]) ).
thf(10332,plain,
( ( ( b @ ( a @ meet ) )
!= c )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= b ) ),
inference(simp,[status(thm)],[10217]) ).
thf(703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ meet ) @ ( A @ meet ) )
!= ( D @ ( C @ meet ) ) )
| ( ( B @ ( A @ meet ) )
= ( C @ ( D @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[405,19]) ).
thf(704,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ ( B @ meet ) @ meet ) ) ),
inference(pattern_uni,[status(thm)],[703:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ ( F @ meet ) ))]]) ).
thf(737,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ ( B @ meet ) @ meet ) ) ),
inference(simp,[status(thm)],[704]) ).
thf(2181,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) @ ( B @ meet ) ) ),
inference(rewrite,[status(thm)],[737,23]) ).
thf(2340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ meet ) @ ( B @ meet ) )
!= ( D @ ( C @ meet ) ) )
| ( ( B @ ( A @ meet ) )
= ( C @ ( D @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[2181,19]) ).
thf(2341,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ meet ) @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(pattern_uni,[status(thm)],[2340:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ meet ) ))]]) ).
thf(2412,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ meet ) @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(simp,[status(thm)],[2341]) ).
thf(4899,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ meet ) @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(rewrite,[status(thm)],[2412,23]) ).
thf(2542,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( ( A @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( b @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,36]) ).
thf(2594,plain,
! [A: $i] :
( ( A != c )
| ( A != a )
| ( ( A @ ( b @ join ) )
!= c )
| ( a != a )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= b )
| ( a != a ) ),
inference(simp,[status(thm)],[2542]) ).
thf(2956,plain,
( ( c != a )
| ( ( a @ ( b @ join ) )
!= c )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= b ) ),
inference(simp,[status(thm)],[2594]) ).
thf(7609,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( c != a )
| ( ( a @ ( b @ join ) )
!= c )
| ( ( A @ ( b @ join ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[15,2956]) ).
thf(7631,plain,
! [A: $i] :
( ( A != c )
| ( A != a )
| ( c != a )
| ( ( a @ ( b @ join ) )
!= c )
| ( ( A @ ( b @ join ) )
!= b ) ),
inference(simp,[status(thm)],[7609]) ).
thf(7660,plain,
( ( c != a )
| ( ( a @ ( b @ join ) )
!= c )
| ( ( a @ ( b @ join ) )
!= b ) ),
inference(simp,[status(thm)],[7631]) ).
thf(2506,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) ) )
| ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( ( A @ ( a @ meet ) )
!= ( b @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,36]) ).
thf(2812,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ meet ) ) )
| ( A != b )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= c )
| ( a != a )
| ( A != b )
| ( a != a ) ),
inference(simp,[status(thm)],[2506]) ).
thf(3169,plain,
( ( ( c @ ( a @ meet ) )
!= b )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= c ) ),
inference(simp,[status(thm)],[2812]) ).
thf(4161,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( ( c @ ( a @ meet ) )
!= b )
| ( ( A @ ( b @ join ) )
!= c ) ),
inference(paramod_ordered,[status(thm)],[15,3169]) ).
thf(4175,plain,
! [A: $i] :
( ( A != c )
| ( A != a )
| ( ( c @ ( a @ meet ) )
!= b )
| ( ( A @ ( b @ join ) )
!= c ) ),
inference(simp,[status(thm)],[4161]) ).
thf(4204,plain,
( ( c != a )
| ( ( c @ ( a @ meet ) )
!= b )
| ( ( a @ ( b @ join ) )
!= c ) ),
inference(simp,[status(thm)],[4175]) ).
thf(5194,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( a @ ( b @ join ) ) )
| ( c != a )
| ( ( c @ ( a @ meet ) )
!= b )
| ( ( A @ ( B @ join ) )
!= c ) ),
inference(paramod_ordered,[status(thm)],[21,4204]) ).
thf(5195,plain,
( ( c != a )
| ( ( c @ ( a @ meet ) )
!= b )
| ( ( b @ ( a @ join ) )
!= c ) ),
inference(pattern_uni,[status(thm)],[5194:[bind(A,$thf( b )),bind(B,$thf( a ))]]) ).
thf(4523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ join ) )
!= ( D @ ( C @ join ) ) )
| ( ( B @ ( B @ join ) @ ( A @ join ) )
= ( C @ ( D @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[4494,21]) ).
thf(4524,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ join ) @ ( A @ join ) )
= ( B @ ( A @ join ) ) ),
inference(pattern_uni,[status(thm)],[4523:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(2640,plain,
( ( c != b )
| ( a != a )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= b )
| ( a != a ) ),
inference(simp,[status(thm)],[2548]) ).
thf(3001,plain,
( ( c != b )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= b ) ),
inference(simp,[status(thm)],[2640]) ).
thf(3316,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( c != b )
| ( ( A @ ( b @ join ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[15,3001]) ).
thf(3335,plain,
! [A: $i] :
( ( A != c )
| ( A != a )
| ( c != b )
| ( ( A @ ( b @ join ) )
!= b ) ),
inference(simp,[status(thm)],[3316]) ).
thf(3342,plain,
( ( c != a )
| ( c != b )
| ( ( a @ ( b @ join ) )
!= b ) ),
inference(simp,[status(thm)],[3335]) ).
thf(4529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( D @ ( D @ join ) ) )
| ( ( A @ ( B @ join ) @ ( C @ join ) )
= ( C @ ( D @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,4494]) ).
thf(4530,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ join ) @ ( B @ join ) )
= ( B @ ( A @ join ) ) ),
inference(pattern_uni,[status(thm)],[4529:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(4766,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ join ) @ ( B @ join ) )
= ( B @ ( A @ join ) ) ),
inference(simp,[status(thm)],[4530]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( C @ ( B @ meet ) @ ( A @ join ) @ meet ) )
= ( C @ ( B @ meet ) @ ( A @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quasi_lattice2) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( C @ ( B @ meet ) @ ( A @ join ) @ meet ) )
= ( C @ ( B @ meet ) @ ( A @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( C @ ( B @ meet ) @ ( A @ join ) @ meet ) )
= ( C @ ( B @ meet ) @ ( A @ join ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(33,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( ( A @ ( b @ ( a @ meet ) @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,13]) ).
thf(37,plain,
! [A: $i] :
( ( A != c )
| ( A != a )
| ( ( A @ ( b @ ( a @ meet ) @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(39,plain,
( ( c != a )
| ( ( a @ ( b @ ( a @ meet ) @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( a @ ( b @ ( a @ meet ) @ join ) ) )
| ( c != a )
| ( ( A @ ( B @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,39]) ).
thf(94,plain,
( ( c != a )
| ( ( b @ ( a @ meet ) @ ( a @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( b @ ( a @ meet ) )),bind(B,$thf( a ))]]) ).
thf(1916,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( c != a )
| ( ( A @ ( b @ join ) @ ( a @ meet ) )
!= ( b @ ( a @ meet ) @ ( a @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,94]) ).
thf(1958,plain,
! [A: $i] :
( ( A != c )
| ( A != a )
| ( c != a )
| ( ( A @ ( b @ join ) @ ( a @ meet ) )
!= ( b @ ( a @ meet ) @ ( a @ join ) ) ) ),
inference(simp,[status(thm)],[1916]) ).
thf(1997,plain,
( ( c != a )
| ( ( a @ ( b @ join ) @ ( a @ meet ) )
!= ( b @ ( a @ meet ) @ ( a @ join ) ) ) ),
inference(simp,[status(thm)],[1958]) ).
thf(2010,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( a @ ( b @ join ) ) )
| ( c != a )
| ( ( A @ ( B @ join ) @ ( a @ meet ) )
!= ( b @ ( a @ meet ) @ ( a @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,1997]) ).
thf(2011,plain,
( ( c != a )
| ( ( b @ ( a @ meet ) @ ( a @ join ) )
!= ( b @ ( a @ join ) @ ( a @ meet ) ) ) ),
inference(pattern_uni,[status(thm)],[2010:[bind(A,$thf( b )),bind(B,$thf( a ))]]) ).
thf(410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= ( D @ ( D @ meet ) ) )
| ( ( A @ ( B @ meet ) @ ( C @ meet ) )
= ( C @ ( D @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,378]) ).
thf(411,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ meet ) @ ( B @ meet ) )
= ( B @ ( A @ meet ) ) ),
inference(pattern_uni,[status(thm)],[410:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(484,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ meet ) @ ( B @ meet ) )
= ( B @ ( A @ meet ) ) ),
inference(simp,[status(thm)],[411]) ).
thf(6023,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ join ) @ ( A @ join ) )
!= ( D @ ( C @ join ) ) )
| ( ( B @ ( A @ join ) )
= ( C @ ( D @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[4524,21]) ).
thf(6024,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ ( B @ join ) @ join ) ) ),
inference(pattern_uni,[status(thm)],[6023:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ ( F @ join ) ))]]) ).
thf(6138,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ ( B @ join ) @ join ) ) ),
inference(simp,[status(thm)],[6024]) ).
thf(8462,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) @ ( B @ join ) ) ),
inference(rewrite,[status(thm)],[6138,25]) ).
thf(6042,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ join ) @ ( A @ join ) )
!= ( C @ ( C @ join ) ) )
| ( ( B @ ( A @ join ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[4524,17]) ).
thf(6043,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ join ) @ join ) )
= ( A @ ( A @ join ) ) ),
inference(pattern_uni,[status(thm)],[6042:[bind(A,$thf( E @ ( E @ join ) )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ join ) ))]]) ).
thf(6145,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ join ) @ join ) )
= ( A @ ( A @ join ) ) ),
inference(simp,[status(thm)],[6043]) ).
thf(9186,plain,
! [A: $i] :
( ( A @ ( A @ join ) @ ( A @ join ) )
= ( A @ ( A @ join ) ) ),
inference(rewrite,[status(thm)],[6145,25]) ).
thf(8007,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( a @ ( b @ join ) ) )
| ( c != a )
| ( ( a @ ( b @ join ) )
!= c )
| ( ( A @ ( B @ join ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[21,7660]) ).
thf(8008,plain,
( ( c != a )
| ( ( a @ ( b @ join ) )
!= c )
| ( ( b @ ( a @ join ) )
!= b ) ),
inference(pattern_uni,[status(thm)],[8007:[bind(A,$thf( b )),bind(B,$thf( a ))]]) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ meet ) @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( c != a )
| ( ( a @ ( C @ ( B @ meet ) @ ( A @ meet ) @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,39]) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ( C != b )
| ( ( B @ ( A @ meet ) )
!= a )
| ( c != a )
| ( ( a @ ( C @ ( B @ meet ) @ ( A @ meet ) @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= a )
| ( c != a )
| ( ( a @ ( b @ ( B @ meet ) @ ( A @ meet ) @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(10388,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) ) )
| ( ( b @ ( a @ meet ) )
!= c )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[17,10332]) ).
thf(10412,plain,
( ( ( c @ ( a @ meet ) )
!= b )
| ( b != b )
| ( ( b @ ( a @ meet ) )
!= c ) ),
inference(simp,[status(thm)],[10388]) ).
thf(10465,plain,
( ( ( c @ ( a @ meet ) )
!= b )
| ( ( b @ ( a @ meet ) )
!= c ) ),
inference(simp,[status(thm)],[10412]) ).
thf(2549,plain,
( ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( b @ ( a @ meet ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[36]) ).
thf(2601,plain,
( ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= c )
| ( a != a )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= b )
| ( a != a )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= b )
| ( a != a ) ),
inference(simp,[status(thm)],[2549]) ).
thf(2963,plain,
( ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= c )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= b ) ),
inference(simp,[status(thm)],[2601]) ).
thf(159,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ meet ) @ meet ) )
!= ( E @ ( D @ meet ) ) )
| ( ( F @ ( C @ ( B @ meet ) @ ( A @ meet ) @ meet ) )
= ( F @ ( E @ meet ) @ ( D @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,23]) ).
thf(160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ meet ) @ ( C @ meet ) @ meet ) )
= ( B @ ( A @ meet ) @ ( D @ ( C @ meet ) @ meet ) ) ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ meet ) )),bind(E,$thf( C ))]]) ).
thf(170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ meet ) @ ( C @ meet ) @ meet ) )
= ( B @ ( A @ meet ) @ ( D @ ( C @ meet ) @ meet ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(7128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ meet ) @ meet ) @ ( C @ meet ) )
= ( B @ ( A @ meet ) @ ( D @ meet ) @ ( C @ meet ) ) ),
inference(rewrite,[status(thm)],[170,23]) ).
thf(54,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( a @ ( b @ ( a @ meet ) @ join ) ) )
| ( c != a )
| ( A
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,39]) ).
thf(59,plain,
( ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= a )
| ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( c != a ) ),
inference(simp,[status(thm)],[54]) ).
thf(8091,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( a @ ( b @ join ) ) )
| ( c != a )
| ( ( A @ ( B @ join ) )
!= c )
| ( ( b @ ( a @ join ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[21,8008]) ).
thf(8092,plain,
( ( c != a )
| ( ( b @ ( a @ join ) )
!= c )
| ( ( b @ ( a @ join ) )
!= b ) ),
inference(pattern_uni,[status(thm)],[8091:[bind(A,$thf( b )),bind(B,$thf( a ))]]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( C @ ( B @ join ) @ ( A @ meet ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quasi_lattice1) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( C @ ( B @ join ) @ ( A @ meet ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( C @ ( B @ join ) @ ( A @ meet ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ meet ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= ( C @ ( D @ meet ) ) )
| ( ( A @ ( B @ meet ) )
= ( D @ ( D @ meet ) @ ( C @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,378]) ).
thf(413,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ meet ) @ ( B @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(pattern_uni,[status(thm)],[412:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(8009,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( a @ ( b @ join ) ) )
| ( c != a )
| ( ( A @ ( B @ join ) )
!= c )
| ( ( a @ ( b @ join ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[21,7660]) ).
thf(8010,plain,
( ( c != a )
| ( ( b @ ( a @ join ) )
!= c )
| ( ( a @ ( b @ join ) )
!= b ) ),
inference(pattern_uni,[status(thm)],[8009:[bind(A,$thf( b )),bind(B,$thf( a ))]]) ).
thf(4519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ join ) @ ( A @ join ) )
!= ( D @ ( C @ join ) ) )
| ( ( A @ ( B @ join ) )
= ( C @ ( D @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[4494,21]) ).
thf(4520,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ join ) @ join ) )
= ( A @ ( B @ join ) ) ),
inference(pattern_uni,[status(thm)],[4519:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ ( F @ join ) ))]]) ).
thf(4763,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ join ) @ join ) )
= ( A @ ( B @ join ) ) ),
inference(simp,[status(thm)],[4520]) ).
thf(6525,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ join ) @ ( B @ join ) )
= ( A @ ( B @ join ) ) ),
inference(rewrite,[status(thm)],[4763,25]) ).
thf(34,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( ( c @ ( a @ meet ) @ ( A @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,13]) ).
thf(38,plain,
! [A: $i] :
( ( A != b )
| ( A != a )
| ( ( c @ ( a @ meet ) @ ( A @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(40,plain,
( ( b != a )
| ( ( c @ ( a @ meet ) @ ( a @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ meet ) @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( b != a )
| ( ( C @ ( B @ meet ) @ ( A @ meet ) @ ( a @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,40]) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ( C != c )
| ( ( B @ ( A @ meet ) )
!= a )
| ( b != a )
| ( ( C @ ( B @ meet ) @ ( A @ meet ) @ ( a @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= a )
| ( b != a )
| ( ( c @ ( B @ meet ) @ ( A @ meet ) @ ( a @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(3306,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) ) )
| ( c != b )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[17,3001]) ).
thf(3323,plain,
( ( ( c @ ( a @ meet ) )
!= b )
| ( b != b )
| ( c != b ) ),
inference(simp,[status(thm)],[3306]) ).
thf(3347,plain,
( ( ( c @ ( a @ meet ) )
!= b )
| ( c != b ) ),
inference(simp,[status(thm)],[3323]) ).
thf(3365,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( A != b )
| ( c != b ) ),
inference(paramod_ordered,[status(thm)],[15,3347]) ).
thf(3368,plain,
( ( c != b )
| ( b != a )
| ( c != b ) ),
inference(simp,[status(thm)],[3365]) ).
thf(3380,plain,
( ( b != a )
| ( c != b ) ),
inference(simp,[status(thm)],[3368]) ).
thf(132,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ meet ) @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( ( C @ ( B @ meet ) @ ( A @ meet ) @ ( b @ ( a @ meet ) @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,13]) ).
thf(167,plain,
! [C: $i,B: $i,A: $i] :
( ( C != c )
| ( ( B @ ( A @ meet ) )
!= a )
| ( ( C @ ( B @ meet ) @ ( A @ meet ) @ ( b @ ( a @ meet ) @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= a )
| ( ( c @ ( B @ meet ) @ ( A @ meet ) @ ( b @ ( a @ meet ) @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ join ) @ meet ) @ join ) )
= ( B @ ( A @ ( B @ ( C @ join ) @ meet ) @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modularity_axiom) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ join ) @ meet ) @ join ) )
= ( B @ ( A @ ( B @ ( C @ join ) @ meet ) @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ join ) @ meet ) @ join ) )
= ( B @ ( A @ ( B @ ( C @ join ) @ meet ) @ join ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(72,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) )
| ( b != a )
| ( A
!= ( c @ ( a @ meet ) @ ( a @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,40]) ).
thf(77,plain,
( ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= ( c @ ( a @ meet ) @ ( a @ join ) ) )
| ( ( c @ ( a @ meet ) @ ( a @ join ) )
!= a )
| ( b != a ) ),
inference(simp,[status(thm)],[72]) ).
thf(4258,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( c @ ( a @ meet ) @ ( a @ join ) ) )
| ( ( c @ ( a @ meet ) @ ( b @ join ) )
!= ( c @ ( a @ meet ) @ ( a @ join ) ) )
| ( A != a )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[17,77]) ).
thf(4293,plain,
( ( ( c @ ( a @ meet ) )
!= a )
| ( a != a )
| ( ( c @ ( a @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( b != a )
| ( b != a ) ),
inference(simp,[status(thm)],[4258]) ).
thf(4436,plain,
( ( ( c @ ( a @ meet ) )
!= a )
| ( b != a ) ),
inference(simp,[status(thm)],[4293]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ meet ) @ meet ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) )
| ( b != a )
| ( ( C @ ( B @ meet ) @ ( A @ meet ) )
!= ( c @ ( a @ meet ) @ ( a @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,40]) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( c @ ( a @ meet ) @ ( b @ join ) ) )
| ( ( B @ ( A @ meet ) )
!= a )
| ( b != a )
| ( ( C @ ( B @ meet ) @ ( A @ meet ) )
!= ( c @ ( a @ meet ) @ ( a @ join ) ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= a )
| ( b != a )
| ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( B @ meet ) @ ( A @ meet ) )
!= ( c @ ( a @ meet ) @ ( a @ join ) ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ meet ) @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( b != a )
| ( ( C @ ( B @ meet ) @ ( A @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) @ ( a @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,40]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ( C != c )
| ( ( B @ ( A @ meet ) )
!= a )
| ( b != a )
| ( ( C @ ( B @ meet ) @ ( A @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) @ ( a @ join ) ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= a )
| ( b != a )
| ( ( c @ ( B @ meet ) @ ( A @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) @ ( a @ join ) ) ) ),
inference(simp,[status(thm)],[161]) ).
thf(3644,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( a @ ( b @ join ) ) )
| ( c != a )
| ( c != b )
| ( ( A @ ( B @ join ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[21,3342]) ).
thf(3645,plain,
( ( c != a )
| ( c != b )
| ( ( b @ ( a @ join ) )
!= b ) ),
inference(pattern_uni,[status(thm)],[3644:[bind(A,$thf( b )),bind(B,$thf( a ))]]) ).
thf(63,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) ) )
| ( b != a )
| ( ( A @ ( a @ meet ) )
!= ( c @ ( a @ meet ) @ ( a @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,40]) ).
thf(75,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ meet ) ) )
| ( A != b )
| ( b != a )
| ( ( A @ ( a @ meet ) )
!= ( c @ ( a @ meet ) @ ( a @ join ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(82,plain,
( ( ( c @ ( a @ meet ) )
!= b )
| ( b != a )
| ( ( c @ ( a @ meet ) @ ( a @ join ) )
!= ( b @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(62,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( c @ ( a @ meet ) @ ( a @ join ) ) )
| ( b != a )
| ( A
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,40]) ).
thf(79,plain,
( ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= a )
| ( b != a ) ),
inference(simp,[status(thm)],[62]) ).
thf(4233,plain,
( ( ( c @ ( a @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( b != a )
| ( ( c @ ( a @ meet ) @ ( a @ join ) )
!= a )
| ( b != a ) ),
inference(simp,[status(thm)],[77]) ).
thf(4427,plain,
( ( ( c @ ( a @ meet ) @ ( a @ join ) )
!= a )
| ( b != a ) ),
inference(simp,[status(thm)],[4233]) ).
thf(57,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( c != a )
| ( ( a @ ( A @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,39]) ).
thf(60,plain,
! [A: $i] :
( ( A != b )
| ( A != a )
| ( c != a )
| ( ( a @ ( A @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(61,plain,
( ( b != a )
| ( c != a )
| ( ( a @ ( a @ join ) )
!= ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(102,plain,
( ( b != a )
| ( c != a )
| ( ( c @ ( a @ meet ) @ ( b @ join ) @ ( a @ meet ) )
!= a ) ),
inference(rewrite,[status(thm)],[61,17]) ).
thf(110,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( c @ ( a @ meet ) ) )
| ( b != a )
| ( c != a )
| ( ( A @ ( b @ join ) @ ( a @ meet ) )
!= a ) ),
inference(paramod_ordered,[status(thm)],[15,102]) ).
thf(113,plain,
! [A: $i] :
( ( A != c )
| ( A != a )
| ( b != a )
| ( c != a )
| ( ( A @ ( b @ join ) @ ( a @ meet ) )
!= a ) ),
inference(simp,[status(thm)],[110]) ).
thf(117,plain,
( ( b != a )
| ( c != a )
| ( ( a @ ( b @ join ) @ ( a @ meet ) )
!= a ) ),
inference(simp,[status(thm)],[113]) ).
thf(126,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( a @ ( b @ join ) @ ( a @ meet ) ) )
| ( b != a )
| ( c != a )
| ( A != a ) ),
inference(paramod_ordered,[status(thm)],[15,117]) ).
thf(129,plain,
( ( ( a @ ( b @ join ) )
!= a )
| ( a != a )
| ( b != a )
| ( c != a ) ),
inference(simp,[status(thm)],[126]) ).
thf(130,plain,
( ( ( a @ ( b @ join ) )
!= a )
| ( b != a )
| ( c != a ) ),
inference(simp,[status(thm)],[129]) ).
thf(329,plain,
! [A: $i] :
( ( ( A @ ( A @ join ) )
!= ( a @ ( b @ join ) ) )
| ( A != a )
| ( b != a )
| ( c != a ) ),
inference(paramod_ordered,[status(thm)],[17,130]) ).
thf(331,plain,
( ( a != a )
| ( b != a )
| ( b != a )
| ( c != a ) ),
inference(simp,[status(thm)],[329]) ).
thf(332,plain,
( ( b != a )
| ( c != a ) ),
inference(simp,[status(thm)],[331]) ).
thf(52937,plain,
$false,
inference(e,[status(thm)],[4532,5663,18,10332,4899,7660,25,24,5195,14,4524,3342,4766,20,29,2011,3169,28,4204,21,484,879,2181,8462,3001,9186,8008,173,13,10465,2963,513,7128,17,59,8092,27,413,22,4494,1997,8010,6525,172,39,2999,3380,177,16,31,4436,11,175,40,26,171,23,2956,378,3645,82,36,30,405,19,3347,79,4427,94,332,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT023-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.11 % 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
% 0.22/0.49 % Computer : n001.cluster.edu
% 0.22/0.49 % Model : x86_64 x86_64
% 0.22/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.49 % Memory : 8046.5625MB
% 0.22/0.49 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Fri Sep 25 20:03:27 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 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
% 1.42/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.93/1.62 % [INFO] Parsing done (275ms).
% 1.93/1.64 % [INFO] Running in sequential loop mode.
% 3.11/2.22 % [INFO] eprover registered as external prover.
% 3.11/2.23 % [INFO] Scanning for conjecture ...
% 3.28/2.36 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 3.44/2.40 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 3.44/2.42 % [INFO] Problem is propositional (TPTP CNF).
% 3.44/2.42 % [INFO] Type checking passed.
% 3.44/2.43 % [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 ...
% 98.37/24.45 % External prover 'e' found a proof!
% 98.37/24.45 % [INFO] Killing All external provers ...
% 98.37/24.45 % Time passed: 23752ms (effective reasoning time: 22799ms)
% 98.37/24.45 % Axioms used in derivation (9): quasi_lattice1, commutativity_of_join, associativity_of_meet, quasi_lattice2, commutativity_of_meet, associativity_of_join, idempotence_of_meet, idempotence_of_join, modularity_axiom
% 98.37/24.45 % No. of inferences in proof: 202
% 98.37/24.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 23752 ms resp. 22799 ms w/o parsing
% 92.76/24.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 92.76/24.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------