TSTP Solution File: LAT145-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT145-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:26:53 EDT 2023
% Result : Unsatisfiable 60.90s 10.77s
% Output : Refutation 60.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 96 ( 47 unt; 5 typ; 0 def)
% Number of atoms : 160 ( 159 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 918 ( 109 ~; 69 |; 0 &; 740 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 165 ( 0 ^; 165 !; 0 ?; 165 :)
% Comments :
%------------------------------------------------------------------------------
thf(meet_type,type,
meet: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(join_type,type,
join: $i > $i > $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(2,axiom,
! [A: $i] :
( ( meet @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(14,plain,
! [A: $i] :
( ( meet @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[18]) ).
thf(328,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( meet @ C @ ( join @ B @ A ) )
= C )
| ( ( join @ A @ B )
!= ( join @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[25,19]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[328:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( join @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(16,plain,
! [A: $i] :
( ( join @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [A: $i] :
( ( join @ A @ A )
= A ),
inference(lifteq,[status(thm)],[16]) ).
thf(15,plain,
! [A: $i] :
( ( meet @ A @ A )
= A ),
inference(lifteq,[status(thm)],[14]) ).
thf(1,negated_conjecture,
( ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) )
!= ( meet @ a @ ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ c @ ( join @ a @ b ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_H6) ).
thf(11,plain,
( ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) )
!= ( meet @ a @ ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ c @ ( join @ a @ b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) )
!= ( meet @ a @ ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ c @ ( join @ a @ b ) ) ) ) ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( meet @ a @ ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ c @ ( join @ a @ b ) ) ) )
!= ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(60,plain,
! [A: $i] :
( ( ( meet @ a @ ( join @ ( meet @ a @ A ) @ ( meet @ c @ ( join @ a @ b ) ) ) )
!= ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) )
| ( ( join @ A @ A )
!= ( join @ b @ ( meet @ a @ c ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,13]) ).
thf(80,plain,
! [A: $i] :
( ( a != a )
| ( ( join @ ( meet @ a @ A ) @ ( meet @ c @ ( join @ a @ b ) ) )
!= ( join @ b @ ( meet @ a @ c ) ) )
| ( A != b )
| ( A
!= ( meet @ a @ c ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(120,plain,
( ( ( join @ ( meet @ a @ b ) @ ( meet @ c @ ( join @ a @ b ) ) )
!= ( join @ b @ ( meet @ a @ c ) ) )
| ( ( meet @ a @ c )
!= b ) ),
inference(simp,[status(thm)],[80]) ).
thf(157,plain,
! [A: $i] :
( ( ( join @ A @ ( meet @ c @ ( join @ a @ b ) ) )
!= ( join @ b @ ( meet @ a @ c ) ) )
| ( ( meet @ a @ c )
!= b )
| ( ( meet @ A @ A )
!= ( meet @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[15,120]) ).
thf(164,plain,
! [A: $i] :
( ( A != b )
| ( ( meet @ c @ ( join @ a @ b ) )
!= ( meet @ a @ c ) )
| ( ( meet @ a @ c )
!= b )
| ( A != a )
| ( A != b ) ),
inference(simp,[status(thm)],[157]) ).
thf(194,plain,
( ( ( meet @ c @ ( join @ a @ b ) )
!= ( meet @ a @ c ) )
| ( ( meet @ a @ c )
!= b )
| ( b != a ) ),
inference(simp,[status(thm)],[164]) ).
thf(248,plain,
! [A: $i] :
( ( ( meet @ c @ A )
!= ( meet @ a @ c ) )
| ( ( meet @ a @ c )
!= b )
| ( b != a )
| ( ( join @ A @ A )
!= ( join @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[17,194]) ).
thf(263,plain,
! [A: $i] :
( ( ( meet @ c @ A )
!= ( meet @ a @ c ) )
| ( ( meet @ a @ c )
!= b )
| ( b != a )
| ( A != a )
| ( A != b ) ),
inference(simp,[status(thm)],[248]) ).
thf(281,plain,
( ( ( meet @ c @ a )
!= ( meet @ a @ c ) )
| ( ( meet @ a @ c )
!= b )
| ( b != a ) ),
inference(simp,[status(thm)],[263]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(989,plain,
( ( ( meet @ a @ c )
!= b )
| ( b != a ) ),
inference(simplifyReflect,[status(thm)],[281,23]) ).
thf(68,plain,
! [A: $i] :
( ( A
!= ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) )
| ( ( meet @ A @ A )
!= ( meet @ a @ ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ c @ ( join @ a @ b ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,13]) ).
thf(105,plain,
( ( ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) )
!= a )
| ( ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ c @ ( join @ a @ b ) ) )
!= ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[20]) ).
thf(217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( join @ C @ ( meet @ B @ A ) )
= C )
| ( ( meet @ A @ B )
!= ( meet @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23,21]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ B @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[217:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( ( meet @ a @ ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ c @ A ) ) )
!= ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) )
| ( ( join @ A @ ( meet @ A @ B ) )
!= ( join @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[21,13]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( a != a )
| ( ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ c @ A ) )
!= ( join @ b @ ( meet @ a @ c ) ) )
| ( ( join @ A @ ( meet @ A @ B ) )
!= ( join @ a @ b ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ c @ A ) )
!= ( join @ b @ ( meet @ a @ c ) ) )
| ( ( join @ A @ ( meet @ A @ B ) )
!= ( join @ a @ b ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(2714,plain,
! [A: $i] :
( ( ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ c @ A ) )
!= ( join @ b @ ( meet @ a @ c ) ) )
| ( A
!= ( join @ a @ b ) ) ),
inference(rewrite,[status(thm)],[109,21]) ).
thf(995,plain,
! [B: $i,A: $i] :
( ( A != b )
| ( b != a )
| ( ( meet @ A @ ( join @ A @ B ) )
!= ( meet @ a @ c ) ) ),
inference(paramod_ordered,[status(thm)],[19,989]) ).
thf(1000,plain,
! [A: $i] :
( ( b != a )
| ( b != a )
| ( ( join @ b @ A )
!= c ) ),
inference(simp,[status(thm)],[995]) ).
thf(1009,plain,
! [A: $i] :
( ( b != a )
| ( ( join @ b @ A )
!= c ) ),
inference(simp,[status(thm)],[1000]) ).
thf(991,plain,
! [B: $i,A: $i] :
( ( A != b )
| ( b != a )
| ( ( meet @ A @ ( join @ B @ A ) )
!= ( meet @ a @ c ) ) ),
inference(paramod_ordered,[status(thm)],[329,989]) ).
thf(998,plain,
! [A: $i] :
( ( b != a )
| ( b != a )
| ( ( join @ A @ b )
!= c ) ),
inference(simp,[status(thm)],[991]) ).
thf(1007,plain,
! [A: $i] :
( ( b != a )
| ( ( join @ A @ b )
!= c ) ),
inference(simp,[status(thm)],[998]) ).
thf(1386,plain,
! [C: $i,B: $i,A: $i] :
( ( b != a )
| ( A != c )
| ( ( join @ A @ ( meet @ A @ B ) )
!= ( join @ C @ b ) ) ),
inference(paramod_ordered,[status(thm)],[21,1007]) ).
thf(1397,plain,
! [B: $i,A: $i] :
( ( b != a )
| ( c != B )
| ( ( meet @ c @ A )
!= b ) ),
inference(simp,[status(thm)],[1386]) ).
thf(1401,plain,
! [A: $i] :
( ( b != a )
| ( ( meet @ c @ A )
!= b ) ),
inference(simp,[status(thm)],[1397]) ).
thf(231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( meet @ D @ C ) )
| ( ( meet @ A @ ( join @ A @ B ) )
!= ( meet @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[19,23]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ( meet @ ( join @ A @ B ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( join @ E @ F ))]]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ( meet @ ( join @ A @ B ) @ A )
= A ),
inference(simp,[status(thm)],[232]) ).
thf(409,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( meet @ ( join @ B @ A ) @ C )
= C )
| ( ( join @ A @ B )
!= ( join @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[25,243]) ).
thf(410,plain,
! [B: $i,A: $i] :
( ( meet @ ( join @ B @ A ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[409:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( meet @ ( join @ B @ A ) @ C )
= C )
| ( ( join @ A @ B )
!= ( join @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25,410]) ).
thf(1127,plain,
! [B: $i,A: $i] :
( ( meet @ ( join @ B @ A ) @ B )
= B ),
inference(pattern_uni,[status(thm)],[1126:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(996,plain,
! [A: $i] :
( ( A != b )
| ( b != a )
| ( ( meet @ A @ A )
!= ( meet @ a @ c ) ) ),
inference(paramod_ordered,[status(thm)],[15,989]) ).
thf(1005,plain,
( ( b != a )
| ( b != a )
| ( c != b ) ),
inference(simp,[status(thm)],[996]) ).
thf(1013,plain,
( ( b != a )
| ( c != b ) ),
inference(simp,[status(thm)],[1005]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(54,plain,
( ( a != a )
| ( ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ c @ ( join @ a @ b ) ) )
!= ( join @ b @ ( meet @ a @ c ) ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(147,plain,
( ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ c @ ( join @ a @ b ) ) )
!= ( join @ b @ ( meet @ a @ c ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(2742,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ B @ A ) )
!= ( join @ b @ ( meet @ a @ c ) ) )
| ( C
!= ( join @ a @ b ) )
| ( ( meet @ A @ B )
!= ( meet @ c @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,2714]) ).
thf(2743,plain,
! [A: $i] :
( ( ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ A @ c ) )
!= ( join @ b @ ( meet @ a @ c ) ) )
| ( A
!= ( join @ a @ b ) ) ),
inference(pattern_uni,[status(thm)],[2742:[bind(A,$thf( c )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2986,plain,
( ( join @ ( meet @ a @ ( join @ b @ ( meet @ a @ c ) ) ) @ ( meet @ ( join @ a @ b ) @ c ) )
!= ( join @ b @ ( meet @ a @ c ) ) ),
inference(simp,[status(thm)],[2743]) ).
thf(411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( meet @ ( join @ A @ B ) @ C )
= C )
| ( ( join @ B @ A )
!= ( join @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[25,243]) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( meet @ ( join @ A @ B ) @ B )
= B ),
inference(pattern_uni,[status(thm)],[411:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(1389,plain,
! [C: $i,B: $i,A: $i] :
( ( b != a )
| ( A != c )
| ( ( join @ A @ ( meet @ B @ A ) )
!= ( join @ C @ b ) ) ),
inference(paramod_ordered,[status(thm)],[218,1007]) ).
thf(1399,plain,
! [B: $i,A: $i] :
( ( b != a )
| ( c != B )
| ( ( meet @ A @ c )
!= b ) ),
inference(simp,[status(thm)],[1389]) ).
thf(1403,plain,
! [A: $i] :
( ( b != a )
| ( ( meet @ A @ c )
!= b ) ),
inference(simp,[status(thm)],[1399]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( meet @ A @ B ) @ C )
= ( meet @ A @ ( meet @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( meet @ A @ B ) @ C )
= ( meet @ A @ ( meet @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( meet @ A @ B ) @ C )
= ( meet @ A @ ( meet @ B @ C ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( join @ D @ C ) )
| ( ( join @ A @ ( meet @ B @ A ) )
!= ( join @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[218,25]) ).
thf(338,plain,
! [B: $i,A: $i] :
( ( join @ ( meet @ A @ B ) @ B )
= B ),
inference(pattern_uni,[status(thm)],[337:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( meet @ E @ F ))]]) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( join @ ( meet @ A @ B ) @ B )
= B ),
inference(simp,[status(thm)],[338]) ).
thf(918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( join @ ( meet @ B @ A ) @ D )
= D )
| ( ( meet @ A @ B )
!= ( meet @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23,382]) ).
thf(919,plain,
! [B: $i,A: $i] :
( ( join @ ( meet @ B @ A ) @ B )
= B ),
inference(pattern_uni,[status(thm)],[918:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( join @ D @ C ) )
| ( ( join @ A @ ( meet @ A @ B ) )
!= ( join @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[21,25]) ).
thf(307,plain,
! [B: $i,A: $i] :
( ( join @ ( meet @ A @ B ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[306:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( meet @ E @ F ))]]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( join @ ( meet @ A @ B ) @ A )
= A ),
inference(simp,[status(thm)],[307]) ).
thf(775,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( join @ ( meet @ B @ A ) @ C )
= C )
| ( ( meet @ A @ B )
!= ( meet @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23,332]) ).
thf(776,plain,
! [B: $i,A: $i] :
( ( join @ ( meet @ B @ A ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[775:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ ( meet @ A @ ( meet @ C @ D ) ) ) )
= ( meet @ A @ ( join @ B @ ( meet @ C @ ( join @ ( meet @ A @ D ) @ ( meet @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H32) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ ( meet @ A @ ( meet @ C @ D ) ) ) )
= ( meet @ A @ ( join @ B @ ( meet @ C @ ( join @ ( meet @ A @ D ) @ ( meet @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ ( meet @ A @ ( meet @ C @ D ) ) ) )
= ( meet @ A @ ( join @ B @ ( meet @ C @ ( join @ ( meet @ A @ D ) @ ( meet @ B @ D ) ) ) ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(30011,plain,
$false,
inference(cvc4,[status(thm)],[14,329,989,13,105,11,218,2714,1009,1401,120,1127,24,25,20,1013,29,147,243,28,21,2986,412,17,1007,22,1403,27,382,919,776,18,16,31,26,23,410,30,19,332,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT145-1 : TPTP v8.1.2. Released v3.1.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n026.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 14:14:21 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.96/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.97 % [INFO] Parsing done (111ms).
% 1.22/0.98 % [INFO] Running in sequential loop mode.
% 1.66/1.18 % [INFO] eprover registered as external prover.
% 1.66/1.18 % [INFO] cvc4 registered as external prover.
% 1.66/1.18 % [INFO] Scanning for conjecture ...
% 1.83/1.24 % [INFO] Found a conjecture and 9 axioms. Running axiom selection ...
% 1.83/1.26 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.83/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.83/1.27 % [INFO] Type checking passed.
% 1.83/1.28 % [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 ...
% 60.90/10.77 % External prover 'cvc4' found a proof!
% 60.90/10.77 % [INFO] Killing All external provers ...
% 60.90/10.77 % Time passed: 10240ms (effective reasoning time: 9788ms)
% 60.90/10.77 % Solved by 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)>
% 60.90/10.77 % Axioms used in derivation (9): absorption1, associativity_of_meet, commutativity_of_meet, associativity_of_join, idempotence_of_meet, equation_H32, commutativity_of_join, idempotence_of_join, absorption2
% 60.90/10.77 % No. of inferences in proof: 91
% 60.90/10.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10240 ms resp. 9788 ms w/o parsing
% 60.90/10.81 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 60.90/10.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------