TSTP Solution File: LAT005-10 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT005-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 11:26:38 EDT 2023
% Result : Unsatisfiable 69.73s 12.28s
% Output : Refutation 69.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 35
% Syntax : Number of formulae : 117 ( 70 unt; 13 typ; 0 def)
% Number of atoms : 167 ( 166 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 632 ( 95 ~; 63 |; 0 &; 474 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 138 ( 0 ^; 138 !; 0 ?; 138 :)
% Comments :
%------------------------------------------------------------------------------
thf(r1_type,type,
r1: $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(join_type,type,
join: $i > $i > $i ).
thf(r2_type,type,
r2: $i ).
thf(b_type,type,
b: $i ).
thf(a_type,type,
a: $i ).
thf(ifeq_type,type,
ifeq: $i > $i > $i > $i > $i ).
thf(ifeq2_type,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(ifeq3_type,type,
ifeq3: $i > $i > $i > $i > $i ).
thf(n1_type,type,
n1: $i ).
thf(n0_type,type,
n0: $i ).
thf(complement_type,type,
complement: $i > $i > $i ).
thf(true_type,type,
true: $i ).
thf(17,axiom,
! [A: $i] :
( ( join @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(56,plain,
! [A: $i] :
( ( join @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq3 @ ( meet @ A @ B ) @ A @ ( meet @ B @ ( join @ A @ C ) ) @ ( join @ A @ ( meet @ C @ B ) ) )
= ( join @ A @ ( meet @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq3 @ ( meet @ A @ B ) @ A @ ( meet @ B @ ( join @ A @ C ) ) @ ( join @ A @ ( meet @ C @ B ) ) )
= ( join @ A @ ( meet @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [A: $i] :
( ( join @ A @ n0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_0) ).
thf(60,plain,
! [A: $i] :
( ( join @ A @ n0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(61,plain,
! [A: $i] :
( ( join @ A @ n0 )
= A ),
inference(lifteq,[status(thm)],[60]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(8,axiom,
! [A: $i] :
( ( join @ A @ n1 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_1) ).
thf(38,plain,
! [A: $i] :
( ( join @ A @ n1 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(39,plain,
! [A: $i] :
( ( join @ A @ n1 )
= n1 ),
inference(lifteq,[status(thm)],[38]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[34]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( ifeq2 @ ( join @ A @ B ) @ n1 @ ( ifeq2 @ ( meet @ A @ B ) @ n0 @ ( complement @ A @ B ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_join_complement) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( ifeq2 @ ( join @ A @ B ) @ n1 @ ( ifeq2 @ ( meet @ A @ B ) @ n0 @ ( complement @ A @ B ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( ifeq2 @ ( join @ A @ B ) @ n1 @ ( ifeq2 @ ( meet @ A @ B ) @ n0 @ ( complement @ A @ B ) @ true ) @ true )
= true ),
inference(lifteq,[status(thm)],[42]) ).
thf(13,axiom,
! [A: $i] :
( ( meet @ A @ n0 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_0) ).
thf(48,plain,
! [A: $i] :
( ( meet @ A @ n0 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(49,plain,
! [A: $i] :
( ( meet @ A @ n0 )
= n0 ),
inference(lifteq,[status(thm)],[48]) ).
thf(1,negated_conjecture,
( r1
!= ( meet @ ( join @ r1 @ ( meet @ r2 @ b ) ) @ ( join @ r1 @ ( meet @ r2 @ a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lemma) ).
thf(23,plain,
( r1
!= ( meet @ ( join @ r1 @ ( meet @ r2 @ b ) ) @ ( join @ r1 @ ( meet @ r2 @ a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(24,plain,
( r1
!= ( meet @ ( join @ r1 @ ( meet @ r2 @ b ) ) @ ( join @ r1 @ ( meet @ r2 @ a ) ) ) ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
( ( meet @ ( join @ r1 @ ( meet @ r2 @ b ) ) @ ( join @ r1 @ ( meet @ r2 @ a ) ) )
!= r1 ),
inference(lifteq,[status(thm)],[24]) ).
thf(77,plain,
! [A: $i] :
( ( n0 != r1 )
| ( ( meet @ A @ n0 )
!= ( meet @ ( join @ r1 @ ( meet @ r2 @ b ) ) @ ( join @ r1 @ ( meet @ r2 @ a ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,25]) ).
thf(82,plain,
! [A: $i] :
( ( n0 != r1 )
| ( A
!= ( join @ r1 @ ( meet @ r2 @ b ) ) )
| ( ( join @ r1 @ ( meet @ r2 @ a ) )
!= n0 ) ),
inference(simp,[status(thm)],[77]) ).
thf(87,plain,
( ( n0 != r1 )
| ( ( join @ r1 @ ( meet @ r2 @ a ) )
!= n0 ) ),
inference(simp,[status(thm)],[82]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(91,plain,
! [A: $i] :
( ( n0 != r1 )
| ( ( join @ r1 @ n0 )
!= n0 )
| ( ( meet @ A @ n0 )
!= ( meet @ r2 @ a ) ) ),
inference(paramod_ordered,[status(thm)],[49,87]) ).
thf(93,plain,
! [A: $i] :
( ( n0 != r1 )
| ( ( join @ r1 @ n0 )
!= n0 )
| ( A != r2 )
| ( n0 != a ) ),
inference(simp,[status(thm)],[91]) ).
thf(95,plain,
( ( n0 != r1 )
| ( ( join @ r1 @ n0 )
!= n0 )
| ( n0 != a ) ),
inference(simp,[status(thm)],[93]) ).
thf(121,plain,
( ( n0 != r1 )
| ( n0 != r1 )
| ( n0 != a ) ),
inference(rewrite,[status(thm)],[95,61]) ).
thf(122,plain,
( ( n0 != r1 )
| ( n0 != a ) ),
inference(simp,[status(thm)],[121]) ).
thf(7,axiom,
! [A: $i] :
( ( meet @ A @ n1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_1) ).
thf(36,plain,
! [A: $i] :
( ( meet @ A @ n1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,plain,
! [A: $i] :
( ( meet @ A @ n1 )
= A ),
inference(lifteq,[status(thm)],[36]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( complement @ A @ B ) @ true @ ( join @ A @ B ) @ n1 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_join) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( complement @ A @ B ) @ true @ ( join @ A @ B ) @ n1 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(57,plain,
! [A: $i] :
( ( join @ A @ A )
= A ),
inference(lifteq,[status(thm)],[56]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
inference(lifteq,[status(thm)],[28]) ).
thf(100,plain,
! [A: $i] :
( ( n0 != r1 )
| ( ( join @ r1 @ A )
!= n0 )
| ( ( meet @ A @ n1 )
!= ( meet @ r2 @ a ) ) ),
inference(paramod_ordered,[status(thm)],[37,87]) ).
thf(111,plain,
! [A: $i] :
( ( n0 != r1 )
| ( ( join @ r1 @ A )
!= n0 )
| ( A != r2 )
| ( n1 != a ) ),
inference(simp,[status(thm)],[100]) ).
thf(117,plain,
( ( n0 != r1 )
| ( ( join @ r1 @ r2 )
!= n0 )
| ( n1 != a ) ),
inference(simp,[status(thm)],[111]) ).
thf(14,axiom,
( ( complement @ r1 @ ( join @ a @ b ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_join_b) ).
thf(50,plain,
( ( complement @ r1 @ ( join @ a @ b ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(51,plain,
( ( complement @ r1 @ ( join @ a @ b ) )
= true ),
inference(lifteq,[status(thm)],[50]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( ( complement @ r1 @ ( join @ B @ A ) )
= true )
| ( ( join @ A @ B )
!= ( join @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[41,51]) ).
thf(260,plain,
( ( complement @ r1 @ ( join @ b @ a ) )
= true ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(20,axiom,
( ( complement @ r2 @ ( meet @ a @ b ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_meet_b) ).
thf(62,plain,
( ( complement @ r2 @ ( meet @ a @ b ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(63,plain,
( ( complement @ r2 @ ( meet @ a @ b ) )
= true ),
inference(lifteq,[status(thm)],[62]) ).
thf(629,plain,
! [B: $i,A: $i] :
( ( ( complement @ r2 @ ( meet @ B @ A ) )
= true )
| ( ( meet @ A @ B )
!= ( meet @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[59,63]) ).
thf(630,plain,
( ( complement @ r2 @ ( meet @ b @ a ) )
= true ),
inference(pattern_uni,[status(thm)],[629:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(5,axiom,
! [A: $i] :
( ( meet @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(32,plain,
! [A: $i] :
( ( meet @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,plain,
! [A: $i] :
( ( meet @ A @ A )
= A ),
inference(lifteq,[status(thm)],[32]) ).
thf(641,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ B @ A )
= C )
| ( ( meet @ A @ B )
!= ( meet @ C @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[59,37]) ).
thf(642,plain,
! [A: $i] :
( ( meet @ n1 @ A )
= A ),
inference(pattern_uni,[status(thm)],[641:[bind(A,$thf( A )),bind(B,$thf( n1 )),bind(C,$thf( A ))]]) ).
thf(92,plain,
! [A: $i] :
( ( n0 != r1 )
| ( n0 != n1 )
| ( ( join @ A @ n1 )
!= ( join @ r1 @ ( meet @ r2 @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,87]) ).
thf(94,plain,
! [A: $i] :
( ( n0 != r1 )
| ( n0 != n1 )
| ( A != r1 )
| ( ( meet @ r2 @ a )
!= n1 ) ),
inference(simp,[status(thm)],[92]) ).
thf(96,plain,
( ( n0 != r1 )
| ( n0 != n1 )
| ( ( meet @ r2 @ a )
!= n1 ) ),
inference(simp,[status(thm)],[94]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ B @ A )
= n1 )
| ( ( join @ A @ B )
!= ( join @ C @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[41,39]) ).
thf(244,plain,
! [A: $i] :
( ( join @ n1 @ A )
= n1 ),
inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( A )),bind(B,$thf( n1 )),bind(C,$thf( A ))]]) ).
thf(329,plain,
! [A: $i] :
( ( n0 != r1 )
| ( n0 != n1 )
| ( ( join @ n1 @ A )
!= ( join @ r1 @ ( meet @ r2 @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[244,87]) ).
thf(338,plain,
! [A: $i] :
( ( n0 != r1 )
| ( n0 != n1 )
| ( n1 != r1 )
| ( A
!= ( meet @ r2 @ a ) ) ),
inference(simp,[status(thm)],[329]) ).
thf(343,plain,
( ( n0 != r1 )
| ( n0 != n1 )
| ( n1 != r1 ) ),
inference(simp,[status(thm)],[338]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[44]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( complement @ A @ B ) @ true @ ( meet @ A @ B ) @ n0 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_meet) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( complement @ A @ B ) @ true @ ( meet @ A @ B ) @ n0 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ B @ A )
= C )
| ( ( join @ A @ B )
!= ( join @ C @ n0 ) ) ),
inference(paramod_ordered,[status(thm)],[41,61]) ).
thf(236,plain,
! [A: $i] :
( ( join @ n0 @ A )
= A ),
inference(pattern_uni,[status(thm)],[235:[bind(A,$thf( A )),bind(B,$thf( n0 )),bind(C,$thf( A ))]]) ).
thf(371,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( join @ n0 @ A )
!= ( join @ B @ ( meet @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[236,35]) ).
thf(372,plain,
! [A: $i] :
( ( meet @ n0 @ A )
= n0 ),
inference(pattern_uni,[status(thm)],[371:[bind(A,$thf( meet @ n0 @ E )),bind(B,$thf( n0 )),bind(C,$thf( E ))]]) ).
thf(402,plain,
! [A: $i] :
( ( meet @ n0 @ A )
= n0 ),
inference(simp,[status(thm)],[372]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(lifteq,[status(thm)],[26]) ).
thf(16,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(54,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)],[16]) ).
thf(125,plain,
! [A: $i] :
( ( n0 != r1 )
| ( A != n0 )
| ( ( join @ A @ n0 )
!= ( join @ r1 @ ( meet @ r2 @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,87]) ).
thf(130,plain,
( ( n0 != r1 )
| ( n0 != r1 )
| ( ( meet @ r2 @ a )
!= n0 ) ),
inference(simp,[status(thm)],[125]) ).
thf(136,plain,
( ( n0 != r1 )
| ( ( meet @ r2 @ a )
!= n0 ) ),
inference(simp,[status(thm)],[130]) ).
thf(459,plain,
! [A: $i] :
( ( n0 != r1 )
| ( ( meet @ n0 @ A )
!= ( meet @ r2 @ a ) ) ),
inference(paramod_ordered,[status(thm)],[402,136]) ).
thf(481,plain,
! [A: $i] :
( ( n0 != r1 )
| ( n0 != r2 )
| ( A != a ) ),
inference(simp,[status(thm)],[459]) ).
thf(483,plain,
( ( n0 != r1 )
| ( n0 != r2 ) ),
inference(simp,[status(thm)],[481]) ).
thf(22,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(66,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)],[22]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq3 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq3 @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq3 @ A @ A @ B @ C )
= B ),
inference(lifteq,[status(thm)],[30]) ).
thf(301,plain,
! [A: $i] :
( ( n0 != r1 )
| ( n0 != n1 )
| ( A != n1 )
| ( ( meet @ A @ n1 )
!= ( meet @ r2 @ a ) ) ),
inference(paramod_ordered,[status(thm)],[37,96]) ).
thf(305,plain,
( ( n0 != r1 )
| ( n0 != n1 )
| ( n1 != r2 )
| ( n1 != a ) ),
inference(simp,[status(thm)],[301]) ).
thf(147,plain,
! [A: $i] :
( ( n0 != r1 )
| ( ( join @ r1 @ A )
!= n0 )
| ( ( meet @ A @ A )
!= ( meet @ r2 @ a ) ) ),
inference(paramod_ordered,[status(thm)],[33,87]) ).
thf(158,plain,
! [A: $i] :
( ( n0 != r1 )
| ( ( join @ r1 @ A )
!= n0 )
| ( A != r2 )
| ( A != a ) ),
inference(simp,[status(thm)],[147]) ).
thf(163,plain,
( ( n0 != r1 )
| ( ( join @ r1 @ r2 )
!= n0 )
| ( a != r2 ) ),
inference(simp,[status(thm)],[158]) ).
thf(41316,plain,
$false,
inference(cvc4,[status(thm)],[56,52,61,41,39,35,43,87,58,122,42,37,25,46,57,29,60,117,260,630,33,28,38,642,96,343,244,45,64,32,34,402,44,59,27,54,49,236,483,66,48,63,50,31,40,26,23,36,30,51,305,136,163,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT005-10 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n028.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 14:18:19 EDT 2023
% 0.16/0.37 % CPUTime :
% 1.07/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/1.06 % [INFO] Parsing done (136ms).
% 1.31/1.07 % [INFO] Running in sequential loop mode.
% 1.70/1.27 % [INFO] eprover registered as external prover.
% 1.70/1.27 % [INFO] cvc4 registered as external prover.
% 1.70/1.28 % [INFO] Scanning for conjecture ...
% 1.92/1.33 % [INFO] Found a conjecture and 21 axioms. Running axiom selection ...
% 2.08/1.37 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 2.08/1.39 % [INFO] Problem is propositional (TPTP CNF).
% 2.08/1.40 % [INFO] Type checking passed.
% 2.08/1.40 % [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 ...
% 69.73/12.28 % External prover 'cvc4' found a proof!
% 69.73/12.28 % [INFO] Killing All external provers ...
% 69.73/12.28 % Time passed: 11756ms (effective reasoning time: 11206ms)
% 69.73/12.28 % 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)>
% 69.73/12.28 % Axioms used in derivation (21): ifeq_axiom_001, meet_join_complement, commutativity_of_meet, x_join_0, x_meet_1, associativity_of_join, idempotence_of_meet, x_meet_0, complement_of_a_meet_b, ifeq_axiom_002, ifeq_axiom, commutativity_of_join, absorption1, x_join_1, modular, associativity_of_meet, complement_join, complement_meet, complement_of_a_join_b, idempotence_of_join, absorption2
% 69.73/12.28 % No. of inferences in proof: 104
% 69.73/12.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11756 ms resp. 11206 ms w/o parsing
% 69.73/12.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 69.73/12.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------