%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT005-10 : TPTP v9.3.1. Released v7.5.0.
% 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 : n016.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 07:46:27 AM UTC 2026
% Result : Unsatisfiable 92.39s 22.95s
% Output : Refutation 92.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 191 ( 97 unt; 0 typ; 0 def)
% Number of atoms : 352 ( 351 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1396 ( 237 ~; 161 |; 0 &; 998 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 209 ( 0 ^; 209 !; 0 ?; 209 :)
% Comments :
%------------------------------------------------------------------------------
thf(r1_decl,type,
r1: $i ).
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(join_decl,type,
join: $i > $i > $i ).
thf(r2_decl,type,
r2: $i ).
thf(b_decl,type,
b: $i ).
thf(a_decl,type,
a: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(ifeq2_decl,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(ifeq3_decl,type,
ifeq3: $i > $i > $i > $i > $i ).
thf(n1_decl,type,
n1: $i ).
thf(n0_decl,type,
n0: $i ).
thf(complement_decl,type,
complement: $i > $i > $i ).
thf(true_decl,type,
true: $i ).
thf(8,axiom,
! [A: $i] :
( ( n1 @ ( A @ join ) )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_join_1) ).
thf(38,plain,
! [A: $i] :
( ( n1 @ ( A @ join ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(39,plain,
! [A: $i] :
( ( n1 @ ( A @ join ) )
= n1 ),
inference(lifteq,[status(thm)],[38]) ).
thf(1,negated_conjecture,
( r1
!= ( a @ ( r2 @ meet ) @ ( r1 @ join ) @ ( b @ ( r2 @ meet ) @ ( r1 @ join ) @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lemma) ).
thf(23,plain,
( r1
!= ( a @ ( r2 @ meet ) @ ( r1 @ join ) @ ( b @ ( r2 @ meet ) @ ( r1 @ join ) @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(24,plain,
( r1
!= ( a @ ( r2 @ meet ) @ ( r1 @ join ) @ ( b @ ( r2 @ meet ) @ ( r1 @ join ) @ meet ) ) ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
( ( a @ ( r2 @ meet ) @ ( r1 @ join ) @ ( b @ ( r2 @ meet ) @ ( r1 @ join ) @ meet ) )
!= r1 ),
inference(lifteq,[status(thm)],[24]) ).
thf(81,plain,
! [A: $i] :
( ( ( n1 @ ( A @ join ) )
!= ( a @ ( r2 @ meet ) @ ( r1 @ join ) ) )
| ( ( n1 @ ( b @ ( r2 @ meet ) @ ( r1 @ join ) @ meet ) )
!= r1 ) ),
inference(paramod_ordered,[status(thm)],[39,25]) ).
thf(84,plain,
! [A: $i] :
( ( ( a @ ( r2 @ meet ) )
!= n1 )
| ( A != r1 )
| ( ( n1 @ ( b @ ( r2 @ meet ) @ ( r1 @ join ) @ meet ) )
!= r1 ) ),
inference(simp,[status(thm)],[81]) ).
thf(89,plain,
( ( ( a @ ( r2 @ meet ) )
!= n1 )
| ( ( n1 @ ( b @ ( r2 @ meet ) @ ( r1 @ join ) @ meet ) )
!= r1 ) ),
inference(simp,[status(thm)],[84]) ).
thf(7,axiom,
! [A: $i] :
( ( n1 @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_meet_1) ).
thf(36,plain,
! [A: $i] :
( ( n1 @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,plain,
! [A: $i] :
( ( n1 @ ( A @ meet ) )
= A ),
inference(lifteq,[status(thm)],[36]) ).
thf(3040,plain,
( ( ( a @ ( r2 @ meet ) )
!= n1 )
| ( ( b @ ( r2 @ meet ) @ ( r1 @ join ) )
!= r1 ) ),
inference(rewrite,[status(thm)],[89,37]) ).
thf(20,axiom,
( ( b @ ( a @ meet ) @ ( r2 @ complement ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_meet_b) ).
thf(62,plain,
( ( b @ ( a @ meet ) @ ( r2 @ complement ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(63,plain,
( ( b @ ( a @ meet ) @ ( r2 @ complement ) )
= true ),
inference(lifteq,[status(thm)],[62]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( n0 @ ( B @ ( A @ meet ) @ ( true @ ( B @ ( A @ complement ) @ ifeq ) ) ) )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_meet) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( n0 @ ( B @ ( A @ meet ) @ ( true @ ( B @ ( A @ complement ) @ ifeq ) ) ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( n0 @ ( B @ ( A @ meet ) @ ( true @ ( B @ ( A @ complement ) @ ifeq ) ) ) )
= n0 ),
inference(lifteq,[status(thm)],[64]) ).
thf(1563,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ meet ) @ ( r2 @ complement ) )
!= ( B @ ( A @ complement ) ) )
| ( ( n0 @ ( B @ ( A @ meet ) @ ( true @ ( true @ ifeq ) ) ) )
= n0 ) ),
inference(paramod_ordered,[status(thm)],[63,65]) ).
thf(1564,plain,
( ( n0 @ ( b @ ( a @ meet ) @ ( r2 @ meet ) @ ( true @ ( true @ ifeq ) ) ) )
= n0 ),
inference(pattern_uni,[status(thm)],[1563:[bind(A,$thf( r2 )),bind(B,$thf( b @ ( a @ meet ) ))]]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(lifteq,[status(thm)],[26]) ).
thf(3393,plain,
( ( b @ ( a @ meet ) @ ( r2 @ meet ) )
= n0 ),
inference(rewrite,[status(thm)],[1564,27]) ).
thf(19,axiom,
! [A: $i] :
( ( n0 @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_join_0) ).
thf(60,plain,
! [A: $i] :
( ( n0 @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(61,plain,
! [A: $i] :
( ( n0 @ ( A @ join ) )
= A ),
inference(lifteq,[status(thm)],[60]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( n0 @ ( C @ join ) ) )
| ( ( A @ ( B @ join ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[41,61]) ).
thf(244,plain,
! [A: $i] :
( ( A @ ( n0 @ join ) )
= A ),
inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( A )),bind(B,$thf( n0 )),bind(C,$thf( A ))]]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
inference(lifteq,[status(thm)],[34]) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( n0 @ join ) )
!= ( C @ ( B @ meet ) @ ( B @ join ) ) )
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[244,35]) ).
thf(400,plain,
! [A: $i] :
( ( A @ ( n0 @ meet ) )
= n0 ),
inference(pattern_uni,[status(thm)],[399:[bind(A,$thf( E @ ( n0 @ meet ) )),bind(B,$thf( n0 )),bind(C,$thf( E ))]]) ).
thf(433,plain,
! [A: $i] :
( ( A @ ( n0 @ meet ) )
= n0 ),
inference(simp,[status(thm)],[400]) ).
thf(13,axiom,
! [A: $i] :
( ( n0 @ ( A @ meet ) )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_meet_0) ).
thf(48,plain,
! [A: $i] :
( ( n0 @ ( A @ meet ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(49,plain,
! [A: $i] :
( ( n0 @ ( A @ meet ) )
= n0 ),
inference(lifteq,[status(thm)],[48]) ).
thf(79,plain,
! [A: $i] :
( ( ( n0 @ ( A @ meet ) )
!= ( a @ ( r2 @ meet ) @ ( r1 @ join ) @ ( b @ ( r2 @ meet ) @ ( r1 @ join ) @ meet ) ) )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[49,25]) ).
thf(87,plain,
! [A: $i] :
( ( ( a @ ( r2 @ meet ) @ ( r1 @ join ) )
!= n0 )
| ( A
!= ( b @ ( r2 @ meet ) @ ( r1 @ join ) ) )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[79]) ).
thf(92,plain,
( ( ( a @ ( r2 @ meet ) @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[87]) ).
thf(132,plain,
! [A: $i] :
( ( ( n0 @ ( A @ join ) )
!= ( a @ ( r2 @ meet ) @ ( r1 @ join ) ) )
| ( A != n0 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[61,92]) ).
thf(134,plain,
( ( ( a @ ( r2 @ meet ) )
!= n0 )
| ( n0 != r1 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[132]) ).
thf(140,plain,
( ( ( a @ ( r2 @ meet ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[134]) ).
thf(446,plain,
! [A: $i] :
( ( ( A @ ( n0 @ meet ) )
!= ( a @ ( r2 @ meet ) ) )
| ( n0 != n0 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[433,140]) ).
thf(447,plain,
! [A: $i] :
( ( ( A @ ( n0 @ meet ) )
!= ( a @ ( r2 @ meet ) ) )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[446]) ).
thf(467,plain,
! [A: $i] :
( ( A != a )
| ( n0 != r2 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[447]) ).
thf(471,plain,
( ( n0 != r2 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[467]) ).
thf(456,plain,
! [A: $i] :
( ( ( A @ ( n0 @ meet ) )
!= ( a @ ( r2 @ meet ) @ ( r1 @ join ) @ ( b @ ( r2 @ meet ) @ ( r1 @ join ) @ meet ) ) )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[433,25]) ).
thf(462,plain,
! [A: $i] :
( ( A
!= ( a @ ( r2 @ meet ) @ ( r1 @ join ) ) )
| ( ( b @ ( r2 @ meet ) @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[456]) ).
thf(473,plain,
( ( ( b @ ( r2 @ meet ) @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[462]) ).
thf(195,plain,
! [A: $i] :
( ( ( n0 @ ( A @ meet ) )
!= ( a @ ( r2 @ meet ) ) )
| ( n0 != n0 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[49,140]) ).
thf(196,plain,
! [A: $i] :
( ( ( n0 @ ( A @ meet ) )
!= ( a @ ( r2 @ meet ) ) )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[195]) ).
thf(200,plain,
! [A: $i] :
( ( n0 != a )
| ( A != r2 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[196]) ).
thf(203,plain,
( ( n0 != a )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[200]) ).
thf(14,axiom,
( ( b @ ( a @ join ) @ ( r1 @ complement ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_join_b) ).
thf(50,plain,
( ( b @ ( a @ join ) @ ( r1 @ complement ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(51,plain,
( ( b @ ( a @ join ) @ ( r1 @ complement ) )
= true ),
inference(lifteq,[status(thm)],[50]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( n1 @ ( B @ ( A @ join ) @ ( true @ ( B @ ( A @ complement ) @ ifeq ) ) ) )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_join) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( n1 @ ( B @ ( A @ join ) @ ( true @ ( B @ ( A @ complement ) @ ifeq ) ) ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( n1 @ ( B @ ( A @ join ) @ ( true @ ( B @ ( A @ complement ) @ ifeq ) ) ) )
= n1 ),
inference(lifteq,[status(thm)],[46]) ).
thf(803,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ join ) @ ( r1 @ complement ) )
!= ( B @ ( A @ complement ) ) )
| ( ( n1 @ ( B @ ( A @ join ) @ ( true @ ( true @ ifeq ) ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[51,47]) ).
thf(804,plain,
( ( n1 @ ( b @ ( a @ join ) @ ( r1 @ join ) @ ( true @ ( true @ ifeq ) ) ) )
= n1 ),
inference(pattern_uni,[status(thm)],[803:[bind(A,$thf( r1 )),bind(B,$thf( b @ ( a @ join ) ))]]) ).
thf(1600,plain,
( ( b @ ( a @ join ) @ ( r1 @ join ) )
= n1 ),
inference(rewrite,[status(thm)],[804,27]) ).
thf(1609,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( b @ ( a @ join ) ) )
| ( ( A @ ( B @ join ) @ ( r1 @ join ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[41,1600]) ).
thf(1610,plain,
( ( a @ ( b @ join ) @ ( r1 @ join ) )
= n1 ),
inference(pattern_uni,[status(thm)],[1609:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(2058,plain,
! [B: $i,A: $i] :
( ( ( a @ ( b @ join ) @ ( r1 @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[1610,41]) ).
thf(2059,plain,
( ( r1 @ ( a @ ( b @ join ) @ join ) )
= n1 ),
inference(pattern_uni,[status(thm)],[2058:[bind(A,$thf( r1 )),bind(B,$thf( a @ ( b @ join ) ))]]) ).
thf(16,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(54,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)],[16]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ join ) ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(2655,plain,
( ( r1 @ ( a @ join ) @ ( b @ join ) )
= n1 ),
inference(rewrite,[status(thm)],[2059,55]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(56,plain,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1604,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ join ) @ ( r1 @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[1600,41]) ).
thf(1605,plain,
( ( r1 @ ( b @ ( a @ join ) @ join ) )
= n1 ),
inference(pattern_uni,[status(thm)],[1604:[bind(A,$thf( r1 )),bind(B,$thf( b @ ( a @ join ) ))]]) ).
thf(1735,plain,
( ( r1 @ ( b @ join ) @ ( a @ join ) )
= n1 ),
inference(rewrite,[status(thm)],[1605,55]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ complement ) @ ( n0 @ ( B @ ( A @ meet ) @ ifeq2 ) ) ) @ ( n1 @ ( B @ ( A @ join ) @ ifeq2 ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_join_complement) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ complement ) @ ( n0 @ ( B @ ( A @ meet ) @ ifeq2 ) ) ) @ ( n1 @ ( B @ ( A @ join ) @ ifeq2 ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(801,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ meet ) @ ( r2 @ complement ) )
!= ( B @ ( A @ complement ) ) )
| ( ( n1 @ ( B @ ( A @ join ) @ ( true @ ( true @ ifeq ) ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[63,47]) ).
thf(802,plain,
( ( n1 @ ( b @ ( a @ meet ) @ ( r2 @ join ) @ ( true @ ( true @ ifeq ) ) ) )
= n1 ),
inference(pattern_uni,[status(thm)],[801:[bind(A,$thf( r2 )),bind(B,$thf( b @ ( a @ meet ) ))]]) ).
thf(828,plain,
( ( b @ ( a @ meet ) @ ( r2 @ join ) )
= n1 ),
inference(rewrite,[status(thm)],[802,27]) ).
thf(849,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ meet ) @ ( r2 @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( n1 @ ( n1 @ ( true @ ( B @ ( A @ complement ) @ ifeq ) ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[828,47]) ).
thf(850,plain,
( ( n1 @ ( n1 @ ( true @ ( b @ ( a @ meet ) @ ( r2 @ complement ) @ ifeq ) ) ) )
= n1 ),
inference(pattern_uni,[status(thm)],[849:[bind(A,$thf( r2 )),bind(B,$thf( b @ ( a @ meet ) ))]]) ).
thf(3140,plain,
( ( n1 @ ( n1 @ ( true @ ( true @ ifeq ) ) ) )
= n1 ),
inference(rewrite,[status(thm)],[850,63]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ meet ) @ ( A @ join ) @ ( C @ ( A @ join ) @ ( B @ meet ) @ ( A @ ( B @ ( A @ meet ) @ ifeq3 ) ) ) )
= ( B @ ( C @ meet ) @ ( A @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modular) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ meet ) @ ( A @ join ) @ ( C @ ( A @ join ) @ ( B @ meet ) @ ( A @ ( B @ ( A @ meet ) @ ifeq3 ) ) ) )
= ( B @ ( C @ meet ) @ ( A @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(94,plain,
! [A: $i] :
( ( ( n1 @ ( A @ join ) )
!= ( a @ ( r2 @ meet ) @ ( r1 @ join ) ) )
| ( n0 != n1 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[39,92]) ).
thf(96,plain,
! [A: $i] :
( ( ( a @ ( r2 @ meet ) )
!= n1 )
| ( A != r1 )
| ( n0 != n1 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[94]) ).
thf(97,plain,
( ( ( a @ ( r2 @ meet ) )
!= n1 )
| ( n0 != n1 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[96]) ).
thf(122,plain,
! [A: $i] :
( ( ( n1 @ ( A @ meet ) )
!= ( a @ ( r2 @ meet ) ) )
| ( A != n1 )
| ( n0 != n1 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[37,97]) ).
thf(125,plain,
( ( n1 != a )
| ( n1 != r2 )
| ( n0 != n1 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[122]) ).
thf(57,plain,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
inference(lifteq,[status(thm)],[56]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
inference(lifteq,[status(thm)],[28]) ).
thf(72,plain,
! [A: $i] :
( ( ( n1 @ ( A @ join ) )
!= ( b @ ( a @ join ) ) )
| ( ( n1 @ ( r1 @ complement ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[39,51]) ).
thf(73,plain,
! [A: $i] :
( ( n1 != b )
| ( A != a )
| ( ( n1 @ ( r1 @ complement ) )
= true ) ),
inference(simp,[status(thm)],[72]) ).
thf(74,plain,
( ( n1 != b )
| ( ( n1 @ ( r1 @ complement ) )
= true ) ),
inference(simp,[status(thm)],[73]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(32,plain,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,plain,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
inference(lifteq,[status(thm)],[32]) ).
thf(914,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( b @ ( r2 @ meet ) ) )
| ( ( A @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[33,473]) ).
thf(943,plain,
! [A: $i] :
( ( A != b )
| ( A != r2 )
| ( ( A @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[914]) ).
thf(957,plain,
( ( b != r2 )
| ( ( r2 @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[943]) ).
thf(921,plain,
! [A: $i] :
( ( ( n1 @ ( A @ meet ) )
!= ( b @ ( r2 @ meet ) ) )
| ( ( A @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[37,473]) ).
thf(937,plain,
! [A: $i] :
( ( n1 != b )
| ( A != r2 )
| ( ( A @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[921]) ).
thf(952,plain,
( ( n1 != b )
| ( ( r2 @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[937]) ).
thf(251,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( n1 @ ( C @ join ) ) )
| ( ( A @ ( B @ join ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[41,39]) ).
thf(252,plain,
! [A: $i] :
( ( A @ ( n1 @ join ) )
= n1 ),
inference(pattern_uni,[status(thm)],[251:[bind(A,$thf( A )),bind(B,$thf( n1 )),bind(C,$thf( A ))]]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
inference(lifteq,[status(thm)],[44]) ).
thf(78,plain,
! [A: $i] :
( ( ( n0 @ ( A @ meet ) )
!= ( b @ ( r2 @ meet ) ) )
| ( ( a @ ( r2 @ meet ) @ ( r1 @ join ) @ ( n0 @ ( r1 @ join ) @ meet ) )
!= r1 ) ),
inference(paramod_ordered,[status(thm)],[49,25]) ).
thf(83,plain,
! [A: $i] :
( ( n0 != b )
| ( A != r2 )
| ( ( a @ ( r2 @ meet ) @ ( r1 @ join ) @ ( n0 @ ( r1 @ join ) @ meet ) )
!= r1 ) ),
inference(simp,[status(thm)],[78]) ).
thf(88,plain,
( ( n0 != b )
| ( ( a @ ( r2 @ meet ) @ ( r1 @ join ) @ ( n0 @ ( r1 @ join ) @ meet ) )
!= r1 ) ),
inference(simp,[status(thm)],[83]) ).
thf(2890,plain,
( ( n0 != b )
| ( ( a @ ( r2 @ meet ) @ ( r1 @ join ) @ ( r1 @ meet ) )
!= r1 ) ),
inference(rewrite,[status(thm)],[88,61]) ).
thf(2908,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) @ ( A @ meet ) )
!= ( a @ ( r2 @ meet ) @ ( r1 @ join ) @ ( r1 @ meet ) ) )
| ( n0 != b )
| ( A != r1 ) ),
inference(paramod_ordered,[status(thm)],[45,2890]) ).
thf(2909,plain,
( ( n0 != b )
| ( r1 != r1 ) ),
inference(pattern_uni,[status(thm)],[2908:[bind(A,$thf( r1 )),bind(B,$thf( a @ ( r2 @ meet ) ))]]) ).
thf(2973,plain,
n0 != b,
inference(simp,[status(thm)],[2909]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ meet ) @ ( A @ join ) @ ( C @ ( A @ join ) @ ( B @ meet ) @ ( A @ ( B @ ( A @ meet ) @ ifeq3 ) ) ) )
= ( B @ ( C @ meet ) @ ( A @ join ) ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(80,plain,
! [A: $i] :
( ( ( n0 @ ( A @ meet ) )
!= ( a @ ( r2 @ meet ) ) )
| ( ( n0 @ ( r1 @ join ) @ ( b @ ( r2 @ meet ) @ ( r1 @ join ) @ meet ) )
!= r1 ) ),
inference(paramod_ordered,[status(thm)],[49,25]) ).
thf(85,plain,
! [A: $i] :
( ( n0 != a )
| ( A != r2 )
| ( ( n0 @ ( r1 @ join ) @ ( b @ ( r2 @ meet ) @ ( r1 @ join ) @ meet ) )
!= r1 ) ),
inference(simp,[status(thm)],[80]) ).
thf(90,plain,
( ( n0 != a )
| ( ( n0 @ ( r1 @ join ) @ ( b @ ( r2 @ meet ) @ ( r1 @ join ) @ meet ) )
!= r1 ) ),
inference(simp,[status(thm)],[85]) ).
thf(3237,plain,
( ( n0 != a )
| ( ( r1 @ ( b @ ( r2 @ meet ) @ ( r1 @ join ) @ meet ) )
!= r1 ) ),
inference(rewrite,[status(thm)],[90,61]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(663,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= ( n1 @ ( C @ meet ) ) )
| ( ( A @ ( B @ meet ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[59,37]) ).
thf(664,plain,
! [A: $i] :
( ( A @ ( n1 @ meet ) )
= A ),
inference(pattern_uni,[status(thm)],[663:[bind(A,$thf( A )),bind(B,$thf( n1 )),bind(C,$thf( A ))]]) ).
thf(753,plain,
! [A: $i] :
( ( ( A @ ( n1 @ meet ) )
!= ( a @ ( r2 @ meet ) ) )
| ( ( A @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[664,92]) ).
thf(773,plain,
! [A: $i] :
( ( A != a )
| ( n1 != r2 )
| ( ( A @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[753]) ).
thf(783,plain,
( ( n1 != r2 )
| ( ( a @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[773]) ).
thf(832,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ meet ) @ ( r2 @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[828,41]) ).
thf(833,plain,
( ( r2 @ ( b @ ( a @ meet ) @ join ) )
= n1 ),
inference(pattern_uni,[status(thm)],[832:[bind(A,$thf( r2 )),bind(B,$thf( b @ ( a @ meet ) ))]]) ).
thf(1130,plain,
! [B: $i,A: $i] :
( ( ( r2 @ ( b @ ( a @ meet ) @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( n1 @ ( n1 @ ( true @ ( B @ ( A @ complement ) @ ifeq ) ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[833,47]) ).
thf(1131,plain,
( ( n1 @ ( n1 @ ( true @ ( r2 @ ( b @ ( a @ meet ) @ complement ) @ ifeq ) ) ) )
= n1 ),
inference(pattern_uni,[status(thm)],[1130:[bind(A,$thf( b @ ( a @ meet ) )),bind(B,$thf( r2 ))]]) ).
thf(265,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( b @ ( a @ join ) ) )
| ( ( A @ ( B @ join ) @ ( r1 @ complement ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[41,51]) ).
thf(266,plain,
( ( a @ ( b @ join ) @ ( r1 @ complement ) )
= true ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(919,plain,
! [A: $i] :
( ( ( n1 @ ( A @ join ) )
!= ( b @ ( r2 @ meet ) @ ( r1 @ join ) ) )
| ( n0 != n1 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[39,473]) ).
thf(938,plain,
! [A: $i] :
( ( ( b @ ( r2 @ meet ) )
!= n1 )
| ( A != r1 )
| ( n0 != n1 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[919]) ).
thf(953,plain,
( ( ( b @ ( r2 @ meet ) )
!= n1 )
| ( n0 != n1 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[938]) ).
thf(1145,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( ( r2 @ ( A @ ( B @ meet ) @ join ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[59,833]) ).
thf(1146,plain,
( ( r2 @ ( a @ ( b @ meet ) @ join ) )
= n1 ),
inference(pattern_uni,[status(thm)],[1145:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(158,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( a @ ( r2 @ meet ) ) )
| ( ( A @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[33,92]) ).
thf(167,plain,
! [A: $i] :
( ( A != a )
| ( A != r2 )
| ( ( A @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[158]) ).
thf(171,plain,
( ( a != r2 )
| ( ( r2 @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[167]) ).
thf(529,plain,
! [A: $i] :
( ( ( n1 @ ( A @ join ) )
!= ( r2 @ ( r1 @ join ) ) )
| ( a != r2 )
| ( n0 != n1 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[39,171]) ).
thf(536,plain,
! [A: $i] :
( ( n1 != r2 )
| ( A != r1 )
| ( a != r2 )
| ( n0 != n1 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[529]) ).
thf(545,plain,
( ( n1 != r2 )
| ( a != r2 )
| ( n0 != n1 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[536]) ).
thf(913,plain,
! [A: $i] :
( ( ( n0 @ ( A @ join ) )
!= ( b @ ( r2 @ meet ) @ ( r1 @ join ) ) )
| ( A != n0 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[61,473]) ).
thf(931,plain,
( ( ( b @ ( r2 @ meet ) )
!= n0 )
| ( n0 != r1 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[913]) ).
thf(947,plain,
( ( ( b @ ( r2 @ meet ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[931]) ).
thf(22,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(66,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)],[22]) ).
thf(928,plain,
! [A: $i] :
( ( ( A @ ( n1 @ meet ) )
!= ( b @ ( r2 @ meet ) ) )
| ( ( A @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[664,473]) ).
thf(946,plain,
! [A: $i] :
( ( A != b )
| ( n1 != r2 )
| ( ( A @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[928]) ).
thf(959,plain,
( ( n1 != r2 )
| ( ( b @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[946]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) @ meet ) )
= ( C @ ( B @ meet ) @ ( A @ meet ) ) ),
inference(lifteq,[status(thm)],[66]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq3 ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq3 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq3 ) ) ) )
= B ),
inference(lifteq,[status(thm)],[30]) ).
thf(655,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( ( A @ ( B @ meet ) @ ( r2 @ complement ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[59,63]) ).
thf(656,plain,
( ( a @ ( b @ meet ) @ ( r2 @ complement ) )
= true ),
inference(pattern_uni,[status(thm)],[655:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(1505,plain,
! [B: $i,A: $i] :
( ( ( r2 @ ( a @ ( b @ meet ) @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( n1 @ ( n1 @ ( true @ ( B @ ( A @ complement ) @ ifeq ) ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[1146,47]) ).
thf(1506,plain,
( ( n1 @ ( n1 @ ( true @ ( r2 @ ( a @ ( b @ meet ) @ complement ) @ ifeq ) ) ) )
= n1 ),
inference(pattern_uni,[status(thm)],[1505:[bind(A,$thf( a @ ( b @ meet ) )),bind(B,$thf( r2 ))]]) ).
thf(3053,plain,
! [A: $i] :
( ( ( A @ ( n1 @ join ) )
!= ( b @ ( r2 @ meet ) @ ( r1 @ join ) ) )
| ( ( a @ ( r2 @ meet ) )
!= n1 )
| ( n1 != r1 ) ),
inference(paramod_ordered,[status(thm)],[252,3040]) ).
thf(3078,plain,
! [A: $i] :
( ( A
!= ( b @ ( r2 @ meet ) ) )
| ( n1 != r1 )
| ( ( a @ ( r2 @ meet ) )
!= n1 )
| ( n1 != r1 ) ),
inference(simp,[status(thm)],[3053]) ).
thf(3117,plain,
( ( ( a @ ( r2 @ meet ) )
!= n1 )
| ( n1 != r1 ) ),
inference(simp,[status(thm)],[3078]) ).
thf(3213,plain,
! [A: $i] :
( ( ( A @ ( A @ meet ) )
!= ( a @ ( r2 @ meet ) ) )
| ( A != n1 )
| ( n1 != r1 ) ),
inference(paramod_ordered,[status(thm)],[33,3117]) ).
thf(3224,plain,
( ( n1 != a )
| ( n1 != r2 )
| ( n1 != r1 ) ),
inference(simp,[status(thm)],[3213]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ complement ) @ ( n0 @ ( B @ ( A @ meet ) @ ifeq2 ) ) ) @ ( n1 @ ( B @ ( A @ join ) @ ifeq2 ) ) ) )
= true ),
inference(lifteq,[status(thm)],[42]) ).
thf(344,plain,
! [A: $i] :
( ( ( A @ ( n1 @ join ) )
!= ( a @ ( r2 @ meet ) @ ( r1 @ join ) ) )
| ( n0 != n1 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[252,92]) ).
thf(345,plain,
! [A: $i] :
( ( A
!= ( a @ ( r2 @ meet ) ) )
| ( n1 != r1 )
| ( n0 != n1 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[344]) ).
thf(351,plain,
( ( n1 != r1 )
| ( n0 != n1 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[345]) ).
thf(1744,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( r1 @ ( b @ join ) ) )
| ( ( A @ ( B @ join ) @ ( a @ join ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[41,1735]) ).
thf(1745,plain,
( ( b @ ( r1 @ join ) @ ( a @ join ) )
= n1 ),
inference(pattern_uni,[status(thm)],[1744:[bind(A,$thf( b )),bind(B,$thf( r1 ))]]) ).
thf(1740,plain,
! [B: $i,A: $i] :
( ( ( r1 @ ( b @ join ) @ ( a @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[1735,41]) ).
thf(1741,plain,
( ( a @ ( r1 @ ( b @ join ) @ join ) )
= n1 ),
inference(pattern_uni,[status(thm)],[1740:[bind(A,$thf( a )),bind(B,$thf( r1 @ ( b @ join ) ))]]) ).
thf(2251,plain,
( ( a @ ( r1 @ join ) @ ( b @ join ) )
= n1 ),
inference(rewrite,[status(thm)],[1741,55]) ).
thf(99,plain,
! [A: $i] :
( ( ( n1 @ ( A @ meet ) )
!= ( a @ ( r2 @ meet ) ) )
| ( ( A @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(paramod_ordered,[status(thm)],[37,92]) ).
thf(111,plain,
! [A: $i] :
( ( n1 != a )
| ( A != r2 )
| ( ( A @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[99]) ).
thf(119,plain,
( ( n1 != a )
| ( ( r2 @ ( r1 @ join ) )
!= n0 )
| ( n0 != r1 ) ),
inference(simp,[status(thm)],[111]) ).
thf(864,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= ( b @ ( a @ meet ) ) )
| ( ( A @ ( B @ meet ) @ ( r2 @ join ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[59,828]) ).
thf(865,plain,
( ( a @ ( b @ meet ) @ ( r2 @ join ) )
= n1 ),
inference(pattern_uni,[status(thm)],[864:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(52472,plain,
$false,
inference(e,[status(thm)],[3040,3393,60,471,39,473,203,2655,56,1735,42,3140,37,25,52,125,46,57,29,61,1600,74,957,952,33,28,38,92,252,65,97,2973,53,3237,783,1131,41,244,266,953,1146,45,64,32,34,44,59,545,27,54,49,947,140,66,959,35,48,63,50,67,31,656,1506,3224,3117,43,26,351,1745,55,171,23,40,2251,433,119,58,30,51,865,833,36,664,828,1610,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT005-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % 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
% 0.14/0.39 % Computer : n016.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Fri Sep 25 19:59:29 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.17 % [INFO] Parsing done (193ms).
% 1.27/1.19 % [INFO] Running in sequential loop mode.
% 1.86/1.59 % [INFO] eprover registered as external prover.
% 2.05/1.60 % [INFO] Scanning for conjecture ...
% 2.05/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 21 axioms. Running axiom selection ...
% 2.23/1.75 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 2.23/1.78 % [INFO] Problem is propositional (TPTP CNF).
% 2.23/1.79 % [INFO] Type checking passed.
% 2.23/1.80 % [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 ...
% 92.39/22.95 % External prover 'e' found a proof!
% 92.39/22.95 % [INFO] Killing All external provers ...
% 92.39/22.95 % Time passed: 22412ms (effective reasoning time: 21759ms)
% 92.39/22.95 % 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
% 92.39/22.95 % No. of inferences in proof: 191
% 92.39/22.95 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22412 ms resp. 21759 ms w/o parsing
% 92.98/23.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 92.98/23.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------