%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT017-1 : TPTP v9.3.1. Bugfixed v2.2.1.
% 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 07:46:29 AM UTC 2026
% Result : Unsatisfiable 35.70s 22.96s
% Output : Refutation 36.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 11
% Syntax : Number of formulae : 110 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 301 ( 300 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1546 ( 253 ~; 191 |; 0 &;1102 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 92 ( 0 ^; 92 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_decl,type,
join: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(complement_decl,type,
complement: $i > $i ).
thf(b_decl,type,
b: $i ).
thf(n1_decl,type,
n1: $i ).
thf(n0_decl,type,
n0: $i ).
thf(9,axiom,
! [A: $i] :
( ( A @ complement @ complement )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_involution) ).
thf(29,plain,
! [A: $i] :
( ( A @ complement @ complement )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,plain,
! [A: $i] :
( ( A @ complement @ complement )
= A ),
inference(lifteq,[status(thm)],[29]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ complement @ meet ) )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( A @ complement @ meet ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,plain,
! [A: $i] :
( ( A @ ( A @ complement @ meet ) )
= n0 ),
inference(lifteq,[status(thm)],[17]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( ( A @ complement @ complement )
!= ( B @ complement ) )
| ( ( B @ ( A @ meet ) )
= n0 ) ),
inference(paramod_ordered,[status(thm)],[30,18]) ).
thf(41,plain,
! [A: $i] :
( ( A @ complement @ ( A @ meet ) )
= n0 ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( C )),bind(B,$thf( C @ complement ))]]) ).
thf(42,plain,
! [A: $i] :
( ( A @ complement @ ( A @ meet ) )
= n0 ),
inference(simp,[status(thm)],[41]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
inference(lifteq,[status(thm)],[19]) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ complement @ ( A @ meet ) )
!= ( C @ ( B @ meet ) ) )
| ( ( n0 @ ( B @ join ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[42,20]) ).
thf(326,plain,
! [A: $i] :
( ( n0 @ ( A @ join ) )
= A ),
inference(pattern_uni,[status(thm)],[325:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ complement ))]]) ).
thf(372,plain,
! [A: $i] :
( ( n0 @ ( A @ join ) )
= A ),
inference(simp,[status(thm)],[326]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( A @ complement @ join ) )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',top) ).
thf(15,plain,
! [A: $i] :
( ( A @ ( A @ complement @ join ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
! [A: $i] :
( ( A @ ( A @ complement @ join ) )
= n1 ),
inference(lifteq,[status(thm)],[15]) ).
thf(404,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( A @ join ) )
!= ( B @ ( B @ complement @ join ) ) )
| ( A = n1 ) ),
inference(paramod_ordered,[status(thm)],[372,16]) ).
thf(405,plain,
( ( n0 @ complement )
= n1 ),
inference(pattern_uni,[status(thm)],[404:[bind(A,$thf( n0 @ complement )),bind(B,$thf( n0 ))]]) ).
thf(470,plain,
! [A: $i] :
( ( ( n0 @ complement )
!= ( A @ complement ) )
| ( ( A @ ( n1 @ meet ) )
= n0 ) ),
inference(paramod_ordered,[status(thm)],[405,18]) ).
thf(471,plain,
( ( n0 @ ( n1 @ meet ) )
= n0 ),
inference(pattern_uni,[status(thm)],[470:[bind(A,$thf( n0 ))]]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( ( A @ complement @ complement )
!= ( B @ complement ) )
| ( ( B @ ( A @ join ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[30,16]) ).
thf(38,plain,
! [A: $i] :
( ( A @ complement @ ( A @ join ) )
= n1 ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( C )),bind(B,$thf( C @ complement ))]]) ).
thf(39,plain,
! [A: $i] :
( ( A @ complement @ ( A @ join ) )
= n1 ),
inference(simp,[status(thm)],[38]) ).
thf(1,negated_conjecture,
( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( b @ complement @ ( a @ join ) @ meet ) @ ( a @ complement @ meet ) @ join ) @ ( a @ join ) )
!= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_e2) ).
thf(12,plain,
( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( b @ complement @ ( a @ join ) @ meet ) @ ( a @ complement @ meet ) @ join ) @ ( a @ join ) )
!= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,plain,
( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( b @ complement @ ( a @ join ) @ meet ) @ ( a @ complement @ meet ) @ join ) @ ( a @ join ) )
!= n1 ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(14,plain,
( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( b @ complement @ ( a @ join ) @ meet ) @ ( a @ complement @ meet ) @ join ) @ ( a @ join ) )
!= n1 ),
inference(lifteq,[status(thm)],[13]) ).
thf(52,plain,
! [A: $i] :
( ( ( A @ complement @ ( A @ join ) )
!= ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( b @ complement @ ( a @ join ) @ meet ) @ ( a @ complement @ meet ) @ join ) @ ( a @ join ) ) )
| ( n1 != n1 ) ),
inference(paramod_ordered,[status(thm)],[39,14]) ).
thf(53,plain,
! [A: $i] :
( ( A @ complement @ ( A @ join ) )
!= ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( b @ complement @ ( a @ join ) @ meet ) @ ( a @ complement @ meet ) @ join ) @ ( a @ join ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(80,plain,
! [A: $i] :
( ( ( A @ complement )
!= ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( b @ complement @ ( a @ join ) @ meet ) @ ( a @ complement @ meet ) @ join ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[53]) ).
thf(99,plain,
( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( b @ complement @ ( a @ join ) @ meet ) @ ( a @ complement @ meet ) @ join ) )
!= ( a @ complement ) ),
inference(simp,[status(thm)],[80]) ).
thf(121,plain,
! [A: $i] :
( ( ( A @ ( A @ complement @ join ) )
!= ( b @ complement @ ( a @ join ) ) )
| ( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( n1 @ meet ) @ ( a @ complement @ meet ) @ join ) )
!= ( a @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[16,99]) ).
thf(128,plain,
! [A: $i] :
( ( A
!= ( b @ complement ) )
| ( ( A @ complement )
!= a )
| ( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( n1 @ meet ) @ ( a @ complement @ meet ) @ join ) )
!= ( a @ complement ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(147,plain,
( ( ( b @ complement @ complement )
!= a )
| ( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( n1 @ meet ) @ ( a @ complement @ meet ) @ join ) )
!= ( a @ complement ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(266,plain,
( ( b != a )
| ( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( n1 @ meet ) @ ( a @ complement @ meet ) @ join ) )
!= ( a @ complement ) ) ),
inference(rewrite,[status(thm)],[147,30]) ).
thf(461,plain,
! [A: $i] :
( ( ( n0 @ complement )
!= ( A @ complement ) )
| ( ( n1 @ ( A @ meet ) )
= n0 ) ),
inference(paramod_ordered,[status(thm)],[405,42]) ).
thf(462,plain,
( ( n1 @ ( n0 @ meet ) )
= n0 ),
inference(pattern_uni,[status(thm)],[461:[bind(A,$thf( n0 ))]]) ).
thf(494,plain,
! [A: $i] :
( ( ( n0 @ complement )
!= ( A @ complement ) )
| ( ( n1 @ complement )
= A ) ),
inference(paramod_ordered,[status(thm)],[405,30]) ).
thf(495,plain,
( ( n1 @ complement )
= n0 ),
inference(pattern_uni,[status(thm)],[494:[bind(A,$thf( n0 ))]]) ).
thf(400,plain,
! [A: $i] :
( ( ( n0 @ ( A @ join ) )
!= ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( n1 @ meet ) @ ( a @ complement @ meet ) @ join ) ) )
| ( b != a )
| ( A
!= ( a @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[372,266]) ).
thf(442,plain,
( ( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) )
!= n0 )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) @ ( a @ complement @ meet ) )
!= ( a @ complement ) )
| ( b != a ) ),
inference(simp,[status(thm)],[400]) ).
thf(604,plain,
! [A: $i] :
( ( ( A @ ( A @ complement @ meet ) )
!= ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) ) )
| ( n0 != n0 )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) @ ( a @ complement @ meet ) )
!= ( a @ complement ) )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[18,442]) ).
thf(605,plain,
! [A: $i] :
( ( ( A @ ( A @ complement @ meet ) )
!= ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) @ ( a @ complement @ meet ) )
!= ( a @ complement ) )
| ( b != a ) ),
inference(simp,[status(thm)],[604]) ).
thf(643,plain,
! [A: $i] :
( ( A
!= ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) ) )
| ( ( A @ complement )
!= ( a @ complement ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) @ ( a @ complement @ meet ) )
!= ( a @ complement ) )
| ( b != a ) ),
inference(simp,[status(thm)],[605]) ).
thf(661,plain,
( ( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ complement )
!= ( a @ complement ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) @ ( a @ complement @ meet ) )
!= ( a @ complement ) )
| ( b != a ) ),
inference(simp,[status(thm)],[643]) ).
thf(837,plain,
( ( ( b @ ( a @ join ) @ ( n1 @ meet ) @ ( a @ complement @ meet ) )
!= ( n1 @ ( n0 @ meet ) ) )
| ( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ complement )
!= ( a @ complement ) )
| ( ( a @ complement )
!= n0 )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[462,661]) ).
thf(881,plain,
( ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( ( a @ complement )
!= n0 )
| ( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) )
!= a )
| ( ( a @ complement )
!= n0 )
| ( b != a ) ),
inference(simp,[status(thm)],[837]) ).
thf(910,plain,
( ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) )
!= a )
| ( ( a @ complement )
!= n0 )
| ( b != a ) ),
inference(simp,[status(thm)],[881]) ).
thf(928,plain,
( ( ( n1 @ complement )
!= ( a @ complement ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) )
!= a )
| ( n0 != n0 )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[495,910]) ).
thf(929,plain,
( ( ( n1 @ complement )
!= ( a @ complement ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) )
!= a )
| ( b != a ) ),
inference(simp,[status(thm)],[928]) ).
thf(969,plain,
( ( n1 != a )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) )
!= a )
| ( b != a ) ),
inference(simp,[status(thm)],[929]) ).
thf(1002,plain,
! [A: $i] :
( ( ( A @ ( A @ complement @ join ) )
!= ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) ) )
| ( n1 != a )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[16,969]) ).
thf(1003,plain,
! [A: $i] :
( ( ( A @ ( A @ complement @ join ) )
!= ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1002]) ).
thf(1026,plain,
! [A: $i] :
( ( A
!= ( b @ complement @ ( a @ complement @ meet ) ) )
| ( ( A @ complement )
!= ( b @ ( a @ complement @ meet ) ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1003]) ).
thf(1048,plain,
( ( ( b @ complement @ ( a @ complement @ meet ) @ complement )
!= ( b @ ( a @ complement @ meet ) ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1026]) ).
thf(1396,plain,
( ( ( n1 @ complement )
!= ( a @ complement ) )
| ( ( b @ ( n0 @ meet ) )
!= ( b @ complement @ ( a @ complement @ meet ) @ complement ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[495,1048]) ).
thf(1413,plain,
( ( n1 != a )
| ( ( b @ ( n0 @ meet ) )
!= ( b @ complement @ ( a @ complement @ meet ) @ complement ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1396]) ).
thf(1438,plain,
( ( ( b @ ( n0 @ meet ) )
!= ( b @ complement @ ( a @ complement @ meet ) @ complement ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1413]) ).
thf(1474,plain,
( ( ( n1 @ complement )
!= ( a @ complement ) )
| ( ( b @ complement @ ( n0 @ meet ) @ complement )
!= ( b @ ( n0 @ meet ) ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[495,1438]) ).
thf(1505,plain,
( ( n1 != a )
| ( ( b @ complement @ ( n0 @ meet ) @ complement )
!= ( b @ ( n0 @ meet ) ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1474]) ).
thf(1522,plain,
( ( ( b @ complement @ ( n0 @ meet ) @ complement )
!= ( b @ ( n0 @ meet ) ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1505]) ).
thf(1554,plain,
! [A: $i] :
( ( ( A @ complement @ complement )
!= ( b @ complement @ ( n0 @ meet ) @ complement ) )
| ( A
!= ( b @ ( n0 @ meet ) ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[30,1522]) ).
thf(1569,plain,
( ( ( b @ complement @ ( n0 @ meet ) )
!= ( b @ ( n0 @ meet ) @ complement ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1554]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(7,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(25,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)],[7]) ).
thf(8,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(27,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)],[8]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ join ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( B @ complement @ ( A @ complement @ join ) @ complement ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_complement) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( B @ complement @ ( A @ complement @ join ) @ complement ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ complement @ ( B @ join ) @ ( A @ join ) )
= ( B @ complement @ ( B @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',join_complement) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ complement @ ( B @ join ) @ ( A @ join ) )
= ( B @ complement @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1548,plain,
! [A: $i] :
( ( ( n0 @ ( A @ join ) )
!= ( b @ ( a @ join ) ) )
| ( ( b @ complement @ ( n0 @ meet ) @ complement )
!= ( b @ ( n0 @ meet ) ) )
| ( ( A @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[372,1522]) ).
thf(1562,plain,
! [A: $i] :
( ( n0 != b )
| ( A != a )
| ( ( b @ complement @ ( n0 @ meet ) @ complement )
!= ( b @ ( n0 @ meet ) ) )
| ( ( A @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1548]) ).
thf(1585,plain,
( ( n0 != b )
| ( ( b @ complement @ ( n0 @ meet ) @ complement )
!= ( b @ ( n0 @ meet ) ) )
| ( ( a @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1562]) ).
thf(1843,plain,
( ( ( n1 @ ( n0 @ meet ) )
!= ( a @ ( n1 @ meet ) ) )
| ( n0 != b )
| ( ( b @ complement @ ( n0 @ meet ) @ complement )
!= ( b @ ( n0 @ meet ) ) )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[462,1585]) ).
thf(1863,plain,
( ( n1 != a )
| ( n0 != n1 )
| ( n0 != b )
| ( ( b @ complement @ ( n0 @ meet ) @ complement )
!= ( b @ ( n0 @ meet ) ) )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1843]) ).
thf(1880,plain,
( ( n0 != b )
| ( ( b @ complement @ ( n0 @ meet ) @ complement )
!= ( b @ ( n0 @ meet ) ) )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1863]) ).
thf(1890,plain,
( ( ( b @ ( n0 @ meet ) )
!= ( n0 @ ( n1 @ meet ) ) )
| ( n0 != b )
| ( ( b @ complement @ ( n0 @ meet ) @ complement )
!= n0 )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[471,1880]) ).
thf(1912,plain,
( ( n0 != b )
| ( n0 != n1 )
| ( n0 != b )
| ( ( b @ complement @ ( n0 @ meet ) @ complement )
!= n0 )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1890]) ).
thf(1928,plain,
( ( n0 != b )
| ( ( b @ complement @ ( n0 @ meet ) @ complement )
!= n0 )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[1912]) ).
thf(2183,plain,
( ( ( b @ complement @ ( n0 @ meet ) @ complement )
!= ( n1 @ complement ) )
| ( n0 != b )
| ( n0 != n0 )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[495,1928]) ).
thf(2184,plain,
( ( ( b @ complement @ ( n0 @ meet ) @ complement )
!= ( n1 @ complement ) )
| ( n0 != b )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[2183]) ).
thf(2190,plain,
( ( ( b @ complement @ ( n0 @ meet ) )
!= n1 )
| ( n0 != b )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[2184]) ).
thf(2208,plain,
( ( ( b @ complement @ ( n0 @ meet ) )
!= ( n0 @ ( n1 @ meet ) ) )
| ( n0 != n1 )
| ( n0 != b )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[471,2190]) ).
thf(2209,plain,
( ( ( b @ complement @ ( n0 @ meet ) )
!= ( n0 @ ( n1 @ meet ) ) )
| ( n0 != b )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[2208]) ).
thf(2229,plain,
( ( ( b @ complement )
!= n0 )
| ( n0 != n1 )
| ( n0 != b )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[2209]) ).
thf(2233,plain,
( ( ( b @ complement )
!= n0 )
| ( n0 != b )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[2229]) ).
thf(2241,plain,
( ( ( n0 @ complement )
!= ( b @ complement ) )
| ( n0 != n1 )
| ( n0 != b )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[405,2233]) ).
thf(2242,plain,
( ( ( n0 @ complement )
!= ( b @ complement ) )
| ( n0 != b )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[2241]) ).
thf(2246,plain,
( ( n0 != b )
| ( n0 != b )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[2242]) ).
thf(2247,plain,
( ( n0 != b )
| ( n0 != n1 )
| ( n1 != a )
| ( b != a ) ),
inference(simp,[status(thm)],[2246]) ).
thf(1535,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= ( b @ ( n0 @ meet ) ) )
| ( ( A @ ( B @ meet ) )
!= ( b @ complement @ ( n0 @ meet ) @ complement ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[22,1522]) ).
thf(1536,plain,
( ( ( n0 @ ( b @ meet ) )
!= ( b @ complement @ ( n0 @ meet ) @ complement ) )
| ( ( b @ ( a @ join ) @ ( n1 @ meet ) )
!= n1 )
| ( n1 != a )
| ( b != a ) ),
inference(pattern_uni,[status(thm)],[1535:[bind(A,$thf( n0 )),bind(B,$thf( b ))]]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) @ meet ) )
= ( C @ ( B @ meet ) @ ( A @ meet ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(468,plain,
! [A: $i] :
( ( ( n0 @ complement )
!= ( A @ complement ) )
| ( ( n1 @ ( A @ join ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[405,39]) ).
thf(469,plain,
( ( n1 @ ( n0 @ join ) )
= n1 ),
inference(pattern_uni,[status(thm)],[468:[bind(A,$thf( n0 ))]]) ).
thf(63,plain,
! [A: $i] :
( ( ( A @ ( A @ complement @ join ) )
!= ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( b @ complement @ ( a @ join ) @ meet ) @ ( a @ complement @ meet ) @ join ) @ ( a @ join ) ) )
| ( n1 != n1 ) ),
inference(paramod_ordered,[status(thm)],[16,14]) ).
thf(64,plain,
! [A: $i] :
( ( A @ ( A @ complement @ join ) )
!= ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( b @ complement @ ( a @ join ) @ meet ) @ ( a @ complement @ meet ) @ join ) @ ( a @ join ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(81,plain,
! [A: $i] :
( ( A
!= ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( b @ complement @ ( a @ join ) @ meet ) @ ( a @ complement @ meet ) @ join ) ) )
| ( ( A @ complement )
!= a ) ),
inference(simp,[status(thm)],[64]) ).
thf(100,plain,
( ( b @ complement @ ( a @ complement @ meet ) @ ( b @ ( a @ complement @ meet ) @ join ) @ ( a @ complement @ meet ) @ ( b @ ( a @ join ) @ ( b @ complement @ ( a @ join ) @ meet ) @ ( a @ complement @ meet ) @ join ) @ complement )
!= a ),
inference(simp,[status(thm)],[81]) ).
thf(7542,plain,
$false,
inference(e,[status(thm)],[471,266,17,12,462,18,1522,1569,42,24,25,14,372,20,969,29,1438,661,910,28,21,33,22,27,1048,39,16,31,2247,1536,1585,99,495,26,23,30,405,19,15,442,469,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT017-1 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.07 % 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
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/15.46 % CPULimit : 300
% 0.12/15.46 % WCLimit : 300
% 0.12/15.46 % DateTime : Fri Sep 25 19:57:49 UTC 2026
% 0.12/15.46 % CPUTime :
% 0.12/15.47 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
% 0.37/15.76 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.37/15.85 % [INFO] Parsing done (95ms).
% 0.37/15.86 % [INFO] Running in sequential loop mode.
% 1.54/16.04 % [INFO] eprover registered as external prover.
% 1.54/16.05 % [INFO] Scanning for conjecture ...
% 1.54/16.09 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 1.54/16.11 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.54/16.12 % [INFO] Problem is propositional (TPTP CNF).
% 1.54/16.12 % [INFO] Type checking passed.
% 1.54/16.12 % [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 ...
% 35.70/22.95 % External prover 'e' found a proof!
% 35.70/22.95 % [INFO] Killing All external provers ...
% 35.70/22.95 % Time passed: 7400ms (effective reasoning time: 7087ms)
% 35.70/22.95 % Axioms used in derivation (10): commutativity_of_join, absorption2, commutativity_of_meet, complement_involution, associativity_of_join, join_complement, top, meet_complement, associativity_of_meet, bottom
% 35.70/22.95 % No. of inferences in proof: 110
% 35.70/22.96 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7400 ms resp. 7087 ms w/o parsing
% 36.16/23.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 36.16/23.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------