%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : REL031+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 08:24:03 AM UTC 2026
% Result : Theorem 22.24s 5.57s
% Output : Refutation 22.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 113 ( 78 unt; 0 typ; 2 def)
% Number of atoms : 165 ( 164 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 940 ( 69 ~; 38 |; 7 &; 821 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 139 ( 0 ^; 137 !; 0 ?; 139 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(join_decl,type,
join: $i > $i > $i ).
thf(composition_decl,type,
composition: $i > $i > $i ).
thf(converse_decl,type,
converse: $i > $i ).
thf(one_decl,type,
one: $i ).
thf(complement_decl,type,
complement: $i > $i ).
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(top_decl,type,
top: $i ).
thf(zero_decl,type,
zero: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( ( one @ ( B @ ( B @ converse @ composition ) @ join ) )
= one )
& ( ( one @ ( A @ ( A @ converse @ composition ) @ join ) )
= one ) )
=> ( ( one @ ( B @ ( A @ composition ) @ ( B @ ( A @ composition ) @ converse @ composition ) @ join ) )
= one ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( ( one @ ( A @ ( A @ converse @ composition ) @ join ) )
= one )
& ( ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) )
= one ) )
=> ( ( one @ ( A @ ( sk1 @ composition ) @ ( A @ ( sk1 @ composition ) @ converse @ composition ) @ join ) )
= one ) ) ) ) ).
thf(15,axiom,
! [A: $i] :
( zero
= ( A @ complement @ ( A @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
thf(60,plain,
! [A: $i] :
( zero
= ( A @ complement @ ( A @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,axiom,
! [A: $i] :
( ( one @ ( A @ composition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
thf(39,plain,
! [A: $i] :
( ( one @ ( A @ composition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(40,plain,
! [A: $i] :
( ( one @ ( A @ composition ) )
= A ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [A: $i] :
( ( one @ ( A @ composition ) )
= A ),
inference(lifteq,[status(thm)],[40]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( ( one @ ( B @ ( B @ converse @ composition ) @ join ) )
= one )
& ( ( one @ ( A @ ( A @ converse @ composition ) @ join ) )
= one ) )
=> ( ( one @ ( B @ ( A @ composition ) @ ( B @ ( A @ composition ) @ converse @ composition ) @ join ) )
= one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( ( one @ ( B @ ( B @ converse @ composition ) @ join ) )
= one )
& ( ( one @ ( A @ ( A @ converse @ composition ) @ join ) )
= one ) )
=> ( ( one @ ( B @ ( A @ composition ) @ ( B @ ( A @ composition ) @ converse @ composition ) @ join ) )
= one ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i,B: $i] :
( ( ( ( one @ ( B @ ( B @ converse @ composition ) @ join ) )
= one )
& ( ( one @ ( A @ ( A @ converse @ composition ) @ join ) )
= one ) )
=> ( ( one @ ( B @ ( A @ composition ) @ ( B @ ( A @ composition ) @ converse @ composition ) @ join ) )
= one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
( ( ( one @ ( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) @ join ) )
!= one )
& ( ( one @ ( sk2 @ ( sk2 @ converse @ composition ) @ join ) )
= one )
& ( ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) )
= one ) ),
inference(cnf,[status(esa)],[16]) ).
thf(20,plain,
( ( one @ ( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) @ join ) )
!= one ),
inference(cnfConj,[status(thm)],[17]) ).
thf(23,plain,
( ( one @ ( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) @ join ) )
!= one ),
inference(lifteq,[status(thm)],[20]) ).
thf(83,plain,
! [A: $i] :
( ( ( one @ ( A @ composition ) )
!= ( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) ) )
| ( ( one @ ( A @ join ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[41,23]) ).
thf(92,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ composition ) )
!= one )
| ( A
!= ( sk2 @ ( sk1 @ composition ) @ converse ) )
| ( ( one @ ( A @ join ) )
!= one ) ),
inference(simp,[status(thm)],[83]) ).
thf(97,plain,
( ( ( sk2 @ ( sk1 @ composition ) )
!= one )
| ( ( one @ ( sk2 @ ( sk1 @ composition ) @ converse @ join ) )
!= one ) ),
inference(simp,[status(thm)],[92]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(18,plain,
( ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) )
= one ),
inference(cnfConj,[status(thm)],[17]) ).
thf(21,plain,
( ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) )
= one ),
inference(lifteq,[status(thm)],[18]) ).
thf(67,plain,
! [A: $i] :
( ( ( one @ ( A @ composition ) )
!= ( sk1 @ ( sk1 @ converse @ composition ) ) )
| ( ( one @ ( A @ join ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[41,21]) ).
thf(69,plain,
! [A: $i] :
( ( sk1 != one )
| ( A
!= ( sk1 @ converse ) )
| ( ( one @ ( A @ join ) )
= one ) ),
inference(simp,[status(thm)],[67]) ).
thf(71,plain,
( ( sk1 != one )
| ( ( one @ ( sk1 @ converse @ join ) )
= one ) ),
inference(simp,[status(thm)],[69]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( one @ ( sk1 @ converse @ join ) ) )
| ( sk1 != one )
| ( ( A @ ( B @ join ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[26,71]) ).
thf(193,plain,
( ( sk1 != one )
| ( ( sk1 @ converse @ ( one @ join ) )
= one ) ),
inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( sk1 @ converse )),bind(B,$thf( one ))]]) ).
thf(19,plain,
( ( one @ ( sk2 @ ( sk2 @ converse @ composition ) @ join ) )
= one ),
inference(cnfConj,[status(thm)],[17]) ).
thf(22,plain,
( ( one @ ( sk2 @ ( sk2 @ converse @ composition ) @ join ) )
= one ),
inference(lifteq,[status(thm)],[19]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( one @ ( sk2 @ ( sk2 @ converse @ composition ) @ join ) ) )
| ( ( A @ ( B @ join ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[26,22]) ).
thf(213,plain,
( ( sk2 @ ( sk2 @ converse @ composition ) @ ( one @ join ) )
= one ),
inference(pattern_uni,[status(thm)],[212:[bind(A,$thf( sk2 @ ( sk2 @ converse @ composition ) )),bind(B,$thf( one ))]]) ).
thf(14,axiom,
! [A: $i] :
( top
= ( A @ complement @ ( A @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
thf(57,plain,
! [A: $i] :
( top
= ( A @ complement @ ( A @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(58,plain,
! [A: $i] :
( top
= ( A @ complement @ ( A @ join ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(59,plain,
! [A: $i] :
( ( A @ complement @ ( A @ join ) )
= top ),
inference(lifteq,[status(thm)],[58]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) ) )
| ( ( A @ ( B @ join ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[26,21]) ).
thf(185,plain,
( ( sk1 @ ( sk1 @ converse @ composition ) @ ( one @ join ) )
= one ),
inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( sk1 @ ( sk1 @ converse @ composition ) )),bind(B,$thf( one ))]]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ join ) @ ( A @ join ) )
= ( C @ ( B @ ( A @ join ) @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
thf(27,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ join ) @ ( A @ join ) )
= ( C @ ( B @ ( A @ join ) @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ join ) @ ( A @ join ) )
= ( C @ ( B @ ( A @ join ) @ join ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ join ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(354,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ converse @ composition ) @ ( one @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( C @ ( one @ join ) )
= ( C @ ( B @ join ) @ ( A @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[185,29]) ).
thf(355,plain,
! [A: $i] :
( ( A @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) @ ( one @ join ) )
= ( A @ ( one @ join ) ) ),
inference(pattern_uni,[status(thm)],[354:[bind(A,$thf( one )),bind(B,$thf( sk1 @ ( sk1 @ converse @ composition ) )),bind(C,$thf( C ))]]) ).
thf(429,plain,
! [A: $i] :
( ( A @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) @ ( one @ join ) )
= ( A @ ( one @ join ) ) ),
inference(simp,[status(thm)],[355]) ).
thf(811,plain,
! [B: $i,A: $i] :
( ( ( A @ complement @ ( A @ join ) )
!= ( B @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) ) )
| ( ( top @ ( one @ join ) )
= ( B @ ( one @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[59,429]) ).
thf(812,plain,
( ( sk1 @ ( sk1 @ converse @ composition ) @ complement @ ( one @ join ) )
= ( top @ ( one @ join ) ) ),
inference(pattern_uni,[status(thm)],[811:[bind(A,$thf( sk1 @ ( sk1 @ converse @ composition ) )),bind(B,$thf( sk1 @ ( sk1 @ converse @ composition ) @ complement ))]]) ).
thf(61,plain,
! [A: $i] :
( zero
= ( A @ complement @ ( A @ meet ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(62,plain,
! [A: $i] :
( ( A @ complement @ ( A @ meet ) )
= zero ),
inference(lifteq,[status(thm)],[61]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ meet ) )
= ( B @ complement @ ( A @ complement @ join ) @ complement ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ meet ) )
= ( B @ complement @ ( A @ complement @ join ) @ complement ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( B @ complement @ ( A @ complement @ join ) @ complement ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( B @ complement @ ( A @ complement @ join ) @ complement ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(890,plain,
! [A: $i] :
( ( A @ complement @ complement @ ( A @ complement @ join ) @ complement )
= zero ),
inference(rewrite,[status(thm)],[62,35]) ).
thf(1094,plain,
( ( top @ complement )
= zero ),
inference(rewrite,[status(thm)],[890,59]) ).
thf(224,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ complement @ ( A @ join ) )
!= ( B @ ( C @ join ) ) )
| ( ( C @ ( B @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[59,26]) ).
thf(225,plain,
! [A: $i] :
( ( A @ ( A @ complement @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[224:[bind(A,$thf( D )),bind(B,$thf( D @ complement )),bind(C,$thf( D ))]]) ).
thf(230,plain,
! [A: $i] :
( ( A @ ( A @ complement @ join ) )
= top ),
inference(simp,[status(thm)],[225]) ).
thf(1103,plain,
! [A: $i] :
( ( ( top @ complement )
!= ( A @ complement ) )
| ( ( A @ ( zero @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[1094,230]) ).
thf(1104,plain,
( ( top @ ( zero @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[1103:[bind(A,$thf( top ))]]) ).
thf(1233,plain,
! [C: $i,B: $i,A: $i] :
( ( ( top @ ( zero @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( C @ ( top @ join ) )
= ( C @ ( B @ join ) @ ( A @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[1104,29]) ).
thf(1234,plain,
! [A: $i] :
( ( A @ ( top @ join ) @ ( zero @ join ) )
= ( A @ ( top @ join ) ) ),
inference(pattern_uni,[status(thm)],[1233:[bind(A,$thf( zero )),bind(B,$thf( top ))]]) ).
thf(1289,plain,
! [A: $i] :
( ( A @ ( top @ join ) @ ( zero @ join ) )
= ( A @ ( top @ join ) ) ),
inference(simp,[status(thm)],[1234]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ converse @ converse )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
thf(45,plain,
! [A: $i] :
( ( A @ converse @ converse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(46,plain,
! [A: $i] :
( ( A @ converse @ converse )
= A ),
inference(cnf,[status(esa)],[45]) ).
thf(47,plain,
! [A: $i] :
( ( A @ converse @ converse )
= A ),
inference(lifteq,[status(thm)],[46]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ join ) @ composition ) )
= ( C @ ( B @ composition ) @ ( C @ ( A @ composition ) @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
thf(42,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ join ) @ composition ) )
= ( C @ ( B @ composition ) @ ( C @ ( A @ composition ) @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(84,plain,
( ( ( one @ ( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) @ join ) )
!= ( one @ ( sk2 @ ( sk2 @ converse @ composition ) @ join ) ) )
| ( one != one ) ),
inference(paramod_ordered,[status(thm)],[22,23]) ).
thf(85,plain,
( ( one @ ( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) @ join ) )
!= ( one @ ( sk2 @ ( sk2 @ converse @ composition ) @ join ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(87,plain,
( ( one != one )
| ( ( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) )
!= ( sk2 @ ( sk2 @ converse @ composition ) ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(93,plain,
( ( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) )
!= ( sk2 @ ( sk2 @ converse @ composition ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(730,plain,
( ( ( sk2 @ ( sk1 @ composition ) )
!= sk2 )
| ( ( sk2 @ ( sk1 @ composition ) @ converse )
!= ( sk2 @ converse ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(753,plain,
( ( ( sk2 @ ( sk1 @ composition ) )
!= sk2 )
| ( ( sk2 @ ( sk1 @ composition ) )
!= sk2 ) ),
inference(simp,[status(thm)],[730]) ).
thf(766,plain,
( ( sk2 @ ( sk1 @ composition ) )
!= sk2 ),
inference(simp,[status(thm)],[753]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ composition ) @ ( A @ composition ) )
= ( C @ ( B @ ( A @ composition ) @ composition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
thf(36,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ composition ) @ ( A @ composition ) )
= ( C @ ( B @ ( A @ composition ) @ composition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ composition ) @ ( A @ composition ) )
= ( C @ ( B @ ( A @ composition ) @ composition ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ composition ) @ composition ) )
= ( C @ ( B @ composition ) @ ( A @ composition ) ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( A
= ( B @ ( A @ complement @ join ) @ complement @ ( B @ complement @ ( A @ complement @ join ) @ complement @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
thf(30,plain,
! [A: $i,B: $i] :
( A
= ( B @ ( A @ complement @ join ) @ complement @ ( B @ complement @ ( A @ complement @ join ) @ complement @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ complement @ join ) @ complement @ ( B @ complement @ ( A @ complement @ join ) @ complement @ join ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement @ join ) @ complement @ ( B @ complement @ ( A @ complement @ join ) @ complement @ join ) )
= A ),
inference(lifteq,[status(thm)],[31]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ composition ) )
= ( C @ ( B @ composition ) @ ( C @ ( A @ composition ) @ join ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ composition ) )
= ( C @ ( B @ composition ) @ ( C @ ( A @ composition ) @ join ) ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ complement @ ( B @ ( A @ composition ) @ complement @ ( A @ converse @ composition ) @ join ) )
= ( B @ complement ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( B @ complement @ ( B @ ( A @ composition ) @ complement @ ( A @ converse @ composition ) @ join ) )
= ( B @ complement ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1106,plain,
! [A: $i] :
( ( ( top @ complement )
!= ( A @ complement ) )
| ( ( zero @ ( A @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[1094,59]) ).
thf(1107,plain,
( ( zero @ ( top @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[1106:[bind(A,$thf( top ))]]) ).
thf(81,plain,
! [A: $i] :
( ( ( one @ ( A @ composition ) )
!= ( sk2 @ ( sk1 @ composition ) ) )
| ( ( one @ ( sk2 @ ( sk1 @ composition ) @ ( A @ converse @ composition ) @ join ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[41,23]) ).
thf(89,plain,
! [A: $i] :
( ( sk2 != one )
| ( A != sk1 )
| ( ( one @ ( sk2 @ ( sk1 @ composition ) @ ( A @ converse @ composition ) @ join ) )
!= one ) ),
inference(simp,[status(thm)],[81]) ).
thf(94,plain,
( ( sk2 != one )
| ( ( one @ ( sk2 @ ( sk1 @ composition ) @ ( sk1 @ converse @ composition ) @ join ) )
!= one ) ),
inference(simp,[status(thm)],[89]) ).
thf(100,plain,
! [A: $i] :
( ( ( one @ ( A @ composition ) )
!= ( sk2 @ ( sk1 @ composition ) ) )
| ( sk2 != one )
| ( ( one @ ( A @ ( sk1 @ converse @ composition ) @ join ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[41,94]) ).
thf(107,plain,
! [A: $i] :
( ( sk2 != one )
| ( A != sk1 )
| ( sk2 != one )
| ( ( one @ ( A @ ( sk1 @ converse @ composition ) @ join ) )
!= one ) ),
inference(simp,[status(thm)],[100]) ).
thf(112,plain,
( ( sk2 != one )
| ( ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) )
!= one ) ),
inference(simp,[status(thm)],[107]) ).
thf(277,plain,
( ( sk2 != one )
| ( one != one ) ),
inference(rewrite,[status(thm)],[112,21]) ).
thf(278,plain,
sk2 != one,
inference(simp,[status(thm)],[277]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ join ) @ converse )
= ( B @ converse @ ( A @ converse @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ join ) @ converse )
= ( B @ converse @ ( A @ converse @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(79,plain,
( ( ( one @ ( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) @ join ) )
!= ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) ) )
| ( one != one ) ),
inference(paramod_ordered,[status(thm)],[21,23]) ).
thf(80,plain,
( ( one @ ( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) @ join ) )
!= ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(90,plain,
( ( one != one )
| ( ( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) )
!= ( sk1 @ ( sk1 @ converse @ composition ) ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(95,plain,
( ( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) )
!= ( sk1 @ ( sk1 @ converse @ composition ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ converse )
= ( B @ converse @ ( A @ converse @ join ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ converse @ ( A @ converse @ join ) )
= ( B @ ( A @ join ) @ converse ) ),
inference(lifteq,[status(thm)],[49]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ composition ) @ converse )
= ( A @ converse @ ( B @ converse @ composition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ composition ) @ converse )
= ( A @ converse @ ( B @ converse @ composition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( one @ ( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) @ join ) ) )
| ( ( A @ ( B @ join ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[26,23]) ).
thf(227,plain,
( ( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) @ ( one @ join ) )
!= one ),
inference(pattern_uni,[status(thm)],[226:[bind(A,$thf( sk2 @ ( sk1 @ composition ) @ ( sk2 @ ( sk1 @ composition ) @ converse @ composition ) )),bind(B,$thf( one ))]]) ).
thf(922,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ converse @ composition ) @ complement @ ( one @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( top @ ( one @ join ) )
= ( A @ ( B @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[812,26]) ).
thf(923,plain,
( ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ complement @ join ) )
= ( top @ ( one @ join ) ) ),
inference(pattern_uni,[status(thm)],[922:[bind(A,$thf( one )),bind(B,$thf( sk1 @ ( sk1 @ converse @ composition ) @ complement ))]]) ).
thf(3992,plain,
$false,
inference(e,[status(thm)],[60,97,193,41,213,812,1094,1289,47,185,42,24,93,57,29,766,1104,38,429,21,33,32,45,22,44,59,27,71,54,1107,230,39,278,35,48,95,50,16,26,23,36,30,51,227,923]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL031+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n007.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 05:32:54 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.00/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.15 % [INFO] Parsing done (182ms).
% 1.55/1.16 % [INFO] Running in sequential loop mode.
% 2.35/1.50 % [INFO] eprover registered as external prover.
% 2.35/1.51 % [INFO] Scanning for conjecture ...
% 2.59/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.59/1.63 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.59/1.66 % [INFO] Problem is first-order (TPTP FOF).
% 2.59/1.66 % [INFO] Type checking passed.
% 2.59/1.67 % [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 ...
% 22.24/5.56 % External prover 'e' found a proof!
% 22.24/5.56 % [INFO] Killing All external provers ...
% 22.24/5.56 % Time passed: 5020ms (effective reasoning time: 4402ms)
% 22.24/5.56 % 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)>
% 22.24/5.57 % Axioms used in derivation (13): converse_cancellativity, composition_identity, converse_idempotence, composition_associativity, maddux3_a_kind_of_de_Morgan, maddux2_join_associativity, maddux1_join_commutativity, converse_multiplicativity, converse_additivity, def_top, def_zero, composition_distributivity, maddux4_definiton_of_meet
% 22.24/5.57 % No. of inferences in proof: 111
% 22.24/5.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5020 ms resp. 4402 ms w/o parsing
% 22.79/5.61 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.79/5.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------