%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : REL042+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 : n004.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 08:24:07 AM UTC 2026
% Result : Theorem 143.01s 47.48s
% Output : Refutation 134.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 15
% Syntax : Number of formulae : 290 ( 121 unt; 0 typ; 1 def)
% Number of atoms : 602 ( 601 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 2462 ( 409 ~; 306 |; 1 &;1742 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 276 ( 0 ^; 275 !; 0 ?; 276 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(composition_decl,type,
composition: $i > $i > $i ).
thf(complement_decl,type,
complement: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(join_decl,type,
join: $i > $i > $i ).
thf(converse_decl,type,
converse: $i > $i ).
thf(one_decl,type,
one: $i ).
thf(top_decl,type,
top: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ! [B: $i] :
( ( B @ complement @ ( A @ composition ) @ ( B @ ( A @ composition ) @ meet ) )
= zero )
=> ( ( one @ ( A @ ( A @ converse @ composition ) @ join ) )
= one ) ) ) ) ).
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(31,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ meet ) )
= ( B @ complement @ ( A @ complement @ join ) @ complement ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( B @ complement @ ( A @ complement @ join ) @ complement ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( B @ complement @ ( A @ complement @ join ) @ complement ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(14,axiom,
! [A: $i] :
( top
= ( A @ complement @ ( A @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
thf(55,plain,
! [A: $i] :
( top
= ( A @ complement @ ( A @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(56,plain,
! [A: $i] :
( top
= ( A @ complement @ ( A @ join ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [A: $i] :
( ( A @ complement @ ( A @ join ) )
= top ),
inference(lifteq,[status(thm)],[56]) ).
thf(245,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ complement @ ( A @ join ) )
!= ( C @ complement @ ( B @ complement @ join ) ) )
| ( ( C @ ( B @ meet ) )
= ( top @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[57,33]) ).
thf(246,plain,
! [A: $i] :
( ( A @ complement @ ( A @ meet ) )
= ( top @ complement ) ),
inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( E @ complement )),bind(B,$thf( E )),bind(C,$thf( E @ complement ))]]) ).
thf(284,plain,
! [A: $i] :
( ( A @ complement @ ( A @ meet ) )
= ( top @ complement ) ),
inference(simp,[status(thm)],[246]) ).
thf(15,axiom,
! [A: $i] :
( zero
= ( A @ complement @ ( A @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
thf(58,plain,
! [A: $i] :
( zero
= ( A @ complement @ ( A @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(59,plain,
! [A: $i] :
( zero
= ( A @ complement @ ( A @ meet ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(60,plain,
! [A: $i] :
( ( A @ complement @ ( A @ meet ) )
= zero ),
inference(lifteq,[status(thm)],[59]) ).
thf(579,plain,
( ( top @ complement )
= zero ),
inference(rewrite,[status(thm)],[284,60]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(111,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ complement @ ( A @ join ) )
!= ( B @ ( C @ join ) ) )
| ( ( C @ ( B @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[57,24]) ).
thf(112,plain,
! [A: $i] :
( ( A @ ( A @ complement @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( D )),bind(B,$thf( D @ complement )),bind(C,$thf( D ))]]) ).
thf(117,plain,
! [A: $i] :
( ( A @ ( A @ complement @ join ) )
= top ),
inference(simp,[status(thm)],[112]) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ complement @ join ) )
!= ( C @ complement @ ( B @ complement @ join ) ) )
| ( ( C @ ( B @ meet ) )
= ( top @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[117,33]) ).
thf(261,plain,
! [A: $i] :
( ( A @ ( A @ complement @ meet ) )
= ( top @ complement ) ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( D @ complement )),bind(B,$thf( D @ complement )),bind(C,$thf( D ))]]) ).
thf(274,plain,
! [A: $i] :
( ( A @ ( A @ complement @ meet ) )
= ( top @ complement ) ),
inference(simp,[status(thm)],[261]) ).
thf(580,plain,
! [A: $i] :
( ( A @ ( A @ complement @ meet ) )
= zero ),
inference(rewrite,[status(thm)],[274,579]) ).
thf(1744,plain,
! [A: $i] :
( ( ( top @ complement )
!= ( A @ complement ) )
| ( ( A @ ( zero @ meet ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[579,580]) ).
thf(1745,plain,
( ( top @ ( zero @ meet ) )
= zero ),
inference(pattern_uni,[status(thm)],[1744:[bind(A,$thf( top ))]]) ).
thf(1787,plain,
! [B: $i,A: $i] :
( ( ( top @ ( zero @ meet ) )
!= ( B @ ( A @ meet ) ) )
| ( ( B @ complement @ ( A @ complement @ join ) @ complement )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1745,33]) ).
thf(1788,plain,
( ( top @ complement @ ( zero @ complement @ join ) @ complement )
= zero ),
inference(pattern_uni,[status(thm)],[1787:[bind(A,$thf( zero )),bind(B,$thf( top ))]]) ).
thf(1946,plain,
( ( zero @ ( zero @ complement @ join ) @ complement )
= zero ),
inference(rewrite,[status(thm)],[1788,579]) ).
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(28,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(29,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ complement @ join ) @ complement @ ( B @ complement @ ( A @ complement @ join ) @ complement @ join ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement @ join ) @ complement @ ( B @ complement @ ( A @ complement @ join ) @ complement @ join ) )
= A ),
inference(lifteq,[status(thm)],[29]) ).
thf(2009,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( zero @ complement @ join ) @ complement )
!= ( B @ ( A @ complement @ join ) @ complement ) )
| ( ( zero @ ( B @ complement @ ( A @ complement @ join ) @ complement @ join ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[1946,30]) ).
thf(2010,plain,
( ( zero @ ( zero @ complement @ ( zero @ complement @ join ) @ complement @ join ) )
= zero ),
inference(pattern_uni,[status(thm)],[2009:[bind(A,$thf( zero )),bind(B,$thf( zero ))]]) ).
thf(2190,plain,
! [B: $i,A: $i] :
( ( ( B @ complement @ ( A @ complement @ join ) @ complement )
!= ( zero @ complement @ ( zero @ complement @ join ) @ complement ) )
| ( ( zero @ ( B @ ( A @ meet ) @ join ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[33,2010]) ).
thf(2191,plain,
( ( zero @ ( zero @ ( zero @ meet ) @ join ) )
= zero ),
inference(pattern_uni,[status(thm)],[2190:[bind(A,$thf( zero )),bind(B,$thf( zero ))]]) ).
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(25,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(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ join ) @ ( A @ join ) )
= ( C @ ( B @ ( A @ join ) @ join ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ join ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ join ) @ join ) )
!= ( D @ complement @ ( D @ join ) ) )
| ( ( C @ ( B @ join ) @ ( A @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[27,57]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ complement @ ( B @ join ) @ ( A @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( I @ ( H @ join ) @ complement )),bind(D,$thf( I @ ( H @ join ) ))]]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ complement @ ( B @ join ) @ ( A @ join ) )
= top ),
inference(simp,[status(thm)],[193]) ).
thf(6672,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( zero @ ( zero @ meet ) @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( zero @ complement @ ( B @ join ) @ ( A @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[2191,209]) ).
thf(6673,plain,
( ( zero @ complement @ ( zero @ join ) @ ( zero @ ( zero @ meet ) @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[6672:[bind(A,$thf( zero @ ( zero @ meet ) )),bind(B,$thf( zero ))]]) ).
thf(9052,plain,
( ( top @ ( zero @ ( zero @ meet ) @ join ) )
= top ),
inference(rewrite,[status(thm)],[6673,57]) ).
thf(606,plain,
! [A: $i] :
( ( ( top @ complement )
!= ( A @ complement ) )
| ( ( zero @ ( A @ meet ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[579,60]) ).
thf(607,plain,
( ( zero @ ( top @ meet ) )
= zero ),
inference(pattern_uni,[status(thm)],[606:[bind(A,$thf( top ))]]) ).
thf(705,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( top @ meet ) )
!= ( B @ ( A @ meet ) ) )
| ( ( B @ complement @ ( A @ complement @ join ) @ complement )
= zero ) ),
inference(paramod_ordered,[status(thm)],[607,33]) ).
thf(706,plain,
( ( zero @ complement @ ( top @ complement @ join ) @ complement )
= zero ),
inference(pattern_uni,[status(thm)],[705:[bind(A,$thf( top )),bind(B,$thf( zero ))]]) ).
thf(839,plain,
( ( zero @ complement @ ( zero @ join ) @ complement )
= zero ),
inference(rewrite,[status(thm)],[706,579]) ).
thf(860,plain,
! [A: $i] :
( ( ( zero @ complement @ ( zero @ join ) @ complement )
!= ( A @ complement ) )
| ( ( zero @ ( A @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[839,57]) ).
thf(861,plain,
( ( zero @ ( zero @ complement @ ( zero @ join ) @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[860:[bind(A,$thf( zero @ complement @ ( zero @ join ) ))]]) ).
thf(1074,plain,
( ( zero @ ( zero @ complement @ join ) @ ( zero @ join ) )
= top ),
inference(rewrite,[status(thm)],[861,27]) ).
thf(1093,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( zero @ complement @ join ) @ ( zero @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[1074,24]) ).
thf(1094,plain,
( ( zero @ ( zero @ ( zero @ complement @ join ) @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[1093:[bind(A,$thf( zero )),bind(B,$thf( zero @ ( zero @ complement @ join ) ))]]) ).
thf(1183,plain,
( ( zero @ ( zero @ join ) @ ( zero @ complement @ join ) )
= top ),
inference(rewrite,[status(thm)],[1094,27]) ).
thf(1196,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( zero @ join ) @ ( zero @ complement @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[1183,24]) ).
thf(1197,plain,
( ( zero @ complement @ ( zero @ ( zero @ join ) @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[1196:[bind(A,$thf( zero @ complement )),bind(B,$thf( zero @ ( zero @ join ) ))]]) ).
thf(1425,plain,
( ( zero @ complement @ ( zero @ join ) @ ( zero @ join ) )
= top ),
inference(rewrite,[status(thm)],[1197,27]) ).
thf(1,conjecture,
! [A: $i] :
( ! [B: $i] :
( ( B @ complement @ ( A @ composition ) @ ( B @ ( A @ composition ) @ meet ) )
= zero )
=> ( ( one @ ( A @ ( A @ converse @ composition ) @ join ) )
= one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ! [B: $i] :
( ( B @ complement @ ( A @ composition ) @ ( B @ ( A @ composition ) @ meet ) )
= zero )
=> ( ( one @ ( A @ ( A @ converse @ composition ) @ join ) )
= one ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i] :
( ! [B: $i] :
( ( B @ complement @ ( A @ composition ) @ ( B @ ( A @ composition ) @ meet ) )
= zero )
=> ( ( one @ ( A @ ( A @ converse @ composition ) @ join ) )
= one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
! [A: $i] :
( ( ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) )
!= one )
& ( ( A @ complement @ ( sk1 @ composition ) @ ( A @ ( sk1 @ composition ) @ meet ) )
= zero ) ),
inference(cnf,[status(esa)],[16]) ).
thf(19,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)],[19]) ).
thf(2353,plain,
( ( ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) )
!= ( zero @ ( zero @ ( zero @ meet ) @ join ) ) )
| ( one != zero ) ),
inference(paramod_ordered,[status(thm)],[2191,21]) ).
thf(2429,plain,
( ( one != zero )
| ( ( sk1 @ ( sk1 @ converse @ composition ) )
!= ( zero @ ( zero @ meet ) ) )
| ( one != zero ) ),
inference(simp,[status(thm)],[2353]) ).
thf(2452,plain,
( ( ( sk1 @ ( sk1 @ converse @ composition ) )
!= ( zero @ ( zero @ meet ) ) )
| ( one != zero ) ),
inference(simp,[status(thm)],[2429]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ converse @ converse )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
thf(43,plain,
! [A: $i] :
( ( A @ converse @ converse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(44,plain,
! [A: $i] :
( ( A @ converse @ converse )
= A ),
inference(cnf,[status(esa)],[43]) ).
thf(45,plain,
! [A: $i] :
( ( A @ converse @ converse )
= A ),
inference(lifteq,[status(thm)],[44]) ).
thf(8,axiom,
! [A: $i] :
( ( one @ ( A @ composition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
thf(37,plain,
! [A: $i] :
( ( one @ ( A @ composition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(38,plain,
! [A: $i] :
( ( one @ ( A @ composition ) )
= A ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [A: $i] :
( ( one @ ( A @ composition ) )
= A ),
inference(lifteq,[status(thm)],[38]) ).
thf(61,plain,
! [A: $i] :
( ( ( one @ ( A @ composition ) )
!= ( sk1 @ ( sk1 @ converse @ composition ) ) )
| ( ( one @ ( A @ join ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[39,21]) ).
thf(62,plain,
! [A: $i] :
( ( sk1 != one )
| ( A
!= ( sk1 @ converse ) )
| ( ( one @ ( A @ join ) )
!= one ) ),
inference(simp,[status(thm)],[61]) ).
thf(63,plain,
( ( sk1 != one )
| ( ( one @ ( sk1 @ converse @ join ) )
!= one ) ),
inference(simp,[status(thm)],[62]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( one @ ( sk1 @ converse @ join ) ) )
| ( sk1 != one )
| ( ( A @ ( B @ join ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[24,63]) ).
thf(104,plain,
( ( sk1 != one )
| ( ( sk1 @ converse @ ( one @ join ) )
!= one ) ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( sk1 @ converse )),bind(B,$thf( one ))]]) ).
thf(132,plain,
! [A: $i] :
( ( ( A @ complement @ ( A @ join ) )
!= ( sk1 @ converse @ ( one @ join ) ) )
| ( sk1 != one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[57,104]) ).
thf(134,plain,
! [A: $i] :
( ( ( A @ complement )
!= ( sk1 @ converse ) )
| ( A != one )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[132]) ).
thf(135,plain,
( ( ( sk1 @ converse )
!= ( one @ complement ) )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[134]) ).
thf(345,plain,
! [A: $i] :
( ( ( A @ converse @ converse )
!= ( sk1 @ converse ) )
| ( A
!= ( one @ complement ) )
| ( sk1 != one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[45,135]) ).
thf(347,plain,
( ( ( one @ complement @ converse )
!= sk1 )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[345]) ).
thf(18,plain,
! [A: $i] :
( ( A @ complement @ ( sk1 @ composition ) @ ( A @ ( sk1 @ composition ) @ meet ) )
= zero ),
inference(cnfConj,[status(thm)],[17]) ).
thf(20,plain,
! [A: $i] :
( ( A @ complement @ ( sk1 @ composition ) @ ( A @ ( sk1 @ composition ) @ meet ) )
= zero ),
inference(lifteq,[status(thm)],[18]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( ( one @ ( A @ composition ) )
!= ( B @ ( sk1 @ composition ) ) )
| ( ( B @ complement @ ( sk1 @ composition ) @ ( A @ meet ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[39,20]) ).
thf(88,plain,
( ( one @ complement @ ( sk1 @ composition ) @ ( sk1 @ meet ) )
= zero ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( sk1 )),bind(B,$thf( one ))]]) ).
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(40,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(41,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ composition ) )
= ( C @ ( B @ composition ) @ ( C @ ( A @ composition ) @ join ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ composition ) @ ( C @ ( A @ composition ) @ join ) )
= ( C @ ( B @ ( A @ join ) @ composition ) ) ),
inference(lifteq,[status(thm)],[41]) ).
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(52,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(72,plain,
! [A: $i] :
( ( ( A @ converse @ converse )
!= ( sk1 @ converse ) )
| ( sk1 != one )
| ( ( one @ ( A @ join ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[45,63]) ).
thf(74,plain,
! [A: $i] :
( ( ( A @ converse )
!= sk1 )
| ( sk1 != one )
| ( ( one @ ( A @ join ) )
!= one ) ),
inference(simp,[status(thm)],[72]) ).
thf(9103,plain,
! [A: $i] :
( ( ( top @ ( zero @ ( zero @ meet ) @ join ) )
!= ( one @ ( A @ join ) ) )
| ( ( A @ converse )
!= sk1 )
| ( sk1 != one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[9052,74]) ).
thf(9240,plain,
! [A: $i] :
( ( top != one )
| ( ( zero @ ( zero @ meet ) )
!= A )
| ( ( A @ converse )
!= sk1 )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[9103]) ).
thf(9315,plain,
( ( ( zero @ ( zero @ meet ) @ converse )
!= sk1 )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[9240]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= ( one @ complement @ ( sk1 @ composition ) @ ( sk1 @ meet ) ) )
| ( ( B @ complement @ ( A @ complement @ join ) @ complement )
= zero ) ),
inference(paramod_ordered,[status(thm)],[33,88]) ).
thf(227,plain,
( ( one @ complement @ ( sk1 @ composition ) @ complement @ ( sk1 @ complement @ join ) @ complement )
= zero ),
inference(pattern_uni,[status(thm)],[226:[bind(A,$thf( sk1 )),bind(B,$thf( one @ complement @ ( sk1 @ composition ) ))]]) ).
thf(459,plain,
! [B: $i,A: $i] :
( ( ( one @ complement @ ( sk1 @ composition ) @ complement @ ( sk1 @ complement @ join ) @ complement )
!= ( B @ complement @ ( A @ complement @ join ) @ complement ) )
| ( ( B @ ( A @ complement @ join ) @ complement @ ( zero @ join ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[227,30]) ).
thf(460,plain,
( ( one @ complement @ ( sk1 @ composition ) @ ( sk1 @ complement @ join ) @ complement @ ( zero @ join ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[459:[bind(A,$thf( sk1 )),bind(B,$thf( one @ complement @ ( sk1 @ composition ) ))]]) ).
thf(96,plain,
! [A: $i] :
( ( ( one @ ( A @ composition ) )
!= ( one @ complement @ ( sk1 @ composition ) ) )
| ( ( A @ ( sk1 @ meet ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[39,88]) ).
thf(101,plain,
! [A: $i] :
( ( ( one @ complement )
!= one )
| ( A != sk1 )
| ( ( A @ ( sk1 @ meet ) )
= zero ) ),
inference(simp,[status(thm)],[96]) ).
thf(102,plain,
( ( ( one @ complement )
!= one )
| ( ( sk1 @ ( sk1 @ meet ) )
= zero ) ),
inference(simp,[status(thm)],[101]) ).
thf(605,plain,
( ( ( top @ complement )
!= ( one @ complement ) )
| ( one != zero )
| ( ( sk1 @ ( sk1 @ meet ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[579,102]) ).
thf(619,plain,
( ( top != one )
| ( one != zero )
| ( ( sk1 @ ( sk1 @ meet ) )
= zero ) ),
inference(simp,[status(thm)],[605]) ).
thf(71,plain,
! [A: $i] :
( ( ( A @ complement @ ( A @ join ) )
!= ( one @ ( sk1 @ converse @ join ) ) )
| ( sk1 != one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[57,63]) ).
thf(73,plain,
! [A: $i] :
( ( ( A @ complement )
!= one )
| ( A
!= ( sk1 @ converse ) )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[71]) ).
thf(75,plain,
( ( ( sk1 @ converse @ complement )
!= one )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[73]) ).
thf(585,plain,
( ( ( sk1 @ converse @ complement )
!= ( top @ complement ) )
| ( one != zero )
| ( sk1 != one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[579,75]) ).
thf(622,plain,
( ( ( sk1 @ converse )
!= top )
| ( one != zero )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[585]) ).
thf(836,plain,
! [A: $i] :
( ( ( A @ converse @ converse )
!= ( sk1 @ converse ) )
| ( A != top )
| ( one != zero )
| ( sk1 != one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[45,622]) ).
thf(838,plain,
( ( ( top @ converse )
!= sk1 )
| ( one != zero )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[836]) ).
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(46,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ join ) @ converse )
= ( B @ converse @ ( A @ converse @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(68,plain,
! [A: $i] :
( ( ( A @ complement @ ( A @ join ) )
!= ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) ) )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[57,21]) ).
thf(69,plain,
! [A: $i] :
( ( ( A @ complement )
!= one )
| ( A
!= ( sk1 @ ( sk1 @ converse @ composition ) ) )
| ( top != one ) ),
inference(simp,[status(thm)],[68]) ).
thf(70,plain,
( ( ( sk1 @ ( sk1 @ converse @ composition ) @ complement )
!= one )
| ( top != one ) ),
inference(simp,[status(thm)],[69]) ).
thf(76,plain,
! [A: $i] :
( ( ( A @ converse @ converse )
!= ( sk1 @ converse ) )
| ( ( sk1 @ ( A @ composition ) @ complement )
!= one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[45,70]) ).
thf(78,plain,
! [A: $i] :
( ( ( A @ converse )
!= sk1 )
| ( ( sk1 @ ( A @ composition ) @ complement )
!= one )
| ( top != one ) ),
inference(simp,[status(thm)],[76]) ).
thf(603,plain,
! [A: $i] :
( ( ( top @ complement )
!= ( A @ complement ) )
| ( ( zero @ ( A @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[579,57]) ).
thf(604,plain,
( ( zero @ ( top @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[603:[bind(A,$thf( top ))]]) ).
thf(6598,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( top @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( top @ complement @ ( B @ join ) @ ( A @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[604,209]) ).
thf(6599,plain,
( ( top @ complement @ ( zero @ join ) @ ( top @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[6598:[bind(A,$thf( top )),bind(B,$thf( zero ))]]) ).
thf(6848,plain,
( ( zero @ ( zero @ join ) @ ( top @ join ) )
= top ),
inference(rewrite,[status(thm)],[6599,579]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) ) )
| ( ( A @ ( B @ join ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[24,21]) ).
thf(114,plain,
( ( sk1 @ ( sk1 @ converse @ composition ) @ ( one @ join ) )
!= one ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( sk1 @ ( sk1 @ converse @ composition ) )),bind(B,$thf( one ))]]) ).
thf(6975,plain,
( ( ( zero @ ( zero @ join ) @ ( top @ join ) )
!= ( sk1 @ ( sk1 @ converse @ composition ) @ ( one @ join ) ) )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[6848,114]) ).
thf(7063,plain,
( ( ( zero @ ( zero @ join ) )
!= ( sk1 @ ( sk1 @ converse @ composition ) ) )
| ( top != one )
| ( top != one ) ),
inference(simp,[status(thm)],[6975]) ).
thf(7094,plain,
( ( ( zero @ ( zero @ join ) )
!= ( sk1 @ ( sk1 @ converse @ composition ) ) )
| ( top != one ) ),
inference(simp,[status(thm)],[7063]) ).
thf(7878,plain,
( ( ( zero @ ( top @ join ) )
!= ( zero @ ( zero @ join ) ) )
| ( ( sk1 @ ( sk1 @ converse @ composition ) )
!= top )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[604,7094]) ).
thf(7896,plain,
( ( zero != zero )
| ( top != zero )
| ( ( sk1 @ ( sk1 @ converse @ composition ) )
!= top )
| ( top != one ) ),
inference(simp,[status(thm)],[7878]) ).
thf(7926,plain,
( ( top != zero )
| ( ( sk1 @ ( sk1 @ converse @ composition ) )
!= top )
| ( top != one ) ),
inference(simp,[status(thm)],[7896]) ).
thf(298,plain,
! [A: $i] :
( ( ( one @ complement @ ( sk1 @ composition ) @ complement @ ( sk1 @ complement @ join ) @ complement )
!= ( A @ complement ) )
| ( ( zero @ ( A @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[227,57]) ).
thf(299,plain,
( ( zero @ ( one @ complement @ ( sk1 @ composition ) @ complement @ ( sk1 @ complement @ join ) @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[298:[bind(A,$thf( one @ complement @ ( sk1 @ composition ) @ complement @ ( sk1 @ complement @ join ) ))]]) ).
thf(348,plain,
( ( zero @ ( one @ complement @ ( sk1 @ composition ) @ complement @ join ) @ ( sk1 @ complement @ join ) )
= top ),
inference(rewrite,[status(thm)],[299,27]) ).
thf(349,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( one @ complement @ ( sk1 @ composition ) @ complement @ join ) @ ( sk1 @ complement @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[348,24]) ).
thf(350,plain,
( ( sk1 @ complement @ ( zero @ ( one @ complement @ ( sk1 @ composition ) @ complement @ join ) @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[349:[bind(A,$thf( sk1 @ complement )),bind(B,$thf( zero @ ( one @ complement @ ( sk1 @ composition ) @ complement @ join ) ))]]) ).
thf(3453,plain,
( ( sk1 @ complement @ ( zero @ join ) @ ( one @ complement @ ( sk1 @ composition ) @ complement @ join ) )
= top ),
inference(rewrite,[status(thm)],[350,27]) ).
thf(581,plain,
( ( ( top @ complement )
!= ( one @ complement ) )
| ( ( zero @ ( sk1 @ composition ) @ ( sk1 @ meet ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[579,88]) ).
thf(623,plain,
( ( top != one )
| ( ( zero @ ( sk1 @ composition ) @ ( sk1 @ meet ) )
= zero ) ),
inference(simp,[status(thm)],[581]) ).
thf(601,plain,
! [A: $i] :
( ( ( top @ complement )
!= ( A @ complement ) )
| ( ( zero @ ( sk1 @ composition ) @ ( A @ ( sk1 @ composition ) @ meet ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[579,20]) ).
thf(602,plain,
( ( zero @ ( sk1 @ composition ) @ ( top @ ( sk1 @ composition ) @ meet ) )
= zero ),
inference(pattern_uni,[status(thm)],[601:[bind(A,$thf( top ))]]) ).
thf(131,plain,
! [A: $i] :
( ( ( A @ converse @ converse )
!= ( sk1 @ converse ) )
| ( sk1 != one )
| ( ( A @ ( one @ join ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[45,104]) ).
thf(133,plain,
! [A: $i] :
( ( ( A @ converse )
!= sk1 )
| ( sk1 != one )
| ( ( A @ ( one @ join ) )
!= one ) ),
inference(simp,[status(thm)],[131]) ).
thf(2153,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( zero @ complement @ ( zero @ complement @ join ) @ complement @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[2010,24]) ).
thf(2154,plain,
( ( zero @ complement @ ( zero @ complement @ join ) @ complement @ ( zero @ join ) )
= zero ),
inference(pattern_uni,[status(thm)],[2153:[bind(A,$thf( zero @ complement @ ( zero @ complement @ join ) @ complement )),bind(B,$thf( zero ))]]) ).
thf(942,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( sk1 @ composition ) @ ( top @ ( sk1 @ composition ) @ meet ) )
!= ( B @ ( A @ meet ) ) )
| ( ( B @ complement @ ( A @ complement @ join ) @ complement )
= zero ) ),
inference(paramod_ordered,[status(thm)],[602,33]) ).
thf(943,plain,
( ( zero @ ( sk1 @ composition ) @ complement @ ( top @ ( sk1 @ composition ) @ complement @ join ) @ complement )
= zero ),
inference(pattern_uni,[status(thm)],[942:[bind(A,$thf( top @ ( sk1 @ composition ) )),bind(B,$thf( zero @ ( sk1 @ composition ) ))]]) ).
thf(4235,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( zero @ ( sk1 @ composition ) @ complement @ ( top @ ( sk1 @ composition ) @ complement @ join ) ) )
| ( ( A @ ( B @ join ) @ complement )
= zero ) ),
inference(paramod_ordered,[status(thm)],[24,943]) ).
thf(4236,plain,
( ( top @ ( sk1 @ composition ) @ complement @ ( zero @ ( sk1 @ composition ) @ complement @ join ) @ complement )
= zero ),
inference(pattern_uni,[status(thm)],[4235:[bind(A,$thf( top @ ( sk1 @ composition ) @ complement )),bind(B,$thf( zero @ ( sk1 @ composition ) @ complement ))]]) ).
thf(5992,plain,
! [B: $i,A: $i] :
( ( ( top @ ( sk1 @ composition ) @ complement @ ( zero @ ( sk1 @ composition ) @ complement @ join ) @ complement )
!= ( B @ complement @ ( A @ complement @ join ) @ complement ) )
| ( ( B @ ( A @ meet ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[4236,33]) ).
thf(5993,plain,
( ( top @ ( sk1 @ composition ) @ ( zero @ ( sk1 @ composition ) @ meet ) )
= zero ),
inference(pattern_uni,[status(thm)],[5992:[bind(A,$thf( zero @ ( sk1 @ composition ) )),bind(B,$thf( top @ ( sk1 @ composition ) ))]]) ).
thf(6234,plain,
! [A: $i] :
( ( ( one @ ( A @ composition ) )
!= ( zero @ ( sk1 @ composition ) ) )
| ( ( top @ ( sk1 @ composition ) @ ( A @ meet ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[39,5993]) ).
thf(6273,plain,
! [A: $i] :
( ( one != zero )
| ( A != sk1 )
| ( ( top @ ( sk1 @ composition ) @ ( A @ meet ) )
= zero ) ),
inference(simp,[status(thm)],[6234]) ).
thf(6282,plain,
( ( one != zero )
| ( ( top @ ( sk1 @ composition ) @ ( sk1 @ meet ) )
= zero ) ),
inference(simp,[status(thm)],[6273]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ meet ) )
!= ( sk1 @ ( sk1 @ meet ) ) )
| ( ( one @ complement )
!= one )
| ( ( B @ complement @ ( A @ complement @ join ) @ complement )
= zero ) ),
inference(paramod_ordered,[status(thm)],[33,102]) ).
thf(248,plain,
( ( ( one @ complement )
!= one )
| ( ( sk1 @ complement @ ( sk1 @ complement @ join ) @ complement )
= zero ) ),
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(6865,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( zero @ join ) @ ( top @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[6848,24]) ).
thf(6866,plain,
( ( top @ ( zero @ ( zero @ join ) @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[6865:[bind(A,$thf( top )),bind(B,$thf( zero @ ( zero @ join ) ))]]) ).
thf(7111,plain,
( ( top @ ( zero @ join ) @ ( zero @ join ) )
= top ),
inference(rewrite,[status(thm)],[6866,27]) ).
thf(7127,plain,
! [B: $i,A: $i] :
( ( ( top @ ( zero @ join ) @ ( zero @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[7111,24]) ).
thf(7128,plain,
( ( zero @ ( top @ ( zero @ join ) @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[7127:[bind(A,$thf( zero )),bind(B,$thf( top @ ( zero @ join ) ))]]) ).
thf(7393,plain,
( ( zero @ ( top @ join ) @ ( zero @ join ) )
= top ),
inference(rewrite,[status(thm)],[7128,27]) ).
thf(121,plain,
! [A: $i] :
( ( ( A @ converse @ converse )
!= ( sk1 @ converse ) )
| ( ( sk1 @ ( A @ composition ) @ ( one @ join ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[45,114]) ).
thf(124,plain,
! [A: $i] :
( ( ( A @ converse )
!= sk1 )
| ( ( sk1 @ ( A @ composition ) @ ( one @ join ) )
!= one ) ),
inference(simp,[status(thm)],[121]) ).
thf(6907,plain,
! [A: $i] :
( ( ( zero @ ( zero @ join ) @ ( top @ join ) )
!= ( A @ ( one @ join ) ) )
| ( ( A @ converse )
!= sk1 )
| ( sk1 != one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[6848,133]) ).
thf(7048,plain,
! [A: $i] :
( ( ( zero @ ( zero @ join ) )
!= A )
| ( top != one )
| ( ( A @ converse )
!= sk1 )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[6907]) ).
thf(7087,plain,
( ( ( zero @ ( zero @ join ) @ converse )
!= sk1 )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[7048]) ).
thf(7790,plain,
( ( ( zero @ ( top @ join ) )
!= ( zero @ ( zero @ join ) ) )
| ( ( top @ converse )
!= sk1 )
| ( sk1 != one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[604,7087]) ).
thf(7818,plain,
( ( zero != zero )
| ( top != zero )
| ( ( top @ converse )
!= sk1 )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[7790]) ).
thf(7841,plain,
( ( top != zero )
| ( ( top @ converse )
!= sk1 )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[7818]) ).
thf(2321,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( zero @ ( zero @ meet ) @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[2191,24]) ).
thf(2322,plain,
( ( zero @ ( zero @ meet ) @ ( zero @ join ) )
= zero ),
inference(pattern_uni,[status(thm)],[2321:[bind(A,$thf( zero @ ( zero @ meet ) )),bind(B,$thf( zero ))]]) ).
thf(6629,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( zero @ meet ) @ ( zero @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( zero @ complement @ ( B @ join ) @ ( A @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[2322,209]) ).
thf(6630,plain,
( ( zero @ complement @ ( zero @ ( zero @ meet ) @ join ) @ ( zero @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[6629:[bind(A,$thf( zero )),bind(B,$thf( zero @ ( zero @ meet ) ))]]) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ complement @ join ) )
!= ( C @ ( B @ join ) ) )
| ( ( D @ ( top @ join ) )
= ( D @ ( C @ join ) @ ( B @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[117,27]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ join ) @ ( B @ complement @ join ) )
= ( A @ ( top @ join ) ) ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( E )),bind(B,$thf( E @ complement )),bind(C,$thf( E ))]]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ join ) @ ( B @ complement @ join ) )
= ( A @ ( top @ join ) ) ),
inference(simp,[status(thm)],[200]) ).
thf(2366,plain,
( ( ( zero @ ( zero @ ( zero @ meet ) @ join ) )
!= ( one @ ( sk1 @ converse @ join ) ) )
| ( sk1 != one )
| ( one != zero ) ),
inference(paramod_ordered,[status(thm)],[2191,63]) ).
thf(2427,plain,
( ( one != zero )
| ( ( zero @ ( zero @ meet ) )
!= ( sk1 @ converse ) )
| ( sk1 != one )
| ( one != zero ) ),
inference(simp,[status(thm)],[2366]) ).
thf(2450,plain,
( ( ( zero @ ( zero @ meet ) )
!= ( sk1 @ converse ) )
| ( sk1 != one )
| ( one != zero ) ),
inference(simp,[status(thm)],[2427]) ).
thf(6974,plain,
( ( ( zero @ ( zero @ join ) @ ( top @ join ) )
!= ( sk1 @ converse @ ( one @ join ) ) )
| ( sk1 != one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[6848,104]) ).
thf(7047,plain,
( ( ( zero @ ( zero @ join ) )
!= ( sk1 @ converse ) )
| ( top != one )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[6974]) ).
thf(7086,plain,
( ( ( zero @ ( zero @ join ) )
!= ( sk1 @ converse ) )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[7047]) ).
thf(2615,plain,
! [A: $i] :
( ( ( A @ ( A @ complement @ meet ) )
!= ( zero @ ( zero @ meet ) ) )
| ( ( sk1 @ converse )
!= zero )
| ( sk1 != one )
| ( one != zero ) ),
inference(paramod_ordered,[status(thm)],[580,2450]) ).
thf(2628,plain,
! [A: $i] :
( ( A != zero )
| ( ( A @ complement )
!= zero )
| ( ( sk1 @ converse )
!= zero )
| ( sk1 != one )
| ( one != zero ) ),
inference(simp,[status(thm)],[2615]) ).
thf(2634,plain,
( ( ( zero @ complement )
!= zero )
| ( ( sk1 @ converse )
!= zero )
| ( sk1 != one )
| ( one != zero ) ),
inference(simp,[status(thm)],[2628]) ).
thf(123,plain,
! [A: $i] :
( ( ( A @ complement @ ( A @ join ) )
!= ( sk1 @ ( sk1 @ converse @ composition ) @ ( one @ join ) ) )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[57,114]) ).
thf(126,plain,
! [A: $i] :
( ( ( A @ complement )
!= ( sk1 @ ( sk1 @ converse @ composition ) ) )
| ( A != one )
| ( top != one ) ),
inference(simp,[status(thm)],[123]) ).
thf(128,plain,
( ( ( sk1 @ ( sk1 @ converse @ composition ) )
!= ( one @ complement ) )
| ( top != one ) ),
inference(simp,[status(thm)],[126]) ).
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(34,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(3984,plain,
! [B: $i,A: $i] :
( ( ( one @ complement @ ( sk1 @ composition ) @ ( sk1 @ complement @ join ) @ complement @ ( zero @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= sk1 ) ),
inference(paramod_ordered,[status(thm)],[460,24]) ).
thf(3985,plain,
( ( zero @ ( one @ complement @ ( sk1 @ composition ) @ ( sk1 @ complement @ join ) @ complement @ join ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[3984:[bind(A,$thf( zero )),bind(B,$thf( one @ complement @ ( sk1 @ composition ) @ ( sk1 @ complement @ join ) @ complement ))]]) ).
thf(9061,plain,
! [B: $i,A: $i] :
( ( ( top @ ( zero @ ( zero @ meet ) @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[9052,24]) ).
thf(9062,plain,
( ( zero @ ( zero @ meet ) @ ( top @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[9061:[bind(A,$thf( zero @ ( zero @ meet ) )),bind(B,$thf( top ))]]) ).
thf(648,plain,
( ( ( zero @ ( top @ join ) )
!= ( sk1 @ converse @ ( one @ join ) ) )
| ( sk1 != one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[604,104]) ).
thf(680,plain,
( ( ( sk1 @ converse )
!= zero )
| ( top != one )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[648]) ).
thf(685,plain,
( ( ( sk1 @ converse )
!= zero )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[680]) ).
thf(709,plain,
! [A: $i] :
( ( ( A @ converse @ converse )
!= ( sk1 @ converse ) )
| ( A != zero )
| ( sk1 != one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[45,685]) ).
thf(711,plain,
( ( ( zero @ converse )
!= sk1 )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[709]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ complement @ ( B @ ( A @ composition ) @ complement @ ( A @ converse @ composition ) @ join ) )
= ( B @ complement ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ complement @ ( B @ ( A @ composition ) @ complement @ ( A @ converse @ composition ) @ join ) )
= ( B @ complement ) ),
inference(lifteq,[status(thm)],[53]) ).
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(49,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ composition ) @ converse )
= ( A @ converse @ ( B @ converse @ composition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6235,plain,
! [A: $i] :
( ( ( one @ ( A @ composition ) )
!= ( top @ ( sk1 @ composition ) ) )
| ( ( A @ ( zero @ ( sk1 @ composition ) @ meet ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[39,5993]) ).
thf(6272,plain,
! [A: $i] :
( ( top != one )
| ( A != sk1 )
| ( ( A @ ( zero @ ( sk1 @ composition ) @ meet ) )
= zero ) ),
inference(simp,[status(thm)],[6235]) ).
thf(6281,plain,
( ( top != one )
| ( ( sk1 @ ( zero @ ( sk1 @ composition ) @ meet ) )
= zero ) ),
inference(simp,[status(thm)],[6272]) ).
thf(2820,plain,
! [A: $i] :
( ( ( zero @ ( zero @ ( zero @ meet ) @ join ) )
!= ( one @ ( A @ join ) ) )
| ( ( A @ converse )
!= sk1 )
| ( sk1 != one )
| ( one != zero ) ),
inference(paramod_ordered,[status(thm)],[2191,74]) ).
thf(2826,plain,
! [A: $i] :
( ( one != zero )
| ( ( zero @ ( zero @ meet ) )
!= A )
| ( ( A @ converse )
!= sk1 )
| ( sk1 != one )
| ( one != zero ) ),
inference(simp,[status(thm)],[2820]) ).
thf(2843,plain,
( ( ( zero @ ( zero @ meet ) @ converse )
!= sk1 )
| ( sk1 != one )
| ( one != zero ) ),
inference(simp,[status(thm)],[2826]) ).
thf(3681,plain,
! [A: $i] :
( ( ( A @ complement @ ( A @ meet ) )
!= ( zero @ ( zero @ meet ) ) )
| ( ( zero @ converse )
!= sk1 )
| ( sk1 != one )
| ( one != zero ) ),
inference(paramod_ordered,[status(thm)],[60,2843]) ).
thf(3700,plain,
! [A: $i] :
( ( ( A @ complement )
!= zero )
| ( A != zero )
| ( ( zero @ converse )
!= sk1 )
| ( sk1 != one )
| ( one != zero ) ),
inference(simp,[status(thm)],[3681]) ).
thf(3710,plain,
( ( ( zero @ complement )
!= zero )
| ( ( zero @ converse )
!= sk1 )
| ( sk1 != one )
| ( one != zero ) ),
inference(simp,[status(thm)],[3700]) ).
thf(302,plain,
! [A: $i] :
( ( ( one @ complement @ ( sk1 @ composition ) @ complement @ ( sk1 @ complement @ join ) @ complement )
!= ( A @ complement ) )
| ( ( zero @ ( A @ meet ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[227,60]) ).
thf(303,plain,
( ( zero @ ( one @ complement @ ( sk1 @ composition ) @ complement @ ( sk1 @ complement @ join ) @ meet ) )
= zero ),
inference(pattern_uni,[status(thm)],[302:[bind(A,$thf( one @ complement @ ( sk1 @ composition ) @ complement @ ( sk1 @ complement @ join ) ))]]) ).
thf(608,plain,
! [A: $i] :
( ( ( top @ complement )
!= ( A @ complement ) )
| ( ( A @ ( zero @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[579,117]) ).
thf(609,plain,
( ( top @ ( zero @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[608:[bind(A,$thf( top ))]]) ).
thf(202,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ join ) @ join ) )
!= ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) ) )
| ( ( C @ ( B @ join ) @ ( A @ join ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[27,21]) ).
thf(203,plain,
! [C: $i,B: $i,A: $i] :
( ( C != one )
| ( ( B @ ( A @ join ) )
!= ( sk1 @ ( sk1 @ converse @ composition ) ) )
| ( ( C @ ( B @ join ) @ ( A @ join ) )
!= one ) ),
inference(simp,[status(thm)],[202]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( sk1 @ ( sk1 @ converse @ composition ) ) )
| ( ( one @ ( B @ join ) @ ( A @ join ) )
!= one ) ),
inference(simp,[status(thm)],[203]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( ( one @ ( A @ composition ) )
!= ( B @ complement @ ( sk1 @ composition ) ) )
| ( ( A @ ( B @ ( sk1 @ composition ) @ meet ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[39,20]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( ( B @ complement )
!= one )
| ( A != sk1 )
| ( ( A @ ( B @ ( sk1 @ composition ) @ meet ) )
= zero ) ),
inference(simp,[status(thm)],[89]) ).
thf(91,plain,
! [A: $i] :
( ( ( A @ complement )
!= one )
| ( ( sk1 @ ( A @ ( sk1 @ composition ) @ meet ) )
= zero ) ),
inference(simp,[status(thm)],[90]) ).
thf(2619,plain,
( ( ( zero @ ( top @ meet ) )
!= ( zero @ ( zero @ meet ) ) )
| ( ( sk1 @ converse )
!= zero )
| ( sk1 != one )
| ( one != zero ) ),
inference(paramod_ordered,[status(thm)],[607,2450]) ).
thf(2627,plain,
( ( zero != zero )
| ( top != zero )
| ( ( sk1 @ converse )
!= zero )
| ( sk1 != one )
| ( one != zero ) ),
inference(simp,[status(thm)],[2619]) ).
thf(2633,plain,
( ( top != zero )
| ( ( sk1 @ converse )
!= zero )
| ( sk1 != one )
| ( one != zero ) ),
inference(simp,[status(thm)],[2627]) ).
thf(2334,plain,
( ( ( sk1 @ ( sk1 @ meet ) )
!= ( zero @ ( zero @ meet ) ) )
| ( ( zero @ ( zero @ join ) )
= zero )
| ( top != one )
| ( one != zero ) ),
inference(paramod_ordered,[status(thm)],[619,2191]) ).
thf(2426,plain,
( ( sk1 != zero )
| ( sk1 != zero )
| ( top != one )
| ( one != zero )
| ( ( zero @ ( zero @ join ) )
= zero ) ),
inference(simp,[status(thm)],[2334]) ).
thf(2449,plain,
( ( sk1 != zero )
| ( top != one )
| ( one != zero )
| ( ( zero @ ( zero @ join ) )
= zero ) ),
inference(simp,[status(thm)],[2426]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ converse )
= ( B @ converse @ ( A @ converse @ join ) ) ),
inference(cnf,[status(esa)],[46]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( B @ converse @ ( A @ converse @ join ) )
= ( B @ ( A @ join ) @ converse ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(64,plain,
! [A: $i] :
( ( ( A @ converse @ converse )
!= ( sk1 @ converse ) )
| ( ( one @ ( sk1 @ ( A @ composition ) @ join ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[45,21]) ).
thf(67,plain,
! [A: $i] :
( ( ( A @ converse )
!= sk1 )
| ( ( one @ ( sk1 @ ( A @ composition ) @ join ) )
!= one ) ),
inference(simp,[status(thm)],[64]) ).
thf(9769,plain,
! [B: $i,A: $i] :
( ( ( top @ ( zero @ join ) )
!= ( A @ ( B @ join ) ) )
| ( ( top @ ( B @ complement @ join ) )
= ( A @ ( top @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[609,212]) ).
thf(9770,plain,
( ( top @ ( zero @ complement @ join ) )
= ( top @ ( top @ join ) ) ),
inference(pattern_uni,[status(thm)],[9769:[bind(A,$thf( top )),bind(B,$thf( zero ))]]) ).
thf(9990,plain,
! [B: $i,A: $i] :
( ( ( top @ ( zero @ complement @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( top @ ( top @ join ) )
= ( A @ ( B @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[9770,24]) ).
thf(9991,plain,
( ( zero @ complement @ ( top @ join ) )
= ( top @ ( top @ join ) ) ),
inference(pattern_uni,[status(thm)],[9990:[bind(A,$thf( zero @ complement )),bind(B,$thf( top ))]]) ).
thf(1716,plain,
! [A: $i] :
( ( ( one @ complement @ ( sk1 @ composition ) @ complement @ ( sk1 @ complement @ join ) @ complement )
!= ( A @ complement ) )
| ( ( A @ ( zero @ meet ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[227,580]) ).
thf(1717,plain,
( ( one @ complement @ ( sk1 @ composition ) @ complement @ ( sk1 @ complement @ join ) @ ( zero @ meet ) )
= zero ),
inference(pattern_uni,[status(thm)],[1716:[bind(A,$thf( one @ complement @ ( sk1 @ composition ) @ complement @ ( sk1 @ complement @ join ) ))]]) ).
thf(3068,plain,
! [A: $i] :
( ( ( A @ converse @ converse )
!= ( sk1 @ converse ) )
| ( top != zero )
| ( A != zero )
| ( sk1 != one )
| ( one != zero ) ),
inference(paramod_ordered,[status(thm)],[45,2633]) ).
thf(3071,plain,
( ( ( zero @ converse )
!= sk1 )
| ( top != zero )
| ( sk1 != one )
| ( one != zero ) ),
inference(simp,[status(thm)],[3068]) ).
thf(9181,plain,
( ( ( top @ ( zero @ ( zero @ meet ) @ join ) )
!= ( one @ ( sk1 @ converse @ join ) ) )
| ( sk1 != one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[9052,63]) ).
thf(9269,plain,
( ( top != one )
| ( ( zero @ ( zero @ meet ) )
!= ( sk1 @ converse ) )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[9181]) ).
thf(9326,plain,
( ( ( zero @ ( zero @ meet ) )
!= ( sk1 @ converse ) )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[9269]) ).
thf(610,plain,
( ( ( sk1 @ ( sk1 @ converse @ composition ) @ complement )
!= ( top @ complement ) )
| ( one != zero )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[579,70]) ).
thf(627,plain,
( ( ( sk1 @ ( sk1 @ converse @ composition ) )
!= top )
| ( one != zero )
| ( top != one ) ),
inference(simp,[status(thm)],[610]) ).
thf(649,plain,
( ( ( zero @ ( top @ join ) )
!= ( sk1 @ ( sk1 @ converse @ composition ) @ ( one @ join ) ) )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[604,114]) ).
thf(671,plain,
( ( ( sk1 @ ( sk1 @ converse @ composition ) )
!= zero )
| ( top != one )
| ( top != one ) ),
inference(simp,[status(thm)],[649]) ).
thf(688,plain,
( ( ( sk1 @ ( sk1 @ converse @ composition ) )
!= zero )
| ( top != one ) ),
inference(simp,[status(thm)],[671]) ).
thf(946,plain,
! [A: $i] :
( ( ( one @ ( A @ composition ) )
!= ( zero @ ( sk1 @ composition ) ) )
| ( ( A @ ( top @ ( sk1 @ composition ) @ meet ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[39,602]) ).
thf(957,plain,
! [A: $i] :
( ( one != zero )
| ( A != sk1 )
| ( ( A @ ( top @ ( sk1 @ composition ) @ meet ) )
= zero ) ),
inference(simp,[status(thm)],[946]) ).
thf(961,plain,
( ( one != zero )
| ( ( sk1 @ ( top @ ( sk1 @ composition ) @ meet ) )
= zero ) ),
inference(simp,[status(thm)],[957]) ).
thf(7704,plain,
( ( ( top @ ( zero @ join ) )
!= ( zero @ ( zero @ join ) ) )
| ( ( sk1 @ converse )
!= top )
| ( sk1 != one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[609,7086]) ).
thf(7744,plain,
( ( top != zero )
| ( zero != zero )
| ( ( sk1 @ converse )
!= top )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[7704]) ).
thf(7747,plain,
( ( top != zero )
| ( ( sk1 @ converse )
!= top )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[7744]) ).
thf(81,plain,
! [A: $i] :
( ( ( A @ converse @ converse )
!= ( sk1 @ converse ) )
| ( ( A @ complement )
!= one )
| ( sk1 != one )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[45,75]) ).
thf(82,plain,
! [A: $i] :
( ( ( A @ converse )
!= sk1 )
| ( ( A @ complement )
!= one )
| ( sk1 != one )
| ( top != one ) ),
inference(simp,[status(thm)],[81]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ composition ) @ ( A @ composition ) )
= ( C @ ( B @ ( A @ composition ) @ composition ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ composition ) @ composition ) )
= ( C @ ( B @ composition ) @ ( A @ composition ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ composition ) @ converse )
= ( A @ converse @ ( B @ converse @ composition ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ composition ) @ converse )
= ( A @ converse @ ( B @ converse @ composition ) ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(304,plain,
! [A: $i] :
( ( ( one @ complement @ ( sk1 @ composition ) @ complement @ ( sk1 @ complement @ join ) @ complement )
!= ( A @ complement ) )
| ( ( A @ ( zero @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[227,117]) ).
thf(305,plain,
( ( one @ complement @ ( sk1 @ composition ) @ complement @ ( sk1 @ complement @ join ) @ ( zero @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[304:[bind(A,$thf( one @ complement @ ( sk1 @ composition ) @ complement @ ( sk1 @ complement @ join ) ))]]) ).
thf(194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ complement @ ( A @ join ) )
!= ( C @ ( B @ join ) ) )
| ( ( D @ ( top @ join ) )
= ( D @ ( C @ join ) @ ( B @ join ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,27]) ).
thf(195,plain,
! [B: $i,A: $i] :
( ( A @ ( top @ join ) )
= ( A @ ( B @ complement @ join ) @ ( B @ join ) ) ),
inference(pattern_uni,[status(thm)],[194:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ complement ))]]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( A @ ( top @ join ) )
= ( A @ ( B @ complement @ join ) @ ( B @ join ) ) ),
inference(simp,[status(thm)],[195]) ).
thf(9122,plain,
( ( ( one @ ( sk1 @ ( sk1 @ converse @ composition ) @ join ) )
!= ( top @ ( zero @ ( zero @ meet ) @ join ) ) )
| ( top != one ) ),
inference(paramod_ordered,[status(thm)],[9052,21]) ).
thf(9268,plain,
( ( top != one )
| ( ( sk1 @ ( sk1 @ converse @ composition ) )
!= ( zero @ ( zero @ meet ) ) )
| ( top != one ) ),
inference(simp,[status(thm)],[9122]) ).
thf(9325,plain,
( ( ( sk1 @ ( sk1 @ converse @ composition ) )
!= ( zero @ ( zero @ meet ) ) )
| ( top != one ) ),
inference(simp,[status(thm)],[9268]) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ join ) )
!= ( zero @ ( one @ complement @ ( sk1 @ composition ) @ complement @ join ) ) )
| ( ( A @ ( B @ join ) @ ( sk1 @ complement @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[24,348]) ).
thf(354,plain,
( ( one @ complement @ ( sk1 @ composition ) @ complement @ ( zero @ join ) @ ( sk1 @ complement @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[353:[bind(A,$thf( one @ complement @ ( sk1 @ composition ) @ complement )),bind(B,$thf( zero ))]]) ).
thf(3759,plain,
! [B: $i,A: $i] :
( ( ( one @ complement @ ( sk1 @ composition ) @ complement @ ( zero @ join ) @ ( sk1 @ complement @ join ) )
!= ( B @ ( A @ join ) ) )
| ( ( A @ ( B @ join ) )
= top ) ),
inference(paramod_ordered,[status(thm)],[354,24]) ).
thf(3760,plain,
( ( sk1 @ complement @ ( one @ complement @ ( sk1 @ composition ) @ complement @ ( zero @ join ) @ join ) )
= top ),
inference(pattern_uni,[status(thm)],[3759:[bind(A,$thf( sk1 @ complement )),bind(B,$thf( one @ complement @ ( sk1 @ composition ) @ complement @ ( zero @ join ) ))]]) ).
thf(5236,plain,
( ( sk1 @ complement @ ( one @ complement @ ( sk1 @ composition ) @ complement @ join ) @ ( zero @ join ) )
= top ),
inference(rewrite,[status(thm)],[3760,27]) ).
thf(2349,plain,
( ( ( sk1 @ ( sk1 @ meet ) )
!= ( zero @ ( zero @ meet ) ) )
| ( ( zero @ ( zero @ join ) )
= zero )
| ( ( one @ complement )
!= one ) ),
inference(paramod_ordered,[status(thm)],[102,2191]) ).
thf(2404,plain,
( ( sk1 != zero )
| ( sk1 != zero )
| ( ( one @ complement )
!= one )
| ( ( zero @ ( zero @ join ) )
= zero ) ),
inference(simp,[status(thm)],[2349]) ).
thf(2438,plain,
( ( sk1 != zero )
| ( ( one @ complement )
!= one )
| ( ( zero @ ( zero @ join ) )
= zero ) ),
inference(simp,[status(thm)],[2404]) ).
thf(134297,plain,
$false,
inference(e,[status(thm)],[9052,1425,2452,347,88,42,24,2010,37,25,52,9315,460,619,838,20,46,57,78,1946,7926,348,3453,623,602,133,2154,74,6282,1074,248,7393,102,60,117,28,70,21,33,6848,5993,124,7111,7841,6630,212,622,2450,7086,2634,128,34,3985,45,9062,22,711,579,27,54,4236,7094,49,6281,604,3710,39,303,609,213,91,943,685,135,2633,209,2449,48,7087,580,63,67,9991,16,2322,31,1717,3071,43,9770,9326,2843,627,688,104,961,40,1745,55,114,75,58,7747,82,36,30,51,305,210,839,9325,5236,607,227,354,2438,2191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL042+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.13/0.40 % Computer : n004.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 05:40:09 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.82/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/1.18 % [INFO] Parsing done (196ms).
% 1.21/1.20 % [INFO] Running in sequential loop mode.
% 1.99/1.60 % [INFO] eprover registered as external prover.
% 1.99/1.61 % [INFO] Scanning for conjecture ...
% 2.14/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.14/1.75 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.14/1.78 % [INFO] Problem is first-order (TPTP FOF).
% 2.14/1.78 % [INFO] Type checking passed.
% 2.14/1.79 % [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 ...
% 143.01/47.47 % External prover 'e' found a proof!
% 143.01/47.47 % [INFO] Killing All external provers ...
% 143.01/47.48 % Time passed: 46929ms (effective reasoning time: 46272ms)
% 143.01/47.48 % 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)>
% 143.01/47.48 % 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
% 143.01/47.48 % No. of inferences in proof: 289
% 143.01/47.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 46929 ms resp. 46272 ms w/o parsing
% 134.95/47.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 134.95/47.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------