TSTP Solution File: ALG272^5 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : ALG272^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 04:01:39 EDT 2024
% Result : Theorem 30.59s 6.51s
% Output : Refutation 30.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 26
% Syntax : Number of formulae : 105 ( 14 unt; 23 typ; 2 def)
% Number of atoms : 370 ( 355 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 1129 ( 148 ~; 119 |; 85 &; 777 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 19 con; 0-6 aty)
% Number of variables : 278 ( 38 ^ 186 !; 54 ?; 278 :)
% Comments :
%------------------------------------------------------------------------------
thf(g_type,type,
g: $tType ).
thf(cGROUP1_type,type,
cGROUP1: ( g > g > g ) > g > $o ).
thf(cGROUP1_def,definition,
( cGROUP1
= ( ^ [A: g > g > g,B: g] :
( ( cGRP_ASSOC @ A )
& ( cGRP_UNIT @ A @ B )
& ( cGRP_INVERSE @ A @ B ) ) ) ) ).
thf(cGROUP2_type,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(cGROUP2_def,definition,
( cGROUP2
= ( ^ [A: g > g > g,B: g] :
( ( cGRP_ASSOC @ A )
& ( cGRP_LEFT_UNIT @ A @ B )
& ( cGRP_LEFT_INVERSE @ A @ B ) ) ) ) ).
thf(sk1_type,type,
sk1: g > g > g ).
thf(sk2_type,type,
sk2: g ).
thf(sk3_type,type,
sk3: g ).
thf(sk4_type,type,
sk4: g ).
thf(sk5_type,type,
sk5: g ).
thf(sk6_type,type,
sk6: g ).
thf(sk7_type,type,
sk7: g ).
thf(sk8_type,type,
sk8: g > g ).
thf(sk9_type,type,
sk9: g > g ).
thf(sk10_type,type,
sk10: g > g ).
thf(sk11_type,type,
sk11: g > g ).
thf(sk12_type,type,
sk12: g > g ).
thf(sk13_type,type,
sk13: g > g ).
thf(sk14_type,type,
sk14: g > g > g > g > g > g > g ).
thf(sk35_type,type,
sk35: g ).
thf(sk61_type,type,
sk61: g ).
thf(sk62_type,type,
sk62: g ).
thf(sk63_type,type,
sk63: g ).
thf(sk71_type,type,
sk71: g ).
thf(sk72_type,type,
sk72: g ).
thf(1,conjecture,
! [A: g > g > g,B: g] :
( ( cGROUP1 @ A @ B )
= ( cGROUP2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEQUIV_01_02) ).
thf(2,negated_conjecture,
~ ! [A: g > g > g,B: g] :
( ( cGROUP1 @ A @ B )
= ( cGROUP2 @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: g > g > g,B: g] :
( ( ! [C: g,D: g,E: g] :
( ( A @ ( A @ C @ D ) @ E )
= ( A @ C @ ( A @ D @ E ) ) )
& ! [C: g] :
( ( ( A @ B @ C )
= C )
& ( ( A @ C @ B )
= C ) )
& ! [C: g] :
? [D: g] :
( ( ( A @ C @ D )
= B )
& ( ( A @ D @ C )
= B ) ) )
= ( ! [C: g,D: g,E: g] :
( ( A @ ( A @ C @ D ) @ E )
= ( A @ C @ ( A @ D @ E ) ) )
& ! [C: g] :
( ( A @ B @ C )
= C )
& ! [C: g] :
? [D: g] :
( ( A @ D @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( sk1 @ sk2 @ A )
= A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( sk1 @ sk2 @ A )
= A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(8,plain,
( ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
| ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( sk1 @ sk2 @ A )
= A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(16,plain,
! [B: g,A: g] :
( ( ( sk1 @ sk2 @ B )
= B )
| ( ( sk1 @ sk2 @ A )
= A ) ),
inference(cnf,[status(esa)],[8]) ).
thf(43,plain,
! [B: g,A: g] :
( ( ( sk1 @ sk2 @ B )
= B )
| ( ( sk1 @ sk2 @ A )
= A ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(44,plain,
! [B: g,A: g] :
( ( ( sk1 @ sk2 @ B )
= B )
| ( ( sk1 @ sk2 @ A )
= A ) ),
inference(simp,[status(thm)],[43]) ).
thf(173,plain,
! [B: g,A: g] :
( ( ( sk1 @ sk2 @ B )
= B )
| ( ( sk1 @ sk2 @ A )
!= ( sk1 @ sk2 @ B ) )
| ( A != B ) ),
inference(eqfactor_ordered,[status(thm)],[44]) ).
thf(176,plain,
! [A: g] :
( ( sk1 @ sk2 @ A )
= A ),
inference(pattern_uni,[status(thm)],[173:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(6,plain,
( ( ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) ) )
!= ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) ) ) )
| ( ( ! [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
( ( sk1 @ sk2 @ A )
= A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
( ( sk1 @ sk2 @ A )
= A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(57,plain,
( ( ( ! [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) ) )
!= ( ! [A: g] :
( ( sk1 @ sk2 @ A )
= A ) ) )
| ( ( ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(179,plain,
( ( ( ! [A: g] :
( ( A = A )
& ( ( sk1 @ A @ sk2 )
= A ) ) )
!= ( ! [A: g] : ( A = A ) ) )
| ( ( ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(rewrite,[status(thm)],[57,176]) ).
thf(180,plain,
( ~ ! [A: g] :
( ( sk1 @ A @ sk2 )
= A )
| ( ( ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(191,plain,
( ( ( ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) )
| ( ( sk1 @ sk35 @ sk2 )
!= sk35 ) ),
inference(cnf,[status(esa)],[180]) ).
thf(192,plain,
( ( ( sk1 @ sk35 @ sk2 )
!= sk35 )
| ( ( ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(376,plain,
! [A: g] :
( ( A != sk35 )
| ( ( ! [B: g] :
? [C: g] :
( ( ( sk1 @ B @ C )
= sk2 )
& ( ( sk1 @ C @ B )
= sk2 ) ) )
!= ( ! [B: g] :
? [C: g] :
( ( sk1 @ C @ B )
= sk2 ) ) )
| ( ( sk1 @ sk2 @ A )
!= ( sk1 @ sk35 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[176,192]) ).
thf(380,plain,
( ( ( ^ [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) )
| ( sk35 != sk2 )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[376]) ).
thf(388,plain,
( ( ( ^ [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[380]) ).
thf(389,plain,
( ( ( ^ [A: g,B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g,B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[388]) ).
thf(393,plain,
( ( ( ( ( sk1 @ sk62 @ sk63 )
= sk2 )
& ( ( sk1 @ sk63 @ sk62 )
= sk2 ) )
!= ( ( sk1 @ sk63 @ sk62 )
= sk2 ) )
| ( sk35 != sk2 ) ),
inference(func_ext,[status(esa)],[389]) ).
thf(923,plain,
( ( sk35 != sk2 )
| ( ( ( sk1 @ sk62 @ sk63 )
= sk2 )
& ( ( sk1 @ sk63 @ sk62 )
= sk2 ) )
| ( ( sk1 @ sk63 @ sk62 )
= sk2 ) ),
inference(bool_ext,[status(thm)],[393]) ).
thf(937,plain,
( ( ( sk1 @ sk63 @ sk62 )
= sk2 )
| ( sk35 != sk2 )
| ( ( ( sk1 @ sk62 @ sk63 )
= sk2 )
& ( ( sk1 @ sk63 @ sk62 )
= sk2 ) ) ),
inference(lifteq,[status(thm)],[923]) ).
thf(961,plain,
( ( ( sk1 @ sk63 @ sk62 )
= sk2 )
| ( sk35 != sk2 )
| ( ( sk1 @ sk63 @ sk62 )
= sk2 ) ),
inference(cnf,[status(esa)],[937]) ).
thf(963,plain,
( ( ( sk1 @ sk63 @ sk62 )
= sk2 )
| ( sk35 != sk2 )
| ( ( sk1 @ sk63 @ sk62 )
= sk2 ) ),
inference(lifteq,[status(thm)],[961]) ).
thf(964,plain,
( ( ( sk1 @ sk63 @ sk62 )
= sk2 )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[963]) ).
thf(984,plain,
( ( sk35 != sk2 )
| ( ( ( sk1 @ sk62 @ sk63 )
= sk2 )
!= ( ( sk1 @ sk63 @ sk62 )
= sk2 ) )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk63 @ sk62 ) ) ),
inference(paramod_ordered,[status(thm)],[964,393]) ).
thf(985,plain,
( ( sk35 != sk2 )
| ( ( ( sk1 @ sk62 @ sk63 )
= sk2 )
!= ( ( sk1 @ sk63 @ sk62 )
= sk2 ) ) ),
inference(pattern_uni,[status(thm)],[984:[]]) ).
thf(1224,plain,
( ( sk35 != sk2 )
| ( ( sk1 @ sk62 @ sk63 )
!= sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk63 @ sk62 ) ) ),
inference(paramod_ordered,[status(thm)],[964,985]) ).
thf(1225,plain,
( ( sk35 != sk2 )
| ( ( sk1 @ sk62 @ sk63 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[1224:[]]) ).
thf(1237,plain,
( ( ( sk1 @ sk62 @ sk63 )
!= sk2 )
| ( sk35 != sk2 ) ),
inference(lifteq,[status(thm)],[1225]) ).
thf(390,plain,
( ( ( ? [A: g] :
( ( ( sk1 @ sk61 @ A )
= sk2 )
& ( ( sk1 @ A @ sk61 )
= sk2 ) ) )
!= ( ? [A: g] :
( ( sk1 @ A @ sk61 )
= sk2 ) ) )
| ( sk35 != sk2 ) ),
inference(func_ext,[status(esa)],[388]) ).
thf(609,plain,
( ( sk35 != sk2 )
| ? [A: g] :
( ( ( sk1 @ sk61 @ A )
= sk2 )
& ( ( sk1 @ A @ sk61 )
= sk2 ) )
| ? [A: g] :
( ( sk1 @ A @ sk61 )
= sk2 ) ),
inference(bool_ext,[status(thm)],[390]) ).
thf(612,plain,
( ( ( sk1 @ sk72 @ sk61 )
= sk2 )
| ( ( sk1 @ sk71 @ sk61 )
= sk2 )
| ( sk35 != sk2 ) ),
inference(cnf,[status(esa)],[609]) ).
thf(614,plain,
( ( ( sk1 @ sk72 @ sk61 )
= sk2 )
| ( ( sk1 @ sk71 @ sk61 )
= sk2 )
| ( sk35 != sk2 ) ),
inference(lifteq,[status(thm)],[612]) ).
thf(637,plain,
( ( ( sk1 @ sk71 @ sk61 )
= sk2 )
| ( sk35 != sk2 )
| ( ( sk1 @ sk72 @ sk61 )
!= ( sk1 @ sk71 @ sk61 ) )
| ( sk2 != sk2 ) ),
inference(eqfactor_ordered,[status(thm)],[614]) ).
thf(647,plain,
( ( ( sk1 @ sk71 @ sk61 )
= sk2 )
| ( sk35 != sk2 )
| ( sk72 != sk71 )
| ( sk61 != sk61 ) ),
inference(simp,[status(thm)],[637]) ).
thf(700,plain,
( ( ( sk1 @ sk71 @ sk61 )
= sk2 )
| ( sk35 != sk2 )
| ( sk72 != sk71 ) ),
inference(simp,[status(thm)],[647]) ).
thf(933,plain,
( ( sk35 != sk2 )
| ( sk72 != sk71 )
| ( ( sk1 @ sk71 @ sk61 )
!= ( sk1 @ sk62 @ sk63 ) ) ),
inference(paramod_ordered,[status(thm)],[700,393]) ).
thf(945,plain,
( ( sk35 != sk2 )
| ( sk72 != sk71 )
| ( sk71 != sk62 )
| ( sk63 != sk61 ) ),
inference(simp,[status(thm)],[933]) ).
thf(986,plain,
( ( sk35 != sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk62 @ sk63 ) ) ),
inference(paramod_ordered,[status(thm)],[964,393]) ).
thf(1057,plain,
( ( sk35 != sk2 )
| ( sk63 != sk62 )
| ( sk63 != sk62 ) ),
inference(simp,[status(thm)],[986]) ).
thf(1079,plain,
( ( sk35 != sk2 )
| ( sk63 != sk62 ) ),
inference(simp,[status(thm)],[1057]) ).
thf(13,plain,
! [F: g,E: g,D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk14 @ F @ E @ D @ C @ B @ A ) @ F )
= sk2 )
| ( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(33,plain,
! [F: g,E: g,D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk14 @ F @ E @ D @ C @ B @ A ) @ F )
= sk2 )
| ( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(34,plain,
! [F: g,E: g,D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk14 @ F @ E @ D @ C @ B @ A ) @ F )
= sk2 )
| ( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(987,plain,
! [A: g] :
( ( sk35 != sk2 )
| ( sk2 = A )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[964,176]) ).
thf(1059,plain,
! [A: g] :
( ( sk2 = A )
| ( sk35 != sk2 )
| ( sk63 != sk2 )
| ( sk62 != A ) ),
inference(simp,[status(thm)],[987]) ).
thf(1081,plain,
( ( sk62 = sk2 )
| ( sk35 != sk2 )
| ( sk63 != sk2 ) ),
inference(simp,[status(thm)],[1059]) ).
thf(104,plain,
( ( ( ^ [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) ) )
!= ( ^ [A: g] :
( ( sk1 @ sk2 @ A )
= A ) ) )
| ( ( ^ [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(187,plain,
( ( ( ^ [A: g] :
( ( A = A )
& ( ( sk1 @ A @ sk2 )
= A ) ) )
!= ( ^ [A: g] : ( A = A ) ) )
| ( ( ^ [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(rewrite,[status(thm)],[104,176]) ).
thf(188,plain,
( ( ( ^ [A: g] :
( ( sk1 @ A @ sk2 )
= A ) )
!= ( ^ [A: g] : $true ) )
| ( ( ^ [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[187]) ).
thf(368,plain,
( ( ( ^ [A: g] :
( ( sk1 @ A @ sk2 )
= A ) )
!= ( ^ [A: g] : $true ) )
| ( ( ^ [A: g,B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g,B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(373,plain,
( ( ( sk1 @ sk35 @ sk2 )
!= sk35 )
| ( ( ^ [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[192]) ).
thf(564,plain,
( ( ( sk1 @ sk35 @ sk2 )
!= sk35 )
| ( ( ^ [A: g,B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g,B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[373]) ).
thf(183,plain,
( ( ! [A: g] :
( ( A = A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] : ( A = A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(rewrite,[status(thm)],[9,176]) ).
thf(184,plain,
( ( ! [A: g] :
( ( sk1 @ A @ sk2 )
= A )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(7,plain,
( ~ ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
| ~ ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( sk1 @ sk2 @ A )
= A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(10,plain,
! [B: g,A: g] :
( ( ( sk1 @ ( sk1 @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ ( sk10 @ A ) )
!= ( sk1 @ ( sk8 @ A ) @ ( sk1 @ ( sk9 @ A ) @ ( sk10 @ A ) ) ) )
| ( ( sk1 @ sk2 @ ( sk11 @ A ) )
!= ( sk11 @ A ) )
| ( ( sk1 @ B @ ( sk12 @ A ) )
!= sk2 )
| ( ( sk1 @ ( sk1 @ sk3 @ sk4 ) @ sk5 )
!= ( sk1 @ sk3 @ ( sk1 @ sk4 @ sk5 ) ) )
| ( ( sk1 @ sk2 @ sk6 )
!= sk6 )
| ( ( sk1 @ sk6 @ sk2 )
!= sk6 )
| ( ( sk1 @ sk7 @ A )
!= sk2 )
| ( ( sk1 @ A @ sk7 )
!= sk2 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(11,plain,
! [B: g,A: g] :
( ( ( sk1 @ ( sk1 @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ ( sk10 @ A ) )
!= ( sk1 @ ( sk8 @ A ) @ ( sk1 @ ( sk9 @ A ) @ ( sk10 @ A ) ) ) )
| ( ( sk1 @ sk2 @ ( sk11 @ A ) )
!= ( sk11 @ A ) )
| ( ( sk1 @ B @ ( sk12 @ A ) )
!= sk2 )
| ( ( sk1 @ ( sk1 @ sk3 @ sk4 ) @ sk5 )
!= ( sk1 @ sk3 @ ( sk1 @ sk4 @ sk5 ) ) )
| ( ( sk1 @ sk2 @ sk6 )
!= sk6 )
| ( ( sk1 @ sk6 @ sk2 )
!= sk6 )
| ( ( sk1 @ sk7 @ A )
!= sk2 )
| ( ( sk1 @ A @ sk7 )
!= sk2 ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(195,plain,
! [B: g,A: g] :
( ( ( sk1 @ ( sk1 @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ ( sk10 @ A ) )
!= ( sk1 @ ( sk8 @ A ) @ ( sk1 @ ( sk9 @ A ) @ ( sk10 @ A ) ) ) )
| ( ( sk11 @ A )
!= ( sk11 @ A ) )
| ( ( sk1 @ B @ ( sk12 @ A ) )
!= sk2 )
| ( ( sk1 @ ( sk1 @ sk3 @ sk4 ) @ sk5 )
!= ( sk1 @ sk3 @ ( sk1 @ sk4 @ sk5 ) ) )
| ( sk6 != sk6 )
| ( ( sk1 @ sk6 @ sk2 )
!= sk6 )
| ( ( sk1 @ sk7 @ A )
!= sk2 )
| ( ( sk1 @ A @ sk7 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[11,176]) ).
thf(196,plain,
! [B: g,A: g] :
( ( ( sk1 @ ( sk1 @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ ( sk10 @ A ) )
!= ( sk1 @ ( sk8 @ A ) @ ( sk1 @ ( sk9 @ A ) @ ( sk10 @ A ) ) ) )
| ( ( sk1 @ B @ ( sk12 @ A ) )
!= sk2 )
| ( ( sk1 @ ( sk1 @ sk3 @ sk4 ) @ sk5 )
!= ( sk1 @ sk3 @ ( sk1 @ sk4 @ sk5 ) ) )
| ( ( sk1 @ sk6 @ sk2 )
!= sk6 )
| ( ( sk1 @ sk7 @ A )
!= sk2 )
| ( ( sk1 @ A @ sk7 )
!= sk2 ) ),
inference(simp,[status(thm)],[195]) ).
thf(14,plain,
! [D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk1 @ B @ C ) @ D )
= ( sk1 @ B @ ( sk1 @ C @ D ) ) )
| ( ( sk1 @ A @ ( sk13 @ A ) )
= sk2 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(27,plain,
! [D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk1 @ B @ C ) @ D )
= ( sk1 @ B @ ( sk1 @ C @ D ) ) )
| ( ( sk1 @ A @ ( sk13 @ A ) )
= sk2 ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(28,plain,
! [D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk1 @ B @ C ) @ D )
= ( sk1 @ B @ ( sk1 @ C @ D ) ) )
| ( ( sk1 @ A @ ( sk13 @ A ) )
= sk2 ) ),
inference(simp,[status(thm)],[27]) ).
thf(1208,plain,
( ( sk35 != sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk62 @ sk63 ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[985]) ).
thf(1266,plain,
( ( sk35 != sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk62 @ sk63 ) ) ),
inference(simp,[status(thm)],[1208]) ).
thf(379,plain,
( ( ( ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) )
| ( sk35 != sk2 )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[376]) ).
thf(387,plain,
( ( ( ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[379]) ).
thf(1269,plain,
! [A: g] :
( ( A != sk2 )
| ( sk35 != sk2 )
| ( ( sk1 @ sk2 @ A )
!= ( sk1 @ sk62 @ sk63 ) ) ),
inference(paramod_ordered,[status(thm)],[176,1237]) ).
thf(1276,plain,
( ( sk35 != sk2 )
| ( sk62 != sk2 )
| ( sk63 != sk2 ) ),
inference(simp,[status(thm)],[1269]) ).
thf(20,plain,
! [F: g,E: g,D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk14 @ F @ E @ D @ C @ B @ A ) @ F )
= sk2 )
| ( ( sk1 @ D @ sk2 )
= D ) ),
inference(cnf,[status(esa)],[8]) ).
thf(29,plain,
! [F: g,E: g,D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk14 @ F @ E @ D @ C @ B @ A ) @ F )
= sk2 )
| ( ( sk1 @ D @ sk2 )
= D ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(30,plain,
! [F: g,E: g,D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk14 @ F @ E @ D @ C @ B @ A ) @ F )
= sk2 )
| ( ( sk1 @ D @ sk2 )
= D ) ),
inference(simp,[status(thm)],[29]) ).
thf(177,plain,
( ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( A = A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] : ( A = A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(rewrite,[status(thm)],[5,176]) ).
thf(178,plain,
( ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( sk1 @ A @ sk2 )
= A )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(607,plain,
( ( ( ^ [A: g] :
( ( ( sk1 @ sk61 @ A )
= sk2 )
& ( ( sk1 @ A @ sk61 )
= sk2 ) ) )
!= ( ^ [A: g] :
( ( sk1 @ A @ sk61 )
= sk2 ) ) )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[390]) ).
thf(5990,plain,
$false,
inference(e,[status(thm)],[1237,614,945,1079,34,176,3,1081,368,564,389,184,196,28,192,188,388,393,985,1266,387,700,964,1276,390,30,373,178,607]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG272^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% 0.10/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jun 19 14:40:55 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.98 % [INFO] Parsing done (114ms).
% 1.18/0.99 % [INFO] Running in sequential loop mode.
% 1.68/1.19 % [INFO] eprover registered as external prover.
% 1.68/1.20 % [INFO] Scanning for conjecture ...
% 1.93/1.27 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.93/1.28 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.93/1.28 % [INFO] Problem is higher-order (TPTP THF).
% 1.93/1.29 % [INFO] Type checking passed.
% 1.93/1.29 % [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 ...
% 30.59/6.50 % External prover 'e' found a proof!
% 30.59/6.51 % [INFO] Killing All external provers ...
% 30.59/6.51 % Time passed: 5979ms (effective reasoning time: 5514ms)
% 30.59/6.51 % 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)>
% 30.59/6.51 % Axioms used in derivation (0):
% 30.59/6.51 % No. of inferences in proof: 80
% 30.59/6.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5979 ms resp. 5514 ms w/o parsing
% 30.64/6.60 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.64/6.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------