%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV040^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.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 : Wed Sep 30 08:36:45 AM UTC 2026
% Result : Theorem 53.77s 14.07s
% Output : Refutation 54.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 16
% Syntax : Number of formulae : 234 ( 23 unt; 0 typ; 15 def)
% Number of atoms : 1392 ( 240 equ; 0 cnn)
% Maximal formula atoms : 75 ( 5 avg)
% Number of connectives : 2815 ( 489 ~; 656 |; 133 &;1452 @)
% ( 0 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 378 ( 8 ^; 355 !; 0 ?; 378 :)
% ( 0 !>; 0 ?*; 0 @-; 15 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: a > a > $o ).
thf(sk3_decl,type,
sk3: a > a > $o ).
thf(sk4_decl,type,
sk4: a ).
thf(sk5_decl,type,
sk5: a ).
thf(sk6_decl,type,
sk6: a ).
thf(sk7_decl,type,
sk7: a ).
thf(sk8_decl,type,
sk8: a ).
thf(sk9_decl,type,
sk9: a > a > $o ).
thf(sk10_decl,type,
sk10: a > a > $o ).
thf(sk11_decl,type,
sk11: a > a > $o ).
thf(sk12_decl,type,
sk12: a ).
thf(sk13_decl,type,
sk13: a ).
thf(sk14_decl,type,
sk14: a ).
thf(sk15_decl,type,
sk15: a ).
thf(sk16_decl,type,
sk16: a ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > a > $o] :
~ ! [B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( A @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( A @ C @ D )
& ( A @ D @ E ) )
=> ( A @ C @ E ) )
& ( A = B ) )
=> ( ! [C: a,D: a] :
( ( B @ C @ D )
=> ( B @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( B @ C @ D )
& ( B @ D @ E ) )
=> ( B @ C @ E ) )
& ( B = A ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a > a > $o] :
~ ( ( ! [B: a,C: a] :
( ( sk2 @ B @ C )
=> ( sk2 @ C @ B ) )
& ! [B: a,C: a,D: a] :
( ( ( sk2 @ B @ C )
& ( sk2 @ C @ D ) )
=> ( sk2 @ B @ D ) )
& ( sk2 = A ) )
=> ( ! [B: a,C: a] :
( ( A @ B @ C )
=> ( A @ C @ B ) )
& ! [B: a,C: a,D: a] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ( A = sk2 ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: a] :
~ ! [B: a] :
( ( sk3 @ A @ B )
=> ( sk3 @ B @ A ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: a] :
~ ( ( sk3 @ sk4 @ A )
=> ( sk3 @ A @ sk4 ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: a] :
~ ! [B: a,C: a] :
( ( ( sk3 @ A @ B )
& ( sk3 @ B @ C ) )
=> ( sk3 @ A @ C ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: a] :
~ ! [B: a] :
( ( ( sk3 @ sk6 @ A )
& ( sk3 @ A @ B ) )
=> ( sk3 @ sk6 @ B ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: a] :
~ ( ( ( sk3 @ sk6 @ sk7 )
& ( sk3 @ sk7 @ A ) )
=> ( sk3 @ sk6 @ A ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: a > a > $o] :
~ ! [B: a > a > $o,C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( A @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( A @ D @ E )
& ( A @ E @ F ) )
=> ( A @ D @ F ) )
& ( A = B )
& ! [D: a,E: a] :
( ( B @ D @ E )
=> ( B @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( B @ D @ E )
& ( B @ E @ F ) )
=> ( B @ D @ F ) )
& ( B = C ) )
=> ( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( A @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( A @ D @ E )
& ( A @ E @ F ) )
=> ( A @ D @ F ) )
& ( A = C ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: a > a > $o] :
~ ! [B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( sk9 @ C @ D )
=> ( sk9 @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( sk9 @ C @ D )
& ( sk9 @ D @ E ) )
=> ( sk9 @ C @ E ) )
& ( sk9 = A )
& ! [C: a,D: a] :
( ( A @ C @ D )
=> ( A @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( A @ C @ D )
& ( A @ D @ E ) )
=> ( A @ C @ E ) )
& ( A = B ) )
=> ( ! [C: a,D: a] :
( ( sk9 @ C @ D )
=> ( sk9 @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( sk9 @ C @ D )
& ( sk9 @ D @ E ) )
=> ( sk9 @ C @ E ) )
& ( sk9 = B ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: a > a > $o] :
~ ( ( ! [B: a,C: a] :
( ( sk9 @ B @ C )
=> ( sk9 @ C @ B ) )
& ! [B: a,C: a,D: a] :
( ( ( sk9 @ B @ C )
& ( sk9 @ C @ D ) )
=> ( sk9 @ B @ D ) )
& ( sk9 = sk10 )
& ! [B: a,C: a] :
( ( sk10 @ B @ C )
=> ( sk10 @ C @ B ) )
& ! [B: a,C: a,D: a] :
( ( ( sk10 @ B @ C )
& ( sk10 @ C @ D ) )
=> ( sk10 @ B @ D ) )
& ( sk10 = A ) )
=> ( ! [B: a,C: a] :
( ( sk9 @ B @ C )
=> ( sk9 @ C @ B ) )
& ! [B: a,C: a,D: a] :
( ( ( sk9 @ B @ C )
& ( sk9 @ C @ D ) )
=> ( sk9 @ B @ D ) )
& ( sk9 = A ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: a] :
~ ! [B: a] :
( ( sk9 @ A @ B )
=> ( sk9 @ B @ A ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: a] :
~ ( ( sk9 @ sk12 @ A )
=> ( sk9 @ A @ sk12 ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: a] :
~ ! [B: a,C: a] :
( ( ( sk9 @ A @ B )
& ( sk9 @ B @ C ) )
=> ( sk9 @ A @ C ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: a] :
~ ! [B: a] :
( ( ( sk9 @ sk14 @ A )
& ( sk9 @ A @ B ) )
=> ( sk9 @ sk14 @ B ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: a] :
~ ( ( ( sk9 @ sk14 @ sk15 )
& ( sk9 @ sk15 @ A ) )
=> ( sk9 @ sk14 @ A ) ) ) ) ).
thf(1,conjecture,
( ! [A: a > a > $o,B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( A @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( A @ C @ D )
& ( A @ D @ E ) )
=> ( A @ C @ E ) )
& ( A = B ) )
=> ( ! [C: a,D: a] :
( ( B @ C @ D )
=> ( B @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( B @ C @ D )
& ( B @ D @ E ) )
=> ( B @ C @ E ) )
& ( B = A ) ) )
& ! [A: a > a > $o,B: a > a > $o,C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( A @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( A @ D @ E )
& ( A @ E @ F ) )
=> ( A @ D @ F ) )
& ( A = B )
& ! [D: a,E: a] :
( ( B @ D @ E )
=> ( B @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( B @ D @ E )
& ( B @ E @ F ) )
=> ( B @ D @ F ) )
& ( B = C ) )
=> ( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( A @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( A @ D @ E )
& ( A @ E @ F ) )
=> ( A @ D @ F ) )
& ( A = C ) ) )
& ( ( ^ [A: a > a > $o,B: a > a > $o] :
( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( A @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( A @ C @ D )
& ( A @ D @ E ) )
=> ( A @ C @ E ) )
& ( A = B ) ) )
= ( ^ [A: a > a > $o,B: a > a > $o] :
( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( A @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( A @ C @ D )
& ( A @ D @ E ) )
=> ( A @ C @ E ) )
& ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM515_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: a > a > $o,B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( A @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( A @ C @ D )
& ( A @ D @ E ) )
=> ( A @ C @ E ) )
& ( A = B ) )
=> ( ! [C: a,D: a] :
( ( B @ C @ D )
=> ( B @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( B @ C @ D )
& ( B @ D @ E ) )
=> ( B @ C @ E ) )
& ( B = A ) ) )
& ! [A: a > a > $o,B: a > a > $o,C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( A @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( A @ D @ E )
& ( A @ E @ F ) )
=> ( A @ D @ F ) )
& ( A = B )
& ! [D: a,E: a] :
( ( B @ D @ E )
=> ( B @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( B @ D @ E )
& ( B @ E @ F ) )
=> ( B @ D @ F ) )
& ( B = C ) )
=> ( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( A @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( A @ D @ E )
& ( A @ E @ F ) )
=> ( A @ D @ F ) )
& ( A = C ) ) )
& ( ( ^ [A: a > a > $o,B: a > a > $o] :
( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( A @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( A @ C @ D )
& ( A @ D @ E ) )
=> ( A @ C @ E ) )
& ( A = B ) ) )
= ( ^ [A: a > a > $o,B: a > a > $o] :
( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( A @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( A @ C @ D )
& ( A @ D @ E ) )
=> ( A @ C @ E ) )
& ( A = B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: a > a > $o,B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( A @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( A @ C @ D )
& ( A @ D @ E ) )
=> ( A @ C @ E ) )
& ( A = B ) )
=> ( ! [C: a,D: a] :
( ( B @ C @ D )
=> ( B @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( B @ C @ D )
& ( B @ D @ E ) )
=> ( B @ C @ E ) )
& ( B = A ) ) )
& ! [A: a > a > $o,B: a > a > $o,C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( A @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( A @ D @ E )
& ( A @ E @ F ) )
=> ( A @ D @ F ) )
& ( A = B )
& ! [D: a,E: a] :
( ( B @ D @ E )
=> ( B @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( B @ D @ E )
& ( B @ E @ F ) )
=> ( B @ D @ F ) )
& ( B = C ) )
=> ( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( A @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( A @ D @ E )
& ( A @ E @ F ) )
=> ( A @ D @ F ) )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [O: a,N: a,M: a,L: a,K: a,J: a,I: a,H: a,G: a,F: a,E: a,D: a,C: a,B: a,A: a] :
( ( ~ ( sk2 @ A @ B )
| ( sk2 @ B @ A )
| ~ sk1 )
& ( ~ ( sk2 @ C @ D )
| ~ ( sk2 @ D @ E )
| ( sk2 @ C @ E )
| ~ sk1 )
& ( ( sk2 = sk3 )
| ~ sk1 )
& ( ( sk3 @ sk4 @ sk5 )
| ( sk3 @ sk6 @ sk7 )
| ( sk3 != sk2 )
| ~ sk1 )
& ( ( sk3 @ sk4 @ sk5 )
| ( sk3 @ sk7 @ sk8 )
| ( sk3 != sk2 )
| ~ sk1 )
& ( ( sk3 @ sk4 @ sk5 )
| ~ ( sk3 @ sk6 @ sk8 )
| ( sk3 != sk2 )
| ~ sk1 )
& ( ~ ( sk3 @ sk5 @ sk4 )
| ( sk3 @ sk6 @ sk7 )
| ( sk3 != sk2 )
| ~ sk1 )
& ( ~ ( sk3 @ sk5 @ sk4 )
| ( sk3 @ sk7 @ sk8 )
| ( sk3 != sk2 )
| ~ sk1 )
& ( ~ ( sk3 @ sk5 @ sk4 )
| ~ ( sk3 @ sk6 @ sk8 )
| ( sk3 != sk2 )
| ~ sk1 )
& ( sk1
| ~ ( sk9 @ F @ G )
| ( sk9 @ G @ F ) )
& ( sk1
| ~ ( sk9 @ H @ I )
| ~ ( sk9 @ I @ J )
| ( sk9 @ H @ J ) )
& ( sk1
| ( sk9 = sk10 ) )
& ( sk1
| ~ ( sk10 @ K @ L )
| ( sk10 @ L @ K ) )
& ( sk1
| ~ ( sk10 @ M @ N )
| ~ ( sk10 @ N @ O )
| ( sk10 @ M @ O ) )
& ( sk1
| ( sk10 = sk11 ) )
& ( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk14 @ sk15 )
| ( sk9 != sk11 ) )
& ( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk15 @ sk16 )
| ( sk9 != sk11 ) )
& ( sk1
| ( sk9 @ sk12 @ sk13 )
| ~ ( sk9 @ sk14 @ sk16 )
| ( sk9 != sk11 ) )
& ( sk1
| ~ ( sk9 @ sk13 @ sk12 )
| ( sk9 @ sk14 @ sk15 )
| ( sk9 != sk11 ) )
& ( sk1
| ~ ( sk9 @ sk13 @ sk12 )
| ( sk9 @ sk15 @ sk16 )
| ( sk9 != sk11 ) )
& ( sk1
| ~ ( sk9 @ sk13 @ sk12 )
| ~ ( sk9 @ sk14 @ sk16 )
| ( sk9 != sk11 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
( ( sk2 = sk3 )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(39,plain,
( ( sk3 = sk2 )
| ~ sk1 ),
inference(lifteq,[status(thm)],[11]) ).
thf(19,plain,
( ( sk3 @ sk4 @ sk5 )
| ~ ( sk3 @ sk6 @ sk8 )
| ( sk3 != sk2 )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(42,plain,
( ( sk3 != sk2 )
| ( sk3 @ sk4 @ sk5 )
| ~ ( sk3 @ sk6 @ sk8 )
| ~ sk1 ),
inference(lifteq,[status(thm)],[19]) ).
thf(2333,plain,
( ~ sk1
| ( sk2 != sk2 )
| ( sk3 @ sk4 @ sk5 )
| ~ ( sk3 @ sk6 @ sk8 )
| ~ sk1
| ( sk3 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[39,42]) ).
thf(2334,plain,
( ~ sk1
| ( sk3 @ sk4 @ sk5 )
| ~ ( sk3 @ sk6 @ sk8 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[2333]) ).
thf(2335,plain,
( ~ sk1
| ( sk3 @ sk4 @ sk5 )
| ~ ( sk3 @ sk6 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[2334:[]]) ).
thf(21,plain,
( sk1
| ( sk9 = sk10 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(30,plain,
( ( sk10 = sk9 )
| sk1 ),
inference(lifteq,[status(thm)],[21]) ).
thf(8,plain,
( sk1
| ( sk10 = sk11 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(41,plain,
( ( sk11 = sk10 )
| sk1 ),
inference(lifteq,[status(thm)],[8]) ).
thf(23,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk14 @ sk15 )
| ( sk9 != sk11 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(40,plain,
( ( sk11 != sk9 )
| sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk14 @ sk15 ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(198,plain,
( sk1
| ( sk10 != sk9 )
| sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk14 @ sk15 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[41,40]) ).
thf(199,plain,
( sk1
| ( sk10 != sk9 )
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk14 @ sk15 )
| ( sk11 != sk11 ) ),
inference(simp,[status(thm)],[198]) ).
thf(200,plain,
( sk1
| ( sk10 != sk9 )
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk14 @ sk15 ) ),
inference(pattern_uni,[status(thm)],[199:[]]) ).
thf(573,plain,
( sk1
| sk1
| ( sk9 != sk9 )
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk14 @ sk15 )
| ( sk10 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[30,200]) ).
thf(574,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk14 @ sk15 )
| ( sk10 != sk10 ) ),
inference(simp,[status(thm)],[573]) ).
thf(575,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk14 @ sk15 ) ),
inference(pattern_uni,[status(thm)],[574:[]]) ).
thf(22,plain,
! [B: a,A: a] :
( sk1
| ~ ( sk9 @ A @ B )
| ( sk9 @ B @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(34,plain,
! [B: a,A: a] :
( sk1
| ~ ( sk9 @ A @ B )
| ( sk9 @ B @ A ) ),
inference(simp,[status(thm)],[22]) ).
thf(1474,plain,
! [B: a,A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| sk1
| ~ $true
| ( sk9 @ B @ A )
| ( ( sk9 @ sk14 @ sk15 )
!= ( sk9 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[575,34]) ).
thf(1475,plain,
! [B: a,A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ B @ A )
| ( ( sk9 @ sk14 @ sk15 )
!= ( sk9 @ A @ B ) ) ),
inference(simp,[status(thm)],[1474]) ).
thf(1476,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk15 @ sk14 ) ),
inference(pattern_uni,[status(thm)],[1475:[bind(A,$thf( sk14 )),bind(B,$thf( sk15 ))]]) ).
thf(47,plain,
! [B: a,A: a] :
( ( ( sk10 @ A @ B )
= ( sk9 @ A @ B ) )
| sk1 ),
inference(func_ext,[status(esa)],[30]) ).
thf(66,plain,
! [B: a,A: a] :
( sk1
| ( sk10 @ A @ B )
| ~ ( sk9 @ A @ B ) ),
inference(bool_ext,[status(thm)],[47]) ).
thf(2225,plain,
! [B: a,A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| sk1
| ( sk10 @ A @ B )
| ~ $true
| ( ( sk9 @ sk15 @ sk14 )
!= ( sk9 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1476,66]) ).
thf(2226,plain,
! [B: a,A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk10 @ A @ B )
| ( ( sk9 @ sk15 @ sk14 )
!= ( sk9 @ A @ B ) ) ),
inference(simp,[status(thm)],[2225]) ).
thf(2227,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk10 @ sk15 @ sk14 ) ),
inference(pattern_uni,[status(thm)],[2226:[bind(A,$thf( sk15 )),bind(B,$thf( sk14 ))]]) ).
thf(10,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk15 @ sk16 )
| ( sk9 != sk11 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(27,plain,
( ( sk11 != sk9 )
| sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk15 @ sk16 ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(97,plain,
( sk1
| ( sk10 != sk9 )
| sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk15 @ sk16 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[41,27]) ).
thf(98,plain,
( sk1
| ( sk10 != sk9 )
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk15 @ sk16 )
| ( sk11 != sk11 ) ),
inference(simp,[status(thm)],[97]) ).
thf(99,plain,
( sk1
| ( sk10 != sk9 )
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk15 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[98:[]]) ).
thf(393,plain,
( sk1
| sk1
| ( sk9 != sk9 )
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk15 @ sk16 )
| ( sk10 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[30,99]) ).
thf(394,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk15 @ sk16 )
| ( sk10 != sk10 ) ),
inference(simp,[status(thm)],[393]) ).
thf(395,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk15 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[394:[]]) ).
thf(1471,plain,
! [B: a,A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| sk1
| ~ $true
| ( sk9 @ B @ A )
| ( ( sk9 @ sk15 @ sk16 )
!= ( sk9 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[395,34]) ).
thf(1472,plain,
! [B: a,A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ B @ A )
| ( ( sk9 @ sk15 @ sk16 )
!= ( sk9 @ A @ B ) ) ),
inference(simp,[status(thm)],[1471]) ).
thf(1473,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk16 @ sk15 ) ),
inference(pattern_uni,[status(thm)],[1472:[bind(A,$thf( sk15 )),bind(B,$thf( sk16 ))]]) ).
thf(2204,plain,
! [B: a,A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| sk1
| ( sk10 @ A @ B )
| ~ $true
| ( ( sk9 @ sk16 @ sk15 )
!= ( sk9 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1473,66]) ).
thf(2205,plain,
! [B: a,A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk10 @ A @ B )
| ( ( sk9 @ sk16 @ sk15 )
!= ( sk9 @ A @ B ) ) ),
inference(simp,[status(thm)],[2204]) ).
thf(2206,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk10 @ sk16 @ sk15 ) ),
inference(pattern_uni,[status(thm)],[2205:[bind(A,$thf( sk16 )),bind(B,$thf( sk15 ))]]) ).
thf(12,plain,
! [C: a,B: a,A: a] :
( sk1
| ~ ( sk10 @ A @ B )
| ~ ( sk10 @ B @ C )
| ( sk10 @ A @ C ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(35,plain,
! [C: a,B: a,A: a] :
( sk1
| ~ ( sk10 @ A @ B )
| ~ ( sk10 @ B @ C )
| ( sk10 @ A @ C ) ),
inference(simp,[status(thm)],[12]) ).
thf(2247,plain,
! [C: a,B: a,A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| sk1
| ~ $true
| ~ ( sk10 @ B @ C )
| ( sk10 @ A @ C )
| ( ( sk10 @ sk16 @ sk15 )
!= ( sk10 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2206,35]) ).
thf(2248,plain,
! [C: a,B: a,A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| ~ ( sk10 @ B @ C )
| ( sk10 @ A @ C )
| ( ( sk10 @ sk16 @ sk15 )
!= ( sk10 @ A @ B ) ) ),
inference(simp,[status(thm)],[2247]) ).
thf(2249,plain,
! [A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| ~ ( sk10 @ sk15 @ A )
| ( sk10 @ sk16 @ A ) ),
inference(pattern_uni,[status(thm)],[2248:[bind(A,$thf( sk16 )),bind(B,$thf( sk15 ))]]) ).
thf(2259,plain,
! [A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| ~ ( sk10 @ sk15 @ A )
| ( sk10 @ sk16 @ A ) ),
inference(simp,[status(thm)],[2249]) ).
thf(5150,plain,
! [A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| sk1
| ( sk9 @ sk12 @ sk13 )
| ~ $true
| ( sk10 @ sk16 @ A )
| ( ( sk10 @ sk15 @ sk14 )
!= ( sk10 @ sk15 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2227,2259]) ).
thf(5151,plain,
! [A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk10 @ sk16 @ A )
| ( ( sk10 @ sk15 @ sk14 )
!= ( sk10 @ sk15 @ A ) ) ),
inference(simp,[status(thm)],[5150]) ).
thf(5152,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk10 @ sk16 @ sk14 ) ),
inference(pattern_uni,[status(thm)],[5151:[bind(A,$thf( sk14 ))]]) ).
thf(16,plain,
! [B: a,A: a] :
( sk1
| ~ ( sk10 @ A @ B )
| ( sk10 @ B @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(38,plain,
! [B: a,A: a] :
( sk1
| ~ ( sk10 @ A @ B )
| ( sk10 @ B @ A ) ),
inference(simp,[status(thm)],[16]) ).
thf(5529,plain,
! [B: a,A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| sk1
| ~ $true
| ( sk10 @ B @ A )
| ( ( sk10 @ sk16 @ sk14 )
!= ( sk10 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5152,38]) ).
thf(5530,plain,
! [B: a,A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk10 @ B @ A )
| ( ( sk10 @ sk16 @ sk14 )
!= ( sk10 @ A @ B ) ) ),
inference(simp,[status(thm)],[5529]) ).
thf(5531,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk10 @ sk14 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[5530:[bind(A,$thf( sk16 )),bind(B,$thf( sk14 ))]]) ).
thf(65,plain,
! [B: a,A: a] :
( sk1
| ~ ( sk10 @ A @ B )
| ( sk9 @ A @ B ) ),
inference(bool_ext,[status(thm)],[47]) ).
thf(6540,plain,
! [B: a,A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| sk1
| ~ $true
| ( sk9 @ A @ B )
| ( ( sk10 @ sk14 @ sk16 )
!= ( sk10 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5531,65]) ).
thf(6541,plain,
! [B: a,A: a] :
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ A @ B )
| ( ( sk10 @ sk14 @ sk16 )
!= ( sk10 @ A @ B ) ) ),
inference(simp,[status(thm)],[6540]) ).
thf(6542,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 @ sk14 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[6541:[bind(A,$thf( sk14 )),bind(B,$thf( sk16 ))]]) ).
thf(18,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ~ ( sk9 @ sk14 @ sk16 )
| ( sk9 != sk11 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(37,plain,
( ( sk11 != sk9 )
| sk1
| ( sk9 @ sk12 @ sk13 )
| ~ ( sk9 @ sk14 @ sk16 ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(9240,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk11 != sk9 )
| sk1
| ( sk9 @ sk12 @ sk13 )
| ~ $true
| ( ( sk9 @ sk14 @ sk16 )
!= ( sk9 @ sk14 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[6542,37]) ).
thf(9241,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk11 != sk9 )
| ( ( sk9 @ sk14 @ sk16 )
!= ( sk9 @ sk14 @ sk16 ) ) ),
inference(simp,[status(thm)],[9240]) ).
thf(9242,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk11 != sk9 ) ),
inference(pattern_uni,[status(thm)],[9241:[]]) ).
thf(9274,plain,
( sk1
| sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk10 != sk9 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[41,9242]) ).
thf(9275,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk10 != sk9 )
| ( sk11 != sk11 ) ),
inference(simp,[status(thm)],[9274]) ).
thf(9276,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk10 != sk9 ) ),
inference(pattern_uni,[status(thm)],[9275:[]]) ).
thf(9278,plain,
( sk1
| sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk9 != sk9 )
| ( sk10 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[30,9276]) ).
thf(9279,plain,
( sk1
| ( sk9 @ sk12 @ sk13 )
| ( sk10 != sk10 ) ),
inference(simp,[status(thm)],[9278]) ).
thf(9280,plain,
( sk1
| ( sk9 @ sk12 @ sk13 ) ),
inference(pattern_uni,[status(thm)],[9279:[]]) ).
thf(9744,plain,
! [B: a,A: a] :
( sk1
| sk1
| ~ $true
| ( sk9 @ B @ A )
| ( ( sk9 @ sk12 @ sk13 )
!= ( sk9 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9280,34]) ).
thf(9745,plain,
! [B: a,A: a] :
( sk1
| ( sk9 @ B @ A )
| ( ( sk9 @ sk12 @ sk13 )
!= ( sk9 @ A @ B ) ) ),
inference(simp,[status(thm)],[9744]) ).
thf(9746,plain,
( sk1
| ( sk9 @ sk13 @ sk12 ) ),
inference(pattern_uni,[status(thm)],[9745:[bind(A,$thf( sk12 )),bind(B,$thf( sk13 ))]]) ).
thf(9,plain,
( sk1
| ~ ( sk9 @ sk13 @ sk12 )
| ( sk9 @ sk14 @ sk15 )
| ( sk9 != sk11 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(31,plain,
( ( sk11 != sk9 )
| sk1
| ~ ( sk9 @ sk13 @ sk12 )
| ( sk9 @ sk14 @ sk15 ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(9780,plain,
( sk1
| ( sk11 != sk9 )
| sk1
| ~ $true
| ( sk9 @ sk14 @ sk15 )
| ( ( sk9 @ sk13 @ sk12 )
!= ( sk9 @ sk13 @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[9746,31]) ).
thf(9781,plain,
( sk1
| ( sk11 != sk9 )
| ( sk9 @ sk14 @ sk15 )
| ( ( sk9 @ sk13 @ sk12 )
!= ( sk9 @ sk13 @ sk12 ) ) ),
inference(simp,[status(thm)],[9780]) ).
thf(9782,plain,
( sk1
| ( sk11 != sk9 )
| ( sk9 @ sk14 @ sk15 ) ),
inference(pattern_uni,[status(thm)],[9781:[]]) ).
thf(10119,plain,
( sk1
| sk1
| ( sk10 != sk9 )
| ( sk9 @ sk14 @ sk15 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[41,9782]) ).
thf(10120,plain,
( sk1
| ( sk10 != sk9 )
| ( sk9 @ sk14 @ sk15 )
| ( sk11 != sk11 ) ),
inference(simp,[status(thm)],[10119]) ).
thf(10121,plain,
( sk1
| ( sk10 != sk9 )
| ( sk9 @ sk14 @ sk15 ) ),
inference(pattern_uni,[status(thm)],[10120:[]]) ).
thf(11138,plain,
( sk1
| sk1
| ( sk9 != sk9 )
| ( sk9 @ sk14 @ sk15 )
| ( sk10 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[30,10121]) ).
thf(11139,plain,
( sk1
| ( sk9 @ sk14 @ sk15 )
| ( sk10 != sk10 ) ),
inference(simp,[status(thm)],[11138]) ).
thf(11140,plain,
( sk1
| ( sk9 @ sk14 @ sk15 ) ),
inference(pattern_uni,[status(thm)],[11139:[]]) ).
thf(6,plain,
( sk1
| ~ ( sk9 @ sk13 @ sk12 )
| ( sk9 @ sk15 @ sk16 )
| ( sk9 != sk11 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(29,plain,
( ( sk11 != sk9 )
| sk1
| ~ ( sk9 @ sk13 @ sk12 )
| ( sk9 @ sk15 @ sk16 ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(9766,plain,
( sk1
| ( sk11 != sk9 )
| sk1
| ~ $true
| ( sk9 @ sk15 @ sk16 )
| ( ( sk9 @ sk13 @ sk12 )
!= ( sk9 @ sk13 @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[9746,29]) ).
thf(9767,plain,
( sk1
| ( sk11 != sk9 )
| ( sk9 @ sk15 @ sk16 )
| ( ( sk9 @ sk13 @ sk12 )
!= ( sk9 @ sk13 @ sk12 ) ) ),
inference(simp,[status(thm)],[9766]) ).
thf(9768,plain,
( sk1
| ( sk11 != sk9 )
| ( sk9 @ sk15 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[9767:[]]) ).
thf(10099,plain,
( sk1
| sk1
| ( sk10 != sk9 )
| ( sk9 @ sk15 @ sk16 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[41,9768]) ).
thf(10100,plain,
( sk1
| ( sk10 != sk9 )
| ( sk9 @ sk15 @ sk16 )
| ( sk11 != sk11 ) ),
inference(simp,[status(thm)],[10099]) ).
thf(10101,plain,
( sk1
| ( sk10 != sk9 )
| ( sk9 @ sk15 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[10100:[]]) ).
thf(10123,plain,
( sk1
| sk1
| ( sk9 != sk9 )
| ( sk9 @ sk15 @ sk16 )
| ( sk10 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[30,10101]) ).
thf(10124,plain,
( sk1
| ( sk9 @ sk15 @ sk16 )
| ( sk10 != sk10 ) ),
inference(simp,[status(thm)],[10123]) ).
thf(10125,plain,
( sk1
| ( sk9 @ sk15 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[10124:[]]) ).
thf(15,plain,
! [C: a,B: a,A: a] :
( sk1
| ~ ( sk9 @ A @ B )
| ~ ( sk9 @ B @ C )
| ( sk9 @ A @ C ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(43,plain,
! [C: a,B: a,A: a] :
( sk1
| ~ ( sk9 @ A @ B )
| ~ ( sk9 @ B @ C )
| ( sk9 @ A @ C ) ),
inference(simp,[status(thm)],[15]) ).
thf(10137,plain,
! [C: a,B: a,A: a] :
( sk1
| sk1
| ~ ( sk9 @ A @ B )
| ~ $true
| ( sk9 @ A @ C )
| ( ( sk9 @ sk15 @ sk16 )
!= ( sk9 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10125,43]) ).
thf(10138,plain,
! [C: a,B: a,A: a] :
( sk1
| ~ ( sk9 @ A @ B )
| ( sk9 @ A @ C )
| ( ( sk9 @ sk15 @ sk16 )
!= ( sk9 @ B @ C ) ) ),
inference(simp,[status(thm)],[10137]) ).
thf(10139,plain,
! [A: a] :
( sk1
| ~ ( sk9 @ A @ sk15 )
| ( sk9 @ A @ sk16 ) ),
inference(pattern_uni,[status(thm)],[10138:[bind(A,$thf( A )),bind(B,$thf( sk15 )),bind(C,$thf( sk16 ))]]) ).
thf(17,plain,
( sk1
| ~ ( sk9 @ sk13 @ sk12 )
| ~ ( sk9 @ sk14 @ sk16 )
| ( sk9 != sk11 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(33,plain,
( ( sk11 != sk9 )
| sk1
| ~ ( sk9 @ sk13 @ sk12 )
| ~ ( sk9 @ sk14 @ sk16 ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(9769,plain,
( sk1
| ( sk11 != sk9 )
| sk1
| ~ $true
| ~ ( sk9 @ sk14 @ sk16 )
| ( ( sk9 @ sk13 @ sk12 )
!= ( sk9 @ sk13 @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[9746,33]) ).
thf(9770,plain,
( sk1
| ( sk11 != sk9 )
| ~ ( sk9 @ sk14 @ sk16 )
| ( ( sk9 @ sk13 @ sk12 )
!= ( sk9 @ sk13 @ sk12 ) ) ),
inference(simp,[status(thm)],[9769]) ).
thf(9771,plain,
( sk1
| ( sk11 != sk9 )
| ~ ( sk9 @ sk14 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[9770:[]]) ).
thf(10105,plain,
( sk1
| sk1
| ( sk10 != sk9 )
| ~ ( sk9 @ sk14 @ sk16 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[41,9771]) ).
thf(10106,plain,
( sk1
| ( sk10 != sk9 )
| ~ ( sk9 @ sk14 @ sk16 )
| ( sk11 != sk11 ) ),
inference(simp,[status(thm)],[10105]) ).
thf(10107,plain,
( sk1
| ( sk10 != sk9 )
| ~ ( sk9 @ sk14 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[10106:[]]) ).
thf(10934,plain,
( sk1
| sk1
| ( sk9 != sk9 )
| ~ ( sk9 @ sk14 @ sk16 )
| ( sk10 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[30,10107]) ).
thf(10935,plain,
( sk1
| ~ ( sk9 @ sk14 @ sk16 )
| ( sk10 != sk10 ) ),
inference(simp,[status(thm)],[10934]) ).
thf(10936,plain,
( sk1
| ~ ( sk9 @ sk14 @ sk16 ) ),
inference(pattern_uni,[status(thm)],[10935:[]]) ).
thf(15859,plain,
! [A: a] :
( sk1
| ~ ( sk9 @ A @ sk15 )
| sk1
| ~ $true
| ( ( sk9 @ A @ sk16 )
!= ( sk9 @ sk14 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[10139,10936]) ).
thf(15860,plain,
! [A: a] :
( sk1
| ~ ( sk9 @ A @ sk15 )
| ( ( sk9 @ A @ sk16 )
!= ( sk9 @ sk14 @ sk16 ) ) ),
inference(simp,[status(thm)],[15859]) ).
thf(15861,plain,
( sk1
| ~ ( sk9 @ sk14 @ sk15 ) ),
inference(pattern_uni,[status(thm)],[15860:[bind(A,$thf( sk14 ))]]) ).
thf(16151,plain,
( sk1
| sk1
| ~ $true
| ( ( sk9 @ sk14 @ sk15 )
!= ( sk9 @ sk14 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[11140,15861]) ).
thf(16152,plain,
( sk1
| ( ( sk9 @ sk14 @ sk15 )
!= ( sk9 @ sk14 @ sk15 ) ) ),
inference(simp,[status(thm)],[16151]) ).
thf(16153,plain,
sk1,
inference(pattern_uni,[status(thm)],[16152:[]]) ).
thf(16639,plain,
( ~ $true
| ( sk3 @ sk4 @ sk5 )
| ~ ( sk3 @ sk6 @ sk8 ) ),
inference(rewrite,[status(thm)],[2335,16153]) ).
thf(16640,plain,
( ( sk3 @ sk4 @ sk5 )
| ~ ( sk3 @ sk6 @ sk8 ) ),
inference(simp,[status(thm)],[16639]) ).
thf(49,plain,
! [B: a,A: a] :
( ( ( sk3 @ A @ B )
= ( sk2 @ A @ B ) )
| ~ sk1 ),
inference(func_ext,[status(esa)],[39]) ).
thf(16739,plain,
! [B: a,A: a] :
( ( ( sk3 @ A @ B )
= ( sk2 @ A @ B ) )
| ~ $true ),
inference(rewrite,[status(thm)],[49,16153]) ).
thf(16740,plain,
! [B: a,A: a] :
( ( sk3 @ A @ B )
= ( sk2 @ A @ B ) ),
inference(simp,[status(thm)],[16739]) ).
thf(16883,plain,
( ( sk2 @ sk4 @ sk5 )
| ~ ( sk2 @ sk6 @ sk8 ) ),
inference(rewrite,[status(thm)],[16640,16740]) ).
thf(13,plain,
( ( sk3 @ sk4 @ sk5 )
| ( sk3 @ sk7 @ sk8 )
| ( sk3 != sk2 )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(32,plain,
( ( sk3 != sk2 )
| ( sk3 @ sk4 @ sk5 )
| ( sk3 @ sk7 @ sk8 )
| ~ sk1 ),
inference(lifteq,[status(thm)],[13]) ).
thf(850,plain,
( ~ sk1
| ( sk2 != sk2 )
| ( sk3 @ sk4 @ sk5 )
| ( sk3 @ sk7 @ sk8 )
| ~ sk1
| ( sk3 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[39,32]) ).
thf(851,plain,
( ~ sk1
| ( sk3 @ sk4 @ sk5 )
| ( sk3 @ sk7 @ sk8 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[850]) ).
thf(852,plain,
( ~ sk1
| ( sk3 @ sk4 @ sk5 )
| ( sk3 @ sk7 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[851:[]]) ).
thf(927,plain,
! [B: a,A: a] :
( ~ sk1
| ( sk3 @ sk4 @ sk5 )
| ( sk2 @ A @ B )
| ~ sk1
| ( ( sk3 @ sk7 @ sk8 )
!= ( sk3 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[852,49]) ).
thf(928,plain,
! [B: a,A: a] :
( ~ sk1
| ( sk3 @ sk4 @ sk5 )
| ( sk2 @ A @ B )
| ( ( sk3 @ sk7 @ sk8 )
!= ( sk3 @ A @ B ) ) ),
inference(simp,[status(thm)],[927]) ).
thf(929,plain,
( ~ sk1
| ( sk3 @ sk4 @ sk5 )
| ( sk2 @ sk7 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[928:[bind(A,$thf( sk7 )),bind(B,$thf( sk8 ))]]) ).
thf(987,plain,
! [B: a,A: a] :
( ~ sk1
| ( sk2 @ sk7 @ sk8 )
| ( sk2 @ A @ B )
| ~ sk1
| ( ( sk3 @ sk4 @ sk5 )
!= ( sk3 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[929,49]) ).
thf(988,plain,
! [B: a,A: a] :
( ~ sk1
| ( sk2 @ sk7 @ sk8 )
| ( sk2 @ A @ B )
| ( ( sk3 @ sk4 @ sk5 )
!= ( sk3 @ A @ B ) ) ),
inference(simp,[status(thm)],[987]) ).
thf(989,plain,
( ~ sk1
| ( sk2 @ sk7 @ sk8 )
| ( sk2 @ sk4 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[988:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(16703,plain,
( ~ $true
| ( sk2 @ sk7 @ sk8 )
| ( sk2 @ sk4 @ sk5 ) ),
inference(rewrite,[status(thm)],[989,16153]) ).
thf(16704,plain,
( ( sk2 @ sk7 @ sk8 )
| ( sk2 @ sk4 @ sk5 ) ),
inference(simp,[status(thm)],[16703]) ).
thf(14,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk2 @ B @ A )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(24,plain,
( ~ ( sk3 @ sk5 @ sk4 )
| ( sk3 @ sk6 @ sk7 )
| ( sk3 != sk2 )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(44,plain,
( ( sk3 != sk2 )
| ~ ( sk3 @ sk5 @ sk4 )
| ( sk3 @ sk6 @ sk7 )
| ~ sk1 ),
inference(lifteq,[status(thm)],[24]) ).
thf(3431,plain,
( ~ sk1
| ( sk2 != sk2 )
| ~ ( sk3 @ sk5 @ sk4 )
| ( sk3 @ sk6 @ sk7 )
| ~ sk1
| ( sk3 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[39,44]) ).
thf(3432,plain,
( ~ sk1
| ~ ( sk3 @ sk5 @ sk4 )
| ( sk3 @ sk6 @ sk7 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[3431]) ).
thf(3433,plain,
( ~ sk1
| ~ ( sk3 @ sk5 @ sk4 )
| ( sk3 @ sk6 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[3432:[]]) ).
thf(3935,plain,
! [B: a,A: a] :
( ~ sk1
| ~ ( sk3 @ sk5 @ sk4 )
| ( sk2 @ A @ B )
| ~ sk1
| ( ( sk3 @ sk6 @ sk7 )
!= ( sk3 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3433,49]) ).
thf(3936,plain,
! [B: a,A: a] :
( ~ sk1
| ~ ( sk3 @ sk5 @ sk4 )
| ( sk2 @ A @ B )
| ( ( sk3 @ sk6 @ sk7 )
!= ( sk3 @ A @ B ) ) ),
inference(simp,[status(thm)],[3935]) ).
thf(3937,plain,
( ~ sk1
| ~ ( sk3 @ sk5 @ sk4 )
| ( sk2 @ sk6 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[3936:[bind(A,$thf( sk6 )),bind(B,$thf( sk7 ))]]) ).
thf(4439,plain,
! [B: a,A: a] :
( ~ sk1
| ~ sk1
| ~ ( sk2 @ A @ B )
| ( sk2 @ sk6 @ sk7 )
| ( ( sk3 @ A @ B )
!= ( sk3 @ sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[49,3937]) ).
thf(4440,plain,
! [B: a,A: a] :
( ~ sk1
| ~ ( sk2 @ A @ B )
| ( sk2 @ sk6 @ sk7 )
| ( ( sk3 @ A @ B )
!= ( sk3 @ sk5 @ sk4 ) ) ),
inference(simp,[status(thm)],[4439]) ).
thf(4441,plain,
( ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ( sk2 @ sk6 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[4440:[bind(A,$thf( sk5 )),bind(B,$thf( sk4 ))]]) ).
thf(25,plain,
( ~ ( sk3 @ sk5 @ sk4 )
| ( sk3 @ sk7 @ sk8 )
| ( sk3 != sk2 )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(45,plain,
( ( sk3 != sk2 )
| ~ ( sk3 @ sk5 @ sk4 )
| ( sk3 @ sk7 @ sk8 )
| ~ sk1 ),
inference(lifteq,[status(thm)],[25]) ).
thf(3793,plain,
( ~ sk1
| ( sk2 != sk2 )
| ~ ( sk3 @ sk5 @ sk4 )
| ( sk3 @ sk7 @ sk8 )
| ~ sk1
| ( sk3 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[39,45]) ).
thf(3794,plain,
( ~ sk1
| ~ ( sk3 @ sk5 @ sk4 )
| ( sk3 @ sk7 @ sk8 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[3793]) ).
thf(3795,plain,
( ~ sk1
| ~ ( sk3 @ sk5 @ sk4 )
| ( sk3 @ sk7 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[3794:[]]) ).
thf(4208,plain,
! [B: a,A: a] :
( ~ sk1
| ~ ( sk3 @ sk5 @ sk4 )
| ( sk2 @ A @ B )
| ~ sk1
| ( ( sk3 @ sk7 @ sk8 )
!= ( sk3 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3795,49]) ).
thf(4209,plain,
! [B: a,A: a] :
( ~ sk1
| ~ ( sk3 @ sk5 @ sk4 )
| ( sk2 @ A @ B )
| ( ( sk3 @ sk7 @ sk8 )
!= ( sk3 @ A @ B ) ) ),
inference(simp,[status(thm)],[4208]) ).
thf(4210,plain,
( ~ sk1
| ~ ( sk3 @ sk5 @ sk4 )
| ( sk2 @ sk7 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[4209:[bind(A,$thf( sk7 )),bind(B,$thf( sk8 ))]]) ).
thf(5228,plain,
! [B: a,A: a] :
( ~ sk1
| ~ sk1
| ~ ( sk2 @ A @ B )
| ( sk2 @ sk7 @ sk8 )
| ( ( sk3 @ A @ B )
!= ( sk3 @ sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[49,4210]) ).
thf(5229,plain,
! [B: a,A: a] :
( ~ sk1
| ~ ( sk2 @ A @ B )
| ( sk2 @ sk7 @ sk8 )
| ( ( sk3 @ A @ B )
!= ( sk3 @ sk5 @ sk4 ) ) ),
inference(simp,[status(thm)],[5228]) ).
thf(5230,plain,
( ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ( sk2 @ sk7 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[5229:[bind(A,$thf( sk5 )),bind(B,$thf( sk4 ))]]) ).
thf(5,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ C )
| ( sk2 @ A @ C )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(26,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ C )
| ( sk2 @ A @ C )
| ~ sk1 ),
inference(simp,[status(thm)],[5]) ).
thf(7,plain,
( ~ ( sk3 @ sk5 @ sk4 )
| ~ ( sk3 @ sk6 @ sk8 )
| ( sk3 != sk2 )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(36,plain,
( ( sk3 != sk2 )
| ~ ( sk3 @ sk5 @ sk4 )
| ~ ( sk3 @ sk6 @ sk8 )
| ~ sk1 ),
inference(lifteq,[status(thm)],[7]) ).
thf(53,plain,
( ~ sk1
| ( sk2 != sk2 )
| ~ ( sk3 @ sk5 @ sk4 )
| ~ ( sk3 @ sk6 @ sk8 )
| ~ sk1
| ( sk3 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[39,36]) ).
thf(54,plain,
( ~ sk1
| ~ ( sk3 @ sk5 @ sk4 )
| ~ ( sk3 @ sk6 @ sk8 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[53]) ).
thf(55,plain,
( ~ sk1
| ~ ( sk3 @ sk5 @ sk4 )
| ~ ( sk3 @ sk6 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[54:[]]) ).
thf(72,plain,
! [B: a,A: a] :
( ~ sk1
| ~ sk1
| ~ ( sk2 @ A @ B )
| ~ ( sk3 @ sk6 @ sk8 )
| ( ( sk3 @ A @ B )
!= ( sk3 @ sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[49,55]) ).
thf(73,plain,
! [B: a,A: a] :
( ~ sk1
| ~ ( sk2 @ A @ B )
| ~ ( sk3 @ sk6 @ sk8 )
| ( ( sk3 @ A @ B )
!= ( sk3 @ sk5 @ sk4 ) ) ),
inference(simp,[status(thm)],[72]) ).
thf(74,plain,
( ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ~ ( sk3 @ sk6 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[73:[bind(A,$thf( sk5 )),bind(B,$thf( sk4 ))]]) ).
thf(83,plain,
! [B: a,A: a] :
( ~ sk1
| ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ~ ( sk2 @ A @ B )
| ( ( sk3 @ A @ B )
!= ( sk3 @ sk6 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[49,74]) ).
thf(84,plain,
! [B: a,A: a] :
( ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ~ ( sk2 @ A @ B )
| ( ( sk3 @ A @ B )
!= ( sk3 @ sk6 @ sk8 ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(85,plain,
( ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ~ ( sk2 @ sk6 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( sk6 )),bind(B,$thf( sk8 ))]]) ).
thf(120,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ C )
| ~ sk1
| ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ~ $true
| ( ( sk2 @ A @ C )
!= ( sk2 @ sk6 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[26,85]) ).
thf(121,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ C )
| ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ( ( sk2 @ A @ C )
!= ( sk2 @ sk6 @ sk8 ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(122,plain,
! [A: a] :
( ~ ( sk2 @ sk6 @ A )
| ~ ( sk2 @ A @ sk8 )
| ~ sk1
| ~ ( sk2 @ sk5 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( sk6 )),bind(B,$thf( B )),bind(C,$thf( sk8 ))]]) ).
thf(145,plain,
! [A: a] :
( ~ ( sk2 @ sk6 @ A )
| ~ ( sk2 @ A @ sk8 )
| ~ sk1
| ~ ( sk2 @ sk5 @ sk4 ) ),
inference(simp,[status(thm)],[122]) ).
thf(10267,plain,
! [A: a] :
( ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ~ ( sk2 @ sk6 @ A )
| ~ $true
| ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ( ( sk2 @ sk7 @ sk8 )
!= ( sk2 @ A @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[5230,145]) ).
thf(10268,plain,
! [A: a] :
( ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ~ ( sk2 @ sk6 @ A )
| ( ( sk2 @ sk7 @ sk8 )
!= ( sk2 @ A @ sk8 ) ) ),
inference(simp,[status(thm)],[10267]) ).
thf(10269,plain,
( ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ~ ( sk2 @ sk6 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[10268:[bind(A,$thf( sk7 ))]]) ).
thf(10527,plain,
( ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ~ $true
| ( ( sk2 @ sk6 @ sk7 )
!= ( sk2 @ sk6 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[4441,10269]) ).
thf(10528,plain,
( ~ sk1
| ~ ( sk2 @ sk5 @ sk4 )
| ( ( sk2 @ sk6 @ sk7 )
!= ( sk2 @ sk6 @ sk7 ) ) ),
inference(simp,[status(thm)],[10527]) ).
thf(10529,plain,
( ~ sk1
| ~ ( sk2 @ sk5 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[10528:[]]) ).
thf(10601,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ sk1
| ~ sk1
| ~ $true
| ( ( sk2 @ B @ A )
!= ( sk2 @ sk5 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[14,10529]) ).
thf(10602,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ sk1
| ( ( sk2 @ B @ A )
!= ( sk2 @ sk5 @ sk4 ) ) ),
inference(simp,[status(thm)],[10601]) ).
thf(10603,plain,
( ~ ( sk2 @ sk4 @ sk5 )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[10602:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(16713,plain,
( ~ ( sk2 @ sk4 @ sk5 )
| ~ $true ),
inference(rewrite,[status(thm)],[10603,16153]) ).
thf(16714,plain,
~ ( sk2 @ sk4 @ sk5 ),
inference(simp,[status(thm)],[16713]) ).
thf(16927,plain,
( ( sk2 @ sk7 @ sk8 )
| $false ),
inference(rewrite,[status(thm)],[16704,16714]) ).
thf(16928,plain,
sk2 @ sk7 @ sk8,
inference(simp,[status(thm)],[16927]) ).
thf(20,plain,
( ( sk3 @ sk4 @ sk5 )
| ( sk3 @ sk6 @ sk7 )
| ( sk3 != sk2 )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(28,plain,
( ( sk3 != sk2 )
| ( sk3 @ sk4 @ sk5 )
| ( sk3 @ sk6 @ sk7 )
| ~ sk1 ),
inference(lifteq,[status(thm)],[20]) ).
thf(210,plain,
( ~ sk1
| ( sk2 != sk2 )
| ( sk3 @ sk4 @ sk5 )
| ( sk3 @ sk6 @ sk7 )
| ~ sk1
| ( sk3 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[39,28]) ).
thf(211,plain,
( ~ sk1
| ( sk3 @ sk4 @ sk5 )
| ( sk3 @ sk6 @ sk7 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[210]) ).
thf(212,plain,
( ~ sk1
| ( sk3 @ sk4 @ sk5 )
| ( sk3 @ sk6 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[211:[]]) ).
thf(264,plain,
! [B: a,A: a] :
( ~ sk1
| ( sk3 @ sk4 @ sk5 )
| ( sk2 @ A @ B )
| ~ sk1
| ( ( sk3 @ sk6 @ sk7 )
!= ( sk3 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[212,49]) ).
thf(265,plain,
! [B: a,A: a] :
( ~ sk1
| ( sk3 @ sk4 @ sk5 )
| ( sk2 @ A @ B )
| ( ( sk3 @ sk6 @ sk7 )
!= ( sk3 @ A @ B ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(266,plain,
( ~ sk1
| ( sk3 @ sk4 @ sk5 )
| ( sk2 @ sk6 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( sk6 )),bind(B,$thf( sk7 ))]]) ).
thf(305,plain,
! [B: a,A: a] :
( ~ sk1
| ( sk2 @ sk6 @ sk7 )
| ( sk2 @ A @ B )
| ~ sk1
| ( ( sk3 @ sk4 @ sk5 )
!= ( sk3 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[266,49]) ).
thf(306,plain,
! [B: a,A: a] :
( ~ sk1
| ( sk2 @ sk6 @ sk7 )
| ( sk2 @ A @ B )
| ( ( sk3 @ sk4 @ sk5 )
!= ( sk3 @ A @ B ) ) ),
inference(simp,[status(thm)],[305]) ).
thf(307,plain,
( ~ sk1
| ( sk2 @ sk6 @ sk7 )
| ( sk2 @ sk4 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[306:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(355,plain,
! [C: a,B: a,A: a] :
( ~ sk1
| ( sk2 @ sk4 @ sk5 )
| ~ $true
| ~ ( sk2 @ B @ C )
| ( sk2 @ A @ C )
| ~ sk1
| ( ( sk2 @ sk6 @ sk7 )
!= ( sk2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[307,26]) ).
thf(356,plain,
! [C: a,B: a,A: a] :
( ~ sk1
| ( sk2 @ sk4 @ sk5 )
| ~ ( sk2 @ B @ C )
| ( sk2 @ A @ C )
| ( ( sk2 @ sk6 @ sk7 )
!= ( sk2 @ A @ B ) ) ),
inference(simp,[status(thm)],[355]) ).
thf(357,plain,
! [A: a] :
( ~ sk1
| ( sk2 @ sk4 @ sk5 )
| ~ ( sk2 @ sk7 @ A )
| ( sk2 @ sk6 @ A ) ),
inference(pattern_uni,[status(thm)],[356:[bind(A,$thf( sk6 )),bind(B,$thf( sk7 ))]]) ).
thf(376,plain,
! [A: a] :
( ~ sk1
| ( sk2 @ sk4 @ sk5 )
| ~ ( sk2 @ sk7 @ A )
| ( sk2 @ sk6 @ A ) ),
inference(simp,[status(thm)],[357]) ).
thf(16948,plain,
! [A: a] :
( ~ $true
| $false
| ~ ( sk2 @ sk7 @ A )
| ( sk2 @ sk6 @ A ) ),
inference(rewrite,[status(thm)],[376,16153,16714]) ).
thf(16949,plain,
! [A: a] :
( ~ ( sk2 @ sk7 @ A )
| ( sk2 @ sk6 @ A ) ),
inference(simp,[status(thm)],[16948]) ).
thf(16950,plain,
! [A: a] :
( ~ $true
| ( sk2 @ sk6 @ A )
| ( ( sk2 @ sk7 @ sk8 )
!= ( sk2 @ sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16928,16949]) ).
thf(16951,plain,
! [A: a] :
( ( sk2 @ sk6 @ A )
| ( ( sk2 @ sk7 @ sk8 )
!= ( sk2 @ sk7 @ A ) ) ),
inference(simp,[status(thm)],[16950]) ).
thf(16952,plain,
sk2 @ sk6 @ sk8,
inference(pattern_uni,[status(thm)],[16951:[bind(A,$thf( sk8 ))]]) ).
thf(16966,plain,
( ( sk2 @ sk4 @ sk5 )
| ~ $true ),
inference(rewrite,[status(thm)],[16883,16952]) ).
thf(16967,plain,
sk2 @ sk4 @ sk5,
inference(simp,[status(thm)],[16966]) ).
thf(16978,plain,
$false,
inference(rewrite,[status(thm)],[16967,16714]) ).
thf(16979,plain,
$false,
inference(simp,[status(thm)],[16978]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV040^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/0.23 % Computer : n026.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 15:07:33 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.02/0.72 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/0.89 % [INFO] Parsing done (170ms).
% 1.51/0.90 % [INFO] Running in sequential loop mode.
% 1.95/1.18 % [INFO] eprover registered as external prover.
% 1.95/1.19 % [INFO] Scanning for conjecture ...
% 2.14/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.14/1.28 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.14/1.28 % [INFO] Problem is higher-order (TPTP THF).
% 2.14/1.29 % [INFO] Type checking passed.
% 2.14/1.29 % [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 ...
% 53.77/14.05 % [INFO] Killing All external provers ...
% 53.77/14.06 % Time passed: 13677ms (effective reasoning time: 13152ms)
% 53.77/14.06 % 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)>
% 53.77/14.07 % Axioms used in derivation (0):
% 53.77/14.07 % No. of inferences in proof: 219
% 53.77/14.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 13677 ms resp. 13152 ms w/o parsing
% 54.57/14.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 54.57/14.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------