%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL861^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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 : n010.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 08:14:15 AM UTC 2026
% Result : Theorem 10.85s 4.09s
% Output : Refutation 11.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 25
% Syntax : Number of formulae : 140 ( 33 unt; 0 typ; 24 def)
% Number of atoms : 869 ( 200 equ; 0 cnn)
% Maximal formula atoms : 135 ( 6 avg)
% Number of connectives : 2385 ( 439 ~; 450 |; 131 &;1318 @)
% ( 0 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 22 con; 0-2 aty)
% Number of variables : 220 ( 3 ^; 196 !; 0 ?; 220 :)
% ( 0 !>; 0 ?*; 0 @-; 21 @+)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mreflexive_decl,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mtransitive_decl,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(meuclidean_decl,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(sk1_decl,type,
sk1: $i > $i > $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk15_decl,type,
sk15: $i ).
thf(sk16_decl,type,
sk16: $i ).
thf(sk17_decl,type,
sk17: $i ).
thf(sk18_decl,type,
sk18: $i ).
thf(sk19_decl,type,
sk19: $i ).
thf(sk20_decl,type,
sk20: $i ).
thf(sk21_decl,type,
sk21: $i ).
thf(mreflexive_def,definition,
( mreflexive
= ( ^ [A: $i > $i > $o] :
! [B: $i] : ( A @ B @ B ) ) ) ).
thf(mtransitive_def,definition,
( mtransitive
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(meuclidean_def,definition,
( meuclidean
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ B @ D ) )
=> ( A @ C @ D ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $o] :
( ( ! [B: $i] : ( A @ B @ B )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ B @ D ) )
=> ( A @ C @ D ) ) )
!= ( ! [B: $i] : ( A @ B @ B )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ B @ D ) )
=> ( A @ C @ D ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( sk1 @ A @ A ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk3 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk3 @ B ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk3 @ sk4 )
& ( sk1 @ sk4 @ A ) )
=> ( sk1 @ sk3 @ A ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk6 @ A )
& ( sk1 @ sk6 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk6 @ sk7 )
& ( sk1 @ sk6 @ A ) )
=> ( sk1 @ sk7 @ A ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ( sk1 @ A @ A ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk10 @ A )
& ( sk1 @ sk10 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk10 @ sk11 )
& ( sk1 @ sk10 @ A ) )
=> ( sk1 @ sk11 @ A ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk13 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk13 @ B ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk13 @ sk14 )
& ( sk1 @ sk14 @ A ) )
=> ( sk1 @ sk13 @ A ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk16 @ A )
& ( sk1 @ sk16 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk16 @ sk17 )
& ( sk1 @ sk16 @ A ) )
=> ( sk1 @ sk17 @ A ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk19 @ A )
& ( sk1 @ sk19 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk19 @ sk20 )
& ( sk1 @ sk19 @ A ) )
=> ( sk1 @ sk20 @ A ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ( ( mreflexive @ A )
& ( meuclidean @ A ) )
= ( ( mreflexive @ A )
& ( mtransitive @ A )
& ( meuclidean @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ( ( mreflexive @ A )
& ( meuclidean @ A ) )
= ( ( mreflexive @ A )
& ( mtransitive @ A )
& ( meuclidean @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o] :
( ( ! [B: $i] : ( A @ B @ B )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ B @ D ) )
=> ( A @ C @ D ) ) )
= ( ! [B: $i] : ( A @ B @ B )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ B @ D ) )
=> ( A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [A: $i] : ( sk1 @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ! [A: $i] : ( sk1 @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [A: $i] : ( sk1 @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ! [A: $i] : ( sk1 @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ( ( ! [A: $i] : ( sk1 @ A @ A ) )
!= ( ! [A: $i] : ( sk1 @ A @ A ) ) )
| ( ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(51,plain,
( ~ ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
| ~ ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(53,plain,
( ( ( sk1 @ sk13 @ sk14 )
| ( sk1 @ sk16 @ sk17 )
| ( sk1 @ sk19 @ sk20 ) )
& ( ( sk1 @ sk13 @ sk14 )
| ( sk1 @ sk16 @ sk17 )
| ( sk1 @ sk19 @ sk21 ) )
& ( ( sk1 @ sk13 @ sk14 )
| ( sk1 @ sk16 @ sk17 )
| ~ ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk13 @ sk14 )
| ( sk1 @ sk16 @ sk18 )
| ( sk1 @ sk19 @ sk20 ) )
& ( ( sk1 @ sk13 @ sk14 )
| ( sk1 @ sk16 @ sk18 )
| ( sk1 @ sk19 @ sk21 ) )
& ( ( sk1 @ sk13 @ sk14 )
| ( sk1 @ sk16 @ sk18 )
| ~ ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk13 @ sk14 )
| ~ ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk19 @ sk20 ) )
& ( ( sk1 @ sk13 @ sk14 )
| ~ ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk19 @ sk21 ) )
& ( ( sk1 @ sk13 @ sk14 )
| ~ ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk16 @ sk17 )
| ( sk1 @ sk19 @ sk20 ) )
& ( ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk16 @ sk17 )
| ( sk1 @ sk19 @ sk21 ) )
& ( ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk16 @ sk17 )
| ~ ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk16 @ sk18 )
| ( sk1 @ sk19 @ sk20 ) )
& ( ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk16 @ sk18 )
| ( sk1 @ sk19 @ sk21 ) )
& ( ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk16 @ sk18 )
| ~ ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk14 @ sk15 )
| ~ ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk19 @ sk20 ) )
& ( ( sk1 @ sk14 @ sk15 )
| ~ ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk19 @ sk21 ) )
& ( ( sk1 @ sk14 @ sk15 )
| ~ ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk20 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk15 )
| ( sk1 @ sk16 @ sk17 )
| ( sk1 @ sk19 @ sk20 ) )
& ( ~ ( sk1 @ sk13 @ sk15 )
| ( sk1 @ sk16 @ sk17 )
| ( sk1 @ sk19 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk15 )
| ( sk1 @ sk16 @ sk17 )
| ~ ( sk1 @ sk20 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk15 )
| ( sk1 @ sk16 @ sk18 )
| ( sk1 @ sk19 @ sk20 ) )
& ( ~ ( sk1 @ sk13 @ sk15 )
| ( sk1 @ sk16 @ sk18 )
| ( sk1 @ sk19 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk15 )
| ( sk1 @ sk16 @ sk18 )
| ~ ( sk1 @ sk20 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk15 )
| ~ ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk19 @ sk20 ) )
& ( ~ ( sk1 @ sk13 @ sk15 )
| ~ ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk19 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk15 )
| ~ ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk20 @ sk21 ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(56,plain,
( ( sk1 @ sk14 @ sk15 )
| ~ ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk19 @ sk20 ) ),
inference(cnfConj,[status(thm)],[53]) ).
thf(57,plain,
( ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk16 @ sk18 )
| ( sk1 @ sk19 @ sk21 ) ),
inference(cnfConj,[status(thm)],[53]) ).
thf(8,plain,
( ( ! [A: $i] : ( sk1 @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
| ( ! [A: $i] : ( sk1 @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(38,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ A @ A )
| ( sk1 @ H @ H ) )
& ( ( sk1 @ A @ A )
| ~ ( sk1 @ I @ J )
| ~ ( sk1 @ I @ K )
| ( sk1 @ J @ K ) )
& ( ~ ( sk1 @ B @ C )
| ~ ( sk1 @ C @ D )
| ( sk1 @ B @ D )
| ( sk1 @ H @ H ) )
& ( ~ ( sk1 @ B @ C )
| ~ ( sk1 @ C @ D )
| ( sk1 @ B @ D )
| ~ ( sk1 @ I @ J )
| ~ ( sk1 @ I @ K )
| ( sk1 @ J @ K ) )
& ( ~ ( sk1 @ E @ F )
| ~ ( sk1 @ E @ G )
| ( sk1 @ F @ G )
| ( sk1 @ H @ H ) )
& ( ~ ( sk1 @ E @ F )
| ~ ( sk1 @ E @ G )
| ( sk1 @ F @ G )
| ~ ( sk1 @ I @ J )
| ~ ( sk1 @ I @ K )
| ( sk1 @ J @ K ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( sk1 @ A @ A )
| ( sk1 @ B @ B ) ),
inference(cnfConj,[status(thm)],[38]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( sk1 @ A @ A )
| ( sk1 @ B @ B ) ),
inference(simp,[status(thm)],[39]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( sk1 @ A @ A )
| ( ( sk1 @ B @ B )
!= ( sk1 @ A @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[48]) ).
thf(87,plain,
! [A: $i] : ( sk1 @ A @ A ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( B ))]]) ).
thf(88,plain,
! [A: $i] : ( sk1 @ A @ A ),
inference(simp,[status(thm)],[87]) ).
thf(74,plain,
( ~ ( sk1 @ sk13 @ sk15 )
| ~ ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk20 @ sk21 ) ),
inference(cnfConj,[status(thm)],[53]) ).
thf(93,plain,
! [A: $i] :
( ~ ( sk1 @ sk13 @ sk15 )
| ~ ( sk1 @ sk17 @ sk18 )
| ~ $true
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk20 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[88,74]) ).
thf(94,plain,
! [A: $i] :
( ~ ( sk1 @ sk13 @ sk15 )
| ~ ( sk1 @ sk17 @ sk18 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk20 @ sk21 ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(119,plain,
! [A: $i] :
( ~ ( sk1 @ sk13 @ sk15 )
| ~ ( sk1 @ sk17 @ sk18 )
| ( A != sk20 )
| ( A != sk21 ) ),
inference(simp,[status(thm)],[94]) ).
thf(128,plain,
( ~ ( sk1 @ sk13 @ sk15 )
| ~ ( sk1 @ sk17 @ sk18 )
| ( sk21 != sk20 ) ),
inference(simp,[status(thm)],[119]) ).
thf(247,plain,
! [A: $i] :
( ~ $true
| ~ ( sk1 @ sk17 @ sk18 )
| ( sk21 != sk20 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk13 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[88,128]) ).
thf(248,plain,
! [A: $i] :
( ~ ( sk1 @ sk17 @ sk18 )
| ( sk21 != sk20 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk13 @ sk15 ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(264,plain,
! [A: $i] :
( ~ ( sk1 @ sk17 @ sk18 )
| ( sk21 != sk20 )
| ( A != sk13 )
| ( A != sk15 ) ),
inference(simp,[status(thm)],[248]) ).
thf(275,plain,
( ~ ( sk1 @ sk17 @ sk18 )
| ( sk21 != sk20 )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[264]) ).
thf(91,plain,
! [A: $i] :
( ~ ( sk1 @ sk13 @ sk15 )
| ~ $true
| ~ ( sk1 @ sk20 @ sk21 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk17 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[88,74]) ).
thf(92,plain,
! [A: $i] :
( ~ ( sk1 @ sk13 @ sk15 )
| ~ ( sk1 @ sk20 @ sk21 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk17 @ sk18 ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(111,plain,
! [A: $i] :
( ~ ( sk1 @ sk13 @ sk15 )
| ~ ( sk1 @ sk20 @ sk21 )
| ( A != sk17 )
| ( A != sk18 ) ),
inference(simp,[status(thm)],[92]) ).
thf(124,plain,
( ~ ( sk1 @ sk13 @ sk15 )
| ~ ( sk1 @ sk20 @ sk21 )
| ( sk18 != sk17 ) ),
inference(simp,[status(thm)],[111]) ).
thf(89,plain,
! [A: $i] :
( ~ $true
| ~ ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk20 @ sk21 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk13 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[88,74]) ).
thf(90,plain,
! [A: $i] :
( ~ ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk20 @ sk21 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk13 @ sk15 ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(120,plain,
! [A: $i] :
( ~ ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk20 @ sk21 )
| ( A != sk13 )
| ( A != sk15 ) ),
inference(simp,[status(thm)],[90]) ).
thf(129,plain,
( ~ ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk20 @ sk21 )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[120]) ).
thf(7,plain,
( ~ ( ! [A: $i] : ( sk1 @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
| ~ ( ! [A: $i] : ( sk1 @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(10,plain,
( ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk6 @ sk7 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk6 @ sk7 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk6 @ sk7 )
| ~ ( sk1 @ sk9 @ sk9 )
| ~ ( sk1 @ sk11 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ~ ( sk1 @ sk11 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ~ ( sk1 @ sk11 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk6 @ sk7 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk6 @ sk7 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk6 @ sk7 )
| ~ ( sk1 @ sk9 @ sk9 )
| ~ ( sk1 @ sk11 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ~ ( sk1 @ sk11 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ~ ( sk1 @ sk11 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ~ ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk6 @ sk7 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ~ ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk6 @ sk7 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ~ ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk6 @ sk7 )
| ~ ( sk1 @ sk9 @ sk9 )
| ~ ( sk1 @ sk11 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ~ ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ~ ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ~ ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ~ ( sk1 @ sk11 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ~ ( sk1 @ sk3 @ sk5 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ~ ( sk1 @ sk3 @ sk5 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk12 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ~ ( sk1 @ sk3 @ sk5 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ~ ( sk1 @ sk11 @ sk12 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(12,plain,
( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ~ ( sk1 @ sk11 @ sk12 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(515,plain,
( ~ $true
| ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ $true
| ~ ( sk1 @ sk11 @ sk12 ) ),
inference(rewrite,[status(thm)],[12,88]) ).
thf(516,plain,
( ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk11 @ sk12 ) ),
inference(simp,[status(thm)],[515]) ).
thf(517,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ~ $true
| ~ ( sk1 @ sk11 @ sk12 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk7 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[88,516]) ).
thf(518,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk11 @ sk12 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk7 @ sk8 ) ) ),
inference(simp,[status(thm)],[517]) ).
thf(546,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk11 @ sk12 )
| ( A != sk7 )
| ( A != sk8 ) ),
inference(simp,[status(thm)],[518]) ).
thf(562,plain,
( ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk11 @ sk12 )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[546]) ).
thf(131,plain,
! [A: $i] :
( ~ $true
| ~ ( sk1 @ sk20 @ sk21 )
| ( sk18 != sk17 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk13 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[88,124]) ).
thf(132,plain,
! [A: $i] :
( ~ ( sk1 @ sk20 @ sk21 )
| ( sk18 != sk17 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk13 @ sk15 ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(146,plain,
! [A: $i] :
( ~ ( sk1 @ sk20 @ sk21 )
| ( sk18 != sk17 )
| ( A != sk13 )
| ( A != sk15 ) ),
inference(simp,[status(thm)],[132]) ).
thf(154,plain,
( ~ ( sk1 @ sk20 @ sk21 )
| ( sk18 != sk17 )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[146]) ).
thf(11,plain,
( ~ ( sk1 @ sk2 @ sk2 )
| ~ ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ~ ( sk1 @ sk11 @ sk12 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(197,plain,
( ~ $true
| ~ ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk6 @ sk8 )
| ~ $true
| ~ ( sk1 @ sk11 @ sk12 ) ),
inference(rewrite,[status(thm)],[11,88]) ).
thf(198,plain,
( ~ ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk11 @ sk12 ) ),
inference(simp,[status(thm)],[197]) ).
thf(199,plain,
! [A: $i] :
( ~ $true
| ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk11 @ sk12 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[88,198]) ).
thf(200,plain,
! [A: $i] :
( ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk11 @ sk12 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(223,plain,
! [A: $i] :
( ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk11 @ sk12 )
| ( A != sk3 )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[200]) ).
thf(231,plain,
( ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk11 @ sk12 )
| ( sk5 != sk3 ) ),
inference(simp,[status(thm)],[223]) ).
thf(55,plain,
( ~ ( sk1 @ sk13 @ sk15 )
| ( sk1 @ sk16 @ sk18 )
| ( sk1 @ sk19 @ sk20 ) ),
inference(cnfConj,[status(thm)],[53]) ).
thf(519,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ $true
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk11 @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[88,516]) ).
thf(520,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk11 @ sk12 ) ) ),
inference(simp,[status(thm)],[519]) ).
thf(556,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ( A != sk11 )
| ( A != sk12 ) ),
inference(simp,[status(thm)],[520]) ).
thf(568,plain,
( ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ( sk12 != sk11 ) ),
inference(simp,[status(thm)],[556]) ).
thf(143,plain,
( ~ ( sk1 @ sk13 @ sk15 )
| ( sk18 != sk17 )
| ( ( sk1 @ sk20 @ sk21 )
!= ( sk1 @ sk13 @ sk15 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[124]) ).
thf(150,plain,
( ~ ( sk1 @ sk13 @ sk15 )
| ( sk18 != sk17 )
| ( sk20 != sk13 )
| ( sk21 != sk15 ) ),
inference(simp,[status(thm)],[143]) ).
thf(329,plain,
! [A: $i] :
( ~ $true
| ( sk18 != sk17 )
| ( sk20 != sk13 )
| ( sk21 != sk15 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk13 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[88,150]) ).
thf(330,plain,
! [A: $i] :
( ( sk18 != sk17 )
| ( sk20 != sk13 )
| ( sk21 != sk15 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk13 @ sk15 ) ) ),
inference(simp,[status(thm)],[329]) ).
thf(337,plain,
! [A: $i] :
( ( sk18 != sk17 )
| ( sk20 != sk13 )
| ( sk21 != sk15 )
| ( A != sk13 )
| ( A != sk15 ) ),
inference(simp,[status(thm)],[330]) ).
thf(341,plain,
( ( sk18 != sk17 )
| ( sk20 != sk13 )
| ( sk21 != sk15 )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[337]) ).
thf(13,plain,
( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk9 @ sk9 )
| ( sk1 @ sk10 @ sk12 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(987,plain,
( ~ $true
| ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ $true
| ( sk1 @ sk10 @ sk12 ) ),
inference(rewrite,[status(thm)],[13,88]) ).
thf(988,plain,
( ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk10 @ sk12 ) ),
inference(simp,[status(thm)],[987]) ).
thf(989,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ~ $true
| ( sk1 @ sk10 @ sk12 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk7 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[88,988]) ).
thf(990,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk10 @ sk12 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk7 @ sk8 ) ) ),
inference(simp,[status(thm)],[989]) ).
thf(1087,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk10 @ sk12 )
| ( A != sk7 )
| ( A != sk8 ) ),
inference(simp,[status(thm)],[990]) ).
thf(1105,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk1 @ sk10 @ sk12 )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[1087]) ).
thf(263,plain,
( ~ ( sk1 @ sk13 @ sk15 )
| ( sk21 != sk20 )
| ( ( sk1 @ sk17 @ sk18 )
!= ( sk1 @ sk13 @ sk15 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[128]) ).
thf(269,plain,
( ~ ( sk1 @ sk13 @ sk15 )
| ( sk21 != sk20 )
| ( sk17 != sk13 )
| ( sk18 != sk15 ) ),
inference(simp,[status(thm)],[263]) ).
thf(61,plain,
( ( sk1 @ sk13 @ sk14 )
| ( sk1 @ sk16 @ sk17 )
| ( sk1 @ sk19 @ sk21 ) ),
inference(cnfConj,[status(thm)],[53]) ).
thf(709,plain,
! [A: $i] :
( ~ $true
| ( sk21 != sk20 )
| ( sk17 != sk13 )
| ( sk18 != sk15 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk13 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[88,269]) ).
thf(710,plain,
! [A: $i] :
( ( sk21 != sk20 )
| ( sk17 != sk13 )
| ( sk18 != sk15 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk13 @ sk15 ) ) ),
inference(simp,[status(thm)],[709]) ).
thf(727,plain,
! [A: $i] :
( ( sk21 != sk20 )
| ( sk17 != sk13 )
| ( sk18 != sk15 )
| ( A != sk13 )
| ( A != sk15 ) ),
inference(simp,[status(thm)],[710]) ).
thf(734,plain,
( ( sk21 != sk20 )
| ( sk17 != sk13 )
| ( sk18 != sk15 )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[727]) ).
thf(54,plain,
( ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk16 @ sk17 )
| ( sk1 @ sk19 @ sk21 ) ),
inference(cnfConj,[status(thm)],[53]) ).
thf(201,plain,
! [A: $i] :
( ~ ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk6 @ sk8 )
| ~ $true
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk11 @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[88,198]) ).
thf(202,plain,
! [A: $i] :
( ~ ( sk1 @ sk3 @ sk5 )
| ( sk1 @ sk6 @ sk8 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk11 @ sk12 ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(216,plain,
! [A: $i] :
( ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk3 @ sk5 )
| ( A != sk11 )
| ( A != sk12 ) ),
inference(simp,[status(thm)],[202]) ).
thf(226,plain,
( ( sk1 @ sk6 @ sk8 )
| ~ ( sk1 @ sk3 @ sk5 )
| ( sk12 != sk11 ) ),
inference(simp,[status(thm)],[216]) ).
thf(401,plain,
! [A: $i] :
( ( sk1 @ sk6 @ sk8 )
| ~ $true
| ( sk12 != sk11 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[88,226]) ).
thf(402,plain,
! [A: $i] :
( ( sk1 @ sk6 @ sk8 )
| ( sk12 != sk11 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[401]) ).
thf(447,plain,
! [A: $i] :
( ( sk1 @ sk6 @ sk8 )
| ( sk12 != sk11 )
| ( A != sk3 )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[402]) ).
thf(466,plain,
( ( sk1 @ sk6 @ sk8 )
| ( sk12 != sk11 )
| ( sk5 != sk3 ) ),
inference(simp,[status(thm)],[447]) ).
thf(1051,plain,
( ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ~ $true
| ( ( sk1 @ sk11 @ sk12 )
!= ( sk1 @ sk10 @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[988,516]) ).
thf(1052,plain,
( ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ( ( sk1 @ sk11 @ sk12 )
!= ( sk1 @ sk10 @ sk12 ) ) ),
inference(simp,[status(thm)],[1051]) ).
thf(1093,plain,
( ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ( sk11 != sk10 )
| ( sk12 != sk12 ) ),
inference(simp,[status(thm)],[1052]) ).
thf(1097,plain,
( ( sk1 @ sk3 @ sk4 )
| ~ ( sk1 @ sk7 @ sk8 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[1093]) ).
thf(1106,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ~ $true
| ( sk11 != sk10 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk7 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[88,1097]) ).
thf(1107,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ( sk11 != sk10 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk7 @ sk8 ) ) ),
inference(simp,[status(thm)],[1106]) ).
thf(1136,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ( sk11 != sk10 )
| ( A != sk7 )
| ( A != sk8 ) ),
inference(simp,[status(thm)],[1107]) ).
thf(1144,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk11 != sk10 )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[1136]) ).
thf(594,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ~ $true
| ( sk8 != sk7 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk11 @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[88,562]) ).
thf(595,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ( sk8 != sk7 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk11 @ sk12 ) ) ),
inference(simp,[status(thm)],[594]) ).
thf(612,plain,
! [A: $i] :
( ( sk1 @ sk3 @ sk4 )
| ( sk8 != sk7 )
| ( A != sk11 )
| ( A != sk12 ) ),
inference(simp,[status(thm)],[595]) ).
thf(616,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk8 != sk7 )
| ( sk12 != sk11 ) ),
inference(simp,[status(thm)],[612]) ).
thf(133,plain,
! [A: $i] :
( ~ ( sk1 @ sk13 @ sk15 )
| ~ $true
| ( sk18 != sk17 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk20 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[88,124]) ).
thf(134,plain,
! [A: $i] :
( ~ ( sk1 @ sk13 @ sk15 )
| ( sk18 != sk17 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk20 @ sk21 ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(147,plain,
! [A: $i] :
( ~ ( sk1 @ sk13 @ sk15 )
| ( sk18 != sk17 )
| ( A != sk20 )
| ( A != sk21 ) ),
inference(simp,[status(thm)],[134]) ).
thf(155,plain,
( ~ ( sk1 @ sk13 @ sk15 )
| ( sk18 != sk17 )
| ( sk21 != sk20 ) ),
inference(simp,[status(thm)],[147]) ).
thf(813,plain,
! [A: $i] :
( ~ $true
| ( sk1 @ sk16 @ sk18 )
| ( sk1 @ sk19 @ sk20 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk13 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[88,55]) ).
thf(814,plain,
! [A: $i] :
( ( sk1 @ sk16 @ sk18 )
| ( sk1 @ sk19 @ sk20 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk13 @ sk15 ) ) ),
inference(simp,[status(thm)],[813]) ).
thf(879,plain,
! [A: $i] :
( ( sk1 @ sk16 @ sk18 )
| ( sk1 @ sk19 @ sk20 )
| ( A != sk13 )
| ( A != sk15 ) ),
inference(simp,[status(thm)],[814]) ).
thf(912,plain,
( ( sk1 @ sk16 @ sk18 )
| ( sk1 @ sk19 @ sk20 )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[879]) ).
thf(181,plain,
! [A: $i] :
( ~ $true
| ( sk18 != sk17 )
| ( sk15 != sk13 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk20 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[88,154]) ).
thf(182,plain,
! [A: $i] :
( ( sk18 != sk17 )
| ( sk15 != sk13 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk20 @ sk21 ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(189,plain,
! [A: $i] :
( ( sk18 != sk17 )
| ( sk15 != sk13 )
| ( A != sk20 )
| ( A != sk21 ) ),
inference(simp,[status(thm)],[182]) ).
thf(194,plain,
( ( sk18 != sk17 )
| ( sk15 != sk13 )
| ( sk21 != sk20 ) ),
inference(simp,[status(thm)],[189]) ).
thf(311,plain,
( ~ ( sk1 @ sk17 @ sk18 )
| ( sk15 != sk13 )
| ( ( sk1 @ sk20 @ sk21 )
!= ( sk1 @ sk17 @ sk18 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[129]) ).
thf(315,plain,
( ~ ( sk1 @ sk17 @ sk18 )
| ( sk15 != sk13 )
| ( sk20 != sk17 )
| ( sk21 != sk18 ) ),
inference(simp,[status(thm)],[311]) ).
thf(2720,plain,
$false,
inference(e,[status(thm)],[56,57,275,9,124,129,128,562,154,231,55,568,341,1105,88,5,269,61,734,988,74,54,466,1144,616,155,198,912,226,3,516,194,48,150,315,1097]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL861^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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
% 0.09/0.18 % Computer : n010.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 10:13:11 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.91/0.76 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.01 % [INFO] Parsing done (249ms).
% 1.29/1.03 % [INFO] Running in sequential loop mode.
% 2.29/1.42 % [INFO] eprover registered as external prover.
% 2.29/1.43 % [INFO] Scanning for conjecture ...
% 2.74/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.74/1.63 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.74/1.63 % [INFO] Problem is higher-order (TPTP THF).
% 2.74/1.64 % [INFO] Type checking passed.
% 2.74/1.64 % [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 ...
% 10.85/4.08 % External prover 'e' found a proof!
% 10.85/4.08 % [INFO] Killing All external provers ...
% 10.85/4.08 % Time passed: 3755ms (effective reasoning time: 3048ms)
% 10.85/4.08 % 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)>
% 10.85/4.09 % Axioms used in derivation (0):
% 10.85/4.09 % No. of inferences in proof: 116
% 10.85/4.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3755 ms resp. 3048 ms w/o parsing
% 11.83/4.15 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.83/4.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------