%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL860^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : 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 08:14:14 AM UTC 2026
% Result : Theorem 14.04s 4.41s
% Output : Refutation 14.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 25
% Syntax : Number of formulae : 131 ( 33 unt; 0 typ; 24 def)
% Number of atoms : 830 ( 146 equ; 0 cnn)
% Maximal formula atoms : 153 ( 6 avg)
% Number of connectives : 2134 ( 417 ~; 438 |; 123 &;1100 @)
% ( 0 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 22 con; 0-2 aty)
% Number of variables : 217 ( 4 ^; 193 !; 0 ?; 217 :)
% ( 0 !>; 0 ?*; 0 @-; 20 @+)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mreflexive_decl,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(msymmetric_decl,type,
msymmetric: ( $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: $o ).
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(msymmetric_def,definition,
( msymmetric
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( A @ B @ C )
=> ( A @ C @ 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] :
( ( A @ B @ C )
=> ( A @ C @ B ) )
& ! [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(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk4 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk4 @ B ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk4 @ sk5 )
& ( sk1 @ sk5 @ A ) )
=> ( sk1 @ sk4 @ A ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( sk1 @ sk7 @ A )
=> ( sk1 @ A @ sk7 ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk9 @ A )
& ( sk1 @ sk9 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk9 @ sk10 )
& ( sk1 @ sk9 @ A ) )
=> ( sk1 @ sk10 @ A ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
~ ( sk1 @ A @ A ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk13 @ A )
& ( sk1 @ sk13 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk13 @ sk14 )
& ( sk1 @ sk13 @ A ) )
=> ( sk1 @ sk14 @ A ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk16 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk16 @ B ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk16 @ sk17 )
& ( sk1 @ sk17 @ A ) )
=> ( sk1 @ sk16 @ 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 )
& ( msymmetric @ A )
& ( meuclidean @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ( ( mreflexive @ A )
& ( meuclidean @ A ) )
= ( ( mreflexive @ A )
& ( mtransitive @ A )
& ( msymmetric @ 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] :
( ( A @ B @ C )
=> ( A @ C @ B ) )
& ! [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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) )
& ! [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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(38,plain,
! [M: $i,L: $i,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 @ J @ J ) )
& ( ( sk1 @ A @ A )
| ~ ( sk1 @ K @ L )
| ~ ( sk1 @ K @ M )
| ( sk1 @ L @ M ) )
& ( ~ ( sk1 @ B @ C )
| ~ ( sk1 @ C @ D )
| ( sk1 @ B @ D )
| ( sk1 @ J @ J ) )
& ( ~ ( sk1 @ B @ C )
| ~ ( sk1 @ C @ D )
| ( sk1 @ B @ D )
| ~ ( sk1 @ K @ L )
| ~ ( sk1 @ K @ M )
| ( sk1 @ L @ M ) )
& ( ~ ( sk1 @ E @ F )
| ( sk1 @ F @ E )
| ( sk1 @ J @ J ) )
& ( ~ ( sk1 @ E @ F )
| ( sk1 @ F @ E )
| ~ ( sk1 @ K @ L )
| ~ ( sk1 @ K @ M )
| ( sk1 @ L @ M ) )
& ( ~ ( sk1 @ G @ H )
| ~ ( sk1 @ G @ I )
| ( sk1 @ H @ I )
| ( sk1 @ J @ J ) )
& ( ~ ( sk1 @ G @ H )
| ~ ( sk1 @ G @ I )
| ( sk1 @ H @ I )
| ~ ( sk1 @ K @ L )
| ~ ( sk1 @ K @ M )
| ( sk1 @ L @ M ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(46,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)],[46]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( sk1 @ A @ A )
| ( ( sk1 @ B @ B )
!= ( sk1 @ A @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[48]) ).
thf(75,plain,
! [A: $i] : ( sk1 @ A @ A ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( B ))]]) ).
thf(76,plain,
! [A: $i] : ( sk1 @ A @ A ),
inference(simp,[status(thm)],[75]) ).
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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) )
& ! [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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) )
& ! [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(55,plain,
( ~ ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) )
& ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) )
& ! [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(57,plain,
( ( ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ( sk1 @ sk19 @ sk20 ) )
& ( ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ( sk1 @ sk19 @ sk21 ) )
& ( ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ~ ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ( sk1 @ sk19 @ sk20 ) )
& ( ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ( sk1 @ sk19 @ sk21 ) )
& ( ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ~ ( sk1 @ sk20 @ sk21 ) )
& ( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ( sk1 @ sk19 @ sk20 ) )
& ( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ( sk1 @ sk19 @ sk21 ) )
& ( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ~ ( sk1 @ sk20 @ sk21 ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(65,plain,
( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ~ ( sk1 @ sk20 @ sk21 ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(77,plain,
! [A: $i] :
( ~ $true
| ~ sk3
| ~ ( sk1 @ sk20 @ sk21 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[76,65]) ).
thf(78,plain,
! [A: $i] :
( ~ sk3
| ~ ( sk1 @ sk20 @ sk21 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(91,plain,
! [A: $i] :
( ~ sk3
| ~ ( sk1 @ sk20 @ sk21 )
| ( A != sk16 )
| ( A != sk18 ) ),
inference(simp,[status(thm)],[78]) ).
thf(101,plain,
( ~ sk3
| ~ ( sk1 @ sk20 @ sk21 )
| ( sk18 != sk16 ) ),
inference(simp,[status(thm)],[91]) ).
thf(62,plain,
( ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ( sk1 @ sk19 @ sk21 ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(63,plain,
( ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ~ ( sk1 @ sk20 @ sk21 ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(490,plain,
( ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ~ $true
| ( ( sk1 @ sk20 @ sk21 )
!= ( sk1 @ sk19 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[62,63]) ).
thf(491,plain,
( ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ( ( sk1 @ sk20 @ sk21 )
!= ( sk1 @ sk19 @ sk21 ) ) ),
inference(simp,[status(thm)],[490]) ).
thf(507,plain,
( ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ( sk20 != sk19 )
| ( sk21 != sk21 ) ),
inference(simp,[status(thm)],[491]) ).
thf(514,plain,
( ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ( sk20 != sk19 ) ),
inference(simp,[status(thm)],[507]) ).
thf(61,plain,
( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ( sk1 @ sk19 @ sk20 ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(60,plain,
( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ( sk1 @ sk19 @ sk21 ) ),
inference(cnfConj,[status(thm)],[57]) ).
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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(10,plain,
( ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ~ sk3
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk14 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ~ sk3
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ~ sk3
| ~ ( sk1 @ sk12 @ sk12 )
| ~ ( sk1 @ sk14 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk5 @ sk6 )
| ~ sk3
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk14 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk5 @ sk6 )
| ~ sk3
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ( sk1 @ sk5 @ sk6 )
| ~ sk3
| ~ ( sk1 @ sk12 @ sk12 )
| ~ ( sk1 @ sk14 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ~ ( sk1 @ sk4 @ sk6 )
| ~ sk3
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk14 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ~ ( sk1 @ sk4 @ sk6 )
| ~ sk3
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| ~ ( sk1 @ sk4 @ sk6 )
| ~ sk3
| ~ ( sk1 @ sk12 @ sk12 )
| ~ ( sk1 @ sk14 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk9 @ sk10 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk14 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk9 @ sk10 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk9 @ sk10 )
| ~ ( sk1 @ sk12 @ sk12 )
| ~ ( sk1 @ sk14 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk9 @ sk11 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk14 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk9 @ sk11 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk9 @ sk11 )
| ~ ( sk1 @ sk12 @ sk12 )
| ~ ( sk1 @ sk14 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk10 @ sk11 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk14 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk10 @ sk11 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk10 @ sk11 )
| ~ ( sk1 @ sk12 @ sk12 )
| ~ ( sk1 @ sk14 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ( sk1 @ sk9 @ sk10 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk14 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ( sk1 @ sk9 @ sk10 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ( sk1 @ sk9 @ sk10 )
| ~ ( sk1 @ sk12 @ sk12 )
| ~ ( sk1 @ sk14 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ( sk1 @ sk9 @ sk11 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk14 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ( sk1 @ sk9 @ sk11 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ( sk1 @ sk9 @ sk11 )
| ~ ( sk1 @ sk12 @ sk12 )
| ~ ( sk1 @ sk14 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ~ ( sk1 @ sk10 @ sk11 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk14 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ~ ( sk1 @ sk10 @ sk11 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk15 ) )
& ( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ~ ( sk1 @ sk10 @ sk11 )
| ~ ( sk1 @ sk12 @ sk12 )
| ~ ( sk1 @ sk14 @ sk15 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(11,plain,
( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ( sk1 @ sk9 @ sk10 )
| ~ ( sk1 @ sk12 @ sk12 )
| ~ ( sk1 @ sk14 @ sk15 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(143,plain,
( ~ $true
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ( sk1 @ sk9 @ sk10 )
| ~ $true
| ~ ( sk1 @ sk14 @ sk15 ) ),
inference(rewrite,[status(thm)],[11,76]) ).
thf(144,plain,
( sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ( sk1 @ sk9 @ sk10 )
| ~ ( sk1 @ sk14 @ sk15 ) ),
inference(simp,[status(thm)],[143]) ).
thf(494,plain,
! [A: $i] :
( ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ~ $true
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk20 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[76,63]) ).
thf(495,plain,
! [A: $i] :
( ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk20 @ sk21 ) ) ),
inference(simp,[status(thm)],[494]) ).
thf(506,plain,
! [A: $i] :
( ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ( A != sk20 )
| ( A != sk21 ) ),
inference(simp,[status(thm)],[495]) ).
thf(513,plain,
( ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ( sk21 != sk20 ) ),
inference(simp,[status(thm)],[506]) ).
thf(79,plain,
! [A: $i] :
( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ~ $true
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk20 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[76,65]) ).
thf(80,plain,
! [A: $i] :
( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk20 @ sk21 ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(96,plain,
! [A: $i] :
( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ( A != sk20 )
| ( A != sk21 ) ),
inference(simp,[status(thm)],[80]) ).
thf(98,plain,
( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ( sk21 != sk20 ) ),
inference(simp,[status(thm)],[96]) ).
thf(536,plain,
( ~ sk3
| ( sk21 != sk20 )
| ~ $true
| ~ sk3
| ( sk21 != sk20 )
| ( ( sk1 @ sk16 @ sk18 )
!= ( sk1 @ sk16 @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[513,98]) ).
thf(537,plain,
( ~ sk3
| ( sk21 != sk20 )
| ( ( sk1 @ sk16 @ sk18 )
!= ( sk1 @ sk16 @ sk17 ) ) ),
inference(simp,[status(thm)],[536]) ).
thf(542,plain,
( ~ sk3
| ( sk21 != sk20 )
| ( sk16 != sk16 )
| ( sk18 != sk17 ) ),
inference(simp,[status(thm)],[537]) ).
thf(553,plain,
( ~ sk3
| ( sk21 != sk20 )
| ( sk18 != sk17 ) ),
inference(simp,[status(thm)],[542]) ).
thf(369,plain,
! [A: $i] :
( ~ $true
| ~ sk3
| ( sk1 @ sk19 @ sk20 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[76,61]) ).
thf(370,plain,
! [A: $i] :
( ~ sk3
| ( sk1 @ sk19 @ sk20 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(simp,[status(thm)],[369]) ).
thf(387,plain,
! [A: $i] :
( ( sk1 @ sk19 @ sk20 )
| ~ sk3
| ( A != sk16 )
| ( A != sk18 ) ),
inference(simp,[status(thm)],[370]) ).
thf(390,plain,
( ( sk1 @ sk19 @ sk20 )
| ~ sk3
| ( sk18 != sk16 ) ),
inference(simp,[status(thm)],[387]) ).
thf(58,plain,
( ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ~ ( sk1 @ sk20 @ sk21 ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(182,plain,
! [A: $i] :
( ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ~ $true
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk20 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[76,58]) ).
thf(183,plain,
! [A: $i] :
( ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk20 @ sk21 ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(187,plain,
! [A: $i] :
( ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ( A != sk20 )
| ( A != sk21 ) ),
inference(simp,[status(thm)],[183]) ).
thf(190,plain,
( ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ( sk21 != sk20 ) ),
inference(simp,[status(thm)],[187]) ).
thf(234,plain,
! [A: $i] :
( ~ $true
| ~ sk3
| ( sk1 @ sk19 @ sk21 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[76,60]) ).
thf(235,plain,
! [A: $i] :
( ~ sk3
| ( sk1 @ sk19 @ sk21 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(simp,[status(thm)],[234]) ).
thf(246,plain,
! [A: $i] :
( ( sk1 @ sk19 @ sk21 )
| ~ sk3
| ( A != sk16 )
| ( A != sk18 ) ),
inference(simp,[status(thm)],[235]) ).
thf(254,plain,
( ( sk1 @ sk19 @ sk21 )
| ~ sk3
| ( sk18 != sk16 ) ),
inference(simp,[status(thm)],[246]) ).
thf(89,plain,
( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ( ( sk1 @ sk20 @ sk21 )
!= ( sk1 @ sk16 @ sk18 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[65]) ).
thf(93,plain,
( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ( ( sk1 @ sk20 @ sk21 )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(64,plain,
( ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ( sk1 @ sk19 @ sk21 ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(714,plain,
( ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ~ $true
| ( ( sk1 @ sk20 @ sk21 )
!= ( sk1 @ sk19 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[64,58]) ).
thf(715,plain,
( ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ( ( sk1 @ sk20 @ sk21 )
!= ( sk1 @ sk19 @ sk21 ) ) ),
inference(simp,[status(thm)],[714]) ).
thf(721,plain,
( ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ( sk20 != sk19 )
| ( sk21 != sk21 ) ),
inference(simp,[status(thm)],[715]) ).
thf(732,plain,
( ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ( sk20 != sk19 ) ),
inference(simp,[status(thm)],[721]) ).
thf(218,plain,
( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ~ $true
| ( ( sk1 @ sk20 @ sk21 )
!= ( sk1 @ sk19 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[60,65]) ).
thf(219,plain,
( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ( ( sk1 @ sk20 @ sk21 )
!= ( sk1 @ sk19 @ sk21 ) ) ),
inference(simp,[status(thm)],[218]) ).
thf(243,plain,
( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ( sk20 != sk19 )
| ( sk21 != sk21 ) ),
inference(simp,[status(thm)],[219]) ).
thf(251,plain,
( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ( sk20 != sk19 ) ),
inference(simp,[status(thm)],[243]) ).
thf(750,plain,
( ~ sk3
| ( sk20 != sk19 )
| ~ $true
| ~ sk3
| ( sk20 != sk19 )
| ( ( sk1 @ sk17 @ sk18 )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[732,251]) ).
thf(751,plain,
( ~ sk3
| ( sk20 != sk19 )
| ( ( sk1 @ sk17 @ sk18 )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(simp,[status(thm)],[750]) ).
thf(761,plain,
( ~ sk3
| ( sk20 != sk19 )
| ( sk17 != sk16 )
| ( sk18 != sk18 ) ),
inference(simp,[status(thm)],[751]) ).
thf(770,plain,
( ~ sk3
| ( sk20 != sk19 )
| ( sk17 != sk16 ) ),
inference(simp,[status(thm)],[761]) ).
thf(637,plain,
( ~ sk3
| ( sk20 != sk19 )
| ~ $true
| ~ sk3
| ( sk20 != sk19 )
| ( ( sk1 @ sk16 @ sk18 )
!= ( sk1 @ sk16 @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[514,251]) ).
thf(638,plain,
( ~ sk3
| ( sk20 != sk19 )
| ( ( sk1 @ sk16 @ sk18 )
!= ( sk1 @ sk16 @ sk17 ) ) ),
inference(simp,[status(thm)],[637]) ).
thf(648,plain,
( ~ sk3
| ( sk20 != sk19 )
| ( sk16 != sk16 )
| ( sk18 != sk17 ) ),
inference(simp,[status(thm)],[638]) ).
thf(657,plain,
( ~ sk3
| ( sk20 != sk19 )
| ( sk18 != sk17 ) ),
inference(simp,[status(thm)],[648]) ).
thf(13,plain,
( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk9 @ sk11 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk14 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(661,plain,
( ~ $true
| sk3
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk9 @ sk11 )
| ~ $true
| ( sk1 @ sk13 @ sk14 ) ),
inference(rewrite,[status(thm)],[13,76]) ).
thf(662,plain,
( sk3
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk9 @ sk11 )
| ( sk1 @ sk13 @ sk14 ) ),
inference(simp,[status(thm)],[661]) ).
thf(12,plain,
( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ( sk1 @ sk9 @ sk10 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk15 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(393,plain,
( ~ $true
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ( sk1 @ sk9 @ sk10 )
| ~ $true
| ( sk1 @ sk13 @ sk15 ) ),
inference(rewrite,[status(thm)],[12,76]) ).
thf(394,plain,
( sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ( sk1 @ sk9 @ sk10 )
| ( sk1 @ sk13 @ sk15 ) ),
inference(simp,[status(thm)],[393]) ).
thf(419,plain,
! [B: $i,A: $i] :
( ( sk1 @ B @ B )
| sk3
| ~ $true
| ( sk1 @ sk9 @ sk10 )
| ( sk1 @ sk13 @ sk15 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk8 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[48,394]) ).
thf(420,plain,
! [B: $i,A: $i] :
( ( sk1 @ B @ B )
| sk3
| ( sk1 @ sk9 @ sk10 )
| ( sk1 @ sk13 @ sk15 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk8 @ sk7 ) ) ),
inference(simp,[status(thm)],[419]) ).
thf(438,plain,
! [B: $i,A: $i] :
( ( sk1 @ B @ B )
| sk3
| ( sk1 @ sk9 @ sk10 )
| ( sk1 @ sk13 @ sk15 )
| ( A != sk8 )
| ( A != sk7 ) ),
inference(simp,[status(thm)],[420]) ).
thf(444,plain,
! [A: $i] :
( ( sk1 @ A @ A )
| sk3
| ( sk1 @ sk9 @ sk10 )
| ( sk1 @ sk13 @ sk15 )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[438]) ).
thf(14,plain,
( ~ ( sk1 @ sk2 @ sk2 )
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ~ ( sk1 @ sk10 @ sk11 )
| ~ ( sk1 @ sk12 @ sk12 )
| ( sk1 @ sk13 @ sk14 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(874,plain,
( ~ $true
| sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ~ ( sk1 @ sk10 @ sk11 )
| ~ $true
| ( sk1 @ sk13 @ sk14 ) ),
inference(rewrite,[status(thm)],[14,76]) ).
thf(875,plain,
( sk3
| ~ ( sk1 @ sk8 @ sk7 )
| ~ ( sk1 @ sk10 @ sk11 )
| ( sk1 @ sk13 @ sk14 ) ),
inference(simp,[status(thm)],[874]) ).
thf(59,plain,
( ( sk1 @ sk17 @ sk18 )
| ~ sk3
| ( sk1 @ sk19 @ sk20 ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(108,plain,
! [A: $i] :
( ~ $true
| ~ sk3
| ( sk21 != sk20 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[76,98]) ).
thf(109,plain,
! [A: $i] :
( ~ sk3
| ( sk21 != sk20 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(112,plain,
! [A: $i] :
( ~ sk3
| ( sk21 != sk20 )
| ( A != sk16 )
| ( A != sk18 ) ),
inference(simp,[status(thm)],[109]) ).
thf(113,plain,
( ~ sk3
| ( sk21 != sk20 )
| ( sk18 != sk16 ) ),
inference(simp,[status(thm)],[112]) ).
thf(266,plain,
! [A: $i] :
( ~ $true
| ~ sk3
| ( sk20 != sk19 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[76,251]) ).
thf(267,plain,
! [A: $i] :
( ~ sk3
| ( sk20 != sk19 )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(272,plain,
! [A: $i] :
( ~ sk3
| ( sk20 != sk19 )
| ( A != sk16 )
| ( A != sk18 ) ),
inference(simp,[status(thm)],[267]) ).
thf(274,plain,
( ~ sk3
| ( sk20 != sk19 )
| ( sk18 != sk16 ) ),
inference(simp,[status(thm)],[272]) ).
thf(66,plain,
( ( sk1 @ sk16 @ sk17 )
| ~ sk3
| ( sk1 @ sk19 @ sk20 ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(203,plain,
( ~ sk3
| ( sk21 != sk20 )
| ~ $true
| ~ sk3
| ( sk21 != sk20 )
| ( ( sk1 @ sk17 @ sk18 )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[190,98]) ).
thf(204,plain,
( ~ sk3
| ( sk21 != sk20 )
| ( ( sk1 @ sk17 @ sk18 )
!= ( sk1 @ sk16 @ sk18 ) ) ),
inference(simp,[status(thm)],[203]) ).
thf(208,plain,
( ~ sk3
| ( sk21 != sk20 )
| ( sk17 != sk16 )
| ( sk18 != sk18 ) ),
inference(simp,[status(thm)],[204]) ).
thf(210,plain,
( ~ sk3
| ( sk21 != sk20 )
| ( sk17 != sk16 ) ),
inference(simp,[status(thm)],[208]) ).
thf(94,plain,
( ~ ( sk1 @ sk16 @ sk18 )
| ~ sk3
| ( sk20 != sk16 )
| ( sk21 != sk18 ) ),
inference(simp,[status(thm)],[89]) ).
thf(2546,plain,
$false,
inference(e,[status(thm)],[101,5,514,61,60,65,9,144,553,390,58,190,62,254,93,770,657,662,513,64,444,732,875,59,113,274,76,98,66,251,394,3,48,63,210,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL860^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.23 % Computer : n026.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 10:15:32 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.10/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.63/1.07 % [INFO] Parsing done (261ms).
% 1.63/1.08 % [INFO] Running in sequential loop mode.
% 2.37/1.48 % [INFO] eprover registered as external prover.
% 2.37/1.49 % [INFO] Scanning for conjecture ...
% 2.84/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.84/1.69 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.84/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 3.09/1.70 % [INFO] Type checking passed.
% 3.09/1.70 % [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 ...
% 14.04/4.41 % External prover 'e' found a proof!
% 14.04/4.41 % [INFO] Killing All external provers ...
% 14.04/4.41 % Time passed: 4040ms (effective reasoning time: 3321ms)
% 14.04/4.41 % 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)>
% 14.04/4.41 % Axioms used in derivation (0):
% 14.04/4.41 % No. of inferences in proof: 107
% 14.04/4.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4040 ms resp. 3321 ms w/o parsing
% 14.54/4.57 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.54/4.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------