%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL867^1 : 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 : n011.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 161.66s 55.94s
% Output : Refutation 163.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 96
% Syntax : Number of formulae : 678 ( 101 unt; 0 typ; 95 def)
% Number of atoms : 6347 (1128 equ; 0 cnn)
% Maximal formula atoms : 216 ( 9 avg)
% Number of connectives : 17206 (2442 ~;2798 |; 857 &;10262 @)
% ( 0 <=>; 847 =>; 0 <=; 0 <~>)
% Maximal formula depth : 59 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 120 ( 117 usr; 115 con; 0-2 aty)
% Number of variables : 1876 ( 841 ^; 943 !; 0 ?;1876 :)
% ( 0 !>; 0 ?*; 0 @-; 92 @+)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
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: $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(sk22_decl,type,
sk22: $i ).
thf(sk23_decl,type,
sk23: $i ).
thf(sk53_decl,type,
sk53: $i ).
thf(sk59_decl,type,
sk59: $i ).
thf(sk60_decl,type,
sk60: $i ).
thf(sk66_decl,type,
sk66: $i ).
thf(sk72_decl,type,
sk72: $i ).
thf(sk73_decl,type,
sk73: $i ).
thf(sk117_decl,type,
sk117: $i ).
thf(sk118_decl,type,
sk118: $i ).
thf(sk119_decl,type,
sk119: $i ).
thf(sk120_decl,type,
sk120: $i ).
thf(sk121_decl,type,
sk121: $i ).
thf(sk122_decl,type,
sk122: $i ).
thf(sk123_decl,type,
sk123: $i ).
thf(sk124_decl,type,
sk124: $i ).
thf(sk144_decl,type,
sk144: $i ).
thf(sk145_decl,type,
sk145: $i ).
thf(sk146_decl,type,
sk146: $i ).
thf(sk147_decl,type,
sk147: $i ).
thf(sk148_decl,type,
sk148: $i ).
thf(sk149_decl,type,
sk149: $i ).
thf(sk150_decl,type,
sk150: $i ).
thf(sk151_decl,type,
sk151: $i ).
thf(sk171_decl,type,
sk171: $i ).
thf(sk172_decl,type,
sk172: $i ).
thf(sk173_decl,type,
sk173: $i ).
thf(sk174_decl,type,
sk174: $i ).
thf(sk175_decl,type,
sk175: $i ).
thf(sk176_decl,type,
sk176: $i ).
thf(sk177_decl,type,
sk177: $i ).
thf(sk178_decl,type,
sk178: $i ).
thf(sk179_decl,type,
sk179: $i ).
thf(sk180_decl,type,
sk180: $i ).
thf(sk181_decl,type,
sk181: $i ).
thf(sk182_decl,type,
sk182: $i ).
thf(sk183_decl,type,
sk183: $i ).
thf(sk184_decl,type,
sk184: $i ).
thf(sk185_decl,type,
sk185: $i ).
thf(sk186_decl,type,
sk186: $i ).
thf(sk187_decl,type,
sk187: $i ).
thf(sk284_decl,type,
sk284: $i ).
thf(sk285_decl,type,
sk285: $i ).
thf(sk286_decl,type,
sk286: $i ).
thf(sk287_decl,type,
sk287: $i ).
thf(sk288_decl,type,
sk288: $i ).
thf(sk289_decl,type,
sk289: $i ).
thf(sk316_decl,type,
sk316: $i ).
thf(sk403_decl,type,
sk403: $i ).
thf(sk498_decl,type,
sk498: $i ).
thf(sk629_decl,type,
sk629: $i ).
thf(sk630_decl,type,
sk630: $i ).
thf(sk668_decl,type,
sk668: $i ).
thf(sk669_decl,type,
sk669: $i ).
thf(sk707_decl,type,
sk707: $i ).
thf(sk811_decl,type,
sk811: $i ).
thf(sk812_decl,type,
sk812: $i ).
thf(sk962_decl,type,
sk962: $i ).
thf(sk963_decl,type,
sk963: $i ).
thf(sk964_decl,type,
sk964: $i ).
thf(sk965_decl,type,
sk965: $i ).
thf(sk1090_decl,type,
sk1090: $i ).
thf(sk1091_decl,type,
sk1091: $i ).
thf(sk1332_decl,type,
sk1332: $i ).
thf(sk1333_decl,type,
sk1333: $i ).
thf(sk1334_decl,type,
sk1334: $i ).
thf(sk1335_decl,type,
sk1335: $i ).
thf(sk1417_decl,type,
sk1417: $i ).
thf(sk1418_decl,type,
sk1418: $i ).
thf(sk1419_decl,type,
sk1419: $i ).
thf(sk1420_decl,type,
sk1420: $i ).
thf(sk1680_decl,type,
sk1680: $i ).
thf(sk1681_decl,type,
sk1681: $i ).
thf(sk1682_decl,type,
sk1682: $i ).
thf(sk1683_decl,type,
sk1683: $i ).
thf(sk1684_decl,type,
sk1684: $i ).
thf(sk1685_decl,type,
sk1685: $i ).
thf(sk1840_decl,type,
sk1840: $i ).
thf(sk2241_decl,type,
sk2241: $i ).
thf(sk2391_decl,type,
sk2391: $i ).
thf(sk2541_decl,type,
sk2541: $i ).
thf(sk2542_decl,type,
sk2542: $i ).
thf(sk2792_decl,type,
sk2792: $i ).
thf(sk4457_decl,type,
sk4457: $i ).
thf(sk4458_decl,type,
sk4458: $i ).
thf(sk4724_decl,type,
sk4724: $i ).
thf(sk4728_decl,type,
sk4728: $i ).
thf(sk4738_decl,type,
sk4738: $i ).
thf(sk4747_decl,type,
sk4747: $i ).
thf(sk4753_decl,type,
sk4753: $i ).
thf(sk4774_decl,type,
sk4774: $i ).
thf(sk4778_decl,type,
sk4778: $i ).
thf(sk4781_decl,type,
sk4781: $i ).
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,C: $i] :
( ( A @ B @ C )
=> ( A @ C @ B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ B @ D ) )
=> ( A @ C @ D ) ) )
!= ( ! [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 ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( sk1 @ sk2 @ A )
=> ( sk1 @ A @ sk2 ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk4 @ A )
& ( sk1 @ sk4 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk4 @ sk5 )
& ( sk1 @ sk4 @ A ) )
=> ( sk1 @ sk5 @ A ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk7 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk7 @ B ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk7 @ sk8 )
& ( sk1 @ sk8 @ A ) )
=> ( sk1 @ sk7 @ A ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
~ ( ( sk1 @ sk10 @ A )
=> ( sk1 @ A @ sk10 ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] :
~ ( ( sk1 @ sk12 @ A )
=> ( sk1 @ A @ sk12 ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk14 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk14 @ B ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk14 @ sk15 )
& ( sk1 @ sk15 @ A ) )
=> ( sk1 @ sk14 @ A ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk17 @ A )
& ( sk1 @ sk17 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk17 @ sk18 )
& ( sk1 @ sk17 @ A ) )
=> ( sk1 @ sk18 @ A ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i] :
~ ( ( sk1 @ sk20 @ A )
=> ( sk1 @ A @ sk20 ) ) ) ) ).
thf(sk117_def,definition,
( sk117
= ( @+[A: $i] :
~ ( ( sk1 @ sk53 @ A )
=> ( sk1 @ A @ sk53 ) ) ) ) ).
thf(sk118_def,definition,
( sk118
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk53 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk53 @ B ) ) ) ) ).
thf(sk119_def,definition,
( sk119
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk53 @ sk118 )
& ( sk1 @ sk118 @ A ) )
=> ( sk1 @ sk53 @ A ) ) ) ) ).
thf(sk120_def,definition,
( sk120
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ) ).
thf(sk121_def,definition,
( sk121
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk120 @ A )
& ( sk1 @ sk120 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk122_def,definition,
( sk122
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk120 @ sk121 )
& ( sk1 @ sk120 @ A ) )
=> ( sk1 @ sk121 @ A ) ) ) ) ).
thf(sk123_def,definition,
( sk123
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ).
thf(sk124_def,definition,
( sk124
= ( @+[A: $i] :
~ ( ( sk1 @ sk123 @ A )
=> ( sk1 @ A @ sk123 ) ) ) ) ).
thf(sk144_def,definition,
( sk144
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk66 @ A )
& ( sk1 @ sk66 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk145_def,definition,
( sk145
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk66 @ sk144 )
& ( sk1 @ sk66 @ A ) )
=> ( sk1 @ sk144 @ A ) ) ) ) ).
thf(sk146_def,definition,
( sk146
= ( @+[A: $i] :
~ ( ( sk1 @ sk66 @ A )
=> ( sk1 @ A @ sk66 ) ) ) ) ).
thf(sk147_def,definition,
( sk147
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ).
thf(sk148_def,definition,
( sk148
= ( @+[A: $i] :
~ ( ( sk1 @ sk147 @ A )
=> ( sk1 @ A @ sk147 ) ) ) ) ).
thf(sk149_def,definition,
( sk149
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ).
thf(sk150_def,definition,
( sk150
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk149 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk149 @ B ) ) ) ) ).
thf(sk151_def,definition,
( sk151
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk149 @ sk150 )
& ( sk1 @ sk150 @ A ) )
=> ( sk1 @ sk149 @ A ) ) ) ) ).
thf(sk171_def,definition,
( sk171
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ).
thf(sk172_def,definition,
( sk172
= ( @+[A: $i] :
~ ( ( sk1 @ sk171 @ A )
=> ( sk1 @ A @ sk171 ) ) ) ) ).
thf(sk173_def,definition,
( sk173
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ).
thf(sk174_def,definition,
( sk174
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk173 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk173 @ B ) ) ) ) ).
thf(sk175_def,definition,
( sk175
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk173 @ sk174 )
& ( sk1 @ sk174 @ A ) )
=> ( sk1 @ sk173 @ A ) ) ) ) ).
thf(sk176_def,definition,
( sk176
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ) ).
thf(sk177_def,definition,
( sk177
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk176 @ A )
& ( sk1 @ sk176 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk178_def,definition,
( sk178
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk176 @ sk177 )
& ( sk1 @ sk176 @ A ) )
=> ( sk1 @ sk177 @ A ) ) ) ) ).
thf(sk179_def,definition,
( sk179
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ).
thf(sk180_def,definition,
( sk180
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk179 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk179 @ B ) ) ) ) ).
thf(sk181_def,definition,
( sk181
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk179 @ sk180 )
& ( sk1 @ sk180 @ A ) )
=> ( sk1 @ sk179 @ A ) ) ) ) ).
thf(sk182_def,definition,
( sk182
= ( @+[A: $i] :
~ ( ( sk1 @ sk22 @ A )
=> ( sk1 @ A @ sk22 ) ) ) ) ).
thf(sk183_def,definition,
( sk183
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk22 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk22 @ B ) ) ) ) ).
thf(sk184_def,definition,
( sk184
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk22 @ sk183 )
& ( sk1 @ sk183 @ A ) )
=> ( sk1 @ sk22 @ A ) ) ) ) ).
thf(sk185_def,definition,
( sk185
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk23 @ A )
& ( sk1 @ sk23 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk186_def,definition,
( sk186
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk23 @ sk185 )
& ( sk1 @ sk23 @ A ) )
=> ( sk1 @ sk185 @ A ) ) ) ) ).
thf(sk187_def,definition,
( sk187
= ( @+[A: $i] :
~ ( ( sk1 @ sk23 @ A )
=> ( sk1 @ A @ sk23 ) ) ) ) ).
thf(sk284_def,definition,
( sk284
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) ) ).
thf(sk285_def,definition,
( sk285
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) ) ) ).
thf(sk286_def,definition,
( sk286
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk285 @ A )
& ( sk1 @ sk285 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk287_def,definition,
( sk287
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk285 @ sk286 )
& ( sk1 @ sk285 @ A ) )
=> ( sk1 @ sk286 @ A ) ) ) ) ).
thf(sk288_def,definition,
( sk288
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ).
thf(sk289_def,definition,
( sk289
= ( @+[A: $i] :
~ ( ( sk1 @ sk288 @ A )
=> ( sk1 @ A @ sk288 ) ) ) ) ).
thf(sk316_def,definition,
( sk316
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) ) ).
thf(sk962_def,definition,
( sk962
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk498 @ A )
& ( sk1 @ sk498 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk963_def,definition,
( sk963
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk498 @ sk962 )
& ( sk1 @ sk498 @ A ) )
=> ( sk1 @ sk962 @ A ) ) ) ) ).
thf(sk964_def,definition,
( sk964
= ( @+[A: $i] :
~ ( ( sk1 @ sk498 @ A )
=> ( sk1 @ A @ sk498 ) ) ) ) ).
thf(sk965_def,definition,
( sk965
= ( @+[A: $i] :
~ ( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) ) ) ).
thf(sk1090_def,definition,
( sk1090
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk629 @ sk630 )
& ( sk1 @ sk629 @ A ) )
=> ( sk1 @ sk630 @ A ) ) ) ) ).
thf(sk1091_def,definition,
( sk1091
= ( @+[A: $i] :
~ ( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) ) ) ).
thf(sk1332_def,definition,
( sk1332
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk403 @ A )
& ( sk1 @ sk403 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk1333_def,definition,
( sk1333
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk403 @ sk1332 )
& ( sk1 @ sk403 @ A ) )
=> ( sk1 @ sk1332 @ A ) ) ) ) ).
thf(sk1334_def,definition,
( sk1334
= ( @+[A: $i] :
~ ( ( sk1 @ sk403 @ A )
=> ( sk1 @ A @ sk403 ) ) ) ) ).
thf(sk1335_def,definition,
( sk1335
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) ) ).
thf(sk1417_def,definition,
( sk1417
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk707 @ A )
& ( sk1 @ sk707 @ B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk1418_def,definition,
( sk1418
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk707 @ sk1417 )
& ( sk1 @ sk707 @ A ) )
=> ( sk1 @ sk1417 @ A ) ) ) ) ).
thf(sk1419_def,definition,
( sk1419
= ( @+[A: $i] :
~ ( ( sk1 @ sk707 @ A )
=> ( sk1 @ A @ sk707 ) ) ) ) ).
thf(sk1420_def,definition,
( sk1420
= ( @+[A: $i] :
~ ( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) ) ) ).
thf(sk1680_def,definition,
( sk1680
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) ) ) ).
thf(sk1681_def,definition,
( sk1681
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ).
thf(sk1682_def,definition,
( sk1682
= ( @+[A: $i] :
~ ( ( sk1 @ sk1681 @ A )
=> ( sk1 @ A @ sk1681 ) ) ) ) ).
thf(sk1683_def,definition,
( sk1683
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ).
thf(sk1684_def,definition,
( sk1684
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk1683 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk1683 @ B ) ) ) ) ).
thf(sk1685_def,definition,
( sk1685
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk1683 @ sk1684 )
& ( sk1 @ sk1684 @ A ) )
=> ( sk1 @ sk1683 @ A ) ) ) ) ).
thf(sk1840_def,definition,
( sk1840
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) ) ) ).
thf(sk4457_def,definition,
( sk4457
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk811 @ sk812 )
& ( sk1 @ sk811 @ A ) )
=> ( sk1 @ sk812 @ A ) ) ) ) ).
thf(sk4458_def,definition,
( sk4458
= ( @+[A: $i] :
~ ( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) ) ) ).
thf(sk4724_def,definition,
( sk4724
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) ) ) ).
thf(sk4728_def,definition,
( sk4728
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) ) ) ).
thf(sk4738_def,definition,
( sk4738
= ( @+[A: $i] :
~ ( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) ) ) ).
thf(sk4747_def,definition,
( sk4747
= ( @+[A: $i] :
~ ( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) ) ) ).
thf(sk4753_def,definition,
( sk4753
= ( @+[A: $i] :
~ ( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) ) ) ).
thf(sk4774_def,definition,
( sk4774
= ( @+[A: $i] :
~ ( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) ) ) ).
thf(sk4778_def,definition,
( sk4778
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) ) ).
thf(sk4781_def,definition,
( sk4781
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ( ( msymmetric @ A )
& ( meuclidean @ A ) )
= ( ( mtransitive @ A )
& ( msymmetric @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ( ( msymmetric @ A )
& ( meuclidean @ A ) )
= ( ( mtransitive @ A )
& ( msymmetric @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o] :
( ( ! [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 ) ) )
= ( ! [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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [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 @ B @ C ) )
=> ( sk1 @ A @ C ) )
& ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [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 @ B @ C ) )
=> ( sk1 @ A @ C ) )
& ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(55,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(1799,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(1814,plain,
( ( ( ( sk1 @ sk59 @ sk60 )
=> ( sk1 @ sk60 @ sk59 ) )
!= ( ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) )
| ( ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(func_ext,[status(esa)],[1799]) ).
thf(11100,plain,
( ( ( ( sk1 @ sk59 @ sk60 )
=> ( sk1 @ sk60 @ sk59 ) )
!= ( ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) )
| ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[1814]) ).
thf(11928,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ( ( sk1 @ sk59 @ sk60 )
=> ( sk1 @ sk60 @ sk59 ) )
| ~ ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ),
inference(bool_ext,[status(thm)],[11100]) ).
thf(12430,plain,
( ( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk60 @ sk316 ) )
& ( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk59 @ sk316 ) )
& ( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk60 @ sk316 ) )
& ( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk316 ) ) ),
inference(cnf,[status(esa)],[11928]) ).
thf(12431,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 ) ),
inference(cnfConj,[status(thm)],[12430]) ).
thf(12437,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk59 @ sk60 ) ),
inference(simp,[status(thm)],[12431]) ).
thf(13981,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( $true
=> ( sk1 @ sk60 @ sk59 ) )
!= ( ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) )
| ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[12437,11100]) ).
thf(13982,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( sk1 @ sk60 @ sk59 )
!= ( ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[13981]) ).
thf(13983,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( sk1 @ sk60 @ sk59 )
!= ( ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[13982:[]]) ).
thf(15099,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( ! [A: $i] :
( ( $true
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) )
!= ( sk1 @ sk60 @ sk59 ) )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[12437,13983]) ).
thf(15100,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) )
!= ( sk1 @ sk60 @ sk59 ) )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[15099]) ).
thf(15101,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(pattern_uni,[status(thm)],[15100:[]]) ).
thf(15744,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(simp,[status(thm)],[15101]) ).
thf(18454,plain,
( ( ( ! [A: $i] :
( ( ( sk1 @ sk629 @ sk630 )
& ( sk1 @ sk629 @ A ) )
=> ( sk1 @ sk630 @ A ) ) )
!= ( ( sk1 @ sk629 @ sk630 )
=> ( sk1 @ sk630 @ sk629 ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(func_ext,[status(esa)],[15744]) ).
thf(23427,plain,
( ~ ! [A: $i] :
( ( ( sk1 @ sk629 @ sk630 )
& ( sk1 @ sk629 @ A ) )
=> ( sk1 @ sk630 @ A ) )
| ~ ( ( sk1 @ sk629 @ sk630 )
=> ( sk1 @ sk630 @ sk629 ) )
| ~ ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) )
| ~ ( sk1 @ sk60 @ sk59 ) ),
inference(bool_ext,[status(thm)],[18454]) ).
thf(23858,plain,
( ( ( sk1 @ sk629 @ sk630 )
| ( sk1 @ sk629 @ sk630 )
| ( sk1 @ sk60 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk629 @ sk630 )
| ( sk1 @ sk629 @ sk630 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk629 @ sk630 )
| ~ ( sk1 @ sk630 @ sk629 )
| ( sk1 @ sk60 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk629 @ sk630 )
| ~ ( sk1 @ sk630 @ sk629 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk629 @ sk1090 )
| ( sk1 @ sk629 @ sk630 )
| ( sk1 @ sk60 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk629 @ sk1090 )
| ( sk1 @ sk629 @ sk630 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk629 @ sk1090 )
| ~ ( sk1 @ sk630 @ sk629 )
| ( sk1 @ sk60 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk629 @ sk1090 )
| ~ ( sk1 @ sk630 @ sk629 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk630 @ sk1090 )
| ( sk1 @ sk629 @ sk630 )
| ( sk1 @ sk60 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk630 @ sk1090 )
| ( sk1 @ sk629 @ sk630 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk630 @ sk1090 )
| ~ ( sk1 @ sk630 @ sk629 )
| ( sk1 @ sk60 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk630 @ sk1090 )
| ~ ( sk1 @ sk630 @ sk629 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) ) ),
inference(cnf,[status(esa)],[23427]) ).
thf(23863,plain,
( ( sk1 @ sk629 @ sk630 )
| ( sk1 @ sk629 @ sk630 )
| ( sk1 @ sk60 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) ),
inference(cnfConj,[status(thm)],[23858]) ).
thf(23872,plain,
( ( sk1 @ sk629 @ sk630 )
| ( sk1 @ sk60 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) ),
inference(simp,[status(thm)],[23863]) ).
thf(56,plain,
( ( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(1826,plain,
( ( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(1840,plain,
( ( ( ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) )
!= ( ( sk1 @ sk72 @ sk73 )
=> ( sk1 @ sk73 @ sk72 ) ) )
| ( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(func_ext,[status(esa)],[1826]) ).
thf(32989,plain,
( ~ ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) )
| ~ ( ( sk1 @ sk72 @ sk73 )
=> ( sk1 @ sk73 @ sk72 ) )
| ~ ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) )
| ~ ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ),
inference(bool_ext,[status(thm)],[1840]) ).
thf(33635,plain,
( ( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1683 @ sk1684 ) )
& ( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1684 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ~ ( sk1 @ sk1683 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1683 @ sk1684 ) )
& ( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1684 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ~ ( sk1 @ sk1683 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk73 @ sk72 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1683 @ sk1684 ) )
& ( ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk73 @ sk72 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1684 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk73 @ sk72 )
| ( sk1 @ sk1681 @ sk1682 )
| ~ ( sk1 @ sk1683 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk73 @ sk72 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1683 @ sk1684 ) )
& ( ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk73 @ sk72 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1684 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk73 @ sk72 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ~ ( sk1 @ sk1683 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk1680 )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1683 @ sk1684 ) )
& ( ( sk1 @ sk72 @ sk1680 )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1684 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk1680 )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ~ ( sk1 @ sk1683 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk1680 )
| ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1683 @ sk1684 ) )
& ( ( sk1 @ sk72 @ sk1680 )
| ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1684 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk1680 )
| ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ~ ( sk1 @ sk1683 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk1680 )
| ~ ( sk1 @ sk73 @ sk72 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1683 @ sk1684 ) )
& ( ( sk1 @ sk72 @ sk1680 )
| ~ ( sk1 @ sk73 @ sk72 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1684 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk1680 )
| ~ ( sk1 @ sk73 @ sk72 )
| ( sk1 @ sk1681 @ sk1682 )
| ~ ( sk1 @ sk1683 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk1680 )
| ~ ( sk1 @ sk73 @ sk72 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1683 @ sk1684 ) )
& ( ( sk1 @ sk72 @ sk1680 )
| ~ ( sk1 @ sk73 @ sk72 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1684 @ sk1685 ) )
& ( ( sk1 @ sk72 @ sk1680 )
| ~ ( sk1 @ sk73 @ sk72 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ~ ( sk1 @ sk1683 @ sk1685 ) )
& ( ~ ( sk1 @ sk73 @ sk1680 )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1683 @ sk1684 ) )
& ( ~ ( sk1 @ sk73 @ sk1680 )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1684 @ sk1685 ) )
& ( ~ ( sk1 @ sk73 @ sk1680 )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ~ ( sk1 @ sk1683 @ sk1685 ) )
& ( ~ ( sk1 @ sk73 @ sk1680 )
| ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1683 @ sk1684 ) )
& ( ~ ( sk1 @ sk73 @ sk1680 )
| ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1684 @ sk1685 ) )
& ( ~ ( sk1 @ sk73 @ sk1680 )
| ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ~ ( sk1 @ sk1683 @ sk1685 ) )
& ( ~ ( sk1 @ sk73 @ sk1680 )
| ~ ( sk1 @ sk73 @ sk72 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1683 @ sk1684 ) )
& ( ~ ( sk1 @ sk73 @ sk1680 )
| ~ ( sk1 @ sk73 @ sk72 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1684 @ sk1685 ) )
& ( ~ ( sk1 @ sk73 @ sk1680 )
| ~ ( sk1 @ sk73 @ sk72 )
| ( sk1 @ sk1681 @ sk1682 )
| ~ ( sk1 @ sk1683 @ sk1685 ) )
& ( ~ ( sk1 @ sk73 @ sk1680 )
| ~ ( sk1 @ sk73 @ sk72 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1683 @ sk1684 ) )
& ( ~ ( sk1 @ sk73 @ sk1680 )
| ~ ( sk1 @ sk73 @ sk72 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1684 @ sk1685 ) )
& ( ~ ( sk1 @ sk73 @ sk1680 )
| ~ ( sk1 @ sk73 @ sk72 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ~ ( sk1 @ sk1683 @ sk1685 ) ) ),
inference(cnf,[status(esa)],[32989]) ).
thf(33645,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ~ ( sk1 @ sk1683 @ sk1685 ) ),
inference(cnfConj,[status(thm)],[33635]) ).
thf(33675,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ~ ( sk1 @ sk1683 @ sk1685 ) ),
inference(simp,[status(thm)],[33645]) ).
thf(32988,plain,
( ( ( ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) )
!= ( ( sk1 @ sk72 @ sk73 )
=> ( sk1 @ sk73 @ sk72 ) ) )
| ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[1840]) ).
thf(34222,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) )
| ~ ( ( sk1 @ sk72 @ sk73 )
=> ( sk1 @ sk73 @ sk72 ) ) ),
inference(bool_ext,[status(thm)],[32988]) ).
thf(34938,plain,
( ( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk72 @ sk73 ) )
& ( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk73 @ sk72 ) )
& ( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk1840 )
| ( sk1 @ sk72 @ sk73 ) )
& ( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk1840 )
| ~ ( sk1 @ sk73 @ sk72 ) )
& ( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ( sk1 @ sk73 @ sk1840 )
| ( sk1 @ sk72 @ sk73 ) )
& ( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ( sk1 @ sk73 @ sk1840 )
| ~ ( sk1 @ sk73 @ sk72 ) ) ),
inference(cnf,[status(esa)],[34222]) ).
thf(34939,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk72 @ sk73 ) ),
inference(cnfConj,[status(thm)],[34938]) ).
thf(34945,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk73 ) ),
inference(simp,[status(thm)],[34939]) ).
thf(35677,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( ! [A: $i] :
( ( $true
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) )
!= ( ( sk1 @ sk72 @ sk73 )
=> ( sk1 @ sk73 @ sk72 ) ) )
| ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( sk1 @ sk72 @ sk73 )
!= ( sk1 @ sk72 @ sk73 ) ) ),
inference(paramod_ordered,[status(thm)],[34945,32988]) ).
thf(35678,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) )
!= ( ( sk1 @ sk72 @ sk73 )
=> ( sk1 @ sk73 @ sk72 ) ) )
| ( ( sk1 @ sk72 @ sk73 )
!= ( sk1 @ sk72 @ sk73 ) ) ),
inference(simp,[status(thm)],[35677]) ).
thf(35679,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) )
!= ( ( sk1 @ sk72 @ sk73 )
=> ( sk1 @ sk73 @ sk72 ) ) ) ),
inference(pattern_uni,[status(thm)],[35678:[]]) ).
thf(8,plain,
( ( ! [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 @ B @ C ) )
=> ( sk1 @ A @ C ) )
& ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(46,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( sk1 @ A @ B )
| ( sk1 @ B @ A )
| ~ ( sk1 @ F @ G )
| ~ ( sk1 @ G @ H )
| ( sk1 @ F @ H ) )
& ( ~ ( sk1 @ A @ B )
| ( sk1 @ B @ A )
| ~ ( sk1 @ I @ J )
| ( sk1 @ J @ I ) )
& ( ~ ( sk1 @ C @ D )
| ~ ( sk1 @ C @ E )
| ( sk1 @ D @ E )
| ~ ( sk1 @ F @ G )
| ~ ( sk1 @ G @ H )
| ( sk1 @ F @ H ) )
& ( ~ ( sk1 @ C @ D )
| ~ ( sk1 @ C @ E )
| ( sk1 @ D @ E )
| ~ ( sk1 @ I @ J )
| ( sk1 @ J @ I ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ( sk1 @ B @ A )
| ~ ( sk1 @ C @ D )
| ( sk1 @ D @ C ) ),
inference(cnfConj,[status(thm)],[46]) ).
thf(52,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ( sk1 @ B @ A )
| ~ ( sk1 @ C @ D )
| ( sk1 @ D @ C ) ),
inference(simp,[status(thm)],[48]) ).
thf(72765,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ( sk1 @ B @ A )
| ( sk1 @ D @ C )
| ( ( sk1 @ C @ D )
!= ( sk1 @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[52]) ).
thf(72767,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ( sk1 @ B @ A )
| ( sk1 @ B @ A ) ),
inference(pattern_uni,[status(thm)],[72765:[bind(A,$thf( C )),bind(B,$thf( D ))]]) ).
thf(72823,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ( sk1 @ B @ A ) ),
inference(simp,[status(thm)],[72767]) ).
thf(7,plain,
( ~ ( ! [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 @ B @ C ) )
=> ( sk1 @ A @ C ) )
& ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) )
& ( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(14,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(10,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(580,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ $true
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[14,10]) ).
thf(581,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(simp,[status(thm)],[580]) ).
thf(683,plain,
( ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[581]) ).
thf(686,plain,
( ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[683]) ).
thf(21,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(23,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(2642,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ $true
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[21,23]) ).
thf(2643,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(simp,[status(thm)],[2642]) ).
thf(2752,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk11 != sk10 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[2643]) ).
thf(2771,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[2752]) ).
thf(2812,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ $true
| ( sk11 != sk10 )
| ( ( sk1 @ sk7 @ sk9 )
!= ( sk1 @ sk7 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[686,2771]) ).
thf(2813,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( ( sk1 @ sk7 @ sk9 )
!= ( sk1 @ sk7 @ sk8 ) ) ),
inference(simp,[status(thm)],[2812]) ).
thf(2895,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( sk7 != sk7 )
| ( sk9 != sk8 ) ),
inference(simp,[status(thm)],[2813]) ).
thf(2919,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( sk9 != sk8 ) ),
inference(simp,[status(thm)],[2895]) ).
thf(73945,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ $true
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( sk9 != sk8 )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[72823,2919]) ).
thf(73946,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( sk9 != sk8 )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[73945]) ).
thf(73947,plain,
( ~ ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( sk9 != sk8 ) ),
inference(pattern_uni,[status(thm)],[73946:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(11,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(12,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(257,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ $true
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[11,12]) ).
thf(258,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(268,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[258]) ).
thf(270,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[268]) ).
thf(32,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(28,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(7066,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ $true
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[32,28]) ).
thf(7067,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(simp,[status(thm)],[7066]) ).
thf(7359,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk11 != sk10 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[7067]) ).
thf(7405,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[7359]) ).
thf(7430,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ $true
| ( sk11 != sk10 )
| ( ( sk1 @ sk7 @ sk9 )
!= ( sk1 @ sk7 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[270,7405]) ).
thf(7431,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( ( sk1 @ sk7 @ sk9 )
!= ( sk1 @ sk7 @ sk8 ) ) ),
inference(simp,[status(thm)],[7430]) ).
thf(7517,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( sk7 != sk7 )
| ( sk9 != sk8 ) ),
inference(simp,[status(thm)],[7431]) ).
thf(7549,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( sk9 != sk8 ) ),
inference(simp,[status(thm)],[7517]) ).
thf(63,plain,
( ( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[6]) ).
thf(64,plain,
( ( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(8822,plain,
( ~ ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ),
inference(bool_ext,[status(thm)],[64]) ).
thf(8841,plain,
( ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk173 @ sk174 )
| ( sk1 @ sk176 @ sk177 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk173 @ sk174 )
| ( sk1 @ sk176 @ sk177 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk173 @ sk174 )
| ( sk1 @ sk176 @ sk177 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk173 @ sk174 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk173 @ sk174 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk173 @ sk174 )
| ( sk1 @ sk176 @ sk178 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk173 @ sk174 )
| ~ ( sk1 @ sk177 @ sk178 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk173 @ sk174 )
| ~ ( sk1 @ sk177 @ sk178 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk173 @ sk174 )
| ~ ( sk1 @ sk177 @ sk178 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk177 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk177 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk177 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk178 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk174 @ sk175 )
| ~ ( sk1 @ sk177 @ sk178 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk174 @ sk175 )
| ~ ( sk1 @ sk177 @ sk178 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk174 @ sk175 )
| ~ ( sk1 @ sk177 @ sk178 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ~ ( sk1 @ sk173 @ sk175 )
| ( sk1 @ sk176 @ sk177 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ~ ( sk1 @ sk173 @ sk175 )
| ( sk1 @ sk176 @ sk177 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ~ ( sk1 @ sk173 @ sk175 )
| ( sk1 @ sk176 @ sk177 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ~ ( sk1 @ sk173 @ sk175 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ~ ( sk1 @ sk173 @ sk175 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ~ ( sk1 @ sk173 @ sk175 )
| ( sk1 @ sk176 @ sk178 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ~ ( sk1 @ sk173 @ sk175 )
| ~ ( sk1 @ sk177 @ sk178 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ~ ( sk1 @ sk173 @ sk175 )
| ~ ( sk1 @ sk177 @ sk178 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ( sk1 @ sk171 @ sk172 )
| ~ ( sk1 @ sk173 @ sk175 )
| ~ ( sk1 @ sk177 @ sk178 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk173 @ sk174 )
| ( sk1 @ sk176 @ sk177 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk173 @ sk174 )
| ( sk1 @ sk176 @ sk177 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk173 @ sk174 )
| ( sk1 @ sk176 @ sk177 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk173 @ sk174 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk173 @ sk174 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk173 @ sk174 )
| ( sk1 @ sk176 @ sk178 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk173 @ sk174 )
| ~ ( sk1 @ sk177 @ sk178 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk173 @ sk174 )
| ~ ( sk1 @ sk177 @ sk178 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk173 @ sk174 )
| ~ ( sk1 @ sk177 @ sk178 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk177 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk177 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk177 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk178 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk174 @ sk175 )
| ~ ( sk1 @ sk177 @ sk178 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk174 @ sk175 )
| ~ ( sk1 @ sk177 @ sk178 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ( sk1 @ sk174 @ sk175 )
| ~ ( sk1 @ sk177 @ sk178 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ~ ( sk1 @ sk173 @ sk175 )
| ( sk1 @ sk176 @ sk177 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ~ ( sk1 @ sk173 @ sk175 )
| ( sk1 @ sk176 @ sk177 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ~ ( sk1 @ sk173 @ sk175 )
| ( sk1 @ sk176 @ sk177 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ~ ( sk1 @ sk173 @ sk175 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ~ ( sk1 @ sk173 @ sk175 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ~ ( sk1 @ sk173 @ sk175 )
| ( sk1 @ sk176 @ sk178 )
| ~ ( sk1 @ sk179 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ~ ( sk1 @ sk173 @ sk175 )
| ~ ( sk1 @ sk177 @ sk178 )
| ( sk1 @ sk179 @ sk180 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ~ ( sk1 @ sk173 @ sk175 )
| ~ ( sk1 @ sk177 @ sk178 )
| ( sk1 @ sk180 @ sk181 ) )
& ( ~ ( sk1 @ sk172 @ sk171 )
| ~ ( sk1 @ sk173 @ sk175 )
| ~ ( sk1 @ sk177 @ sk178 )
| ~ ( sk1 @ sk179 @ sk181 ) ) ),
inference(cnf,[status(esa)],[8822]) ).
thf(8843,plain,
( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk173 @ sk174 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk180 @ sk181 ) ),
inference(cnfConj,[status(thm)],[8841]) ).
thf(33643,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1684 @ sk1685 ) ),
inference(cnfConj,[status(thm)],[33635]) ).
thf(33672,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1684 @ sk1685 ) ),
inference(simp,[status(thm)],[33643]) ).
thf(52535,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ~ $true
| ( ( sk1 @ sk1684 @ sk1685 )
!= ( sk1 @ sk1683 @ sk1685 ) ) ),
inference(paramod_ordered,[status(thm)],[33672,33675]) ).
thf(52536,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( ( sk1 @ sk1684 @ sk1685 )
!= ( sk1 @ sk1683 @ sk1685 ) ) ),
inference(simp,[status(thm)],[52535]) ).
thf(52645,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1684 != sk1683 )
| ( sk1685 != sk1685 ) ),
inference(simp,[status(thm)],[52536]) ).
thf(52694,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1684 != sk1683 ) ),
inference(simp,[status(thm)],[52645]) ).
thf(33638,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1684 @ sk1685 ) ),
inference(cnfConj,[status(thm)],[33635]) ).
thf(33676,plain,
( ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1684 @ sk1685 ) ),
inference(simp,[status(thm)],[33638]) ).
thf(33649,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ~ ( sk1 @ sk1683 @ sk1685 ) ),
inference(cnfConj,[status(thm)],[33635]) ).
thf(33677,plain,
( ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ~ ( sk1 @ sk1683 @ sk1685 ) ),
inference(simp,[status(thm)],[33649]) ).
thf(70533,plain,
( ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ~ $true
| ( ( sk1 @ sk1684 @ sk1685 )
!= ( sk1 @ sk1683 @ sk1685 ) ) ),
inference(paramod_ordered,[status(thm)],[33676,33677]) ).
thf(70534,plain,
( ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( ( sk1 @ sk1684 @ sk1685 )
!= ( sk1 @ sk1683 @ sk1685 ) ) ),
inference(simp,[status(thm)],[70533]) ).
thf(70780,plain,
( ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1684 != sk1683 )
| ( sk1685 != sk1685 ) ),
inference(simp,[status(thm)],[70534]) ).
thf(70898,plain,
( ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1684 != sk1683 ) ),
inference(simp,[status(thm)],[70780]) ).
thf(70928,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1684 != sk1683 )
| ( sk1 @ sk72 @ sk73 )
| ~ $true
| ( sk1684 != sk1683 )
| ( ( sk1 @ sk1682 @ sk1681 )
!= ( sk1 @ sk1681 @ sk1682 ) ) ),
inference(paramod_ordered,[status(thm)],[52694,70898]) ).
thf(70929,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1684 != sk1683 )
| ( ( sk1 @ sk1682 @ sk1681 )
!= ( sk1 @ sk1681 @ sk1682 ) ) ),
inference(simp,[status(thm)],[70928]) ).
thf(71024,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1684 != sk1683 )
| ( sk1682 != sk1681 )
| ( sk1682 != sk1681 ) ),
inference(simp,[status(thm)],[70929]) ).
thf(71087,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1684 != sk1683 )
| ( sk1682 != sk1681 ) ),
inference(simp,[status(thm)],[71024]) ).
thf(79428,plain,
! [B: $i,A: $i] :
( ( sk1684 != sk1683 )
| ( sk1682 != sk1681 )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk72 @ sk73 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[71087,72823]) ).
thf(79429,plain,
! [B: $i,A: $i] :
( ( sk1684 != sk1683 )
| ( sk1682 != sk1681 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk72 @ sk73 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[79428]) ).
thf(79430,plain,
( ( sk1684 != sk1683 )
| ( sk1682 != sk1681 )
| ( sk1 @ sk73 @ sk72 ) ),
inference(pattern_uni,[status(thm)],[79429:[bind(A,$thf( sk72 )),bind(B,$thf( sk73 ))]]) ).
thf(8855,plain,
( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk177 )
| ( sk1 @ sk179 @ sk180 ) ),
inference(cnfConj,[status(thm)],[8841]) ).
thf(1828,plain,
( ( ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk66 @ A )
& ( sk1 @ sk66 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ! [A: $i] :
( ( sk1 @ sk66 @ A )
=> ( sk1 @ A @ sk66 ) ) ) )
| ( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(func_ext,[status(esa)],[56]) ).
thf(6199,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk66 @ A )
& ( sk1 @ sk66 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ^ [A: $i] :
( ( sk1 @ sk66 @ A )
=> ( sk1 @ A @ sk66 ) ) ) )
| ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[1828]) ).
thf(11101,plain,
( ~ ( ( sk1 @ sk59 @ sk60 )
=> ( sk1 @ sk60 @ sk59 ) )
| ~ ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) )
| ~ ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) )
| ~ ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ),
inference(bool_ext,[status(thm)],[1814]) ).
thf(11861,plain,
( ( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk286 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk286 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk60 @ sk284 )
| ( sk1 @ sk285 @ sk286 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk60 @ sk284 )
| ( sk1 @ sk285 @ sk286 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk60 @ sk284 )
| ( sk1 @ sk285 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk60 @ sk284 )
| ( sk1 @ sk285 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk60 @ sk284 )
| ~ ( sk1 @ sk286 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk60 @ sk284 )
| ~ ( sk1 @ sk286 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk59 @ sk284 )
| ( sk1 @ sk285 @ sk286 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk59 @ sk284 )
| ( sk1 @ sk285 @ sk286 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk59 @ sk284 )
| ( sk1 @ sk285 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk59 @ sk284 )
| ( sk1 @ sk285 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk59 @ sk284 )
| ~ ( sk1 @ sk286 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk59 @ sk284 )
| ~ ( sk1 @ sk286 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk286 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk286 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk60 @ sk284 )
| ( sk1 @ sk285 @ sk286 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk60 @ sk284 )
| ( sk1 @ sk285 @ sk286 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk60 @ sk284 )
| ( sk1 @ sk285 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk60 @ sk284 )
| ( sk1 @ sk285 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk60 @ sk284 )
| ~ ( sk1 @ sk286 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk60 @ sk284 )
| ~ ( sk1 @ sk286 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk284 )
| ( sk1 @ sk285 @ sk286 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk284 )
| ( sk1 @ sk285 @ sk286 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk284 )
| ( sk1 @ sk285 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk284 )
| ( sk1 @ sk285 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk284 )
| ~ ( sk1 @ sk286 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) )
& ( ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk284 )
| ~ ( sk1 @ sk286 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) ) ),
inference(cnf,[status(esa)],[11101]) ).
thf(11880,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) ),
inference(cnfConj,[status(thm)],[11861]) ).
thf(11901,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) ),
inference(simp,[status(thm)],[11880]) ).
thf(73639,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk288 @ sk289 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11901,72823]) ).
thf(73640,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk288 @ sk289 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[73639]) ).
thf(73641,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ( sk1 @ sk289 @ sk288 ) ),
inference(pattern_uni,[status(thm)],[73640:[bind(A,$thf( sk288 )),bind(B,$thf( sk289 ))]]) ).
thf(11897,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) ),
inference(cnfConj,[status(thm)],[11861]) ).
thf(11899,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) ),
inference(simp,[status(thm)],[11897]) ).
thf(97947,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ~ $true
| ( ( sk1 @ sk289 @ sk288 )
!= ( sk1 @ sk289 @ sk288 ) ) ),
inference(paramod_ordered,[status(thm)],[73641,11899]) ).
thf(97948,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ( ( sk1 @ sk289 @ sk288 )
!= ( sk1 @ sk289 @ sk288 ) ) ),
inference(simp,[status(thm)],[97947]) ).
thf(97949,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 ) ),
inference(pattern_uni,[status(thm)],[97948:[]]) ).
thf(99185,plain,
( ( sk1 @ sk59 @ sk60 )
| ( ( sk1 @ sk285 @ sk287 )
!= ( sk1 @ sk59 @ sk60 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[97949]) ).
thf(99247,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk285 != sk59 )
| ( sk287 != sk60 ) ),
inference(simp,[status(thm)],[99185]) ).
thf(23868,plain,
( ( sk1 @ sk629 @ sk630 )
| ( sk1 @ sk629 @ sk630 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) ),
inference(cnfConj,[status(thm)],[23858]) ).
thf(23871,plain,
( ( sk1 @ sk629 @ sk630 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) ),
inference(simp,[status(thm)],[23868]) ).
thf(23866,plain,
( ~ ( sk1 @ sk630 @ sk1090 )
| ~ ( sk1 @ sk630 @ sk629 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 ) ),
inference(cnfConj,[status(thm)],[23858]) ).
thf(24880,plain,
( ~ ( sk1 @ sk630 @ sk629 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( ( sk1 @ sk630 @ sk1090 )
!= ( sk1 @ sk630 @ sk629 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[23866]) ).
thf(24969,plain,
( ~ ( sk1 @ sk630 @ sk629 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk630 != sk630 )
| ( sk1090 != sk629 ) ),
inference(simp,[status(thm)],[24880]) ).
thf(25044,plain,
( ~ ( sk1 @ sk630 @ sk629 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1090 != sk629 ) ),
inference(simp,[status(thm)],[24969]) ).
thf(39588,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ $true
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1090 != sk629 )
| ( ( sk1 @ sk630 @ sk629 )
!= ( sk1 @ sk629 @ sk630 ) ) ),
inference(paramod_ordered,[status(thm)],[23871,25044]) ).
thf(39589,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1090 != sk629 )
| ( ( sk1 @ sk630 @ sk629 )
!= ( sk1 @ sk629 @ sk630 ) ) ),
inference(simp,[status(thm)],[39588]) ).
thf(39810,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk630 != sk629 ) ),
inference(simp,[status(thm)],[39589]) ).
thf(40253,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 ) ),
inference(simp,[status(thm)],[39810]) ).
thf(73765,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ $true
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(paramod_ordered,[status(thm)],[72823,40253]) ).
thf(73766,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ sk59 @ sk1091 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(simp,[status(thm)],[73765]) ).
thf(73767,plain,
( ~ ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 ) ),
inference(pattern_uni,[status(thm)],[73766:[bind(A,$thf( sk59 )),bind(B,$thf( sk60 ))]]) ).
thf(86703,plain,
( ~ ( sk1 @ sk59 @ sk60 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( ( sk1 @ sk59 @ sk1091 )
!= ( sk1 @ sk59 @ sk60 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[73767]) ).
thf(86794,plain,
( ~ ( sk1 @ sk59 @ sk60 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk59 != sk59 )
| ( sk1091 != sk60 ) ),
inference(simp,[status(thm)],[86703]) ).
thf(86832,plain,
( ~ ( sk1 @ sk59 @ sk60 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 ) ),
inference(simp,[status(thm)],[86794]) ).
thf(111624,plain,
( ( sk285 != sk59 )
| ( sk287 != sk60 )
| ~ $true
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[99247,86832]) ).
thf(111625,plain,
( ( sk285 != sk59 )
| ( sk287 != sk60 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[111624]) ).
thf(111626,plain,
( ( sk285 != sk59 )
| ( sk287 != sk60 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 ) ),
inference(pattern_uni,[status(thm)],[111625:[]]) ).
thf(98823,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk59 @ sk60 )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk285 @ sk287 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[97949,72823]) ).
thf(98824,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk285 @ sk287 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[98823]) ).
thf(98825,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk287 @ sk285 ) ),
inference(pattern_uni,[status(thm)],[98824:[bind(A,$thf( sk285 )),bind(B,$thf( sk287 ))]]) ).
thf(100360,plain,
( ( sk1 @ sk59 @ sk60 )
| ( ( sk1 @ sk287 @ sk285 )
!= ( sk1 @ sk59 @ sk60 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[98825]) ).
thf(100566,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk287 != sk59 )
| ( sk285 != sk60 ) ),
inference(simp,[status(thm)],[100360]) ).
thf(116099,plain,
( ( sk287 != sk59 )
| ( sk285 != sk60 )
| ~ $true
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[100566,86832]) ).
thf(116100,plain,
( ( sk287 != sk59 )
| ( sk285 != sk60 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[116099]) ).
thf(116101,plain,
( ( sk287 != sk59 )
| ( sk285 != sk60 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 ) ),
inference(pattern_uni,[status(thm)],[116100:[]]) ).
thf(58,plain,
( ~ ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(78,plain,
( ( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk17 @ sk19 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk17 @ sk19 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk14 @ sk15 )
| ~ ( sk1 @ sk18 @ sk19 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk14 @ sk15 )
| ~ ( sk1 @ sk18 @ sk19 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk15 @ sk16 )
| ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk15 @ sk16 )
| ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk15 @ sk16 )
| ( sk1 @ sk17 @ sk19 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk15 @ sk16 )
| ( sk1 @ sk17 @ sk19 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk15 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk15 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ~ ( sk1 @ sk14 @ sk16 )
| ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ~ ( sk1 @ sk14 @ sk16 )
| ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ~ ( sk1 @ sk14 @ sk16 )
| ( sk1 @ sk17 @ sk19 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ~ ( sk1 @ sk14 @ sk16 )
| ( sk1 @ sk17 @ sk19 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ~ ( sk1 @ sk14 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ( sk1 @ sk12 @ sk13 )
| ~ ( sk1 @ sk14 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk17 @ sk19 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk17 @ sk19 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ( sk1 @ sk14 @ sk15 )
| ~ ( sk1 @ sk18 @ sk19 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ( sk1 @ sk14 @ sk15 )
| ~ ( sk1 @ sk18 @ sk19 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ( sk1 @ sk15 @ sk16 )
| ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ( sk1 @ sk15 @ sk16 )
| ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ( sk1 @ sk15 @ sk16 )
| ( sk1 @ sk17 @ sk19 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ( sk1 @ sk15 @ sk16 )
| ( sk1 @ sk17 @ sk19 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ( sk1 @ sk15 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ( sk1 @ sk15 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ~ ( sk1 @ sk14 @ sk16 )
| ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ~ ( sk1 @ sk14 @ sk16 )
| ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ~ ( sk1 @ sk14 @ sk16 )
| ( sk1 @ sk17 @ sk19 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ~ ( sk1 @ sk14 @ sk16 )
| ( sk1 @ sk17 @ sk19 )
| ~ ( sk1 @ sk21 @ sk20 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ~ ( sk1 @ sk14 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ( sk1 @ sk20 @ sk21 ) )
& ( ~ ( sk1 @ sk13 @ sk12 )
| ~ ( sk1 @ sk14 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ~ ( sk1 @ sk21 @ sk20 ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(103,plain,
( ~ ( sk1 @ sk13 @ sk12 )
| ~ ( sk1 @ sk14 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ~ ( sk1 @ sk21 @ sk20 ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(149,plain,
( ~ ( sk1 @ sk13 @ sk12 )
| ~ ( sk1 @ sk14 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ( ( sk1 @ sk21 @ sk20 )
!= ( sk1 @ sk13 @ sk12 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[103]) ).
thf(153,plain,
( ~ ( sk1 @ sk13 @ sk12 )
| ~ ( sk1 @ sk14 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ( sk21 != sk13 )
| ( sk20 != sk12 ) ),
inference(simp,[status(thm)],[149]) ).
thf(13984,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( ! [A: $i] :
( ( $true
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) )
!= ( ( sk1 @ sk59 @ sk60 )
=> ( sk1 @ sk60 @ sk59 ) ) )
| ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[12437,11100]) ).
thf(13985,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) )
!= ( ( sk1 @ sk59 @ sk60 )
=> ( sk1 @ sk60 @ sk59 ) ) )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[13984]) ).
thf(13986,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) )
!= ( ( sk1 @ sk59 @ sk60 )
=> ( sk1 @ sk60 @ sk59 ) ) ) ),
inference(pattern_uni,[status(thm)],[13985:[]]) ).
thf(18990,plain,
( ( ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk707 @ A )
& ( sk1 @ sk707 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ! [A: $i] :
( ( sk1 @ sk707 @ A )
=> ( sk1 @ A @ sk707 ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) )
!= ( ( sk1 @ sk59 @ sk60 )
=> ( sk1 @ sk60 @ sk59 ) ) ) ),
inference(func_ext,[status(esa)],[13986]) ).
thf(27865,plain,
( ~ ! [A: $i,B: $i] :
( ( ( sk1 @ sk707 @ A )
& ( sk1 @ sk707 @ B ) )
=> ( sk1 @ A @ B ) )
| ~ ! [A: $i] :
( ( sk1 @ sk707 @ A )
=> ( sk1 @ A @ sk707 ) )
| ~ ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) )
| ~ ( ( sk1 @ sk59 @ sk60 )
=> ( sk1 @ sk60 @ sk59 ) ) ),
inference(bool_ext,[status(thm)],[18990]) ).
thf(28359,plain,
( ( ( sk1 @ sk707 @ sk1417 )
| ( sk1 @ sk707 @ sk1419 )
| ( sk1 @ sk60 @ sk1420 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk707 @ sk1417 )
| ( sk1 @ sk707 @ sk1419 )
| ( sk1 @ sk60 @ sk1420 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk707 @ sk1417 )
| ( sk1 @ sk707 @ sk1419 )
| ~ ( sk1 @ sk59 @ sk1420 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk707 @ sk1417 )
| ( sk1 @ sk707 @ sk1419 )
| ~ ( sk1 @ sk59 @ sk1420 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk707 @ sk1417 )
| ~ ( sk1 @ sk1419 @ sk707 )
| ( sk1 @ sk60 @ sk1420 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk707 @ sk1417 )
| ~ ( sk1 @ sk1419 @ sk707 )
| ( sk1 @ sk60 @ sk1420 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk707 @ sk1417 )
| ~ ( sk1 @ sk1419 @ sk707 )
| ~ ( sk1 @ sk59 @ sk1420 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk707 @ sk1417 )
| ~ ( sk1 @ sk1419 @ sk707 )
| ~ ( sk1 @ sk59 @ sk1420 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk707 @ sk1418 )
| ( sk1 @ sk707 @ sk1419 )
| ( sk1 @ sk60 @ sk1420 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk707 @ sk1418 )
| ( sk1 @ sk707 @ sk1419 )
| ( sk1 @ sk60 @ sk1420 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk707 @ sk1418 )
| ( sk1 @ sk707 @ sk1419 )
| ~ ( sk1 @ sk59 @ sk1420 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk707 @ sk1418 )
| ( sk1 @ sk707 @ sk1419 )
| ~ ( sk1 @ sk59 @ sk1420 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk707 @ sk1418 )
| ~ ( sk1 @ sk1419 @ sk707 )
| ( sk1 @ sk60 @ sk1420 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk707 @ sk1418 )
| ~ ( sk1 @ sk1419 @ sk707 )
| ( sk1 @ sk60 @ sk1420 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk707 @ sk1418 )
| ~ ( sk1 @ sk1419 @ sk707 )
| ~ ( sk1 @ sk59 @ sk1420 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk707 @ sk1418 )
| ~ ( sk1 @ sk1419 @ sk707 )
| ~ ( sk1 @ sk59 @ sk1420 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk1417 @ sk1418 )
| ( sk1 @ sk707 @ sk1419 )
| ( sk1 @ sk60 @ sk1420 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ~ ( sk1 @ sk1417 @ sk1418 )
| ( sk1 @ sk707 @ sk1419 )
| ( sk1 @ sk60 @ sk1420 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk1417 @ sk1418 )
| ( sk1 @ sk707 @ sk1419 )
| ~ ( sk1 @ sk59 @ sk1420 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ~ ( sk1 @ sk1417 @ sk1418 )
| ( sk1 @ sk707 @ sk1419 )
| ~ ( sk1 @ sk59 @ sk1420 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk1417 @ sk1418 )
| ~ ( sk1 @ sk1419 @ sk707 )
| ( sk1 @ sk60 @ sk1420 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ~ ( sk1 @ sk1417 @ sk1418 )
| ~ ( sk1 @ sk1419 @ sk707 )
| ( sk1 @ sk60 @ sk1420 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk1417 @ sk1418 )
| ~ ( sk1 @ sk1419 @ sk707 )
| ~ ( sk1 @ sk59 @ sk1420 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ~ ( sk1 @ sk1417 @ sk1418 )
| ~ ( sk1 @ sk1419 @ sk707 )
| ~ ( sk1 @ sk59 @ sk1420 )
| ~ ( sk1 @ sk60 @ sk59 ) ) ),
inference(cnf,[status(esa)],[27865]) ).
thf(28366,plain,
( ~ ( sk1 @ sk1417 @ sk1418 )
| ~ ( sk1 @ sk1419 @ sk707 )
| ~ ( sk1 @ sk59 @ sk1420 )
| ~ ( sk1 @ sk60 @ sk59 ) ),
inference(cnfConj,[status(thm)],[28359]) ).
thf(6200,plain,
( ~ ! [A: $i,B: $i] :
( ( ( sk1 @ sk66 @ A )
& ( sk1 @ sk66 @ B ) )
=> ( sk1 @ A @ B ) )
| ~ ! [A: $i] :
( ( sk1 @ sk66 @ A )
=> ( sk1 @ A @ sk66 ) )
| ~ ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) )
| ~ ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ),
inference(bool_ext,[status(thm)],[1828]) ).
thf(6220,plain,
( ( ( sk1 @ sk66 @ sk144 )
| ( sk1 @ sk66 @ sk146 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk149 @ sk150 ) )
& ( ( sk1 @ sk66 @ sk144 )
| ( sk1 @ sk66 @ sk146 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk150 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk144 )
| ( sk1 @ sk66 @ sk146 )
| ( sk1 @ sk147 @ sk148 )
| ~ ( sk1 @ sk149 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk144 )
| ( sk1 @ sk66 @ sk146 )
| ~ ( sk1 @ sk148 @ sk147 )
| ( sk1 @ sk149 @ sk150 ) )
& ( ( sk1 @ sk66 @ sk144 )
| ( sk1 @ sk66 @ sk146 )
| ~ ( sk1 @ sk148 @ sk147 )
| ( sk1 @ sk150 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk144 )
| ( sk1 @ sk66 @ sk146 )
| ~ ( sk1 @ sk148 @ sk147 )
| ~ ( sk1 @ sk149 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk144 )
| ~ ( sk1 @ sk146 @ sk66 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk149 @ sk150 ) )
& ( ( sk1 @ sk66 @ sk144 )
| ~ ( sk1 @ sk146 @ sk66 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk150 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk144 )
| ~ ( sk1 @ sk146 @ sk66 )
| ( sk1 @ sk147 @ sk148 )
| ~ ( sk1 @ sk149 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk144 )
| ~ ( sk1 @ sk146 @ sk66 )
| ~ ( sk1 @ sk148 @ sk147 )
| ( sk1 @ sk149 @ sk150 ) )
& ( ( sk1 @ sk66 @ sk144 )
| ~ ( sk1 @ sk146 @ sk66 )
| ~ ( sk1 @ sk148 @ sk147 )
| ( sk1 @ sk150 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk144 )
| ~ ( sk1 @ sk146 @ sk66 )
| ~ ( sk1 @ sk148 @ sk147 )
| ~ ( sk1 @ sk149 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk145 )
| ( sk1 @ sk66 @ sk146 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk149 @ sk150 ) )
& ( ( sk1 @ sk66 @ sk145 )
| ( sk1 @ sk66 @ sk146 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk150 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk145 )
| ( sk1 @ sk66 @ sk146 )
| ( sk1 @ sk147 @ sk148 )
| ~ ( sk1 @ sk149 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk145 )
| ( sk1 @ sk66 @ sk146 )
| ~ ( sk1 @ sk148 @ sk147 )
| ( sk1 @ sk149 @ sk150 ) )
& ( ( sk1 @ sk66 @ sk145 )
| ( sk1 @ sk66 @ sk146 )
| ~ ( sk1 @ sk148 @ sk147 )
| ( sk1 @ sk150 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk145 )
| ( sk1 @ sk66 @ sk146 )
| ~ ( sk1 @ sk148 @ sk147 )
| ~ ( sk1 @ sk149 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk149 @ sk150 ) )
& ( ( sk1 @ sk66 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk150 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ( sk1 @ sk147 @ sk148 )
| ~ ( sk1 @ sk149 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ~ ( sk1 @ sk148 @ sk147 )
| ( sk1 @ sk149 @ sk150 ) )
& ( ( sk1 @ sk66 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ~ ( sk1 @ sk148 @ sk147 )
| ( sk1 @ sk150 @ sk151 ) )
& ( ( sk1 @ sk66 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ~ ( sk1 @ sk148 @ sk147 )
| ~ ( sk1 @ sk149 @ sk151 ) )
& ( ~ ( sk1 @ sk144 @ sk145 )
| ( sk1 @ sk66 @ sk146 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk149 @ sk150 ) )
& ( ~ ( sk1 @ sk144 @ sk145 )
| ( sk1 @ sk66 @ sk146 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk150 @ sk151 ) )
& ( ~ ( sk1 @ sk144 @ sk145 )
| ( sk1 @ sk66 @ sk146 )
| ( sk1 @ sk147 @ sk148 )
| ~ ( sk1 @ sk149 @ sk151 ) )
& ( ~ ( sk1 @ sk144 @ sk145 )
| ( sk1 @ sk66 @ sk146 )
| ~ ( sk1 @ sk148 @ sk147 )
| ( sk1 @ sk149 @ sk150 ) )
& ( ~ ( sk1 @ sk144 @ sk145 )
| ( sk1 @ sk66 @ sk146 )
| ~ ( sk1 @ sk148 @ sk147 )
| ( sk1 @ sk150 @ sk151 ) )
& ( ~ ( sk1 @ sk144 @ sk145 )
| ( sk1 @ sk66 @ sk146 )
| ~ ( sk1 @ sk148 @ sk147 )
| ~ ( sk1 @ sk149 @ sk151 ) )
& ( ~ ( sk1 @ sk144 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk149 @ sk150 ) )
& ( ~ ( sk1 @ sk144 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk150 @ sk151 ) )
& ( ~ ( sk1 @ sk144 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ( sk1 @ sk147 @ sk148 )
| ~ ( sk1 @ sk149 @ sk151 ) )
& ( ~ ( sk1 @ sk144 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ~ ( sk1 @ sk148 @ sk147 )
| ( sk1 @ sk149 @ sk150 ) )
& ( ~ ( sk1 @ sk144 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ~ ( sk1 @ sk148 @ sk147 )
| ( sk1 @ sk150 @ sk151 ) )
& ( ~ ( sk1 @ sk144 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ~ ( sk1 @ sk148 @ sk147 )
| ~ ( sk1 @ sk149 @ sk151 ) ) ),
inference(cnf,[status(esa)],[6200]) ).
thf(6246,plain,
( ( sk1 @ sk66 @ sk144 )
| ( sk1 @ sk66 @ sk146 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk149 @ sk150 ) ),
inference(cnfConj,[status(thm)],[6220]) ).
thf(8848,plain,
( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk180 @ sk181 ) ),
inference(cnfConj,[status(thm)],[8841]) ).
thf(57,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(119,plain,
( ( ( ! [A: $i] :
( ( sk1 @ sk22 @ A )
=> ( sk1 @ A @ sk22 ) ) )
!= ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk22 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk22 @ B ) ) ) )
| ( ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk23 @ A )
& ( sk1 @ sk23 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ! [A: $i] :
( ( sk1 @ sk23 @ A )
=> ( sk1 @ A @ sk23 ) ) ) ) ),
inference(func_ext,[status(esa)],[57]) ).
thf(8898,plain,
( ( ( ^ [A: $i] :
( ( sk1 @ sk22 @ A )
=> ( sk1 @ A @ sk22 ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk22 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk22 @ B ) ) ) )
| ( ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk23 @ A )
& ( sk1 @ sk23 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ! [A: $i] :
( ( sk1 @ sk23 @ A )
=> ( sk1 @ A @ sk23 ) ) ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(42,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(24,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(37,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(25,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(1802,plain,
( ( ( ! [A: $i] :
( ( sk1 @ sk53 @ A )
=> ( sk1 @ A @ sk53 ) ) )
!= ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk53 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk53 @ B ) ) ) )
| ( ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(func_ext,[status(esa)],[55]) ).
thf(4896,plain,
( ( ( ^ [A: $i] :
( ( sk1 @ sk53 @ A )
=> ( sk1 @ A @ sk53 ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk53 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk53 @ B ) ) ) )
| ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[1802]) ).
thf(8901,plain,
( ~ ! [A: $i] :
( ( sk1 @ sk22 @ A )
=> ( sk1 @ A @ sk22 ) )
| ~ ! [A: $i,B: $i] :
( ( ( sk1 @ sk22 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk22 @ B ) )
| ~ ! [A: $i,B: $i] :
( ( ( sk1 @ sk23 @ A )
& ( sk1 @ sk23 @ B ) )
=> ( sk1 @ A @ B ) )
| ~ ! [A: $i] :
( ( sk1 @ sk23 @ A )
=> ( sk1 @ A @ sk23 ) ) ),
inference(bool_ext,[status(thm)],[119]) ).
thf(8921,plain,
( ( ( sk1 @ sk22 @ sk182 )
| ( sk1 @ sk22 @ sk183 )
| ( sk1 @ sk23 @ sk185 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ( sk1 @ sk22 @ sk183 )
| ( sk1 @ sk23 @ sk185 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ( sk1 @ sk22 @ sk183 )
| ( sk1 @ sk23 @ sk186 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ( sk1 @ sk22 @ sk183 )
| ( sk1 @ sk23 @ sk186 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ( sk1 @ sk22 @ sk183 )
| ~ ( sk1 @ sk185 @ sk186 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ( sk1 @ sk22 @ sk183 )
| ~ ( sk1 @ sk185 @ sk186 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ( sk1 @ sk183 @ sk184 )
| ( sk1 @ sk23 @ sk185 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ( sk1 @ sk183 @ sk184 )
| ( sk1 @ sk23 @ sk185 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ( sk1 @ sk183 @ sk184 )
| ( sk1 @ sk23 @ sk186 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ( sk1 @ sk183 @ sk184 )
| ( sk1 @ sk23 @ sk186 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ( sk1 @ sk183 @ sk184 )
| ~ ( sk1 @ sk185 @ sk186 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ( sk1 @ sk183 @ sk184 )
| ~ ( sk1 @ sk185 @ sk186 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ~ ( sk1 @ sk22 @ sk184 )
| ( sk1 @ sk23 @ sk185 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ~ ( sk1 @ sk22 @ sk184 )
| ( sk1 @ sk23 @ sk185 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ~ ( sk1 @ sk22 @ sk184 )
| ( sk1 @ sk23 @ sk186 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ~ ( sk1 @ sk22 @ sk184 )
| ( sk1 @ sk23 @ sk186 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ~ ( sk1 @ sk22 @ sk184 )
| ~ ( sk1 @ sk185 @ sk186 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ( sk1 @ sk22 @ sk182 )
| ~ ( sk1 @ sk22 @ sk184 )
| ~ ( sk1 @ sk185 @ sk186 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ( sk1 @ sk22 @ sk183 )
| ( sk1 @ sk23 @ sk185 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ( sk1 @ sk22 @ sk183 )
| ( sk1 @ sk23 @ sk185 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ( sk1 @ sk22 @ sk183 )
| ( sk1 @ sk23 @ sk186 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ( sk1 @ sk22 @ sk183 )
| ( sk1 @ sk23 @ sk186 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ( sk1 @ sk22 @ sk183 )
| ~ ( sk1 @ sk185 @ sk186 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ( sk1 @ sk22 @ sk183 )
| ~ ( sk1 @ sk185 @ sk186 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ( sk1 @ sk183 @ sk184 )
| ( sk1 @ sk23 @ sk185 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ( sk1 @ sk183 @ sk184 )
| ( sk1 @ sk23 @ sk185 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ( sk1 @ sk183 @ sk184 )
| ( sk1 @ sk23 @ sk186 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ( sk1 @ sk183 @ sk184 )
| ( sk1 @ sk23 @ sk186 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ( sk1 @ sk183 @ sk184 )
| ~ ( sk1 @ sk185 @ sk186 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ( sk1 @ sk183 @ sk184 )
| ~ ( sk1 @ sk185 @ sk186 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ~ ( sk1 @ sk22 @ sk184 )
| ( sk1 @ sk23 @ sk185 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ~ ( sk1 @ sk22 @ sk184 )
| ( sk1 @ sk23 @ sk185 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ~ ( sk1 @ sk22 @ sk184 )
| ( sk1 @ sk23 @ sk186 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ~ ( sk1 @ sk22 @ sk184 )
| ( sk1 @ sk23 @ sk186 )
| ~ ( sk1 @ sk187 @ sk23 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ~ ( sk1 @ sk22 @ sk184 )
| ~ ( sk1 @ sk185 @ sk186 )
| ( sk1 @ sk23 @ sk187 ) )
& ( ~ ( sk1 @ sk182 @ sk22 )
| ~ ( sk1 @ sk22 @ sk184 )
| ~ ( sk1 @ sk185 @ sk186 )
| ~ ( sk1 @ sk187 @ sk23 ) ) ),
inference(cnf,[status(esa)],[8901]) ).
thf(8951,plain,
( ~ ( sk1 @ sk182 @ sk22 )
| ~ ( sk1 @ sk22 @ sk184 )
| ~ ( sk1 @ sk185 @ sk186 )
| ~ ( sk1 @ sk187 @ sk23 ) ),
inference(cnfConj,[status(thm)],[8921]) ).
thf(39710,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk630 @ sk1090 )
| ~ $true
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( ( sk1 @ sk630 @ sk629 )
!= ( sk1 @ sk629 @ sk630 ) ) ),
inference(paramod_ordered,[status(thm)],[23871,23866]) ).
thf(39711,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk630 @ sk1090 )
| ( ( sk1 @ sk630 @ sk629 )
!= ( sk1 @ sk629 @ sk630 ) ) ),
inference(simp,[status(thm)],[39710]) ).
thf(39868,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk630 @ sk1090 )
| ( sk630 != sk629 )
| ( sk630 != sk629 ) ),
inference(simp,[status(thm)],[39711]) ).
thf(40284,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk630 @ sk1090 )
| ( sk630 != sk629 ) ),
inference(simp,[status(thm)],[39868]) ).
thf(44984,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ $true
| ( sk630 != sk629 )
| ( ( sk1 @ sk630 @ sk1090 )
!= ( sk1 @ sk629 @ sk630 ) ) ),
inference(paramod_ordered,[status(thm)],[23871,40284]) ).
thf(44985,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk630 != sk629 )
| ( ( sk1 @ sk630 @ sk1090 )
!= ( sk1 @ sk629 @ sk630 ) ) ),
inference(simp,[status(thm)],[44984]) ).
thf(45275,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk630 != sk629 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 ) ),
inference(simp,[status(thm)],[44985]) ).
thf(45351,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 ) ),
inference(simp,[status(thm)],[45275]) ).
thf(35680,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( $true
=> ( sk1 @ sk73 @ sk72 ) )
!= ( ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) ) )
| ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( sk1 @ sk72 @ sk73 )
!= ( sk1 @ sk72 @ sk73 ) ) ),
inference(paramod_ordered,[status(thm)],[34945,32988]) ).
thf(35681,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) ) )
| ( ( sk1 @ sk72 @ sk73 )
!= ( sk1 @ sk72 @ sk73 ) ) ),
inference(simp,[status(thm)],[35680]) ).
thf(35682,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[35681:[]]) ).
thf(73325,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk1684 @ sk1685 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[33672,72823]) ).
thf(73326,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk1684 @ sk1685 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[73325]) ).
thf(73327,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1685 @ sk1684 ) ),
inference(pattern_uni,[status(thm)],[73326:[bind(A,$thf( sk1684 )),bind(B,$thf( sk1685 ))]]) ).
thf(11893,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 )
| ( sk1 @ sk288 @ sk289 ) ),
inference(cnfConj,[status(thm)],[11861]) ).
thf(11902,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 )
| ( sk1 @ sk288 @ sk289 ) ),
inference(simp,[status(thm)],[11893]) ).
thf(73468,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk288 @ sk289 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11902,72823]) ).
thf(73469,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk288 @ sk289 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[73468]) ).
thf(73470,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 )
| ( sk1 @ sk289 @ sk288 ) ),
inference(pattern_uni,[status(thm)],[73469:[bind(A,$thf( sk288 )),bind(B,$thf( sk289 ))]]) ).
thf(11863,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 )
| ~ ( sk1 @ sk289 @ sk288 ) ),
inference(cnfConj,[status(thm)],[11861]) ).
thf(11898,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 )
| ~ ( sk1 @ sk289 @ sk288 ) ),
inference(simp,[status(thm)],[11863]) ).
thf(87066,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 )
| ~ $true
| ( ( sk1 @ sk289 @ sk288 )
!= ( sk1 @ sk289 @ sk288 ) ) ),
inference(paramod_ordered,[status(thm)],[73470,11898]) ).
thf(87067,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 )
| ( ( sk1 @ sk289 @ sk288 )
!= ( sk1 @ sk289 @ sk288 ) ) ),
inference(simp,[status(thm)],[87066]) ).
thf(87068,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk286 ) ),
inference(pattern_uni,[status(thm)],[87067:[]]) ).
thf(88402,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk59 @ sk60 )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk285 @ sk286 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[87068,72823]) ).
thf(88403,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk285 @ sk286 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[88402]) ).
thf(88404,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk286 @ sk285 ) ),
inference(pattern_uni,[status(thm)],[88403:[bind(A,$thf( sk285 )),bind(B,$thf( sk286 ))]]) ).
thf(11879,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk286 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) ),
inference(cnfConj,[status(thm)],[11861]) ).
thf(11903,plain,
( ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk286 @ sk287 )
| ( sk1 @ sk288 @ sk289 ) ),
inference(simp,[status(thm)],[11879]) ).
thf(11896,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk286 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) ),
inference(cnfConj,[status(thm)],[11861]) ).
thf(11900,plain,
( ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk286 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) ),
inference(simp,[status(thm)],[11896]) ).
thf(21604,plain,
( ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk286 @ sk287 )
| ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk286 @ sk287 )
| ~ $true
| ( ( sk1 @ sk289 @ sk288 )
!= ( sk1 @ sk288 @ sk289 ) ) ),
inference(paramod_ordered,[status(thm)],[11903,11900]) ).
thf(21605,plain,
( ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk286 @ sk287 )
| ( ( sk1 @ sk289 @ sk288 )
!= ( sk1 @ sk288 @ sk289 ) ) ),
inference(simp,[status(thm)],[21604]) ).
thf(21772,plain,
( ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk286 @ sk287 )
| ( sk289 != sk288 )
| ( sk289 != sk288 ) ),
inference(simp,[status(thm)],[21605]) ).
thf(21991,plain,
( ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk286 @ sk287 )
| ( sk289 != sk288 ) ),
inference(simp,[status(thm)],[21772]) ).
thf(89901,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk59 @ sk60 )
| ~ $true
| ( sk289 != sk288 )
| ( ( sk1 @ sk286 @ sk287 )
!= ( sk1 @ sk286 @ sk285 ) ) ),
inference(paramod_ordered,[status(thm)],[88404,21991]) ).
thf(89902,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk289 != sk288 )
| ( ( sk1 @ sk286 @ sk287 )
!= ( sk1 @ sk286 @ sk285 ) ) ),
inference(simp,[status(thm)],[89901]) ).
thf(89988,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk289 != sk288 )
| ( sk286 != sk286 )
| ( sk287 != sk285 ) ),
inference(simp,[status(thm)],[89902]) ).
thf(90427,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk289 != sk288 )
| ( sk287 != sk285 ) ),
inference(simp,[status(thm)],[89988]) ).
thf(104659,plain,
! [B: $i,A: $i] :
( ( sk289 != sk288 )
| ( sk287 != sk285 )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[90427,72823]) ).
thf(104660,plain,
! [B: $i,A: $i] :
( ( sk289 != sk288 )
| ( sk287 != sk285 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[104659]) ).
thf(104661,plain,
( ( sk289 != sk288 )
| ( sk287 != sk285 )
| ( sk1 @ sk60 @ sk59 ) ),
inference(pattern_uni,[status(thm)],[104660:[bind(A,$thf( sk59 )),bind(B,$thf( sk60 ))]]) ).
thf(151,plain,
( ~ ( sk1 @ sk13 @ sk12 )
| ~ ( sk1 @ sk14 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ( ( sk1 @ sk21 @ sk20 )
!= ( sk1 @ sk18 @ sk19 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[103]) ).
thf(157,plain,
( ~ ( sk1 @ sk13 @ sk12 )
| ~ ( sk1 @ sk14 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ( sk21 != sk18 )
| ( sk20 != sk19 ) ),
inference(simp,[status(thm)],[151]) ).
thf(35396,plain,
( ( sk1 @ sk72 @ sk73 )
| ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[34945]) ).
thf(73451,plain,
! [B: $i,A: $i] :
( ( ( ^ [C: $i,D: $i] :
( ( sk1 @ C @ D )
=> ( sk1 @ D @ C ) ) )
!= ( ^ [C: $i,D: $i] :
! [E: $i] :
( ( ( sk1 @ C @ D )
& ( sk1 @ D @ E ) )
=> ( sk1 @ C @ E ) ) ) )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk72 @ sk73 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35396,72823]) ).
thf(73452,plain,
! [B: $i,A: $i] :
( ( ( ^ [C: $i,D: $i] :
( ( sk1 @ C @ D )
=> ( sk1 @ D @ C ) ) )
!= ( ^ [C: $i,D: $i] :
! [E: $i] :
( ( ( sk1 @ C @ D )
& ( sk1 @ D @ E ) )
=> ( sk1 @ C @ E ) ) ) )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk72 @ sk73 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[73451]) ).
thf(73453,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk73 @ sk72 ) ),
inference(pattern_uni,[status(thm)],[73452:[bind(A,$thf( sk72 )),bind(B,$thf( sk73 ))]]) ).
thf(42233,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) )
!= ( ( sk1 @ sk72 @ sk73 )
=> ( sk1 @ sk73 @ sk72 ) ) ) ),
inference(simp,[status(thm)],[35679]) ).
thf(74509,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( ( sk1 @ sk72 @ sk73 )
=> $true )
!= ( ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(paramod_ordered,[status(thm)],[73453,42233]) ).
thf(74510,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(simp,[status(thm)],[74509]) ).
thf(74511,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) ),
inference(pattern_uni,[status(thm)],[74510:[]]) ).
thf(75281,plain,
( ( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk4738 ) )
& ( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ( sk1 @ sk73 @ sk4738 ) ) ),
inference(cnf,[status(esa)],[74511]) ).
thf(75282,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk4738 ) ),
inference(cnfConj,[status(thm)],[75281]) ).
thf(4897,plain,
( ~ ! [A: $i] :
( ( sk1 @ sk53 @ A )
=> ( sk1 @ A @ sk53 ) )
| ~ ! [A: $i,B: $i] :
( ( ( sk1 @ sk53 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk53 @ B ) )
| ~ ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) )
| ~ ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ),
inference(bool_ext,[status(thm)],[1802]) ).
thf(4917,plain,
( ( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk53 @ sk118 )
| ( sk1 @ sk120 @ sk121 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk53 @ sk118 )
| ( sk1 @ sk120 @ sk121 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk53 @ sk118 )
| ( sk1 @ sk120 @ sk122 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk53 @ sk118 )
| ( sk1 @ sk120 @ sk122 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk53 @ sk118 )
| ~ ( sk1 @ sk121 @ sk122 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk53 @ sk118 )
| ~ ( sk1 @ sk121 @ sk122 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk118 @ sk119 )
| ( sk1 @ sk120 @ sk121 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk118 @ sk119 )
| ( sk1 @ sk120 @ sk121 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk118 @ sk119 )
| ( sk1 @ sk120 @ sk122 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk118 @ sk119 )
| ( sk1 @ sk120 @ sk122 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk118 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk118 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ~ ( sk1 @ sk53 @ sk119 )
| ( sk1 @ sk120 @ sk121 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ~ ( sk1 @ sk53 @ sk119 )
| ( sk1 @ sk120 @ sk121 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ~ ( sk1 @ sk53 @ sk119 )
| ( sk1 @ sk120 @ sk122 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ~ ( sk1 @ sk53 @ sk119 )
| ( sk1 @ sk120 @ sk122 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ~ ( sk1 @ sk53 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ( sk1 @ sk53 @ sk117 )
| ~ ( sk1 @ sk53 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ( sk1 @ sk53 @ sk118 )
| ( sk1 @ sk120 @ sk121 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ( sk1 @ sk53 @ sk118 )
| ( sk1 @ sk120 @ sk121 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ( sk1 @ sk53 @ sk118 )
| ( sk1 @ sk120 @ sk122 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ( sk1 @ sk53 @ sk118 )
| ( sk1 @ sk120 @ sk122 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ( sk1 @ sk53 @ sk118 )
| ~ ( sk1 @ sk121 @ sk122 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ( sk1 @ sk53 @ sk118 )
| ~ ( sk1 @ sk121 @ sk122 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ( sk1 @ sk118 @ sk119 )
| ( sk1 @ sk120 @ sk121 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ( sk1 @ sk118 @ sk119 )
| ( sk1 @ sk120 @ sk121 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ( sk1 @ sk118 @ sk119 )
| ( sk1 @ sk120 @ sk122 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ( sk1 @ sk118 @ sk119 )
| ( sk1 @ sk120 @ sk122 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ( sk1 @ sk118 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ( sk1 @ sk118 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ~ ( sk1 @ sk53 @ sk119 )
| ( sk1 @ sk120 @ sk121 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ~ ( sk1 @ sk53 @ sk119 )
| ( sk1 @ sk120 @ sk121 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ~ ( sk1 @ sk53 @ sk119 )
| ( sk1 @ sk120 @ sk122 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ~ ( sk1 @ sk53 @ sk119 )
| ( sk1 @ sk120 @ sk122 )
| ~ ( sk1 @ sk124 @ sk123 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ~ ( sk1 @ sk53 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ( sk1 @ sk123 @ sk124 ) )
& ( ~ ( sk1 @ sk117 @ sk53 )
| ~ ( sk1 @ sk53 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ~ ( sk1 @ sk124 @ sk123 ) ) ),
inference(cnf,[status(esa)],[4897]) ).
thf(4952,plain,
( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk53 @ sk118 )
| ( sk1 @ sk120 @ sk122 )
| ( sk1 @ sk123 @ sk124 ) ),
inference(cnfConj,[status(thm)],[4917]) ).
thf(89920,plain,
( ( sk1 @ sk59 @ sk60 )
| ( ( sk1 @ sk286 @ sk285 )
!= ( sk1 @ sk59 @ sk60 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[88404]) ).
thf(89995,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk286 != sk59 )
| ( sk285 != sk60 ) ),
inference(simp,[status(thm)],[89920]) ).
thf(103409,plain,
! [B: $i,A: $i] :
( ( sk286 != sk59 )
| ( sk285 != sk60 )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[89995,72823]) ).
thf(103410,plain,
! [B: $i,A: $i] :
( ( sk286 != sk59 )
| ( sk285 != sk60 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[103409]) ).
thf(103411,plain,
( ( sk286 != sk59 )
| ( sk285 != sk60 )
| ( sk1 @ sk60 @ sk59 ) ),
inference(pattern_uni,[status(thm)],[103410:[bind(A,$thf( sk59 )),bind(B,$thf( sk60 ))]]) ).
thf(29,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(20,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(34,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(8293,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ $true
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[34,20]) ).
thf(8294,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(simp,[status(thm)],[8293]) ).
thf(8555,plain,
( ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[8294]) ).
thf(8632,plain,
( ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[8555]) ).
thf(2875,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( ( sk1 @ sk7 @ sk9 )
!= ( sk1 @ sk5 @ sk6 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2771]) ).
thf(2912,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( sk7 != sk5 )
| ( sk9 != sk6 ) ),
inference(simp,[status(thm)],[2875]) ).
thf(3804,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk7 != sk5 )
| ( sk9 != sk6 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk3 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2912]) ).
thf(3835,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk7 != sk5 )
| ( sk9 != sk6 )
| ( sk5 != sk3 )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[3804]) ).
thf(13924,plain,
( ( sk1 @ sk59 @ sk60 )
| ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[12437]) ).
thf(73562,plain,
! [B: $i,A: $i] :
( ( ( ^ [C: $i,D: $i] :
! [E: $i] :
( ( ( sk1 @ C @ D )
& ( sk1 @ C @ E ) )
=> ( sk1 @ D @ E ) ) )
!= ( ^ [C: $i,D: $i] :
( ( sk1 @ C @ D )
=> ( sk1 @ D @ C ) ) ) )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13924,72823]) ).
thf(73563,plain,
! [B: $i,A: $i] :
( ( ( ^ [C: $i,D: $i] :
! [E: $i] :
( ( ( sk1 @ C @ D )
& ( sk1 @ C @ E ) )
=> ( sk1 @ D @ E ) ) )
!= ( ^ [C: $i,D: $i] :
( ( sk1 @ C @ D )
=> ( sk1 @ D @ C ) ) ) )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[73562]) ).
thf(73564,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk60 @ sk59 ) ),
inference(pattern_uni,[status(thm)],[73563:[bind(A,$thf( sk59 )),bind(B,$thf( sk60 ))]]) ).
thf(18989,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) )
!= ( ( sk1 @ sk59 @ sk60 )
=> ( sk1 @ sk60 @ sk59 ) ) ) ),
inference(simp,[status(thm)],[13986]) ).
thf(75492,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( ( sk1 @ sk59 @ sk60 )
=> $true )
!= ( ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) ) )
| ( ( sk1 @ sk60 @ sk59 )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(paramod_ordered,[status(thm)],[73564,18989]) ).
thf(75493,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) )
| ( ( sk1 @ sk60 @ sk59 )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(simp,[status(thm)],[75492]) ).
thf(75494,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) ),
inference(pattern_uni,[status(thm)],[75493:[]]) ).
thf(76267,plain,
( ( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk60 @ sk4774 ) )
& ( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ( sk1 @ sk59 @ sk4774 ) ) ),
inference(cnf,[status(esa)],[75494]) ).
thf(76269,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ( sk1 @ sk59 @ sk4774 ) ),
inference(cnfConj,[status(thm)],[76267]) ).
thf(108533,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ $true
| ( ( sk1 @ sk59 @ sk4774 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[13924,76269]) ).
thf(108534,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( sk1 @ sk59 @ sk4774 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[108533]) ).
thf(108697,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk59 != sk59 )
| ( sk4774 != sk60 ) ),
inference(simp,[status(thm)],[108534]) ).
thf(108718,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk4774 != sk60 ) ),
inference(simp,[status(thm)],[108697]) ).
thf(75412,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) )
| ( ( sk1 @ sk60 @ sk59 )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(paramod_ordered,[status(thm)],[73564,15744]) ).
thf(75413,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) )
| ( ( sk1 @ sk60 @ sk59 )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(simp,[status(thm)],[75412]) ).
thf(75414,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) ),
inference(pattern_uni,[status(thm)],[75413:[]]) ).
thf(76191,plain,
( ( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk60 @ sk4753 ) )
& ( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ( sk1 @ sk59 @ sk4753 ) ) ),
inference(cnf,[status(esa)],[75414]) ).
thf(76192,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk60 @ sk4753 ) ),
inference(cnfConj,[status(thm)],[76191]) ).
thf(76193,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ( sk1 @ sk59 @ sk4753 ) ),
inference(cnfConj,[status(thm)],[76191]) ).
thf(107034,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ $true
| ( ( sk1 @ sk60 @ sk4753 )
!= ( sk1 @ sk59 @ sk4753 ) ) ),
inference(paramod_ordered,[status(thm)],[76192,76193]) ).
thf(107035,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( sk1 @ sk60 @ sk4753 )
!= ( sk1 @ sk59 @ sk4753 ) ) ),
inference(simp,[status(thm)],[107034]) ).
thf(107194,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk60 != sk59 )
| ( sk4753 != sk4753 ) ),
inference(simp,[status(thm)],[107035]) ).
thf(107210,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk60 != sk59 ) ),
inference(simp,[status(thm)],[107194]) ).
thf(2874,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( ( sk1 @ sk7 @ sk9 )
!= ( sk1 @ sk3 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2771]) ).
thf(2880,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk10 )
| ( sk7 != sk3 )
| ( sk9 != sk2 ) ),
inference(simp,[status(thm)],[2874]) ).
thf(106,plain,
( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk15 @ sk16 )
| ( sk1 @ sk17 @ sk19 )
| ( sk1 @ sk20 @ sk21 ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(107010,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ $true
| ( ( sk1 @ sk59 @ sk4753 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[12437,76193]) ).
thf(107011,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( sk1 @ sk59 @ sk4753 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[107010]) ).
thf(107142,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk59 != sk59 )
| ( sk4753 != sk60 ) ),
inference(simp,[status(thm)],[107011]) ).
thf(107203,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk4753 != sk60 ) ),
inference(simp,[status(thm)],[107142]) ).
thf(66,plain,
( ( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(3621,plain,
( ( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(88762,plain,
( ( sk1 @ sk59 @ sk60 )
| ( ( sk1 @ sk285 @ sk286 )
!= ( sk1 @ sk59 @ sk60 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[87068]) ).
thf(88819,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk285 != sk59 )
| ( sk286 != sk60 ) ),
inference(simp,[status(thm)],[88762]) ).
thf(94157,plain,
( ( sk285 != sk59 )
| ( sk286 != sk60 )
| ~ $true
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[88819,86832]) ).
thf(94158,plain,
( ( sk285 != sk59 )
| ( sk286 != sk60 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[94157]) ).
thf(94159,plain,
( ( sk285 != sk59 )
| ( sk286 != sk60 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 ) ),
inference(pattern_uni,[status(thm)],[94158:[]]) ).
thf(121,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[57]) ).
thf(132,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(116,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(65,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(3588,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(73809,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ $true
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1090 != sk629 )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk630 @ sk629 ) ) ),
inference(paramod_ordered,[status(thm)],[72823,25044]) ).
thf(73810,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1090 != sk629 )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk630 @ sk629 ) ) ),
inference(simp,[status(thm)],[73809]) ).
thf(73811,plain,
( ~ ( sk1 @ sk629 @ sk630 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1090 != sk629 ) ),
inference(pattern_uni,[status(thm)],[73810:[bind(A,$thf( sk629 )),bind(B,$thf( sk630 ))]]) ).
thf(127138,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ $true
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1090 != sk629 )
| ( ( sk1 @ sk629 @ sk630 )
!= ( sk1 @ sk629 @ sk630 ) ) ),
inference(paramod_ordered,[status(thm)],[23871,73811]) ).
thf(127139,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1090 != sk629 )
| ( ( sk1 @ sk629 @ sk630 )
!= ( sk1 @ sk629 @ sk630 ) ) ),
inference(simp,[status(thm)],[127138]) ).
thf(127140,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1090 != sk629 ) ),
inference(pattern_uni,[status(thm)],[127139:[]]) ).
thf(7707,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk66 @ A )
& ( sk1 @ sk66 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ^ [A: $i] :
( ( sk1 @ sk66 @ A )
=> ( sk1 @ A @ sk66 ) ) ) )
| ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[6199]) ).
thf(15070,plain,
( ( ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk403 @ A )
& ( sk1 @ sk403 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ! [A: $i] :
( ( sk1 @ sk403 @ A )
=> ( sk1 @ A @ sk403 ) ) ) )
| ( ( sk1 @ sk60 @ sk59 )
!= ( ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) ) ),
inference(func_ext,[status(esa)],[13983]) ).
thf(26602,plain,
( ~ ! [A: $i,B: $i] :
( ( ( sk1 @ sk403 @ A )
& ( sk1 @ sk403 @ B ) )
=> ( sk1 @ A @ B ) )
| ~ ! [A: $i] :
( ( sk1 @ sk403 @ A )
=> ( sk1 @ A @ sk403 ) )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ),
inference(bool_ext,[status(thm)],[15070]) ).
thf(27457,plain,
( ( ( sk1 @ sk403 @ sk1332 )
| ( sk1 @ sk403 @ sk1334 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk403 @ sk1332 )
| ( sk1 @ sk403 @ sk1334 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk60 @ sk1335 ) )
& ( ( sk1 @ sk403 @ sk1332 )
| ( sk1 @ sk403 @ sk1334 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk1335 ) )
& ( ( sk1 @ sk403 @ sk1332 )
| ~ ( sk1 @ sk1334 @ sk403 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk403 @ sk1332 )
| ~ ( sk1 @ sk1334 @ sk403 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk60 @ sk1335 ) )
& ( ( sk1 @ sk403 @ sk1332 )
| ~ ( sk1 @ sk1334 @ sk403 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk1335 ) )
& ( ( sk1 @ sk403 @ sk1333 )
| ( sk1 @ sk403 @ sk1334 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk403 @ sk1333 )
| ( sk1 @ sk403 @ sk1334 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk60 @ sk1335 ) )
& ( ( sk1 @ sk403 @ sk1333 )
| ( sk1 @ sk403 @ sk1334 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk1335 ) )
& ( ( sk1 @ sk403 @ sk1333 )
| ~ ( sk1 @ sk1334 @ sk403 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk403 @ sk1333 )
| ~ ( sk1 @ sk1334 @ sk403 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk60 @ sk1335 ) )
& ( ( sk1 @ sk403 @ sk1333 )
| ~ ( sk1 @ sk1334 @ sk403 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk1335 ) )
& ( ~ ( sk1 @ sk1332 @ sk1333 )
| ( sk1 @ sk403 @ sk1334 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ~ ( sk1 @ sk1332 @ sk1333 )
| ( sk1 @ sk403 @ sk1334 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk60 @ sk1335 ) )
& ( ~ ( sk1 @ sk1332 @ sk1333 )
| ( sk1 @ sk403 @ sk1334 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk1335 ) )
& ( ~ ( sk1 @ sk1332 @ sk1333 )
| ~ ( sk1 @ sk1334 @ sk403 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ~ ( sk1 @ sk1332 @ sk1333 )
| ~ ( sk1 @ sk1334 @ sk403 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk1 @ sk60 @ sk1335 ) )
& ( ~ ( sk1 @ sk1332 @ sk1333 )
| ~ ( sk1 @ sk1334 @ sk403 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk1335 ) ) ),
inference(cnf,[status(esa)],[26602]) ).
thf(27474,plain,
( ~ ( sk1 @ sk1332 @ sk1333 )
| ~ ( sk1 @ sk1334 @ sk403 )
| ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk1335 ) ),
inference(cnfConj,[status(thm)],[27457]) ).
thf(117,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(73404,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ $true
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(paramod_ordered,[status(thm)],[72823,45351]) ).
thf(73405,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ sk59 @ sk1091 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(simp,[status(thm)],[73404]) ).
thf(73406,plain,
( ~ ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 ) ),
inference(pattern_uni,[status(thm)],[73405:[bind(A,$thf( sk59 )),bind(B,$thf( sk60 ))]]) ).
thf(77798,plain,
( ~ ( sk1 @ sk59 @ sk60 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( ( sk1 @ sk59 @ sk1091 )
!= ( sk1 @ sk59 @ sk60 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[73406]) ).
thf(77895,plain,
( ~ ( sk1 @ sk59 @ sk60 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk59 != sk59 )
| ( sk1091 != sk60 ) ),
inference(simp,[status(thm)],[77798]) ).
thf(77921,plain,
( ~ ( sk1 @ sk59 @ sk60 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 ) ),
inference(simp,[status(thm)],[77895]) ).
thf(111491,plain,
( ( sk285 != sk59 )
| ( sk287 != sk60 )
| ~ $true
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[99247,77921]) ).
thf(111492,plain,
( ( sk285 != sk59 )
| ( sk287 != sk60 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[111491]) ).
thf(111493,plain,
( ( sk285 != sk59 )
| ( sk287 != sk60 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 ) ),
inference(pattern_uni,[status(thm)],[111492:[]]) ).
thf(3635,plain,
( ( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[3621]) ).
thf(93791,plain,
! [B: $i,A: $i] :
( ( sk285 != sk59 )
| ( sk286 != sk60 )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[88819,72823]) ).
thf(93792,plain,
! [B: $i,A: $i] :
( ( sk285 != sk59 )
| ( sk286 != sk60 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[93791]) ).
thf(93793,plain,
( ( sk285 != sk59 )
| ( sk286 != sk60 )
| ( sk1 @ sk60 @ sk59 ) ),
inference(pattern_uni,[status(thm)],[93792:[bind(A,$thf( sk59 )),bind(B,$thf( sk60 ))]]) ).
thf(4925,plain,
( ~ ( sk1 @ sk117 @ sk53 )
| ~ ( sk1 @ sk53 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ~ ( sk1 @ sk124 @ sk123 ) ),
inference(cnfConj,[status(thm)],[4917]) ).
thf(42234,plain,
( ( ( ! [A: $i] :
( ( sk1 @ sk2241 @ A )
=> ( sk1 @ A @ sk2241 ) ) )
!= ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk2241 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk2241 @ B ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) )
!= ( ( sk1 @ sk72 @ sk73 )
=> ( sk1 @ sk73 @ sk72 ) ) ) ),
inference(func_ext,[status(esa)],[35679]) ).
thf(15069,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( sk1 @ sk60 @ sk59 )
!= ( ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) ) ),
inference(simp,[status(thm)],[13983]) ).
thf(75519,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) )
| ( ( sk1 @ sk60 @ sk59 )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(paramod_ordered,[status(thm)],[73564,15069]) ).
thf(75520,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) )
| ( ( sk1 @ sk60 @ sk59 )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(simp,[status(thm)],[75519]) ).
thf(75521,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ),
inference(pattern_uni,[status(thm)],[75520:[]]) ).
thf(76283,plain,
( ( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk60 @ sk4778 ) )
& ( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ( sk1 @ sk59 @ sk4778 ) ) ),
inference(cnf,[status(esa)],[75521]) ).
thf(76286,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ( sk1 @ sk59 @ sk4778 ) ),
inference(cnfConj,[status(thm)],[76283]) ).
thf(114125,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ $true
| ( ( sk1 @ sk59 @ sk4778 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[13924,76286]) ).
thf(114126,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( sk1 @ sk59 @ sk4778 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[114125]) ).
thf(114240,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk59 != sk59 )
| ( sk4778 != sk60 ) ),
inference(simp,[status(thm)],[114126]) ).
thf(114313,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk4778 != sk60 ) ),
inference(simp,[status(thm)],[114240]) ).
thf(11927,plain,
( ( ( ( sk1 @ sk59 @ sk60 )
=> ( sk1 @ sk60 @ sk59 ) )
!= ( ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[11100]) ).
thf(75530,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( ( sk1 @ sk59 @ sk60 )
=> $true )
!= ( ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( sk1 @ sk60 @ sk59 )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(paramod_ordered,[status(thm)],[73564,11927]) ).
thf(75531,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) )
| ( ( sk1 @ sk60 @ sk59 )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(simp,[status(thm)],[75530]) ).
thf(75532,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ),
inference(pattern_uni,[status(thm)],[75531:[]]) ).
thf(76299,plain,
( ( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk60 @ sk4781 ) )
& ( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ( sk1 @ sk59 @ sk4781 ) ) ),
inference(cnf,[status(esa)],[75532]) ).
thf(76302,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ ( sk1 @ sk59 @ sk4781 ) ),
inference(cnfConj,[status(thm)],[76299]) ).
thf(3708,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk7 != sk3 )
| ( sk9 != sk2 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk3 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2880]) ).
thf(3735,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk7 != sk3 )
| ( sk9 != sk2 )
| ( sk5 != sk3 )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[3708]) ).
thf(89994,plain,
( ( sk1 @ sk59 @ sk60 )
| ( ( sk1 @ sk286 @ sk285 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[89920]) ).
thf(140,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk3 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[23]) ).
thf(144,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk11 != sk3 )
| ( sk10 != sk2 ) ),
inference(simp,[status(thm)],[140]) ).
thf(291,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk3 )
| ( sk10 != sk2 )
| ( ( sk1 @ sk7 @ sk9 )
!= ( sk1 @ sk5 @ sk6 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[144]) ).
thf(297,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk11 != sk3 )
| ( sk10 != sk2 )
| ( sk7 != sk5 )
| ( sk9 != sk6 ) ),
inference(simp,[status(thm)],[291]) ).
thf(8899,plain,
( ( ( ! [A: $i] :
( ( sk1 @ sk22 @ A )
=> ( sk1 @ A @ sk22 ) ) )
!= ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk22 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk22 @ B ) ) ) )
| ( ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk23 @ A )
& ( sk1 @ sk23 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ^ [A: $i] :
( ( sk1 @ sk23 @ A )
=> ( sk1 @ A @ sk23 ) ) ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(19651,plain,
( ( ( ! [A: $i] :
( ( ( sk1 @ sk811 @ sk812 )
& ( sk1 @ sk811 @ A ) )
=> ( sk1 @ sk812 @ A ) ) )
!= ( ( sk1 @ sk811 @ sk812 )
=> ( sk1 @ sk812 @ sk811 ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) )
!= ( ( sk1 @ sk59 @ sk60 )
=> ( sk1 @ sk60 @ sk59 ) ) ) ),
inference(func_ext,[status(esa)],[18989]) ).
thf(66892,plain,
( ~ ! [A: $i] :
( ( ( sk1 @ sk811 @ sk812 )
& ( sk1 @ sk811 @ A ) )
=> ( sk1 @ sk812 @ A ) )
| ~ ( ( sk1 @ sk811 @ sk812 )
=> ( sk1 @ sk812 @ sk811 ) )
| ~ ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) )
| ~ ( ( sk1 @ sk59 @ sk60 )
=> ( sk1 @ sk60 @ sk59 ) ) ),
inference(bool_ext,[status(thm)],[19651]) ).
thf(68080,plain,
( ( ( sk1 @ sk811 @ sk812 )
| ( sk1 @ sk811 @ sk812 )
| ( sk1 @ sk60 @ sk4458 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk811 @ sk812 )
| ( sk1 @ sk811 @ sk812 )
| ( sk1 @ sk60 @ sk4458 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk811 @ sk812 )
| ( sk1 @ sk811 @ sk812 )
| ~ ( sk1 @ sk59 @ sk4458 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk811 @ sk812 )
| ( sk1 @ sk811 @ sk812 )
| ~ ( sk1 @ sk59 @ sk4458 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk811 @ sk812 )
| ~ ( sk1 @ sk812 @ sk811 )
| ( sk1 @ sk60 @ sk4458 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk811 @ sk812 )
| ~ ( sk1 @ sk812 @ sk811 )
| ( sk1 @ sk60 @ sk4458 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk811 @ sk812 )
| ~ ( sk1 @ sk812 @ sk811 )
| ~ ( sk1 @ sk59 @ sk4458 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk811 @ sk812 )
| ~ ( sk1 @ sk812 @ sk811 )
| ~ ( sk1 @ sk59 @ sk4458 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk811 @ sk4457 )
| ( sk1 @ sk811 @ sk812 )
| ( sk1 @ sk60 @ sk4458 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk811 @ sk4457 )
| ( sk1 @ sk811 @ sk812 )
| ( sk1 @ sk60 @ sk4458 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk811 @ sk4457 )
| ( sk1 @ sk811 @ sk812 )
| ~ ( sk1 @ sk59 @ sk4458 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk811 @ sk4457 )
| ( sk1 @ sk811 @ sk812 )
| ~ ( sk1 @ sk59 @ sk4458 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk811 @ sk4457 )
| ~ ( sk1 @ sk812 @ sk811 )
| ( sk1 @ sk60 @ sk4458 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk811 @ sk4457 )
| ~ ( sk1 @ sk812 @ sk811 )
| ( sk1 @ sk60 @ sk4458 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk811 @ sk4457 )
| ~ ( sk1 @ sk812 @ sk811 )
| ~ ( sk1 @ sk59 @ sk4458 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ( sk1 @ sk811 @ sk4457 )
| ~ ( sk1 @ sk812 @ sk811 )
| ~ ( sk1 @ sk59 @ sk4458 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk812 @ sk4457 )
| ( sk1 @ sk811 @ sk812 )
| ( sk1 @ sk60 @ sk4458 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ~ ( sk1 @ sk812 @ sk4457 )
| ( sk1 @ sk811 @ sk812 )
| ( sk1 @ sk60 @ sk4458 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk812 @ sk4457 )
| ( sk1 @ sk811 @ sk812 )
| ~ ( sk1 @ sk59 @ sk4458 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ~ ( sk1 @ sk812 @ sk4457 )
| ( sk1 @ sk811 @ sk812 )
| ~ ( sk1 @ sk59 @ sk4458 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk812 @ sk4457 )
| ~ ( sk1 @ sk812 @ sk811 )
| ( sk1 @ sk60 @ sk4458 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ~ ( sk1 @ sk812 @ sk4457 )
| ~ ( sk1 @ sk812 @ sk811 )
| ( sk1 @ sk60 @ sk4458 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk812 @ sk4457 )
| ~ ( sk1 @ sk812 @ sk811 )
| ~ ( sk1 @ sk59 @ sk4458 )
| ( sk1 @ sk59 @ sk60 ) )
& ( ~ ( sk1 @ sk812 @ sk4457 )
| ~ ( sk1 @ sk812 @ sk811 )
| ~ ( sk1 @ sk59 @ sk4458 )
| ~ ( sk1 @ sk60 @ sk59 ) ) ),
inference(cnf,[status(esa)],[66892]) ).
thf(68082,plain,
( ( sk1 @ sk811 @ sk812 )
| ( sk1 @ sk811 @ sk812 )
| ( sk1 @ sk60 @ sk4458 )
| ( sk1 @ sk59 @ sk60 ) ),
inference(cnfConj,[status(thm)],[68080]) ).
thf(68105,plain,
( ( sk1 @ sk811 @ sk812 )
| ( sk1 @ sk60 @ sk4458 )
| ( sk1 @ sk59 @ sk60 ) ),
inference(simp,[status(thm)],[68082]) ).
thf(33,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(38,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(13663,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ~ $true
| ( ( sk1 @ sk289 @ sk288 )
!= ( sk1 @ sk288 @ sk289 ) ) ),
inference(paramod_ordered,[status(thm)],[11901,11899]) ).
thf(13664,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ( ( sk1 @ sk289 @ sk288 )
!= ( sk1 @ sk288 @ sk289 ) ) ),
inference(simp,[status(thm)],[13663]) ).
thf(13718,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ( sk289 != sk288 )
| ( sk289 != sk288 ) ),
inference(simp,[status(thm)],[13664]) ).
thf(13726,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk285 @ sk287 )
| ( sk289 != sk288 ) ),
inference(simp,[status(thm)],[13718]) ).
thf(25723,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk289 != sk288 )
| ( sk1 @ sk59 @ sk60 )
| ~ $true
| ( sk289 != sk288 )
| ( ( sk1 @ sk286 @ sk287 )
!= ( sk1 @ sk285 @ sk287 ) ) ),
inference(paramod_ordered,[status(thm)],[13726,21991]) ).
thf(25724,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk289 != sk288 )
| ( ( sk1 @ sk286 @ sk287 )
!= ( sk1 @ sk285 @ sk287 ) ) ),
inference(simp,[status(thm)],[25723]) ).
thf(25761,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk289 != sk288 )
| ( sk286 != sk285 )
| ( sk287 != sk287 ) ),
inference(simp,[status(thm)],[25724]) ).
thf(25800,plain,
( ( sk1 @ sk59 @ sk60 )
| ( sk289 != sk288 )
| ( sk286 != sk285 ) ),
inference(simp,[status(thm)],[25761]) ).
thf(86941,plain,
( ( sk289 != sk288 )
| ( sk286 != sk285 )
| ~ $true
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[25800,86832]) ).
thf(86942,plain,
( ( sk289 != sk288 )
| ( sk286 != sk285 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[86941]) ).
thf(86943,plain,
( ( sk289 != sk288 )
| ( sk286 != sk285 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 ) ),
inference(pattern_uni,[status(thm)],[86942:[]]) ).
thf(115960,plain,
( ( sk287 != sk59 )
| ( sk285 != sk60 )
| ~ $true
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[100566,77921]) ).
thf(115961,plain,
( ( sk287 != sk59 )
| ( sk285 != sk60 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[115960]) ).
thf(115962,plain,
( ( sk287 != sk59 )
| ( sk285 != sk60 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 ) ),
inference(pattern_uni,[status(thm)],[115961:[]]) ).
thf(97,plain,
( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk15 @ sk16 )
| ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk20 @ sk21 ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(49,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ~ ( sk1 @ D @ E )
| ~ ( sk1 @ E @ F )
| ( sk1 @ D @ F ) ),
inference(cnfConj,[status(thm)],[46]) ).
thf(53,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ A @ C )
| ( sk1 @ B @ C )
| ~ ( sk1 @ D @ E )
| ~ ( sk1 @ E @ F )
| ( sk1 @ D @ F ) ),
inference(simp,[status(thm)],[49]) ).
thf(76301,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk60 @ sk4781 ) ),
inference(cnfConj,[status(thm)],[76299]) ).
thf(27864,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk707 @ A )
& ( sk1 @ sk707 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ^ [A: $i] :
( ( sk1 @ sk707 @ A )
=> ( sk1 @ A @ sk707 ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) )
!= ( ( sk1 @ sk59 @ sk60 )
=> ( sk1 @ sk60 @ sk59 ) ) ) ),
inference(simp,[status(thm)],[18990]) ).
thf(88818,plain,
( ( sk1 @ sk59 @ sk60 )
| ( ( sk1 @ sk285 @ sk286 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[88762]) ).
thf(48454,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) ) ) ),
inference(simp,[status(thm)],[35682]) ).
thf(74441,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(paramod_ordered,[status(thm)],[73453,48454]) ).
thf(74442,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(simp,[status(thm)],[74441]) ).
thf(74443,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) ),
inference(pattern_uni,[status(thm)],[74442:[]]) ).
thf(75224,plain,
( ( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk73 ) )
& ( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk4724 ) )
& ( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ( sk1 @ sk73 @ sk4724 ) ) ),
inference(cnf,[status(esa)],[74443]) ).
thf(75226,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk4724 ) ),
inference(cnfConj,[status(thm)],[75224]) ).
thf(75227,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ( sk1 @ sk73 @ sk4724 ) ),
inference(cnfConj,[status(thm)],[75224]) ).
thf(85117,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ $true
| ( ( sk1 @ sk73 @ sk4724 )
!= ( sk1 @ sk72 @ sk4724 ) ) ),
inference(paramod_ordered,[status(thm)],[75226,75227]) ).
thf(85118,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( sk1 @ sk73 @ sk4724 )
!= ( sk1 @ sk72 @ sk4724 ) ) ),
inference(simp,[status(thm)],[85117]) ).
thf(85174,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk73 != sk72 )
| ( sk4724 != sk4724 ) ),
inference(simp,[status(thm)],[85118]) ).
thf(85235,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk73 != sk72 ) ),
inference(simp,[status(thm)],[85174]) ).
thf(19,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(22,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(3288,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ~ $true
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[19,22]) ).
thf(3289,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(simp,[status(thm)],[3288]) ).
thf(3318,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[3289]) ).
thf(3333,plain,
( ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[3318]) ).
thf(41,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(73567,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ $true
| ~ ( sk1 @ sk630 @ sk1090 )
| ( sk630 != sk629 )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(paramod_ordered,[status(thm)],[72823,40284]) ).
thf(73568,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk630 @ sk1090 )
| ( sk630 != sk629 )
| ( ( sk1 @ B @ A )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(simp,[status(thm)],[73567]) ).
thf(73569,plain,
( ~ ( sk1 @ sk59 @ sk60 )
| ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk630 @ sk1090 )
| ( sk630 != sk629 ) ),
inference(pattern_uni,[status(thm)],[73568:[bind(A,$thf( sk59 )),bind(B,$thf( sk60 ))]]) ).
thf(13,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(34221,plain,
( ( ( ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) )
!= ( ( sk1 @ sk72 @ sk73 )
=> ( sk1 @ sk73 @ sk72 ) ) )
| ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[32988]) ).
thf(76569,plain,
! [B: $i,A: $i] :
( ( ( ^ [C: $i,D: $i] :
( ( sk1 @ C @ D )
=> ( sk1 @ D @ C ) ) )
!= ( ^ [C: $i,D: $i] :
! [E: $i] :
( ( ( sk1 @ C @ D )
& ( sk1 @ D @ E ) )
=> ( sk1 @ C @ E ) ) ) )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk72 @ sk4724 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[75226,72823]) ).
thf(76570,plain,
! [B: $i,A: $i] :
( ( ( ^ [C: $i,D: $i] :
( ( sk1 @ C @ D )
=> ( sk1 @ D @ C ) ) )
!= ( ^ [C: $i,D: $i] :
! [E: $i] :
( ( ( sk1 @ C @ D )
& ( sk1 @ D @ E ) )
=> ( sk1 @ C @ E ) ) ) )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk72 @ sk4724 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[76569]) ).
thf(76571,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk4724 @ sk72 ) ),
inference(pattern_uni,[status(thm)],[76570:[bind(A,$thf( sk72 )),bind(B,$thf( sk4724 ))]]) ).
thf(5123,plain,
( ~ ( sk1 @ sk117 @ sk53 )
| ~ ( sk1 @ sk53 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ( ( sk1 @ sk124 @ sk123 )
!= ( sk1 @ sk53 @ sk119 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4925]) ).
thf(5126,plain,
( ~ ( sk1 @ sk117 @ sk53 )
| ~ ( sk1 @ sk53 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ( sk124 != sk53 )
| ( sk123 != sk119 ) ),
inference(simp,[status(thm)],[5123]) ).
thf(45179,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk630 != sk629 )
| ( ( sk1 @ sk630 @ sk1090 )
!= ( sk1 @ sk60 @ sk59 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[40284]) ).
thf(45283,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ~ ( sk1 @ sk60 @ sk59 )
| ( sk630 != sk629 )
| ( sk630 != sk60 )
| ( sk1090 != sk59 ) ),
inference(simp,[status(thm)],[45179]) ).
thf(95018,plain,
! [B: $i,A: $i] :
( ( ( ^ [C: $i,D: $i] :
( ( sk1 @ C @ D )
=> ( sk1 @ D @ C ) ) )
!= ( ^ [C: $i,D: $i] :
! [E: $i] :
( ( ( sk1 @ C @ D )
& ( sk1 @ D @ E ) )
=> ( sk1 @ C @ E ) ) ) )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk72 @ sk4738 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[75282,72823]) ).
thf(95019,plain,
! [B: $i,A: $i] :
( ( ( ^ [C: $i,D: $i] :
( ( sk1 @ C @ D )
=> ( sk1 @ D @ C ) ) )
!= ( ^ [C: $i,D: $i] :
! [E: $i] :
( ( ( sk1 @ C @ D )
& ( sk1 @ D @ E ) )
=> ( sk1 @ C @ E ) ) ) )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk72 @ sk4738 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[95018]) ).
thf(95020,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk4738 @ sk72 ) ),
inference(pattern_uni,[status(thm)],[95019:[bind(A,$thf( sk72 )),bind(B,$thf( sk4738 ))]]) ).
thf(45,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(74469,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( ( sk1 @ sk72 @ sk73 )
=> $true )
!= ( ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) ) )
| ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(paramod_ordered,[status(thm)],[73453,34221]) ).
thf(74470,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(simp,[status(thm)],[74469]) ).
thf(74471,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) ),
inference(pattern_uni,[status(thm)],[74470:[]]) ).
thf(75240,plain,
( ( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk73 ) )
& ( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk4728 ) )
& ( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ( sk1 @ sk73 @ sk4728 ) ) ),
inference(cnf,[status(esa)],[74471]) ).
thf(75243,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ( sk1 @ sk73 @ sk4728 ) ),
inference(cnfConj,[status(thm)],[75240]) ).
thf(90756,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ $true
| ( ( sk1 @ sk73 @ sk4728 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(paramod_ordered,[status(thm)],[73453,75243]) ).
thf(90757,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( sk1 @ sk73 @ sk4728 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(simp,[status(thm)],[90756]) ).
thf(90891,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk73 != sk73 )
| ( sk4728 != sk72 ) ),
inference(simp,[status(thm)],[90757]) ).
thf(90898,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk4728 != sk72 ) ),
inference(simp,[status(thm)],[90891]) ).
thf(17,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(42310,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( $true
=> ( sk1 @ sk73 @ sk72 ) )
!= ( ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) ) )
| ( ( sk1 @ sk72 @ sk73 )
!= ( sk1 @ sk72 @ sk73 ) ) ),
inference(paramod_ordered,[status(thm)],[34945,35679]) ).
thf(42311,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) ) )
| ( ( sk1 @ sk72 @ sk73 )
!= ( sk1 @ sk72 @ sk73 ) ) ),
inference(simp,[status(thm)],[42310]) ).
thf(42312,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[42311:[]]) ).
thf(43182,plain,
( ( ( ! [A: $i] :
( ( sk1 @ sk2391 @ A )
=> ( sk1 @ A @ sk2391 ) ) )
!= ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk2391 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk2391 @ B ) ) ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) ) ) ),
inference(func_ext,[status(esa)],[42312]) ).
thf(50084,plain,
( ( ( ^ [A: $i] :
( ( sk1 @ sk2391 @ A )
=> ( sk1 @ A @ sk2391 ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk2391 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk2391 @ B ) ) ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) ) ) ),
inference(simp,[status(thm)],[43182]) ).
thf(142,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk7 @ sk9 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[23]) ).
thf(148,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk11 != sk7 )
| ( sk10 != sk9 ) ),
inference(simp,[status(thm)],[142]) ).
thf(6229,plain,
( ( sk1 @ sk66 @ sk144 )
| ( sk1 @ sk66 @ sk146 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk150 @ sk151 ) ),
inference(cnfConj,[status(thm)],[6220]) ).
thf(118,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(27,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(44,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(8900,plain,
( ( ( ^ [A: $i] :
( ( sk1 @ sk22 @ A )
=> ( sk1 @ A @ sk22 ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk22 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk22 @ B ) ) ) )
| ( ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk23 @ A )
& ( sk1 @ sk23 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ^ [A: $i] :
( ( sk1 @ sk23 @ A )
=> ( sk1 @ A @ sk23 ) ) ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(78011,plain,
( ( sk289 != sk288 )
| ( sk286 != sk285 )
| ~ $true
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[25800,77921]) ).
thf(78012,plain,
( ( sk289 != sk288 )
| ( sk286 != sk285 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[78011]) ).
thf(78013,plain,
( ( sk289 != sk288 )
| ( sk286 != sk285 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 ) ),
inference(pattern_uni,[status(thm)],[78012:[]]) ).
thf(33652,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1683 @ sk1684 ) ),
inference(cnfConj,[status(thm)],[33635]) ).
thf(33673,plain,
( ( sk1 @ sk72 @ sk73 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ( sk1 @ sk1683 @ sk1684 ) ),
inference(simp,[status(thm)],[33652]) ).
thf(5124,plain,
( ~ ( sk1 @ sk117 @ sk53 )
| ~ ( sk1 @ sk53 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ( ( sk1 @ sk124 @ sk123 )
!= ( sk1 @ sk121 @ sk122 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4925]) ).
thf(5190,plain,
( ~ ( sk1 @ sk117 @ sk53 )
| ~ ( sk1 @ sk53 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ( sk124 != sk121 )
| ( sk123 != sk122 ) ),
inference(simp,[status(thm)],[5124]) ).
thf(18648,plain,
( ( ( ! [A: $i] :
( ( ( sk1 @ sk668 @ sk669 )
& ( sk1 @ sk668 @ A ) )
=> ( sk1 @ sk669 @ A ) ) )
!= ( ( sk1 @ sk668 @ sk669 )
=> ( sk1 @ sk669 @ sk668 ) ) )
| ( ( sk1 @ sk60 @ sk59 )
!= ( ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) ) ),
inference(func_ext,[status(esa)],[15069]) ).
thf(33641,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1683 @ sk1684 ) ),
inference(cnfConj,[status(thm)],[33635]) ).
thf(33674,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1683 @ sk1684 ) ),
inference(simp,[status(thm)],[33641]) ).
thf(73990,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk1683 @ sk1684 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[33674,72823]) ).
thf(73991,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk1683 @ sk1684 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[73990]) ).
thf(73992,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk1684 @ sk1683 ) ),
inference(pattern_uni,[status(thm)],[73991:[bind(A,$thf( sk1683 )),bind(B,$thf( sk1684 ))]]) ).
thf(81,plain,
( ~ ( sk1 @ sk13 @ sk12 )
| ~ ( sk1 @ sk14 @ sk16 )
| ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk20 @ sk21 ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(118874,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ~ $true
| ( ( sk1 @ sk59 @ sk4781 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[12437,76302]) ).
thf(118875,plain,
( ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( ( sk1 @ sk59 @ sk4781 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[118874]) ).
thf(119045,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ 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] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk59 != sk59 )
| ( sk4781 != sk60 ) ),
inference(simp,[status(thm)],[118875]) ).
thf(119076,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk4781 != sk60 ) ),
inference(simp,[status(thm)],[119045]) ).
thf(39,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(6197,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk66 @ A )
& ( sk1 @ sk66 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ^ [A: $i] :
( ( sk1 @ sk66 @ A )
=> ( sk1 @ A @ sk66 ) ) ) )
| ( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[1828]) ).
thf(15745,plain,
( ( ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk498 @ A )
& ( sk1 @ sk498 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ! [A: $i] :
( ( sk1 @ sk498 @ A )
=> ( sk1 @ A @ sk498 ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(func_ext,[status(esa)],[15101]) ).
thf(22195,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk498 @ A )
& ( sk1 @ sk498 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ^ [A: $i] :
( ( sk1 @ sk498 @ A )
=> ( sk1 @ A @ sk498 ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) ) )
!= ( sk1 @ sk60 @ sk59 ) ) ),
inference(simp,[status(thm)],[15745]) ).
thf(94025,plain,
( ( sk285 != sk59 )
| ( sk286 != sk60 )
| ~ $true
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[88819,77921]) ).
thf(94026,plain,
( ( sk285 != sk59 )
| ( sk286 != sk60 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[94025]) ).
thf(94027,plain,
( ( sk285 != sk59 )
| ( sk286 != sk60 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 ) ),
inference(pattern_uni,[status(thm)],[94026:[]]) ).
thf(76285,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk60 @ sk4778 ) ),
inference(cnfConj,[status(thm)],[76283]) ).
thf(150,plain,
( ~ ( sk1 @ sk13 @ sk12 )
| ~ ( sk1 @ sk14 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ( ( sk1 @ sk21 @ sk20 )
!= ( sk1 @ sk14 @ sk16 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[103]) ).
thf(155,plain,
( ~ ( sk1 @ sk13 @ sk12 )
| ~ ( sk1 @ sk14 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ( sk21 != sk14 )
| ( sk20 != sk16 ) ),
inference(simp,[status(thm)],[150]) ).
thf(99246,plain,
( ( sk1 @ sk59 @ sk60 )
| ( ( sk1 @ sk285 @ sk287 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[99185]) ).
thf(6255,plain,
( ( sk1 @ sk66 @ sk145 )
| ( sk1 @ sk66 @ sk146 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk150 @ sk151 ) ),
inference(cnfConj,[status(thm)],[6220]) ).
thf(130,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(26601,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk403 @ A )
& ( sk1 @ sk403 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ^ [A: $i] :
( ( sk1 @ sk403 @ A )
=> ( sk1 @ A @ sk403 ) ) ) )
| ( ( sk1 @ sk60 @ sk59 )
!= ( ! [A: $i] :
( ( ( sk1 @ sk59 @ sk60 )
& ( sk1 @ sk60 @ A ) )
=> ( sk1 @ sk59 @ A ) ) ) ) ),
inference(simp,[status(thm)],[15070]) ).
thf(1161,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ~ $true
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[27,17]) ).
thf(1162,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(simp,[status(thm)],[1161]) ).
thf(1167,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ( sk11 != sk10 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[1162]) ).
thf(1176,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk8 @ sk9 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[1167]) ).
thf(80,plain,
( ( sk1 @ sk12 @ sk13 )
| ~ ( sk1 @ sk14 @ sk16 )
| ~ ( sk1 @ sk18 @ sk19 )
| ~ ( sk1 @ sk21 @ sk20 ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(35,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(48455,plain,
( ( ( ! [A: $i] :
( ( sk1 @ sk2792 @ A )
=> ( sk1 @ A @ sk2792 ) ) )
!= ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk2792 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk2792 @ B ) ) ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) ) ) ),
inference(func_ext,[status(esa)],[35682]) ).
thf(16,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(1083,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ $true
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[13,16]) ).
thf(1084,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk10 @ sk11 ) ) ),
inference(simp,[status(thm)],[1083]) ).
thf(1137,plain,
( ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk11 != sk10 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[1084]) ).
thf(1145,plain,
( ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[1137]) ).
thf(4065,plain,
( ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk3 @ sk2 )
| ~ $true
| ( sk11 != sk10 )
| ( ( sk1 @ sk8 @ sk9 )
!= ( sk1 @ sk7 @ sk9 ) ) ),
inference(paramod_ordered,[status(thm)],[3333,1145]) ).
thf(4066,plain,
( ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( ( sk1 @ sk8 @ sk9 )
!= ( sk1 @ sk7 @ sk9 ) ) ),
inference(simp,[status(thm)],[4065]) ).
thf(4313,plain,
( ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk8 != sk7 )
| ( sk9 != sk9 ) ),
inference(simp,[status(thm)],[4066]) ).
thf(4331,plain,
( ( sk1 @ sk4 @ sk5 )
| ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[4313]) ).
thf(73853,plain,
! [B: $i,A: $i] :
( ( sk289 != sk288 )
| ( sk286 != sk285 )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25800,72823]) ).
thf(73854,plain,
! [B: $i,A: $i] :
( ( sk289 != sk288 )
| ( sk286 != sk285 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[73853]) ).
thf(73855,plain,
( ( sk289 != sk288 )
| ( sk286 != sk285 )
| ( sk1 @ sk60 @ sk59 ) ),
inference(pattern_uni,[status(thm)],[73854:[bind(A,$thf( sk59 )),bind(B,$thf( sk60 ))]]) ).
thf(73530,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk60 @ sk4458 )
| ( sk1 @ sk59 @ sk60 )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk811 @ sk812 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[68105,72823]) ).
thf(73531,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk60 @ sk4458 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk811 @ sk812 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[73530]) ).
thf(73532,plain,
( ( sk1 @ sk60 @ sk4458 )
| ( sk1 @ sk59 @ sk60 )
| ( sk1 @ sk812 @ sk811 ) ),
inference(pattern_uni,[status(thm)],[73531:[bind(A,$thf( sk811 )),bind(B,$thf( sk812 ))]]) ).
thf(55600,plain,
( ( ( ^ [A: $i] :
( ( sk1 @ sk2241 @ A )
=> ( sk1 @ A @ sk2241 ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk2241 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk2241 @ B ) ) ) )
| ( ( ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) )
!= ( ( sk1 @ sk72 @ sk73 )
=> ( sk1 @ sk73 @ sk72 ) ) ) ),
inference(simp,[status(thm)],[42234]) ).
thf(18,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(4894,plain,
( ( ( ^ [A: $i] :
( ( sk1 @ sk53 @ A )
=> ( sk1 @ A @ sk53 ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk53 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk53 @ B ) ) ) )
| ( ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[1802]) ).
thf(43181,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) ) ) ),
inference(simp,[status(thm)],[42312]) ).
thf(74744,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(paramod_ordered,[status(thm)],[73453,43181]) ).
thf(74745,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(simp,[status(thm)],[74744]) ).
thf(74746,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) ),
inference(pattern_uni,[status(thm)],[74745:[]]) ).
thf(75320,plain,
( ( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk4747 ) )
& ( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ( sk1 @ sk73 @ sk4747 ) ) ),
inference(cnf,[status(esa)],[74746]) ).
thf(75321,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk4747 ) ),
inference(cnfConj,[status(thm)],[75320]) ).
thf(44771,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( ( sk1 @ sk60 @ sk59 )
!= ( sk1 @ sk59 @ sk1091 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[40253]) ).
thf(44858,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk60 != sk59 )
| ( sk1091 != sk59 ) ),
inference(simp,[status(thm)],[44771]) ).
thf(67,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(22196,plain,
( ~ ! [A: $i,B: $i] :
( ( ( sk1 @ sk498 @ A )
& ( sk1 @ sk498 @ B ) )
=> ( sk1 @ A @ B ) )
| ~ ! [A: $i] :
( ( sk1 @ sk498 @ A )
=> ( sk1 @ A @ sk498 ) )
| ~ ! [A: $i] :
( ( sk1 @ sk60 @ A )
=> ( sk1 @ sk59 @ A ) )
| ~ ( sk1 @ sk60 @ sk59 ) ),
inference(bool_ext,[status(thm)],[15745]) ).
thf(22584,plain,
( ( ( sk1 @ sk498 @ sk962 )
| ( sk1 @ sk498 @ sk964 )
| ( sk1 @ sk60 @ sk965 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk498 @ sk962 )
| ( sk1 @ sk498 @ sk964 )
| ~ ( sk1 @ sk59 @ sk965 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk498 @ sk962 )
| ~ ( sk1 @ sk964 @ sk498 )
| ( sk1 @ sk60 @ sk965 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk498 @ sk962 )
| ~ ( sk1 @ sk964 @ sk498 )
| ~ ( sk1 @ sk59 @ sk965 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk498 @ sk963 )
| ( sk1 @ sk498 @ sk964 )
| ( sk1 @ sk60 @ sk965 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk498 @ sk963 )
| ( sk1 @ sk498 @ sk964 )
| ~ ( sk1 @ sk59 @ sk965 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk498 @ sk963 )
| ~ ( sk1 @ sk964 @ sk498 )
| ( sk1 @ sk60 @ sk965 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ( sk1 @ sk498 @ sk963 )
| ~ ( sk1 @ sk964 @ sk498 )
| ~ ( sk1 @ sk59 @ sk965 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk962 @ sk963 )
| ( sk1 @ sk498 @ sk964 )
| ( sk1 @ sk60 @ sk965 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk962 @ sk963 )
| ( sk1 @ sk498 @ sk964 )
| ~ ( sk1 @ sk59 @ sk965 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk962 @ sk963 )
| ~ ( sk1 @ sk964 @ sk498 )
| ( sk1 @ sk60 @ sk965 )
| ~ ( sk1 @ sk60 @ sk59 ) )
& ( ~ ( sk1 @ sk962 @ sk963 )
| ~ ( sk1 @ sk964 @ sk498 )
| ~ ( sk1 @ sk59 @ sk965 )
| ~ ( sk1 @ sk60 @ sk59 ) ) ),
inference(cnf,[status(esa)],[22196]) ).
thf(22593,plain,
( ~ ( sk1 @ sk962 @ sk963 )
| ~ ( sk1 @ sk964 @ sk498 )
| ~ ( sk1 @ sk59 @ sk965 )
| ~ ( sk1 @ sk60 @ sk59 ) ),
inference(cnfConj,[status(thm)],[22584]) ).
thf(4895,plain,
( ( ( ! [A: $i] :
( ( sk1 @ sk53 @ A )
=> ( sk1 @ A @ sk53 ) ) )
!= ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk53 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk53 @ B ) ) ) )
| ( ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[1802]) ).
thf(6174,plain,
( ( ( ! [A: $i] :
( ( sk1 @ sk53 @ A )
=> ( sk1 @ A @ sk53 ) ) )
!= ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk53 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk53 @ B ) ) ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[4895]) ).
thf(31,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(6226,plain,
( ~ ( sk1 @ sk144 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ~ ( sk1 @ sk148 @ sk147 )
| ~ ( sk1 @ sk149 @ sk151 ) ),
inference(cnfConj,[status(thm)],[6220]) ).
thf(6441,plain,
( ~ ( sk1 @ sk144 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ~ ( sk1 @ sk148 @ sk147 )
| ( ( sk1 @ sk149 @ sk151 )
!= ( sk1 @ sk146 @ sk66 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6226]) ).
thf(6457,plain,
( ~ ( sk1 @ sk144 @ sk145 )
| ~ ( sk1 @ sk146 @ sk66 )
| ~ ( sk1 @ sk148 @ sk147 )
| ( sk149 != sk146 )
| ( sk151 != sk66 ) ),
inference(simp,[status(thm)],[6441]) ).
thf(75322,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ( sk1 @ sk73 @ sk4747 ) ),
inference(cnfConj,[status(thm)],[75320]) ).
thf(101211,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ $true
| ( ( sk1 @ sk73 @ sk4747 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(paramod_ordered,[status(thm)],[73453,75322]) ).
thf(101212,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( sk1 @ sk73 @ sk4747 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(simp,[status(thm)],[101211]) ).
thf(101291,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk73 != sk73 )
| ( sk4747 != sk72 ) ),
inference(simp,[status(thm)],[101212]) ).
thf(101359,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk4747 != sk72 ) ),
inference(simp,[status(thm)],[101291]) ).
thf(8861,plain,
( ( sk1 @ sk171 @ sk172 )
| ( sk1 @ sk174 @ sk175 )
| ( sk1 @ sk176 @ sk178 )
| ( sk1 @ sk179 @ sk180 ) ),
inference(cnfConj,[status(thm)],[8841]) ).
thf(6198,plain,
( ( ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk66 @ A )
& ( sk1 @ sk66 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ! [A: $i] :
( ( sk1 @ sk66 @ A )
=> ( sk1 @ A @ sk66 ) ) ) )
| ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[1828]) ).
thf(7720,plain,
( ( ( ! [A: $i,B: $i] :
( ( ( sk1 @ sk66 @ A )
& ( sk1 @ sk66 @ B ) )
=> ( sk1 @ A @ B ) ) )
!= ( ! [A: $i] :
( ( sk1 @ sk66 @ A )
=> ( sk1 @ A @ sk66 ) ) ) )
| ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[6198]) ).
thf(43,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(131,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(1180,plain,
( ( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(4944,plain,
( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk118 @ sk119 )
| ( sk1 @ sk120 @ sk121 )
| ( sk1 @ sk123 @ sk124 ) ),
inference(cnfConj,[status(thm)],[4917]) ).
thf(33647,plain,
( ~ ( sk1 @ sk73 @ sk1680 )
| ~ ( sk1 @ sk73 @ sk72 )
| ~ ( sk1 @ sk1682 @ sk1681 )
| ~ ( sk1 @ sk1683 @ sk1685 ) ),
inference(cnfConj,[status(thm)],[33635]) ).
thf(2974,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk9 != sk8 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk3 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2919]) ).
thf(2997,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk9 != sk8 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[2974]) ).
thf(76268,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) )
| ( sk1 @ sk60 @ sk4774 ) ),
inference(cnfConj,[status(thm)],[76267]) ).
thf(63604,plain,
( ( ( ^ [A: $i] :
( ( sk1 @ sk2792 @ A )
=> ( sk1 @ A @ sk2792 ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk2792 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk2792 @ B ) ) ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( ! [A: $i] :
( ( ( sk1 @ sk72 @ sk73 )
& ( sk1 @ sk72 @ A ) )
=> ( sk1 @ sk73 @ A ) ) ) ) ),
inference(simp,[status(thm)],[48455]) ).
thf(40,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk7 @ sk8 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(26,plain,
( ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(8854,plain,
( ~ ( sk1 @ sk172 @ sk171 )
| ~ ( sk1 @ sk173 @ sk175 )
| ~ ( sk1 @ sk177 @ sk178 )
| ~ ( sk1 @ sk179 @ sk181 ) ),
inference(cnfConj,[status(thm)],[8841]) ).
thf(85099,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ $true
| ( ( sk1 @ sk73 @ sk4724 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(paramod_ordered,[status(thm)],[73453,75227]) ).
thf(85100,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( sk1 @ sk73 @ sk4724 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(simp,[status(thm)],[85099]) ).
thf(85204,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk73 != sk73 )
| ( sk4724 != sk72 ) ),
inference(simp,[status(thm)],[85100]) ).
thf(85237,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk4724 != sk72 ) ),
inference(simp,[status(thm)],[85204]) ).
thf(75242,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk72 @ sk4728 ) ),
inference(cnfConj,[status(thm)],[75240]) ).
thf(137,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[118]) ).
thf(139,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[137]) ).
thf(4969,plain,
( ( ( ^ [A: $i] :
( ( sk1 @ sk53 @ A )
=> ( sk1 @ A @ sk53 ) ) )
!= ( ^ [A: $i] :
! [B: $i] :
( ( ( sk1 @ sk53 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk53 @ B ) ) ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ A @ C ) )
=> ( sk1 @ B @ C ) ) )
!= ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[4896]) ).
thf(103782,plain,
( ( sk286 != sk59 )
| ( sk285 != sk60 )
| ~ $true
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[89995,86832]) ).
thf(103783,plain,
( ( sk286 != sk59 )
| ( sk285 != sk60 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[103782]) ).
thf(103784,plain,
( ( sk286 != sk59 )
| ( sk285 != sk60 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 ) ),
inference(pattern_uni,[status(thm)],[103783:[]]) ).
thf(100565,plain,
( ( sk1 @ sk59 @ sk60 )
| ( ( sk1 @ sk287 @ sk285 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[100360]) ).
thf(51307,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( ( sk1 @ sk60 @ sk59 )
!= ( sk1 @ sk59 @ sk1091 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[45351]) ).
thf(51386,plain,
( ~ ( sk1 @ sk59 @ sk1091 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk60 != sk59 )
| ( sk1091 != sk59 ) ),
inference(simp,[status(thm)],[51307]) ).
thf(5122,plain,
( ~ ( sk1 @ sk117 @ sk53 )
| ~ ( sk1 @ sk53 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ( ( sk1 @ sk124 @ sk123 )
!= ( sk1 @ sk117 @ sk53 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4925]) ).
thf(5144,plain,
( ~ ( sk1 @ sk117 @ sk53 )
| ~ ( sk1 @ sk53 @ sk119 )
| ~ ( sk1 @ sk121 @ sk122 )
| ( sk124 != sk117 )
| ( sk123 != sk53 ) ),
inference(simp,[status(thm)],[5122]) ).
thf(85431,plain,
! [B: $i,A: $i] :
( ( ( ^ [C: $i,D: $i] :
( ( sk1 @ C @ D )
=> ( sk1 @ D @ C ) ) )
!= ( ^ [C: $i,D: $i] :
! [E: $i] :
( ( ( sk1 @ C @ D )
& ( sk1 @ D @ E ) )
=> ( sk1 @ C @ E ) ) ) )
| ~ $true
| ( sk1 @ B @ A )
| ( ( sk1 @ sk72 @ sk4728 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[75242,72823]) ).
thf(85432,plain,
! [B: $i,A: $i] :
( ( ( ^ [C: $i,D: $i] :
( ( sk1 @ C @ D )
=> ( sk1 @ D @ C ) ) )
!= ( ^ [C: $i,D: $i] :
! [E: $i] :
( ( ( sk1 @ C @ D )
& ( sk1 @ D @ E ) )
=> ( sk1 @ C @ E ) ) ) )
| ( sk1 @ B @ A )
| ( ( sk1 @ sk72 @ sk4728 )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[85431]) ).
thf(85433,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk1 @ sk4728 @ sk72 ) ),
inference(pattern_uni,[status(thm)],[85432:[bind(A,$thf( sk72 )),bind(B,$thf( sk4728 ))]]) ).
thf(36,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ~ ( sk1 @ sk11 @ sk10 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(141,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( ( sk1 @ sk11 @ sk10 )
!= ( sk1 @ sk5 @ sk6 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[23]) ).
thf(146,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk1 @ sk7 @ sk9 )
| ( sk11 != sk5 )
| ( sk10 != sk6 ) ),
inference(simp,[status(thm)],[141]) ).
thf(30,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk5 )
| ( sk1 @ sk7 @ sk8 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(11871,plain,
( ~ ( sk1 @ sk60 @ sk59 )
| ~ ( sk1 @ sk59 @ sk284 )
| ~ ( sk1 @ sk286 @ sk287 )
| ~ ( sk1 @ sk289 @ sk288 ) ),
inference(cnfConj,[status(thm)],[11861]) ).
thf(104901,plain,
( ( sk289 != sk288 )
| ( sk287 != sk285 )
| ~ $true
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[90427,77921]) ).
thf(104902,plain,
( ( sk289 != sk288 )
| ( sk287 != sk285 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[104901]) ).
thf(104903,plain,
( ( sk289 != sk288 )
| ( sk287 != sk285 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 ) ),
inference(pattern_uni,[status(thm)],[104902:[]]) ).
thf(107,plain,
( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk17 @ sk19 )
| ( sk1 @ sk20 @ sk21 ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(4476,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk8 != sk7 )
| ~ ( sk1 @ sk3 @ sk2 )
| ~ $true
| ( sk11 != sk10 )
| ( sk9 != sk8 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[4331,2919]) ).
thf(4477,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk8 != sk7 )
| ( sk9 != sk8 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk4 @ sk5 ) ) ),
inference(simp,[status(thm)],[4476]) ).
thf(4565,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk8 != sk7 )
| ( sk9 != sk8 )
| ( sk5 != sk4 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[4477]) ).
thf(43840,plain,
( ( ( ( sk1 @ sk2541 @ sk2542 )
=> ( sk1 @ sk2542 @ sk2541 ) )
!= ( ! [A: $i] :
( ( ( sk1 @ sk2541 @ sk2542 )
& ( sk1 @ sk2542 @ A ) )
=> ( sk1 @ sk2541 @ A ) ) ) )
| ( ( sk1 @ sk73 @ sk72 )
!= ( ! [A: $i] :
( ( sk1 @ sk72 @ A )
=> ( sk1 @ sk73 @ A ) ) ) ) ),
inference(func_ext,[status(esa)],[43181]) ).
thf(79,plain,
( ~ ( sk1 @ sk13 @ sk12 )
| ( sk1 @ sk15 @ sk16 )
| ( sk1 @ sk17 @ sk18 )
| ~ ( sk1 @ sk21 @ sk20 ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(75283,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ ( sk1 @ sk73 @ sk4738 ) ),
inference(cnfConj,[status(thm)],[75281]) ).
thf(96091,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ 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 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ~ $true
| ( ( sk1 @ sk73 @ sk4738 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(paramod_ordered,[status(thm)],[73453,75283]) ).
thf(96092,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( ( sk1 @ sk73 @ sk4738 )
!= ( sk1 @ sk73 @ sk72 ) ) ),
inference(simp,[status(thm)],[96091]) ).
thf(96231,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk73 != sk73 )
| ( sk4738 != sk72 ) ),
inference(simp,[status(thm)],[96092]) ).
thf(96240,plain,
( ( ( ^ [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
! [C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) )
| ( sk4738 != sk72 ) ),
inference(simp,[status(thm)],[96231]) ).
thf(103651,plain,
( ( sk286 != sk59 )
| ( sk285 != sk60 )
| ~ $true
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[89995,77921]) ).
thf(103652,plain,
( ( sk286 != sk59 )
| ( sk285 != sk60 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[103651]) ).
thf(103653,plain,
( ( sk286 != sk59 )
| ( sk285 != sk60 )
| ( sk630 != sk629 )
| ( sk1090 != sk630 )
| ( sk1091 != sk60 ) ),
inference(pattern_uni,[status(thm)],[103652:[]]) ).
thf(15,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1 @ sk4 @ sk6 )
| ( sk1 @ sk8 @ sk9 )
| ( sk1 @ sk10 @ sk11 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(105032,plain,
( ( sk289 != sk288 )
| ( sk287 != sk285 )
| ~ $true
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(paramod_ordered,[status(thm)],[90427,86832]) ).
thf(105033,plain,
( ( sk289 != sk288 )
| ( sk287 != sk285 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 )
| ( ( sk1 @ sk59 @ sk60 )
!= ( sk1 @ sk59 @ sk60 ) ) ),
inference(simp,[status(thm)],[105032]) ).
thf(105034,plain,
( ( sk289 != sk288 )
| ( sk287 != sk285 )
| ( sk1090 != sk629 )
| ( sk630 != sk629 )
| ( sk1091 != sk60 ) ),
inference(pattern_uni,[status(thm)],[105033:[]]) ).
thf(4936,plain,
( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk53 @ sk118 )
| ( sk1 @ sk120 @ sk121 )
| ( sk1 @ sk123 @ sk124 ) ),
inference(cnfConj,[status(thm)],[4917]) ).
thf(111,plain,
( ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk14 @ sk15 )
| ( sk1 @ sk17 @ sk18 )
| ( sk1 @ sk20 @ sk21 ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(4949,plain,
( ( sk1 @ sk53 @ sk117 )
| ( sk1 @ sk118 @ sk119 )
| ( sk1 @ sk120 @ sk122 )
| ( sk1 @ sk123 @ sk124 ) ),
inference(cnfConj,[status(thm)],[4917]) ).
thf(2998,plain,
( ~ ( sk1 @ sk3 @ sk2 )
| ( sk11 != sk10 )
| ( sk9 != sk8 )
| ( sk5 != sk3 )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[2974]) ).
thf(6254,plain,
( ( sk1 @ sk66 @ sk145 )
| ( sk1 @ sk66 @ sk146 )
| ( sk1 @ sk147 @ sk148 )
| ( sk1 @ sk149 @ sk150 ) ),
inference(cnfConj,[status(thm)],[6220]) ).
thf(52615,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ~ $true
| ( ( sk1 @ sk1683 @ sk1685 )
!= ( sk1 @ sk1683 @ sk1684 ) ) ),
inference(paramod_ordered,[status(thm)],[33674,33675]) ).
thf(52616,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( ( sk1 @ sk1683 @ sk1685 )
!= ( sk1 @ sk1683 @ sk1684 ) ) ),
inference(simp,[status(thm)],[52615]) ).
thf(52637,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1683 != sk1683 )
| ( sk1685 != sk1684 ) ),
inference(simp,[status(thm)],[52616]) ).
thf(52693,plain,
( ( sk1 @ sk72 @ sk73 )
| ( sk1 @ sk1681 @ sk1682 )
| ( sk1685 != sk1684 ) ),
inference(simp,[status(thm)],[52637]) ).
thf(143042,plain,
$false,
inference(e,[status(thm)],[23872,33675,35679,1840,73947,7549,8843,79430,8855,6199,33672,5,111626,10,56,116101,153,28366,7405,6246,8848,8898,42,24,100566,37,25,14,4896,8951,45351,35682,1826,73327,104661,157,75282,4952,15744,103411,29,20,11100,8632,3835,108718,35396,57,107210,52694,2880,106,107203,1828,3621,94159,132,116,3588,127140,7707,27474,6,117,111493,270,3635,23871,93793,4925,73767,42234,99247,114313,76302,88819,3735,12437,89994,297,21,8899,68105,33,28,38,34945,65,86943,115962,18989,97,13924,53,33676,40284,76301,686,71087,27864,88818,76192,72823,85235,48454,15069,70898,3333,41,11927,73569,1799,13,73453,34221,76571,1814,15101,5126,76193,73406,45283,95020,45,90898,64,87068,17,32,34,50084,148,42233,15070,22,18990,6229,118,27,44,8900,12,75226,78013,144,33673,5190,11900,18648,73992,81,119076,39,89995,6197,22195,94027,97949,15745,66,76285,155,99246,103,6255,130,26601,1176,3,80,35,48455,4331,42312,75227,1145,73855,43182,19651,73532,55600,25800,18,4894,75321,44858,67,22593,16,6174,73564,31,33677,90427,6457,13983,1802,77921,11,101359,8861,7720,43,32988,1180,4944,33647,2997,2919,76268,63604,76269,76286,40,26,8854,85237,55,75242,139,18454,4969,23,103784,100565,33674,51386,119,2912,88404,5144,23866,85433,6198,43181,36,75243,146,30,11871,19,6226,104903,13986,107,4565,4895,21991,98825,43840,79,11903,96240,103653,86832,131,15,105034,75283,4936,111,75322,4949,2998,6254,52693,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL867^1 : 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
% 0.11/0.22 % Computer : n011.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 10:16:01 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.52/1.05 % [INFO] Parsing done (252ms).
% 1.52/1.06 % [INFO] Running in sequential loop mode.
% 2.07/1.47 % [INFO] eprover registered as external prover.
% 2.07/1.48 % [INFO] Scanning for conjecture ...
% 2.46/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.46/1.67 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.46/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 2.46/1.68 % [INFO] Type checking passed.
% 2.46/1.69 % [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 ...
% 161.66/55.93 % External prover 'e' found a proof!
% 161.66/55.93 % [INFO] Killing All external provers ...
% 161.66/55.94 % Time passed: 55568ms (effective reasoning time: 54868ms)
% 161.66/55.94 % 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)>
% 161.66/55.94 % Axioms used in derivation (0):
% 161.66/55.94 % No. of inferences in proof: 583
% 161.66/55.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 55568 ms resp. 54868 ms w/o parsing
% 163.67/56.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 163.67/56.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------