%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL652+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:52:20 AM UTC 2026
% Result : Theorem 95.54s 29.53s
% Output : Refutation 90.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 24
% Syntax : Number of formulae : 1183 ( 43 unt; 0 typ; 23 def)
% Number of atoms : 5551 (1424 equ; 0 cnn)
% Maximal formula atoms : 167 ( 4 avg)
% Number of connectives : 15679 (3553 ~;3049 |; 84 &;8993 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 74 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 7 con; 0-3 aty)
% Number of variables : 1052 ( 36 ^; 989 !; 4 ?;1052 :)
% ( 0 !>; 0 ?*; 0 @-; 23 @+)
% Comments :
%------------------------------------------------------------------------------
thf(r1_decl,type,
r1: $i > $i > $o ).
thf(p4_decl,type,
p4: $i > $o ).
thf(p1_decl,type,
p1: $i > $o ).
thf(p3_decl,type,
p3: $i > $o ).
thf(p2_decl,type,
p2: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $o ).
thf(sk7_decl,type,
sk7: $i > $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $o ).
thf(sk10_decl,type,
sk10: $i > $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk13_decl,type,
sk13: $i > $o ).
thf(sk14_decl,type,
sk14: $i > $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i > $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i > $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i ).
thf(sk20_decl,type,
sk20: $i > $i ).
thf(sk21_decl,type,
sk21: $i ).
thf(sk22_decl,type,
sk22: $i ).
thf(sk23_decl,type,
sk23: $i ).
thf(sk24_decl,type,
sk24: $i ).
thf(sk25_decl,type,
sk25: $i > $i ).
thf(sk26_decl,type,
sk26: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p3 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p1 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ~ ( D @ p1 )
| ~ ( D @ ( A @ r1 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( A @ r1 ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C @ p3 )
| ~ ( C @ ( B @ ( A @ sk4 ) @ r1 ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( D @ p3 )
| ~ ( D @ ( A @ r1 ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( A @ r1 ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( A @ r1 ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( D @ p3 )
| ~ ( D @ ( C @ ( B @ ( A @ sk10 ) ) @ r1 ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( A @ r1 ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( A @ r1 ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( A @ r1 ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( D @ p3 )
| ~ ( D @ ( C @ ( B @ ( A @ sk16 ) ) @ r1 ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ( B @ p2 )
| ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p3 )
| ~ ( B @ ( A @ sk18 @ r1 ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i] :
~ ( ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( @+[A: $i] :
~ ( ~ ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk21 @ r1 ) ) ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( @+[A: $i] :
~ ( ( A @ p1 )
| ~ ( A @ ( sk21 @ r1 ) ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( @+[A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(1,conjecture,
~ ? [A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p3 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p1 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
thf(2,negated_conjecture,
~ ~ ? [A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p3 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p1 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ? [A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p3 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p1 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
? [A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p3 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p1 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p3 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p1 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(miniscope,[status(thm)],[4]) ).
thf(6,plain,
! [Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( W @ sk26 @ p1 )
| ~ ( Y @ p1 )
| ~ ( Y @ ( X @ r1 ) )
| ~ ( X @ ( W @ r1 ) )
| ~ ( W @ ( sk1 @ r1 ) ) )
& ( ( W @ sk26 @ ( W @ r1 ) )
| ~ ( Y @ p1 )
| ~ ( Y @ ( X @ r1 ) )
| ~ ( X @ ( W @ r1 ) )
| ~ ( W @ ( sk1 @ r1 ) ) )
& ( ~ ( V @ sk25 @ p2 )
| ~ ( V @ ( sk24 @ r1 ) ) )
& ( ( V @ sk25 @ ( V @ r1 ) )
| ~ ( V @ ( sk24 @ r1 ) ) )
& ( sk24 @ ( sk1 @ r1 ) )
& ~ ( sk23 @ p1 )
& ( sk23 @ ( sk21 @ r1 ) )
& ( ( U @ p1 )
| ~ ( U @ ( sk22 @ r1 ) ) )
& ( sk22 @ ( sk21 @ r1 ) )
& ( sk21 @ ( sk1 @ r1 ) )
& ( ~ ( R @ sk20 @ p1 )
| ( T @ p1 )
| ~ ( T @ ( S @ r1 ) )
| ~ ( S @ ( R @ r1 ) )
| ~ ( R @ ( sk1 @ r1 ) ) )
& ( ( R @ sk20 @ ( R @ r1 ) )
| ( T @ p1 )
| ~ ( T @ ( S @ r1 ) )
| ~ ( S @ ( R @ r1 ) )
| ~ ( R @ ( sk1 @ r1 ) ) )
& ( ~ ( F @ sk9 )
| ( F @ sk18 @ p2 )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( F @ sk9 )
| ~ ( F @ sk19 @ p3 )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( F @ sk9 )
| ( F @ sk19 @ ( F @ sk18 @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( F @ sk9 )
| ( F @ sk18 @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ( F @ ( O @ ( Q @ sk16 ) ) @ p2 )
| ~ ( Q @ ( F @ ( O @ sk15 ) @ r1 ) )
| ( O @ sk13 )
| ~ ( O @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( F @ ( O @ ( Q @ sk17 ) ) @ p3 )
| ~ ( Q @ ( F @ ( O @ sk15 ) @ r1 ) )
| ( O @ sk13 )
| ~ ( O @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ( F @ ( O @ ( Q @ sk17 ) ) @ ( F @ ( O @ ( Q @ sk16 ) ) @ r1 ) )
| ~ ( Q @ ( F @ ( O @ sk15 ) @ r1 ) )
| ( O @ sk13 )
| ~ ( O @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ( F @ ( O @ ( Q @ sk16 ) ) @ ( Q @ r1 ) )
| ~ ( Q @ ( F @ ( O @ sk15 ) @ r1 ) )
| ( O @ sk13 )
| ~ ( O @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ( F @ ( O @ sk15 ) @ ( O @ r1 ) )
| ( O @ sk13 )
| ~ ( O @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( O @ sk13 )
| ~ ( P @ p2 )
| ~ ( P @ ( F @ ( O @ sk14 ) @ r1 ) )
| ~ ( O @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( O @ sk13 )
| ( F @ ( O @ sk14 ) @ ( O @ r1 ) )
| ~ ( O @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( N @ p2 )
| ~ ( N @ ( F @ sk12 @ r1 ) )
| ( F @ sk9 )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ( F @ sk12 @ ( F @ r1 ) )
| ( F @ sk9 )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( F @ sk9 )
| ( F @ ( L @ ( M @ sk10 ) ) @ p2 )
| ~ ( M @ ( L @ r1 ) )
| ~ ( L @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( F @ sk9 )
| ~ ( F @ ( L @ ( M @ sk11 ) ) @ p3 )
| ~ ( M @ ( L @ r1 ) )
| ~ ( L @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( F @ sk9 )
| ( F @ ( L @ ( M @ sk11 ) ) @ ( F @ ( L @ ( M @ sk10 ) ) @ r1 ) )
| ~ ( M @ ( L @ r1 ) )
| ~ ( L @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( F @ sk9 )
| ( F @ ( L @ ( M @ sk10 ) ) @ ( M @ r1 ) )
| ~ ( M @ ( L @ r1 ) )
| ~ ( L @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( K @ p2 )
| ~ ( K @ ( F @ ( H @ ( J @ sk8 ) ) @ r1 ) )
| ~ ( J @ ( H @ r1 ) )
| ~ ( H @ p2 )
| ( H @ sk6 )
| ~ ( H @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ( F @ ( H @ ( J @ sk8 ) ) @ ( J @ r1 ) )
| ~ ( J @ ( H @ r1 ) )
| ~ ( H @ p2 )
| ( H @ sk6 )
| ~ ( H @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( H @ sk6 )
| ( I @ p2 )
| ~ ( I @ ( H @ r1 ) )
| ~ ( H @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( H @ sk6 )
| ~ ( F @ ( H @ ( I @ sk7 ) ) @ p3 )
| ~ ( I @ ( H @ r1 ) )
| ~ ( H @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( H @ sk6 )
| ( F @ ( H @ ( I @ sk7 ) ) @ ( I @ r1 ) )
| ~ ( I @ ( H @ r1 ) )
| ~ ( H @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ( F @ ( G @ sk4 ) @ p2 )
| ~ ( G @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( F @ ( G @ sk5 ) @ p3 )
| ~ ( G @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ( F @ ( G @ sk5 ) @ ( F @ ( G @ sk4 ) @ r1 ) )
| ~ ( G @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ( F @ ( G @ sk4 ) @ ( G @ r1 ) )
| ~ ( G @ ( F @ r1 ) )
| ~ ( F @ ( sk1 @ r1 ) ) )
& ( ~ ( E @ p1 )
| ~ ( E @ ( B @ sk3 @ r1 ) )
| ( B @ ( C @ ( D @ sk2 ) ) @ p1 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ( B @ sk3 @ ( B @ r1 ) )
| ( B @ ( C @ ( D @ sk2 ) ) @ p1 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( E @ p1 )
| ~ ( E @ ( B @ sk3 @ r1 ) )
| ( B @ ( C @ ( D @ sk2 ) ) @ ( D @ r1 ) )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ( B @ sk3 @ ( B @ r1 ) )
| ( B @ ( C @ ( D @ sk2 ) ) @ ( D @ r1 ) )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( A @ p4 )
| ~ ( A @ ( sk1 @ r1 ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(12,plain,
! [A: $i] :
( ~ ( A @ sk9 )
| ( A @ sk18 @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(69,plain,
! [A: $i] :
( ~ ( A @ sk9 )
| ( A @ sk18 @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(13,plain,
sk22 @ ( sk21 @ r1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(4900,plain,
! [B: $i,A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[13,61]) ).
thf(4901,plain,
! [B: $i,A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[4900]) ).
thf(4902,plain,
( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
| ~ ( sk21 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[4901:[bind(A,$thf( sk21 )),bind(B,$thf( sk22 ))]]) ).
thf(42,plain,
sk21 @ ( sk1 @ r1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(5468,plain,
( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
| ~ $true ),
inference(rewrite,[status(thm)],[4902,42]) ).
thf(5469,plain,
sk21 @ ( sk22 @ sk4 ) @ p2,
inference(simp,[status(thm)],[5468]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk4 ) @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk4 ) @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(526,plain,
! [B: $i,A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk4 ) @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[13,53]) ).
thf(527,plain,
! [B: $i,A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk4 ) @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[526]) ).
thf(528,plain,
( ( sk21 @ ( sk22 @ sk5 ) @ ( sk21 @ ( sk22 @ sk4 ) @ r1 ) )
| ~ ( sk21 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[527:[bind(A,$thf( sk21 )),bind(B,$thf( sk22 ))]]) ).
thf(618,plain,
( ( sk21 @ ( sk22 @ sk5 ) @ ( sk21 @ ( sk22 @ sk4 ) @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[528,42]) ).
thf(619,plain,
sk21 @ ( sk22 @ sk5 ) @ ( sk21 @ ( sk22 @ sk4 ) @ r1 ),
inference(simp,[status(thm)],[618]) ).
thf(34,plain,
sk24 @ ( sk1 @ r1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(8,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(803,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,54]) ).
thf(804,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[803]) ).
thf(805,plain,
! [A: $i] :
( ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ ( A @ ( sk24 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[804:[bind(A,$thf( sk24 ))]]) ).
thf(845,plain,
! [A: $i] :
( ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ ( A @ ( sk24 @ r1 ) ) ),
inference(simp,[status(thm)],[805]) ).
thf(3271,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk5 ) @ ( sk21 @ ( sk22 @ sk4 ) @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[619,845]) ).
thf(3272,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk5 ) @ ( sk21 @ ( sk22 @ sk4 ) @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3271]) ).
thf(3323,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk5 ) )
!= A )
| ( ( sk21 @ ( sk22 @ sk4 ) )
!= sk24 )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3272]) ).
thf(3345,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= sk24 )
| ~ ( sk24 @ ( sk21 @ ( sk22 @ sk5 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3323]) ).
thf(47,plain,
! [A: $i] :
( ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(85,plain,
! [A: $i] :
( ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(142,plain,
! [A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,85]) ).
thf(143,plain,
! [A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 ) ),
inference(simp,[status(thm)],[142]) ).
thf(144,plain,
( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
| ( sk21 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( sk21 ))]]) ).
thf(4934,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[144,61]) ).
thf(4935,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[4934]) ).
thf(4936,plain,
( ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 )
| ~ ( sk21 @ ( sk1 @ r1 ) )
| ( sk21 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[4935:[bind(A,$thf( sk21 )),bind(B,$thf( sk21 @ sk12 ))]]) ).
thf(6854,plain,
( ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 )
| ~ $true
| ( sk21 @ sk9 ) ),
inference(rewrite,[status(thm)],[4936,42]) ).
thf(6855,plain,
( ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[6854]) ).
thf(40,plain,
! [A: $i] :
( ~ ( A @ sk25 @ p2 )
| ~ ( A @ ( sk24 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(79,plain,
! [A: $i] :
( ~ ( A @ sk25 @ p2 )
| ~ ( A @ ( sk24 @ r1 ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(639,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk5 ) @ ( sk21 @ ( sk22 @ sk4 ) @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[619,79]) ).
thf(640,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk5 ) @ ( sk21 @ ( sk22 @ sk4 ) @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[639]) ).
thf(657,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk5 ) )
!= A )
| ( ( sk21 @ ( sk22 @ sk4 ) )
!= sk24 )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[640]) ).
thf(666,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= sk24 )
| ~ ( sk21 @ ( sk22 @ sk5 ) @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[657]) ).
thf(5002,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[61]) ).
thf(5017,plain,
( ( sk1 @ ( sk1 @ sk4 ) @ p2 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[5002:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(6246,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk1 @ sk4 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,5017]) ).
thf(6247,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk1 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[6246]) ).
thf(6332,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk1 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[6247]) ).
thf(6374,plain,
( ( sk21 != sk1 )
| ( sk1 @ ( sk1 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[6332]) ).
thf(19,plain,
! [A: $i] :
( ( A @ p1 )
| ~ ( A @ ( sk22 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(84,plain,
! [A: $i] :
( ( A @ p1 )
| ~ ( A @ ( sk22 @ r1 ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( ( A @ sk12 @ ( A @ r1 ) )
!= ( B @ ( sk22 @ r1 ) ) )
| ( B @ p1 )
| ~ $true
| ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[85,84]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( ( A @ sk12 @ ( A @ r1 ) )
!= ( B @ ( sk22 @ r1 ) ) )
| ( B @ p1 )
| ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(133,plain,
( ( sk22 @ sk12 @ p1 )
| ( sk22 @ sk9 )
| ~ ( sk22 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( sk22 )),bind(B,$thf( sk22 @ sk12 ))]]) ).
thf(1435,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ( sk22 @ sk12 @ p1 )
| ( sk22 @ sk9 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,133]) ).
thf(1436,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ( sk22 @ sk12 @ p1 )
| ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[1435]) ).
thf(1457,plain,
( ( sk24 != sk22 )
| ( sk1 != sk1 )
| ( sk22 @ sk12 @ p1 )
| ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[1436]) ).
thf(1465,plain,
( ( sk24 != sk22 )
| ( sk22 @ sk12 @ p1 )
| ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[1457]) ).
thf(13406,plain,
! [A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk18 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,69]) ).
thf(13407,plain,
! [A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[13406]) ).
thf(13408,plain,
( ~ ( sk24 @ sk9 )
| ( sk24 @ sk18 @ p2 ) ),
inference(pattern_uni,[status(thm)],[13407:[bind(A,$thf( sk24 ))]]) ).
thf(13670,plain,
( ( ( sk24 @ sk9 )
!= ( sk22 @ sk9 ) )
| ~ $true
| ( sk24 @ sk18 @ p2 )
| ( sk24 != sk22 )
| ( sk22 @ sk12 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[1465,13408]) ).
thf(13671,plain,
( ( ( sk24 @ sk9 )
!= ( sk22 @ sk9 ) )
| ( sk24 @ sk18 @ p2 )
| ( sk24 != sk22 )
| ( sk22 @ sk12 @ p1 ) ),
inference(simp,[status(thm)],[13670]) ).
thf(13735,plain,
( ( sk24 != sk22 )
| ( sk24 != sk22 )
| ( sk24 @ sk18 @ p2 )
| ( sk22 @ sk12 @ p1 ) ),
inference(simp,[status(thm)],[13671]) ).
thf(13746,plain,
( ( sk24 != sk22 )
| ( sk24 @ sk18 @ p2 )
| ( sk22 @ sk12 @ p1 ) ),
inference(simp,[status(thm)],[13735]) ).
thf(22,plain,
~ ( sk23 @ p1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(23874,plain,
( ( ( sk22 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk24 != sk22 )
| ( sk24 @ sk18 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[13746,22]) ).
thf(23875,plain,
( ( ( sk22 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ( sk24 != sk22 )
| ( sk24 @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[23874]) ).
thf(23904,plain,
( ( ( sk22 @ sk12 )
!= sk23 )
| ( sk24 != sk22 )
| ( sk24 @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[23875]) ).
thf(24,plain,
sk23 @ ( sk21 @ r1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(43,plain,
! [A: $i] :
( ( A @ sk25 @ ( A @ r1 ) )
| ~ ( A @ ( sk24 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(78,plain,
! [A: $i] :
( ( A @ sk25 @ ( A @ r1 ) )
| ~ ( A @ ( sk24 @ r1 ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(28105,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk23 @ ( sk21 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,78]) ).
thf(28106,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk23 @ ( sk21 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[28105]) ).
thf(28485,plain,
! [A: $i] :
( ( A != sk23 )
| ( sk24 != sk21 )
| ( A @ sk25 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[28106]) ).
thf(28571,plain,
( ( sk24 != sk21 )
| ( sk23 @ sk25 @ ( sk23 @ r1 ) ) ),
inference(simp,[status(thm)],[28485]) ).
thf(28694,plain,
! [A: $i] :
( ( ( sk23 @ sk25 @ ( sk23 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk24 != sk21 ) ),
inference(paramod_ordered,[status(thm)],[28571,84]) ).
thf(28695,plain,
! [A: $i] :
( ( ( sk23 @ sk25 @ ( sk23 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[28694]) ).
thf(28928,plain,
! [A: $i] :
( ( ( sk23 @ sk25 )
!= A )
| ( sk23 != sk22 )
| ( sk24 != sk21 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[28695]) ).
thf(28964,plain,
( ( sk23 != sk22 )
| ( sk24 != sk21 )
| ( sk23 @ sk25 @ p1 ) ),
inference(simp,[status(thm)],[28928]) ).
thf(32348,plain,
( ( ( sk23 @ sk25 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk23 != sk22 )
| ( sk24 != sk21 ) ),
inference(paramod_ordered,[status(thm)],[28964,22]) ).
thf(32349,plain,
( ( ( sk23 @ sk25 @ p1 )
!= ( sk23 @ p1 ) )
| ( sk23 != sk22 )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[32348]) ).
thf(32356,plain,
( ( ( sk23 @ sk25 )
!= sk23 )
| ( sk23 != sk22 )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[32349]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(7615,plain,
! [B: $i,A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ ( B @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,65]) ).
thf(7616,plain,
! [B: $i,A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[7615]) ).
thf(7617,plain,
( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
| ~ ( sk21 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[7616:[bind(A,$thf( sk21 )),bind(B,$thf( sk23 ))]]) ).
thf(9408,plain,
( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[7617,42]) ).
thf(9409,plain,
sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ),
inference(simp,[status(thm)],[9408]) ).
thf(9442,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[9409,61]) ).
thf(9443,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[9442]) ).
thf(9444,plain,
( ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk4 ) @ p2 )
| ~ ( sk23 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[9443:[bind(A,$thf( sk23 )),bind(B,$thf( sk21 @ ( sk23 @ sk4 ) ))]]) ).
thf(21409,plain,
( ( ( sk23 @ ( sk1 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk4 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,9444]) ).
thf(21410,plain,
( ( ( sk23 @ ( sk1 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[21409]) ).
thf(21603,plain,
( ( sk23 != sk21 )
| ( sk1 != sk1 )
| ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[21410]) ).
thf(21645,plain,
( ( sk23 != sk21 )
| ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[21603]) ).
thf(7718,plain,
! [B: $i,A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ ( B @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[13,65]) ).
thf(7719,plain,
! [B: $i,A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[7718]) ).
thf(7720,plain,
( ( sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ) )
| ~ ( sk21 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[7719:[bind(A,$thf( sk21 )),bind(B,$thf( sk22 ))]]) ).
thf(10649,plain,
( ( sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[7720,42]) ).
thf(10650,plain,
sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ),
inference(simp,[status(thm)],[10649]) ).
thf(10684,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[10650,61]) ).
thf(10685,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[10684]) ).
thf(10686,plain,
( ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk4 ) @ p2 )
| ~ ( sk22 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[10685:[bind(A,$thf( sk22 )),bind(B,$thf( sk21 @ ( sk22 @ sk4 ) ))]]) ).
thf(41090,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk4 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,10686]) ).
thf(41091,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[41090]) ).
thf(41240,plain,
( ( sk24 != sk22 )
| ( sk1 != sk1 )
| ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[41091]) ).
thf(41329,plain,
( ( sk24 != sk22 )
| ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[41240]) ).
thf(7915,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[65]) ).
thf(7947,plain,
( ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[7915:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(13921,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,7947]) ).
thf(13922,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[13921]) ).
thf(14154,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[13922]) ).
thf(14200,plain,
( ( sk24 != sk1 )
| ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[14154]) ).
thf(4840,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[42,61]) ).
thf(4841,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[4840]) ).
thf(4842,plain,
( ( sk1 @ ( sk21 @ sk4 ) @ p2 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[4841:[bind(A,$thf( sk1 )),bind(B,$thf( sk21 ))]]) ).
thf(5075,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk21 @ sk4 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,4842]) ).
thf(5076,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk21 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[5075]) ).
thf(5173,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk21 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[5076]) ).
thf(5195,plain,
( ( sk21 != sk1 )
| ( sk1 @ ( sk21 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[5173]) ).
thf(245,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk22 @ ( sk21 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,79]) ).
thf(246,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk22 @ ( sk21 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[245]) ).
thf(256,plain,
! [A: $i] :
( ( A != sk22 )
| ( sk24 != sk21 )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[246]) ).
thf(257,plain,
( ( sk24 != sk21 )
| ~ ( sk22 @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[256]) ).
thf(5200,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) @ p2 )
!= ( sk22 @ sk25 @ p2 ) )
| ( sk24 != sk21 )
| ~ $true
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[5195,257]) ).
thf(5201,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) @ p2 )
!= ( sk22 @ sk25 @ p2 ) )
| ( sk24 != sk21 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[5200]) ).
thf(5225,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) )
!= ( sk22 @ sk25 ) )
| ( sk24 != sk21 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[5201]) ).
thf(17,plain,
! [A: $i] :
( ~ ( A @ p4 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( ( A @ sk12 @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( B @ p4 )
| ~ $true
| ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[85,17]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( ( A @ sk12 @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( B @ p4 )
| ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(152,plain,
( ~ ( sk1 @ sk12 @ p4 )
| ( sk1 @ sk9 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[151:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk12 ))]]) ).
thf(4076,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk12 @ p4 )
| ( sk1 @ sk9 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,152]) ).
thf(4077,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk12 @ p4 )
| ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[4076]) ).
thf(4134,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ~ ( sk1 @ sk12 @ p4 )
| ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[4077]) ).
thf(4156,plain,
( ( sk21 != sk1 )
| ~ ( sk1 @ sk12 @ p4 )
| ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[4134]) ).
thf(11,plain,
! [A: $i] :
( ~ ( A @ sk9 )
| ( A @ sk18 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(77,plain,
! [A: $i] :
( ~ ( A @ sk9 )
| ( A @ sk18 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(25923,plain,
! [A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk18 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,77]) ).
thf(25924,plain,
! [A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk18 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[25923]) ).
thf(25925,plain,
( ~ ( sk21 @ sk9 )
| ( sk21 @ sk18 @ ( sk21 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[25924:[bind(A,$thf( sk21 ))]]) ).
thf(26690,plain,
! [A: $i] :
( ( ( sk21 @ sk18 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ~ ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[25925,17]) ).
thf(26691,plain,
! [A: $i] :
( ( ( sk21 @ sk18 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[26690]) ).
thf(26850,plain,
! [A: $i] :
( ( ( sk21 @ sk18 )
!= A )
| ( sk21 != sk1 )
| ~ ( A @ p4 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[26691]) ).
thf(26931,plain,
( ( sk21 != sk1 )
| ~ ( sk21 @ sk18 @ p4 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[26850]) ).
thf(27541,plain,
( ( ( sk21 @ sk9 )
!= ( sk1 @ sk9 ) )
| ( sk21 != sk1 )
| ~ ( sk21 @ sk18 @ p4 )
| ~ $true
| ( sk21 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(paramod_ordered,[status(thm)],[4156,26931]) ).
thf(27542,plain,
( ( ( sk21 @ sk9 )
!= ( sk1 @ sk9 ) )
| ~ ( sk21 @ sk18 @ p4 )
| ( sk21 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[27541]) ).
thf(27573,plain,
( ( sk21 != sk1 )
| ~ ( sk21 @ sk18 @ p4 )
| ( sk21 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[27542]) ).
thf(27575,plain,
( ~ ( sk21 @ sk18 @ p4 )
| ( sk21 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[27573]) ).
thf(10768,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10650,845]) ).
thf(10769,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[10768]) ).
thf(10835,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= A )
| ( sk24 != sk22 )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[10769]) ).
thf(10876,plain,
( ( sk24 != sk22 )
| ~ ( sk24 @ ( sk21 @ ( sk22 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[10835]) ).
thf(787,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,54]) ).
thf(788,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[787]) ).
thf(789,plain,
! [A: $i] :
( ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ~ ( A @ ( sk21 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[788:[bind(A,$thf( sk21 ))]]) ).
thf(850,plain,
! [A: $i] :
( ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ~ ( A @ ( sk21 @ r1 ) ) ),
inference(simp,[status(thm)],[789]) ).
thf(4559,plain,
! [A: $i] :
( ( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ~ $true
| ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[144,850]) ).
thf(4560,plain,
! [A: $i] :
( ( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[4559]) ).
thf(4561,plain,
( ~ ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ p3 )
| ( sk21 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[4560:[bind(A,$thf( sk21 @ sk12 ))]]) ).
thf(10,plain,
! [A: $i] :
( ~ ( A @ sk9 )
| ~ ( A @ sk19 @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(50,plain,
! [A: $i] :
( ~ ( A @ sk9 )
| ~ ( A @ sk19 @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(103,plain,
! [A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ~ ( A @ sk19 @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,50]) ).
thf(104,plain,
! [A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ~ ( A @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[103]) ).
thf(105,plain,
( ~ ( sk21 @ sk9 )
| ~ ( sk21 @ sk19 @ p3 ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( sk21 ))]]) ).
thf(4811,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ~ $true
| ~ ( sk21 @ sk19 @ p3 )
| ~ ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ p3 ) ),
inference(paramod_ordered,[status(thm)],[4561,105]) ).
thf(4812,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ~ ( sk21 @ sk19 @ p3 )
| ~ ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[4811]) ).
thf(4813,plain,
( ~ ( sk21 @ sk19 @ p3 )
| ~ ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[4812:[]]) ).
thf(7514,plain,
( ~ $true
| ( ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ p3 )
!= ( sk21 @ sk19 @ p3 ) )
| ~ ( sk21 @ sk19 @ p3 ) ),
inference(eqfactor_ordered,[status(thm)],[4813]) ).
thf(7516,plain,
( ( ( sk21 @ ( sk21 @ sk12 @ sk5 ) )
!= ( sk21 @ sk19 ) )
| ~ ( sk21 @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[7514]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk6 )
| ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk6 )
| ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(6284,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk1 @ sk4 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,5017]) ).
thf(6285,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk1 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[6284]) ).
thf(6339,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk1 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[6285]) ).
thf(6369,plain,
( ( sk24 != sk1 )
| ( sk1 @ ( sk1 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[6339]) ).
thf(247,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,79]) ).
thf(248,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[247]) ).
thf(253,plain,
! [A: $i] :
( ( A != sk21 )
| ( sk24 != sk1 )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[248]) ).
thf(258,plain,
( ( sk24 != sk1 )
| ~ ( sk21 @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[253]) ).
thf(6395,plain,
( ( ( sk1 @ ( sk1 @ sk4 ) @ p2 )
!= ( sk21 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6369,258]) ).
thf(6396,plain,
( ( ( sk1 @ ( sk1 @ sk4 ) @ p2 )
!= ( sk21 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[6395]) ).
thf(6401,plain,
( ( ( sk1 @ ( sk1 @ sk4 ) )
!= ( sk21 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[6396]) ).
thf(554,plain,
! [B: $i,A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk4 ) @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,53]) ).
thf(555,plain,
! [B: $i,A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk4 ) @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[554]) ).
thf(556,plain,
( ( sk21 @ ( sk23 @ sk5 ) @ ( sk21 @ ( sk23 @ sk4 ) @ r1 ) )
| ~ ( sk21 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[555:[bind(A,$thf( sk21 )),bind(B,$thf( sk23 ))]]) ).
thf(1932,plain,
( ( sk21 @ ( sk23 @ sk5 ) @ ( sk21 @ ( sk23 @ sk4 ) @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[556,42]) ).
thf(1933,plain,
sk21 @ ( sk23 @ sk5 ) @ ( sk21 @ ( sk23 @ sk4 ) @ r1 ),
inference(simp,[status(thm)],[1932]) ).
thf(1942,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk5 ) @ ( sk21 @ ( sk23 @ sk4 ) @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1933,84]) ).
thf(1943,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk5 ) @ ( sk21 @ ( sk23 @ sk4 ) @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[1942]) ).
thf(2001,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk5 ) )
!= A )
| ( ( sk21 @ ( sk23 @ sk4 ) )
!= sk22 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[1943]) ).
thf(2018,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= sk22 )
| ( sk21 @ ( sk23 @ sk5 ) @ p1 ) ),
inference(simp,[status(thm)],[2001]) ).
thf(2033,plain,
( ( ( sk21 @ ( sk23 @ sk5 ) @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( ( sk21 @ ( sk23 @ sk4 ) )
!= sk22 ) ),
inference(paramod_ordered,[status(thm)],[2018,22]) ).
thf(2034,plain,
( ( ( sk21 @ ( sk23 @ sk5 ) @ p1 )
!= ( sk23 @ p1 ) )
| ( ( sk21 @ ( sk23 @ sk4 ) )
!= sk22 ) ),
inference(simp,[status(thm)],[2033]) ).
thf(2035,plain,
( ( ( sk21 @ ( sk23 @ sk5 ) )
!= sk23 )
| ( ( sk21 @ ( sk23 @ sk4 ) )
!= sk22 ) ),
inference(simp,[status(thm)],[2034]) ).
thf(4096,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk12 @ p4 )
| ( sk1 @ sk9 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,152]) ).
thf(4097,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk12 @ p4 )
| ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[4096]) ).
thf(4127,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ~ ( sk1 @ sk12 @ p4 )
| ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[4097]) ).
thf(4154,plain,
( ( sk24 != sk1 )
| ~ ( sk1 @ sk12 @ p4 )
| ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[4127]) ).
thf(13701,plain,
( ( ( sk24 @ sk9 )
!= ( sk1 @ sk9 ) )
| ~ $true
| ( sk24 @ sk18 @ p2 )
| ( sk24 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(paramod_ordered,[status(thm)],[4154,13408]) ).
thf(13702,plain,
( ( ( sk24 @ sk9 )
!= ( sk1 @ sk9 ) )
| ( sk24 @ sk18 @ p2 )
| ( sk24 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[13701]) ).
thf(13739,plain,
( ( sk24 != sk1 )
| ( sk24 != sk1 )
| ~ ( sk1 @ sk12 @ p4 )
| ( sk24 @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[13702]) ).
thf(13747,plain,
( ( sk24 != sk1 )
| ~ ( sk1 @ sk12 @ p4 )
| ( sk24 @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[13739]) ).
thf(7736,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ ( B @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[34,65]) ).
thf(7737,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[7736]) ).
thf(7738,plain,
( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[7737:[bind(A,$thf( sk1 )),bind(B,$thf( sk24 ))]]) ).
thf(11958,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,7738]) ).
thf(11959,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) ) ),
inference(simp,[status(thm)],[11958]) ).
thf(12212,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) ) ),
inference(simp,[status(thm)],[11959]) ).
thf(12296,plain,
( ( sk21 != sk1 )
| ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) ) ),
inference(simp,[status(thm)],[12212]) ).
thf(12477,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[12296,79]) ).
thf(12478,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[12477]) ).
thf(12479,plain,
( ~ ( sk1 @ ( sk24 @ sk4 ) @ sk25 @ p2 )
| ( sk21 != sk1 ) ),
inference(pattern_uni,[status(thm)],[12478:[bind(A,$thf( sk1 @ ( sk24 @ sk4 ) ))]]) ).
thf(7610,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ ( B @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[42,65]) ).
thf(7611,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[7610]) ).
thf(7612,plain,
( ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[7611:[bind(A,$thf( sk1 )),bind(B,$thf( sk21 ))]]) ).
thf(8149,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,7612]) ).
thf(8150,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) ) ),
inference(simp,[status(thm)],[8149]) ).
thf(8344,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) ) ),
inference(simp,[status(thm)],[8150]) ).
thf(8413,plain,
( ( sk21 != sk1 )
| ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) ) ),
inference(simp,[status(thm)],[8344]) ).
thf(8528,plain,
! [A: $i] :
( ( ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[8413,17]) ).
thf(8529,plain,
! [A: $i] :
( ( ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[8528]) ).
thf(8625,plain,
! [A: $i] :
( ( ( sk1 @ ( sk21 @ sk4 ) )
!= A )
| ( sk21 != sk1 )
| ~ ( A @ p4 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[8529]) ).
thf(8667,plain,
( ~ ( sk1 @ ( sk21 @ sk4 ) @ p4 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[8625]) ).
thf(3258,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk22 @ ( sk21 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,845]) ).
thf(3259,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk22 @ ( sk21 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3258]) ).
thf(3316,plain,
! [A: $i] :
( ( A != sk22 )
| ( sk24 != sk21 )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3259]) ).
thf(3338,plain,
( ( sk24 != sk21 )
| ~ ( sk24 @ ( sk22 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3316]) ).
thf(26116,plain,
! [B: $i,A: $i] :
( ( ( A @ sk18 @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( B @ p4 )
| ~ $true
| ~ ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[77,17]) ).
thf(26117,plain,
! [B: $i,A: $i] :
( ( ( A @ sk18 @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( B @ p4 )
| ~ ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[26116]) ).
thf(26118,plain,
( ~ ( sk1 @ sk18 @ p4 )
| ~ ( sk1 @ sk9 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[26117:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk18 ))]]) ).
thf(41605,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk18 @ p4 )
| ~ ( sk1 @ sk9 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,26118]) ).
thf(41606,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk18 @ p4 )
| ~ ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[41605]) ).
thf(41774,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ~ ( sk1 @ sk18 @ p4 )
| ~ ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[41606]) ).
thf(41815,plain,
( ( sk24 != sk1 )
| ~ ( sk1 @ sk18 @ p4 )
| ~ ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[41774]) ).
thf(108,plain,
! [A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ~ ( A @ sk19 @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,50]) ).
thf(109,plain,
! [A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ~ ( A @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[108]) ).
thf(110,plain,
( ~ ( sk24 @ sk9 )
| ~ ( sk24 @ sk19 @ p3 ) ),
inference(pattern_uni,[status(thm)],[109:[bind(A,$thf( sk24 ))]]) ).
thf(2136,plain,
( ( ( sk24 @ sk9 )
!= ( sk22 @ sk9 ) )
| ~ $true
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk22 )
| ( sk22 @ sk12 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[1465,110]) ).
thf(2137,plain,
( ( ( sk24 @ sk9 )
!= ( sk22 @ sk9 ) )
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk22 )
| ( sk22 @ sk12 @ p1 ) ),
inference(simp,[status(thm)],[2136]) ).
thf(2153,plain,
( ( sk24 != sk22 )
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk22 )
| ( sk22 @ sk12 @ p1 ) ),
inference(simp,[status(thm)],[2137]) ).
thf(2159,plain,
( ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk22 )
| ( sk22 @ sk12 @ p1 ) ),
inference(simp,[status(thm)],[2153]) ).
thf(8906,plain,
( ( ( sk22 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk22 ) ),
inference(paramod_ordered,[status(thm)],[2159,22]) ).
thf(8907,plain,
( ( ( sk22 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk22 ) ),
inference(simp,[status(thm)],[8906]) ).
thf(8911,plain,
( ( ( sk22 @ sk12 )
!= sk23 )
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk22 ) ),
inference(simp,[status(thm)],[8907]) ).
thf(13343,plain,
! [A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk18 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,69]) ).
thf(13344,plain,
! [A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[13343]) ).
thf(13345,plain,
( ~ ( sk21 @ sk9 )
| ( sk21 @ sk18 @ p2 ) ),
inference(pattern_uni,[status(thm)],[13344:[bind(A,$thf( sk21 ))]]) ).
thf(249,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk23 @ ( sk21 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,79]) ).
thf(250,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk23 @ ( sk21 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[249]) ).
thf(255,plain,
! [A: $i] :
( ( A != sk23 )
| ( sk24 != sk21 )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[250]) ).
thf(260,plain,
( ( sk24 != sk21 )
| ~ ( sk23 @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[255]) ).
thf(13585,plain,
( ( ( sk23 @ sk25 @ p2 )
!= ( sk21 @ sk18 @ p2 ) )
| ( sk24 != sk21 )
| ~ $true
| ~ ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[13345,260]) ).
thf(13586,plain,
( ( ( sk23 @ sk25 @ p2 )
!= ( sk21 @ sk18 @ p2 ) )
| ( sk24 != sk21 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[13585]) ).
thf(13626,plain,
( ( ( sk23 @ sk25 )
!= ( sk21 @ sk18 ) )
| ( sk24 != sk21 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[13586]) ).
thf(277,plain,
! [A: $i] :
( ( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[144,17]) ).
thf(278,plain,
! [A: $i] :
( ( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[277]) ).
thf(282,plain,
! [A: $i] :
( ( ( sk21 @ sk12 )
!= A )
| ( sk21 != sk1 )
| ~ ( A @ p4 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[278]) ).
thf(288,plain,
( ( sk21 != sk1 )
| ~ ( sk21 @ sk12 @ p4 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[282]) ).
thf(1423,plain,
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ( sk22 @ sk12 @ p1 )
| ( sk22 @ sk9 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,133]) ).
thf(1424,plain,
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ( sk22 @ sk12 @ p1 )
| ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[1423]) ).
thf(1458,plain,
( ( sk22 != sk22 )
| ( sk21 != sk1 )
| ( sk22 @ sk12 @ p1 )
| ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[1424]) ).
thf(1466,plain,
( ( sk21 != sk1 )
| ( sk22 @ sk12 @ p1 )
| ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[1458]) ).
thf(13397,plain,
! [A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk18 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,69]) ).
thf(13398,plain,
! [A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[13397]) ).
thf(13492,plain,
! [A: $i] :
( ( sk22 != A )
| ( sk21 != sk1 )
| ~ ( A @ sk9 )
| ( A @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[13398]) ).
thf(13531,plain,
( ( sk21 != sk1 )
| ~ ( sk22 @ sk9 )
| ( sk22 @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[13492]) ).
thf(14486,plain,
( ( ( sk22 @ sk9 )
!= ( sk22 @ sk9 ) )
| ( sk21 != sk1 )
| ~ $true
| ( sk22 @ sk18 @ p2 )
| ( sk21 != sk1 )
| ( sk22 @ sk12 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[1466,13531]) ).
thf(14487,plain,
( ( ( sk22 @ sk9 )
!= ( sk22 @ sk9 ) )
| ( sk22 @ sk18 @ p2 )
| ( sk21 != sk1 )
| ( sk22 @ sk12 @ p1 ) ),
inference(simp,[status(thm)],[14486]) ).
thf(14488,plain,
( ( sk22 @ sk18 @ p2 )
| ( sk21 != sk1 )
| ( sk22 @ sk12 @ p1 ) ),
inference(pattern_uni,[status(thm)],[14487:[]]) ).
thf(1996,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk5 ) @ ( sk21 @ ( sk23 @ sk4 ) @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1933,79]) ).
thf(1997,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk5 ) @ ( sk21 @ ( sk23 @ sk4 ) @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[1996]) ).
thf(2003,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk5 ) )
!= A )
| ( ( sk21 @ ( sk23 @ sk4 ) )
!= sk24 )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[1997]) ).
thf(2020,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= sk24 )
| ~ ( sk21 @ ( sk23 @ sk5 ) @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[2003]) ).
thf(4916,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[34,61]) ).
thf(4917,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[4916]) ).
thf(4918,plain,
( ( sk1 @ ( sk24 @ sk4 ) @ p2 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[4917:[bind(A,$thf( sk1 )),bind(B,$thf( sk24 ))]]) ).
thf(5510,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk24 @ sk4 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,4918]) ).
thf(5511,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk24 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[5510]) ).
thf(5624,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk24 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[5511]) ).
thf(5634,plain,
( ( sk21 != sk1 )
| ( sk1 @ ( sk24 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[5624]) ).
thf(12857,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) @ sk25 @ p2 )
!= ( sk1 @ ( sk24 @ sk4 ) @ p2 ) )
| ~ $true
| ( sk21 != sk1 )
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[5634,12479]) ).
thf(12858,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) @ sk25 @ p2 )
!= ( sk1 @ ( sk24 @ sk4 ) @ p2 ) )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[12857]) ).
thf(12879,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) @ sk25 )
!= ( sk1 @ ( sk24 @ sk4 ) ) )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[12858]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk9 )
| ( A @ ( B @ ( C @ sk10 ) ) @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk9 )
| ( A @ ( B @ ( C @ sk10 ) ) @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(4849,plain,
! [B: $i,A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,61]) ).
thf(4850,plain,
! [B: $i,A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[4849]) ).
thf(4851,plain,
( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
| ~ ( sk21 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[4850:[bind(A,$thf( sk21 )),bind(B,$thf( sk23 ))]]) ).
thf(5270,plain,
( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
| ~ $true ),
inference(rewrite,[status(thm)],[4851,42]) ).
thf(5271,plain,
sk21 @ ( sk23 @ sk4 ) @ p2,
inference(simp,[status(thm)],[5270]) ).
thf(5292,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk21 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5271,258]) ).
thf(5293,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk21 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[5292]) ).
thf(5306,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= ( sk21 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[5293]) ).
thf(10724,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10650,17]) ).
thf(10725,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[10724]) ).
thf(10822,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= A )
| ( sk22 != sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[10725]) ).
thf(10865,plain,
( ( sk22 != sk1 )
| ~ ( sk21 @ ( sk22 @ sk4 ) @ p4 ) ),
inference(simp,[status(thm)],[10822]) ).
thf(28238,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk22 @ ( sk21 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,78]) ).
thf(28239,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk22 @ ( sk21 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[28238]) ).
thf(28509,plain,
! [A: $i] :
( ( A != sk22 )
| ( sk24 != sk21 )
| ( A @ sk25 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[28239]) ).
thf(28597,plain,
( ( sk24 != sk21 )
| ( sk22 @ sk25 @ ( sk22 @ r1 ) ) ),
inference(simp,[status(thm)],[28509]) ).
thf(29139,plain,
! [A: $i] :
( ( ( sk22 @ sk25 @ ( sk22 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk24 != sk21 ) ),
inference(paramod_ordered,[status(thm)],[28597,17]) ).
thf(29140,plain,
! [A: $i] :
( ( ( sk22 @ sk25 @ ( sk22 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[29139]) ).
thf(29268,plain,
! [A: $i] :
( ( ( sk22 @ sk25 )
!= A )
| ( sk22 != sk1 )
| ~ ( A @ p4 )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[29140]) ).
thf(29330,plain,
( ( sk22 != sk1 )
| ~ ( sk22 @ sk25 @ p4 )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[29268]) ).
thf(21474,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk23 @ ( sk1 @ r1 ) ) )
| ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk4 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,9444]) ).
thf(21475,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk23 @ ( sk1 @ r1 ) ) )
| ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[21474]) ).
thf(21625,plain,
( ( sk24 != sk23 )
| ( sk1 != sk1 )
| ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[21475]) ).
thf(21652,plain,
( ( sk24 != sk23 )
| ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[21625]) ).
thf(147,plain,
! [A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,85]) ).
thf(148,plain,
! [A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 ) ),
inference(simp,[status(thm)],[147]) ).
thf(149,plain,
( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
| ( sk24 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[148:[bind(A,$thf( sk24 ))]]) ).
thf(3284,plain,
! [A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[149,845]) ).
thf(3285,plain,
! [A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[3284]) ).
thf(3286,plain,
( ~ ( sk24 @ ( sk24 @ sk12 @ sk5 ) @ p3 )
| ( sk24 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[3285:[bind(A,$thf( sk24 @ sk12 ))]]) ).
thf(3472,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ $true
| ~ ( sk24 @ sk19 @ p3 )
| ~ ( sk24 @ ( sk24 @ sk12 @ sk5 ) @ p3 ) ),
inference(paramod_ordered,[status(thm)],[3286,110]) ).
thf(3473,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ ( sk24 @ sk19 @ p3 )
| ~ ( sk24 @ ( sk24 @ sk12 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3472]) ).
thf(3474,plain,
( ~ ( sk24 @ sk19 @ p3 )
| ~ ( sk24 @ ( sk24 @ sk12 @ sk5 ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[3473:[]]) ).
thf(3936,plain,
( ~ $true
| ( ( sk24 @ ( sk24 @ sk12 @ sk5 ) @ p3 )
!= ( sk24 @ sk19 @ p3 ) )
| ~ ( sk24 @ sk19 @ p3 ) ),
inference(eqfactor_ordered,[status(thm)],[3474]) ).
thf(3938,plain,
( ( ( sk24 @ ( sk24 @ sk12 @ sk5 ) )
!= ( sk24 @ sk19 ) )
| ~ ( sk24 @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[3936]) ).
thf(568,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk4 ) @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[34,53]) ).
thf(569,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk4 ) @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[568]) ).
thf(570,plain,
( ( sk1 @ ( sk24 @ sk5 ) @ ( sk1 @ ( sk24 @ sk4 ) @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[569:[bind(A,$thf( sk1 )),bind(B,$thf( sk24 ))]]) ).
thf(395,plain,
! [A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[149,79]) ).
thf(396,plain,
! [A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[395]) ).
thf(397,plain,
( ~ ( sk24 @ sk12 @ sk25 @ p2 )
| ( sk24 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[396:[bind(A,$thf( sk24 @ sk12 ))]]) ).
thf(26101,plain,
! [A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk18 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,77]) ).
thf(26102,plain,
! [A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk18 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[26101]) ).
thf(26103,plain,
( ~ ( sk24 @ sk9 )
| ( sk24 @ sk18 @ ( sk24 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[26102:[bind(A,$thf( sk24 ))]]) ).
thf(26989,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ $true
| ( sk24 @ sk18 @ ( sk24 @ r1 ) )
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[397,26103]) ).
thf(26990,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ( sk24 @ sk18 @ ( sk24 @ r1 ) )
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[26989]) ).
thf(26991,plain,
( ( sk24 @ sk18 @ ( sk24 @ r1 ) )
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(pattern_uni,[status(thm)],[26990:[]]) ).
thf(784,plain,
! [B: $i,A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[13,54]) ).
thf(785,plain,
! [B: $i,A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[784]) ).
thf(786,plain,
( ~ ( sk21 @ ( sk22 @ sk5 ) @ p3 )
| ~ ( sk21 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[785:[bind(A,$thf( sk21 )),bind(B,$thf( sk22 ))]]) ).
thf(852,plain,
( ~ ( sk21 @ ( sk22 @ sk5 ) @ p3 )
| ~ $true ),
inference(rewrite,[status(thm)],[786,42]) ).
thf(853,plain,
~ ( sk21 @ ( sk22 @ sk5 ) @ p3 ),
inference(simp,[status(thm)],[852]) ).
thf(406,plain,
! [A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[149,17]) ).
thf(407,plain,
! [A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[406]) ).
thf(409,plain,
! [A: $i] :
( ( ( sk24 @ sk12 )
!= A )
| ( sk24 != sk1 )
| ~ ( A @ p4 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[407]) ).
thf(416,plain,
( ( sk24 != sk1 )
| ~ ( sk24 @ sk12 @ p4 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[409]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( B @ p2 )
| ~ ( B @ ( A @ sk12 @ r1 ) )
| ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( B @ p2 )
| ~ ( B @ ( A @ sk12 @ r1 ) )
| ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(91,plain,
! [A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,17]) ).
thf(92,plain,
! [A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[91]) ).
thf(93,plain,
~ ( sk24 @ p4 ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( sk24 ))]]) ).
thf(4552,plain,
! [A: $i] :
( ( ( A @ ( sk21 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,850]) ).
thf(4553,plain,
! [A: $i] :
( ( ( A @ ( sk21 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[4552]) ).
thf(4599,plain,
! [A: $i] :
( ( A != sk24 )
| ( sk21 != sk1 )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[4553]) ).
thf(4622,plain,
( ( sk21 != sk1 )
| ~ ( sk21 @ ( sk24 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[4599]) ).
thf(9494,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[9409,54]) ).
thf(9495,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[9494]) ).
thf(9496,plain,
( ~ ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 )
| ~ ( sk23 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[9495:[bind(A,$thf( sk23 )),bind(B,$thf( sk21 @ ( sk23 @ sk4 ) ))]]) ).
thf(23129,plain,
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( sk23 @ ( sk1 @ r1 ) ) )
| ~ ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,9496]) ).
thf(23130,plain,
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( sk23 @ ( sk1 @ r1 ) ) )
| ~ ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[23129]) ).
thf(23246,plain,
( ( sk23 != sk23 )
| ( sk21 != sk1 )
| ~ ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[23130]) ).
thf(23290,plain,
( ( sk21 != sk1 )
| ~ ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[23246]) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk26 @ p1 )
| ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk26 @ p1 )
| ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(177,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( A @ sk26 @ p1 )
| ~ ( C @ p1 )
| ~ $true
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[13,51]) ).
thf(178,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( A @ sk26 @ p1 )
| ~ ( C @ p1 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(179,plain,
! [A: $i] :
( ( A @ sk26 @ p1 )
| ~ ( sk22 @ p1 )
| ~ ( sk21 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( A )),bind(B,$thf( sk21 )),bind(C,$thf( sk22 ))]]) ).
thf(27197,plain,
! [A: $i] :
( ( ( sk24 @ sk18 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[26103,79]) ).
thf(27198,plain,
! [A: $i] :
( ( ( sk24 @ sk18 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[27197]) ).
thf(27199,plain,
( ~ ( sk24 @ sk18 @ sk25 @ p2 )
| ~ ( sk24 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[27198:[bind(A,$thf( sk24 @ sk18 ))]]) ).
thf(27379,plain,
( ( ( sk24 @ sk18 @ sk25 @ p2 )
!= ( sk24 @ sk18 @ p2 ) )
| ~ $true
| ~ ( sk24 @ sk9 )
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[13408,27199]) ).
thf(27380,plain,
( ( ( sk24 @ sk18 @ sk25 @ p2 )
!= ( sk24 @ sk18 @ p2 ) )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[27379]) ).
thf(27483,plain,
( ( ( sk24 @ sk18 @ sk25 )
!= ( sk24 @ sk18 ) )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[27380]) ).
thf(23167,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk23 @ ( sk1 @ r1 ) ) )
| ~ ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,9496]) ).
thf(23168,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk23 @ ( sk1 @ r1 ) ) )
| ~ ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[23167]) ).
thf(23271,plain,
( ( sk24 != sk23 )
| ( sk1 != sk1 )
| ~ ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[23168]) ).
thf(23301,plain,
( ( sk24 != sk23 )
| ~ ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[23271]) ).
thf(29052,plain,
! [A: $i] :
( ( ( sk22 @ sk25 @ ( sk22 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk24 != sk21 ) ),
inference(paramod_ordered,[status(thm)],[28597,84]) ).
thf(29053,plain,
! [A: $i] :
( ( ( sk22 @ sk25 @ ( sk22 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[29052]) ).
thf(29054,plain,
( ( sk22 @ sk25 @ p1 )
| ( sk24 != sk21 ) ),
inference(pattern_uni,[status(thm)],[29053:[bind(A,$thf( sk22 @ sk25 ))]]) ).
thf(29386,plain,
( ( ( sk22 @ sk25 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk24 != sk21 ) ),
inference(paramod_ordered,[status(thm)],[29054,22]) ).
thf(29387,plain,
( ( ( sk22 @ sk25 @ p1 )
!= ( sk23 @ p1 ) )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[29386]) ).
thf(29395,plain,
( ( ( sk22 @ sk25 )
!= sk23 )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[29387]) ).
thf(28254,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,78]) ).
thf(28255,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[28254]) ).
thf(28525,plain,
! [A: $i] :
( ( A != sk24 )
| ( sk24 != sk1 )
| ( A @ sk25 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[28255]) ).
thf(28616,plain,
( ( sk24 != sk1 )
| ( sk24 @ sk25 @ ( sk24 @ r1 ) ) ),
inference(simp,[status(thm)],[28525]) ).
thf(30164,plain,
! [A: $i] :
( ( ( sk24 @ sk25 @ ( sk24 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[28616,84]) ).
thf(30165,plain,
! [A: $i] :
( ( ( sk24 @ sk25 @ ( sk24 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[30164]) ).
thf(30429,plain,
! [A: $i] :
( ( ( sk24 @ sk25 )
!= A )
| ( sk24 != sk22 )
| ( sk24 != sk1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[30165]) ).
thf(30505,plain,
( ( sk24 != sk22 )
| ( sk24 != sk1 )
| ( sk24 @ sk25 @ p1 ) ),
inference(simp,[status(thm)],[30429]) ).
thf(34913,plain,
( ( ( sk24 @ sk25 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk24 != sk22 )
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[30505,22]) ).
thf(34914,plain,
( ( ( sk24 @ sk25 @ p1 )
!= ( sk23 @ p1 ) )
| ( sk24 != sk22 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[34913]) ).
thf(34924,plain,
( ( ( sk24 @ sk25 )
!= sk23 )
| ( sk24 != sk22 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[34914]) ).
thf(10796,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10650,79]) ).
thf(10797,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[10796]) ).
thf(10834,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= A )
| ( sk24 != sk22 )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[10797]) ).
thf(10875,plain,
( ( sk24 != sk22 )
| ~ ( sk21 @ ( sk22 @ sk4 ) @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[10834]) ).
thf(10891,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ sk25 @ p2 )
!= ( sk21 @ ( sk22 @ sk4 ) @ p2 ) )
| ( sk24 != sk22 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5469,10875]) ).
thf(10892,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ sk25 @ p2 )
!= ( sk21 @ ( sk22 @ sk4 ) @ p2 ) )
| ( sk24 != sk22 ) ),
inference(simp,[status(thm)],[10891]) ).
thf(10933,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ sk25 )
!= ( sk21 @ ( sk22 @ sk4 ) ) )
| ( sk24 != sk22 ) ),
inference(simp,[status(thm)],[10892]) ).
thf(251,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,79]) ).
thf(252,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[251]) ).
thf(254,plain,
! [A: $i] :
( ( A != sk24 )
| ( sk24 != sk1 )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[252]) ).
thf(259,plain,
( ( sk24 != sk1 )
| ~ ( sk24 @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[254]) ).
thf(13699,plain,
( ( ( sk24 @ sk25 @ p2 )
!= ( sk24 @ sk18 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[13408,259]) ).
thf(13700,plain,
( ( ( sk24 @ sk25 @ p2 )
!= ( sk24 @ sk18 @ p2 ) )
| ( sk24 != sk1 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13699]) ).
thf(13725,plain,
( ( ( sk24 @ sk25 )
!= ( sk24 @ sk18 ) )
| ( sk24 != sk1 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13700]) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( A @ sk3 @ r1 ) )
| ( A @ ( B @ ( C @ sk2 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(74,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( A @ sk3 @ r1 ) )
| ( A @ ( B @ ( C @ sk2 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(13934,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[7947,17]) ).
thf(13935,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[13934]) ).
thf(13936,plain,
( ~ ( sk1 @ ( sk1 @ sk4 ) @ p4 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[13935:[bind(A,$thf( sk1 @ ( sk1 @ sk4 ) ))]]) ).
thf(531,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk4 ) @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[144,53]) ).
thf(532,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk4 ) @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[531]) ).
thf(533,plain,
( ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ r1 ) )
| ~ ( sk21 @ ( sk1 @ r1 ) )
| ( sk21 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[532:[bind(A,$thf( sk21 )),bind(B,$thf( sk21 @ sk12 ))]]) ).
thf(4628,plain,
( ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ r1 ) )
| ~ $true
| ( sk21 @ sk9 ) ),
inference(rewrite,[status(thm)],[533,42]) ).
thf(4629,plain,
( ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ r1 ) )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[4628]) ).
thf(806,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[34,54]) ).
thf(807,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[806]) ).
thf(808,plain,
( ~ ( sk1 @ ( sk24 @ sk5 ) @ p3 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[807:[bind(A,$thf( sk1 )),bind(B,$thf( sk24 ))]]) ).
thf(904,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk24 @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,808]) ).
thf(905,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk24 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[904]) ).
thf(915,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( sk24 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[905]) ).
thf(925,plain,
( ( sk24 != sk1 )
| ~ ( sk1 @ ( sk24 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[915]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( B @ r1 ) )
| ( B @ sk13 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( B @ r1 ) )
| ( B @ sk13 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(9087,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk15 ) @ ( B @ r1 ) )
| ( B @ sk13 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[149,66]) ).
thf(9088,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk15 ) @ ( B @ r1 ) )
| ( B @ sk13 )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[9087]) ).
thf(9089,plain,
( ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ ( sk24 @ sk12 @ r1 ) )
| ( sk24 @ sk12 @ sk13 )
| ~ ( sk24 @ ( sk1 @ r1 ) )
| ( sk24 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[9088:[bind(A,$thf( sk24 )),bind(B,$thf( sk24 @ sk12 ))]]) ).
thf(9691,plain,
( ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ ( sk24 @ sk12 @ r1 ) )
| ( sk24 @ sk12 @ sk13 )
| ~ $true
| ( sk24 @ sk9 ) ),
inference(rewrite,[status(thm)],[9089,34]) ).
thf(9692,plain,
( ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ ( sk24 @ sk12 @ r1 ) )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[9691]) ).
thf(9783,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ ( sk24 @ sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk15 ) @ ( B @ r1 ) )
| ( B @ sk13 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[9692,66]) ).
thf(9784,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ ( sk24 @ sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk15 ) @ ( B @ r1 ) )
| ( B @ sk13 )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[9783]) ).
thf(9785,plain,
( ( sk24 @ sk12 @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk15 ) @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk13 )
| ~ ( sk24 @ sk12 @ ( sk1 @ r1 ) )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[9784:[bind(A,$thf( sk24 @ sk12 )),bind(B,$thf( sk24 @ ( sk24 @ sk12 @ sk15 ) ))]]) ).
thf(12167,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[7738,79]) ).
thf(12168,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[12167]) ).
thf(12169,plain,
( ~ ( sk1 @ ( sk24 @ sk4 ) @ sk25 @ p2 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[12168:[bind(A,$thf( sk1 @ ( sk24 @ sk4 ) ))]]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk13 )
| ~ ( C @ p2 )
| ~ ( C @ ( A @ ( B @ sk14 ) @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk13 )
| ~ ( C @ p2 )
| ~ ( C @ ( A @ ( B @ sk14 ) @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(9546,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9409,79]) ).
thf(9547,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[9546]) ).
thf(9593,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= A )
| ( sk24 != sk23 )
| ~ ( A @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[9547]) ).
thf(9631,plain,
( ( sk24 != sk23 )
| ~ ( sk21 @ ( sk23 @ sk4 ) @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[9593]) ).
thf(9640,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk21 @ ( sk23 @ sk4 ) @ sk25 @ p2 ) )
| ( sk24 != sk23 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5469,9631]) ).
thf(9641,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk21 @ ( sk23 @ sk4 ) @ sk25 @ p2 ) )
| ( sk24 != sk23 ) ),
inference(simp,[status(thm)],[9640]) ).
thf(9682,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= ( sk21 @ ( sk23 @ sk4 ) @ sk25 ) )
| ( sk24 != sk23 ) ),
inference(simp,[status(thm)],[9641]) ).
thf(4527,plain,
! [A: $i] :
( ( ( A @ ( sk21 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,850]) ).
thf(4528,plain,
! [A: $i] :
( ( ( A @ ( sk21 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[4527]) ).
thf(4587,plain,
! [A: $i] :
( ( A != sk21 )
| ( sk21 != sk1 )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[4528]) ).
thf(4609,plain,
( ( sk21 != sk1 )
| ~ ( sk21 @ ( sk21 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[4587]) ).
thf(13563,plain,
( ( ( sk21 @ sk9 )
!= ( sk1 @ sk9 ) )
| ~ $true
| ( sk21 @ sk18 @ p2 )
| ( sk21 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(paramod_ordered,[status(thm)],[4156,13345]) ).
thf(13564,plain,
( ( ( sk21 @ sk9 )
!= ( sk1 @ sk9 ) )
| ( sk21 @ sk18 @ p2 )
| ( sk21 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[13563]) ).
thf(13630,plain,
( ( sk21 != sk1 )
| ( sk21 != sk1 )
| ~ ( sk1 @ sk12 @ p4 )
| ( sk21 @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[13564]) ).
thf(13649,plain,
( ( sk21 != sk1 )
| ~ ( sk1 @ sk12 @ p4 )
| ( sk21 @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[13630]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk6 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk6 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(15897,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[14200,845]) ).
thf(15898,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[15897]) ).
thf(15965,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) )
!= A )
| ( sk24 != sk1 )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[15898]) ).
thf(16016,plain,
( ~ ( sk24 @ ( sk1 @ ( sk1 @ sk4 ) @ sk5 ) @ p3 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[15965]) ).
thf(25967,plain,
! [B: $i,A: $i] :
( ( ( A @ sk18 @ ( A @ r1 ) )
!= ( B @ ( sk22 @ r1 ) ) )
| ( B @ p1 )
| ~ $true
| ~ ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[77,84]) ).
thf(25968,plain,
! [B: $i,A: $i] :
( ( ( A @ sk18 @ ( A @ r1 ) )
!= ( B @ ( sk22 @ r1 ) ) )
| ( B @ p1 )
| ~ ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[25967]) ).
thf(25969,plain,
( ( sk22 @ sk18 @ p1 )
| ~ ( sk22 @ sk9 )
| ~ ( sk22 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[25968:[bind(A,$thf( sk22 )),bind(B,$thf( sk22 @ sk18 ))]]) ).
thf(44399,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ( sk22 @ sk18 @ p1 )
| ~ ( sk22 @ sk9 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,25969]) ).
thf(44400,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ( sk22 @ sk18 @ p1 )
| ~ ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[44399]) ).
thf(44576,plain,
( ( sk24 != sk22 )
| ( sk1 != sk1 )
| ~ ( sk22 @ sk9 )
| ( sk22 @ sk18 @ p1 ) ),
inference(simp,[status(thm)],[44400]) ).
thf(44612,plain,
( ( sk24 != sk22 )
| ~ ( sk22 @ sk9 )
| ( sk22 @ sk18 @ p1 ) ),
inference(simp,[status(thm)],[44576]) ).
thf(30317,plain,
! [A: $i] :
( ( ( sk24 @ sk25 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[28616,845]) ).
thf(30318,plain,
! [A: $i] :
( ( ( sk24 @ sk25 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[30317]) ).
thf(30319,plain,
( ~ ( sk24 @ ( sk24 @ sk25 @ sk5 ) @ p3 )
| ( sk24 != sk1 ) ),
inference(pattern_uni,[status(thm)],[30318:[bind(A,$thf( sk24 @ sk25 ))]]) ).
thf(27404,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk24 @ sk18 @ sk25 @ p2 ) )
| ~ $true
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[5271,27199]) ).
thf(27405,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk24 @ sk18 @ sk25 @ p2 ) )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[27404]) ).
thf(27454,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= ( sk24 @ sk18 @ sk25 ) )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[27405]) ).
thf(5113,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk21 @ sk4 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,4842]) ).
thf(5114,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk21 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[5113]) ).
thf(5182,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk21 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[5114]) ).
thf(5197,plain,
( ( sk24 != sk1 )
| ( sk1 @ ( sk21 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[5182]) ).
thf(28445,plain,
! [B: $i,A: $i] :
( ( ( A @ sk25 @ ( A @ r1 ) )
!= ( B @ ( sk24 @ r1 ) ) )
| ~ ( B @ sk25 @ p2 )
| ~ $true
| ~ ( A @ ( sk24 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[78,79]) ).
thf(28446,plain,
! [B: $i,A: $i] :
( ( ( A @ sk25 @ ( A @ r1 ) )
!= ( B @ ( sk24 @ r1 ) ) )
| ~ ( B @ sk25 @ p2 )
| ~ ( A @ ( sk24 @ r1 ) ) ),
inference(simp,[status(thm)],[28445]) ).
thf(28447,plain,
( ~ ( sk24 @ sk25 @ sk25 @ p2 )
| ~ ( sk24 @ ( sk24 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[28446:[bind(A,$thf( sk24 )),bind(B,$thf( sk24 @ sk25 ))]]) ).
thf(29530,plain,
( ( ( sk24 @ ( sk24 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ~ ( sk24 @ sk25 @ sk25 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,28447]) ).
thf(29531,plain,
( ( ( sk24 @ ( sk24 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ~ ( sk24 @ sk25 @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[29530]) ).
thf(29682,plain,
( ( sk24 != sk24 )
| ( sk24 != sk1 )
| ~ ( sk24 @ sk25 @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[29531]) ).
thf(29771,plain,
( ( sk24 != sk1 )
| ~ ( sk24 @ sk25 @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[29682]) ).
thf(31768,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[5197,29771]) ).
thf(31769,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[31768]) ).
thf(31822,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) )
!= ( sk24 @ sk25 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[31769]) ).
thf(431,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ $true
| ~ ( sk24 @ sk19 @ p3 )
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[397,110]) ).
thf(432,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ ( sk24 @ sk19 @ p3 )
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[431]) ).
thf(433,plain,
( ~ ( sk24 @ sk19 @ p3 )
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(pattern_uni,[status(thm)],[432:[]]) ).
thf(5294,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk24 @ sk12 @ sk25 @ p2 ) )
| ~ ( sk24 @ sk19 @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5271,433]) ).
thf(5295,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk24 @ sk12 @ sk25 @ p2 ) )
| ~ ( sk24 @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[5294]) ).
thf(5302,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= ( sk24 @ sk12 @ sk25 ) )
| ~ ( sk24 @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[5295]) ).
thf(13560,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ~ $true
| ( sk21 @ sk18 @ p2 )
| ( sk21 != sk1 )
| ~ ( sk21 @ sk12 @ p4 ) ),
inference(paramod_ordered,[status(thm)],[288,13345]) ).
thf(13561,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ( sk21 @ sk18 @ p2 )
| ( sk21 != sk1 )
| ~ ( sk21 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[13560]) ).
thf(13562,plain,
( ( sk21 @ sk18 @ p2 )
| ( sk21 != sk1 )
| ~ ( sk21 @ sk12 @ p4 ) ),
inference(pattern_uni,[status(thm)],[13561:[]]) ).
thf(89,plain,
! [A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,17]) ).
thf(90,plain,
! [A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[89]) ).
thf(95,plain,
! [A: $i] :
( ( sk22 != A )
| ( sk21 != sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[90]) ).
thf(97,plain,
( ( sk21 != sk1 )
| ~ ( sk22 @ p4 ) ),
inference(simp,[status(thm)],[95]) ).
thf(12843,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) @ p2 )
!= ( sk1 @ ( sk24 @ sk4 ) @ sk25 @ p2 ) )
| ~ $true
| ( sk21 != sk1 )
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[5195,12479]) ).
thf(12844,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) @ p2 )
!= ( sk1 @ ( sk24 @ sk4 ) @ sk25 @ p2 ) )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[12843]) ).
thf(12881,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) )
!= ( sk1 @ ( sk24 @ sk4 ) @ sk25 ) )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[12844]) ).
thf(829,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[54]) ).
thf(830,plain,
( ~ ( sk1 @ ( sk1 @ sk5 ) @ p3 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[829:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(31,plain,
! [A: $i] :
( ~ ( A @ sk9 )
| ( A @ sk19 @ ( A @ sk18 @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(76,plain,
! [A: $i] :
( ~ ( A @ sk9 )
| ( A @ sk19 @ ( A @ sk18 @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(24096,plain,
! [A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk19 @ ( A @ sk18 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,76]) ).
thf(24097,plain,
! [A: $i] :
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk19 @ ( A @ sk18 @ r1 ) ) ),
inference(simp,[status(thm)],[24096]) ).
thf(24098,plain,
( ~ ( sk24 @ sk9 )
| ( sk24 @ sk19 @ ( sk24 @ sk18 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[24097:[bind(A,$thf( sk24 ))]]) ).
thf(24970,plain,
! [A: $i] :
( ( ( sk24 @ sk19 @ ( sk24 @ sk18 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[24098,84]) ).
thf(24971,plain,
! [A: $i] :
( ( ( sk24 @ sk19 @ ( sk24 @ sk18 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[24970]) ).
thf(25211,plain,
! [A: $i] :
( ( ( sk24 @ sk19 )
!= A )
| ( ( sk24 @ sk18 )
!= sk22 )
| ~ ( sk24 @ sk9 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[24971]) ).
thf(25284,plain,
( ( ( sk24 @ sk18 )
!= sk22 )
| ~ ( sk24 @ sk9 )
| ( sk24 @ sk19 @ p1 ) ),
inference(simp,[status(thm)],[25211]) ).
thf(381,plain,
! [A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[149,84]) ).
thf(382,plain,
! [A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[381]) ).
thf(412,plain,
! [A: $i] :
( ( ( sk24 @ sk12 )
!= A )
| ( sk24 != sk22 )
| ( A @ p1 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[382]) ).
thf(419,plain,
( ( sk24 != sk22 )
| ( sk24 @ sk12 @ p1 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[412]) ).
thf(751,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ $true
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk22 )
| ( sk24 @ sk12 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[419,110]) ).
thf(752,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk22 )
| ( sk24 @ sk12 @ p1 ) ),
inference(simp,[status(thm)],[751]) ).
thf(753,plain,
( ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk22 )
| ( sk24 @ sk12 @ p1 ) ),
inference(pattern_uni,[status(thm)],[752:[]]) ).
thf(7586,plain,
( ( ( sk24 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk22 ) ),
inference(paramod_ordered,[status(thm)],[753,22]) ).
thf(7587,plain,
( ( ( sk24 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk22 ) ),
inference(simp,[status(thm)],[7586]) ).
thf(7591,plain,
( ( ( sk24 @ sk12 )
!= sk23 )
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk22 ) ),
inference(simp,[status(thm)],[7587]) ).
thf(6391,plain,
( ( ( sk1 @ ( sk1 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6369,259]) ).
thf(6392,plain,
( ( ( sk1 @ ( sk1 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[6391]) ).
thf(6402,plain,
( ( ( sk1 @ ( sk1 @ sk4 ) )
!= ( sk24 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[6392]) ).
thf(549,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk4 ) @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[42,53]) ).
thf(550,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk4 ) @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[549]) ).
thf(551,plain,
( ( sk1 @ ( sk21 @ sk5 ) @ ( sk1 @ ( sk21 @ sk4 ) @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[550:[bind(A,$thf( sk1 )),bind(B,$thf( sk21 ))]]) ).
thf(13820,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,7947]) ).
thf(13821,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[13820]) ).
thf(14100,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[13821]) ).
thf(14165,plain,
( ( sk21 != sk1 )
| ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[14100]) ).
thf(15653,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ~ $true
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[14165,850]) ).
thf(15654,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[15653]) ).
thf(15681,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) )
!= A )
| ( sk21 != sk1 )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[15654]) ).
thf(15724,plain,
( ~ ( sk21 @ ( sk1 @ ( sk1 @ sk4 ) @ sk5 ) @ p3 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[15681]) ).
thf(23937,plain,
! [A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk19 @ ( A @ sk18 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,76]) ).
thf(23938,plain,
! [A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk19 @ ( A @ sk18 @ r1 ) ) ),
inference(simp,[status(thm)],[23937]) ).
thf(23939,plain,
( ~ ( sk21 @ sk9 )
| ( sk21 @ sk19 @ ( sk21 @ sk18 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[23938:[bind(A,$thf( sk21 ))]]) ).
thf(24581,plain,
! [A: $i] :
( ( ( sk21 @ sk19 @ ( sk21 @ sk18 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ~ ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[23939,84]) ).
thf(24582,plain,
! [A: $i] :
( ( ( sk21 @ sk19 @ ( sk21 @ sk18 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[24581]) ).
thf(24830,plain,
! [A: $i] :
( ( ( sk21 @ sk19 )
!= A )
| ( ( sk21 @ sk18 )
!= sk22 )
| ~ ( sk21 @ sk9 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[24582]) ).
thf(24932,plain,
( ( ( sk21 @ sk18 )
!= sk22 )
| ~ ( sk21 @ sk9 )
| ( sk21 @ sk19 @ p1 ) ),
inference(simp,[status(thm)],[24830]) ).
thf(620,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk5 ) @ ( sk21 @ ( sk22 @ sk4 ) @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[619,84]) ).
thf(621,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk5 ) @ ( sk21 @ ( sk22 @ sk4 ) @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[620]) ).
thf(656,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk5 ) )
!= A )
| ( ( sk21 @ ( sk22 @ sk4 ) )
!= sk22 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[621]) ).
thf(665,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= sk22 )
| ( sk21 @ ( sk22 @ sk5 ) @ p1 ) ),
inference(simp,[status(thm)],[656]) ).
thf(13684,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ $true
| ( sk24 @ sk18 @ p2 )
| ~ ( sk24 @ ( sk24 @ sk12 @ sk5 ) @ p3 ) ),
inference(paramod_ordered,[status(thm)],[3286,13408]) ).
thf(13685,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ( sk24 @ sk18 @ p2 )
| ~ ( sk24 @ ( sk24 @ sk12 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[13684]) ).
thf(13686,plain,
( ( sk24 @ sk18 @ p2 )
| ~ ( sk24 @ ( sk24 @ sk12 @ sk5 ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[13685:[]]) ).
thf(12448,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[12296,845]) ).
thf(12449,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[12448]) ).
thf(12450,plain,
( ~ ( sk24 @ ( sk1 @ ( sk24 @ sk4 ) @ sk5 ) @ p3 )
| ( sk21 != sk1 ) ),
inference(pattern_uni,[status(thm)],[12449:[bind(A,$thf( sk1 @ ( sk24 @ sk4 ) ))]]) ).
thf(275,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk21 @ sk12 @ ( sk21 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true
| ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[144,79]) ).
thf(276,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk21 @ sk12 @ ( sk21 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[275]) ).
thf(279,plain,
! [A: $i] :
( ( A
!= ( sk21 @ sk12 ) )
| ( sk24 != sk21 )
| ~ ( A @ sk25 @ p2 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[276]) ).
thf(285,plain,
( ( sk24 != sk21 )
| ~ ( sk21 @ sk12 @ sk25 @ p2 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[279]) ).
thf(145,plain,
! [A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,85]) ).
thf(146,plain,
! [A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 ) ),
inference(simp,[status(thm)],[145]) ).
thf(154,plain,
! [A: $i] :
( ( sk23 != A )
| ( sk21 != sk1 )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 ) ),
inference(simp,[status(thm)],[146]) ).
thf(156,plain,
( ( sk21 != sk1 )
| ( sk23 @ sk12 @ ( sk23 @ r1 ) )
| ( sk23 @ sk9 ) ),
inference(simp,[status(thm)],[154]) ).
thf(5548,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk24 @ sk4 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,4918]) ).
thf(5549,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk24 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[5548]) ).
thf(5627,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk24 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[5549]) ).
thf(5635,plain,
( ( sk24 != sk1 )
| ( sk1 @ ( sk24 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[5627]) ).
thf(5484,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk23 @ sk25 @ p2 ) )
| ( sk24 != sk21 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5469,260]) ).
thf(5485,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk23 @ sk25 @ p2 ) )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[5484]) ).
thf(5502,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= ( sk23 @ sk25 ) )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[5485]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ( ( A @ sk12 @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( B @ sk9 )
| ~ ( B @ sk19 @ p3 )
| ~ $true
| ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[85,50]) ).
thf(140,plain,
! [B: $i,A: $i] :
( ( ( A @ sk12 @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( B @ sk9 )
| ~ ( B @ sk19 @ p3 )
| ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
( ~ ( sk1 @ sk12 @ sk9 )
| ~ ( sk1 @ sk12 @ sk19 @ p3 )
| ( sk1 @ sk9 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk12 ))]]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( A @ sk26 @ p1 )
| ~ ( C @ p1 )
| ~ $true
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[42,51]) ).
thf(187,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( A @ sk26 @ p1 )
| ~ ( C @ p1 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(188,plain,
! [A: $i] :
( ( A @ sk26 @ p1 )
| ~ ( sk21 @ p1 )
| ~ ( sk1 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk21 ))]]) ).
thf(9434,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9409,84]) ).
thf(9435,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[9434]) ).
thf(9584,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= A )
| ( sk23 != sk22 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[9435]) ).
thf(9624,plain,
( ( sk23 != sk22 )
| ( sk21 @ ( sk23 @ sk4 ) @ p1 ) ),
inference(simp,[status(thm)],[9584]) ).
thf(13674,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ $true
| ( sk24 @ sk18 @ p2 )
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[397,13408]) ).
thf(13675,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ( sk24 @ sk18 @ p2 )
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[13674]) ).
thf(13676,plain,
( ( sk24 @ sk18 @ p2 )
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(pattern_uni,[status(thm)],[13675:[]]) ).
thf(8229,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,7612]) ).
thf(8230,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) ) ),
inference(simp,[status(thm)],[8229]) ).
thf(8376,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) ) ),
inference(simp,[status(thm)],[8230]) ).
thf(8429,plain,
( ( sk24 != sk1 )
| ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) ) ),
inference(simp,[status(thm)],[8376]) ).
thf(5486,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5469,259]) ).
thf(5487,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[5486]) ).
thf(5497,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= ( sk24 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[5487]) ).
thf(28780,plain,
! [A: $i] :
( ( ( sk23 @ sk25 @ ( sk23 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk24 != sk21 ) ),
inference(paramod_ordered,[status(thm)],[28571,17]) ).
thf(28781,plain,
! [A: $i] :
( ( ( sk23 @ sk25 @ ( sk23 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[28780]) ).
thf(28934,plain,
! [A: $i] :
( ( ( sk23 @ sk25 )
!= A )
| ( sk23 != sk1 )
| ~ ( A @ p4 )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[28781]) ).
thf(28967,plain,
( ( sk23 != sk1 )
| ~ ( sk23 @ sk25 @ p4 )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[28934]) ).
thf(31760,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5271,29771]) ).
thf(31761,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[31760]) ).
thf(31810,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= ( sk24 @ sk25 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[31761]) ).
thf(87,plain,
! [A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,17]) ).
thf(88,plain,
! [A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[87]) ).
thf(94,plain,
! [A: $i] :
( ( sk23 != A )
| ( sk21 != sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[88]) ).
thf(96,plain,
( ( sk21 != sk1 )
| ~ ( sk23 @ p4 ) ),
inference(simp,[status(thm)],[94]) ).
thf(13602,plain,
( ( ( sk24 @ sk25 @ p2 )
!= ( sk21 @ sk18 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true
| ~ ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[13345,259]) ).
thf(13603,plain,
( ( ( sk24 @ sk25 @ p2 )
!= ( sk21 @ sk18 @ p2 ) )
| ( sk24 != sk1 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[13602]) ).
thf(13635,plain,
( ( ( sk24 @ sk25 )
!= ( sk21 @ sk18 ) )
| ( sk24 != sk1 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[13603]) ).
thf(24545,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ~ $true
| ( sk21 @ sk19 @ ( sk21 @ sk18 @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 ) ),
inference(paramod_ordered,[status(thm)],[6855,23939]) ).
thf(24546,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ( sk21 @ sk19 @ ( sk21 @ sk18 @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[24545]) ).
thf(24547,plain,
( ( sk21 @ sk19 @ ( sk21 @ sk18 @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 ) ),
inference(pattern_uni,[status(thm)],[24546:[]]) ).
thf(4787,plain,
( ( ( sk21 @ sk9 )
!= ( sk1 @ sk9 ) )
| ~ $true
| ~ ( sk21 @ sk19 @ p3 )
| ( sk21 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(paramod_ordered,[status(thm)],[4156,105]) ).
thf(4788,plain,
( ( ( sk21 @ sk9 )
!= ( sk1 @ sk9 ) )
| ~ ( sk21 @ sk19 @ p3 )
| ( sk21 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[4787]) ).
thf(4802,plain,
( ( sk21 != sk1 )
| ~ ( sk21 @ sk19 @ p3 )
| ( sk21 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[4788]) ).
thf(4804,plain,
( ~ ( sk21 @ sk19 @ p3 )
| ( sk21 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[4802]) ).
thf(14267,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk1 @ sk4 ) @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,13936]) ).
thf(14268,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk1 @ sk4 ) @ p4 ) ),
inference(simp,[status(thm)],[14267]) ).
thf(14346,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( sk1 @ sk4 ) @ p4 ) ),
inference(simp,[status(thm)],[14268]) ).
thf(14369,plain,
( ( sk24 != sk1 )
| ~ ( sk1 @ ( sk1 @ sk4 ) @ p4 ) ),
inference(simp,[status(thm)],[14346]) ).
thf(5286,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk23 @ sk25 @ p2 ) )
| ( sk24 != sk21 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5271,260]) ).
thf(5287,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk23 @ sk25 @ p2 ) )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[5286]) ).
thf(5305,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= ( sk23 @ sk25 ) )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[5287]) ).
thf(9113,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk15 ) @ ( B @ r1 ) )
| ( B @ sk13 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[144,66]) ).
thf(9114,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk15 ) @ ( B @ r1 ) )
| ( B @ sk13 )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[9113]) ).
thf(9115,plain,
( ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ ( sk21 @ sk12 @ r1 ) )
| ( sk21 @ sk12 @ sk13 )
| ~ ( sk21 @ ( sk1 @ r1 ) )
| ( sk21 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[9114:[bind(A,$thf( sk21 )),bind(B,$thf( sk21 @ sk12 ))]]) ).
thf(23398,plain,
( ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ ( sk21 @ sk12 @ r1 ) )
| ( sk21 @ sk12 @ sk13 )
| ~ $true
| ( sk21 @ sk9 ) ),
inference(rewrite,[status(thm)],[9115,42]) ).
thf(23399,plain,
( ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ ( sk21 @ sk12 @ r1 ) )
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[23398]) ).
thf(23539,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ ( sk21 @ sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk15 ) @ ( B @ r1 ) )
| ( B @ sk13 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[23399,66]) ).
thf(23540,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ ( sk21 @ sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk15 ) @ ( B @ r1 ) )
| ( B @ sk13 )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[23539]) ).
thf(23541,plain,
( ( sk21 @ sk12 @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk15 ) @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk13 )
| ~ ( sk21 @ sk12 @ ( sk1 @ r1 ) )
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[23540:[bind(A,$thf( sk21 @ sk12 )),bind(B,$thf( sk21 @ ( sk21 @ sk12 @ sk15 ) ))]]) ).
thf(42036,plain,
( ( ( sk21 @ sk12 @ ( sk1 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ( sk21 @ sk12 @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk15 ) @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk13 )
| ~ $true
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[34,23541]) ).
thf(42037,plain,
( ( ( sk21 @ sk12 @ ( sk1 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ( sk21 @ sk12 @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk15 ) @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk13 )
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[42036]) ).
thf(42353,plain,
( ( ( sk21 @ sk12 )
!= sk24 )
| ( sk1 != sk1 )
| ( sk21 @ sk12 @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk15 ) @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk13 )
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[42037]) ).
thf(42505,plain,
( ( ( sk21 @ sk12 )
!= sk24 )
| ( sk21 @ sk12 @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk15 ) @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk13 )
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[42353]) ).
thf(3937,plain,
( ( ( sk24 @ ( sk24 @ sk12 @ sk5 ) @ p3 )
!= ( sk24 @ sk19 @ p3 ) )
| ~ ( sk24 @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[3936]) ).
thf(1263,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk21 @ sk5 ) @ ( sk1 @ ( sk21 @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,551]) ).
thf(1264,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk21 @ sk5 ) @ ( sk1 @ ( sk21 @ sk4 ) @ r1 ) ) ),
inference(simp,[status(thm)],[1263]) ).
thf(1311,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk21 @ sk5 ) @ ( sk1 @ ( sk21 @ sk4 ) @ r1 ) ) ),
inference(simp,[status(thm)],[1264]) ).
thf(1333,plain,
( ( sk24 != sk1 )
| ( sk1 @ ( sk21 @ sk5 ) @ ( sk1 @ ( sk21 @ sk4 ) @ r1 ) ) ),
inference(simp,[status(thm)],[1311]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk20 @ p1 )
| ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk20 @ p1 )
| ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(117,plain,
! [A: $i] :
( ( ( A @ ( sk22 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,84]) ).
thf(118,plain,
! [A: $i] :
( ( ( A @ ( sk22 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[117]) ).
thf(124,plain,
! [A: $i] :
( ( A != sk21 )
| ( sk22 != sk1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[118]) ).
thf(128,plain,
( ( sk22 != sk1 )
| ( sk21 @ p1 ) ),
inference(simp,[status(thm)],[124]) ).
thf(790,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[42,54]) ).
thf(791,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[790]) ).
thf(792,plain,
( ~ ( sk1 @ ( sk21 @ sk5 ) @ p3 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[791:[bind(A,$thf( sk1 )),bind(B,$thf( sk21 ))]]) ).
thf(756,plain,
( ( ( sk24 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk24 != sk22 )
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[419,22]) ).
thf(757,plain,
( ( ( sk24 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ( sk24 != sk22 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[756]) ).
thf(765,plain,
( ( ( sk24 @ sk12 )
!= sk23 )
| ( sk24 != sk22 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[757]) ).
thf(28269,plain,
! [A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) )
| ~ $true
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[149,78]) ).
thf(28270,plain,
! [A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[28269]) ).
thf(28271,plain,
( ( sk24 @ sk12 @ sk25 @ ( sk24 @ sk12 @ r1 ) )
| ( sk24 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[28270:[bind(A,$thf( sk24 @ sk12 ))]]) ).
thf(28103,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,78]) ).
thf(28104,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[28103]) ).
thf(28530,plain,
! [A: $i] :
( ( A != sk21 )
| ( sk24 != sk1 )
| ( A @ sk25 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[28104]) ).
thf(28621,plain,
( ( sk24 != sk1 )
| ( sk21 @ sk25 @ ( sk21 @ r1 ) ) ),
inference(simp,[status(thm)],[28530]) ).
thf(31581,plain,
! [A: $i] :
( ( ( sk21 @ sk25 @ ( sk21 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[28621,850]) ).
thf(31582,plain,
! [A: $i] :
( ( ( sk21 @ sk25 @ ( sk21 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[31581]) ).
thf(31583,plain,
( ~ ( sk21 @ ( sk21 @ sk25 @ sk5 ) @ p3 )
| ( sk24 != sk1 ) ),
inference(pattern_uni,[status(thm)],[31582:[bind(A,$thf( sk21 @ sk25 ))]]) ).
thf(23461,plain,
! [A: $i] :
( ( ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ ( sk21 @ sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ~ $true
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[23399,85]) ).
thf(23462,plain,
! [A: $i] :
( ( ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ ( sk21 @ sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[23461]) ).
thf(23674,plain,
! [A: $i] :
( ( ( sk21 @ ( sk21 @ sk12 @ sk15 ) )
!= A )
| ( ( sk21 @ sk12 )
!= sk1 )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[23462]) ).
thf(23725,plain,
( ( ( sk21 @ sk12 )
!= sk1 )
| ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk12 @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk9 )
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[23674]) ).
thf(866,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk21 @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,792]) ).
thf(867,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk21 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[866]) ).
thf(885,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( sk21 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[867]) ).
thf(888,plain,
( ( sk24 != sk1 )
| ~ ( sk1 @ ( sk21 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[885]) ).
thf(41080,plain,
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk4 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,10686]) ).
thf(41081,plain,
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[41080]) ).
thf(41230,plain,
( ( sk22 != sk22 )
| ( sk21 != sk1 )
| ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[41081]) ).
thf(41325,plain,
( ( sk21 != sk1 )
| ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[41230]) ).
thf(898,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk24 @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,808]) ).
thf(899,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk24 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[898]) ).
thf(921,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( sk24 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[899]) ).
thf(926,plain,
( ( sk21 != sk1 )
| ~ ( sk1 @ ( sk24 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[921]) ).
thf(31754,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[5635,29771]) ).
thf(31755,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[31754]) ).
thf(31827,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) )
!= ( sk24 @ sk25 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[31755]) ).
thf(672,plain,
( ( ( sk21 @ ( sk22 @ sk5 ) @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( ( sk21 @ ( sk22 @ sk4 ) )
!= sk22 ) ),
inference(paramod_ordered,[status(thm)],[665,22]) ).
thf(673,plain,
( ( ( sk21 @ ( sk22 @ sk5 ) @ p1 )
!= ( sk23 @ p1 ) )
| ( ( sk21 @ ( sk22 @ sk4 ) )
!= sk22 ) ),
inference(simp,[status(thm)],[672]) ).
thf(674,plain,
( ( ( sk21 @ ( sk22 @ sk5 ) )
!= sk23 )
| ( ( sk21 @ ( sk22 @ sk4 ) )
!= sk22 ) ),
inference(simp,[status(thm)],[673]) ).
thf(13703,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ $true
| ( sk24 @ sk18 @ p2 )
| ( sk24 != sk22 )
| ( sk24 @ sk12 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[419,13408]) ).
thf(13704,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ( sk24 @ sk18 @ p2 )
| ( sk24 != sk22 )
| ( sk24 @ sk12 @ p1 ) ),
inference(simp,[status(thm)],[13703]) ).
thf(13705,plain,
( ( sk24 @ sk18 @ p2 )
| ( sk24 != sk22 )
| ( sk24 @ sk12 @ p1 ) ),
inference(pattern_uni,[status(thm)],[13704:[]]) ).
thf(23788,plain,
( ( ( sk24 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk24 @ sk18 @ p2 )
| ( sk24 != sk22 ) ),
inference(paramod_ordered,[status(thm)],[13705,22]) ).
thf(23789,plain,
( ( ( sk24 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ( sk24 @ sk18 @ p2 )
| ( sk24 != sk22 ) ),
inference(simp,[status(thm)],[23788]) ).
thf(23823,plain,
( ( ( sk24 @ sk12 )
!= sk23 )
| ( sk24 != sk22 )
| ( sk24 @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[23789]) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( ( A @ sk12 @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ( B @ sk12 @ ( B @ r1 ) )
| ( B @ sk9 )
| ~ $true
| ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[85,85]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( ( A @ sk12 @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ( B @ sk12 @ ( B @ r1 ) )
| ( B @ sk9 )
| ( A @ sk9 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(136,plain,
( ( sk1 @ sk12 @ sk12 @ ( sk1 @ sk12 @ r1 ) )
| ( sk1 @ sk12 @ sk9 )
| ( sk1 @ sk9 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk12 ))]]) ).
thf(967,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ sk12 @ sk12 @ ( sk1 @ sk12 @ r1 ) )
| ( sk1 @ sk12 @ sk9 )
| ( sk1 @ sk9 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,136]) ).
thf(968,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ sk12 @ sk12 @ ( sk1 @ sk12 @ r1 ) )
| ( sk1 @ sk12 @ sk9 )
| ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[967]) ).
thf(1011,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ sk12 @ sk12 @ ( sk1 @ sk12 @ r1 ) )
| ( sk1 @ sk12 @ sk9 )
| ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[968]) ).
thf(1026,plain,
( ( sk24 != sk1 )
| ( sk1 @ sk12 @ sk12 @ ( sk1 @ sk12 @ r1 ) )
| ( sk1 @ sk12 @ sk9 )
| ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[1011]) ).
thf(13714,plain,
( ( ( sk21 @ sk25 @ p2 )
!= ( sk24 @ sk18 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[13408,258]) ).
thf(13715,plain,
( ( ( sk21 @ sk25 @ p2 )
!= ( sk24 @ sk18 @ p2 ) )
| ( sk24 != sk1 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13714]) ).
thf(13726,plain,
( ( ( sk21 @ sk25 )
!= ( sk24 @ sk18 ) )
| ( sk24 != sk1 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13715]) ).
thf(1185,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk1 @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,830]) ).
thf(1186,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk1 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[1185]) ).
thf(1214,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( sk1 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[1186]) ).
thf(1219,plain,
( ( sk21 != sk1 )
| ~ ( sk1 @ ( sk1 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[1214]) ).
thf(8589,plain,
! [A: $i] :
( ( ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ~ $true
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[8413,850]) ).
thf(8590,plain,
! [A: $i] :
( ( ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[8589]) ).
thf(8591,plain,
( ~ ( sk21 @ ( sk1 @ ( sk21 @ sk4 ) @ sk5 ) @ p3 )
| ( sk21 != sk1 ) ),
inference(pattern_uni,[status(thm)],[8590:[bind(A,$thf( sk1 @ ( sk21 @ sk4 ) ))]]) ).
thf(41,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( A @ ( B @ ( C @ sk8 ) ) @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk6 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(64,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( A @ ( B @ ( C @ sk8 ) ) @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk6 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(28370,plain,
! [A: $i] :
( ( ( sk24 @ sk18 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) )
| ~ $true
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[26103,78]) ).
thf(28371,plain,
! [A: $i] :
( ( ( sk24 @ sk18 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[28370]) ).
thf(28372,plain,
( ( sk24 @ sk18 @ sk25 @ ( sk24 @ sk18 @ r1 ) )
| ~ ( sk24 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[28371:[bind(A,$thf( sk24 @ sk18 ))]]) ).
thf(15490,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[14165,84]) ).
thf(15491,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[15490]) ).
thf(15674,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) )
!= A )
| ( sk22 != sk1 )
| ( sk21 != sk1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[15491]) ).
thf(15715,plain,
( ( sk22 != sk1 )
| ( sk21 != sk1 )
| ( sk1 @ ( sk1 @ sk4 ) @ p1 ) ),
inference(simp,[status(thm)],[15674]) ).
thf(15928,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[14200,79]) ).
thf(15929,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[15928]) ).
thf(15962,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) )
!= A )
| ( sk24 != sk1 )
| ~ ( A @ sk25 @ p2 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[15929]) ).
thf(16012,plain,
( ~ ( sk1 @ ( sk1 @ sk4 ) @ sk25 @ p2 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[15962]) ).
thf(24674,plain,
! [A: $i] :
( ( ( sk21 @ sk19 @ ( sk21 @ sk18 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ~ ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[23939,17]) ).
thf(24675,plain,
! [A: $i] :
( ( ( sk21 @ sk19 @ ( sk21 @ sk18 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[24674]) ).
thf(24822,plain,
! [A: $i] :
( ( ( sk21 @ sk19 )
!= A )
| ( ( sk21 @ sk18 )
!= sk1 )
| ~ ( A @ p4 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[24675]) ).
thf(24925,plain,
( ( ( sk21 @ sk18 )
!= sk1 )
| ~ ( sk21 @ sk19 @ p4 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[24822]) ).
thf(10675,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10650,84]) ).
thf(10676,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[10675]) ).
thf(10677,plain,
sk21 @ ( sk22 @ sk4 ) @ p1,
inference(pattern_uni,[status(thm)],[10676:[bind(A,$thf( sk21 @ ( sk22 @ sk4 ) ))]]) ).
thf(10885,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10677,22]) ).
thf(10886,plain,
( ( sk21 @ ( sk22 @ sk4 ) @ p1 )
!= ( sk23 @ p1 ) ),
inference(simp,[status(thm)],[10885]) ).
thf(10890,plain,
( ( sk21 @ ( sk22 @ sk4 ) )
!= sk23 ),
inference(simp,[status(thm)],[10886]) ).
thf(731,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ $true
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk1 )
| ~ ( sk24 @ sk12 @ p4 ) ),
inference(paramod_ordered,[status(thm)],[416,110]) ).
thf(732,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk1 )
| ~ ( sk24 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[731]) ).
thf(733,plain,
( ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk1 )
| ~ ( sk24 @ sk12 @ p4 ) ),
inference(pattern_uni,[status(thm)],[732:[]]) ).
thf(13055,plain,
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( sk24 @ sk12 @ ( sk1 @ r1 ) ) )
| ( sk24 @ sk12 @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk15 ) @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk13 )
| ~ $true
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 )
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[149,9785]) ).
thf(13056,plain,
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( sk24 @ sk12 @ ( sk1 @ r1 ) ) )
| ( sk24 @ sk12 @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk15 ) @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk13 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13055]) ).
thf(13203,plain,
( ( ( sk24 @ sk12 )
!= ( sk24 @ sk12 ) )
| ( sk24 != sk1 )
| ( sk24 @ sk12 @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk15 ) @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk13 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13056]) ).
thf(13296,plain,
( ( sk24 != sk1 )
| ( sk24 @ sk12 @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk15 ) @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk13 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13203]) ).
thf(5472,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk22 @ sk25 @ p2 ) )
| ( sk24 != sk21 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5469,257]) ).
thf(5473,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk22 @ sk25 @ p2 ) )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[5472]) ).
thf(5503,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= ( sk22 @ sk25 ) )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[5473]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk3 @ ( A @ r1 ) )
| ( A @ ( B @ ( C @ sk2 ) ) @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk3 @ ( A @ r1 ) )
| ( A @ ( B @ ( C @ sk2 ) ) @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(8330,plain,
! [A: $i] :
( ( ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ~ $true
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[7612,850]) ).
thf(8331,plain,
! [A: $i] :
( ( ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[8330]) ).
thf(8332,plain,
( ~ ( sk21 @ ( sk1 @ ( sk21 @ sk4 ) @ sk5 ) @ p3 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[8331:[bind(A,$thf( sk1 @ ( sk21 @ sk4 ) ))]]) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk16 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( A @ ( B @ sk15 ) @ r1 ) )
| ( B @ sk13 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk16 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( A @ ( B @ sk15 ) @ r1 ) )
| ( B @ sk13 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(12354,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[12296,84]) ).
thf(12355,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[12354]) ).
thf(12525,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) )
!= A )
| ( sk24 != sk22 )
| ( sk21 != sk1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[12355]) ).
thf(12566,plain,
( ( sk24 != sk22 )
| ( sk21 != sk1 )
| ( sk1 @ ( sk24 @ sk4 ) @ p1 ) ),
inference(simp,[status(thm)],[12525]) ).
thf(12044,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,7738]) ).
thf(12045,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) ) ),
inference(simp,[status(thm)],[12044]) ).
thf(12229,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) ) ),
inference(simp,[status(thm)],[12045]) ).
thf(12302,plain,
( ( sk24 != sk1 )
| ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) ) ),
inference(simp,[status(thm)],[12229]) ).
thf(12651,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[12302,17]) ).
thf(12652,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[12651]) ).
thf(12778,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) )
!= A )
| ( sk24 != sk1 )
| ~ ( A @ p4 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[12652]) ).
thf(12830,plain,
( ~ ( sk1 @ ( sk24 @ sk4 ) @ p4 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[12778]) ).
thf(13617,plain,
( ( ( sk21 @ sk25 @ p2 )
!= ( sk21 @ sk18 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true
| ~ ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[13345,258]) ).
thf(13618,plain,
( ( ( sk21 @ sk25 @ p2 )
!= ( sk21 @ sk18 @ p2 ) )
| ( sk24 != sk1 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[13617]) ).
thf(13638,plain,
( ( ( sk21 @ sk25 )
!= ( sk21 @ sk18 ) )
| ( sk24 != sk1 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[13618]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk20 @ ( A @ r1 ) )
| ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk20 @ ( A @ r1 ) )
| ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(26802,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk21 @ sk18 @ ( sk21 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true
| ~ ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[25925,79]) ).
thf(26803,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk21 @ sk18 @ ( sk21 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[26802]) ).
thf(26872,plain,
! [A: $i] :
( ( A
!= ( sk21 @ sk18 ) )
| ( sk24 != sk21 )
| ~ ( A @ sk25 @ p2 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[26803]) ).
thf(26945,plain,
( ( sk24 != sk21 )
| ~ ( sk21 @ sk18 @ sk25 @ p2 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[26872]) ).
thf(13565,plain,
( ( ( sk22 @ sk25 @ p2 )
!= ( sk21 @ sk18 @ p2 ) )
| ( sk24 != sk21 )
| ~ $true
| ~ ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[13345,257]) ).
thf(13566,plain,
( ( ( sk22 @ sk25 @ p2 )
!= ( sk21 @ sk18 @ p2 ) )
| ( sk24 != sk21 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[13565]) ).
thf(13633,plain,
( ( ( sk22 @ sk25 )
!= ( sk21 @ sk18 ) )
| ( sk24 != sk21 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[13566]) ).
thf(106,plain,
! [A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ~ ( A @ sk19 @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,50]) ).
thf(107,plain,
! [A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ~ ( A @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[106]) ).
thf(112,plain,
! [A: $i] :
( ( sk23 != A )
| ( sk21 != sk1 )
| ~ ( A @ sk9 )
| ~ ( A @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[107]) ).
thf(113,plain,
( ( sk21 != sk1 )
| ~ ( sk23 @ sk9 )
| ~ ( sk23 @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[112]) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( A @ sk3 @ r1 ) )
| ( A @ ( B @ ( C @ sk2 ) ) @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(81,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( A @ sk3 @ r1 ) )
| ( A @ ( B @ ( C @ sk2 ) ) @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(5281,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk24 @ sk12 @ sk25 @ p2 ) )
| ~ $true
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[5271,397]) ).
thf(5282,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk24 @ sk12 @ sk25 @ p2 ) )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[5281]) ).
thf(5303,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= ( sk24 @ sk12 @ sk25 ) )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[5282]) ).
thf(5250,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[5197,259]) ).
thf(5251,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[5250]) ).
thf(5267,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) )
!= ( sk24 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[5251]) ).
thf(31720,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5469,29771]) ).
thf(31721,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[31720]) ).
thf(31799,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= ( sk24 @ sk25 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[31721]) ).
thf(27372,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ ( sk24 @ sk18 @ sk25 @ p2 )
| ~ $true
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[397,27199]) ).
thf(27373,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ ( sk24 @ sk18 @ sk25 @ p2 )
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[27372]) ).
thf(27374,plain,
( ~ ( sk24 @ sk18 @ sk25 @ p2 )
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(pattern_uni,[status(thm)],[27373:[]]) ).
thf(1239,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk21 @ sk5 ) @ ( sk1 @ ( sk21 @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,551]) ).
thf(1240,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk21 @ sk5 ) @ ( sk1 @ ( sk21 @ sk4 ) @ r1 ) ) ),
inference(simp,[status(thm)],[1239]) ).
thf(1323,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk21 @ sk5 ) @ ( sk1 @ ( sk21 @ sk4 ) @ r1 ) ) ),
inference(simp,[status(thm)],[1240]) ).
thf(1339,plain,
( ( sk21 != sk1 )
| ( sk1 @ ( sk21 @ sk5 ) @ ( sk1 @ ( sk21 @ sk4 ) @ r1 ) ) ),
inference(simp,[status(thm)],[1323]) ).
thf(42082,plain,
( ( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
!= ( sk21 @ sk12 @ ( sk1 @ r1 ) ) )
| ( sk21 @ sk12 @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk15 ) @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk13 )
| ~ $true
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 )
| ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[144,23541]) ).
thf(42083,plain,
( ( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
!= ( sk21 @ sk12 @ ( sk1 @ r1 ) ) )
| ( sk21 @ sk12 @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk15 ) @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk13 )
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[42082]) ).
thf(42400,plain,
( ( ( sk21 @ sk12 )
!= ( sk21 @ sk12 ) )
| ( sk21 != sk1 )
| ( sk21 @ sk12 @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk15 ) @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk13 )
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[42083]) ).
thf(42535,plain,
( ( sk21 != sk1 )
| ( sk21 @ sk12 @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk15 ) @ ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk15 ) @ sk13 )
| ( sk21 @ sk12 @ sk13 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[42400]) ).
thf(23127,plain,
( ( ( sk23 @ ( sk1 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ~ ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,9496]) ).
thf(23128,plain,
( ( ( sk23 @ ( sk1 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ~ ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[23127]) ).
thf(23278,plain,
( ( sk23 != sk21 )
| ( sk1 != sk1 )
| ~ ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[23128]) ).
thf(23303,plain,
( ( sk23 != sk21 )
| ~ ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[23278]) ).
thf(12695,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[12302,845]) ).
thf(12696,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[12695]) ).
thf(12697,plain,
( ~ ( sk24 @ ( sk1 @ ( sk24 @ sk4 ) @ sk5 ) @ p3 )
| ( sk24 != sk1 ) ),
inference(pattern_uni,[status(thm)],[12696:[bind(A,$thf( sk1 @ ( sk24 @ sk4 ) ))]]) ).
thf(137,plain,
! [A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,85]) ).
thf(138,plain,
! [A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 ) ),
inference(simp,[status(thm)],[137]) ).
thf(153,plain,
! [A: $i] :
( ( sk22 != A )
| ( sk21 != sk1 )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 ) ),
inference(simp,[status(thm)],[138]) ).
thf(155,plain,
( ( sk21 != sk1 )
| ( sk22 @ sk12 @ ( sk22 @ r1 ) )
| ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[153]) ).
thf(121,plain,
! [A: $i] :
( ( ( A @ ( sk22 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,84]) ).
thf(122,plain,
! [A: $i] :
( ( ( A @ ( sk22 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[121]) ).
thf(126,plain,
! [A: $i] :
( ( A != sk24 )
| ( sk22 != sk1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[122]) ).
thf(130,plain,
( ( sk22 != sk1 )
| ( sk24 @ p1 ) ),
inference(simp,[status(thm)],[126]) ).
thf(12601,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[12302,84]) ).
thf(12602,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[12601]) ).
thf(12752,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) )
!= A )
| ( sk24 != sk22 )
| ( sk24 != sk1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[12602]) ).
thf(12802,plain,
( ( sk24 != sk22 )
| ( sk24 != sk1 )
| ( sk1 @ ( sk24 @ sk4 ) @ p1 ) ),
inference(simp,[status(thm)],[12752]) ).
thf(25064,plain,
! [A: $i] :
( ( ( sk24 @ sk19 @ ( sk24 @ sk18 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[24098,17]) ).
thf(25065,plain,
! [A: $i] :
( ( ( sk24 @ sk19 @ ( sk24 @ sk18 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[25064]) ).
thf(25235,plain,
! [A: $i] :
( ( ( sk24 @ sk19 )
!= A )
| ( ( sk24 @ sk18 )
!= sk1 )
| ~ ( A @ p4 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[25065]) ).
thf(25297,plain,
( ( ( sk24 @ sk18 )
!= sk1 )
| ~ ( sk24 @ sk19 @ p4 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[25235]) ).
thf(13664,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ $true
| ( sk24 @ sk18 @ p2 )
| ( sk24 != sk1 )
| ~ ( sk24 @ sk12 @ p4 ) ),
inference(paramod_ordered,[status(thm)],[416,13408]) ).
thf(13665,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ( sk24 @ sk18 @ p2 )
| ( sk24 != sk1 )
| ~ ( sk24 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[13664]) ).
thf(13666,plain,
( ( sk24 @ sk18 @ p2 )
| ( sk24 != sk1 )
| ~ ( sk24 @ sk12 @ p4 ) ),
inference(pattern_uni,[status(thm)],[13665:[]]) ).
thf(951,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ sk12 @ sk12 @ ( sk1 @ sk12 @ r1 ) )
| ( sk1 @ sk12 @ sk9 )
| ( sk1 @ sk9 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,136]) ).
thf(952,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ sk12 @ sk12 @ ( sk1 @ sk12 @ r1 ) )
| ( sk1 @ sk12 @ sk9 )
| ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[951]) ).
thf(994,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ sk12 @ sk12 @ ( sk1 @ sk12 @ r1 ) )
| ( sk1 @ sk12 @ sk9 )
| ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[952]) ).
thf(1015,plain,
( ( sk21 != sk1 )
| ( sk1 @ sk12 @ sk12 @ ( sk1 @ sk12 @ r1 ) )
| ( sk1 @ sk12 @ sk9 )
| ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[994]) ).
thf(5288,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5271,259]) ).
thf(5289,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[5288]) ).
thf(5299,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= ( sk24 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[5289]) ).
thf(9736,plain,
! [A: $i] :
( ( ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ ( sk24 @ sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ~ $true
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[9692,85]) ).
thf(9737,plain,
! [A: $i] :
( ( ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ ( sk24 @ sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[9736]) ).
thf(9876,plain,
! [A: $i] :
( ( ( sk24 @ ( sk24 @ sk12 @ sk15 ) )
!= A )
| ( ( sk24 @ sk12 )
!= sk1 )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[9737]) ).
thf(9894,plain,
( ( ( sk24 @ sk12 )
!= sk1 )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk12 @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk9 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[9876]) ).
thf(27157,plain,
! [A: $i] :
( ( ( sk24 @ sk18 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[26103,845]) ).
thf(27158,plain,
! [A: $i] :
( ( ( sk24 @ sk18 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[27157]) ).
thf(27159,plain,
( ~ ( sk24 @ ( sk24 @ sk18 @ sk5 ) @ p3 )
| ~ ( sk24 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[27158:[bind(A,$thf( sk24 @ sk18 ))]]) ).
thf(26987,plain,
! [A: $i] :
( ( ( sk24 @ sk18 @ ( sk24 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[26103,84]) ).
thf(26988,plain,
! [A: $i] :
( ( ( sk24 @ sk18 @ ( sk24 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[26987]) ).
thf(27280,plain,
! [A: $i] :
( ( ( sk24 @ sk18 )
!= A )
| ( sk24 != sk22 )
| ~ ( sk24 @ sk9 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[26988]) ).
thf(27335,plain,
( ( sk24 != sk22 )
| ~ ( sk24 @ sk9 )
| ( sk24 @ sk18 @ p1 ) ),
inference(simp,[status(thm)],[27280]) ).
thf(1975,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk5 ) @ ( sk21 @ ( sk23 @ sk4 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1933,17]) ).
thf(1976,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk5 ) @ ( sk21 @ ( sk23 @ sk4 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[1975]) ).
thf(2006,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk5 ) )
!= A )
| ( ( sk21 @ ( sk23 @ sk4 ) )
!= sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[1976]) ).
thf(2022,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= sk1 )
| ~ ( sk21 @ ( sk23 @ sk5 ) @ p4 ) ),
inference(simp,[status(thm)],[2006]) ).
thf(2140,plain,
( ( ( sk22 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk24 != sk22 )
| ( sk22 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[1465,22]) ).
thf(2141,plain,
( ( ( sk22 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ( sk24 != sk22 )
| ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[2140]) ).
thf(2156,plain,
( ( ( sk22 @ sk12 )
!= sk23 )
| ( sk24 != sk22 )
| ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[2141]) ).
thf(434,plain,
( ( ( sk24 @ sk9 )
!= ( sk21 @ sk9 ) )
| ~ $true
| ~ ( sk21 @ sk19 @ p3 )
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[397,105]) ).
thf(435,plain,
( ( ( sk24 @ sk9 )
!= ( sk21 @ sk9 ) )
| ~ ( sk21 @ sk19 @ p3 )
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[434]) ).
thf(438,plain,
( ( sk24 != sk21 )
| ~ ( sk21 @ sk19 @ p3 )
| ~ ( sk24 @ sk12 @ sk25 @ p2 ) ),
inference(simp,[status(thm)],[435]) ).
thf(236,plain,
( ( ( sk24 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk22 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[130,22]) ).
thf(237,plain,
( ( ( sk24 @ p1 )
!= ( sk23 @ p1 ) )
| ( sk22 != sk1 ) ),
inference(simp,[status(thm)],[236]) ).
thf(241,plain,
( ( sk24 != sk23 )
| ( sk22 != sk1 ) ),
inference(simp,[status(thm)],[237]) ).
thf(13682,plain,
( ( ( sk23 @ sk25 @ p2 )
!= ( sk24 @ sk18 @ p2 ) )
| ( sk24 != sk21 )
| ~ $true
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[13408,260]) ).
thf(13683,plain,
( ( ( sk23 @ sk25 @ p2 )
!= ( sk24 @ sk18 @ p2 ) )
| ( sk24 != sk21 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13682]) ).
thf(13727,plain,
( ( ( sk23 @ sk25 )
!= ( sk24 @ sk18 ) )
| ( sk24 != sk21 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13683]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ sk17 ) ) @ p3 )
| ~ ( C @ ( A @ ( B @ sk15 ) @ r1 ) )
| ( B @ sk13 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ sk17 ) ) @ p3 )
| ~ ( C @ ( A @ ( B @ sk15 ) @ r1 ) )
| ( B @ sk13 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(160,plain,
( ( ( sk23 @ p1 )
!= ( sk21 @ p1 ) )
| ~ $true
| ( sk22 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[128,22]) ).
thf(161,plain,
( ( ( sk23 @ p1 )
!= ( sk21 @ p1 ) )
| ( sk22 != sk1 ) ),
inference(simp,[status(thm)],[160]) ).
thf(162,plain,
( ( sk23 != sk21 )
| ( sk22 != sk1 ) ),
inference(simp,[status(thm)],[161]) ).
thf(649,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk5 ) @ ( sk21 @ ( sk22 @ sk4 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[619,17]) ).
thf(650,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk5 ) @ ( sk21 @ ( sk22 @ sk4 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[649]) ).
thf(654,plain,
! [A: $i] :
( ( ( sk21 @ ( sk22 @ sk5 ) )
!= A )
| ( ( sk21 @ ( sk22 @ sk4 ) )
!= sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[650]) ).
thf(663,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= sk1 )
| ~ ( sk21 @ ( sk22 @ sk5 ) @ p4 ) ),
inference(simp,[status(thm)],[654]) ).
thf(13553,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ~ $true
| ( sk21 @ sk18 @ p2 )
| ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 ) ),
inference(paramod_ordered,[status(thm)],[6855,13345]) ).
thf(13554,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ( sk21 @ sk18 @ p2 )
| ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[13553]) ).
thf(13555,plain,
( ( sk21 @ sk18 @ p2 )
| ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 ) ),
inference(pattern_uni,[status(thm)],[13554:[]]) ).
thf(9634,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk23 != sk22 ) ),
inference(paramod_ordered,[status(thm)],[9624,22]) ).
thf(9635,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p1 )
!= ( sk23 @ p1 ) )
| ( sk23 != sk22 ) ),
inference(simp,[status(thm)],[9634]) ).
thf(9639,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= sk23 )
| ( sk23 != sk22 ) ),
inference(simp,[status(thm)],[9635]) ).
thf(9658,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ sk25 @ p2 )
!= ( sk21 @ ( sk23 @ sk4 ) @ p2 ) )
| ( sk24 != sk23 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5271,9631]) ).
thf(9659,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ sk25 @ p2 )
!= ( sk21 @ ( sk23 @ sk4 ) @ p2 ) )
| ( sk24 != sk23 ) ),
inference(simp,[status(thm)],[9658]) ).
thf(9678,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ sk25 )
!= ( sk21 @ ( sk23 @ sk4 ) ) )
| ( sk24 != sk23 ) ),
inference(simp,[status(thm)],[9659]) ).
thf(15775,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[14200,84]) ).
thf(15776,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[15775]) ).
thf(15952,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk4 ) )
!= A )
| ( sk22 != sk1 )
| ( sk24 != sk1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[15776]) ).
thf(16001,plain,
( ( sk22 != sk1 )
| ( sk24 != sk1 )
| ( sk1 @ ( sk1 @ sk4 ) @ p1 ) ),
inference(simp,[status(thm)],[15952]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk6 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk6 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(860,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk21 @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,792]) ).
thf(861,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk21 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[860]) ).
thf(882,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( sk21 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[861]) ).
thf(887,plain,
( ( sk21 != sk1 )
| ~ ( sk1 @ ( sk21 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[882]) ).
thf(101,plain,
! [A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ~ ( A @ sk19 @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,50]) ).
thf(102,plain,
! [A: $i] :
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ~ ( A @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[101]) ).
thf(111,plain,
! [A: $i] :
( ( sk22 != A )
| ( sk21 != sk1 )
| ~ ( A @ sk9 )
| ~ ( A @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[102]) ).
thf(114,plain,
( ( sk21 != sk1 )
| ~ ( sk22 @ sk9 )
| ~ ( sk22 @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[111]) ).
thf(2511,plain,
( ( ( sk22 @ sk9 )
!= ( sk22 @ sk9 ) )
| ( sk21 != sk1 )
| ~ $true
| ~ ( sk22 @ sk19 @ p3 )
| ( sk21 != sk1 )
| ( sk22 @ sk12 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[1466,114]) ).
thf(2512,plain,
( ( ( sk22 @ sk9 )
!= ( sk22 @ sk9 ) )
| ~ ( sk22 @ sk19 @ p3 )
| ( sk21 != sk1 )
| ( sk22 @ sk12 @ p1 ) ),
inference(simp,[status(thm)],[2511]) ).
thf(2513,plain,
( ~ ( sk22 @ sk19 @ p3 )
| ( sk21 != sk1 )
| ( sk22 @ sk12 @ p1 ) ),
inference(pattern_uni,[status(thm)],[2512:[]]) ).
thf(500,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ~ $true
| ~ ( sk21 @ sk19 @ p3 )
| ( sk21 != sk1 )
| ~ ( sk21 @ sk12 @ p4 ) ),
inference(paramod_ordered,[status(thm)],[288,105]) ).
thf(501,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ~ ( sk21 @ sk19 @ p3 )
| ( sk21 != sk1 )
| ~ ( sk21 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[500]) ).
thf(502,plain,
( ~ ( sk21 @ sk19 @ p3 )
| ( sk21 != sk1 )
| ~ ( sk21 @ sk12 @ p4 ) ),
inference(pattern_uni,[status(thm)],[501:[]]) ).
thf(4665,plain,
! [A: $i] :
( ( ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ~ $true
| ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[4629,85]) ).
thf(4666,plain,
! [A: $i] :
( ( ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[4665]) ).
thf(4752,plain,
! [A: $i] :
( ( ( sk21 @ ( sk21 @ sk12 @ sk5 ) )
!= A )
| ( ( sk21 @ ( sk21 @ sk12 @ sk4 ) )
!= sk1 )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[4666]) ).
thf(4768,plain,
( ( ( sk21 @ ( sk21 @ sk12 @ sk4 ) )
!= sk1 )
| ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ sk12 @ ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ sk9 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[4752]) ).
thf(13041,plain,
( ( ( sk24 @ sk12 @ ( sk1 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ( sk24 @ sk12 @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk15 ) @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk13 )
| ~ $true
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[34,9785]) ).
thf(13042,plain,
( ( ( sk24 @ sk12 @ ( sk1 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ( sk24 @ sk12 @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk15 ) @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk13 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13041]) ).
thf(13252,plain,
( ( ( sk24 @ sk12 )
!= sk24 )
| ( sk1 != sk1 )
| ( sk24 @ sk12 @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk15 ) @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk13 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13042]) ).
thf(13320,plain,
( ( ( sk24 @ sk12 )
!= sk24 )
| ( sk24 @ sk12 @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk15 ) @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk13 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13252]) ).
thf(1193,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk1 @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,830]) ).
thf(1194,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk1 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[1193]) ).
thf(1211,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( sk1 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[1194]) ).
thf(1218,plain,
( ( sk24 != sk1 )
| ~ ( sk1 @ ( sk1 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[1211]) ).
thf(41534,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk18 @ p4 )
| ~ ( sk1 @ sk9 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,26118]) ).
thf(41535,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk18 @ p4 )
| ~ ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[41534]) ).
thf(41788,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ~ ( sk1 @ sk18 @ p4 )
| ~ ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[41535]) ).
thf(41820,plain,
( ( sk21 != sk1 )
| ~ ( sk1 @ sk18 @ p4 )
| ~ ( sk1 @ sk9 ) ),
inference(simp,[status(thm)],[41788]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk9 )
| ( A @ ( B @ ( C @ sk10 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk9 )
| ( A @ ( B @ ( C @ sk10 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(2352,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk24 @ sk5 ) @ ( sk1 @ ( sk24 @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,570]) ).
thf(2353,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk24 @ sk5 ) @ ( sk1 @ ( sk24 @ sk4 ) @ r1 ) ) ),
inference(simp,[status(thm)],[2352]) ).
thf(2468,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk24 @ sk5 ) @ ( sk1 @ ( sk24 @ sk4 ) @ r1 ) ) ),
inference(simp,[status(thm)],[2353]) ).
thf(2486,plain,
( ( sk21 != sk1 )
| ( sk1 @ ( sk24 @ sk5 ) @ ( sk1 @ ( sk24 @ sk4 ) @ r1 ) ) ),
inference(simp,[status(thm)],[2468]) ).
thf(44655,plain,
( ( ( sk22 @ sk18 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk24 != sk22 )
| ~ ( sk22 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[44612,22]) ).
thf(44656,plain,
( ( ( sk22 @ sk18 @ p1 )
!= ( sk23 @ p1 ) )
| ( sk24 != sk22 )
| ~ ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[44655]) ).
thf(44681,plain,
( ( ( sk22 @ sk18 )
!= sk23 )
| ( sk24 != sk22 )
| ~ ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[44656]) ).
thf(12724,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[12302,79]) ).
thf(12725,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( A @ sk25 @ p2 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[12724]) ).
thf(12726,plain,
( ~ ( sk1 @ ( sk24 @ sk4 ) @ sk25 @ p2 )
| ( sk24 != sk1 ) ),
inference(pattern_uni,[status(thm)],[12725:[bind(A,$thf( sk1 @ ( sk24 @ sk4 ) ))]]) ).
thf(27083,plain,
! [A: $i] :
( ( ( sk24 @ sk18 @ ( sk24 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[26103,17]) ).
thf(27084,plain,
! [A: $i] :
( ( ( sk24 @ sk18 @ ( sk24 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[27083]) ).
thf(27265,plain,
! [A: $i] :
( ( ( sk24 @ sk18 )
!= A )
| ( sk24 != sk1 )
| ~ ( A @ p4 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[27084]) ).
thf(27322,plain,
( ( sk24 != sk1 )
| ~ ( sk24 @ sk18 @ p4 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[27265]) ).
thf(5479,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk24 @ sk12 @ sk25 @ p2 ) )
| ~ $true
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[5469,397]) ).
thf(5480,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk24 @ sk12 @ sk25 @ p2 ) )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[5479]) ).
thf(5504,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= ( sk24 @ sk12 @ sk25 ) )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[5480]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk6 )
| ~ ( A @ ( B @ ( C @ sk7 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk6 )
| ~ ( A @ ( B @ ( C @ sk7 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(4921,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[149,61]) ).
thf(4922,plain,
! [B: $i,A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk4 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[4921]) ).
thf(4923,plain,
( ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 )
| ~ ( sk24 @ ( sk1 @ r1 ) )
| ( sk24 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[4922:[bind(A,$thf( sk24 )),bind(B,$thf( sk24 @ sk12 ))]]) ).
thf(6411,plain,
( ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 )
| ~ $true
| ( sk24 @ sk9 ) ),
inference(rewrite,[status(thm)],[4923,34]) ).
thf(6412,plain,
( ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[6411]) ).
thf(6428,plain,
( ( ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 )
!= ( sk24 @ sk12 @ sk25 @ p2 ) )
| ~ $true
| ( sk24 @ sk9 )
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[6412,397]) ).
thf(6429,plain,
( ( ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 )
!= ( sk24 @ sk12 @ sk25 @ p2 ) )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[6428]) ).
thf(6467,plain,
( ( ( sk24 @ ( sk24 @ sk12 @ sk4 ) )
!= ( sk24 @ sk12 @ sk25 ) )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[6429]) ).
thf(9482,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9409,17]) ).
thf(9483,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[9482]) ).
thf(9580,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= A )
| ( sk23 != sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[9483]) ).
thf(9622,plain,
( ( sk23 != sk1 )
| ~ ( sk21 @ ( sk23 @ sk4 ) @ p4 ) ),
inference(simp,[status(thm)],[9580]) ).
thf(26559,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ~ $true
| ( sk21 @ sk18 @ ( sk21 @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 ) ),
inference(paramod_ordered,[status(thm)],[6855,25925]) ).
thf(26560,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ( sk21 @ sk18 @ ( sk21 @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[26559]) ).
thf(26561,plain,
( ( sk21 @ sk18 @ ( sk21 @ r1 ) )
| ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 ) ),
inference(pattern_uni,[status(thm)],[26560:[]]) ).
thf(12837,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk1 @ ( sk24 @ sk4 ) @ sk25 @ p2 ) )
| ~ $true
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[5469,12479]) ).
thf(12838,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk1 @ ( sk24 @ sk4 ) @ sk25 @ p2 ) )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[12837]) ).
thf(12883,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= ( sk1 @ ( sk24 @ sk4 ) @ sk25 ) )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[12838]) ).
thf(31776,plain,
( ( ( sk1 @ ( sk1 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6369,29771]) ).
thf(31777,plain,
( ( ( sk1 @ ( sk1 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[31776]) ).
thf(31817,plain,
( ( ( sk1 @ ( sk1 @ sk4 ) )
!= ( sk24 @ sk25 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[31777]) ).
thf(8823,plain,
! [A: $i] :
( ( ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[8429,850]) ).
thf(8824,plain,
! [A: $i] :
( ( ( sk1 @ ( sk21 @ sk4 ) @ ( sk21 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[8823]) ).
thf(8825,plain,
( ~ ( sk21 @ ( sk1 @ ( sk21 @ sk4 ) @ sk5 ) @ p3 )
| ( sk24 != sk1 ) ),
inference(pattern_uni,[status(thm)],[8824:[bind(A,$thf( sk1 @ ( sk21 @ sk4 ) ))]]) ).
thf(3282,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,845]) ).
thf(3283,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk24 @ ( sk1 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3282]) ).
thf(3324,plain,
! [A: $i] :
( ( A != sk24 )
| ( sk24 != sk1 )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3283]) ).
thf(3346,plain,
( ( sk24 != sk1 )
| ~ ( sk24 @ ( sk24 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3324]) ).
thf(27184,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ $true
| ( sk24 @ sk18 @ ( sk24 @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(paramod_ordered,[status(thm)],[6412,26103]) ).
thf(27185,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ( sk24 @ sk18 @ ( sk24 @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[27184]) ).
thf(27186,plain,
( ( sk24 @ sk18 @ ( sk24 @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(pattern_uni,[status(thm)],[27185:[]]) ).
thf(31869,plain,
! [A: $i] :
( ( ( sk24 @ sk18 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) )
| ~ $true
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(paramod_ordered,[status(thm)],[27186,78]) ).
thf(31870,plain,
! [A: $i] :
( ( ( sk24 @ sk18 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[31869]) ).
thf(31871,plain,
( ( sk24 @ sk18 @ sk25 @ ( sk24 @ sk18 @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(pattern_uni,[status(thm)],[31870:[bind(A,$thf( sk24 @ sk18 ))]]) ).
thf(4654,plain,
! [A: $i] :
( ( ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[4629,84]) ).
thf(4655,plain,
! [A: $i] :
( ( ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[4654]) ).
thf(4755,plain,
! [A: $i] :
( ( ( sk21 @ ( sk21 @ sk12 @ sk5 ) )
!= A )
| ( ( sk21 @ ( sk21 @ sk12 @ sk4 ) )
!= sk22 )
| ( A @ p1 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[4655]) ).
thf(4770,plain,
( ( ( sk21 @ ( sk21 @ sk12 @ sk4 ) )
!= sk22 )
| ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ p1 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[4755]) ).
thf(12128,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[7738,845]) ).
thf(12129,plain,
! [A: $i] :
( ( ( sk1 @ ( sk24 @ sk4 ) @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[12128]) ).
thf(12130,plain,
( ~ ( sk24 @ ( sk1 @ ( sk24 @ sk4 ) @ sk5 ) @ p3 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[12129:[bind(A,$thf( sk1 @ ( sk24 @ sk4 ) ))]]) ).
thf(25858,plain,
( ( ( sk22 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk22 @ sk18 @ p2 )
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[14488,22]) ).
thf(25859,plain,
( ( ( sk22 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ( sk22 @ sk18 @ p2 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[25858]) ).
thf(25886,plain,
( ( ( sk22 @ sk12 )
!= sk23 )
| ( sk21 != sk1 )
| ( sk22 @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[25859]) ).
thf(28387,plain,
! [B: $i,A: $i] :
( ( ( A @ sk25 @ ( A @ r1 ) )
!= ( B @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( B @ sk5 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk24 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[78,845]) ).
thf(28388,plain,
! [B: $i,A: $i] :
( ( ( A @ sk25 @ ( A @ r1 ) )
!= ( B @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( B @ sk5 ) @ p3 )
| ~ ( A @ ( sk24 @ r1 ) ) ),
inference(simp,[status(thm)],[28387]) ).
thf(28389,plain,
( ~ ( sk24 @ ( sk24 @ sk25 @ sk5 ) @ p3 )
| ~ ( sk24 @ ( sk24 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[28388:[bind(A,$thf( sk24 )),bind(B,$thf( sk24 @ sk25 ))]]) ).
thf(795,plain,
! [B: $i,A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,54]) ).
thf(796,plain,
! [B: $i,A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[795]) ).
thf(797,plain,
( ~ ( sk21 @ ( sk23 @ sk5 ) @ p3 )
| ~ ( sk21 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[796:[bind(A,$thf( sk21 )),bind(B,$thf( sk23 ))]]) ).
thf(890,plain,
( ~ ( sk21 @ ( sk23 @ sk5 ) @ p3 )
| ~ $true ),
inference(rewrite,[status(thm)],[797,42]) ).
thf(891,plain,
~ ( sk21 @ ( sk23 @ sk5 ) @ p3 ),
inference(simp,[status(thm)],[890]) ).
thf(18786,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk24 != sk22 )
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[12802,22]) ).
thf(18787,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) @ p1 )
!= ( sk23 @ p1 ) )
| ( sk24 != sk22 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[18786]) ).
thf(18794,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) )
!= sk23 )
| ( sk24 != sk22 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[18787]) ).
thf(9548,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9409,850]) ).
thf(9549,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[9548]) ).
thf(9570,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= A )
| ( sk23 != sk21 )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[9549]) ).
thf(9615,plain,
( ( sk23 != sk21 )
| ~ ( sk21 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[9570]) ).
thf(13352,plain,
! [A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk18 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,69]) ).
thf(13353,plain,
! [A: $i] :
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk9 )
| ( A @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[13352]) ).
thf(13510,plain,
! [A: $i] :
( ( sk23 != A )
| ( sk21 != sk1 )
| ~ ( A @ sk9 )
| ( A @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[13353]) ).
thf(13549,plain,
( ( sk21 != sk1 )
| ~ ( sk23 @ sk9 )
| ( sk23 @ sk18 @ p2 ) ),
inference(simp,[status(thm)],[13510]) ).
thf(30159,plain,
! [A: $i] :
( ( ( sk24 @ sk25 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[28616,78]) ).
thf(30160,plain,
! [A: $i] :
( ( ( sk24 @ sk25 @ ( sk24 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ( A @ sk25 @ ( A @ r1 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[30159]) ).
thf(30161,plain,
( ( sk24 @ sk25 @ sk25 @ ( sk24 @ sk25 @ r1 ) )
| ( sk24 != sk1 ) ),
inference(pattern_uni,[status(thm)],[30160:[bind(A,$thf( sk24 @ sk25 ))]]) ).
thf(6870,plain,
( ( ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 )
!= ( sk24 @ sk12 @ sk25 @ p2 ) )
| ~ $true
| ( sk24 @ sk9 )
| ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[6855,397]) ).
thf(6871,plain,
( ( ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 )
!= ( sk24 @ sk12 @ sk25 @ p2 ) )
| ( sk24 @ sk9 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[6870]) ).
thf(6910,plain,
( ( ( sk21 @ ( sk21 @ sk12 @ sk4 ) )
!= ( sk24 @ sk12 @ sk25 ) )
| ( sk24 @ sk9 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[6871]) ).
thf(3267,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk23 @ ( sk21 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,845]) ).
thf(3268,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk23 @ ( sk21 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3267]) ).
thf(3309,plain,
! [A: $i] :
( ( A != sk23 )
| ( sk24 != sk21 )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3268]) ).
thf(3331,plain,
( ( sk24 != sk21 )
| ~ ( sk24 @ ( sk23 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3309]) ).
thf(5492,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk24 @ sk12 @ sk25 @ p2 ) )
| ~ ( sk24 @ sk19 @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5469,433]) ).
thf(5493,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk24 @ sk12 @ sk25 @ p2 ) )
| ~ ( sk24 @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[5492]) ).
thf(5505,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= ( sk24 @ sk12 @ sk25 ) )
| ~ ( sk24 @ sk19 @ p3 ) ),
inference(simp,[status(thm)],[5493]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk9 )
| ~ ( A @ ( B @ ( C @ sk11 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk9 )
| ~ ( A @ ( B @ ( C @ sk11 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(27538,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ( sk21 != sk1 )
| ~ ( sk21 @ sk18 @ p4 )
| ~ $true
| ( sk21 != sk1 )
| ~ ( sk21 @ sk12 @ p4 ) ),
inference(paramod_ordered,[status(thm)],[288,26931]) ).
thf(27539,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ~ ( sk21 @ sk18 @ p4 )
| ( sk21 != sk1 )
| ~ ( sk21 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[27538]) ).
thf(27540,plain,
( ~ ( sk21 @ sk18 @ p4 )
| ( sk21 != sk1 )
| ~ ( sk21 @ sk12 @ p4 ) ),
inference(pattern_uni,[status(thm)],[27539:[]]) ).
thf(14231,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk1 @ sk4 ) @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,13936]) ).
thf(14232,plain,
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( sk1 @ sk4 ) @ p4 ) ),
inference(simp,[status(thm)],[14231]) ).
thf(14341,plain,
( ( sk21 != sk1 )
| ( sk1 != sk1 )
| ~ ( sk1 @ ( sk1 @ sk4 ) @ p4 ) ),
inference(simp,[status(thm)],[14232]) ).
thf(14368,plain,
( ( sk21 != sk1 )
| ~ ( sk1 @ ( sk1 @ sk4 ) @ p4 ) ),
inference(simp,[status(thm)],[14341]) ).
thf(4163,plain,
( ( ( sk24 @ sk9 )
!= ( sk1 @ sk9 ) )
| ~ $true
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(paramod_ordered,[status(thm)],[4154,110]) ).
thf(4164,plain,
( ( ( sk24 @ sk9 )
!= ( sk1 @ sk9 ) )
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[4163]) ).
thf(4180,plain,
( ( sk24 != sk1 )
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[4164]) ).
thf(4182,plain,
( ~ ( sk24 @ sk19 @ p3 )
| ( sk24 != sk1 )
| ~ ( sk1 @ sk12 @ p4 ) ),
inference(simp,[status(thm)],[4180]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk3 @ ( A @ r1 ) )
| ( A @ ( B @ ( C @ sk2 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk3 @ ( A @ r1 ) )
| ( A @ ( B @ ( C @ sk2 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(119,plain,
! [A: $i] :
( ( ( A @ ( sk22 @ r1 ) )
!= ( sk23 @ ( sk21 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,84]) ).
thf(120,plain,
! [A: $i] :
( ( ( A @ ( sk22 @ r1 ) )
!= ( sk23 @ ( sk21 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[119]) ).
thf(125,plain,
! [A: $i] :
( ( A != sk23 )
| ( sk22 != sk21 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[120]) ).
thf(129,plain,
( ( sk22 != sk21 )
| ( sk23 @ p1 ) ),
inference(simp,[status(thm)],[125]) ).
thf(234,plain,
( ( sk22 != sk21 )
| $false ),
inference(rewrite,[status(thm)],[129,22]) ).
thf(235,plain,
sk22 != sk21,
inference(simp,[status(thm)],[234]) ).
thf(10736,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[10650,54]) ).
thf(10737,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ ( sk22 @ sk4 ) @ ( sk22 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk5 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[10736]) ).
thf(10738,plain,
( ~ ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk5 ) @ p3 )
| ~ ( sk22 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[10737:[bind(A,$thf( sk22 )),bind(B,$thf( sk21 @ ( sk22 @ sk4 ) ))]]) ).
thf(25164,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ $true
| ( sk24 @ sk19 @ ( sk24 @ sk18 @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(paramod_ordered,[status(thm)],[6412,24098]) ).
thf(25165,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ( sk24 @ sk19 @ ( sk24 @ sk18 @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[25164]) ).
thf(25166,plain,
( ( sk24 @ sk19 @ ( sk24 @ sk18 @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(pattern_uni,[status(thm)],[25165:[]]) ).
thf(9718,plain,
! [A: $i] :
( ( ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ ( sk24 @ sk12 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[9692,84]) ).
thf(9719,plain,
! [A: $i] :
( ( ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ ( sk24 @ sk12 @ r1 ) )
!= ( A @ ( sk22 @ r1 ) ) )
| ( A @ p1 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[9718]) ).
thf(9865,plain,
! [A: $i] :
( ( ( sk24 @ ( sk24 @ sk12 @ sk15 ) )
!= A )
| ( ( sk24 @ sk12 )
!= sk22 )
| ( A @ p1 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[9719]) ).
thf(9887,plain,
( ( ( sk24 @ sk12 )
!= sk22 )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ p1 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[9865]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( B @ sk13 )
| ( A @ ( B @ sk14 ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( B @ sk13 )
| ( A @ ( B @ sk14 ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(263,plain,
! [A: $i] :
( ( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ~ $true
| ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[144,85]) ).
thf(264,plain,
! [A: $i] :
( ( ( sk21 @ sk12 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[263]) ).
thf(281,plain,
! [A: $i] :
( ( ( sk21 @ sk12 )
!= A )
| ( sk21 != sk1 )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[264]) ).
thf(287,plain,
( ( sk21 != sk1 )
| ( sk21 @ sk12 @ sk12 @ ( sk21 @ sk12 @ r1 ) )
| ( sk21 @ sk12 @ sk9 )
| ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[281]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk9 )
| ( A @ ( B @ ( C @ sk11 ) ) @ ( A @ ( B @ ( C @ sk10 ) ) @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk9 )
| ( A @ ( B @ ( C @ sk11 ) ) @ ( A @ ( B @ ( C @ sk10 ) ) @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(10909,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk21 @ ( sk22 @ sk4 ) @ sk25 @ p2 ) )
| ( sk24 != sk22 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5271,10875]) ).
thf(10910,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk21 @ ( sk22 @ sk4 ) @ sk25 @ p2 ) )
| ( sk24 != sk22 ) ),
inference(simp,[status(thm)],[10909]) ).
thf(10937,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= ( sk21 @ ( sk22 @ sk4 ) @ sk25 ) )
| ( sk24 != sk22 ) ),
inference(simp,[status(thm)],[10910]) ).
thf(43468,plain,
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ~ ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,10738]) ).
thf(43469,plain,
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ~ ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[43468]) ).
thf(43614,plain,
( ( sk22 != sk22 )
| ( sk21 != sk1 )
| ~ ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[43469]) ).
thf(43675,plain,
( ( sk21 != sk1 )
| ~ ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[43614]) ).
thf(26811,plain,
! [A: $i] :
( ( ( sk21 @ sk18 @ ( sk21 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ~ $true
| ~ ( sk21 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[25925,850]) ).
thf(26812,plain,
! [A: $i] :
( ( ( sk21 @ sk18 @ ( sk21 @ r1 ) )
!= ( A @ ( sk21 @ r1 ) ) )
| ~ ( sk21 @ ( A @ sk5 ) @ p3 )
| ~ ( sk21 @ sk9 ) ),
inference(simp,[status(thm)],[26811]) ).
thf(26813,plain,
( ~ ( sk21 @ ( sk21 @ sk18 @ sk5 ) @ p3 )
| ~ ( sk21 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[26812:[bind(A,$thf( sk21 @ sk18 ))]]) ).
thf(30250,plain,
! [A: $i] :
( ( ( sk24 @ sk25 @ ( sk24 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[28616,17]) ).
thf(30251,plain,
! [A: $i] :
( ( ( sk24 @ sk25 @ ( sk24 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[30250]) ).
thf(30410,plain,
! [A: $i] :
( ( ( sk24 @ sk25 )
!= A )
| ( sk24 != sk1 )
| ~ ( A @ p4 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[30251]) ).
thf(30485,plain,
( ~ ( sk24 @ sk25 @ p4 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[30410]) ).
thf(2501,plain,
( ( ( sk22 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk21 != sk1 )
| ( sk22 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[1466,22]) ).
thf(2502,plain,
( ( ( sk22 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ( sk21 != sk1 )
| ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[2501]) ).
thf(2517,plain,
( ( ( sk22 @ sk12 )
!= sk23 )
| ( sk21 != sk1 )
| ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[2502]) ).
thf(9917,plain,
( ( ( sk22 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ~ ( sk22 @ sk19 @ p3 )
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[2513,22]) ).
thf(9918,plain,
( ( ( sk22 @ sk12 @ p1 )
!= ( sk23 @ p1 ) )
| ~ ( sk22 @ sk19 @ p3 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[9917]) ).
thf(9922,plain,
( ( ( sk22 @ sk12 )
!= sk23 )
| ~ ( sk22 @ sk19 @ p3 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[9918]) ).
thf(18777,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk24 != sk22 )
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[12566,22]) ).
thf(18778,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) @ p1 )
!= ( sk23 @ p1 ) )
| ( sk24 != sk22 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[18777]) ).
thf(18785,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) )
!= sk23 )
| ( sk24 != sk22 )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[18778]) ).
thf(6222,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[5635,259]) ).
thf(6223,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) @ p2 )
!= ( sk24 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[6222]) ).
thf(6237,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) )
!= ( sk24 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[6223]) ).
thf(21415,plain,
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( sk23 @ ( sk1 @ r1 ) ) )
| ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk4 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,9444]) ).
thf(21416,plain,
( ( ( sk23 @ ( sk21 @ r1 ) )
!= ( sk23 @ ( sk1 @ r1 ) ) )
| ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[21415]) ).
thf(21578,plain,
( ( sk23 != sk23 )
| ( sk21 != sk1 )
| ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[21416]) ).
thf(21638,plain,
( ( sk21 != sk1 )
| ( sk23 @ ( sk21 @ ( sk23 @ sk4 ) @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[21578]) ).
thf(44386,plain,
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ( sk22 @ sk18 @ p1 )
| ~ ( sk22 @ sk9 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,25969]) ).
thf(44387,plain,
( ( ( sk22 @ ( sk21 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ( sk22 @ sk18 @ p1 )
| ~ ( sk22 @ sk9 ) ),
inference(simp,[status(thm)],[44386]) ).
thf(44589,plain,
( ( sk22 != sk22 )
| ( sk21 != sk1 )
| ~ ( sk22 @ sk9 )
| ( sk22 @ sk18 @ p1 ) ),
inference(simp,[status(thm)],[44387]) ).
thf(44614,plain,
( ( sk21 != sk1 )
| ~ ( sk22 @ sk9 )
| ( sk22 @ sk18 @ p1 ) ),
inference(simp,[status(thm)],[44589]) ).
thf(5254,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) @ p2 )
!= ( sk21 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[5197,258]) ).
thf(5255,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) @ p2 )
!= ( sk21 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[5254]) ).
thf(5268,plain,
( ( ( sk1 @ ( sk21 @ sk4 ) )
!= ( sk21 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[5255]) ).
thf(12841,plain,
( ( ( sk1 @ ( sk1 @ sk4 ) @ p2 )
!= ( sk1 @ ( sk24 @ sk4 ) @ sk25 @ p2 ) )
| ~ $true
| ( sk21 != sk1 )
| ( sk21 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6374,12479]) ).
thf(12842,plain,
( ( ( sk1 @ ( sk1 @ sk4 ) @ p2 )
!= ( sk1 @ ( sk24 @ sk4 ) @ sk25 @ p2 ) )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[12841]) ).
thf(12876,plain,
( ( ( sk1 @ ( sk1 @ sk4 ) )
!= ( sk1 @ ( sk24 @ sk4 ) @ sk25 ) )
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[12842]) ).
thf(32311,plain,
( ( ( sk24 @ sk18 @ p1 )
!= ( sk23 @ p1 ) )
| ~ $true
| ( sk24 != sk22 )
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[27335,22]) ).
thf(32312,plain,
( ( ( sk24 @ sk18 @ p1 )
!= ( sk23 @ p1 ) )
| ( sk24 != sk22 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[32311]) ).
thf(32338,plain,
( ( ( sk24 @ sk18 )
!= sk23 )
| ( sk24 != sk22 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[32312]) ).
thf(43478,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ~ ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,10738]) ).
thf(43479,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk22 @ ( sk1 @ r1 ) ) )
| ~ ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[43478]) ).
thf(43627,plain,
( ( sk24 != sk22 )
| ( sk1 != sk1 )
| ~ ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[43479]) ).
thf(43679,plain,
( ( sk24 != sk22 )
| ~ ( sk22 @ ( sk21 @ ( sk22 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[43627]) ).
thf(383,plain,
! [A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ~ $true
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[149,85]) ).
thf(384,plain,
! [A: $i] :
( ( ( sk24 @ sk12 @ ( sk24 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[383]) ).
thf(408,plain,
! [A: $i] :
( ( ( sk24 @ sk12 )
!= A )
| ( sk24 != sk1 )
| ( A @ sk12 @ ( A @ r1 ) )
| ( A @ sk9 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[384]) ).
thf(415,plain,
( ( sk24 != sk1 )
| ( sk24 @ sk12 @ sk12 @ ( sk24 @ sk12 @ r1 ) )
| ( sk24 @ sk12 @ sk9 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[408]) ).
thf(13612,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ~ $true
| ( sk21 @ sk18 @ p2 )
| ~ ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ p3 ) ),
inference(paramod_ordered,[status(thm)],[4561,13345]) ).
thf(13613,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ( sk21 @ sk18 @ p2 )
| ~ ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[13612]) ).
thf(13614,plain,
( ( sk21 @ sk18 @ p2 )
| ~ ( sk21 @ ( sk21 @ sk12 @ sk5 ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[13613:[]]) ).
thf(3265,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,845]) ).
thf(3266,plain,
! [A: $i] :
( ( ( A @ ( sk24 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3265]) ).
thf(3325,plain,
! [A: $i] :
( ( A != sk21 )
| ( sk24 != sk1 )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3266]) ).
thf(3347,plain,
( ( sk24 != sk1 )
| ~ ( sk24 @ ( sk21 @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3325]) ).
thf(5490,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk21 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5469,258]) ).
thf(5491,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk21 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[5490]) ).
thf(5500,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= ( sk21 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[5491]) ).
thf(13660,plain,
( ( ( sk22 @ sk25 @ p2 )
!= ( sk24 @ sk18 @ p2 ) )
| ( sk24 != sk21 )
| ~ $true
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[13408,257]) ).
thf(13661,plain,
( ( ( sk22 @ sk25 @ p2 )
!= ( sk24 @ sk18 @ p2 ) )
| ( sk24 != sk21 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13660]) ).
thf(13728,plain,
( ( ( sk22 @ sk25 )
!= ( sk24 @ sk18 ) )
| ( sk24 != sk21 )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13661]) ).
thf(6226,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) @ p2 )
!= ( sk21 @ sk25 @ p2 ) )
| ( sk24 != sk1 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[5635,258]) ).
thf(6227,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) @ p2 )
!= ( sk21 @ sk25 @ p2 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[6226]) ).
thf(6233,plain,
( ( ( sk1 @ ( sk24 @ sk4 ) )
!= ( sk21 @ sk25 ) )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[6227]) ).
thf(13718,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ $true
| ( sk24 @ sk18 @ p2 )
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(paramod_ordered,[status(thm)],[6412,13408]) ).
thf(13719,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ( sk24 @ sk18 @ p2 )
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[13718]) ).
thf(13720,plain,
( ( sk24 @ sk18 @ p2 )
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(pattern_uni,[status(thm)],[13719:[]]) ).
thf(9518,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9409,845]) ).
thf(9519,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) @ ( sk23 @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[9518]) ).
thf(9595,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= A )
| ( sk24 != sk23 )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[9519]) ).
thf(9633,plain,
( ( sk24 != sk23 )
| ~ ( sk24 @ ( sk21 @ ( sk23 @ sk4 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[9595]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk17 ) ) @ ( A @ ( B @ ( C @ sk16 ) ) @ r1 ) )
| ~ ( C @ ( A @ ( B @ sk15 ) @ r1 ) )
| ( B @ sk13 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk17 ) ) @ ( A @ ( B @ ( C @ sk16 ) ) @ r1 ) )
| ~ ( C @ ( A @ ( B @ sk15 ) @ r1 ) )
| ( B @ sk13 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk26 @ ( A @ r1 ) )
| ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk26 @ ( A @ r1 ) )
| ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(3289,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk5 ) @ ( sk21 @ ( sk23 @ sk4 ) @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1933,845]) ).
thf(3290,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk5 ) @ ( sk21 @ ( sk23 @ sk4 ) @ r1 ) )
!= ( A @ ( sk24 @ r1 ) ) )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3289]) ).
thf(3319,plain,
! [A: $i] :
( ( ( sk21 @ ( sk23 @ sk5 ) )
!= A )
| ( ( sk21 @ ( sk23 @ sk4 ) )
!= sk24 )
| ~ ( sk24 @ ( A @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3290]) ).
thf(3341,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= sk24 )
| ~ ( sk24 @ ( sk21 @ ( sk23 @ sk5 ) @ sk5 ) @ p3 ) ),
inference(simp,[status(thm)],[3319]) ).
thf(6422,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ $true
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(paramod_ordered,[status(thm)],[6412,110]) ).
thf(6423,plain,
( ( ( sk24 @ sk9 )
!= ( sk24 @ sk9 ) )
| ~ ( sk24 @ sk19 @ p3 )
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[6422]) ).
thf(6424,plain,
( ~ ( sk24 @ sk19 @ p3 )
| ( sk24 @ ( sk24 @ sk12 @ sk4 ) @ p2 ) ),
inference(pattern_uni,[status(thm)],[6423:[]]) ).
thf(27343,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk24 @ sk18 @ sk25 @ p2 ) )
| ~ $true
| ~ ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[5469,27199]) ).
thf(27344,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) @ p2 )
!= ( sk24 @ sk18 @ sk25 @ p2 ) )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[27343]) ).
thf(27465,plain,
( ( ( sk21 @ ( sk22 @ sk4 ) )
!= ( sk24 @ sk18 @ sk25 ) )
| ~ ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[27344]) ).
thf(5274,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk22 @ sk25 @ p2 ) )
| ( sk24 != sk21 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5271,257]) ).
thf(5275,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) @ p2 )
!= ( sk22 @ sk25 @ p2 ) )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[5274]) ).
thf(5307,plain,
( ( ( sk21 @ ( sk23 @ sk4 ) )
!= ( sk22 @ sk25 ) )
| ( sk24 != sk21 ) ),
inference(simp,[status(thm)],[5275]) ).
thf(31462,plain,
! [A: $i] :
( ( ( sk21 @ sk25 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk24 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[28621,17]) ).
thf(31463,plain,
! [A: $i] :
( ( ( sk21 @ sk25 @ ( sk21 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[31462]) ).
thf(31649,plain,
! [A: $i] :
( ( ( sk21 @ sk25 )
!= A )
| ( sk21 != sk1 )
| ~ ( A @ p4 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[31463]) ).
thf(31707,plain,
( ( sk21 != sk1 )
| ~ ( sk21 @ sk25 @ p4 )
| ( sk24 != sk1 ) ),
inference(simp,[status(thm)],[31649]) ).
thf(2392,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk24 @ sk5 ) @ ( sk1 @ ( sk24 @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,570]) ).
thf(2393,plain,
( ( ( sk24 @ ( sk1 @ r1 ) )
!= ( sk1 @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk24 @ sk5 ) @ ( sk1 @ ( sk24 @ sk4 ) @ r1 ) ) ),
inference(simp,[status(thm)],[2392]) ).
thf(2433,plain,
( ( sk24 != sk1 )
| ( sk1 != sk1 )
| ( sk1 @ ( sk24 @ sk5 ) @ ( sk1 @ ( sk24 @ sk4 ) @ r1 ) ) ),
inference(simp,[status(thm)],[2393]) ).
thf(2470,plain,
( ( sk24 != sk1 )
| ( sk1 @ ( sk24 @ sk5 ) @ ( sk1 @ ( sk24 @ sk4 ) @ r1 ) ) ),
inference(simp,[status(thm)],[2433]) ).
thf(6877,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ~ $true
| ~ ( sk21 @ sk19 @ p3 )
| ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 ) ),
inference(paramod_ordered,[status(thm)],[6855,105]) ).
thf(6878,plain,
( ( ( sk21 @ sk9 )
!= ( sk21 @ sk9 ) )
| ~ ( sk21 @ sk19 @ p3 )
| ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 ) ),
inference(simp,[status(thm)],[6877]) ).
thf(6879,plain,
( ~ ( sk21 @ sk19 @ p3 )
| ( sk21 @ ( sk21 @ sk12 @ sk4 ) @ p2 ) ),
inference(pattern_uni,[status(thm)],[6878:[]]) ).
thf(98,plain,
! [A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,17]) ).
thf(99,plain,
! [A: $i] :
( ( ( sk21 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
~ ( sk21 @ p4 ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( sk21 ))]]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk16 ) ) @ p2 )
| ~ ( C @ ( A @ ( B @ sk15 ) @ r1 ) )
| ( B @ sk13 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk16 ) ) @ p2 )
| ~ ( C @ ( A @ ( B @ sk15 ) @ r1 ) )
| ( B @ sk13 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(12949,plain,
( ( ( sk24 @ sk12 @ ( sk1 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ( sk24 @ sk12 @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk15 ) @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk13 )
| ~ $true
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[42,9785]) ).
thf(12950,plain,
( ( ( sk24 @ sk12 @ ( sk1 @ r1 ) )
!= ( sk21 @ ( sk1 @ r1 ) ) )
| ( sk24 @ sk12 @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk15 ) @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk13 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[12949]) ).
thf(13227,plain,
( ( ( sk24 @ sk12 )
!= sk21 )
| ( sk1 != sk1 )
| ( sk24 @ sk12 @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk15 ) @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk13 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[12950]) ).
thf(13306,plain,
( ( ( sk24 @ sk12 )
!= sk21 )
| ( sk24 @ sk12 @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk15 ) @ ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ r1 ) )
| ( sk24 @ ( sk24 @ sk12 @ sk15 ) @ sk13 )
| ( sk24 @ sk12 @ sk13 )
| ( sk24 @ sk9 ) ),
inference(simp,[status(thm)],[13227]) ).
thf(73508,plain,
$false,
inference(e,[status(thm)],[69,5469,3345,6855,666,6374,23904,32356,21645,41329,28964,14200,5225,27575,10876,7516,56,6401,2035,13747,12479,8667,3338,41815,8911,13626,42,288,14488,4156,2020,24,5195,12879,257,52,5306,10865,110,29330,619,21652,3938,570,26991,853,416,57,78,93,4622,10650,152,23290,1465,179,27483,12296,23301,29395,84,397,34924,133,10933,13725,74,27199,4842,61,13936,4629,925,9785,12169,60,9682,13408,10875,85,5017,13746,260,4609,13649,70,16016,44612,30319,3286,27454,31822,5302,65,13562,97,12881,830,25284,7591,6402,551,15724,24932,665,13686,12450,285,156,5635,5502,9444,53,25925,141,188,9624,13676,8429,5497,28967,77,753,31810,96,13635,24547,4804,14369,7738,5305,42505,13,3937,1333,29054,73,128,105,792,765,1466,28271,31583,23725,888,41325,926,31827,674,23823,1026,13726,1219,34,8591,64,28372,15715,16012,17,24925,149,10890,733,13296,22,5271,28621,5503,259,59,8332,71,12566,144,12830,9496,13638,28616,86,26118,26945,13633,54,5634,13531,23939,113,81,5303,1933,13705,4154,5267,31799,419,10677,76,27374,28597,1339,42535,23303,66,23541,8413,12697,155,130,12802,25297,5197,13666,1015,3,5299,26931,9894,27159,27335,4918,2022,2156,438,241,13727,80,162,4813,663,29771,13555,9639,9678,16001,63,887,2513,9631,50,502,4768,7947,13320,1218,41820,67,4561,2486,808,24098,44681,12726,27322,6369,5504,72,6467,26103,25969,7612,9622,26561,845,12883,31817,8825,3346,31871,4770,27186,12130,25886,28389,891,18794,9615,13549,12302,30161,13345,258,6910,3331,5505,9692,55,114,27540,14368,4182,30505,58,235,10738,6412,25166,14165,9887,82,287,75,10937,433,28571,43675,26813,30485,2517,9922,18785,51,6237,21638,44614,5268,12876,23399,32338,136,43679,79,9409,415,13614,3347,5500,2159,13728,6233,13720,9633,62,850,68,3341,6424,27465,3474,5307,2018,31707,2470,6879,100,28447,83,13306,10686]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL652+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/5.41 % Computer : n026.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Fri Sep 25 23:01:15 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.18/5.74 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/5.85 % [INFO] Parsing done (109ms).
% 0.18/5.86 % [INFO] Running in sequential loop mode.
% 1.42/6.05 % [INFO] eprover registered as external prover.
% 1.42/6.05 % [INFO] Scanning for conjecture ...
% 1.71/6.13 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.71/6.16 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.71/6.16 % [INFO] Problem is first-order (TPTP FOF).
% 1.71/6.16 % [INFO] Type checking passed.
% 1.71/6.17 % [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 ...
% 95.54/29.53 % External prover 'e' found a proof!
% 95.54/29.53 % [INFO] Killing All external provers ...
% 95.54/29.53 % Time passed: 23995ms (effective reasoning time: 23665ms)
% 95.54/29.53 % 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)>
% 95.54/29.53 % Axioms used in derivation (0):
% 95.54/29.53 % No. of inferences in proof: 1160
% 95.54/29.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 23995 ms resp. 23665 ms w/o parsing
% 90.50/29.92 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 90.50/29.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------