%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL642+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 : n017.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 07:52:15 AM UTC 2026
% Result : Theorem 101.45s 22.02s
% Output : Refutation 105.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 31
% Syntax : Number of formulae : 1255 ( 65 unt; 0 typ; 30 def)
% Number of atoms : 7926 (1508 equ; 0 cnn)
% Maximal formula atoms : 293 ( 6 avg)
% Number of connectives : 19526 (4564 ~;5249 |; 96 &;9617 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 97 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 15 con; 0-4 aty)
% Number of variables : 1055 ( 33 ^; 988 !; 4 ?;1055 :)
% ( 0 !>; 0 ?*; 0 @-; 30 @+)
% Comments :
%------------------------------------------------------------------------------
thf(r1_decl,type,
r1: $i > $i > $o ).
thf(p3_decl,type,
p3: $i > $o ).
thf(p2_decl,type,
p2: $i > $o ).
thf(p1_decl,type,
p1: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i ).
thf(sk11_decl,type,
sk11: $o ).
thf(sk12_decl,type,
sk12: $o ).
thf(sk13_decl,type,
sk13: $i > $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i > $i ).
thf(sk15_decl,type,
sk15: $i ).
thf(sk16_decl,type,
sk16: $i ).
thf(sk17_decl,type,
sk17: $i ).
thf(sk18_decl,type,
sk18: $i ).
thf(sk19_decl,type,
sk19: $o ).
thf(sk20_decl,type,
sk20: $i ).
thf(sk21_decl,type,
sk21: $i ).
thf(sk22_decl,type,
sk22: $i > $i ).
thf(sk23_decl,type,
sk23: $i > $i ).
thf(sk24_decl,type,
sk24: $i > $o ).
thf(sk25_decl,type,
sk25: $i > $o ).
thf(sk26_decl,type,
sk26: $i > $i > $i > $i > $i ).
thf(sk27_decl,type,
sk27: $i > $i > $i > $i > $i ).
thf(sk28_decl,type,
sk28: $i > $i > $i ).
thf(sk29_decl,type,
sk29: $i > $i > $i ).
thf(sk30_decl,type,
sk30: $i > $i > $i ).
thf(sk31_decl,type,
sk31: $i > $o ).
thf(sk32_decl,type,
sk32: $i > $i ).
thf(sk33_decl,type,
sk33: $i > $i ).
thf(sk34_decl,type,
sk34: $i > $i > $i ).
thf(sk35_decl,type,
sk35: $i > $i > $i ).
thf(sk36_decl,type,
sk36: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ~ ( ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
& ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( ( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 ) )
& ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ! [D: $i] :
( ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p2 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) ) )
| ! [D: $i] :
( ( ( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 ) )
& ( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p2 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ! [E: $i] :
( ! [F: $i] :
( ~ ! [G: $i] :
( ~ ( G @ p2 )
| ! [H: $i] :
( ( H @ p2 )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( ( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 ) )
& ( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( ( ~ ! [B: $i] :
( ~ ( B @ p2 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p2 ) )
& ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p3 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ( B @ p3 )
| ! [C: $i] :
( ( C @ p3 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p3 )
| ~ ( B @ ( A @ sk3 @ r1 ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ( B @ p2 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p2 )
| ~ ( B @ ( A @ sk6 @ r1 ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( A @ p1 )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ( B @ p1 )
| ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p1 )
| ~ ( B @ ( A @ sk9 @ r1 ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( A @ r1 ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C @ p2 )
| ~ ( C @ ( B @ ( A @ sk13 ) @ r1 ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] :
~ ( ~ ! [B: $i] :
( ~ ( B @ p2 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: $i] :
~ ( ~ ( A @ p2 )
| ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i] :
~ ( ( A @ p2 )
| ~ ( A @ ( sk16 @ r1 ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: $i] :
~ ( ~ ! [B: $i] :
( ~ ( ( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 ) )
& ( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) ) )
| ! [C: $i] :
( ( ( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 ) )
& ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ! [D: $i] :
( ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p2 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( ( ~ ! [B: $i] :
( ~ ( B @ p2 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p2 ) )
& ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( @+[A: $i] :
~ ( ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk18 @ r1 ) ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i] :
~ ( ~ ! [B: $i] :
( ~ ( B @ p2 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p2 )
| ~ ( A @ ( sk20 @ r1 ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ( B @ p2 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p2 )
| ~ ( B @ ( A @ sk22 @ r1 ) ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
@+[E: $i] :
~ ( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( A @ r1 ) ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
@+[E: $i] :
~ ( ( E @ p2 )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ sk26 ) ) ) @ r1 ) ) ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( A @ r1 ) ) ) ) ) ).
thf(sk29_def,definition,
( sk29
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( A @ r1 ) ) ) ) ) ).
thf(sk30_def,definition,
( sk30
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C @ p2 )
| ~ ( C @ ( B @ ( A @ sk29 ) @ r1 ) ) ) ) ) ).
thf(sk32_def,definition,
( sk32
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk33_def,definition,
( sk33
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ sk32 @ r1 ) ) ) ) ) ).
thf(sk34_def,definition,
( sk34
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( A @ r1 ) ) ) ) ) ).
thf(sk35_def,definition,
( sk35
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C @ p2 )
| ~ ( C @ ( B @ ( A @ sk34 ) @ r1 ) ) ) ) ) ).
thf(sk36_def,definition,
( sk36
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(1,conjecture,
~ ? [A: $i] :
~ ( ~ ( ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
& ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( ( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 ) )
& ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ! [D: $i] :
( ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p2 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) ) )
| ! [D: $i] :
( ( ( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 ) )
& ( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p2 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ! [E: $i] :
( ! [F: $i] :
( ~ ! [G: $i] :
( ~ ( G @ p2 )
| ! [H: $i] :
( ( H @ p2 )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( ( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 ) )
& ( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( ( ~ ! [B: $i] :
( ~ ( B @ p2 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p2 ) )
& ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p3 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
thf(2,negated_conjecture,
~ ~ ? [A: $i] :
~ ( ~ ( ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
& ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( ( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 ) )
& ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ! [D: $i] :
( ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p2 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) ) )
| ! [D: $i] :
( ( ( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 ) )
& ( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p2 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ! [E: $i] :
( ! [F: $i] :
( ~ ! [G: $i] :
( ~ ( G @ p2 )
| ! [H: $i] :
( ( H @ p2 )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( ( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 ) )
& ( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( ( ~ ! [B: $i] :
( ~ ( B @ p2 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p2 ) )
& ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p3 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ? [A: $i] :
~ ( ~ ( ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
& ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( ( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 ) )
& ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ! [D: $i] :
( ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p2 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) ) )
| ! [D: $i] :
( ( ( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 ) )
& ( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p2 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ! [E: $i] :
( ! [F: $i] :
( ~ ! [G: $i] :
( ~ ( G @ p2 )
| ! [H: $i] :
( ( H @ p2 )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( ( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 ) )
& ( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( ( ~ ! [B: $i] :
( ~ ( B @ p2 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p2 ) )
& ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p3 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
? [A: $i] :
~ ( ~ ( ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
& ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( ( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 ) )
& ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ! [D: $i] :
( ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p2 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) ) )
| ! [D: $i] :
( ( ( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 ) )
& ( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p2 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ! [E: $i] :
( ! [F: $i] :
( ~ ! [G: $i] :
( ~ ( G @ p2 )
| ! [H: $i] :
( ( H @ p2 )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( ( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 ) )
& ( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( ( ~ ! [B: $i] :
( ~ ( B @ p2 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p2 ) )
& ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p3 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
~ ! [A: $i] :
( ~ ( ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
& ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( ( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 ) )
& ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ! [D: $i] :
( ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p2 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) ) )
| ! [D: $i] :
( ( ( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 ) )
& ( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ! [G: $i] :
( ( G @ p2 )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ! [E: $i] :
( ! [F: $i] :
( ~ ! [G: $i] :
( ~ ( G @ p2 )
| ! [H: $i] :
( ( H @ p2 )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( ( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 ) )
& ( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( ( ~ ! [B: $i] :
( ~ ( B @ p2 )
| ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ( A @ p2 ) )
& ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p3 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p3 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(miniscope,[status(thm)],[4]) ).
thf(6,plain,
! [Z: $i,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] :
( ( ~ ( Y @ p2 )
| ( Z @ p2 )
| ~ ( Z @ ( Y @ r1 ) )
| ~ ( Y @ ( X @ sk36 @ r1 ) )
| ( X @ p2 )
| ~ ( X @ ( sk1 @ r1 ) ) )
& ( ~ ( X @ sk36 @ p2 )
| ( X @ p2 )
| ~ ( X @ ( sk1 @ r1 ) ) )
& ( ( X @ sk36 @ ( X @ r1 ) )
| ( X @ p2 )
| ~ ( X @ ( sk1 @ r1 ) ) )
& ( ~ ( V @ p2 )
| ( W @ p2 )
| ~ ( W @ ( V @ r1 ) )
| ~ ( V @ ( M @ r1 ) )
| ( M @ sk31 )
| ~ ( M @ sk24 )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ~ ( M @ p2 )
| ( M @ sk31 )
| ~ ( M @ sk24 )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ~ ( M @ sk31 )
| ( M @ ( U @ sk34 ) @ p2 )
| ( U @ p2 )
| ~ ( U @ ( M @ r1 ) )
| ~ ( M @ sk24 )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ~ ( M @ sk31 )
| ~ ( M @ ( U @ sk35 ) @ p2 )
| ( U @ p2 )
| ~ ( U @ ( M @ r1 ) )
| ~ ( M @ sk24 )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ~ ( M @ sk31 )
| ( M @ ( U @ sk35 ) @ ( M @ ( U @ sk34 ) @ r1 ) )
| ( U @ p2 )
| ~ ( U @ ( M @ r1 ) )
| ~ ( M @ sk24 )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ~ ( M @ sk31 )
| ( M @ ( U @ sk34 ) @ ( U @ r1 ) )
| ( U @ p2 )
| ~ ( U @ ( M @ r1 ) )
| ~ ( M @ sk24 )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ~ ( M @ sk31 )
| ~ ( S @ p2 )
| ( T @ p2 )
| ~ ( T @ ( S @ r1 ) )
| ~ ( S @ ( M @ sk33 @ r1 ) )
| ~ ( M @ sk24 )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ~ ( M @ sk31 )
| ~ ( M @ sk33 @ p2 )
| ~ ( M @ sk24 )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ~ ( M @ sk31 )
| ( M @ sk33 @ ( M @ sk32 @ r1 ) )
| ~ ( M @ sk24 )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ~ ( M @ sk31 )
| ( M @ sk32 @ ( M @ r1 ) )
| ~ ( M @ sk24 )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ( M @ sk24 )
| ( M @ ( N @ sk29 ) @ p2 )
| ( N @ p2 )
| ~ ( N @ ( M @ r1 ) )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ( M @ sk24 )
| ~ ( M @ ( N @ sk30 ) @ p2 )
| ( N @ p2 )
| ~ ( N @ ( M @ r1 ) )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ( M @ sk24 )
| ( M @ ( N @ sk30 ) @ ( M @ ( N @ sk29 ) @ r1 ) )
| ( N @ p2 )
| ~ ( N @ ( M @ r1 ) )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ( M @ sk24 )
| ( M @ ( N @ sk29 ) @ ( N @ r1 ) )
| ( N @ p2 )
| ~ ( N @ ( M @ r1 ) )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ( M @ sk24 )
| ~ ( Q @ p2 )
| ( R @ p2 )
| ~ ( R @ ( Q @ r1 ) )
| ~ ( Q @ ( M @ ( N @ sk28 ) @ r1 ) )
| ~ ( N @ sk25 )
| ~ ( N @ ( M @ r1 ) )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ( M @ sk24 )
| ~ ( M @ ( N @ sk28 ) @ p2 )
| ~ ( N @ sk25 )
| ~ ( N @ ( M @ r1 ) )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ( M @ sk24 )
| ( M @ ( N @ sk28 ) @ ( N @ r1 ) )
| ~ ( N @ sk25 )
| ~ ( N @ ( M @ r1 ) )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ( M @ sk24 )
| ( N @ sk25 )
| ( M @ ( N @ ( O @ ( P @ sk26 ) ) ) @ p2 )
| ( P @ p2 )
| ~ ( P @ ( O @ r1 ) )
| ~ ( O @ ( N @ r1 ) )
| ~ ( N @ ( M @ r1 ) )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ( M @ sk24 )
| ( N @ sk25 )
| ~ ( M @ ( N @ ( O @ ( P @ sk27 ) ) ) @ p2 )
| ( P @ p2 )
| ~ ( P @ ( O @ r1 ) )
| ~ ( O @ ( N @ r1 ) )
| ~ ( N @ ( M @ r1 ) )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ( M @ sk24 )
| ( N @ sk25 )
| ( M @ ( N @ ( O @ ( P @ sk27 ) ) ) @ ( M @ ( N @ ( O @ ( P @ sk26 ) ) ) @ r1 ) )
| ( P @ p2 )
| ~ ( P @ ( O @ r1 ) )
| ~ ( O @ ( N @ r1 ) )
| ~ ( N @ ( M @ r1 ) )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ( M @ sk24 )
| ( N @ sk25 )
| ( M @ ( N @ ( O @ ( P @ sk26 ) ) ) @ ( P @ r1 ) )
| ( P @ p2 )
| ~ ( P @ ( O @ r1 ) )
| ~ ( O @ ( N @ r1 ) )
| ~ ( N @ ( M @ r1 ) )
| ~ ( M @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ~ ( K @ p2 )
| ( L @ p2 )
| ~ ( L @ ( K @ r1 ) )
| ~ ( K @ ( sk18 @ r1 ) )
| sk19
| ~ sk11 )
& ( ~ ( sk18 @ p2 )
| sk19
| ~ sk11 )
& ( ~ sk19
| ( J @ sk22 @ p2 )
| ( J @ p2 )
| ~ ( J @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ~ sk19
| ~ ( J @ sk23 @ p2 )
| ( J @ p2 )
| ~ ( J @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ~ sk19
| ( J @ sk23 @ ( J @ sk22 @ r1 ) )
| ( J @ p2 )
| ~ ( J @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ~ sk19
| ( J @ sk22 @ ( J @ r1 ) )
| ( J @ p2 )
| ~ ( J @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ~ sk19
| ~ ( H @ p2 )
| ( I @ p2 )
| ~ ( I @ ( H @ r1 ) )
| ~ ( H @ ( sk21 @ r1 ) )
| ~ sk11 )
& ( ~ sk19
| ~ ( sk21 @ p2 )
| ~ sk11 )
& ( ~ sk19
| ( sk21 @ ( sk20 @ r1 ) )
| ~ sk11 )
& ( ~ sk19
| ( sk20 @ ( sk18 @ r1 ) )
| ~ sk11 )
& ( ( sk18 @ ( sk1 @ r1 ) )
| ~ sk11 )
& ( sk11
| ( sk16 @ p2 )
| ( sk1 @ p2 ) )
& ( sk11
| ~ ( sk17 @ p2 )
| ( sk1 @ p2 ) )
& ( sk11
| ( sk17 @ ( sk16 @ r1 ) )
| ( sk1 @ p2 ) )
& ( sk11
| ( sk16 @ ( sk1 @ r1 ) )
| ( sk1 @ p2 ) )
& ( sk11
| ~ ( F @ p2 )
| ( G @ p2 )
| ~ ( G @ ( F @ r1 ) )
| ~ ( F @ ( sk15 @ r1 ) )
| ~ sk12 )
& ( sk11
| ~ ( sk15 @ p2 )
| ~ sk12 )
& ( sk11
| ( sk15 @ ( sk1 @ r1 ) )
| ~ sk12 )
& ( sk11
| sk12
| ( D @ ( E @ sk13 ) @ p2 )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) ) )
& ( sk11
| sk12
| ~ ( D @ ( E @ sk14 ) @ p2 )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) ) )
& ( sk11
| sk12
| ( D @ ( E @ sk14 ) @ ( D @ ( E @ sk13 ) @ r1 ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) ) )
& ( sk11
| sk12
| ( D @ ( E @ sk13 ) @ ( E @ r1 ) )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) ) )
& ( ( C @ sk9 @ p1 )
| ( C @ p1 )
| ~ ( C @ ( sk1 @ r1 ) ) )
& ( ~ ( C @ sk10 @ p1 )
| ( C @ p1 )
| ~ ( C @ ( sk1 @ r1 ) ) )
& ( ( C @ sk10 @ ( C @ sk9 @ r1 ) )
| ( C @ p1 )
| ~ ( C @ ( sk1 @ r1 ) ) )
& ( ( C @ sk9 @ ( C @ r1 ) )
| ( C @ p1 )
| ~ ( C @ ( sk1 @ r1 ) ) )
& ~ ( sk8 @ p1 )
& ( sk8 @ ( sk1 @ r1 ) )
& ( ( B @ sk6 @ p2 )
| ( B @ p2 )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( B @ sk7 @ p2 )
| ( B @ p2 )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ( B @ sk7 @ ( B @ sk6 @ r1 ) )
| ( B @ p2 )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ( B @ sk6 @ ( B @ r1 ) )
| ( B @ p2 )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ~ ( sk5 @ p2 )
& ( sk5 @ ( sk1 @ r1 ) )
& ( ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) )
& ( ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) )
& ( ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) )
& ( ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) )
& ~ ( sk2 @ p3 )
& ( sk2 @ ( sk1 @ r1 ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(8,plain,
sk2 @ ( sk1 @ r1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(17,plain,
! [A: $i] :
( ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(176,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,17]) ).
thf(177,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[176]) ).
thf(178,plain,
( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
| ( sk2 @ p3 ) ),
inference(pattern_uni,[status(thm)],[177:[bind(A,$thf( sk2 ))]]) ).
thf(32,plain,
~ ( sk2 @ p3 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(206,plain,
( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
| $false ),
inference(rewrite,[status(thm)],[178,32]) ).
thf(207,plain,
sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ),
inference(simp,[status(thm)],[206]) ).
thf(10,plain,
! [A: $i] :
( ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(75,plain,
! [A: $i] :
( ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(2131,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,75]) ).
thf(2132,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[2131]) ).
thf(2145,plain,
! [A: $i] :
( ( ( sk2 @ sk4 )
!= A )
| ( ( sk2 @ sk3 )
!= sk1 )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[2132]) ).
thf(2163,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ( sk2 @ sk4 @ sk6 @ ( sk2 @ sk4 @ r1 ) )
| ( sk2 @ sk4 @ p2 ) ),
inference(simp,[status(thm)],[2145]) ).
thf(33,plain,
! [A: $i] :
( ~ ( A @ sk31 )
| ( A @ sk32 @ ( A @ r1 ) )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(87,plain,
! [A: $i] :
( ~ ( A @ sk31 )
| ( A @ sk32 @ ( A @ r1 ) )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[33]) ).
thf(26,plain,
! [A: $i] :
( ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(106,plain,
! [A: $i] :
( ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[26]) ).
thf(8958,plain,
! [B: $i,A: $i] :
( ( ( A @ sk32 @ ( A @ r1 ) )
!= ( B @ ( sk18 @ r1 ) ) )
| ~ ( B @ sk31 )
| ~ ( B @ sk33 @ p2 )
| ~ ( B @ sk24 )
| ~ $true
| ~ sk11
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[87,106]) ).
thf(8959,plain,
! [B: $i,A: $i] :
( ( ( A @ sk32 @ ( A @ r1 ) )
!= ( B @ ( sk18 @ r1 ) ) )
| ~ ( B @ sk31 )
| ~ ( B @ sk33 @ p2 )
| ~ ( B @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[8958]) ).
thf(8960,plain,
( ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ ( sk18 @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[8959:[bind(A,$thf( sk18 )),bind(B,$thf( sk18 @ sk32 ))]]) ).
thf(18,plain,
! [A: $i] :
( ~ ( A @ sk36 @ p2 )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(101,plain,
! [A: $i] :
( ~ ( A @ sk36 @ p2 )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(19,plain,
sk8 @ ( sk1 @ r1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(42,plain,
! [A: $i] :
( ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(77,plain,
! [A: $i] :
( ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(3077,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,77]) ).
thf(3078,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[3077]) ).
thf(3079,plain,
( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
| ( sk8 @ p1 ) ),
inference(pattern_uni,[status(thm)],[3078:[bind(A,$thf( sk8 ))]]) ).
thf(51,plain,
~ ( sk8 @ p1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(3313,plain,
( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
| $false ),
inference(rewrite,[status(thm)],[3079,51]) ).
thf(3314,plain,
sk8 @ sk9 @ ( sk8 @ r1 ),
inference(simp,[status(thm)],[3313]) ).
thf(3369,plain,
! [A: $i] :
( ( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3314,75]) ).
thf(3370,plain,
! [A: $i] :
( ( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[3369]) ).
thf(3383,plain,
! [A: $i] :
( ( ( sk8 @ sk9 )
!= A )
| ( sk8 != sk1 )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[3370]) ).
thf(3399,plain,
( ( sk8 != sk1 )
| ( sk8 @ sk9 @ sk6 @ ( sk8 @ sk9 @ r1 ) )
| ( sk8 @ sk9 @ p2 ) ),
inference(simp,[status(thm)],[3383]) ).
thf(39,plain,
! [A: $i] :
( ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(331,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,39]) ).
thf(332,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[331]) ).
thf(333,plain,
( ( sk8 @ sk3 @ p3 )
| ( sk8 @ p3 ) ),
inference(pattern_uni,[status(thm)],[332:[bind(A,$thf( sk8 ))]]) ).
thf(61,plain,
! [A: $i] :
( ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(3327,plain,
! [A: $i] :
( ( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3314,61]) ).
thf(3328,plain,
! [A: $i] :
( ( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[3327]) ).
thf(3381,plain,
! [A: $i] :
( ( ( sk8 @ sk9 )
!= A )
| ( sk8 != sk1 )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[3328]) ).
thf(3397,plain,
( ( sk8 != sk1 )
| ( sk8 @ sk9 @ sk3 @ ( sk8 @ sk9 @ r1 ) )
| ( sk8 @ sk9 @ p3 ) ),
inference(simp,[status(thm)],[3381]) ).
thf(11,plain,
( ~ sk19
| ( sk20 @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(21,plain,
! [A: $i] :
( ~ sk19
| ( A @ sk22 @ p2 )
| ( A @ p2 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(86,plain,
! [A: $i] :
( ~ sk19
| ( A @ sk22 @ p2 )
| ( A @ p2 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[21]) ).
thf(8602,plain,
! [A: $i] :
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ sk19
| ( A @ sk22 @ p2 )
| ( A @ p2 )
| ~ $true
| ~ sk11
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[11,86]) ).
thf(8603,plain,
! [A: $i] :
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ( A @ sk22 @ p2 )
| ( A @ p2 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[8602]) ).
thf(8604,plain,
( ( sk20 @ sk22 @ p2 )
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[8603:[bind(A,$thf( sk20 ))]]) ).
thf(37,plain,
! [A: $i] :
( ~ sk19
| ~ ( A @ sk23 @ p2 )
| ( A @ p2 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(79,plain,
! [A: $i] :
( ~ sk19
| ~ ( A @ sk23 @ p2 )
| ( A @ p2 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[37]) ).
thf(4314,plain,
! [A: $i] :
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ sk19
| ~ ( A @ sk23 @ p2 )
| ( A @ p2 )
| ~ $true
| ~ sk11
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[11,79]) ).
thf(4315,plain,
! [A: $i] :
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ ( A @ sk23 @ p2 )
| ( A @ p2 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[4314]) ).
thf(4316,plain,
( ~ ( sk20 @ sk23 @ p2 )
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[4315:[bind(A,$thf( sk20 ))]]) ).
thf(8805,plain,
( ( ( sk20 @ sk23 @ p2 )
!= ( sk20 @ sk22 @ p2 ) )
| ~ $true
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[8604,4316]) ).
thf(8806,plain,
( ( ( sk20 @ sk23 @ p2 )
!= ( sk20 @ sk22 @ p2 ) )
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[8805]) ).
thf(8887,plain,
( ( ( sk20 @ sk23 )
!= ( sk20 @ sk22 ) )
| ~ sk19
| ~ sk11
| ( sk20 @ p2 ) ),
inference(simp,[status(thm)],[8806]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk31 )
| ~ ( B @ p2 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ sk33 @ r1 ) )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk31 )
| ~ ( B @ p2 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ sk33 @ r1 ) )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[38]) ).
thf(48,plain,
sk5 @ ( sk1 @ r1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(306,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,39]) ).
thf(307,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[306]) ).
thf(308,plain,
( ( sk5 @ sk3 @ p3 )
| ( sk5 @ p3 ) ),
inference(pattern_uni,[status(thm)],[307:[bind(A,$thf( sk5 ))]]) ).
thf(350,plain,
( ~ $true
| ( ( sk5 @ sk3 @ p3 )
!= ( sk5 @ p3 ) )
| ( sk5 @ p3 ) ),
inference(eqfactor_ordered,[status(thm)],[308]) ).
thf(352,plain,
( ( ( sk5 @ sk3 @ p3 )
!= ( sk5 @ p3 ) )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[350]) ).
thf(46,plain,
! [A: $i] :
( ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(83,plain,
! [A: $i] :
( ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(6288,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,83]) ).
thf(6289,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6288]) ).
thf(6290,plain,
( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
| ( sk8 @ p1 ) ),
inference(pattern_uni,[status(thm)],[6289:[bind(A,$thf( sk8 ))]]) ).
thf(6694,plain,
( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
| $false ),
inference(rewrite,[status(thm)],[6290,51]) ).
thf(6695,plain,
sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ),
inference(simp,[status(thm)],[6694]) ).
thf(6743,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6695,39]) ).
thf(6744,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[6743]) ).
thf(6788,plain,
! [A: $i] :
( ( ( sk8 @ sk10 )
!= A )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( A @ sk3 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[6744]) ).
thf(6811,plain,
( ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ sk3 @ p3 )
| ( sk8 @ sk10 @ p3 ) ),
inference(simp,[status(thm)],[6788]) ).
thf(41,plain,
! [A: $i] :
( ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(440,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,41]) ).
thf(441,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[440]) ).
thf(442,plain,
( ~ ( sk2 @ sk4 @ p3 )
| ( sk2 @ p3 ) ),
inference(pattern_uni,[status(thm)],[441:[bind(A,$thf( sk2 ))]]) ).
thf(749,plain,
( ~ ( sk2 @ sk4 @ p3 )
| $false ),
inference(rewrite,[status(thm)],[442,32]) ).
thf(750,plain,
~ ( sk2 @ sk4 @ p3 ),
inference(simp,[status(thm)],[749]) ).
thf(9258,plain,
( ( ( sk8 @ sk10 @ sk3 @ p3 )
!= ( sk2 @ sk4 @ p3 ) )
| ~ $true
| ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[6811,750]) ).
thf(9259,plain,
( ( ( sk8 @ sk10 @ sk3 @ p3 )
!= ( sk2 @ sk4 @ p3 ) )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ p3 ) ),
inference(simp,[status(thm)],[9258]) ).
thf(9273,plain,
( ( ( sk8 @ sk10 @ sk3 )
!= ( sk2 @ sk4 ) )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ p3 ) ),
inference(simp,[status(thm)],[9259]) ).
thf(7,plain,
( sk11
| ( sk16 @ p2 )
| ( sk1 @ p2 ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(134,plain,
( ~ $true
| ( ( sk16 @ p2 )
!= ( sk1 @ p2 ) )
| sk11
| ( sk1 @ p2 ) ),
inference(eqfactor_ordered,[status(thm)],[7]) ).
thf(138,plain,
( ( sk16 != sk1 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[134]) ).
thf(6727,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6695,77]) ).
thf(6728,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6727]) ).
thf(6790,plain,
! [A: $i] :
( ( ( sk8 @ sk10 )
!= A )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6728]) ).
thf(6813,plain,
( ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ sk9 @ ( sk8 @ sk10 @ r1 ) )
| ( sk8 @ sk10 @ p1 ) ),
inference(simp,[status(thm)],[6790]) ).
thf(43,plain,
! [A: $i] :
( ~ ( A @ sk10 @ p1 )
| ( A @ p1 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(105,plain,
! [A: $i] :
( ~ ( A @ sk10 @ p1 )
| ( A @ p1 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(29909,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk10 @ p1 )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,105]) ).
thf(29910,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk10 @ p1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[29909]) ).
thf(29911,plain,
( ~ ( sk8 @ sk10 @ p1 )
| ( sk8 @ p1 ) ),
inference(pattern_uni,[status(thm)],[29910:[bind(A,$thf( sk8 ))]]) ).
thf(30090,plain,
( ~ ( sk8 @ sk10 @ p1 )
| $false ),
inference(rewrite,[status(thm)],[29911,51]) ).
thf(30091,plain,
~ ( sk8 @ sk10 @ p1 ),
inference(simp,[status(thm)],[30090]) ).
thf(30092,plain,
( ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ sk9 @ ( sk8 @ sk10 @ r1 ) )
| $false ),
inference(rewrite,[status(thm)],[6813,30091]) ).
thf(30093,plain,
( ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ sk9 @ ( sk8 @ sk10 @ r1 ) ) ),
inference(simp,[status(thm)],[30092]) ).
thf(753,plain,
( ( ( sk2 @ sk4 @ p3 )
!= ( sk5 @ sk3 @ p3 ) )
| ~ $true
| ( sk5 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[308,750]) ).
thf(754,plain,
( ( ( sk2 @ sk4 @ p3 )
!= ( sk5 @ sk3 @ p3 ) )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[753]) ).
thf(760,plain,
( ( ( sk2 @ sk4 )
!= ( sk5 @ sk3 ) )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[754]) ).
thf(70,plain,
( sk11
| ~ ( sk17 @ p2 )
| ( sk1 @ p2 ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(160,plain,
( ( ( sk17 @ p2 )
!= ( sk16 @ p2 ) )
| sk11
| ~ $true
| ( sk1 @ p2 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[7,70]) ).
thf(161,plain,
( ( ( sk17 @ p2 )
!= ( sk16 @ p2 ) )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[160]) ).
thf(162,plain,
( ( sk17 != sk16 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[161]) ).
thf(52,plain,
! [A: $i] :
( ~ ( A @ sk7 @ p2 )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(81,plain,
! [A: $i] :
( ~ ( A @ sk7 @ p2 )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(5065,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,81]) ).
thf(5066,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[5065]) ).
thf(5067,plain,
( ~ ( sk8 @ sk7 @ p2 )
| ( sk8 @ p2 ) ),
inference(pattern_uni,[status(thm)],[5066:[bind(A,$thf( sk8 ))]]) ).
thf(5196,plain,
( ( ( sk8 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk8 @ p2 )
| ( sk17 != sk16 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[162,5067]) ).
thf(5197,plain,
( ( ( sk8 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk8 @ p2 )
| ( sk17 != sk16 )
| sk11 ),
inference(simp,[status(thm)],[5196]) ).
thf(5205,plain,
( ( ( sk8 @ sk7 )
!= sk1 )
| ( sk17 != sk16 )
| ( sk8 @ p2 )
| sk11 ),
inference(simp,[status(thm)],[5197]) ).
thf(6718,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6695,61]) ).
thf(6719,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[6718]) ).
thf(6796,plain,
! [A: $i] :
( ( ( sk8 @ sk10 )
!= A )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[6719]) ).
thf(6819,plain,
( ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ sk3 @ ( sk8 @ sk10 @ r1 ) )
| ( sk8 @ sk10 @ p3 ) ),
inference(simp,[status(thm)],[6796]) ).
thf(50,plain,
! [A: $i] :
( ( A @ sk6 @ p2 )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(102,plain,
! [A: $i] :
( ( A @ sk6 @ p2 )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(26290,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,102]) ).
thf(26291,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[26290]) ).
thf(26292,plain,
( ( sk5 @ sk6 @ p2 )
| ( sk5 @ p2 ) ),
inference(pattern_uni,[status(thm)],[26291:[bind(A,$thf( sk5 ))]]) ).
thf(40,plain,
~ ( sk5 @ p2 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(26511,plain,
( ( sk5 @ sk6 @ p2 )
| $false ),
inference(rewrite,[status(thm)],[26292,40]) ).
thf(26512,plain,
sk5 @ sk6 @ p2,
inference(simp,[status(thm)],[26511]) ).
thf(20,plain,
( ~ sk19
| ( sk21 @ ( sk20 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(482,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk21 @ ( sk20 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( B @ p2 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ sk33 @ r1 ) )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[20,88]) ).
thf(483,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk21 @ ( sk20 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( B @ p2 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ sk33 @ r1 ) )
| ~ ( A @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[482]) ).
thf(596,plain,
! [C: $i,B: $i,A: $i] :
( ( sk21 != A )
| ( sk20 != sk18 )
| ~ ( A @ sk31 )
| ~ ( B @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ sk33 @ r1 ) )
| ~ ( A @ sk24 )
| ~ sk19
| ~ sk11
| ( C @ p2 ) ),
inference(simp,[status(thm)],[483]) ).
thf(621,plain,
! [B: $i,A: $i] :
( ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( A @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk21 @ sk33 @ r1 ) )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( B @ p2 ) ),
inference(simp,[status(thm)],[596]) ).
thf(861,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk21 @ sk33 @ r1 ) )
!= ( sk8 @ ( sk1 @ r1 ) ) )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( A @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ $true
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( B @ p2 ) ),
inference(paramod_ordered,[status(thm)],[19,621]) ).
thf(862,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk21 @ sk33 @ r1 ) )
!= ( sk8 @ ( sk1 @ r1 ) ) )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( A @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( B @ p2 ) ),
inference(simp,[status(thm)],[861]) ).
thf(869,plain,
! [B: $i,A: $i] :
( ( A != sk8 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( A @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( B @ p2 ) ),
inference(simp,[status(thm)],[862]) ).
thf(881,plain,
! [A: $i] :
( ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( A @ ( sk8 @ r1 ) )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[869]) ).
thf(891,plain,
! [A: $i] :
( ( ( A @ ( sk8 @ r1 ) )
!= ( sk5 @ ( sk1 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ $true
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(paramod_ordered,[status(thm)],[48,881]) ).
thf(892,plain,
! [A: $i] :
( ( ( A @ ( sk8 @ r1 ) )
!= ( sk5 @ ( sk1 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[891]) ).
thf(939,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk8 != sk1 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[892]) ).
thf(949,plain,
( ( sk8 != sk1 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( sk5 @ p2 ) ),
inference(simp,[status(thm)],[939]) ).
thf(1756,plain,
( ( sk8 != sk1 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| $false ),
inference(rewrite,[status(thm)],[949,40]) ).
thf(1757,plain,
( ( sk8 != sk1 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[1756]) ).
thf(26666,plain,
( ( ( sk5 @ sk6 @ p2 )
!= ( sk8 @ p2 ) )
| ( sk8 != sk1 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ $true
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,1757]) ).
thf(26667,plain,
( ( ( sk5 @ sk6 @ p2 )
!= ( sk8 @ p2 ) )
| ( sk8 != sk1 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26666]) ).
thf(26746,plain,
( ( ( sk5 @ sk6 )
!= sk8 )
| ( sk8 != sk1 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26667]) ).
thf(22041,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,101]) ).
thf(22042,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[22041]) ).
thf(22043,plain,
( ~ ( sk5 @ sk36 @ p2 )
| ( sk5 @ p2 ) ),
inference(pattern_uni,[status(thm)],[22042:[bind(A,$thf( sk5 ))]]) ).
thf(22252,plain,
( ~ ( sk5 @ sk36 @ p2 )
| $false ),
inference(rewrite,[status(thm)],[22043,40]) ).
thf(22253,plain,
~ ( sk5 @ sk36 @ p2 ),
inference(simp,[status(thm)],[22252]) ).
thf(22264,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk16 @ p2 ) )
| ~ $true
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[7,22253]) ).
thf(22265,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk16 @ p2 ) )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[22264]) ).
thf(22279,plain,
( ( ( sk5 @ sk36 )
!= sk16 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[22265]) ).
thf(716,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,61]) ).
thf(717,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[716]) ).
thf(718,plain,
( ( sk2 @ sk3 @ ( sk2 @ r1 ) )
| ( sk2 @ p3 ) ),
inference(pattern_uni,[status(thm)],[717:[bind(A,$thf( sk2 ))]]) ).
thf(1158,plain,
( ( sk2 @ sk3 @ ( sk2 @ r1 ) )
| $false ),
inference(rewrite,[status(thm)],[718,32]) ).
thf(1159,plain,
sk2 @ sk3 @ ( sk2 @ r1 ),
inference(simp,[status(thm)],[1158]) ).
thf(1169,plain,
! [A: $i] :
( ( ( A @ ( sk8 @ r1 ) )
!= ( sk2 @ sk3 @ ( sk2 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ $true
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(paramod_ordered,[status(thm)],[1159,881]) ).
thf(1170,plain,
! [A: $i] :
( ( ( A @ ( sk8 @ r1 ) )
!= ( sk2 @ sk3 @ ( sk2 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[1169]) ).
thf(1195,plain,
! [A: $i] :
( ( A
!= ( sk2 @ sk3 ) )
| ( sk8 != sk2 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[1170]) ).
thf(1205,plain,
( ( sk8 != sk2 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( sk2 @ sk3 @ p2 ) ),
inference(simp,[status(thm)],[1195]) ).
thf(35,plain,
( sk11
| ( sk16 @ ( sk1 @ r1 ) )
| ( sk1 @ p2 ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(433,plain,
! [A: $i] :
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| ~ $true
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[35,41]) ).
thf(434,plain,
! [A: $i] :
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[433]) ).
thf(435,plain,
( ~ ( sk16 @ sk4 @ p3 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(pattern_uni,[status(thm)],[434:[bind(A,$thf( sk16 ))]]) ).
thf(4572,plain,
( ( ( sk5 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ~ ( sk16 @ sk4 @ p3 )
| ( sk16 @ p3 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[435,40]) ).
thf(4573,plain,
( ( ( sk5 @ p2 )
!= ( sk1 @ p2 ) )
| ~ ( sk16 @ sk4 @ p3 )
| ( sk16 @ p3 )
| sk11 ),
inference(simp,[status(thm)],[4572]) ).
thf(4592,plain,
( ( sk5 != sk1 )
| ~ ( sk16 @ sk4 @ p3 )
| ( sk16 @ p3 )
| sk11 ),
inference(simp,[status(thm)],[4573]) ).
thf(49,plain,
! [A: $i] :
( ( A @ sk36 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(99,plain,
! [A: $i] :
( ( A @ sk36 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(23863,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk36 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,99]) ).
thf(23864,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk36 @ ( A @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[23863]) ).
thf(23865,plain,
( ( sk5 @ sk36 @ ( sk5 @ r1 ) )
| ( sk5 @ p2 ) ),
inference(pattern_uni,[status(thm)],[23864:[bind(A,$thf( sk5 ))]]) ).
thf(24158,plain,
( ( sk5 @ sk36 @ ( sk5 @ r1 ) )
| $false ),
inference(rewrite,[status(thm)],[23865,40]) ).
thf(24159,plain,
sk5 @ sk36 @ ( sk5 @ r1 ),
inference(simp,[status(thm)],[24158]) ).
thf(24254,plain,
! [A: $i] :
( ( ( sk5 @ sk36 @ ( sk5 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24159,39]) ).
thf(24255,plain,
! [A: $i] :
( ( ( sk5 @ sk36 @ ( sk5 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[24254]) ).
thf(24330,plain,
! [A: $i] :
( ( ( sk5 @ sk36 )
!= A )
| ( sk5 != sk1 )
| ( A @ sk3 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[24255]) ).
thf(24373,plain,
( ( sk5 != sk1 )
| ( sk5 @ sk36 @ sk3 @ p3 )
| ( sk5 @ sk36 @ p3 ) ),
inference(simp,[status(thm)],[24330]) ).
thf(15,plain,
! [A: $i] :
( ( A @ sk9 @ p1 )
| ( A @ p1 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(111,plain,
! [A: $i] :
( ( A @ sk9 @ p1 )
| ( A @ p1 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(35250,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ p1 )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,111]) ).
thf(35251,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ p1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[35250]) ).
thf(35252,plain,
( ( sk5 @ sk9 @ p1 )
| ( sk5 @ p1 ) ),
inference(pattern_uni,[status(thm)],[35251:[bind(A,$thf( sk5 ))]]) ).
thf(29867,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk10 @ p1 )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,105]) ).
thf(29868,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk10 @ p1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[29867]) ).
thf(29869,plain,
( ~ ( sk5 @ sk10 @ p1 )
| ( sk5 @ p1 ) ),
inference(pattern_uni,[status(thm)],[29868:[bind(A,$thf( sk5 ))]]) ).
thf(35487,plain,
( ( ( sk5 @ sk10 @ p1 )
!= ( sk5 @ sk9 @ p1 ) )
| ~ $true
| ( sk5 @ p1 )
| ( sk5 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[35252,29869]) ).
thf(35488,plain,
( ( ( sk5 @ sk10 @ p1 )
!= ( sk5 @ sk9 @ p1 ) )
| ( sk5 @ p1 ) ),
inference(simp,[status(thm)],[35487]) ).
thf(35500,plain,
( ( ( sk5 @ sk10 )
!= ( sk5 @ sk9 ) )
| ( sk5 @ p1 ) ),
inference(simp,[status(thm)],[35488]) ).
thf(317,plain,
! [A: $i] :
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[35,39]) ).
thf(318,plain,
! [A: $i] :
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[317]) ).
thf(319,plain,
( ( sk16 @ sk3 @ p3 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( sk16 ))]]) ).
thf(403,plain,
( ( ( sk5 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk16 @ sk3 @ p3 )
| ( sk16 @ p3 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[319,40]) ).
thf(404,plain,
( ( ( sk5 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk16 @ sk3 @ p3 )
| ( sk16 @ p3 )
| sk11 ),
inference(simp,[status(thm)],[403]) ).
thf(408,plain,
( ( sk5 != sk1 )
| ( sk16 @ sk3 @ p3 )
| ( sk16 @ p3 )
| sk11 ),
inference(simp,[status(thm)],[404]) ).
thf(25,plain,
! [A: $i] :
( ~ ( A @ sk31 )
| ( A @ sk33 @ ( A @ sk32 @ r1 ) )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(80,plain,
! [A: $i] :
( ~ ( A @ sk31 )
| ( A @ sk33 @ ( A @ sk32 @ r1 ) )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[25]) ).
thf(4626,plain,
! [B: $i,A: $i] :
( ( ( A @ sk33 @ ( A @ sk32 @ r1 ) )
!= ( B @ ( sk18 @ r1 ) ) )
| ~ ( B @ sk31 )
| ~ ( B @ sk33 @ p2 )
| ~ ( B @ sk24 )
| ~ $true
| ~ sk11
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[80,106]) ).
thf(4627,plain,
! [B: $i,A: $i] :
( ( ( A @ sk33 @ ( A @ sk32 @ r1 ) )
!= ( B @ ( sk18 @ r1 ) ) )
| ~ ( B @ sk31 )
| ~ ( B @ sk33 @ p2 )
| ~ ( B @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[4626]) ).
thf(4778,plain,
! [B: $i,A: $i] :
( ( ( A @ sk33 )
!= B )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( B @ sk31 )
| ~ ( B @ sk33 @ p2 )
| ~ ( B @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[4627]) ).
thf(4821,plain,
! [A: $i] :
( ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[4778]) ).
thf(5299,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk2 @ ( sk1 @ r1 ) ) )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[8,4821]) ).
thf(5300,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk2 @ ( sk1 @ r1 ) ) )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[5299]) ).
thf(5329,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk18 != sk1 )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[5300]) ).
thf(5351,plain,
( ( sk18 != sk1 )
| ( ( sk2 @ sk32 )
!= sk18 )
| ~ ( sk2 @ sk33 @ sk31 )
| ~ ( sk2 @ sk33 @ sk33 @ p2 )
| ~ ( sk2 @ sk33 @ sk24 )
| ~ ( sk2 @ sk31 )
| ~ ( sk2 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[5329]) ).
thf(7931,plain,
( ~ $true
| ( ( sk2 @ sk33 @ sk31 )
!= ( sk2 @ sk31 ) )
| ( sk18 != sk1 )
| ( ( sk2 @ sk32 )
!= sk18 )
| ~ ( sk2 @ sk33 @ sk33 @ p2 )
| ~ ( sk2 @ sk33 @ sk24 )
| ~ ( sk2 @ sk31 )
| ~ ( sk2 @ sk24 )
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[5351]) ).
thf(7934,plain,
( ( ( sk2 @ sk33 )
!= sk2 )
| ( sk18 != sk1 )
| ( ( sk2 @ sk32 )
!= sk18 )
| ~ ( sk2 @ sk33 @ sk33 @ p2 )
| ~ ( sk2 @ sk33 @ sk24 )
| ~ ( sk2 @ sk31 )
| ~ ( sk2 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[7931]) ).
thf(19136,plain,
( ~ $true
| ( ( sk2 @ sk33 @ sk24 )
!= ( sk2 @ sk24 ) )
| ( ( sk2 @ sk33 )
!= sk2 )
| ( sk18 != sk1 )
| ( ( sk2 @ sk32 )
!= sk18 )
| ~ ( sk2 @ sk33 @ sk33 @ p2 )
| ~ ( sk2 @ sk31 )
| ~ ( sk2 @ sk24 )
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[7934]) ).
thf(19141,plain,
( ( ( sk2 @ sk33 )
!= sk2 )
| ( ( sk2 @ sk33 )
!= sk2 )
| ( sk18 != sk1 )
| ( ( sk2 @ sk32 )
!= sk18 )
| ~ ( sk2 @ sk33 @ sk33 @ p2 )
| ~ ( sk2 @ sk31 )
| ~ ( sk2 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[19136]) ).
thf(19142,plain,
( ( ( sk2 @ sk33 )
!= sk2 )
| ( sk18 != sk1 )
| ( ( sk2 @ sk32 )
!= sk18 )
| ~ ( sk2 @ sk33 @ sk33 @ p2 )
| ~ ( sk2 @ sk31 )
| ~ ( sk2 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[19141]) ).
thf(264,plain,
( ( ( sk5 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk16 != sk1 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[138,40]) ).
thf(265,plain,
( ( ( sk5 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk16 != sk1 )
| sk11 ),
inference(simp,[status(thm)],[264]) ).
thf(276,plain,
( ( sk5 != sk1 )
| ( sk16 != sk1 )
| sk11 ),
inference(simp,[status(thm)],[265]) ).
thf(320,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,39]) ).
thf(321,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[320]) ).
thf(322,plain,
( ( sk2 @ sk3 @ p3 )
| ( sk2 @ p3 ) ),
inference(pattern_uni,[status(thm)],[321:[bind(A,$thf( sk2 ))]]) ).
thf(354,plain,
( ( sk2 @ sk3 @ p3 )
| $false ),
inference(rewrite,[status(thm)],[322,32]) ).
thf(355,plain,
sk2 @ sk3 @ p3,
inference(simp,[status(thm)],[354]) ).
thf(58,plain,
( ( sk18 @ ( sk1 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(443,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,41]) ).
thf(444,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| ~ sk11 ),
inference(simp,[status(thm)],[443]) ).
thf(445,plain,
( ~ ( sk18 @ sk4 @ p3 )
| ( sk18 @ p3 )
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[444:[bind(A,$thf( sk18 ))]]) ).
thf(1518,plain,
( ( ( sk18 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ~ $true
| ( sk18 @ p3 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[355,445]) ).
thf(1519,plain,
( ( ( sk18 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ( sk18 @ p3 )
| ~ sk11 ),
inference(simp,[status(thm)],[1518]) ).
thf(1522,plain,
( ( ( sk18 @ sk4 )
!= ( sk2 @ sk3 ) )
| ~ sk11
| ( sk18 @ p3 ) ),
inference(simp,[status(thm)],[1519]) ).
thf(16,plain,
! [A: $i] :
( ( A @ sk7 @ ( A @ sk6 @ r1 ) )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(104,plain,
! [A: $i] :
( ( A @ sk7 @ ( A @ sk6 @ r1 ) )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(29072,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk7 @ ( A @ sk6 @ r1 ) )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,104]) ).
thf(29073,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk7 @ ( A @ sk6 @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[29072]) ).
thf(29074,plain,
( ( sk5 @ sk7 @ ( sk5 @ sk6 @ r1 ) )
| ( sk5 @ p2 ) ),
inference(pattern_uni,[status(thm)],[29073:[bind(A,$thf( sk5 ))]]) ).
thf(29456,plain,
( ( sk5 @ sk7 @ ( sk5 @ sk6 @ r1 ) )
| $false ),
inference(rewrite,[status(thm)],[29074,40]) ).
thf(29457,plain,
sk5 @ sk7 @ ( sk5 @ sk6 @ r1 ),
inference(simp,[status(thm)],[29456]) ).
thf(29487,plain,
! [A: $i] :
( ( ( sk5 @ sk7 @ ( sk5 @ sk6 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[29457,106]) ).
thf(29488,plain,
! [A: $i] :
( ( ( sk5 @ sk7 @ ( sk5 @ sk6 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[29487]) ).
thf(29668,plain,
! [A: $i] :
( ( ( sk5 @ sk7 )
!= A )
| ( ( sk5 @ sk6 )
!= sk18 )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[29488]) ).
thf(29724,plain,
( ( ( sk5 @ sk6 )
!= sk18 )
| ~ ( sk5 @ sk7 @ sk31 )
| ~ ( sk5 @ sk7 @ sk33 @ p2 )
| ~ ( sk5 @ sk7 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[29668]) ).
thf(32609,plain,
( ( ( sk5 @ sk7 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( ( sk5 @ sk6 )
!= sk18 )
| ~ ( sk5 @ sk7 @ sk31 )
| ~ $true
| ~ ( sk5 @ sk7 @ sk24 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,29724]) ).
thf(32610,plain,
( ( ( sk5 @ sk7 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( ( sk5 @ sk6 )
!= sk18 )
| ~ ( sk5 @ sk7 @ sk31 )
| ~ ( sk5 @ sk7 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[32609]) ).
thf(32631,plain,
( ( ( sk5 @ sk7 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( ( sk5 @ sk6 )
!= sk18 )
| ~ ( sk5 @ sk7 @ sk31 )
| ~ ( sk5 @ sk7 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[32610]) ).
thf(2035,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,75]) ).
thf(2036,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[2035]) ).
thf(2037,plain,
( ( sk5 @ sk6 @ ( sk5 @ r1 ) )
| ( sk5 @ p2 ) ),
inference(pattern_uni,[status(thm)],[2036:[bind(A,$thf( sk5 ))]]) ).
thf(2181,plain,
( ( sk5 @ sk6 @ ( sk5 @ r1 ) )
| $false ),
inference(rewrite,[status(thm)],[2037,40]) ).
thf(2182,plain,
sk5 @ sk6 @ ( sk5 @ r1 ),
inference(simp,[status(thm)],[2181]) ).
thf(2192,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk5 @ sk6 @ ( sk5 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[2182,106]) ).
thf(2193,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk5 @ sk6 @ ( sk5 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[2192]) ).
thf(2231,plain,
! [A: $i] :
( ( A
!= ( sk5 @ sk6 ) )
| ( sk18 != sk5 )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[2193]) ).
thf(2248,plain,
( ( sk18 != sk5 )
| ~ ( sk5 @ sk6 @ sk31 )
| ~ ( sk5 @ sk6 @ sk33 @ p2 )
| ~ ( sk5 @ sk6 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[2231]) ).
thf(26312,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,102]) ).
thf(26313,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[26312]) ).
thf(26314,plain,
( ( sk2 @ sk6 @ p2 )
| ( sk2 @ p2 ) ),
inference(pattern_uni,[status(thm)],[26313:[bind(A,$thf( sk2 ))]]) ).
thf(3350,plain,
! [A: $i] :
( ( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3314,39]) ).
thf(3351,plain,
! [A: $i] :
( ( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[3350]) ).
thf(3386,plain,
! [A: $i] :
( ( ( sk8 @ sk9 )
!= A )
| ( sk8 != sk1 )
| ( A @ sk3 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[3351]) ).
thf(3402,plain,
( ( sk8 != sk1 )
| ( sk8 @ sk9 @ sk3 @ p3 )
| ( sk8 @ sk9 @ p3 ) ),
inference(simp,[status(thm)],[3386]) ).
thf(22060,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,101]) ).
thf(22061,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[22060]) ).
thf(22062,plain,
( ~ ( sk2 @ sk36 @ p2 )
| ( sk2 @ p2 ) ),
inference(pattern_uni,[status(thm)],[22061:[bind(A,$thf( sk2 ))]]) ).
thf(26668,plain,
( ( ( sk2 @ sk36 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ~ $true
| ( sk2 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26512,22062]) ).
thf(26669,plain,
( ( ( sk2 @ sk36 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26668]) ).
thf(26679,plain,
( ( ( sk2 @ sk36 )
!= ( sk5 @ sk6 ) )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26669]) ).
thf(3066,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,77]) ).
thf(3067,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[3066]) ).
thf(3098,plain,
! [A: $i] :
( ( ( sk2 @ sk4 )
!= A )
| ( ( sk2 @ sk3 )
!= sk1 )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[3067]) ).
thf(3120,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ( sk2 @ sk4 @ sk9 @ ( sk2 @ sk4 @ r1 ) )
| ( sk2 @ sk4 @ p1 ) ),
inference(simp,[status(thm)],[3098]) ).
thf(26926,plain,
( ~ $true
| ( ( sk2 @ sk6 @ p2 )
!= ( sk2 @ p2 ) )
| ( sk2 @ p2 ) ),
inference(eqfactor_ordered,[status(thm)],[26314]) ).
thf(26950,plain,
( ( ( sk2 @ sk6 )
!= sk2 )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26926]) ).
thf(139,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk18 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,106]) ).
thf(140,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk18 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
! [A: $i] :
( ( A != sk18 )
| ( sk18 != sk1 )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[140]) ).
thf(142,plain,
( ( sk18 != sk1 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk33 @ p2 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[141]) ).
thf(145,plain,
! [A: $i] :
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[11,106]) ).
thf(146,plain,
! [A: $i] :
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[145]) ).
thf(147,plain,
( ~ ( sk20 @ sk31 )
| ~ ( sk20 @ sk33 @ p2 )
| ~ ( sk20 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( sk20 ))]]) ).
thf(26556,plain,
( ( ( sk20 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ~ ( sk20 @ sk31 )
| ~ $true
| ~ ( sk20 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,147]) ).
thf(26557,plain,
( ( ( sk20 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ~ ( sk20 @ sk31 )
| ~ ( sk20 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26556]) ).
thf(26699,plain,
( ( ( sk20 @ sk33 )
!= ( sk5 @ sk6 ) )
| ~ ( sk20 @ sk31 )
| ~ ( sk20 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26557]) ).
thf(2139,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,75]) ).
thf(2140,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[2139]) ).
thf(2141,plain,
( ( sk8 @ sk6 @ ( sk8 @ r1 ) )
| ( sk8 @ p2 ) ),
inference(pattern_uni,[status(thm)],[2140:[bind(A,$thf( sk8 ))]]) ).
thf(26332,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,102]) ).
thf(26333,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[26332]) ).
thf(26334,plain,
( ( sk8 @ sk6 @ p2 )
| ( sk8 @ p2 ) ),
inference(pattern_uni,[status(thm)],[26333:[bind(A,$thf( sk8 ))]]) ).
thf(27112,plain,
( ( ( sk8 @ sk7 @ p2 )
!= ( sk8 @ sk6 @ p2 ) )
| ~ $true
| ( sk8 @ p2 )
| ( sk8 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26334,5067]) ).
thf(27113,plain,
( ( ( sk8 @ sk7 @ p2 )
!= ( sk8 @ sk6 @ p2 ) )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[27112]) ).
thf(27227,plain,
( ( ( sk8 @ sk7 )
!= ( sk8 @ sk6 ) )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[27113]) ).
thf(926,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk8 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ $true
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(paramod_ordered,[status(thm)],[207,881]) ).
thf(927,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk8 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[926]) ).
thf(935,plain,
! [A: $i] :
( ( ( sk2 @ sk4 )
!= A )
| ( ( sk2 @ sk3 )
!= sk8 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[927]) ).
thf(945,plain,
( ( ( sk2 @ sk3 )
!= sk8 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( sk2 @ sk4 @ p2 ) ),
inference(simp,[status(thm)],[935]) ).
thf(9268,plain,
( ~ $true
| ( ( sk8 @ sk10 @ sk3 @ p3 )
!= ( sk8 @ sk10 @ p3 ) )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ p3 ) ),
inference(eqfactor_ordered,[status(thm)],[6811]) ).
thf(9278,plain,
( ( ( sk8 @ sk10 @ sk3 @ p3 )
!= ( sk8 @ sk10 @ p3 ) )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ p3 ) ),
inference(simp,[status(thm)],[9268]) ).
thf(45,plain,
( ~ ( sk18 @ p2 )
| sk19
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(26611,plain,
( ( ( sk5 @ sk6 @ p2 )
!= ( sk18 @ p2 ) )
| ~ $true
| sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,45]) ).
thf(26612,plain,
( ( ( sk5 @ sk6 @ p2 )
!= ( sk18 @ p2 ) )
| sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26611]) ).
thf(26753,plain,
( ( ( sk5 @ sk6 )
!= sk18 )
| ~ sk11
| sk19 ),
inference(simp,[status(thm)],[26612]) ).
thf(6716,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[6695,106]) ).
thf(6717,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[6716]) ).
thf(6783,plain,
! [A: $i] :
( ( ( sk8 @ sk10 )
!= A )
| ( ( sk8 @ sk9 )
!= sk18 )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[6717]) ).
thf(6834,plain,
( ( ( sk8 @ sk9 )
!= sk18 )
| ~ ( sk8 @ sk10 @ sk31 )
| ~ ( sk8 @ sk10 @ sk33 @ p2 )
| ~ ( sk8 @ sk10 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[6783]) ).
thf(26628,plain,
( ( ( sk8 @ sk10 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( ( sk8 @ sk9 )
!= sk18 )
| ~ ( sk8 @ sk10 @ sk31 )
| ~ $true
| ~ ( sk8 @ sk10 @ sk24 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,6834]) ).
thf(26629,plain,
( ( ( sk8 @ sk10 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( ( sk8 @ sk9 )
!= sk18 )
| ~ ( sk8 @ sk10 @ sk31 )
| ~ ( sk8 @ sk10 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26628]) ).
thf(26702,plain,
( ( ( sk8 @ sk10 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( ( sk8 @ sk9 )
!= sk18 )
| ~ ( sk8 @ sk10 @ sk31 )
| ~ ( sk8 @ sk10 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26629]) ).
thf(418,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,41]) ).
thf(419,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[418]) ).
thf(420,plain,
( ~ ( sk5 @ sk4 @ p3 )
| ( sk5 @ p3 ) ),
inference(pattern_uni,[status(thm)],[419:[bind(A,$thf( sk5 ))]]) ).
thf(664,plain,
( ( ( sk5 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ~ $true
| ( sk5 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[355,420]) ).
thf(665,plain,
( ( ( sk5 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[664]) ).
thf(670,plain,
( ( ( sk5 @ sk4 )
!= ( sk2 @ sk3 ) )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[665]) ).
thf(35274,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ p1 )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,111]) ).
thf(35275,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ p1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[35274]) ).
thf(35276,plain,
( ( sk2 @ sk9 @ p1 )
| ( sk2 @ p1 ) ),
inference(pattern_uni,[status(thm)],[35275:[bind(A,$thf( sk2 ))]]) ).
thf(35516,plain,
( ( ( sk8 @ sk10 @ p1 )
!= ( sk2 @ sk9 @ p1 ) )
| ~ $true
| ( sk2 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[35276,30091]) ).
thf(35517,plain,
( ( ( sk8 @ sk10 @ p1 )
!= ( sk2 @ sk9 @ p1 ) )
| ( sk2 @ p1 ) ),
inference(simp,[status(thm)],[35516]) ).
thf(35527,plain,
( ( ( sk8 @ sk10 )
!= ( sk2 @ sk9 ) )
| ( sk2 @ p1 ) ),
inference(simp,[status(thm)],[35517]) ).
thf(3336,plain,
! [A: $i] :
( ( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3314,41]) ).
thf(3337,plain,
! [A: $i] :
( ( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[3336]) ).
thf(3380,plain,
! [A: $i] :
( ( ( sk8 @ sk9 )
!= A )
| ( sk8 != sk1 )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[3337]) ).
thf(3396,plain,
( ( sk8 != sk1 )
| ~ ( sk8 @ sk9 @ sk4 @ p3 )
| ( sk8 @ sk9 @ p3 ) ),
inference(simp,[status(thm)],[3380]) ).
thf(4396,plain,
( ( ( sk8 @ sk9 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ( sk8 != sk1 )
| ~ $true
| ( sk8 @ sk9 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[355,3396]) ).
thf(4397,plain,
( ( ( sk8 @ sk9 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ( sk8 != sk1 )
| ( sk8 @ sk9 @ p3 ) ),
inference(simp,[status(thm)],[4396]) ).
thf(4403,plain,
( ( ( sk8 @ sk9 @ sk4 )
!= ( sk2 @ sk3 ) )
| ( sk8 != sk1 )
| ( sk8 @ sk9 @ p3 ) ),
inference(simp,[status(thm)],[4397]) ).
thf(253,plain,
! [A: $i] :
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| ~ $true
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[35,17]) ).
thf(254,plain,
! [A: $i] :
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[253]) ).
thf(255,plain,
( ( sk16 @ sk4 @ ( sk16 @ sk3 @ r1 ) )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(pattern_uni,[status(thm)],[254:[bind(A,$thf( sk16 ))]]) ).
thf(714,plain,
! [A: $i] :
( ( ( sk16 @ sk4 @ ( sk16 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ $true
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[255,61]) ).
thf(715,plain,
! [A: $i] :
( ( ( sk16 @ sk4 @ ( sk16 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[714]) ).
thf(734,plain,
! [A: $i] :
( ( ( sk16 @ sk4 )
!= A )
| ( ( sk16 @ sk3 )
!= sk1 )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[715]) ).
thf(747,plain,
( ( ( sk16 @ sk3 )
!= sk1 )
| ( sk16 @ sk4 @ sk3 @ ( sk16 @ sk4 @ r1 ) )
| ( sk16 @ sk4 @ p3 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[734]) ).
thf(9427,plain,
( ( ( sk18 @ ( sk18 @ r1 ) )
!= ( sk18 @ ( sk1 @ r1 ) ) )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ $true
| ~ sk11
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,8960]) ).
thf(9428,plain,
( ( ( sk18 @ ( sk18 @ r1 ) )
!= ( sk18 @ ( sk1 @ r1 ) ) )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[9427]) ).
thf(9468,plain,
( ( sk18 != sk18 )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[9428]) ).
thf(9500,plain,
( ( sk18 != sk1 )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[9468]) ).
thf(10723,plain,
( ~ $true
| ( ( sk18 @ sk32 @ sk31 )
!= ( sk18 @ sk31 ) )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[9500]) ).
thf(10726,plain,
( ( ( sk18 @ sk32 @ sk31 )
!= ( sk18 @ sk31 ) )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[10723]) ).
thf(5051,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,81]) ).
thf(5052,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[5051]) ).
thf(5053,plain,
( ~ ( sk2 @ sk7 @ p2 )
| ( sk2 @ p2 ) ),
inference(pattern_uni,[status(thm)],[5052:[bind(A,$thf( sk2 ))]]) ).
thf(5172,plain,
( ( ( sk2 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk2 @ p2 )
| ( sk17 != sk16 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[162,5053]) ).
thf(5173,plain,
( ( ( sk2 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk2 @ p2 )
| ( sk17 != sk16 )
| sk11 ),
inference(simp,[status(thm)],[5172]) ).
thf(5178,plain,
( ( ( sk2 @ sk7 )
!= sk1 )
| ( sk17 != sk16 )
| ( sk2 @ p2 )
| sk11 ),
inference(simp,[status(thm)],[5173]) ).
thf(6226,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2182,83]) ).
thf(6227,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6226]) ).
thf(6313,plain,
! [A: $i] :
( ( ( sk5 @ sk6 )
!= A )
| ( sk5 != sk1 )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6227]) ).
thf(6370,plain,
( ( sk5 != sk1 )
| ( sk5 @ sk6 @ sk10 @ ( sk5 @ sk6 @ sk9 @ r1 ) )
| ( sk5 @ sk6 @ p1 ) ),
inference(simp,[status(thm)],[6313]) ).
thf(27177,plain,
( ~ $true
| ( ( sk8 @ sk6 @ p2 )
!= ( sk8 @ p2 ) )
| ( sk8 @ p2 ) ),
inference(eqfactor_ordered,[status(thm)],[26334]) ).
thf(27230,plain,
( ( ( sk8 @ sk6 )
!= sk8 )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[27177]) ).
thf(5054,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,81]) ).
thf(5055,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 )
| ~ sk11 ),
inference(simp,[status(thm)],[5054]) ).
thf(5056,plain,
( ~ ( sk18 @ sk7 @ p2 )
| ( sk18 @ p2 )
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[5055:[bind(A,$thf( sk18 ))]]) ).
thf(28,plain,
( sk11
| ~ ( sk15 @ p2 )
| ~ sk12 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(293,plain,
( ( ( sk15 @ p2 )
!= ( sk1 @ p2 ) )
| sk11
| ~ $true
| ~ sk12
| ( sk17 != sk16 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[162,28]) ).
thf(294,plain,
( ( ( sk15 @ p2 )
!= ( sk1 @ p2 ) )
| ~ sk12
| ( sk17 != sk16 )
| sk11 ),
inference(simp,[status(thm)],[293]) ).
thf(301,plain,
( ( sk15 != sk1 )
| ~ sk12
| ( sk17 != sk16 )
| sk11 ),
inference(simp,[status(thm)],[294]) ).
thf(4422,plain,
( ( ( sk8 @ sk9 @ sk4 @ p3 )
!= ( sk8 @ sk9 @ sk3 @ p3 ) )
| ( sk8 != sk1 )
| ~ $true
| ( sk8 @ sk9 @ p3 )
| ( sk8 != sk1 )
| ( sk8 @ sk9 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[3402,3396]) ).
thf(4423,plain,
( ( ( sk8 @ sk9 @ sk4 @ p3 )
!= ( sk8 @ sk9 @ sk3 @ p3 ) )
| ( sk8 != sk1 )
| ( sk8 @ sk9 @ p3 ) ),
inference(simp,[status(thm)],[4422]) ).
thf(4439,plain,
( ( ( sk8 @ sk9 @ sk4 )
!= ( sk8 @ sk9 @ sk3 ) )
| ( sk8 != sk1 )
| ( sk8 @ sk9 @ p3 ) ),
inference(simp,[status(thm)],[4423]) ).
thf(446,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,41]) ).
thf(447,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[446]) ).
thf(460,plain,
! [A: $i] :
( ( ( sk2 @ sk4 )
!= A )
| ( ( sk2 @ sk3 )
!= sk1 )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[447]) ).
thf(468,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ~ ( sk2 @ sk4 @ sk4 @ p3 )
| ( sk2 @ sk4 @ p3 ) ),
inference(simp,[status(thm)],[460]) ).
thf(4862,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ~ ( sk2 @ sk4 @ sk4 @ p3 )
| $false ),
inference(rewrite,[status(thm)],[468,750]) ).
thf(4863,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ~ ( sk2 @ sk4 @ sk4 @ p3 ) ),
inference(simp,[status(thm)],[4862]) ).
thf(4864,plain,
( ( ( sk2 @ sk4 @ sk4 @ p3 )
!= ( sk8 @ sk3 @ p3 ) )
| ( ( sk2 @ sk3 )
!= sk1 )
| ~ $true
| ( sk8 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[333,4863]) ).
thf(4865,plain,
( ( ( sk2 @ sk4 @ sk4 @ p3 )
!= ( sk8 @ sk3 @ p3 ) )
| ( ( sk2 @ sk3 )
!= sk1 )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[4864]) ).
thf(4896,plain,
( ( ( sk2 @ sk4 @ sk4 )
!= ( sk8 @ sk3 ) )
| ( ( sk2 @ sk3 )
!= sk1 )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[4865]) ).
thf(30,plain,
( sk11
| ( sk15 @ ( sk1 @ r1 ) )
| ~ sk12 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(182,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| ~ $true
| sk11
| ~ sk12 ),
inference(paramod_ordered,[status(thm)],[30,17]) ).
thf(183,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| sk11
| ~ sk12 ),
inference(simp,[status(thm)],[182]) ).
thf(184,plain,
( ( sk15 @ sk4 @ ( sk15 @ sk3 @ r1 ) )
| ( sk15 @ p3 )
| sk11
| ~ sk12 ),
inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( sk15 ))]]) ).
thf(10727,plain,
( ( ( sk18 @ sk32 )
!= sk18 )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[10723]) ).
thf(10746,plain,
( ~ $true
| ( ( sk18 @ sk32 @ sk24 )
!= ( sk18 @ sk24 ) )
| ( ( sk18 @ sk32 )
!= sk18 )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[10727]) ).
thf(10748,plain,
( ( ( sk18 @ sk32 )
!= sk18 )
| ( ( sk18 @ sk32 )
!= sk18 )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[10746]) ).
thf(10751,plain,
( ( ( sk18 @ sk32 )
!= sk18 )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[10748]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk31 )
| ( A @ ( B @ sk34 ) @ ( B @ r1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk31 )
| ( A @ ( B @ sk34 ) @ ( B @ r1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[47]) ).
thf(323,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,39]) ).
thf(324,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ sk11 ),
inference(simp,[status(thm)],[323]) ).
thf(325,plain,
( ( sk18 @ sk3 @ p3 )
| ( sk18 @ p3 )
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[324:[bind(A,$thf( sk18 ))]]) ).
thf(1504,plain,
( ~ $true
| ( ( sk18 @ sk3 @ p3 )
!= ( sk18 @ p3 ) )
| ( sk18 @ p3 )
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[325]) ).
thf(1511,plain,
( ( ( sk18 @ sk3 )
!= sk18 )
| ~ sk11
| ( sk18 @ p3 ) ),
inference(simp,[status(thm)],[1504]) ).
thf(122,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk5 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[48,106]) ).
thf(123,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk5 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[122]) ).
thf(124,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk18 != sk1 )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[123]) ).
thf(125,plain,
( ( sk18 != sk1 )
| ~ ( sk5 @ sk31 )
| ~ ( sk5 @ sk33 @ p2 )
| ~ ( sk5 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[124]) ).
thf(21960,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1159,101]) ).
thf(21961,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[21960]) ).
thf(22115,plain,
! [A: $i] :
( ( ( sk2 @ sk3 )
!= A )
| ( sk2 != sk1 )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[21961]) ).
thf(22229,plain,
( ( sk2 != sk1 )
| ~ ( sk2 @ sk3 @ sk36 @ p2 )
| ( sk2 @ sk3 @ p2 ) ),
inference(simp,[status(thm)],[22115]) ).
thf(114,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk2 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[8,106]) ).
thf(115,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk2 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk18 != sk1 )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[115]) ).
thf(117,plain,
( ( sk18 != sk1 )
| ~ ( sk2 @ sk31 )
| ~ ( sk2 @ sk33 @ p2 )
| ~ ( sk2 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[116]) ).
thf(26569,plain,
( ( ( sk2 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk1 )
| ~ ( sk2 @ sk31 )
| ~ $true
| ~ ( sk2 @ sk24 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,117]) ).
thf(26570,plain,
( ( ( sk2 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk1 )
| ~ ( sk2 @ sk31 )
| ~ ( sk2 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26569]) ).
thf(26718,plain,
( ( ( sk2 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( sk18 != sk1 )
| ~ ( sk2 @ sk31 )
| ~ ( sk2 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26570]) ).
thf(54,plain,
( ~ sk19
| ~ ( sk21 @ p2 )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(8827,plain,
( ( ( sk20 @ sk22 @ p2 )
!= ( sk21 @ p2 ) )
| ~ sk19
| ~ $true
| ~ sk11
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[8604,54]) ).
thf(8828,plain,
( ( ( sk20 @ sk22 @ p2 )
!= ( sk21 @ p2 ) )
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[8827]) ).
thf(8880,plain,
( ( ( sk20 @ sk22 )
!= sk21 )
| ~ sk19
| ~ sk11
| ( sk20 @ p2 ) ),
inference(simp,[status(thm)],[8828]) ).
thf(22078,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,101]) ).
thf(22079,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[22078]) ).
thf(22080,plain,
( ~ ( sk8 @ sk36 @ p2 )
| ( sk8 @ p2 ) ),
inference(pattern_uni,[status(thm)],[22079:[bind(A,$thf( sk8 ))]]) ).
thf(26819,plain,
( ( ( sk8 @ sk36 @ p2 )
!= ( sk2 @ sk6 @ p2 ) )
| ~ $true
| ( sk8 @ p2 )
| ( sk2 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26314,22080]) ).
thf(26820,plain,
( ( ( sk8 @ sk36 @ p2 )
!= ( sk2 @ sk6 @ p2 ) )
| ( sk8 @ p2 )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26819]) ).
thf(26934,plain,
( ( ( sk8 @ sk36 )
!= ( sk2 @ sk6 ) )
| ( sk8 @ p2 )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26820]) ).
thf(5062,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 )
| ~ $true
| sk11
| ~ sk12 ),
inference(paramod_ordered,[status(thm)],[30,81]) ).
thf(5063,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 )
| sk11
| ~ sk12 ),
inference(simp,[status(thm)],[5062]) ).
thf(5064,plain,
( ~ ( sk15 @ sk7 @ p2 )
| ( sk15 @ p2 )
| sk11
| ~ sk12 ),
inference(pattern_uni,[status(thm)],[5063:[bind(A,$thf( sk15 ))]]) ).
thf(5003,plain,
! [A: $i] :
( ( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3314,81]) ).
thf(5004,plain,
! [A: $i] :
( ( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[5003]) ).
thf(5104,plain,
! [A: $i] :
( ( ( sk8 @ sk9 )
!= A )
| ( sk8 != sk1 )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[5004]) ).
thf(5130,plain,
( ( sk8 != sk1 )
| ~ ( sk8 @ sk9 @ sk7 @ p2 )
| ( sk8 @ sk9 @ p2 ) ),
inference(simp,[status(thm)],[5104]) ).
thf(132,plain,
( ( ( sk16 @ p2 )
!= ( sk5 @ p2 ) )
| ~ $true
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[7,40]) ).
thf(133,plain,
( ( ( sk16 @ p2 )
!= ( sk5 @ p2 ) )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[132]) ).
thf(135,plain,
( ( sk16 != sk5 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[133]) ).
thf(4981,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,81]) ).
thf(4982,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[4981]) ).
thf(4983,plain,
( ~ ( sk5 @ sk7 @ p2 )
| ( sk5 @ p2 ) ),
inference(pattern_uni,[status(thm)],[4982:[bind(A,$thf( sk5 ))]]) ).
thf(5136,plain,
( ~ ( sk5 @ sk7 @ p2 )
| $false ),
inference(rewrite,[status(thm)],[4983,40]) ).
thf(5137,plain,
~ ( sk5 @ sk7 @ p2 ),
inference(simp,[status(thm)],[5136]) ).
thf(5146,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk16 != sk5 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[135,5137]) ).
thf(5147,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk16 != sk5 )
| sk11 ),
inference(simp,[status(thm)],[5146]) ).
thf(5160,plain,
( ( ( sk5 @ sk7 )
!= sk1 )
| ( sk16 != sk5 )
| sk11 ),
inference(simp,[status(thm)],[5147]) ).
thf(5310,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk8 @ ( sk1 @ r1 ) ) )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[19,4821]) ).
thf(5311,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk8 @ ( sk1 @ r1 ) ) )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[5310]) ).
thf(5333,plain,
! [A: $i] :
( ( A != sk8 )
| ( sk18 != sk1 )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[5311]) ).
thf(5355,plain,
( ( sk18 != sk1 )
| ( ( sk8 @ sk32 )
!= sk18 )
| ~ ( sk8 @ sk33 @ sk31 )
| ~ ( sk8 @ sk33 @ sk33 @ p2 )
| ~ ( sk8 @ sk33 @ sk24 )
| ~ ( sk8 @ sk31 )
| ~ ( sk8 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[5333]) ).
thf(711,plain,
! [A: $i] :
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ $true
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[35,61]) ).
thf(712,plain,
! [A: $i] :
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[711]) ).
thf(713,plain,
( ( sk16 @ sk3 @ ( sk16 @ r1 ) )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(pattern_uni,[status(thm)],[712:[bind(A,$thf( sk16 ))]]) ).
thf(34,plain,
! [B: $i,A: $i] :
( sk11
| sk12
| ( A @ ( B @ sk14 ) @ ( A @ ( B @ sk13 ) @ r1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(93,plain,
! [B: $i,A: $i] :
( sk11
| sk12
| ( A @ ( B @ sk14 ) @ ( A @ ( B @ sk13 ) @ r1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(14596,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ sk3 @ ( sk16 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| sk11
| sk12
| ( A @ ( B @ sk14 ) @ ( A @ ( B @ sk13 ) @ r1 ) )
| ( B @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[713,93]) ).
thf(14597,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ sk3 @ ( sk16 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| sk12
| ( A @ ( B @ sk14 ) @ ( A @ ( B @ sk13 ) @ r1 ) )
| ( B @ p2 )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[14596]) ).
thf(14598,plain,
( sk12
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
| ( sk16 @ sk3 @ p2 )
| ~ ( sk16 @ ( sk1 @ r1 ) )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(pattern_uni,[status(thm)],[14597:[bind(A,$thf( sk16 )),bind(B,$thf( sk16 @ sk3 ))]]) ).
thf(16013,plain,
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( sk16 @ ( sk1 @ r1 ) ) )
| sk12
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
| ( sk16 @ sk3 @ p2 )
| ~ $true
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[35,14598]) ).
thf(16014,plain,
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( sk16 @ ( sk1 @ r1 ) ) )
| sk12
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[16013]) ).
thf(16015,plain,
( sk12
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(pattern_uni,[status(thm)],[16014:[]]) ).
thf(17373,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ $true
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[16015,77]) ).
thf(17374,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17373]) ).
thf(17456,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) )
!= A )
| ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17374]) ).
thf(17466,plain,
( ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ sk9 @ ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ r1 ) )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ p1 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17456]) ).
thf(26315,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ p2 )
| ( A @ p2 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,102]) ).
thf(26316,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ p2 )
| ( A @ p2 )
| ~ sk11 ),
inference(simp,[status(thm)],[26315]) ).
thf(26317,plain,
( ( sk18 @ sk6 @ p2 )
| ( sk18 @ p2 )
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[26316:[bind(A,$thf( sk18 ))]]) ).
thf(28614,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk18 @ sk6 @ p2 ) )
| ~ $true
| ( sk18 @ p2 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26317,5137]) ).
thf(28615,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk18 @ sk6 @ p2 ) )
| ( sk18 @ p2 )
| ~ sk11 ),
inference(simp,[status(thm)],[28614]) ).
thf(28751,plain,
( ( ( sk5 @ sk7 )
!= ( sk18 @ sk6 ) )
| ~ sk11
| ( sk18 @ p2 ) ),
inference(simp,[status(thm)],[28615]) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk24 )
| ( B @ sk25 )
| ( A @ ( B @ ( C @ ( D @ sk26 ) ) ) @ p2 )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(78,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk24 )
| ( B @ sk25 )
| ( A @ ( B @ ( C @ ( D @ sk26 ) ) ) @ p2 )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[24]) ).
thf(26565,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26512,5137]) ).
thf(26566,plain,
( ( sk5 @ sk7 @ p2 )
!= ( sk5 @ sk6 @ p2 ) ),
inference(simp,[status(thm)],[26565]) ).
thf(26696,plain,
( ( sk5 @ sk7 )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[26566]) ).
thf(29110,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk7 @ ( A @ sk6 @ r1 ) )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,104]) ).
thf(29111,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk7 @ ( A @ sk6 @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[29110]) ).
thf(29112,plain,
( ( sk2 @ sk7 @ ( sk2 @ sk6 @ r1 ) )
| ( sk2 @ p2 ) ),
inference(pattern_uni,[status(thm)],[29111:[bind(A,$thf( sk2 ))]]) ).
thf(328,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true
| sk11
| ~ sk12 ),
inference(paramod_ordered,[status(thm)],[30,39]) ).
thf(329,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| sk11
| ~ sk12 ),
inference(simp,[status(thm)],[328]) ).
thf(330,plain,
( ( sk15 @ sk3 @ p3 )
| ( sk15 @ p3 )
| sk11
| ~ sk12 ),
inference(pattern_uni,[status(thm)],[329:[bind(A,$thf( sk15 ))]]) ).
thf(2506,plain,
( ( ( sk2 @ sk4 @ p3 )
!= ( sk15 @ sk3 @ p3 ) )
| ~ $true
| ( sk15 @ p3 )
| sk11
| ~ sk12 ),
inference(paramod_ordered,[status(thm)],[330,750]) ).
thf(2507,plain,
( ( ( sk2 @ sk4 @ p3 )
!= ( sk15 @ sk3 @ p3 ) )
| ( sk15 @ p3 )
| sk11
| ~ sk12 ),
inference(simp,[status(thm)],[2506]) ).
thf(2520,plain,
( ( ( sk2 @ sk4 )
!= ( sk15 @ sk3 ) )
| ~ sk12
| ( sk15 @ p3 )
| sk11 ),
inference(simp,[status(thm)],[2507]) ).
thf(2215,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2182,39]) ).
thf(2216,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[2215]) ).
thf(2229,plain,
! [A: $i] :
( ( ( sk5 @ sk6 )
!= A )
| ( sk5 != sk1 )
| ( A @ sk3 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[2216]) ).
thf(2246,plain,
( ( sk5 != sk1 )
| ( sk5 @ sk6 @ sk3 @ p3 )
| ( sk5 @ sk6 @ p3 ) ),
inference(simp,[status(thm)],[2229]) ).
thf(4204,plain,
( ~ $true
| ( ( sk5 @ sk6 @ sk3 @ p3 )
!= ( sk5 @ sk6 @ p3 ) )
| ( sk5 != sk1 )
| ( sk5 @ sk6 @ p3 ) ),
inference(eqfactor_ordered,[status(thm)],[2246]) ).
thf(4205,plain,
( ( ( sk5 @ sk6 @ sk3 @ p3 )
!= ( sk5 @ sk6 @ p3 ) )
| ( sk5 != sk1 )
| ( sk5 @ sk6 @ p3 ) ),
inference(simp,[status(thm)],[4204]) ).
thf(6241,plain,
! [A: $i] :
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| ~ $true
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[35,83]) ).
thf(6242,plain,
! [A: $i] :
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[6241]) ).
thf(6243,plain,
( ( sk16 @ sk10 @ ( sk16 @ sk9 @ r1 ) )
| ( sk16 @ p1 )
| sk11
| ( sk1 @ p2 ) ),
inference(pattern_uni,[status(thm)],[6242:[bind(A,$thf( sk16 ))]]) ).
thf(7054,plain,
! [A: $i] :
( ( ( sk16 @ sk10 @ ( sk16 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true
| ( sk16 @ p1 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[6243,39]) ).
thf(7055,plain,
! [A: $i] :
( ( ( sk16 @ sk10 @ ( sk16 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ( sk16 @ p1 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[7054]) ).
thf(7097,plain,
! [A: $i] :
( ( ( sk16 @ sk10 )
!= A )
| ( ( sk16 @ sk9 )
!= sk1 )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ( sk16 @ p1 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[7055]) ).
thf(7107,plain,
( ( ( sk16 @ sk9 )
!= sk1 )
| ( sk16 @ sk10 @ sk3 @ p3 )
| ( sk16 @ sk10 @ p3 )
| ( sk16 @ p1 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[7097]) ).
thf(4420,plain,
( ( ( sk8 @ sk9 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ~ $true
| ( sk8 != sk1 )
| ( sk8 @ sk9 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[3402,32]) ).
thf(4421,plain,
( ( ( sk8 @ sk9 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ( sk8 != sk1 )
| ( sk8 @ sk9 @ p3 ) ),
inference(simp,[status(thm)],[4420]) ).
thf(4443,plain,
( ( ( sk8 @ sk9 @ sk3 )
!= sk2 )
| ( sk8 != sk1 )
| ( sk8 @ sk9 @ p3 ) ),
inference(simp,[status(thm)],[4421]) ).
thf(846,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk21 @ sk33 @ r1 ) )
!= ( sk18 @ ( sk1 @ r1 ) ) )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( A @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ $true
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( B @ p2 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,621]) ).
thf(847,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk21 @ sk33 @ r1 ) )
!= ( sk18 @ ( sk1 @ r1 ) ) )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( A @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ( B @ p2 )
| ~ sk11 ),
inference(simp,[status(thm)],[846]) ).
thf(871,plain,
! [B: $i,A: $i] :
( ( A != sk18 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( A @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( B @ p2 ) ),
inference(simp,[status(thm)],[847]) ).
thf(883,plain,
! [A: $i] :
( ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[871]) ).
thf(3362,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk8 @ sk9 @ ( sk8 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ $true
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(paramod_ordered,[status(thm)],[3314,883]) ).
thf(3363,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk8 @ sk9 @ ( sk8 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[3362]) ).
thf(3377,plain,
! [A: $i] :
( ( A
!= ( sk8 @ sk9 ) )
| ( sk18 != sk8 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[3363]) ).
thf(3393,plain,
( ( sk18 != sk8 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( sk8 @ sk9 @ p2 ) ),
inference(simp,[status(thm)],[3377]) ).
thf(6133,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,83]) ).
thf(6134,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6133]) ).
thf(6135,plain,
( ( sk5 @ sk10 @ ( sk5 @ sk9 @ r1 ) )
| ( sk5 @ p1 ) ),
inference(pattern_uni,[status(thm)],[6134:[bind(A,$thf( sk5 ))]]) ).
thf(118,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk8 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[19,106]) ).
thf(119,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk8 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[118]) ).
thf(120,plain,
! [A: $i] :
( ( A != sk8 )
| ( sk18 != sk1 )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[119]) ).
thf(121,plain,
( ( sk18 != sk1 )
| ~ ( sk8 @ sk31 )
| ~ ( sk8 @ sk33 @ p2 )
| ~ ( sk8 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[120]) ).
thf(5148,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk17 != sk16 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[162,5137]) ).
thf(5149,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk17 != sk16 )
| sk11 ),
inference(simp,[status(thm)],[5148]) ).
thf(5156,plain,
( ( ( sk5 @ sk7 )
!= sk1 )
| ( sk17 != sk16 )
| sk11 ),
inference(simp,[status(thm)],[5149]) ).
thf(57,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk24 )
| ( B @ sk25 )
| ~ ( A @ ( B @ ( C @ ( D @ sk27 ) ) ) @ p2 )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(84,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk24 )
| ( B @ sk25 )
| ~ ( A @ ( B @ ( C @ ( D @ sk27 ) ) ) @ p2 )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[57]) ).
thf(353,plain,
( ( ( sk5 @ sk3 )
!= sk5 )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[350]) ).
thf(26878,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk2 @ sk6 @ p2 ) )
| ~ $true
| ( sk2 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26314,22253]) ).
thf(26879,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk2 @ sk6 @ p2 ) )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26878]) ).
thf(26955,plain,
( ( ( sk5 @ sk36 )
!= ( sk2 @ sk6 ) )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26879]) ).
thf(6729,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6695,41]) ).
thf(6730,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[6729]) ).
thf(6795,plain,
! [A: $i] :
( ( ( sk8 @ sk10 )
!= A )
| ( ( sk8 @ sk9 )
!= sk1 )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[6730]) ).
thf(6818,plain,
( ( ( sk8 @ sk9 )
!= sk1 )
| ~ ( sk8 @ sk10 @ sk4 @ p3 )
| ( sk8 @ sk10 @ p3 ) ),
inference(simp,[status(thm)],[6795]) ).
thf(9302,plain,
( ( ( sk8 @ sk10 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ( ( sk8 @ sk9 )
!= sk1 )
| ~ $true
| ( sk8 @ sk10 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[355,6818]) ).
thf(9303,plain,
( ( ( sk8 @ sk10 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ p3 ) ),
inference(simp,[status(thm)],[9302]) ).
thf(9319,plain,
( ( ( sk8 @ sk10 @ sk4 )
!= ( sk2 @ sk3 ) )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ p3 ) ),
inference(simp,[status(thm)],[9303]) ).
thf(6745,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6695,81]) ).
thf(6746,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[6745]) ).
thf(6786,plain,
! [A: $i] :
( ( ( sk8 @ sk10 )
!= A )
| ( ( sk8 @ sk9 )
!= sk1 )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[6746]) ).
thf(6809,plain,
( ( ( sk8 @ sk9 )
!= sk1 )
| ~ ( sk8 @ sk10 @ sk7 @ p2 )
| ( sk8 @ sk10 @ p2 ) ),
inference(simp,[status(thm)],[6786]) ).
thf(22063,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,101]) ).
thf(22064,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 )
| ~ sk11 ),
inference(simp,[status(thm)],[22063]) ).
thf(22065,plain,
( ~ ( sk18 @ sk36 @ p2 )
| ( sk18 @ p2 )
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[22064:[bind(A,$thf( sk18 ))]]) ).
thf(451,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,41]) ).
thf(452,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[451]) ).
thf(453,plain,
( ~ ( sk8 @ sk4 @ p3 )
| ( sk8 @ p3 ) ),
inference(pattern_uni,[status(thm)],[452:[bind(A,$thf( sk8 ))]]) ).
thf(26538,plain,
( ( ( sk5 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk1 )
| ~ ( sk5 @ sk31 )
| ~ $true
| ~ ( sk5 @ sk24 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,125]) ).
thf(26539,plain,
( ( ( sk5 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk1 )
| ~ ( sk5 @ sk31 )
| ~ ( sk5 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26538]) ).
thf(26750,plain,
( ( ( sk5 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( sk18 != sk1 )
| ~ ( sk5 @ sk31 )
| ~ ( sk5 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26539]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ p2 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ p2 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[9]) ).
thf(26526,plain,
( ( ( sk18 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk31 )
| ~ $true
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,142]) ).
thf(26527,plain,
( ( ( sk18 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26526]) ).
thf(26724,plain,
( ( ( sk18 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26527]) ).
thf(407,plain,
( ~ $true
| ( ( sk16 @ sk3 @ p3 )
!= ( sk16 @ p3 ) )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(eqfactor_ordered,[status(thm)],[319]) ).
thf(411,plain,
( ( ( sk16 @ sk3 )
!= sk16 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[407]) ).
thf(4196,plain,
( ( ( sk5 @ sk6 @ sk3 @ p3 )
!= ( sk2 @ sk4 @ p3 ) )
| ~ $true
| ( sk5 != sk1 )
| ( sk5 @ sk6 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[2246,750]) ).
thf(4197,plain,
( ( ( sk5 @ sk6 @ sk3 @ p3 )
!= ( sk2 @ sk4 @ p3 ) )
| ( sk5 != sk1 )
| ( sk5 @ sk6 @ p3 ) ),
inference(simp,[status(thm)],[4196]) ).
thf(4211,plain,
( ( ( sk5 @ sk6 @ sk3 )
!= ( sk2 @ sk4 ) )
| ( sk5 != sk1 )
| ( sk5 @ sk6 @ p3 ) ),
inference(simp,[status(thm)],[4197]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( A @ sk24 )
| ~ ( A @ ( B @ sk28 ) @ p2 )
| ~ ( B @ sk25 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( A @ sk24 )
| ~ ( A @ ( B @ sk28 ) @ p2 )
| ~ ( B @ sk25 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[66]) ).
thf(128,plain,
( ( ( sk16 @ p2 )
!= ( sk15 @ p2 ) )
| sk11
| ~ $true
| ~ sk12
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[7,28]) ).
thf(129,plain,
( ( ( sk16 @ p2 )
!= ( sk15 @ p2 ) )
| ~ sk12
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[128]) ).
thf(136,plain,
( ( sk16 != sk15 )
| ~ sk12
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[129]) ).
thf(5152,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk16 != sk15 )
| ~ sk12
| sk11 ),
inference(paramod_ordered,[status(thm)],[136,5137]) ).
thf(5153,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk16 != sk15 )
| ~ sk12
| sk11 ),
inference(simp,[status(thm)],[5152]) ).
thf(5157,plain,
( ( ( sk5 @ sk7 )
!= sk1 )
| ( sk16 != sk15 )
| ~ sk12
| sk11 ),
inference(simp,[status(thm)],[5153]) ).
thf(22272,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk16 != sk15 )
| ~ sk12
| sk11 ),
inference(paramod_ordered,[status(thm)],[136,22253]) ).
thf(22273,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk16 != sk15 )
| ~ sk12
| sk11 ),
inference(simp,[status(thm)],[22272]) ).
thf(22282,plain,
( ( ( sk5 @ sk36 )
!= sk1 )
| ( sk16 != sk15 )
| ~ sk12
| sk11 ),
inference(simp,[status(thm)],[22273]) ).
thf(35294,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ p1 )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,111]) ).
thf(35295,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ p1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[35294]) ).
thf(35296,plain,
( ( sk8 @ sk9 @ p1 )
| ( sk8 @ p1 ) ),
inference(pattern_uni,[status(thm)],[35295:[bind(A,$thf( sk8 ))]]) ).
thf(35529,plain,
( ( sk8 @ sk9 @ p1 )
| $false ),
inference(rewrite,[status(thm)],[35296,51]) ).
thf(35530,plain,
sk8 @ sk9 @ p1,
inference(simp,[status(thm)],[35529]) ).
thf(35531,plain,
( ( ( sk5 @ sk10 @ p1 )
!= ( sk8 @ sk9 @ p1 ) )
| ~ $true
| ( sk5 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[35530,29869]) ).
thf(35532,plain,
( ( ( sk5 @ sk10 @ p1 )
!= ( sk8 @ sk9 @ p1 ) )
| ( sk5 @ p1 ) ),
inference(simp,[status(thm)],[35531]) ).
thf(35547,plain,
( ( ( sk5 @ sk10 )
!= ( sk8 @ sk9 ) )
| ( sk5 @ p1 ) ),
inference(simp,[status(thm)],[35532]) ).
thf(35520,plain,
( ~ $true
| ( ( sk2 @ sk9 @ p1 )
!= ( sk2 @ p1 ) )
| ( sk2 @ p1 ) ),
inference(eqfactor_ordered,[status(thm)],[35276]) ).
thf(35522,plain,
( ( ( sk2 @ sk9 )
!= sk2 )
| ( sk2 @ p1 ) ),
inference(simp,[status(thm)],[35520]) ).
thf(27070,plain,
( ( ( sk8 @ sk36 @ p2 )
!= ( sk8 @ sk6 @ p2 ) )
| ~ $true
| ( sk8 @ p2 )
| ( sk8 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26334,22080]) ).
thf(27071,plain,
( ( ( sk8 @ sk36 @ p2 )
!= ( sk8 @ sk6 @ p2 ) )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[27070]) ).
thf(27253,plain,
( ( ( sk8 @ sk36 )
!= ( sk8 @ sk6 ) )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[27071]) ).
thf(27129,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk8 @ sk6 @ p2 ) )
| ~ $true
| ( sk8 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26334,22253]) ).
thf(27130,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk8 @ sk6 @ p2 ) )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[27129]) ).
thf(27221,plain,
( ( ( sk5 @ sk36 )
!= ( sk8 @ sk6 ) )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[27130]) ).
thf(5291,plain,
! [A: $i] :
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[11,4821]) ).
thf(5292,plain,
! [A: $i] :
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[5291]) ).
thf(5293,plain,
( ( ( sk20 @ sk32 )
!= sk18 )
| ~ ( sk20 @ sk33 @ sk31 )
| ~ ( sk20 @ sk33 @ sk33 @ p2 )
| ~ ( sk20 @ sk33 @ sk24 )
| ~ ( sk20 @ sk31 )
| ~ ( sk20 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[5292:[bind(A,$thf( sk20 ))]]) ).
thf(5379,plain,
( ~ $true
| ( ( sk20 @ sk33 @ sk31 )
!= ( sk20 @ sk31 ) )
| ( ( sk20 @ sk32 )
!= sk18 )
| ~ ( sk20 @ sk33 @ sk33 @ p2 )
| ~ ( sk20 @ sk33 @ sk24 )
| ~ ( sk20 @ sk31 )
| ~ ( sk20 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[5293]) ).
thf(5381,plain,
( ( ( sk20 @ sk33 )
!= sk20 )
| ( ( sk20 @ sk32 )
!= sk18 )
| ~ ( sk20 @ sk33 @ sk33 @ p2 )
| ~ ( sk20 @ sk33 @ sk24 )
| ~ ( sk20 @ sk31 )
| ~ ( sk20 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[5379]) ).
thf(6088,plain,
( ~ $true
| ( ( sk20 @ sk33 @ sk24 )
!= ( sk20 @ sk24 ) )
| ( ( sk20 @ sk33 )
!= sk20 )
| ( ( sk20 @ sk32 )
!= sk18 )
| ~ ( sk20 @ sk33 @ sk33 @ p2 )
| ~ ( sk20 @ sk31 )
| ~ ( sk20 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[5381]) ).
thf(6091,plain,
( ( ( sk20 @ sk33 )
!= sk20 )
| ( ( sk20 @ sk33 )
!= sk20 )
| ( ( sk20 @ sk32 )
!= sk18 )
| ~ ( sk20 @ sk33 @ sk33 @ p2 )
| ~ ( sk20 @ sk31 )
| ~ ( sk20 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[6088]) ).
thf(6092,plain,
( ( ( sk20 @ sk33 )
!= sk20 )
| ( ( sk20 @ sk32 )
!= sk18 )
| ~ ( sk20 @ sk33 @ sk33 @ p2 )
| ~ ( sk20 @ sk31 )
| ~ ( sk20 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[6091]) ).
thf(4880,plain,
( ( ( sk2 @ sk4 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ( ( sk2 @ sk3 )
!= sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[355,4863]) ).
thf(4881,plain,
( ( ( sk2 @ sk4 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[4880]) ).
thf(4893,plain,
( ( ( sk2 @ sk4 @ sk4 )
!= ( sk2 @ sk3 ) )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[4881]) ).
thf(3586,plain,
( ~ $true
| ( ( sk16 @ sk3 @ p3 )
!= ( sk16 @ p3 ) )
| ( sk5 != sk1 )
| ( sk16 @ p3 )
| sk11 ),
inference(eqfactor_ordered,[status(thm)],[408]) ).
thf(3591,plain,
( ( ( sk16 @ sk3 )
!= sk16 )
| ( sk5 != sk1 )
| ( sk16 @ p3 )
| sk11 ),
inference(simp,[status(thm)],[3586]) ).
thf(29,plain,
! [A: $i] :
( ~ sk19
| ( A @ sk22 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(85,plain,
! [A: $i] :
( ~ sk19
| ( A @ sk22 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[29]) ).
thf(9417,plain,
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( sk18 @ ( sk18 @ r1 ) ) )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ $true
| ~ sk11
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[11,8960]) ).
thf(9418,plain,
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( sk18 @ ( sk18 @ r1 ) ) )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[9417]) ).
thf(9458,plain,
( ( sk20 != sk18 )
| ( sk18 != sk18 )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[9418]) ).
thf(9496,plain,
( ( sk20 != sk18 )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[9458]) ).
thf(12251,plain,
( ~ $true
| ( ( sk18 @ sk32 @ sk31 )
!= ( sk18 @ sk31 ) )
| ( sk20 != sk18 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[9496]) ).
thf(12254,plain,
( ( ( sk18 @ sk32 )
!= sk18 )
| ( sk20 != sk18 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[12251]) ).
thf(13514,plain,
( ~ $true
| ( ( sk18 @ sk32 @ sk24 )
!= ( sk18 @ sk24 ) )
| ( ( sk18 @ sk32 )
!= sk18 )
| ( sk20 != sk18 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[12254]) ).
thf(13517,plain,
( ( ( sk18 @ sk32 )
!= sk18 )
| ( ( sk18 @ sk32 )
!= sk18 )
| ( sk20 != sk18 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[13514]) ).
thf(13519,plain,
( ( ( sk18 @ sk32 )
!= sk18 )
| ( sk20 != sk18 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[13517]) ).
thf(26573,plain,
( ( ( sk18 @ sk32 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( ( sk18 @ sk32 )
!= sk18 )
| ( sk20 != sk18 )
| ~ $true
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,13519]) ).
thf(26574,plain,
( ( ( sk18 @ sk32 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( ( sk18 @ sk32 )
!= sk18 )
| ( sk20 != sk18 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26573]) ).
thf(26703,plain,
( ( ( sk18 @ sk32 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( ( sk18 @ sk32 )
!= sk18 )
| ( sk20 != sk18 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26574]) ).
thf(755,plain,
( ( ( sk2 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[355,750]) ).
thf(756,plain,
( ( sk2 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) ),
inference(simp,[status(thm)],[755]) ).
thf(761,plain,
( ( sk2 @ sk4 )
!= ( sk2 @ sk3 ) ),
inference(simp,[status(thm)],[756]) ).
thf(208,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[207,106]) ).
thf(209,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[208]) ).
thf(212,plain,
! [A: $i] :
( ( ( sk2 @ sk4 )
!= A )
| ( ( sk2 @ sk3 )
!= sk18 )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[209]) ).
thf(214,plain,
( ( ( sk2 @ sk3 )
!= sk18 )
| ~ ( sk2 @ sk4 @ sk31 )
| ~ ( sk2 @ sk4 @ sk33 @ p2 )
| ~ ( sk2 @ sk4 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[212]) ).
thf(26660,plain,
( ( ( sk2 @ sk4 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( ( sk2 @ sk3 )
!= sk18 )
| ~ ( sk2 @ sk4 @ sk31 )
| ~ $true
| ~ ( sk2 @ sk4 @ sk24 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,214]) ).
thf(26661,plain,
( ( ( sk2 @ sk4 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( ( sk2 @ sk3 )
!= sk18 )
| ~ ( sk2 @ sk4 @ sk31 )
| ~ ( sk2 @ sk4 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26660]) ).
thf(26678,plain,
( ( ( sk2 @ sk4 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( ( sk2 @ sk3 )
!= sk18 )
| ~ ( sk2 @ sk4 @ sk31 )
| ~ ( sk2 @ sk4 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26661]) ).
thf(148,plain,
! [A: $i] :
( ( ( sk21 @ ( sk20 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[20,106]) ).
thf(149,plain,
! [A: $i] :
( ( ( sk21 @ ( sk20 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
! [A: $i] :
( ( sk21 != A )
| ( sk20 != sk18 )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[149]) ).
thf(151,plain,
( ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk21 @ sk33 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[150]) ).
thf(26662,plain,
( ( ( sk21 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ $true
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,151]) ).
thf(26663,plain,
( ( ( sk21 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26662]) ).
thf(26735,plain,
( ( ( sk21 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26663]) ).
thf(2201,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2182,41]) ).
thf(2202,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[2201]) ).
thf(2232,plain,
! [A: $i] :
( ( ( sk5 @ sk6 )
!= A )
| ( sk5 != sk1 )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[2202]) ).
thf(2249,plain,
( ( sk5 != sk1 )
| ~ ( sk5 @ sk6 @ sk4 @ p3 )
| ( sk5 @ sk6 @ p3 ) ),
inference(simp,[status(thm)],[2232]) ).
thf(22512,plain,
( ( ( sk2 @ sk36 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk2 @ p2 )
| ( sk16 != sk5 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[135,22062]) ).
thf(22513,plain,
( ( ( sk2 @ sk36 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk2 @ p2 )
| ( sk16 != sk5 )
| sk11 ),
inference(simp,[status(thm)],[22512]) ).
thf(22524,plain,
( ( ( sk2 @ sk36 )
!= sk1 )
| ( sk16 != sk5 )
| ( sk2 @ p2 )
| sk11 ),
inference(simp,[status(thm)],[22513]) ).
thf(4432,plain,
( ~ $true
| ( ( sk8 @ sk9 @ sk3 @ p3 )
!= ( sk8 @ sk9 @ p3 ) )
| ( sk8 != sk1 )
| ( sk8 @ sk9 @ p3 ) ),
inference(eqfactor_ordered,[status(thm)],[3402]) ).
thf(4434,plain,
( ( ( sk8 @ sk9 @ sk3 )
!= ( sk8 @ sk9 ) )
| ( sk8 != sk1 )
| ( sk8 @ sk9 @ p3 ) ),
inference(simp,[status(thm)],[4432]) ).
thf(137,plain,
( ( ( sk16 @ p2 )
!= ( sk1 @ p2 ) )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[134]) ).
thf(6262,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,83]) ).
thf(6263,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| ~ sk11 ),
inference(simp,[status(thm)],[6262]) ).
thf(6264,plain,
( ( sk18 @ sk10 @ ( sk18 @ sk9 @ r1 ) )
| ( sk18 @ p1 )
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[6263:[bind(A,$thf( sk18 ))]]) ).
thf(5227,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk5 @ ( sk1 @ r1 ) ) )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[48,4821]) ).
thf(5228,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk5 @ ( sk1 @ r1 ) ) )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[5227]) ).
thf(5327,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk18 != sk1 )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[5228]) ).
thf(5349,plain,
( ( sk18 != sk1 )
| ( ( sk5 @ sk32 )
!= sk18 )
| ~ ( sk5 @ sk33 @ sk31 )
| ~ ( sk5 @ sk33 @ sk33 @ p2 )
| ~ ( sk5 @ sk33 @ sk24 )
| ~ ( sk5 @ sk31 )
| ~ ( sk5 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[5327]) ).
thf(26843,plain,
( ( ( sk2 @ sk7 @ p2 )
!= ( sk2 @ sk6 @ p2 ) )
| ~ $true
| ( sk2 @ p2 )
| ( sk2 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26314,5053]) ).
thf(26844,plain,
( ( ( sk2 @ sk7 @ p2 )
!= ( sk2 @ sk6 @ p2 ) )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26843]) ).
thf(26983,plain,
( ( ( sk2 @ sk7 )
!= ( sk2 @ sk6 ) )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26844]) ).
thf(23901,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk36 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,99]) ).
thf(23902,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk36 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ sk11 ),
inference(simp,[status(thm)],[23901]) ).
thf(23903,plain,
( ( sk18 @ sk36 @ ( sk18 @ r1 ) )
| ( sk18 @ p2 )
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[23902:[bind(A,$thf( sk18 ))]]) ).
thf(26532,plain,
( ( ( sk18 @ sk7 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ~ $true
| ( sk18 @ p2 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,5056]) ).
thf(26533,plain,
( ( ( sk18 @ sk7 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 @ p2 )
| ~ sk11 ),
inference(simp,[status(thm)],[26532]) ).
thf(26747,plain,
( ( ( sk18 @ sk7 )
!= ( sk5 @ sk6 ) )
| ~ sk11
| ( sk18 @ p2 ) ),
inference(simp,[status(thm)],[26533]) ).
thf(8851,plain,
( ( ( sk20 @ sk22 @ p2 )
!= ( sk5 @ p2 ) )
| ~ $true
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[8604,40]) ).
thf(8852,plain,
( ( ( sk20 @ sk22 @ p2 )
!= ( sk5 @ p2 ) )
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[8851]) ).
thf(8899,plain,
( ( ( sk20 @ sk22 )
!= sk5 )
| ~ sk19
| ~ sk11
| ( sk20 @ p2 ) ),
inference(simp,[status(thm)],[8852]) ).
thf(727,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,61]) ).
thf(728,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[727]) ).
thf(729,plain,
( ( sk8 @ sk3 @ ( sk8 @ r1 ) )
| ( sk8 @ p3 ) ),
inference(pattern_uni,[status(thm)],[728:[bind(A,$thf( sk8 ))]]) ).
thf(26268,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ p2 )
| ( A @ p2 )
| ~ $true
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[16015,102]) ).
thf(26269,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ p2 )
| ( A @ p2 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[26268]) ).
thf(26379,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) )
!= A )
| ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( A @ sk6 @ p2 )
| ( A @ p2 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[26269]) ).
thf(26445,plain,
( ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ sk6 @ p2 )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ p2 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[26379]) ).
thf(17349,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ $true
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[16015,61]) ).
thf(17350,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17349]) ).
thf(17457,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) )
!= A )
| ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17350]) ).
thf(17467,plain,
( ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ sk3 @ ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ r1 ) )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ p3 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17457]) ).
thf(9367,plain,
( ( ( sk18 @ ( sk18 @ r1 ) )
!= ( sk2 @ sk3 @ ( sk2 @ r1 ) ) )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[1159,8960]) ).
thf(9368,plain,
( ( ( sk18 @ ( sk18 @ r1 ) )
!= ( sk2 @ sk3 @ ( sk2 @ r1 ) ) )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[9367]) ).
thf(9455,plain,
( ( ( sk2 @ sk3 )
!= sk18 )
| ( sk18 != sk2 )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[9368]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( A @ sk24 )
| ( A @ ( B @ sk28 ) @ ( B @ r1 ) )
| ~ ( B @ sk25 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( A @ sk24 )
| ( A @ ( B @ sk28 ) @ ( B @ r1 ) )
| ~ ( B @ sk25 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[64]) ).
thf(22268,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk17 != sk16 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[162,22253]) ).
thf(22269,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk17 != sk16 )
| sk11 ),
inference(simp,[status(thm)],[22268]) ).
thf(22278,plain,
( ( ( sk5 @ sk36 )
!= sk1 )
| ( sk17 != sk16 )
| sk11 ),
inference(simp,[status(thm)],[22269]) ).
thf(22266,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk16 != sk5 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[135,22253]) ).
thf(22267,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk16 != sk5 )
| sk11 ),
inference(simp,[status(thm)],[22266]) ).
thf(22284,plain,
( ( ( sk5 @ sk36 )
!= sk1 )
| ( sk16 != sk5 )
| sk11 ),
inference(simp,[status(thm)],[22267]) ).
thf(3063,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,77]) ).
thf(3064,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ sk11 ),
inference(simp,[status(thm)],[3063]) ).
thf(3065,plain,
( ( sk18 @ sk9 @ ( sk18 @ r1 ) )
| ( sk18 @ p1 )
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[3064:[bind(A,$thf( sk18 ))]]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ~ ( A @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| sk19
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ~ ( A @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| sk19
| ~ sk11 ),
inference(simp,[status(thm)],[27]) ).
thf(35541,plain,
( ( ( sk8 @ sk9 @ p1 )
!= ( sk8 @ p1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35530,51]) ).
thf(35542,plain,
( ( sk8 @ sk9 @ p1 )
!= ( sk8 @ p1 ) ),
inference(simp,[status(thm)],[35541]) ).
thf(35543,plain,
( ( sk8 @ sk9 )
!= sk8 ),
inference(simp,[status(thm)],[35542]) ).
thf(28682,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk18 @ sk6 @ p2 ) )
| ~ $true
| ( sk18 @ p2 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26317,22253]) ).
thf(28683,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk18 @ sk6 @ p2 ) )
| ( sk18 @ p2 )
| ~ sk11 ),
inference(simp,[status(thm)],[28682]) ).
thf(28785,plain,
( ( ( sk5 @ sk36 )
!= ( sk18 @ sk6 ) )
| ~ sk11
| ( sk18 @ p2 ) ),
inference(simp,[status(thm)],[28683]) ).
thf(23898,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk36 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,99]) ).
thf(23899,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk36 @ ( A @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[23898]) ).
thf(23900,plain,
( ( sk2 @ sk36 @ ( sk2 @ r1 ) )
| ( sk2 @ p2 ) ),
inference(pattern_uni,[status(thm)],[23899:[bind(A,$thf( sk2 ))]]) ).
thf(26869,plain,
( ( ( sk2 @ sk6 @ p2 )
!= ( sk21 @ p2 ) )
| ~ sk19
| ~ $true
| ~ sk11
| ( sk2 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26314,54]) ).
thf(26870,plain,
( ( ( sk2 @ sk6 @ p2 )
!= ( sk21 @ p2 ) )
| ~ sk19
| ~ sk11
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26869]) ).
thf(26966,plain,
( ( ( sk2 @ sk6 )
!= sk21 )
| ~ sk19
| ~ sk11
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26870]) ).
thf(3034,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2182,77]) ).
thf(3035,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[3034]) ).
thf(3100,plain,
! [A: $i] :
( ( ( sk5 @ sk6 )
!= A )
| ( sk5 != sk1 )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[3035]) ).
thf(3122,plain,
( ( sk5 != sk1 )
| ( sk5 @ sk6 @ sk9 @ ( sk5 @ sk6 @ r1 ) )
| ( sk5 @ sk6 @ p1 ) ),
inference(simp,[status(thm)],[3100]) ).
thf(5301,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk18 @ ( sk1 @ r1 ) ) )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,4821]) ).
thf(5302,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk18 @ ( sk1 @ r1 ) ) )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[5301]) ).
thf(5323,plain,
! [A: $i] :
( ( A != sk18 )
| ( sk18 != sk1 )
| ( ( A @ sk32 )
!= sk18 )
| ~ ( A @ sk33 @ sk31 )
| ~ ( A @ sk33 @ sk33 @ p2 )
| ~ ( A @ sk33 @ sk24 )
| ~ ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[5302]) ).
thf(5345,plain,
( ( sk18 != sk1 )
| ( ( sk18 @ sk32 )
!= sk18 )
| ~ ( sk18 @ sk33 @ sk31 )
| ~ ( sk18 @ sk33 @ sk33 @ p2 )
| ~ ( sk18 @ sk33 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[5323]) ).
thf(4226,plain,
( ( ( sk5 @ sk6 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ( sk5 != sk1 )
| ~ $true
| ( sk5 @ sk6 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[355,2249]) ).
thf(4227,plain,
( ( ( sk5 @ sk6 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ( sk5 != sk1 )
| ( sk5 @ sk6 @ p3 ) ),
inference(simp,[status(thm)],[4226]) ).
thf(4233,plain,
( ( ( sk5 @ sk6 @ sk4 )
!= ( sk2 @ sk3 ) )
| ( sk5 != sk1 )
| ( sk5 @ sk6 @ p3 ) ),
inference(simp,[status(thm)],[4227]) ).
thf(167,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,17]) ).
thf(168,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[167]) ).
thf(169,plain,
( ( sk5 @ sk4 @ ( sk5 @ sk3 @ r1 ) )
| ( sk5 @ p3 ) ),
inference(pattern_uni,[status(thm)],[168:[bind(A,$thf( sk5 ))]]) ).
thf(35495,plain,
( ( ( sk8 @ sk10 @ p1 )
!= ( sk5 @ sk9 @ p1 ) )
| ~ $true
| ( sk5 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[35252,30091]) ).
thf(35496,plain,
( ( ( sk8 @ sk10 @ p1 )
!= ( sk5 @ sk9 @ p1 ) )
| ( sk5 @ p1 ) ),
inference(simp,[status(thm)],[35495]) ).
thf(35504,plain,
( ( ( sk8 @ sk10 )
!= ( sk5 @ sk9 ) )
| ( sk5 @ p1 ) ),
inference(simp,[status(thm)],[35496]) ).
thf(35277,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ p1 )
| ( A @ p1 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,111]) ).
thf(35278,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ p1 )
| ( A @ p1 )
| ~ sk11 ),
inference(simp,[status(thm)],[35277]) ).
thf(35279,plain,
( ( sk18 @ sk9 @ p1 )
| ( sk18 @ p1 )
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[35278:[bind(A,$thf( sk18 ))]]) ).
thf(2508,plain,
( ( ( sk15 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ~ $true
| ( sk15 @ p3 )
| sk11
| ~ sk12 ),
inference(paramod_ordered,[status(thm)],[330,32]) ).
thf(2509,plain,
( ( ( sk15 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ( sk15 @ p3 )
| sk11
| ~ sk12 ),
inference(simp,[status(thm)],[2508]) ).
thf(2515,plain,
( ( ( sk15 @ sk3 )
!= sk2 )
| ~ sk12
| ( sk15 @ p3 )
| sk11 ),
inference(simp,[status(thm)],[2509]) ).
thf(2811,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk5 @ ( sk1 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ $true
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(paramod_ordered,[status(thm)],[48,883]) ).
thf(2812,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk5 @ ( sk1 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[2811]) ).
thf(2888,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk18 != sk1 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[2812]) ).
thf(2905,plain,
( ( sk18 != sk1 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( sk5 @ p2 ) ),
inference(simp,[status(thm)],[2888]) ).
thf(2914,plain,
( ( sk18 != sk1 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| $false ),
inference(rewrite,[status(thm)],[2905,40]) ).
thf(2915,plain,
( ( sk18 != sk1 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[2914]) ).
thf(26605,plain,
( ( ( sk5 @ sk6 @ p2 )
!= ( sk18 @ p2 ) )
| ( sk18 != sk1 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ $true
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,2915]) ).
thf(26606,plain,
( ( ( sk5 @ sk6 @ p2 )
!= ( sk18 @ p2 ) )
| ( sk18 != sk1 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26605]) ).
thf(26700,plain,
( ( ( sk5 @ sk6 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26606]) ).
thf(36,plain,
! [B: $i,A: $i] :
( sk11
| sk12
| ( A @ ( B @ sk13 ) @ ( B @ r1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(109,plain,
! [B: $i,A: $i] :
( sk11
| sk12
| ( A @ ( B @ sk13 ) @ ( B @ r1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(26552,plain,
( ( ( sk8 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk1 )
| ~ ( sk8 @ sk31 )
| ~ $true
| ~ ( sk8 @ sk24 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,121]) ).
thf(26553,plain,
( ( ( sk8 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk1 )
| ~ ( sk8 @ sk31 )
| ~ ( sk8 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26552]) ).
thf(26695,plain,
( ( ( sk8 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( sk18 != sk1 )
| ~ ( sk8 @ sk31 )
| ~ ( sk8 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26553]) ).
thf(662,plain,
( ( ( sk5 @ sk4 @ p3 )
!= ( sk5 @ sk3 @ p3 ) )
| ~ $true
| ( sk5 @ p3 )
| ( sk5 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[308,420]) ).
thf(663,plain,
( ( ( sk5 @ sk4 @ p3 )
!= ( sk5 @ sk3 @ p3 ) )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[662]) ).
thf(669,plain,
( ( ( sk5 @ sk4 )
!= ( sk5 @ sk3 ) )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[663]) ).
thf(326,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,39]) ).
thf(327,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[326]) ).
thf(339,plain,
! [A: $i] :
( ( ( sk2 @ sk4 )
!= A )
| ( ( sk2 @ sk3 )
!= sk1 )
| ( A @ sk3 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[327]) ).
thf(346,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ( sk2 @ sk4 @ sk3 @ p3 )
| ( sk2 @ sk4 @ p3 ) ),
inference(simp,[status(thm)],[339]) ).
thf(4827,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ( sk2 @ sk4 @ sk3 @ p3 )
| $false ),
inference(rewrite,[status(thm)],[346,750]) ).
thf(4828,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ( sk2 @ sk4 @ sk3 @ p3 ) ),
inference(simp,[status(thm)],[4827]) ).
thf(4830,plain,
( ( ( sk8 @ sk4 @ p3 )
!= ( sk2 @ sk4 @ sk3 @ p3 ) )
| ~ $true
| ( sk8 @ p3 )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[4828,453]) ).
thf(4831,plain,
( ( ( sk8 @ sk4 @ p3 )
!= ( sk2 @ sk4 @ sk3 @ p3 ) )
| ( sk8 @ p3 )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[4830]) ).
thf(4861,plain,
( ( ( sk8 @ sk4 )
!= ( sk2 @ sk4 @ sk3 ) )
| ( ( sk2 @ sk3 )
!= sk1 )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[4831]) ).
thf(6265,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,83]) ).
thf(6266,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6265]) ).
thf(6337,plain,
! [A: $i] :
( ( ( sk2 @ sk4 )
!= A )
| ( ( sk2 @ sk3 )
!= sk1 )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6266]) ).
thf(6395,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ( sk2 @ sk4 @ sk10 @ ( sk2 @ sk4 @ sk9 @ r1 ) )
| ( sk2 @ sk4 @ p1 ) ),
inference(simp,[status(thm)],[6337]) ).
thf(1171,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk2 @ sk3 @ ( sk2 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[1159,106]) ).
thf(1172,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk2 @ sk3 @ ( sk2 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[1171]) ).
thf(1197,plain,
! [A: $i] :
( ( A
!= ( sk2 @ sk3 ) )
| ( sk18 != sk2 )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[1172]) ).
thf(1207,plain,
( ( sk18 != sk2 )
| ~ ( sk2 @ sk3 @ sk31 )
| ~ ( sk2 @ sk3 @ sk33 @ p2 )
| ~ ( sk2 @ sk3 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[1197]) ).
thf(677,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,61]) ).
thf(678,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[677]) ).
thf(679,plain,
( ( sk5 @ sk3 @ ( sk5 @ r1 ) )
| ( sk5 @ p3 ) ),
inference(pattern_uni,[status(thm)],[678:[bind(A,$thf( sk5 ))]]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk31 )
| ( A @ ( B @ sk34 ) @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk31 )
| ( A @ ( B @ sk34 ) @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[59]) ).
thf(22075,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 )
| ~ $true
| sk11
| ~ sk12 ),
inference(paramod_ordered,[status(thm)],[30,101]) ).
thf(22076,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 )
| sk11
| ~ sk12 ),
inference(simp,[status(thm)],[22075]) ).
thf(22077,plain,
( ~ ( sk15 @ sk36 @ p2 )
| ( sk15 @ p2 )
| sk11
| ~ sk12 ),
inference(pattern_uni,[status(thm)],[22076:[bind(A,$thf( sk15 ))]]) ).
thf(26571,plain,
( ( ( sk8 @ sk36 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ~ $true
| ( sk8 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26512,22080]) ).
thf(26572,plain,
( ( ( sk8 @ sk36 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[26571]) ).
thf(26727,plain,
( ( ( sk8 @ sk36 )
!= ( sk5 @ sk6 ) )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[26572]) ).
thf(2208,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2182,17]) ).
thf(2209,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[2208]) ).
thf(2240,plain,
! [A: $i] :
( ( ( sk5 @ sk6 )
!= A )
| ( sk5 != sk1 )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[2209]) ).
thf(2243,plain,
( ( sk5 != sk1 )
| ( sk5 @ sk6 @ sk4 @ ( sk5 @ sk6 @ sk3 @ r1 ) )
| ( sk5 @ sk6 @ p3 ) ),
inference(simp,[status(thm)],[2240]) ).
thf(3325,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk8 @ sk9 @ ( sk8 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[3314,106]) ).
thf(3326,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk8 @ sk9 @ ( sk8 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[3325]) ).
thf(3374,plain,
! [A: $i] :
( ( A
!= ( sk8 @ sk9 ) )
| ( sk18 != sk8 )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[3326]) ).
thf(3390,plain,
( ( sk18 != sk8 )
| ~ ( sk8 @ sk9 @ sk31 )
| ~ ( sk8 @ sk9 @ sk33 @ p2 )
| ~ ( sk8 @ sk9 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[3374]) ).
thf(2513,plain,
( ~ $true
| ( ( sk15 @ sk3 @ p3 )
!= ( sk15 @ p3 ) )
| ( sk15 @ p3 )
| sk11
| ~ sk12 ),
inference(eqfactor_ordered,[status(thm)],[330]) ).
thf(2519,plain,
( ( ( sk15 @ sk3 )
!= sk15 )
| ~ sk12
| ( sk15 @ p3 )
| sk11 ),
inference(simp,[status(thm)],[2513]) ).
thf(6777,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6695,75]) ).
thf(6778,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[6777]) ).
thf(6804,plain,
! [A: $i] :
( ( ( sk8 @ sk10 )
!= A )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[6778]) ).
thf(6827,plain,
( ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ sk6 @ ( sk8 @ sk10 @ r1 ) )
| ( sk8 @ sk10 @ p2 ) ),
inference(simp,[status(thm)],[6804]) ).
thf(8272,plain,
( ~ $true
| ( ( sk8 @ sk33 @ sk31 )
!= ( sk8 @ sk31 ) )
| ( sk18 != sk1 )
| ( ( sk8 @ sk32 )
!= sk18 )
| ~ ( sk8 @ sk33 @ sk33 @ p2 )
| ~ ( sk8 @ sk33 @ sk24 )
| ~ ( sk8 @ sk31 )
| ~ ( sk8 @ sk24 )
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[5355]) ).
thf(8275,plain,
( ( ( sk8 @ sk33 )
!= sk8 )
| ( sk18 != sk1 )
| ( ( sk8 @ sk32 )
!= sk18 )
| ~ ( sk8 @ sk33 @ sk33 @ p2 )
| ~ ( sk8 @ sk33 @ sk24 )
| ~ ( sk8 @ sk31 )
| ~ ( sk8 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[8272]) ).
thf(20659,plain,
( ~ $true
| ( ( sk8 @ sk33 @ sk24 )
!= ( sk8 @ sk24 ) )
| ( ( sk8 @ sk33 )
!= sk8 )
| ( sk18 != sk1 )
| ( ( sk8 @ sk32 )
!= sk18 )
| ~ ( sk8 @ sk33 @ sk33 @ p2 )
| ~ ( sk8 @ sk31 )
| ~ ( sk8 @ sk24 )
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[8275]) ).
thf(20665,plain,
( ( ( sk8 @ sk33 )
!= sk8 )
| ( ( sk8 @ sk33 )
!= sk8 )
| ( sk18 != sk1 )
| ( ( sk8 @ sk32 )
!= sk18 )
| ~ ( sk8 @ sk33 @ sk33 @ p2 )
| ~ ( sk8 @ sk31 )
| ~ ( sk8 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[20659]) ).
thf(20666,plain,
( ( ( sk8 @ sk33 )
!= sk8 )
| ( sk18 != sk1 )
| ( ( sk8 @ sk32 )
!= sk18 )
| ~ ( sk8 @ sk33 @ sk33 @ p2 )
| ~ ( sk8 @ sk31 )
| ~ ( sk8 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[20665]) ).
thf(719,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,61]) ).
thf(720,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ sk11 ),
inference(simp,[status(thm)],[719]) ).
thf(721,plain,
( ( sk18 @ sk3 @ ( sk18 @ r1 ) )
| ( sk18 @ p3 )
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[720:[bind(A,$thf( sk18 ))]]) ).
thf(8125,plain,
! [A: $i] :
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ~ sk19
| ( A @ sk22 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true
| ~ sk11
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[11,85]) ).
thf(8126,plain,
! [A: $i] :
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( A @ ( sk18 @ r1 ) ) )
| ( A @ sk22 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[8125]) ).
thf(8127,plain,
( ( sk20 @ sk22 @ ( sk20 @ r1 ) )
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[8126:[bind(A,$thf( sk20 ))]]) ).
thf(3576,plain,
( ( ( sk16 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ~ $true
| ( sk5 != sk1 )
| ( sk16 @ p3 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[408,32]) ).
thf(3577,plain,
( ( ( sk16 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ( sk5 != sk1 )
| ( sk16 @ p3 )
| sk11 ),
inference(simp,[status(thm)],[3576]) ).
thf(3587,plain,
( ( ( sk16 @ sk3 )
!= sk2 )
| ( sk5 != sk1 )
| ( sk16 @ p3 )
| sk11 ),
inference(simp,[status(thm)],[3577]) ).
thf(722,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,61]) ).
thf(723,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[722]) ).
thf(733,plain,
! [A: $i] :
( ( ( sk2 @ sk4 )
!= A )
| ( ( sk2 @ sk3 )
!= sk1 )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[723]) ).
thf(746,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ( sk2 @ sk4 @ sk3 @ ( sk2 @ sk4 @ r1 ) )
| ( sk2 @ sk4 @ p3 ) ),
inference(simp,[status(thm)],[733]) ).
thf(14156,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ( sk2 @ sk4 @ sk3 @ ( sk2 @ sk4 @ r1 ) )
| $false ),
inference(rewrite,[status(thm)],[746,750]) ).
thf(14157,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ( sk2 @ sk4 @ sk3 @ ( sk2 @ sk4 @ r1 ) ) ),
inference(simp,[status(thm)],[14156]) ).
thf(9254,plain,
( ( ( sk8 @ sk10 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ~ $true
| ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[6811,32]) ).
thf(9255,plain,
( ( ( sk8 @ sk10 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ p3 ) ),
inference(simp,[status(thm)],[9254]) ).
thf(9269,plain,
( ( ( sk8 @ sk10 @ sk3 )
!= sk2 )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ p3 ) ),
inference(simp,[status(thm)],[9255]) ).
thf(5192,plain,
( ( ( sk8 @ sk7 @ p2 )
!= ( sk16 @ p2 ) )
| ~ $true
| ( sk8 @ p2 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[7,5067]) ).
thf(5193,plain,
( ( ( sk8 @ sk7 @ p2 )
!= ( sk16 @ p2 ) )
| ( sk8 @ p2 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[5192]) ).
thf(5209,plain,
( ( ( sk8 @ sk7 )
!= sk16 )
| ( sk8 @ p2 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[5193]) ).
thf(767,plain,
( ( ( sk8 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ~ $true
| ( sk8 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[355,453]) ).
thf(768,plain,
( ( ( sk8 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[767]) ).
thf(773,plain,
( ( ( sk8 @ sk4 )
!= ( sk2 @ sk3 ) )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[768]) ).
thf(2809,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk2 @ sk3 @ ( sk2 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ $true
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(paramod_ordered,[status(thm)],[1159,883]) ).
thf(2810,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk2 @ sk3 @ ( sk2 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[2809]) ).
thf(2892,plain,
! [A: $i] :
( ( A
!= ( sk2 @ sk3 ) )
| ( sk18 != sk2 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[2810]) ).
thf(2909,plain,
( ( sk18 != sk2 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk18 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( sk2 @ sk3 @ p2 ) ),
inference(simp,[status(thm)],[2892]) ).
thf(5057,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,81]) ).
thf(5058,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[5057]) ).
thf(5078,plain,
! [A: $i] :
( ( ( sk2 @ sk4 )
!= A )
| ( ( sk2 @ sk3 )
!= sk1 )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[5058]) ).
thf(5112,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ~ ( sk2 @ sk4 @ sk7 @ p2 )
| ( sk2 @ sk4 @ p2 ) ),
inference(simp,[status(thm)],[5078]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( A @ sk24 )
| ( A @ ( B @ sk30 ) @ ( A @ ( B @ sk29 ) @ r1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( A @ sk24 )
| ( A @ ( B @ sk30 ) @ ( A @ ( B @ sk29 ) @ r1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[65]) ).
thf(27153,plain,
( ( ( sk8 @ sk6 @ p2 )
!= ( sk5 @ p2 ) )
| ~ $true
| ( sk8 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26334,40]) ).
thf(27154,plain,
( ( ( sk8 @ sk6 @ p2 )
!= ( sk5 @ p2 ) )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[27153]) ).
thf(27249,plain,
( ( ( sk8 @ sk6 )
!= sk5 )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[27154]) ).
thf(26861,plain,
( ( ( sk8 @ sk7 @ p2 )
!= ( sk2 @ sk6 @ p2 ) )
| ~ $true
| ( sk8 @ p2 )
| ( sk2 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26314,5067]) ).
thf(26862,plain,
( ( ( sk8 @ sk7 @ p2 )
!= ( sk2 @ sk6 @ p2 ) )
| ( sk8 @ p2 )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26861]) ).
thf(26932,plain,
( ( ( sk8 @ sk7 )
!= ( sk2 @ sk6 ) )
| ( sk8 @ p2 )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26862]) ).
thf(26597,plain,
( ( ( sk2 @ sk3 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk2 )
| ~ ( sk2 @ sk3 @ sk31 )
| ~ $true
| ~ ( sk2 @ sk3 @ sk24 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,1207]) ).
thf(26598,plain,
( ( ( sk2 @ sk3 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk2 )
| ~ ( sk2 @ sk3 @ sk31 )
| ~ ( sk2 @ sk3 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26597]) ).
thf(26691,plain,
( ( ( sk2 @ sk3 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( sk18 != sk2 )
| ~ ( sk2 @ sk3 @ sk31 )
| ~ ( sk2 @ sk3 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26598]) ).
thf(28581,plain,
( ( ( sk18 @ sk7 @ p2 )
!= ( sk18 @ sk6 @ p2 ) )
| ~ $true
| ( sk18 @ p2 )
| ~ sk11
| ( sk18 @ p2 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26317,5056]) ).
thf(28582,plain,
( ( ( sk18 @ sk7 @ p2 )
!= ( sk18 @ sk6 @ p2 ) )
| ( sk18 @ p2 )
| ~ sk11 ),
inference(simp,[status(thm)],[28581]) ).
thf(28744,plain,
( ( ( sk18 @ sk7 )
!= ( sk18 @ sk6 ) )
| ~ sk11
| ( sk18 @ p2 ) ),
inference(simp,[status(thm)],[28582]) ).
thf(29891,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk10 @ p1 )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,105]) ).
thf(29892,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk10 @ p1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[29891]) ).
thf(29893,plain,
( ~ ( sk2 @ sk10 @ p1 )
| ( sk2 @ p1 ) ),
inference(pattern_uni,[status(thm)],[29892:[bind(A,$thf( sk2 ))]]) ).
thf(28609,plain,
( ( ( sk18 @ sk36 @ p2 )
!= ( sk18 @ sk6 @ p2 ) )
| ~ $true
| ( sk18 @ p2 )
| ~ sk11
| ( sk18 @ p2 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26317,22065]) ).
thf(28610,plain,
( ( ( sk18 @ sk36 @ p2 )
!= ( sk18 @ sk6 @ p2 ) )
| ( sk18 @ p2 )
| ~ sk11 ),
inference(simp,[status(thm)],[28609]) ).
thf(28731,plain,
( ( ( sk18 @ sk36 )
!= ( sk18 @ sk6 ) )
| ~ sk11
| ( sk18 @ p2 ) ),
inference(simp,[status(thm)],[28610]) ).
thf(1510,plain,
( ( ( sk18 @ sk3 @ p3 )
!= ( sk18 @ p3 ) )
| ~ sk11
| ( sk18 @ p3 ) ),
inference(simp,[status(thm)],[1504]) ).
thf(26621,plain,
( ( ( sk5 @ sk6 @ p2 )
!= ( sk21 @ p2 ) )
| ~ sk19
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,54]) ).
thf(26622,plain,
( ( ( sk5 @ sk6 @ p2 )
!= ( sk21 @ p2 ) )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26621]) ).
thf(26748,plain,
( ( ( sk5 @ sk6 )
!= sk21 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26622]) ).
thf(8788,plain,
( ( ( sk20 @ sk22 @ p2 )
!= ( sk5 @ sk7 @ p2 ) )
| ~ $true
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[8604,5137]) ).
thf(8789,plain,
( ( ( sk20 @ sk22 @ p2 )
!= ( sk5 @ sk7 @ p2 ) )
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[8788]) ).
thf(8909,plain,
( ( ( sk20 @ sk22 )
!= ( sk5 @ sk7 ) )
| ~ sk19
| ~ sk11
| ( sk20 @ p2 ) ),
inference(simp,[status(thm)],[8789]) ).
thf(17438,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[16015,75]) ).
thf(17439,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17438]) ).
thf(17458,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) )
!= A )
| ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17439]) ).
thf(17468,plain,
( ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ sk6 @ ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ r1 ) )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ p2 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17458]) ).
thf(22260,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk20 @ sk22 @ p2 ) )
| ~ $true
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[8604,22253]) ).
thf(22261,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk20 @ sk22 @ p2 ) )
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[22260]) ).
thf(22277,plain,
( ( ( sk5 @ sk36 )
!= ( sk20 @ sk22 ) )
| ~ sk19
| ~ sk11
| ( sk20 @ p2 ) ),
inference(simp,[status(thm)],[22261]) ).
thf(399,plain,
( ( ( sk16 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ~ $true
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[319,32]) ).
thf(400,plain,
( ( ( sk16 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[399]) ).
thf(413,plain,
( ( ( sk16 @ sk3 )
!= sk2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[400]) ).
thf(765,plain,
( ( ( sk8 @ sk4 @ p3 )
!= ( sk5 @ sk3 @ p3 ) )
| ~ $true
| ( sk8 @ p3 )
| ( sk5 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[308,453]) ).
thf(766,plain,
( ( ( sk8 @ sk4 @ p3 )
!= ( sk5 @ sk3 @ p3 ) )
| ( sk8 @ p3 )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[765]) ).
thf(772,plain,
( ( ( sk8 @ sk4 )
!= ( sk5 @ sk3 ) )
| ( sk8 @ p3 )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[766]) ).
thf(26595,plain,
( ( ( sk2 @ sk7 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ~ $true
| ( sk2 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26512,5053]) ).
thf(26596,plain,
( ( ( sk2 @ sk7 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26595]) ).
thf(26736,plain,
( ( ( sk2 @ sk7 )
!= ( sk5 @ sk6 ) )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26596]) ).
thf(26859,plain,
( ( ( sk2 @ sk6 @ p2 )
!= ( sk18 @ p2 ) )
| ~ $true
| sk19
| ~ sk11
| ( sk2 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26314,45]) ).
thf(26860,plain,
( ( ( sk2 @ sk6 @ p2 )
!= ( sk18 @ p2 ) )
| sk19
| ~ sk11
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26859]) ).
thf(26967,plain,
( ( ( sk2 @ sk6 )
!= sk18 )
| ~ sk11
| sk19
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26860]) ).
thf(6781,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6695,83]) ).
thf(6782,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6781]) ).
thf(6787,plain,
! [A: $i] :
( ( ( sk8 @ sk10 )
!= A )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6782]) ).
thf(6810,plain,
( ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ sk10 @ ( sk8 @ sk10 @ sk9 @ r1 ) )
| ( sk8 @ sk10 @ p1 ) ),
inference(simp,[status(thm)],[6787]) ).
thf(30094,plain,
( ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ sk10 @ ( sk8 @ sk10 @ sk9 @ r1 ) )
| $false ),
inference(rewrite,[status(thm)],[6810,30091]) ).
thf(30095,plain,
( ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ sk10 @ ( sk8 @ sk10 @ sk9 @ r1 ) ) ),
inference(simp,[status(thm)],[30094]) ).
thf(5186,plain,
( ( ( sk8 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk8 @ p2 )
| ( sk16 != sk1 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[138,5067]) ).
thf(5187,plain,
( ( ( sk8 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk8 @ p2 )
| ( sk16 != sk1 )
| sk11 ),
inference(simp,[status(thm)],[5186]) ).
thf(5207,plain,
( ( ( sk8 @ sk7 )
!= sk1 )
| ( sk16 != sk1 )
| ( sk8 @ p2 )
| sk11 ),
inference(simp,[status(thm)],[5187]) ).
thf(4844,plain,
( ( ( sk2 @ sk4 @ sk3 @ p3 )
!= ( sk2 @ sk4 @ p3 ) )
| ~ $true
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[4828,750]) ).
thf(4845,plain,
( ( ( sk2 @ sk4 @ sk3 @ p3 )
!= ( sk2 @ sk4 @ p3 ) )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[4844]) ).
thf(4854,plain,
( ( ( sk2 @ sk4 @ sk3 )
!= ( sk2 @ sk4 ) )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[4845]) ).
thf(179,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,17]) ).
thf(180,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| ~ sk11 ),
inference(simp,[status(thm)],[179]) ).
thf(181,plain,
( ( sk18 @ sk4 @ ( sk18 @ sk3 @ r1 ) )
| ( sk18 @ p3 )
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[180:[bind(A,$thf( sk18 ))]]) ).
thf(895,plain,
! [A: $i] :
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( A @ ( sk8 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ $true
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 )
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[11,881]) ).
thf(896,plain,
! [A: $i] :
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( A @ ( sk8 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ( A @ p2 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[895]) ).
thf(937,plain,
! [A: $i] :
( ( sk20 != A )
| ( sk18 != sk8 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[896]) ).
thf(947,plain,
( ( sk18 != sk8 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( sk20 @ p2 ) ),
inference(simp,[status(thm)],[937]) ).
thf(4870,plain,
( ( ( sk2 @ sk4 @ sk4 @ p3 )
!= ( sk5 @ sk3 @ p3 ) )
| ( ( sk2 @ sk3 )
!= sk1 )
| ~ $true
| ( sk5 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[308,4863]) ).
thf(4871,plain,
( ( ( sk2 @ sk4 @ sk4 @ p3 )
!= ( sk5 @ sk3 @ p3 ) )
| ( ( sk2 @ sk3 )
!= sk1 )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[4870]) ).
thf(4887,plain,
( ( ( sk2 @ sk4 @ sk4 )
!= ( sk5 @ sk3 ) )
| ( ( sk2 @ sk3 )
!= sk1 )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[4871]) ).
thf(4433,plain,
( ( ( sk8 @ sk9 @ sk3 @ p3 )
!= ( sk8 @ sk9 @ p3 ) )
| ( sk8 != sk1 )
| ( sk8 @ sk9 @ p3 ) ),
inference(simp,[status(thm)],[4432]) ).
thf(6259,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,83]) ).
thf(6260,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6259]) ).
thf(6261,plain,
( ( sk2 @ sk10 @ ( sk2 @ sk9 @ r1 ) )
| ( sk2 @ p1 ) ),
inference(pattern_uni,[status(thm)],[6260:[bind(A,$thf( sk2 ))]]) ).
thf(69,plain,
! [B: $i,A: $i] :
( sk11
| sk12
| ~ ( A @ ( B @ sk14 ) @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(71,plain,
! [B: $i,A: $i] :
( sk11
| sk12
| ~ ( A @ ( B @ sk14 ) @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(5170,plain,
( ( ( sk2 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk2 @ p2 )
| ( sk16 != sk5 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[135,5053]) ).
thf(5171,plain,
( ( ( sk2 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk2 @ p2 )
| ( sk16 != sk5 )
| sk11 ),
inference(simp,[status(thm)],[5170]) ).
thf(5185,plain,
( ( ( sk2 @ sk7 )
!= sk1 )
| ( sk16 != sk5 )
| ( sk2 @ p2 )
| sk11 ),
inference(simp,[status(thm)],[5171]) ).
thf(2948,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1159,77]) ).
thf(2949,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[2948]) ).
thf(3096,plain,
! [A: $i] :
( ( ( sk2 @ sk3 )
!= A )
| ( sk2 != sk1 )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[2949]) ).
thf(3118,plain,
( ( sk2 != sk1 )
| ( sk2 @ sk3 @ sk9 @ ( sk2 @ sk3 @ r1 ) )
| ( sk2 @ sk3 @ p1 ) ),
inference(simp,[status(thm)],[3096]) ).
thf(8869,plain,
( ~ $true
| ( ( sk20 @ sk22 @ p2 )
!= ( sk20 @ p2 ) )
| ( sk20 @ p2 )
| ~ sk19
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[8604]) ).
thf(8877,plain,
( ( ( sk20 @ sk22 )
!= sk20 )
| ~ sk19
| ~ sk11
| ( sk20 @ p2 ) ),
inference(simp,[status(thm)],[8869]) ).
thf(4222,plain,
( ( ( sk5 @ sk6 @ sk4 @ p3 )
!= ( sk5 @ sk6 @ sk3 @ p3 ) )
| ( sk5 != sk1 )
| ~ $true
| ( sk5 @ sk6 @ p3 )
| ( sk5 != sk1 )
| ( sk5 @ sk6 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[2246,2249]) ).
thf(4223,plain,
( ( ( sk5 @ sk6 @ sk4 @ p3 )
!= ( sk5 @ sk6 @ sk3 @ p3 ) )
| ( sk5 != sk1 )
| ( sk5 @ sk6 @ p3 ) ),
inference(simp,[status(thm)],[4222]) ).
thf(4236,plain,
( ( ( sk5 @ sk6 @ sk4 )
!= ( sk5 @ sk6 @ sk3 ) )
| ( sk5 != sk1 )
| ( sk5 @ sk6 @ p3 ) ),
inference(simp,[status(thm)],[4223]) ).
thf(185,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,17]) ).
thf(186,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[185]) ).
thf(187,plain,
( ( sk8 @ sk4 @ ( sk8 @ sk3 @ r1 ) )
| ( sk8 @ p3 ) ),
inference(pattern_uni,[status(thm)],[186:[bind(A,$thf( sk8 ))]]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( A @ sk24 )
| ~ ( A @ ( B @ sk30 ) @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( A @ sk24 )
| ~ ( A @ ( B @ sk30 ) @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[62]) ).
thf(12,plain,
! [B: $i,A: $i] :
( sk11
| sk12
| ( A @ ( B @ sk13 ) @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(98,plain,
! [B: $i,A: $i] :
( sk11
| sk12
| ( A @ ( B @ sk13 ) @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(35535,plain,
( ( ( sk2 @ sk10 @ p1 )
!= ( sk8 @ sk9 @ p1 ) )
| ~ $true
| ( sk2 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[35530,29893]) ).
thf(35536,plain,
( ( ( sk2 @ sk10 @ p1 )
!= ( sk8 @ sk9 @ p1 ) )
| ( sk2 @ p1 ) ),
inference(simp,[status(thm)],[35535]) ).
thf(35544,plain,
( ( ( sk2 @ sk10 )
!= ( sk8 @ sk9 ) )
| ( sk2 @ p1 ) ),
inference(simp,[status(thm)],[35536]) ).
thf(1516,plain,
( ( ( sk18 @ sk4 @ p3 )
!= ( sk18 @ sk3 @ p3 ) )
| ~ $true
| ( sk18 @ p3 )
| ~ sk11
| ( sk18 @ p3 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[325,445]) ).
thf(1517,plain,
( ( ( sk18 @ sk4 @ p3 )
!= ( sk18 @ sk3 @ p3 ) )
| ( sk18 @ p3 )
| ~ sk11 ),
inference(simp,[status(thm)],[1516]) ).
thf(1524,plain,
( ( ( sk18 @ sk4 )
!= ( sk18 @ sk3 ) )
| ~ sk11
| ( sk18 @ p3 ) ),
inference(simp,[status(thm)],[1517]) ).
thf(3048,plain,
! [A: $i] :
( ( ( sk16 @ sk4 @ ( sk16 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ $true
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[255,77]) ).
thf(3049,plain,
! [A: $i] :
( ( ( sk16 @ sk4 @ ( sk16 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[3048]) ).
thf(3086,plain,
! [A: $i] :
( ( ( sk16 @ sk4 )
!= A )
| ( ( sk16 @ sk3 )
!= sk1 )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[3049]) ).
thf(3106,plain,
( ( ( sk16 @ sk3 )
!= sk1 )
| ( sk16 @ sk4 @ sk9 @ ( sk16 @ sk4 @ r1 ) )
| ( sk16 @ sk4 @ p1 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[3086]) ).
thf(26560,plain,
( ( ( sk18 @ sk36 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ~ $true
| ( sk18 @ p2 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,22065]) ).
thf(26561,plain,
( ( ( sk18 @ sk36 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 @ p2 )
| ~ sk11 ),
inference(simp,[status(thm)],[26560]) ).
thf(26741,plain,
( ( ( sk18 @ sk36 )
!= ( sk5 @ sk6 ) )
| ~ sk11
| ( sk18 @ p2 ) ),
inference(simp,[status(thm)],[26561]) ).
thf(359,plain,
( ( ( sk8 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ~ $true
| ( sk8 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[333,32]) ).
thf(360,plain,
( ( ( sk8 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[359]) ).
thf(362,plain,
( ( ( sk8 @ sk3 )
!= sk2 )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[360]) ).
thf(56,plain,
! [B: $i,A: $i] :
( sk11
| ~ ( A @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk15 @ r1 ) )
| ~ sk12 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(76,plain,
! [B: $i,A: $i] :
( sk11
| ~ ( A @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk15 @ r1 ) )
| ~ sk12 ),
inference(simp,[status(thm)],[56]) ).
thf(448,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| ~ $true
| sk11
| ~ sk12 ),
inference(paramod_ordered,[status(thm)],[30,41]) ).
thf(449,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk4 @ p3 )
| ( A @ p3 )
| sk11
| ~ sk12 ),
inference(simp,[status(thm)],[448]) ).
thf(450,plain,
( ~ ( sk15 @ sk4 @ p3 )
| ( sk15 @ p3 )
| sk11
| ~ sk12 ),
inference(pattern_uni,[status(thm)],[449:[bind(A,$thf( sk15 ))]]) ).
thf(2936,plain,
( ( ( sk15 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ~ $true
| ( sk15 @ p3 )
| sk11
| ~ sk12 ),
inference(paramod_ordered,[status(thm)],[355,450]) ).
thf(2937,plain,
( ( ( sk15 @ sk4 @ p3 )
!= ( sk2 @ sk3 @ p3 ) )
| ( sk15 @ p3 )
| sk11
| ~ sk12 ),
inference(simp,[status(thm)],[2936]) ).
thf(2943,plain,
( ( ( sk15 @ sk4 )
!= ( sk2 @ sk3 ) )
| ~ sk12
| ( sk15 @ p3 )
| sk11 ),
inference(simp,[status(thm)],[2937]) ).
thf(2934,plain,
( ( ( sk15 @ sk4 @ p3 )
!= ( sk15 @ sk3 @ p3 ) )
| ~ $true
| ( sk15 @ p3 )
| sk11
| ~ sk12
| ( sk15 @ p3 )
| sk11
| ~ sk12 ),
inference(paramod_ordered,[status(thm)],[330,450]) ).
thf(2935,plain,
( ( ( sk15 @ sk4 @ p3 )
!= ( sk15 @ sk3 @ p3 ) )
| ( sk15 @ p3 )
| sk11
| ~ sk12 ),
inference(simp,[status(thm)],[2934]) ).
thf(2945,plain,
( ( ( sk15 @ sk4 )
!= ( sk15 @ sk3 ) )
| ~ sk12
| ( sk15 @ p3 )
| sk11 ),
inference(simp,[status(thm)],[2935]) ).
thf(35518,plain,
( ( ( sk2 @ sk9 @ p1 )
!= ( sk8 @ p1 ) )
| ~ $true
| ( sk2 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[35276,51]) ).
thf(35519,plain,
( ( ( sk2 @ sk9 @ p1 )
!= ( sk8 @ p1 ) )
| ( sk2 @ p1 ) ),
inference(simp,[status(thm)],[35518]) ).
thf(35523,plain,
( ( ( sk2 @ sk9 )
!= sk8 )
| ( sk2 @ p1 ) ),
inference(simp,[status(thm)],[35519]) ).
thf(67,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk24 )
| ~ ( C @ p2 )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( A @ ( B @ sk28 ) @ r1 ) )
| ~ ( B @ sk25 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk24 )
| ~ ( C @ p2 )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( A @ ( B @ sk28 ) @ r1 ) )
| ~ ( B @ sk25 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[67]) ).
thf(724,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ $true
| sk11
| ~ sk12 ),
inference(paramod_ordered,[status(thm)],[30,61]) ).
thf(725,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| sk11
| ~ sk12 ),
inference(simp,[status(thm)],[724]) ).
thf(726,plain,
( ( sk15 @ sk3 @ ( sk15 @ r1 ) )
| ( sk15 @ p3 )
| sk11
| ~ sk12 ),
inference(pattern_uni,[status(thm)],[725:[bind(A,$thf( sk15 ))]]) ).
thf(4194,plain,
( ( ( sk5 @ sk6 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ~ $true
| ( sk5 != sk1 )
| ( sk5 @ sk6 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[2246,32]) ).
thf(4195,plain,
( ( ( sk5 @ sk6 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ( sk5 != sk1 )
| ( sk5 @ sk6 @ p3 ) ),
inference(simp,[status(thm)],[4194]) ).
thf(4208,plain,
( ( ( sk5 @ sk6 @ sk3 )
!= sk2 )
| ( sk5 != sk1 )
| ( sk5 @ sk6 @ p3 ) ),
inference(simp,[status(thm)],[4195]) ).
thf(232,plain,
( ( ( sk5 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk16 != sk5 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[135,40]) ).
thf(233,plain,
( ( ( sk5 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk16 != sk5 )
| sk11 ),
inference(simp,[status(thm)],[232]) ).
thf(240,plain,
( ( sk5 != sk1 )
| ( sk16 != sk5 )
| sk11 ),
inference(simp,[status(thm)],[233]) ).
thf(1022,plain,
( ( ( sk5 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk16 != sk15 )
| ~ sk12
| sk11 ),
inference(paramod_ordered,[status(thm)],[136,40]) ).
thf(1023,plain,
( ( ( sk5 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk16 != sk15 )
| ~ sk12
| sk11 ),
inference(simp,[status(thm)],[1022]) ).
thf(1029,plain,
( ( sk5 != sk1 )
| ( sk16 != sk15 )
| ~ sk12
| sk11 ),
inference(simp,[status(thm)],[1023]) ).
thf(35497,plain,
( ( ( sk5 @ sk9 @ p1 )
!= ( sk8 @ p1 ) )
| ~ $true
| ( sk5 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[35252,51]) ).
thf(35498,plain,
( ( ( sk5 @ sk9 @ p1 )
!= ( sk8 @ p1 ) )
| ( sk5 @ p1 ) ),
inference(simp,[status(thm)],[35497]) ).
thf(35503,plain,
( ( ( sk5 @ sk9 )
!= sk8 )
| ( sk5 @ p1 ) ),
inference(simp,[status(thm)],[35498]) ).
thf(5168,plain,
( ( ( sk2 @ sk7 @ p2 )
!= ( sk16 @ p2 ) )
| ~ $true
| ( sk2 @ p2 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[7,5053]) ).
thf(5169,plain,
( ( ( sk2 @ sk7 @ p2 )
!= ( sk16 @ p2 ) )
| ( sk2 @ p2 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[5168]) ).
thf(5180,plain,
( ( ( sk2 @ sk7 )
!= sk16 )
| ( sk2 @ p2 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[5169]) ).
thf(2194,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2182,61]) ).
thf(2195,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[2194]) ).
thf(2235,plain,
! [A: $i] :
( ( ( sk5 @ sk6 )
!= A )
| ( sk5 != sk1 )
| ( A @ sk3 @ ( A @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[2195]) ).
thf(2252,plain,
( ( sk5 != sk1 )
| ( sk5 @ sk6 @ sk3 @ ( sk5 @ sk6 @ r1 ) )
| ( sk5 @ sk6 @ p3 ) ),
inference(simp,[status(thm)],[2235]) ).
thf(660,plain,
( ( ( sk5 @ sk4 @ p3 )
!= ( sk8 @ sk3 @ p3 ) )
| ~ $true
| ( sk5 @ p3 )
| ( sk8 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[333,420]) ).
thf(661,plain,
( ( ( sk5 @ sk4 @ p3 )
!= ( sk8 @ sk3 @ p3 ) )
| ( sk5 @ p3 )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[660]) ).
thf(668,plain,
( ( ( sk5 @ sk4 )
!= ( sk8 @ sk3 ) )
| ( sk5 @ p3 )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[661]) ).
thf(26534,plain,
( ( ( sk18 @ sk32 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( ( sk18 @ sk32 )
!= sk18 )
| ( sk18 != sk1 )
| ~ $true
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,10751]) ).
thf(26535,plain,
( ( ( sk18 @ sk32 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( ( sk18 @ sk32 )
!= sk18 )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26534]) ).
thf(26716,plain,
( ( ( sk18 @ sk32 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( ( sk18 @ sk32 )
!= sk18 )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26535]) ).
thf(26329,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ p2 )
| ( A @ p2 )
| ~ $true
| sk11
| ~ sk12 ),
inference(paramod_ordered,[status(thm)],[30,102]) ).
thf(26330,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ p2 )
| ( A @ p2 )
| sk11
| ~ sk12 ),
inference(simp,[status(thm)],[26329]) ).
thf(26331,plain,
( ( sk15 @ sk6 @ p2 )
| ( sk15 @ p2 )
| sk11
| ~ sk12 ),
inference(pattern_uni,[status(thm)],[26330:[bind(A,$thf( sk15 ))]]) ).
thf(5194,plain,
( ( ( sk8 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk8 @ p2 )
| ( sk16 != sk5 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[135,5067]) ).
thf(5195,plain,
( ( ( sk8 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk8 @ p2 )
| ( sk16 != sk5 )
| sk11 ),
inference(simp,[status(thm)],[5194]) ).
thf(5202,plain,
( ( ( sk8 @ sk7 )
!= sk1 )
| ( sk16 != sk5 )
| ( sk8 @ p2 )
| sk11 ),
inference(simp,[status(thm)],[5195]) ).
thf(7911,plain,
( ~ $true
| ( ( sk5 @ sk33 @ sk31 )
!= ( sk5 @ sk31 ) )
| ( sk18 != sk1 )
| ( ( sk5 @ sk32 )
!= sk18 )
| ~ ( sk5 @ sk33 @ sk33 @ p2 )
| ~ ( sk5 @ sk33 @ sk24 )
| ~ ( sk5 @ sk31 )
| ~ ( sk5 @ sk24 )
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[5349]) ).
thf(7914,plain,
( ( ( sk5 @ sk33 )
!= sk5 )
| ( sk18 != sk1 )
| ( ( sk5 @ sk32 )
!= sk18 )
| ~ ( sk5 @ sk33 @ sk33 @ p2 )
| ~ ( sk5 @ sk33 @ sk24 )
| ~ ( sk5 @ sk31 )
| ~ ( sk5 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[7911]) ).
thf(8746,plain,
( ~ $true
| ( ( sk5 @ sk33 @ sk24 )
!= ( sk5 @ sk24 ) )
| ( ( sk5 @ sk33 )
!= sk5 )
| ( sk18 != sk1 )
| ( ( sk5 @ sk32 )
!= sk18 )
| ~ ( sk5 @ sk33 @ sk33 @ p2 )
| ~ ( sk5 @ sk31 )
| ~ ( sk5 @ sk24 )
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[7914]) ).
thf(8749,plain,
( ( ( sk5 @ sk33 )
!= sk5 )
| ( ( sk5 @ sk33 )
!= sk5 )
| ( sk18 != sk1 )
| ( ( sk5 @ sk32 )
!= sk18 )
| ~ ( sk5 @ sk33 @ sk33 @ p2 )
| ~ ( sk5 @ sk31 )
| ~ ( sk5 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[8746]) ).
thf(8750,plain,
( ( ( sk5 @ sk33 )
!= sk5 )
| ( sk18 != sk1 )
| ( ( sk5 @ sk32 )
!= sk18 )
| ~ ( sk5 @ sk33 @ sk33 @ p2 )
| ~ ( sk5 @ sk31 )
| ~ ( sk5 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[8749]) ).
thf(13,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk24 )
| ( B @ sk25 )
| ( A @ ( B @ ( C @ ( D @ sk26 ) ) ) @ ( D @ r1 ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(91,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk24 )
| ( B @ sk25 )
| ( A @ ( B @ ( C @ ( D @ sk26 ) ) ) @ ( D @ r1 ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[13]) ).
thf(23,plain,
! [A: $i] :
( ~ ( A @ p2 )
| ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(108,plain,
! [A: $i] :
( ~ ( A @ p2 )
| ( A @ sk31 )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[23]) ).
thf(2115,plain,
! [A: $i] :
( ( ( sk16 @ sk4 @ ( sk16 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[255,75]) ).
thf(2116,plain,
! [A: $i] :
( ( ( sk16 @ sk4 @ ( sk16 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[2115]) ).
thf(2151,plain,
! [A: $i] :
( ( ( sk16 @ sk4 )
!= A )
| ( ( sk16 @ sk3 )
!= sk1 )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[2116]) ).
thf(2171,plain,
( ( ( sk16 @ sk3 )
!= sk1 )
| ( sk16 @ sk4 @ sk6 @ ( sk16 @ sk4 @ r1 ) )
| ( sk16 @ sk4 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[2151]) ).
thf(287,plain,
( ( ( sk5 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk17 != sk16 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[162,40]) ).
thf(288,plain,
( ( ( sk5 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk17 != sk16 )
| sk11 ),
inference(simp,[status(thm)],[287]) ).
thf(299,plain,
( ( sk5 != sk1 )
| ( sk17 != sk16 )
| sk11 ),
inference(simp,[status(thm)],[288]) ).
thf(29894,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk10 @ p1 )
| ( A @ p1 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,105]) ).
thf(29895,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk10 @ p1 )
| ( A @ p1 )
| ~ sk11 ),
inference(simp,[status(thm)],[29894]) ).
thf(29896,plain,
( ~ ( sk18 @ sk10 @ p1 )
| ( sk18 @ p1 )
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[29895:[bind(A,$thf( sk18 ))]]) ).
thf(6736,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6695,17]) ).
thf(6737,plain,
! [A: $i] :
( ( ( sk8 @ sk10 @ ( sk8 @ sk9 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[6736]) ).
thf(6793,plain,
! [A: $i] :
( ( ( sk8 @ sk10 )
!= A )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[6737]) ).
thf(6816,plain,
( ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ sk4 @ ( sk8 @ sk10 @ sk3 @ r1 ) )
| ( sk8 @ sk10 @ p3 ) ),
inference(simp,[status(thm)],[6793]) ).
thf(24189,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk5 @ sk36 @ ( sk5 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[24159,106]) ).
thf(24190,plain,
! [A: $i] :
( ( ( A @ ( sk18 @ r1 ) )
!= ( sk5 @ sk36 @ ( sk5 @ r1 ) ) )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[24189]) ).
thf(24360,plain,
! [A: $i] :
( ( A
!= ( sk5 @ sk36 ) )
| ( sk18 != sk5 )
| ~ ( A @ sk31 )
| ~ ( A @ sk33 @ p2 )
| ~ ( A @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[24190]) ).
thf(24403,plain,
( ( sk18 != sk5 )
| ~ ( sk5 @ sk36 @ sk31 )
| ~ ( sk5 @ sk36 @ sk33 @ p2 )
| ~ ( sk5 @ sk36 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[24360]) ).
thf(26641,plain,
( ( ( sk5 @ sk36 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk5 )
| ~ ( sk5 @ sk36 @ sk31 )
| ~ $true
| ~ ( sk5 @ sk36 @ sk24 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,24403]) ).
thf(26642,plain,
( ( ( sk5 @ sk36 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk5 )
| ~ ( sk5 @ sk36 @ sk31 )
| ~ ( sk5 @ sk36 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26641]) ).
thf(26690,plain,
( ( ( sk5 @ sk36 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( sk18 != sk5 )
| ~ ( sk5 @ sk36 @ sk31 )
| ~ ( sk5 @ sk36 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26642]) ).
thf(35539,plain,
( ( ( sk8 @ sk10 @ p1 )
!= ( sk8 @ sk9 @ p1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35530,30091]) ).
thf(35540,plain,
( ( sk8 @ sk10 @ p1 )
!= ( sk8 @ sk9 @ p1 ) ),
inference(simp,[status(thm)],[35539]) ).
thf(35545,plain,
( ( sk8 @ sk10 )
!= ( sk8 @ sk9 ) ),
inference(simp,[status(thm)],[35540]) ).
thf(2950,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,77]) ).
thf(2951,plain,
! [A: $i] :
( ( ( sk5 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[2950]) ).
thf(2952,plain,
( ( sk5 @ sk9 @ ( sk5 @ r1 ) )
| ( sk5 @ p1 ) ),
inference(pattern_uni,[status(thm)],[2951:[bind(A,$thf( sk5 ))]]) ).
thf(4876,plain,
( ( ( sk2 @ sk4 @ sk4 @ p3 )
!= ( sk2 @ sk4 @ sk3 @ p3 ) )
| ( ( sk2 @ sk3 )
!= sk1 )
| ~ $true
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[4828,4863]) ).
thf(4877,plain,
( ( ( sk2 @ sk4 @ sk4 @ p3 )
!= ( sk2 @ sk4 @ sk3 @ p3 ) )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[4876]) ).
thf(4886,plain,
( ( ( sk2 @ sk4 @ sk4 )
!= ( sk2 @ sk4 @ sk3 ) )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[4877]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ p2 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ sk36 @ r1 ) )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ p2 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ sk36 @ r1 ) )
| ( A @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(4840,plain,
( ( ( sk2 @ sk4 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ~ $true
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[4828,32]) ).
thf(4841,plain,
( ( ( sk2 @ sk4 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[4840]) ).
thf(4859,plain,
( ( ( sk2 @ sk4 @ sk3 )
!= sk2 )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[4841]) ).
thf(27064,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk8 @ sk6 @ p2 ) )
| ~ $true
| ( sk8 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26334,5137]) ).
thf(27065,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk8 @ sk6 @ p2 ) )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[27064]) ).
thf(27235,plain,
( ( ( sk5 @ sk7 )
!= ( sk8 @ sk6 ) )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[27065]) ).
thf(27229,plain,
( ( ( sk8 @ sk6 @ p2 )
!= ( sk8 @ p2 ) )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[27177]) ).
thf(899,plain,
! [A: $i] :
( ( ( sk21 @ ( sk20 @ r1 ) )
!= ( A @ ( sk8 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ $true
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 )
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[20,881]) ).
thf(900,plain,
! [A: $i] :
( ( ( sk21 @ ( sk20 @ r1 ) )
!= ( A @ ( sk8 @ r1 ) ) )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ( A @ p2 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[899]) ).
thf(934,plain,
! [A: $i] :
( ( sk21 != A )
| ( sk20 != sk8 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( A @ p2 ) ),
inference(simp,[status(thm)],[900]) ).
thf(944,plain,
( ( sk20 != sk8 )
| ( ( sk21 @ sk33 )
!= sk1 )
| ( sk20 != sk18 )
| ~ ( sk21 @ sk31 )
| ~ ( sk8 @ p2 )
| ~ ( sk21 @ sk24 )
| ~ sk19
| ~ sk11
| ( sk21 @ p2 ) ),
inference(simp,[status(thm)],[934]) ).
thf(26613,plain,
( ( ( sk8 @ sk7 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ~ $true
| ( sk8 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26512,5067]) ).
thf(26614,plain,
( ( ( sk8 @ sk7 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[26613]) ).
thf(26707,plain,
( ( ( sk8 @ sk7 )
!= ( sk5 @ sk6 ) )
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[26614]) ).
thf(21964,plain,
! [A: $i] :
( ( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3314,101]) ).
thf(21965,plain,
! [A: $i] :
( ( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[21964]) ).
thf(22154,plain,
! [A: $i] :
( ( ( sk8 @ sk9 )
!= A )
| ( sk8 != sk1 )
| ~ ( A @ sk36 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[21965]) ).
thf(22192,plain,
( ( sk8 != sk1 )
| ~ ( sk8 @ sk9 @ sk36 @ p2 )
| ( sk8 @ sk9 @ p2 ) ),
inference(simp,[status(thm)],[22154]) ).
thf(26575,plain,
( ( ( sk20 @ sk33 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( ( sk20 @ sk33 )
!= sk20 )
| ( ( sk20 @ sk32 )
!= sk18 )
| ~ $true
| ~ ( sk20 @ sk31 )
| ~ ( sk20 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,6092]) ).
thf(26576,plain,
( ( ( sk20 @ sk33 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( ( sk20 @ sk33 )
!= sk20 )
| ( ( sk20 @ sk32 )
!= sk18 )
| ~ ( sk20 @ sk31 )
| ~ ( sk20 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26575]) ).
thf(26739,plain,
( ( ( sk20 @ sk33 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( ( sk20 @ sk33 )
!= sk20 )
| ( ( sk20 @ sk32 )
!= sk18 )
| ~ ( sk20 @ sk31 )
| ~ ( sk20 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[26576]) ).
thf(26828,plain,
( ( ( sk2 @ sk6 @ p2 )
!= ( sk15 @ p2 ) )
| sk11
| ~ $true
| ~ sk12
| ( sk2 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26314,28]) ).
thf(26829,plain,
( ( ( sk2 @ sk6 @ p2 )
!= ( sk15 @ p2 ) )
| sk11
| ~ sk12
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26828]) ).
thf(26972,plain,
( ( ( sk2 @ sk6 )
!= sk15 )
| ~ sk12
| sk11
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26829]) ).
thf(210,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,17]) ).
thf(211,plain,
! [A: $i] :
( ( ( sk2 @ sk4 @ ( sk2 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[210]) ).
thf(213,plain,
! [A: $i] :
( ( ( sk2 @ sk4 )
!= A )
| ( ( sk2 @ sk3 )
!= sk1 )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[211]) ).
thf(215,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ( sk2 @ sk4 @ sk4 @ ( sk2 @ sk4 @ sk3 @ r1 ) )
| ( sk2 @ sk4 @ p3 ) ),
inference(simp,[status(thm)],[213]) ).
thf(19924,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ( sk2 @ sk4 @ sk4 @ ( sk2 @ sk4 @ sk3 @ r1 ) )
| $false ),
inference(rewrite,[status(thm)],[215,750]) ).
thf(19925,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ( sk2 @ sk4 @ sk4 @ ( sk2 @ sk4 @ sk3 @ r1 ) ) ),
inference(simp,[status(thm)],[19924]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ sk19
| ~ ( A @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk21 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ~ sk19
| ~ ( A @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk21 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[44]) ).
thf(6178,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1159,83]) ).
thf(6179,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6178]) ).
thf(6331,plain,
! [A: $i] :
( ( ( sk2 @ sk3 )
!= A )
| ( sk2 != sk1 )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6179]) ).
thf(6389,plain,
( ( sk2 != sk1 )
| ( sk2 @ sk3 @ sk10 @ ( sk2 @ sk3 @ sk9 @ r1 ) )
| ( sk2 @ sk3 @ p1 ) ),
inference(simp,[status(thm)],[6331]) ).
thf(9300,plain,
( ( ( sk8 @ sk10 @ sk4 @ p3 )
!= ( sk8 @ sk10 @ sk3 @ p3 ) )
| ( ( sk8 @ sk9 )
!= sk1 )
| ~ $true
| ( sk8 @ sk10 @ p3 )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[6811,6818]) ).
thf(9301,plain,
( ( ( sk8 @ sk10 @ sk4 @ p3 )
!= ( sk8 @ sk10 @ sk3 @ p3 ) )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ p3 ) ),
inference(simp,[status(thm)],[9300]) ).
thf(9313,plain,
( ( ( sk8 @ sk10 @ sk4 )
!= ( sk8 @ sk10 @ sk3 ) )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ p3 ) ),
inference(simp,[status(thm)],[9301]) ).
thf(31,plain,
( sk11
| ( sk17 @ ( sk16 @ r1 ) )
| ( sk1 @ p2 ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(35499,plain,
( ~ $true
| ( ( sk5 @ sk9 @ p1 )
!= ( sk5 @ p1 ) )
| ( sk5 @ p1 ) ),
inference(eqfactor_ordered,[status(thm)],[35252]) ).
thf(35502,plain,
( ( ( sk5 @ sk9 )
!= sk5 )
| ( sk5 @ p1 ) ),
inference(simp,[status(thm)],[35499]) ).
thf(23931,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk36 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,99]) ).
thf(23932,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk36 @ ( A @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[23931]) ).
thf(23933,plain,
( ( sk8 @ sk36 @ ( sk8 @ r1 ) )
| ( sk8 @ p2 ) ),
inference(pattern_uni,[status(thm)],[23932:[bind(A,$thf( sk8 ))]]) ).
thf(28730,plain,
( ~ $true
| ( ( sk18 @ sk6 @ p2 )
!= ( sk18 @ p2 ) )
| ( sk18 @ p2 )
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[26317]) ).
thf(28750,plain,
( ( ( sk18 @ sk6 )
!= sk18 )
| ~ sk11
| ( sk18 @ p2 ) ),
inference(simp,[status(thm)],[28730]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk31 )
| ~ ( A @ ( B @ sk35 ) @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk31 )
| ~ ( A @ ( B @ sk35 ) @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[60]) ).
thf(26601,plain,
( ( ( sk8 @ sk9 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk8 )
| ~ ( sk8 @ sk9 @ sk31 )
| ~ $true
| ~ ( sk8 @ sk9 @ sk24 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,3390]) ).
thf(26602,plain,
( ( ( sk8 @ sk9 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk8 )
| ~ ( sk8 @ sk9 @ sk31 )
| ~ ( sk8 @ sk9 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26601]) ).
thf(26698,plain,
( ( ( sk8 @ sk9 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( sk18 != sk8 )
| ~ ( sk8 @ sk9 @ sk31 )
| ~ ( sk8 @ sk9 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26602]) ).
thf(22254,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk16 != sk1 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[138,22253]) ).
thf(22255,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk16 != sk1 )
| sk11 ),
inference(simp,[status(thm)],[22254]) ).
thf(22280,plain,
( ( ( sk5 @ sk36 )
!= sk1 )
| ( sk16 != sk1 )
| sk11 ),
inference(simp,[status(thm)],[22255]) ).
thf(9279,plain,
( ( ( sk8 @ sk10 @ sk3 )
!= ( sk8 @ sk10 ) )
| ( ( sk8 @ sk9 )
!= sk1 )
| ( sk8 @ sk10 @ p3 ) ),
inference(simp,[status(thm)],[9268]) ).
thf(361,plain,
( ~ $true
| ( ( sk8 @ sk3 @ p3 )
!= ( sk8 @ p3 ) )
| ( sk8 @ p3 ) ),
inference(eqfactor_ordered,[status(thm)],[333]) ).
thf(363,plain,
( ( ( sk8 @ sk3 @ p3 )
!= ( sk8 @ p3 ) )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[361]) ).
thf(35512,plain,
( ( ( sk2 @ sk10 @ p1 )
!= ( sk2 @ sk9 @ p1 ) )
| ~ $true
| ( sk2 @ p1 )
| ( sk2 @ p1 ) ),
inference(paramod_ordered,[status(thm)],[35276,29893]) ).
thf(35513,plain,
( ( ( sk2 @ sk10 @ p1 )
!= ( sk2 @ sk9 @ p1 ) )
| ( sk2 @ p1 ) ),
inference(simp,[status(thm)],[35512]) ).
thf(35526,plain,
( ( ( sk2 @ sk10 )
!= ( sk2 @ sk9 ) )
| ( sk2 @ p1 ) ),
inference(simp,[status(thm)],[35513]) ).
thf(4999,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1159,81]) ).
thf(5000,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[4999]) ).
thf(5087,plain,
! [A: $i] :
( ( ( sk2 @ sk3 )
!= A )
| ( sk2 != sk1 )
| ~ ( A @ sk7 @ p2 )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[5000]) ).
thf(5115,plain,
( ( sk2 != sk1 )
| ~ ( sk2 @ sk3 @ sk7 @ p2 )
| ( sk2 @ sk3 @ p2 ) ),
inference(simp,[status(thm)],[5087]) ).
thf(751,plain,
( ( ( sk2 @ sk4 @ p3 )
!= ( sk8 @ sk3 @ p3 ) )
| ~ $true
| ( sk8 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[333,750]) ).
thf(752,plain,
( ( ( sk2 @ sk4 @ p3 )
!= ( sk8 @ sk3 @ p3 ) )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[751]) ).
thf(759,plain,
( ( ( sk2 @ sk4 )
!= ( sk8 @ sk3 ) )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[752]) ).
thf(763,plain,
( ( ( sk8 @ sk4 @ p3 )
!= ( sk8 @ sk3 @ p3 ) )
| ~ $true
| ( sk8 @ p3 )
| ( sk8 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[333,453]) ).
thf(764,plain,
( ( ( sk8 @ sk4 @ p3 )
!= ( sk8 @ sk3 @ p3 ) )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[763]) ).
thf(771,plain,
( ( ( sk8 @ sk4 )
!= ( sk8 @ sk3 ) )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[764]) ).
thf(5162,plain,
( ( ( sk2 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk2 @ p2 )
| ( sk16 != sk1 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[138,5053]) ).
thf(5163,plain,
( ( ( sk2 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk2 @ p2 )
| ( sk16 != sk1 )
| sk11 ),
inference(simp,[status(thm)],[5162]) ).
thf(5179,plain,
( ( ( sk2 @ sk7 )
!= sk1 )
| ( sk16 != sk1 )
| ( sk2 @ p2 )
| sk11 ),
inference(simp,[status(thm)],[5163]) ).
thf(26902,plain,
( ( ( sk2 @ sk6 @ p2 )
!= ( sk5 @ p2 ) )
| ~ $true
| ( sk2 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26314,40]) ).
thf(26903,plain,
( ( ( sk2 @ sk6 @ p2 )
!= ( sk5 @ p2 ) )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26902]) ).
thf(27000,plain,
( ( ( sk2 @ sk6 )
!= sk5 )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26903]) ).
thf(1502,plain,
( ( ( sk18 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ~ $true
| ( sk18 @ p3 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[325,32]) ).
thf(1503,plain,
( ( ( sk18 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ( sk18 @ p3 )
| ~ sk11 ),
inference(simp,[status(thm)],[1502]) ).
thf(1508,plain,
( ( ( sk18 @ sk3 )
!= sk2 )
| ~ sk11
| ( sk18 @ p3 ) ),
inference(simp,[status(thm)],[1503]) ).
thf(9371,plain,
( ( ( sk18 @ ( sk18 @ r1 ) )
!= ( sk8 @ sk9 @ ( sk8 @ r1 ) ) )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[3314,8960]) ).
thf(9372,plain,
( ( ( sk18 @ ( sk18 @ r1 ) )
!= ( sk8 @ sk9 @ ( sk8 @ r1 ) ) )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[9371]) ).
thf(9482,plain,
( ( ( sk8 @ sk9 )
!= sk18 )
| ( sk18 != sk8 )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[9372]) ).
thf(2128,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[58,75]) ).
thf(2129,plain,
! [A: $i] :
( ( ( sk18 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ sk11 ),
inference(simp,[status(thm)],[2128]) ).
thf(2130,plain,
( ( sk18 @ sk6 @ ( sk18 @ r1 ) )
| ( sk18 @ p2 )
| ~ sk11 ),
inference(pattern_uni,[status(thm)],[2129:[bind(A,$thf( sk18 ))]]) ).
thf(348,plain,
( ( ( sk5 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ~ $true
| ( sk5 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[308,32]) ).
thf(349,plain,
( ( ( sk5 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[348]) ).
thf(351,plain,
( ( ( sk5 @ sk3 )
!= sk2 )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[349]) ).
thf(4836,plain,
( ( ( sk5 @ sk4 @ p3 )
!= ( sk2 @ sk4 @ sk3 @ p3 ) )
| ~ $true
| ( sk5 @ p3 )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[4828,420]) ).
thf(4837,plain,
( ( ( sk5 @ sk4 @ p3 )
!= ( sk2 @ sk4 @ sk3 @ p3 ) )
| ( sk5 @ p3 )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[4836]) ).
thf(4855,plain,
( ( ( sk5 @ sk4 )
!= ( sk2 @ sk4 @ sk3 ) )
| ( ( sk2 @ sk3 )
!= sk1 )
| ( sk5 @ p3 ) ),
inference(simp,[status(thm)],[4837]) ).
thf(23817,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk36 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[16015,99]) ).
thf(23818,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk36 @ ( A @ r1 ) )
| ( A @ p2 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[23817]) ).
thf(24005,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) )
!= A )
| ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( A @ sk36 @ ( A @ r1 ) )
| ( A @ p2 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[23818]) ).
thf(24115,plain,
( ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ sk36 @ ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ r1 ) )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ p2 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[24005]) ).
thf(29141,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk7 @ ( A @ sk6 @ r1 ) )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,104]) ).
thf(29142,plain,
! [A: $i] :
( ( ( sk8 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk7 @ ( A @ sk6 @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[29141]) ).
thf(29143,plain,
( ( sk8 @ sk7 @ ( sk8 @ sk6 @ r1 ) )
| ( sk8 @ p2 ) ),
inference(pattern_uni,[status(thm)],[29142:[bind(A,$thf( sk8 ))]]) ).
thf(26648,plain,
( ( ( sk18 @ sk32 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ $true
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,9500]) ).
thf(26649,plain,
( ( ( sk18 @ sk32 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26648]) ).
thf(26701,plain,
( ( ( sk18 @ sk32 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( sk18 != sk1 )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26649]) ).
thf(26654,plain,
( ( ( sk5 @ sk6 @ p2 )
!= ( sk5 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26512,40]) ).
thf(26655,plain,
( ( sk5 @ sk6 @ p2 )
!= ( sk5 @ p2 ) ),
inference(simp,[status(thm)],[26654]) ).
thf(26680,plain,
( ( sk5 @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[26655]) ).
thf(28706,plain,
( ( ( sk18 @ sk6 @ p2 )
!= ( sk5 @ p2 ) )
| ~ $true
| ( sk18 @ p2 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26317,40]) ).
thf(28707,plain,
( ( ( sk18 @ sk6 @ p2 )
!= ( sk5 @ p2 ) )
| ( sk18 @ p2 )
| ~ sk11 ),
inference(simp,[status(thm)],[28706]) ).
thf(28770,plain,
( ( ( sk18 @ sk6 )
!= sk5 )
| ~ sk11
| ( sk18 @ p2 ) ),
inference(simp,[status(thm)],[28707]) ).
thf(26949,plain,
( ( ( sk2 @ sk6 @ p2 )
!= ( sk2 @ p2 ) )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26926]) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk24 )
| ( B @ sk25 )
| ( A @ ( B @ ( C @ ( D @ sk27 ) ) ) @ ( A @ ( B @ ( C @ ( D @ sk26 ) ) ) @ r1 ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(82,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk24 )
| ( B @ sk25 )
| ( A @ ( B @ ( C @ ( D @ sk27 ) ) ) @ ( A @ ( B @ ( C @ ( D @ sk26 ) ) ) @ r1 ) )
| ( D @ p2 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[14]) ).
thf(1013,plain,
( ( ( sk15 @ p2 )
!= ( sk1 @ p2 ) )
| sk11
| ~ $true
| ~ sk12
| ( sk16 != sk15 )
| ~ sk12
| sk11 ),
inference(paramod_ordered,[status(thm)],[136,28]) ).
thf(1014,plain,
( ( ( sk15 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk16 != sk15 )
| ~ sk12
| sk11 ),
inference(simp,[status(thm)],[1013]) ).
thf(1030,plain,
( ( sk15 != sk1 )
| ( sk16 != sk15 )
| ~ sk12
| sk11 ),
inference(simp,[status(thm)],[1014]) ).
thf(7003,plain,
( ~ $true
| ( ( sk18 @ sk33 @ sk31 )
!= ( sk18 @ sk31 ) )
| ( sk18 != sk1 )
| ( ( sk18 @ sk32 )
!= sk18 )
| ~ ( sk18 @ sk33 @ sk33 @ p2 )
| ~ ( sk18 @ sk33 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[5345]) ).
thf(7006,plain,
( ( ( sk18 @ sk33 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk18 @ sk32 )
!= sk18 )
| ~ ( sk18 @ sk33 @ sk33 @ p2 )
| ~ ( sk18 @ sk33 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[7003]) ).
thf(8292,plain,
( ~ $true
| ( ( sk18 @ sk33 @ sk24 )
!= ( sk18 @ sk24 ) )
| ( ( sk18 @ sk33 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk18 @ sk32 )
!= sk18 )
| ~ ( sk18 @ sk33 @ sk33 @ p2 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(eqfactor_ordered,[status(thm)],[7006]) ).
thf(8295,plain,
( ( ( sk18 @ sk33 )
!= sk18 )
| ( ( sk18 @ sk33 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk18 @ sk32 )
!= sk18 )
| ~ ( sk18 @ sk33 @ sk33 @ p2 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[8292]) ).
thf(8296,plain,
( ( ( sk18 @ sk33 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk18 @ sk32 )
!= sk18 )
| ~ ( sk18 @ sk33 @ sk33 @ p2 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[8295]) ).
thf(26630,plain,
( ( ( sk5 @ sk36 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26512,22253]) ).
thf(26631,plain,
( ( sk5 @ sk36 @ p2 )
!= ( sk5 @ sk6 @ p2 ) ),
inference(simp,[status(thm)],[26630]) ).
thf(26734,plain,
( ( sk5 @ sk36 )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[26631]) ).
thf(17452,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| ~ $true
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[16015,83]) ).
thf(17453,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17452]) ).
thf(17455,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) )
!= A )
| ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( A @ sk10 @ ( A @ sk9 @ r1 ) )
| ( A @ p1 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17453]) ).
thf(17465,plain,
( ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ sk10 @ ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ sk9 @ r1 ) )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ p1 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17455]) ).
thf(3060,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,77]) ).
thf(3061,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[3060]) ).
thf(3062,plain,
( ( sk2 @ sk9 @ ( sk2 @ r1 ) )
| ( sk2 @ p1 ) ),
inference(pattern_uni,[status(thm)],[3061:[bind(A,$thf( sk2 ))]]) ).
thf(26916,plain,
( ( ( sk2 @ sk36 @ p2 )
!= ( sk2 @ sk6 @ p2 ) )
| ~ $true
| ( sk2 @ p2 )
| ( sk2 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26314,22062]) ).
thf(26917,plain,
( ( ( sk2 @ sk36 @ p2 )
!= ( sk2 @ sk6 @ p2 ) )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26916]) ).
thf(26933,plain,
( ( ( sk2 @ sk36 )
!= ( sk2 @ sk6 ) )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26917]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( A @ sk24 )
| ( A @ ( B @ sk29 ) @ ( B @ r1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( A @ sk24 )
| ( A @ ( B @ sk29 ) @ ( B @ r1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[55]) ).
thf(35228,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ p1 )
| ( A @ p1 )
| ~ $true
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[16015,111]) ).
thf(35229,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ p1 )
| ( A @ p1 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[35228]) ).
thf(35338,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) )
!= A )
| ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( A @ sk9 @ p1 )
| ( A @ p1 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[35229]) ).
thf(35413,plain,
( ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ sk9 @ p1 )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ p1 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[35338]) ).
thf(12253,plain,
( ( ( sk18 @ sk32 @ sk31 )
!= ( sk18 @ sk31 ) )
| ( sk20 != sk18 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[12251]) ).
thf(35243,plain,
! [A: $i] :
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ p1 )
| ( A @ p1 )
| ~ $true
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[35,111]) ).
thf(35244,plain,
! [A: $i] :
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ p1 )
| ( A @ p1 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[35243]) ).
thf(35245,plain,
( ( sk16 @ sk9 @ p1 )
| ( sk16 @ p1 )
| sk11
| ( sk1 @ p2 ) ),
inference(pattern_uni,[status(thm)],[35244:[bind(A,$thf( sk16 ))]]) ).
thf(4424,plain,
( ( ( sk8 @ sk9 @ sk3 @ p3 )
!= ( sk2 @ sk4 @ p3 ) )
| ~ $true
| ( sk8 != sk1 )
| ( sk8 @ sk9 @ p3 ) ),
inference(paramod_ordered,[status(thm)],[3402,750]) ).
thf(4425,plain,
( ( ( sk8 @ sk9 @ sk3 @ p3 )
!= ( sk2 @ sk4 @ p3 ) )
| ( sk8 != sk1 )
| ( sk8 @ sk9 @ p3 ) ),
inference(simp,[status(thm)],[4424]) ).
thf(4442,plain,
( ( ( sk8 @ sk9 @ sk3 )
!= ( sk2 @ sk4 ) )
| ( sk8 != sk1 )
| ( sk8 @ sk9 @ p3 ) ),
inference(simp,[status(thm)],[4425]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( A @ sk24 )
| ( A @ ( B @ sk29 ) @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( A @ sk24 )
| ( A @ ( B @ sk29 ) @ p2 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[22]) ).
thf(234,plain,
( ( ( sk15 @ p2 )
!= ( sk1 @ p2 ) )
| sk11
| ~ $true
| ~ sk12
| ( sk16 != sk5 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[135,28]) ).
thf(235,plain,
( ( ( sk15 @ p2 )
!= ( sk1 @ p2 ) )
| ~ sk12
| ( sk16 != sk5 )
| sk11 ),
inference(simp,[status(thm)],[234]) ).
thf(242,plain,
( ( sk15 != sk1 )
| ~ sk12
| ( sk16 != sk5 )
| sk11 ),
inference(simp,[status(thm)],[235]) ).
thf(9399,plain,
( ( ( sk18 @ ( sk18 @ r1 ) )
!= ( sk5 @ sk6 @ ( sk5 @ r1 ) ) )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ $true
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[2182,8960]) ).
thf(9400,plain,
( ( ( sk18 @ ( sk18 @ r1 ) )
!= ( sk5 @ sk6 @ ( sk5 @ r1 ) ) )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[9399]) ).
thf(9466,plain,
( ( ( sk5 @ sk6 )
!= sk18 )
| ( sk18 != sk5 )
| ~ ( sk18 @ sk32 @ sk31 )
| ~ ( sk18 @ sk32 @ sk33 @ p2 )
| ~ ( sk18 @ sk32 @ sk24 )
| ~ ( sk18 @ sk31 )
| ~ ( sk18 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[9400]) ).
thf(5138,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ~ $true
| ( sk16 != sk1 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[138,5137]) ).
thf(5139,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk1 @ p2 ) )
| ( sk16 != sk1 )
| sk11 ),
inference(simp,[status(thm)],[5138]) ).
thf(5159,plain,
( ( ( sk5 @ sk7 )
!= sk1 )
| ( sk16 != sk1 )
| sk11 ),
inference(simp,[status(thm)],[5139]) ).
thf(311,plain,
! [A: $i] :
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true
| ~ sk19
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[11,39]) ).
thf(312,plain,
! [A: $i] :
( ( ( sk20 @ ( sk18 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ sk19
| ~ sk11 ),
inference(simp,[status(thm)],[311]) ).
thf(334,plain,
! [A: $i] :
( ( sk20 != A )
| ( sk18 != sk1 )
| ~ sk19
| ~ sk11
| ( A @ sk3 @ p3 )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[312]) ).
thf(341,plain,
( ( sk18 != sk1 )
| ~ sk19
| ~ sk11
| ( sk20 @ sk3 @ p3 )
| ( sk20 @ p3 ) ),
inference(simp,[status(thm)],[334]) ).
thf(356,plain,
( ( ( sk2 @ sk3 @ p3 )
!= ( sk2 @ p3 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[355,32]) ).
thf(357,plain,
( ( sk2 @ sk3 @ p3 )
!= ( sk2 @ p3 ) ),
inference(simp,[status(thm)],[356]) ).
thf(358,plain,
( ( sk2 @ sk3 )
!= sk2 ),
inference(simp,[status(thm)],[357]) ).
thf(26524,plain,
( ( ( sk5 @ sk6 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk5 )
| ~ ( sk5 @ sk6 @ sk31 )
| ~ $true
| ~ ( sk5 @ sk6 @ sk24 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[26512,2248]) ).
thf(26525,plain,
( ( ( sk5 @ sk6 @ sk33 @ p2 )
!= ( sk5 @ sk6 @ p2 ) )
| ( sk18 != sk5 )
| ~ ( sk5 @ sk6 @ sk31 )
| ~ ( sk5 @ sk6 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26524]) ).
thf(26689,plain,
( ( ( sk5 @ sk6 @ sk33 )
!= ( sk5 @ sk6 ) )
| ( sk18 != sk5 )
| ~ ( sk5 @ sk6 @ sk31 )
| ~ ( sk5 @ sk6 @ sk24 )
| ~ sk11 ),
inference(simp,[status(thm)],[26525]) ).
thf(26813,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk2 @ sk6 @ p2 ) )
| ~ $true
| ( sk2 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26314,5137]) ).
thf(26814,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk2 @ sk6 @ p2 ) )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26813]) ).
thf(26943,plain,
( ( ( sk5 @ sk7 )
!= ( sk2 @ sk6 ) )
| ( sk2 @ p2 ) ),
inference(simp,[status(thm)],[26814]) ).
thf(27110,plain,
( ( ( sk8 @ sk6 @ p2 )
!= ( sk18 @ p2 ) )
| ~ $true
| sk19
| ~ sk11
| ( sk8 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26334,45]) ).
thf(27111,plain,
( ( ( sk8 @ sk6 @ p2 )
!= ( sk18 @ p2 ) )
| sk19
| ~ sk11
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[27110]) ).
thf(27180,plain,
( ( ( sk8 @ sk6 )
!= sk18 )
| ~ sk11
| sk19
| ( sk8 @ p2 ) ),
inference(simp,[status(thm)],[27111]) ).
thf(2125,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,75]) ).
thf(2126,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[2125]) ).
thf(2127,plain,
( ( sk2 @ sk6 @ ( sk2 @ r1 ) )
| ( sk2 @ p2 ) ),
inference(pattern_uni,[status(thm)],[2126:[bind(A,$thf( sk2 ))]]) ).
thf(35501,plain,
( ( ( sk5 @ sk9 @ p1 )
!= ( sk5 @ p1 ) )
| ( sk5 @ p1 ) ),
inference(simp,[status(thm)],[35499]) ).
thf(4206,plain,
( ( ( sk5 @ sk6 @ sk3 )
!= ( sk5 @ sk6 ) )
| ( sk5 != sk1 )
| ( sk5 @ sk6 @ p3 ) ),
inference(simp,[status(thm)],[4204]) ).
thf(1500,plain,
( ( ( sk2 @ sk4 @ p3 )
!= ( sk18 @ sk3 @ p3 ) )
| ~ $true
| ( sk18 @ p3 )
| ~ sk11 ),
inference(paramod_ordered,[status(thm)],[325,750]) ).
thf(1501,plain,
( ( ( sk2 @ sk4 @ p3 )
!= ( sk18 @ sk3 @ p3 ) )
| ( sk18 @ p3 )
| ~ sk11 ),
inference(simp,[status(thm)],[1500]) ).
thf(1505,plain,
( ( ( sk2 @ sk4 )
!= ( sk18 @ sk3 ) )
| ~ sk11
| ( sk18 @ p3 ) ),
inference(simp,[status(thm)],[1501]) ).
thf(26577,plain,
( ( ( sk5 @ sk6 @ p2 )
!= ( sk17 @ p2 ) )
| sk11
| ~ $true
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[26512,70]) ).
thf(26578,plain,
( ( ( sk5 @ sk6 @ p2 )
!= ( sk17 @ p2 ) )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[26577]) ).
thf(26749,plain,
( ( ( sk5 @ sk6 )
!= sk17 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[26578]) ).
thf(3074,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ $true
| sk11
| ~ sk12 ),
inference(paramod_ordered,[status(thm)],[30,77]) ).
thf(3075,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| sk11
| ~ sk12 ),
inference(simp,[status(thm)],[3074]) ).
thf(3076,plain,
( ( sk15 @ sk9 @ ( sk15 @ r1 ) )
| ( sk15 @ p1 )
| sk11
| ~ sk12 ),
inference(pattern_uni,[status(thm)],[3075:[bind(A,$thf( sk15 ))]]) ).
thf(270,plain,
( ( ( sk15 @ p2 )
!= ( sk1 @ p2 ) )
| sk11
| ~ $true
| ~ sk12
| ( sk16 != sk1 )
| sk11 ),
inference(paramod_ordered,[status(thm)],[138,28]) ).
thf(271,plain,
( ( ( sk15 @ p2 )
!= ( sk1 @ p2 ) )
| ~ sk12
| ( sk16 != sk1 )
| sk11 ),
inference(simp,[status(thm)],[270]) ).
thf(277,plain,
( ( sk15 != sk1 )
| ~ sk12
| ( sk16 != sk1 )
| sk11 ),
inference(simp,[status(thm)],[271]) ).
thf(3343,plain,
! [A: $i] :
( ( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3314,17]) ).
thf(3344,plain,
! [A: $i] :
( ( ( sk8 @ sk9 @ ( sk8 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[3343]) ).
thf(3378,plain,
! [A: $i] :
( ( ( sk8 @ sk9 )
!= A )
| ( sk8 != sk1 )
| ( A @ sk4 @ ( A @ sk3 @ r1 ) )
| ( A @ p3 ) ),
inference(simp,[status(thm)],[3344]) ).
thf(3394,plain,
( ( sk8 != sk1 )
| ( sk8 @ sk9 @ sk4 @ ( sk8 @ sk9 @ sk3 @ r1 ) )
| ( sk8 @ sk9 @ p3 ) ),
inference(simp,[status(thm)],[3378]) ).
thf(17391,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[16015,39]) ).
thf(17392,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ ( sk16 @ ( sk16 @ sk3 @ sk13 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17391]) ).
thf(17459,plain,
! [A: $i] :
( ( ( sk16 @ ( sk16 @ sk3 @ sk14 ) )
!= A )
| ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17392]) ).
thf(17469,plain,
( ( ( sk16 @ ( sk16 @ sk3 @ sk13 ) )
!= sk1 )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ sk3 @ p3 )
| ( sk16 @ ( sk16 @ sk3 @ sk14 ) @ p3 )
| sk12
| ( sk16 @ sk3 @ p2 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[17459]) ).
thf(2136,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true
| sk11
| ~ sk12 ),
inference(paramod_ordered,[status(thm)],[30,75]) ).
thf(2137,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| sk11
| ~ sk12 ),
inference(simp,[status(thm)],[2136]) ).
thf(2138,plain,
( ( sk15 @ sk6 @ ( sk15 @ r1 ) )
| ( sk15 @ p2 )
| sk11
| ~ sk12 ),
inference(pattern_uni,[status(thm)],[2137:[bind(A,$thf( sk15 ))]]) ).
thf(5144,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk16 @ p2 ) )
| ~ $true
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[7,5137]) ).
thf(5145,plain,
( ( ( sk5 @ sk7 @ p2 )
!= ( sk16 @ p2 ) )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[5144]) ).
thf(5155,plain,
( ( ( sk5 @ sk7 )
!= sk16 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[5145]) ).
thf(26580,plain,
( ( ( sk5 @ sk6 @ p2 )
!= ( sk15 @ p2 ) )
| sk11
| ~ $true
| ~ sk12 ),
inference(paramod_ordered,[status(thm)],[26512,28]) ).
thf(26581,plain,
( ( ( sk5 @ sk6 @ p2 )
!= ( sk15 @ p2 ) )
| sk11
| ~ sk12 ),
inference(simp,[status(thm)],[26580]) ).
thf(26693,plain,
( ( ( sk5 @ sk6 )
!= sk15 )
| ~ sk12
| sk11 ),
inference(simp,[status(thm)],[26581]) ).
thf(652,plain,
! [A: $i] :
( ( ( sk16 @ sk4 @ ( sk16 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ~ $true
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[255,39]) ).
thf(653,plain,
! [A: $i] :
( ( ( sk16 @ sk4 @ ( sk16 @ sk3 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[652]) ).
thf(655,plain,
! [A: $i] :
( ( ( sk16 @ sk4 )
!= A )
| ( ( sk16 @ sk3 )
!= sk1 )
| ( A @ sk3 @ p3 )
| ( A @ p3 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[653]) ).
thf(659,plain,
( ( ( sk16 @ sk3 )
!= sk1 )
| ( sk16 @ sk4 @ sk3 @ p3 )
| ( sk16 @ sk4 @ p3 )
| ( sk16 @ p3 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[655]) ).
thf(2033,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1159,75]) ).
thf(2034,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[2033]) ).
thf(2150,plain,
! [A: $i] :
( ( ( sk2 @ sk3 )
!= A )
| ( sk2 != sk1 )
| ( A @ sk6 @ ( A @ r1 ) )
| ( A @ p2 ) ),
inference(simp,[status(thm)],[2034]) ).
thf(2170,plain,
( ( sk2 != sk1 )
| ( sk2 @ sk3 @ sk6 @ ( sk2 @ sk3 @ r1 ) )
| ( sk2 @ sk3 @ p2 ) ),
inference(simp,[status(thm)],[2150]) ).
thf(3045,plain,
! [A: $i] :
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| ~ $true
| sk11
| ( sk1 @ p2 ) ),
inference(paramod_ordered,[status(thm)],[35,77]) ).
thf(3046,plain,
! [A: $i] :
( ( ( sk16 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk9 @ ( A @ r1 ) )
| ( A @ p1 )
| sk11
| ( sk1 @ p2 ) ),
inference(simp,[status(thm)],[3045]) ).
thf(3047,plain,
( ( sk16 @ sk9 @ ( sk16 @ r1 ) )
| ( sk16 @ p1 )
| sk11
| ( sk1 @ p2 ) ),
inference(pattern_uni,[status(thm)],[3046:[bind(A,$thf( sk16 ))]]) ).
thf(364,plain,
( ( ( sk8 @ sk3 )
!= sk8 )
| ( sk8 @ p3 ) ),
inference(simp,[status(thm)],[361]) ).
thf(63,plain,
! [A: $i] :
( ~ sk19
| ( A @ sk23 @ ( A @ sk22 @ r1 ) )
| ( A @ p2 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(100,plain,
! [A: $i] :
( ~ sk19
| ( A @ sk23 @ ( A @ sk22 @ r1 ) )
| ( A @ p2 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[63]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk31 )
| ( A @ ( B @ sk35 ) @ ( A @ ( B @ sk34 ) @ r1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk31 )
| ( A @ ( B @ sk35 ) @ ( A @ ( B @ sk34 ) @ r1 ) )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ sk24 )
| ~ ( A @ ( sk18 @ r1 ) )
| ~ sk11 ),
inference(simp,[status(thm)],[53]) ).
thf(45871,plain,
$false,
inference(e,[status(thm)],[2163,8960,101,3399,333,3397,8887,88,352,9273,138,30093,760,5205,6819,26746,22279,1205,4592,24373,35500,408,19142,276,1522,6695,32631,308,2248,26314,3402,26679,3120,26950,142,26699,2141,27227,945,9278,26753,26702,670,35527,4403,747,10726,5178,6370,27230,5056,301,4439,4896,184,10751,110,1511,125,22229,26718,8880,26934,5064,5130,5160,5355,20,29869,17466,93,881,325,28751,78,26696,29112,2520,4205,7107,4443,3393,6135,106,121,5156,84,353,26955,9319,147,6809,61,22065,453,26750,89,26724,411,5137,4211,74,29457,5157,117,22282,35547,35522,27253,22080,102,27221,6092,4893,3591,85,26703,761,26678,26735,13519,2249,22524,4434,137,35252,6264,28,5349,26983,23903,26747,70,4821,8899,729,26445,17467,9455,92,22278,22284,3065,97,35543,28785,26334,1159,4316,23900,435,3314,26966,3122,5345,8604,4233,169,35504,35279,5053,2515,26700,420,109,26695,77,669,4861,6395,1207,679,96,22077,26727,2243,3390,41,2519,6827,20666,721,8127,105,3587,14157,9269,2915,5209,773,2909,5112,73,27249,26932,26691,28744,29893,28731,32,45,6243,17,3396,750,1510,26748,8909,17468,22277,413,772,5067,26512,445,26736,26967,30095,5207,9496,4854,181,947,4887,4433,6261,86,71,5185,3118,54,8877,713,4236,187,113,2246,7,39,98,35544,81,1524,4828,3106,26741,362,76,2943,2945,6834,2182,35523,16015,103,22253,726,4208,240,1029,35503,5180,2252,668,26716,26331,5202,8750,621,91,108,330,6811,2171,883,135,299,3,80,29896,6816,35276,26690,35,35545,2952,4886,255,112,4859,27235,355,27229,162,944,24403,26707,22192,26739,26972,48,19925,95,6389,30091,9313,31,35502,23933,28750,9500,11,72,26698,22280,9279,450,363,87,29724,35526,5115,759,104,771,5179,99,27000,40,1508,9482,2130,319,6818,5351,35530,351,8,4855,58,24115,29143,26701,26680,28770,26949,82,214,75,1030,207,26317,151,8296,30,51,26734,19,1757,17465,3062,24159,26933,107,136,35413,12253,35245,4442,94,242,9466,5159,341,358,79,26689,22062,26943,27180,2127,35501,4206,1505,26749,3076,277,3394,17469,2138,5155,26693,83,659,4863,2170,5293,3047,364,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL642+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41 % Computer : n017.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Fri Sep 25 22:48:02 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 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
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.19 % [INFO] Parsing done (195ms).
% 1.50/1.20 % [INFO] Running in sequential loop mode.
% 2.18/1.61 % [INFO] eprover registered as external prover.
% 2.18/1.61 % [INFO] Scanning for conjecture ...
% 2.39/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.60/1.81 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.60/1.81 % [INFO] Problem is first-order (TPTP FOF).
% 2.60/1.82 % [INFO] Type checking passed.
% 2.60/1.83 % [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 ...
% 101.45/22.01 % External prover 'e' found a proof!
% 101.45/22.01 % [INFO] Killing All external provers ...
% 101.45/22.01 % Time passed: 21453ms (effective reasoning time: 20803ms)
% 101.45/22.01 % 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)>
% 101.45/22.02 % Axioms used in derivation (0):
% 101.45/22.02 % No. of inferences in proof: 1225
% 101.45/22.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21453 ms resp. 20803 ms w/o parsing
% 105.69/22.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 105.69/22.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------