%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL670+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n012.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 07:52:27 AM UTC 2026
% Result : Theorem 135.99s 36.22s
% Output : Refutation 134.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 2300 ( 140 unt; 0 typ; 15 def)
% Number of atoms : 10134 (2997 equ; 0 cnn)
% Maximal formula atoms : 100 ( 4 avg)
% Number of connectives : 29164 (6011 ~;5242 |; 51 &;17860 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 52 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 7 con; 0-3 aty)
% Number of variables : 1786 ( 20 ^;1747 !; 4 ?;1786 :)
% ( 0 !>; 0 ?*; 0 @-; 15 @+)
% Comments :
%------------------------------------------------------------------------------
thf(r1_decl,type,
r1: $i > $i > $o ).
thf(p4_decl,type,
p4: $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 > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $o ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $o ).
thf(sk8_decl,type,
sk8: $i > $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk15_decl,type,
sk15: $i ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ~ ( C @ p2 )
| ! [D: $i] :
( ( D @ p3 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( A @ r1 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C @ p3 )
| ~ ( C @ ( B @ ( A @ sk2 ) @ r1 ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( D @ p3 )
| ~ ( D @ ( A @ r1 ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( A @ r1 ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( A @ r1 ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( D @ p3 )
| ~ ( D @ ( C @ ( B @ ( A @ sk8 ) ) @ r1 ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ! [C: $i] :
( ~ ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
~ ( ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] :
~ ( ~ ! [B: $i] :
( ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk12 @ r1 ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
~ ( ( A @ p1 )
| ~ ( A @ ( sk12 @ r1 ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( sk1 @ r1 ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) ).
thf(1,conjecture,
~ ? [A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
thf(2,negated_conjecture,
~ ~ ? [A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ~ ? [A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
? [A: $i] :
~ ( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ! [C: $i] :
( ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ! [D: $i] :
( ~ ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ~ ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ~ ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ! [C: $i] :
( ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ( D @ p1 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ( ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ! [D: $i] :
( ~ ! [E: $i] :
( ~ ( E @ p2 )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ! [E: $i] :
( ~ ! [F: $i] :
( ~ ( F @ p2 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
& ( C @ p2 )
& ~ ! [D: $i] :
( ~ ( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ~ ! [D: $i] :
( ~ ( D @ p2 )
| ! [E: $i] :
( ( E @ p3 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( B @ p4 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(miniscope,[status(thm)],[5]) ).
thf(7,plain,
! [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] :
( ( ( P @ sk17 @ p1 )
| ~ ( R @ p1 )
| ~ ( R @ ( Q @ r1 ) )
| ~ ( Q @ ( P @ r1 ) )
| ~ ( P @ ( sk1 @ r1 ) ) )
& ( ( P @ sk17 @ ( P @ r1 ) )
| ~ ( R @ p1 )
| ~ ( R @ ( Q @ r1 ) )
| ~ ( Q @ ( P @ r1 ) )
| ~ ( P @ ( sk1 @ r1 ) ) )
& ( ~ ( O @ sk16 @ p2 )
| ~ ( O @ ( sk15 @ r1 ) ) )
& ( ( O @ sk16 @ ( O @ r1 ) )
| ~ ( O @ ( sk15 @ r1 ) ) )
& ( sk15 @ ( sk1 @ r1 ) )
& ~ ( sk14 @ p1 )
& ( sk14 @ ( sk12 @ r1 ) )
& ( ( N @ p1 )
| ~ ( N @ ( sk13 @ r1 ) ) )
& ( sk13 @ ( sk12 @ r1 ) )
& ( sk12 @ ( sk1 @ r1 ) )
& ( ~ ( K @ sk11 @ p1 )
| ( M @ p1 )
| ~ ( M @ ( L @ r1 ) )
| ~ ( L @ ( K @ r1 ) )
| ~ ( K @ ( sk1 @ r1 ) ) )
& ( ( K @ sk11 @ ( K @ r1 ) )
| ( M @ p1 )
| ~ ( M @ ( L @ r1 ) )
| ~ ( L @ ( K @ r1 ) )
| ~ ( K @ ( sk1 @ r1 ) ) )
& ( ~ ( J @ p2 )
| ~ ( J @ ( B @ sk10 @ r1 ) )
| ( B @ sk7 )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ( B @ sk10 @ ( B @ r1 ) )
| ( B @ sk7 )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( B @ sk7 )
| ( B @ ( H @ ( I @ sk8 ) ) @ p2 )
| ~ ( I @ ( H @ r1 ) )
| ~ ( H @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( B @ sk7 )
| ~ ( B @ ( H @ ( I @ sk9 ) ) @ p3 )
| ~ ( I @ ( H @ r1 ) )
| ~ ( H @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( B @ sk7 )
| ( B @ ( H @ ( I @ sk9 ) ) @ ( B @ ( H @ ( I @ sk8 ) ) @ r1 ) )
| ~ ( I @ ( H @ r1 ) )
| ~ ( H @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( B @ sk7 )
| ( B @ ( H @ ( I @ sk8 ) ) @ ( I @ r1 ) )
| ~ ( I @ ( H @ r1 ) )
| ~ ( H @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( G @ p2 )
| ~ ( G @ ( B @ ( D @ ( F @ sk6 ) ) @ r1 ) )
| ~ ( F @ ( D @ r1 ) )
| ~ ( D @ p2 )
| ( D @ sk4 )
| ~ ( D @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ( B @ ( D @ ( F @ sk6 ) ) @ ( F @ r1 ) )
| ~ ( F @ ( D @ r1 ) )
| ~ ( D @ p2 )
| ( D @ sk4 )
| ~ ( D @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( D @ sk4 )
| ( E @ p2 )
| ~ ( E @ ( D @ r1 ) )
| ~ ( D @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( D @ sk4 )
| ~ ( B @ ( D @ ( E @ sk5 ) ) @ p3 )
| ~ ( E @ ( D @ r1 ) )
| ~ ( D @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( D @ sk4 )
| ( B @ ( D @ ( E @ sk5 ) ) @ ( E @ r1 ) )
| ~ ( E @ ( D @ r1 ) )
| ~ ( D @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ( B @ ( C @ sk2 ) @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( B @ ( C @ sk3 ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ( B @ ( C @ sk3 ) @ ( B @ ( C @ sk2 ) @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ( B @ ( C @ sk2 ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) )
& ( ~ ( A @ p4 )
| ~ ( A @ ( sk1 @ r1 ) ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(24,plain,
sk12 @ ( sk1 @ r1 ),
inference(cnfConj,[status(thm)],[7]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(1728,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,42]) ).
thf(1729,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[1728]) ).
thf(1730,plain,
( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[1729:[bind(A,$thf( sk1 )),bind(B,$thf( sk12 ))]]) ).
thf(3,axiom,
! [A: $i] : ( A @ ( A @ r1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(58,plain,
! [A: $i] : ( A @ ( A @ r1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(59,plain,
! [A: $i] : ( A @ ( A @ r1 ) ),
inference(cnf,[status(esa)],[58]) ).
thf(4526,plain,
( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1730,59]) ).
thf(4527,plain,
sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ),
inference(simp,[status(thm)],[4526]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk2 ) @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk2 ) @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(4563,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[4527,45]) ).
thf(4564,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[4563]) ).
thf(4565,plain,
( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[4564:[bind(A,$thf( sk12 )),bind(B,$thf( sk1 @ ( sk12 @ sk2 ) ))]]) ).
thf(9928,plain,
( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
| ~ $true ),
inference(rewrite,[status(thm)],[4565,24]) ).
thf(9929,plain,
sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2,
inference(simp,[status(thm)],[9928]) ).
thf(32,plain,
! [A: $i] :
( ( A @ sk16 @ ( A @ r1 ) )
| ~ ( A @ ( sk15 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(48,plain,
! [A: $i] :
( ( A @ sk16 @ ( A @ r1 ) )
| ~ ( A @ ( sk15 @ r1 ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(919,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk15 @ r1 ) ) )
| ( B @ sk16 @ ( B @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,48]) ).
thf(920,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk15 @ r1 ) ) )
| ( B @ sk16 @ ( B @ r1 ) ) ),
inference(simp,[status(thm)],[919]) ).
thf(921,plain,
sk15 @ sk16 @ ( sk15 @ r1 ),
inference(pattern_uni,[status(thm)],[920:[bind(A,$thf( sk15 )),bind(B,$thf( sk15 ))]]) ).
thf(25,plain,
! [A: $i] :
( ( A @ p1 )
| ~ ( A @ ( sk13 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(43,plain,
! [A: $i] :
( ( A @ p1 )
| ~ ( A @ ( sk13 @ r1 ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(979,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[921,43]) ).
thf(980,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[979]) ).
thf(1029,plain,
! [A: $i] :
( ( ( sk15 @ sk16 )
!= A )
| ( sk15 != sk13 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[980]) ).
thf(1036,plain,
( ( sk15 != sk13 )
| ( sk15 @ sk16 @ p1 ) ),
inference(simp,[status(thm)],[1029]) ).
thf(28,plain,
sk15 @ ( sk1 @ r1 ),
inference(cnfConj,[status(thm)],[7]) ).
thf(34,plain,
! [A: $i] :
( ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(49,plain,
! [A: $i] :
( ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( ( A @ sk10 @ ( A @ r1 ) )
!= ( B @ ( sk13 @ r1 ) ) )
| ( B @ p1 )
| ~ $true
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[49,43]) ).
thf(292,plain,
! [B: $i,A: $i] :
( ( ( A @ sk10 @ ( A @ r1 ) )
!= ( B @ ( sk13 @ r1 ) ) )
| ( B @ p1 )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[291]) ).
thf(293,plain,
( ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 )
| ~ ( sk13 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[292:[bind(A,$thf( sk13 )),bind(B,$thf( sk13 @ sk10 ))]]) ).
thf(4767,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,293]) ).
thf(4768,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[4767]) ).
thf(4830,plain,
( ( sk15 != sk13 )
| ( sk1 != sk1 )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[4768]) ).
thf(4843,plain,
( ( sk15 != sk13 )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[4830]) ).
thf(18,plain,
~ ( sk14 @ p1 ),
inference(cnfConj,[status(thm)],[7]) ).
thf(6828,plain,
( ( ( sk13 @ sk10 @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( sk15 != sk13 )
| ( sk13 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[4843,18]) ).
thf(6829,plain,
( ( ( sk13 @ sk10 @ p1 )
!= ( sk14 @ p1 ) )
| ( sk15 != sk13 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[6828]) ).
thf(6836,plain,
( ( ( sk13 @ sk10 )
!= sk14 )
| ( sk15 != sk13 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[6829]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ( B @ sk10 @ ( B @ r1 ) )
| ( B @ sk7 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,49]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ( B @ sk10 @ ( B @ r1 ) )
| ( B @ sk7 ) ),
inference(simp,[status(thm)],[326]) ).
thf(328,plain,
( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
| ( sk1 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[327:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(4771,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,293]) ).
thf(4772,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[4771]) ).
thf(4810,plain,
( ( ( sk1 @ sk10 )
!= sk13 )
| ( sk1 != sk1 )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[4772]) ).
thf(4835,plain,
( ( ( sk1 @ sk10 )
!= sk13 )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[4810]) ).
thf(29,plain,
sk13 @ ( sk12 @ r1 ),
inference(cnfConj,[status(thm)],[7]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( A @ ( B @ sk2 ) @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( A @ ( B @ sk2 ) @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(6275,plain,
! [B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk3 ) @ ( A @ ( B @ sk2 ) @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[29,54]) ).
thf(6276,plain,
! [B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk3 ) @ ( A @ ( B @ sk2 ) @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[6275]) ).
thf(6277,plain,
( ( sk12 @ ( sk13 @ sk3 ) @ ( sk12 @ ( sk13 @ sk2 ) @ r1 ) )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[6276:[bind(A,$thf( sk12 )),bind(B,$thf( sk13 ))]]) ).
thf(69946,plain,
( ( sk12 @ ( sk13 @ sk3 ) @ ( sk12 @ ( sk13 @ sk2 ) @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[6277,24]) ).
thf(69947,plain,
sk12 @ ( sk13 @ sk3 ) @ ( sk12 @ ( sk13 @ sk2 ) @ r1 ),
inference(simp,[status(thm)],[69946]) ).
thf(70192,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk3 ) @ ( sk12 @ ( sk13 @ sk2 ) @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69947,43]) ).
thf(70193,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk3 ) @ ( sk12 @ ( sk13 @ sk2 ) @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[70192]) ).
thf(70366,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk3 ) )
!= A )
| ( ( sk12 @ ( sk13 @ sk2 ) )
!= sk13 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[70193]) ).
thf(70507,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= sk13 )
| ( sk12 @ ( sk13 @ sk3 ) @ p1 ) ),
inference(simp,[status(thm)],[70366]) ).
thf(70542,plain,
( ( ( sk12 @ ( sk13 @ sk3 ) @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( ( sk12 @ ( sk13 @ sk2 ) )
!= sk13 ) ),
inference(paramod_ordered,[status(thm)],[70507,18]) ).
thf(70543,plain,
( ( ( sk12 @ ( sk13 @ sk3 ) @ p1 )
!= ( sk14 @ p1 ) )
| ( ( sk12 @ ( sk13 @ sk2 ) )
!= sk13 ) ),
inference(simp,[status(thm)],[70542]) ).
thf(70549,plain,
( ( ( sk12 @ ( sk13 @ sk3 ) )
!= sk14 )
| ( ( sk12 @ ( sk13 @ sk2 ) )
!= sk13 ) ),
inference(simp,[status(thm)],[70543]) ).
thf(12,plain,
sk14 @ ( sk12 @ r1 ),
inference(cnfConj,[status(thm)],[7]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(2023,plain,
! [B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[12,44]) ).
thf(2024,plain,
! [B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[2023]) ).
thf(2025,plain,
( ~ ( sk12 @ ( sk14 @ sk3 ) @ p3 )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[2024:[bind(A,$thf( sk12 )),bind(B,$thf( sk14 ))]]) ).
thf(2108,plain,
( ~ ( sk12 @ ( sk14 @ sk3 ) @ p3 )
| ~ $true ),
inference(rewrite,[status(thm)],[2025,24]) ).
thf(2109,plain,
~ ( sk12 @ ( sk14 @ sk3 ) @ p3 ),
inference(simp,[status(thm)],[2108]) ).
thf(2275,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,45]) ).
thf(2276,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[2275]) ).
thf(2277,plain,
! [A: $i] :
( ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ ( A @ ( sk15 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[2276:[bind(A,$thf( sk15 ))]]) ).
thf(2409,plain,
! [A: $i] :
( ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ ( A @ ( sk15 @ r1 ) ) ),
inference(simp,[status(thm)],[2277]) ).
thf(26698,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,2409]) ).
thf(26699,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26698]) ).
thf(26921,plain,
! [A: $i] :
( ( A != sk12 )
| ( sk15 != sk1 )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26699]) ).
thf(26992,plain,
( ( sk15 != sk1 )
| ( sk15 @ ( sk12 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26921]) ).
thf(14,plain,
! [A: $i] :
( ~ ( A @ sk16 @ p2 )
| ~ ( A @ ( sk15 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(37,plain,
! [A: $i] :
( ~ ( A @ sk16 @ p2 )
| ~ ( A @ ( sk15 @ r1 ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(180,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ ( sk12 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,37]) ).
thf(181,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ ( sk12 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[180]) ).
thf(196,plain,
! [A: $i] :
( ( A != sk13 )
| ( sk15 != sk12 )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[181]) ).
thf(200,plain,
( ( sk15 != sk12 )
| ~ ( sk13 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[196]) ).
thf(28371,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[26992,200]) ).
thf(28372,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28371]) ).
thf(28394,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28372]) ).
thf(2018,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( C @ sk3 ) @ p3 )
| ~ $true
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[59,44]) ).
thf(2019,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( C @ sk3 ) @ p3 )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[2018]) ).
thf(2020,plain,
! [A: $i] :
( ~ ( A @ ( A @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[2019:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(92845,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,2020]) ).
thf(92846,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( A @ sk3 ) @ p3 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[92845]) ).
thf(92847,plain,
( ~ ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk3 ) @ p3 )
| ( sk1 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[92846:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(2361,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[45]) ).
thf(2376,plain,
( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[2361:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(3449,plain,
( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
| ~ $true ),
inference(rewrite,[status(thm)],[2376,59]) ).
thf(3450,plain,
sk1 @ ( sk1 @ sk2 ) @ p2,
inference(simp,[status(thm)],[3449]) ).
thf(1013,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[921,48]) ).
thf(1014,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[1013]) ).
thf(1015,plain,
sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ),
inference(pattern_uni,[status(thm)],[1014:[bind(A,$thf( sk15 @ sk16 ))]]) ).
thf(1052,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,37]) ).
thf(1053,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[1052]) ).
thf(1095,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 )
!= A )
| ( ( sk15 @ sk16 )
!= sk15 )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[1053]) ).
thf(1106,plain,
( ( ( sk15 @ sk16 )
!= sk15 )
| ~ ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[1095]) ).
thf(3456,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) )
| ( ( sk15 @ sk16 )
!= sk15 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3450,1106]) ).
thf(3457,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) )
| ( ( sk15 @ sk16 )
!= sk15 ) ),
inference(simp,[status(thm)],[3456]) ).
thf(3477,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 @ sk16 ) )
| ( ( sk15 @ sk16 )
!= sk15 ) ),
inference(simp,[status(thm)],[3457]) ).
thf(26770,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( B @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,2409]) ).
thf(26771,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( B @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26770]) ).
thf(26772,plain,
sk15 @ ( sk15 @ sk2 ) @ p2,
inference(pattern_uni,[status(thm)],[26771:[bind(A,$thf( sk15 )),bind(B,$thf( sk15 ))]]) ).
thf(314,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,49]) ).
thf(315,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 ) ),
inference(simp,[status(thm)],[314]) ).
thf(316,plain,
( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
| ( sk15 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[315:[bind(A,$thf( sk15 ))]]) ).
thf(554,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[316,37]) ).
thf(555,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[554]) ).
thf(556,plain,
( ~ ( sk15 @ sk10 @ sk16 @ p2 )
| ( sk15 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[555:[bind(A,$thf( sk15 @ sk10 ))]]) ).
thf(28056,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[26772,556]) ).
thf(28057,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[28056]) ).
thf(28097,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) )
!= ( sk15 @ sk10 @ sk16 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[28057]) ).
thf(922,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ ( sk12 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,48]) ).
thf(923,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ ( sk12 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[922]) ).
thf(960,plain,
! [A: $i] :
( ( A != sk14 )
| ( sk15 != sk12 )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[923]) ).
thf(962,plain,
( ( sk15 != sk12 )
| ( sk14 @ sk16 @ ( sk14 @ r1 ) ) ),
inference(simp,[status(thm)],[960]) ).
thf(2260,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,45]) ).
thf(2261,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[2260]) ).
thf(2262,plain,
( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[2261:[bind(A,$thf( sk1 )),bind(B,$thf( sk12 ))]]) ).
thf(2412,plain,
( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
| ~ $true ),
inference(rewrite,[status(thm)],[2262,59]) ).
thf(2413,plain,
sk1 @ ( sk12 @ sk2 ) @ p2,
inference(simp,[status(thm)],[2412]) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(120,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[36]) ).
thf(124,plain,
! [A: $i] :
( ( sk1 @ ( sk1 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ~ ( sk1 @ p2 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(138,plain,
! [A: $i] :
( ( sk1 @ ( sk1 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ~ ( sk1 @ p2 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(25738,plain,
! [A: $i] :
( ( sk1 @ ( sk1 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ~ ( sk1 @ p2 )
| ( sk1 @ sk4 )
| ~ $true ),
inference(rewrite,[status(thm)],[138,59]) ).
thf(25739,plain,
! [A: $i] :
( ( sk1 @ ( sk1 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ~ ( sk1 @ p2 )
| ( sk1 @ sk4 ) ),
inference(simp,[status(thm)],[25738]) ).
thf(25887,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk1 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ $true
| ~ ( sk1 @ p2 )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,25739]) ).
thf(25888,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( sk1 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( sk1 @ p2 )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[25887]) ).
thf(25889,plain,
( ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ~ ( sk1 @ p2 )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[25888:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(31178,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ~ $true
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[2413,25889]) ).
thf(31179,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31178]) ).
thf(31408,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31179]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(254,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[28,38]) ).
thf(255,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[254]) ).
thf(256,plain,
! [A: $i] :
( ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk15 @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( sk1 )),bind(B,$thf( sk15 ))]]) ).
thf(268,plain,
! [A: $i] :
( ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk15 @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(629,plain,
! [A: $i] :
( ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk15 @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[268,59]) ).
thf(630,plain,
! [A: $i] :
( ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk15 @ r1 ) ) ),
inference(simp,[status(thm)],[629]) ).
thf(643,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[316,630]) ).
thf(644,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[643]) ).
thf(645,plain,
( ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk5 ) ) @ p3 )
| ( sk15 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[644:[bind(A,$thf( sk15 @ sk10 ))]]) ).
thf(8,plain,
! [A: $i] :
( ~ ( A @ p4 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(66,plain,
! [A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,8]) ).
thf(67,plain,
! [A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[66]) ).
thf(68,plain,
! [A: $i] :
( ( sk14 != A )
| ( sk12 != sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[67]) ).
thf(69,plain,
( ( sk12 != sk1 )
| ~ ( sk14 @ p4 ) ),
inference(simp,[status(thm)],[68]) ).
thf(1741,plain,
! [B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[29,42]) ).
thf(1742,plain,
! [B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[1741]) ).
thf(1743,plain,
( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[1742:[bind(A,$thf( sk12 )),bind(B,$thf( sk13 ))]]) ).
thf(5347,plain,
( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1743,24]) ).
thf(5348,plain,
sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ),
inference(simp,[status(thm)],[5347]) ).
thf(5394,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[5348,45]) ).
thf(5395,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[5394]) ).
thf(5396,plain,
( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
| ~ ( sk13 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[5395:[bind(A,$thf( sk13 )),bind(B,$thf( sk12 @ ( sk13 @ sk2 ) ))]]) ).
thf(11313,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,5396]) ).
thf(11314,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[11313]) ).
thf(11427,plain,
! [A: $i] :
( ( A != sk13 )
| ( A != sk1 )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[11314]) ).
thf(11470,plain,
( ( sk13 != sk1 )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[11427]) ).
thf(989,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[921,37]) ).
thf(990,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[989]) ).
thf(991,plain,
~ ( sk15 @ sk16 @ sk16 @ p2 ),
inference(pattern_uni,[status(thm)],[990:[bind(A,$thf( sk15 @ sk16 ))]]) ).
thf(11883,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk13 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[11470,991]) ).
thf(11884,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[11883]) ).
thf(11922,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[11884]) ).
thf(70229,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk3 ) @ ( sk12 @ ( sk13 @ sk2 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69947,8]) ).
thf(70230,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk3 ) @ ( sk12 @ ( sk13 @ sk2 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[70229]) ).
thf(70363,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk3 ) )
!= A )
| ( ( sk12 @ ( sk13 @ sk2 ) )
!= sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[70230]) ).
thf(70502,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= sk1 )
| ~ ( sk12 @ ( sk13 @ sk3 ) @ p4 ) ),
inference(simp,[status(thm)],[70363]) ).
thf(1750,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[28,42]) ).
thf(1751,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[1750]) ).
thf(1752,plain,
( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[1751:[bind(A,$thf( sk1 )),bind(B,$thf( sk15 ))]]) ).
thf(5839,plain,
( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1752,59]) ).
thf(5840,plain,
sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ),
inference(simp,[status(thm)],[5839]) ).
thf(5910,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5840,48]) ).
thf(5911,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[5910]) ).
thf(5912,plain,
sk1 @ ( sk15 @ sk2 ) @ sk16 @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ),
inference(pattern_uni,[status(thm)],[5911:[bind(A,$thf( sk1 @ ( sk15 @ sk2 ) ))]]) ).
thf(6119,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5912,8]) ).
thf(6120,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[6119]) ).
thf(6149,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ sk16 )
!= A )
| ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[6120]) ).
thf(6172,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk1 )
| ~ ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p4 ) ),
inference(simp,[status(thm)],[6149]) ).
thf(1795,plain,
! [B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[12,42]) ).
thf(1796,plain,
! [B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[1795]) ).
thf(1797,plain,
( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[1796:[bind(A,$thf( sk12 )),bind(B,$thf( sk14 ))]]) ).
thf(6621,plain,
( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1797,24]) ).
thf(6622,plain,
sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ),
inference(simp,[status(thm)],[6621]) ).
thf(6628,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6622,37]) ).
thf(6629,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[6628]) ).
thf(6751,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= A )
| ( sk15 != sk14 )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[6629]) ).
thf(6783,plain,
( ( sk15 != sk14 )
| ~ ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[6751]) ).
thf(6805,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2413,6783]) ).
thf(6806,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[6805]) ).
thf(6819,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[6806]) ).
thf(26860,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4527,2409]) ).
thf(26861,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26860]) ).
thf(26955,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= A )
| ( sk15 != sk12 )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26861]) ).
thf(27017,plain,
( ( sk15 != sk12 )
| ( sk15 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26955]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk15 @ r1 ) ) )
| ~ ( B @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,37]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk15 @ r1 ) ) )
| ~ ( B @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[184]) ).
thf(186,plain,
~ ( sk15 @ sk16 @ p2 ),
inference(pattern_uni,[status(thm)],[185:[bind(A,$thf( sk15 )),bind(B,$thf( sk15 ))]]) ).
thf(33064,plain,
( ( ( sk15 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27017,186]) ).
thf(33065,plain,
( ( ( sk15 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[33064]) ).
thf(33103,plain,
( ( ( sk15 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[33065]) ).
thf(614,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,49]) ).
thf(615,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[614]) ).
thf(616,plain,
( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[615:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(1824,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[616,42]) ).
thf(1825,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[1824]) ).
thf(1826,plain,
( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ ( sk1 @ sk10 @ sk10 @ r1 ) )
| ~ ( sk1 @ sk10 @ ( sk1 @ r1 ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[1825:[bind(A,$thf( sk1 @ sk10 )),bind(B,$thf( sk1 @ sk10 @ sk10 ))]]) ).
thf(12810,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ ( sk1 @ sk10 @ sk10 @ r1 ) )
| ~ $true
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,1826]) ).
thf(12811,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ ( sk1 @ sk10 @ sk10 @ r1 ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[12810]) ).
thf(12812,plain,
( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ ( sk1 @ sk10 @ sk10 @ r1 ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[12811:[]]) ).
thf(28015,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) )
| ( ( sk15 @ sk16 )
!= sk15 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26772,1106]) ).
thf(28016,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) )
| ( ( sk15 @ sk16 )
!= sk15 ) ),
inference(simp,[status(thm)],[28015]) ).
thf(28114,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 @ sk16 ) )
| ( ( sk15 @ sk16 )
!= sk15 ) ),
inference(simp,[status(thm)],[28016]) ).
thf(92868,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[921,2020]) ).
thf(92869,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[92868]) ).
thf(93048,plain,
! [A: $i] :
( ( ( sk15 @ sk16 )
!= A )
| ( sk15 != sk1 )
| ~ ( A @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[92869]) ).
thf(93141,plain,
( ( sk15 != sk1 )
| ~ ( sk15 @ sk16 @ ( sk15 @ sk16 @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[93048]) ).
thf(1993,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,44]) ).
thf(1994,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[1993]) ).
thf(1995,plain,
! [A: $i] :
( ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ ( A @ ( sk15 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[1994:[bind(A,$thf( sk15 ))]]) ).
thf(2077,plain,
! [A: $i] :
( ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ ( A @ ( sk15 @ r1 ) ) ),
inference(simp,[status(thm)],[1995]) ).
thf(245,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,38]) ).
thf(246,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[245]) ).
thf(247,plain,
! [A: $i] :
( ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk12 @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[246:[bind(A,$thf( sk1 )),bind(B,$thf( sk12 ))]]) ).
thf(280,plain,
! [A: $i] :
( ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk12 @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(68166,plain,
! [A: $i] :
( ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk12 @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[280,59]) ).
thf(68167,plain,
! [A: $i] :
( ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk12 @ r1 ) ) ),
inference(simp,[status(thm)],[68166]) ).
thf(68209,plain,
! [A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,68167]) ).
thf(68210,plain,
! [A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[68209]) ).
thf(68211,plain,
( ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( sk13 @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[68210:[bind(A,$thf( sk13 ))]]) ).
thf(2278,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[28,45]) ).
thf(2279,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[2278]) ).
thf(2280,plain,
( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[2279:[bind(A,$thf( sk1 )),bind(B,$thf( sk15 ))]]) ).
thf(2972,plain,
( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
| ~ $true ),
inference(rewrite,[status(thm)],[2280,59]) ).
thf(2973,plain,
sk1 @ ( sk15 @ sk2 ) @ p2,
inference(simp,[status(thm)],[2972]) ).
thf(896,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,48]) ).
thf(897,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[896]) ).
thf(959,plain,
! [A: $i] :
( ( A != sk12 )
| ( sk15 != sk1 )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[897]) ).
thf(978,plain,
( ( sk15 != sk1 )
| ( sk12 @ sk16 @ ( sk12 @ r1 ) ) ),
inference(simp,[status(thm)],[959]) ).
thf(1618,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk16 @ ( sk12 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[978,37]) ).
thf(1619,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk16 @ ( sk12 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[1618]) ).
thf(1665,plain,
! [A: $i] :
( ( A
!= ( sk12 @ sk16 ) )
| ( sk15 != sk12 )
| ~ ( A @ sk16 @ p2 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[1619]) ).
thf(1674,plain,
( ( sk15 != sk12 )
| ~ ( sk12 @ sk16 @ sk16 @ p2 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[1665]) ).
thf(7504,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[2973,1674]) ).
thf(7505,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[7504]) ).
thf(7517,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= ( sk12 @ sk16 @ sk16 ) )
| ( sk15 != sk12 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[7505]) ).
thf(236,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( E @ ( D @ r1 ) ) )
| ~ ( E @ sk4 )
| ~ ( D @ ( E @ ( F @ sk5 ) ) @ p3 )
| ~ ( F @ ( E @ r1 ) )
| ~ $true
| ~ ( D @ ( sk1 @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[36,38]) ).
thf(237,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( E @ ( D @ r1 ) ) )
| ~ ( E @ sk4 )
| ~ ( D @ ( E @ ( F @ sk5 ) ) @ p3 )
| ~ ( F @ ( E @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[236]) ).
thf(238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ sk6 ) ) @ sk4 )
| ~ ( B @ ( D @ ( C @ ( B @ sk6 ) ) @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( D @ ( C @ ( B @ sk6 ) ) @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) )
| ~ ( B @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[237:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( G )),bind(E,$thf( I @ ( H @ ( G @ sk6 ) ) ))]]) ).
thf(276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ sk6 ) ) @ sk4 )
| ~ ( B @ ( D @ ( C @ ( B @ sk6 ) ) @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( D @ ( C @ ( B @ sk6 ) ) @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) )
| ~ ( B @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(992,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[921,630]) ).
thf(993,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[992]) ).
thf(994,plain,
( ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( sk15 @ sk16 @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[993:[bind(A,$thf( sk15 @ sk16 ))]]) ).
thf(306,plain,
! [A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,49]) ).
thf(307,plain,
! [A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 ) ),
inference(simp,[status(thm)],[306]) ).
thf(308,plain,
( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
| ( sk12 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[307:[bind(A,$thf( sk12 ))]]) ).
thf(6695,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6622,48]) ).
thf(6696,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[6695]) ).
thf(6744,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= A )
| ( sk15 != sk14 )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[6696]) ).
thf(6776,plain,
( ( sk15 != sk14 )
| ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ ( sk12 @ ( sk14 @ sk2 ) @ r1 ) ) ),
inference(simp,[status(thm)],[6744]) ).
thf(6677,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[6622,44]) ).
thf(6678,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[6677]) ).
thf(6679,plain,
( ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 )
| ~ ( sk14 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[6678:[bind(A,$thf( sk14 )),bind(B,$thf( sk12 @ ( sk14 @ sk2 ) ))]]) ).
thf(17923,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,6679]) ).
thf(17924,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[17923]) ).
thf(18001,plain,
( ( sk15 != sk14 )
| ( sk1 != sk1 )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[17924]) ).
thf(18052,plain,
( ( sk15 != sk14 )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[18001]) ).
thf(189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( D @ ( sk15 @ r1 ) ) )
| ~ ( D @ sk16 @ p2 )
| ~ $true
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[36,37]) ).
thf(190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( D @ ( sk15 @ r1 ) ) )
| ~ ( D @ sk16 @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[189]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( sk15 @ sk6 ) ) @ sk16 @ p2 )
| ~ ( sk15 @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( sk15 )),bind(D,$thf( G @ ( F @ ( sk15 @ sk6 ) ) ))]]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( sk15 @ sk6 ) ) @ sk16 @ p2 )
| ~ ( sk15 @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[191]) ).
thf(6672,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[6622,45]) ).
thf(6673,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[6672]) ).
thf(6674,plain,
( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
| ~ ( sk14 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[6673:[bind(A,$thf( sk14 )),bind(B,$thf( sk12 @ ( sk14 @ sk2 ) ))]]) ).
thf(17583,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,6674]) ).
thf(17584,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17583]) ).
thf(17757,plain,
! [A: $i] :
( ( A != sk14 )
| ( A != sk1 )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17584]) ).
thf(17796,plain,
( ( sk14 != sk1 )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17757]) ).
thf(18567,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk14 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[17796,186]) ).
thf(18568,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk14 != sk1 ) ),
inference(simp,[status(thm)],[18567]) ).
thf(18603,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk14 != sk1 ) ),
inference(simp,[status(thm)],[18568]) ).
thf(26712,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ ( sk12 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,2409]) ).
thf(26713,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ ( sk12 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26712]) ).
thf(26967,plain,
! [A: $i] :
( ( A != sk13 )
| ( sk15 != sk12 )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26713]) ).
thf(27023,plain,
( ( sk15 != sk12 )
| ( sk15 @ ( sk13 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26967]) ).
thf(2299,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ( B @ ( C @ sk2 ) @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,45]) ).
thf(2300,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ( B @ ( C @ sk2 ) @ p2 )
| ~ ( C @ ( B @ r1 ) ) ),
inference(simp,[status(thm)],[2299]) ).
thf(2301,plain,
! [A: $i] :
( ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[2300:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(2411,plain,
! [A: $i] :
( ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[2301]) ).
thf(33652,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[616,2411]) ).
thf(33653,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[33652]) ).
thf(33823,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 )
!= A )
| ( ( sk1 @ sk10 )
!= sk1 )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[33653]) ).
thf(33885,plain,
( ( ( sk1 @ sk10 )
!= sk1 )
| ( sk1 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[33823]) ).
thf(92801,plain,
! [A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,2020]) ).
thf(92802,plain,
! [A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[92801]) ).
thf(93087,plain,
! [A: $i] :
( ( sk13 != A )
| ( sk12 != sk1 )
| ~ ( A @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[92802]) ).
thf(93180,plain,
( ( sk12 != sk1 )
| ~ ( sk13 @ ( sk13 @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[93087]) ).
thf(904,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ ( sk12 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,48]) ).
thf(905,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ ( sk12 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[904]) ).
thf(955,plain,
! [A: $i] :
( ( A != sk13 )
| ( sk15 != sk12 )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[905]) ).
thf(972,plain,
( ( sk15 != sk12 )
| ( sk13 @ sk16 @ ( sk13 @ r1 ) ) ),
inference(simp,[status(thm)],[955]) ).
thf(2060,plain,
! [B: $i,A: $i] :
( ( ( sk13 @ sk16 @ ( sk13 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[972,44]) ).
thf(2061,plain,
! [B: $i,A: $i] :
( ( ( sk13 @ sk16 @ ( sk13 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2060]) ).
thf(2062,plain,
( ~ ( sk13 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ~ ( sk13 @ ( sk1 @ r1 ) )
| ( sk15 != sk12 ) ),
inference(pattern_uni,[status(thm)],[2061:[bind(A,$thf( sk13 )),bind(B,$thf( sk13 @ sk16 ))]]) ).
thf(1865,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[42]) ).
thf(1875,plain,
( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[1865:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(7282,plain,
( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1875,59]) ).
thf(7283,plain,
sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ),
inference(simp,[status(thm)],[7282]) ).
thf(2257,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,45]) ).
thf(2258,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[2257]) ).
thf(2259,plain,
! [A: $i] :
( ( sk12 @ ( A @ sk2 ) @ p2 )
| ~ ( A @ ( sk12 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[2258:[bind(A,$thf( sk12 ))]]) ).
thf(2408,plain,
! [A: $i] :
( ( sk12 @ ( A @ sk2 ) @ p2 )
| ~ ( A @ ( sk12 @ r1 ) ) ),
inference(simp,[status(thm)],[2259]) ).
thf(21786,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,2408]) ).
thf(21787,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21786]) ).
thf(21891,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= A )
| ( sk12 != sk1 )
| ( sk12 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21787]) ).
thf(21951,plain,
( ( sk12 != sk1 )
| ( sk12 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21891]) ).
thf(25198,plain,
( ( ( sk12 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21951,186]) ).
thf(25199,plain,
( ( ( sk12 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[25198]) ).
thf(25228,plain,
( ( ( sk12 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[25199]) ).
thf(68220,plain,
! [A: $i] :
( ( ( A @ ( sk12 @ r1 ) )
!= ( sk15 @ ( sk1 @ r1 ) ) )
| ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,68167]) ).
thf(68221,plain,
! [A: $i] :
( ( ( A @ ( sk12 @ r1 ) )
!= ( sk15 @ ( sk1 @ r1 ) ) )
| ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[68220]) ).
thf(68384,plain,
! [A: $i] :
( ( A != sk15 )
| ( sk12 != sk1 )
| ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[68221]) ).
thf(68440,plain,
( ( sk12 != sk1 )
| ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( sk15 @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[68384]) ).
thf(21673,plain,
! [A: $i] :
( ( ( sk14 @ sk16 @ ( sk14 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[962,2408]) ).
thf(21674,plain,
! [A: $i] :
( ( ( sk14 @ sk16 @ ( sk14 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[21673]) ).
thf(21920,plain,
! [A: $i] :
( ( ( sk14 @ sk16 )
!= A )
| ( sk14 != sk12 )
| ( sk15 != sk12 )
| ( sk12 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21674]) ).
thf(21967,plain,
( ( sk14 != sk12 )
| ( sk15 != sk12 )
| ( sk12 @ ( sk14 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21920]) ).
thf(5923,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5840,43]) ).
thf(5924,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[5923]) ).
thf(5961,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= A )
| ( sk15 != sk13 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[5924]) ).
thf(5982,plain,
( ( sk15 != sk13 )
| ( sk1 @ ( sk15 @ sk2 ) @ p1 ) ),
inference(simp,[status(thm)],[5961]) ).
thf(1977,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,44]) ).
thf(1978,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[1977]) ).
thf(1979,plain,
! [A: $i] :
( ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ~ ( A @ ( sk12 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[1978:[bind(A,$thf( sk12 ))]]) ).
thf(2100,plain,
! [A: $i] :
( ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ~ ( A @ ( sk12 @ r1 ) ) ),
inference(simp,[status(thm)],[1979]) ).
thf(19059,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[921,2100]) ).
thf(19060,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19059]) ).
thf(19171,plain,
! [A: $i] :
( ( ( sk15 @ sk16 )
!= A )
| ( sk15 != sk12 )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19060]) ).
thf(19213,plain,
( ( sk15 != sk12 )
| ~ ( sk12 @ ( sk15 @ sk16 @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19171]) ).
thf(2243,plain,
! [B: $i,A: $i] :
( ( ( sk14 @ sk16 @ ( sk14 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[962,45]) ).
thf(2244,plain,
! [B: $i,A: $i] :
( ( ( sk14 @ sk16 @ ( sk14 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2243]) ).
thf(2245,plain,
( ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 )
| ~ ( sk14 @ ( sk1 @ r1 ) )
| ( sk15 != sk12 ) ),
inference(pattern_uni,[status(thm)],[2244:[bind(A,$thf( sk14 )),bind(B,$thf( sk14 @ sk16 ))]]) ).
thf(96334,plain,
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[12,2245]) ).
thf(96335,plain,
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[96334]) ).
thf(96700,plain,
( ( sk14 != sk14 )
| ( sk12 != sk1 )
| ( sk15 != sk12 )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[96335]) ).
thf(96748,plain,
( ( sk12 != sk1 )
| ( sk15 != sk12 )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[96700]) ).
thf(6236,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk3 ) @ ( A @ ( B @ sk2 ) @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,54]) ).
thf(6237,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk3 ) @ ( A @ ( B @ sk2 ) @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[6236]) ).
thf(6238,plain,
( ( sk1 @ ( sk12 @ sk3 ) @ ( sk1 @ ( sk12 @ sk2 ) @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[6237:[bind(A,$thf( sk1 )),bind(B,$thf( sk12 ))]]) ).
thf(67006,plain,
( ( sk1 @ ( sk12 @ sk3 ) @ ( sk1 @ ( sk12 @ sk2 ) @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[6238,59]) ).
thf(67007,plain,
sk1 @ ( sk12 @ sk3 ) @ ( sk1 @ ( sk12 @ sk2 ) @ r1 ),
inference(simp,[status(thm)],[67006]) ).
thf(67282,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk3 ) @ ( sk1 @ ( sk12 @ sk2 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67007,8]) ).
thf(67283,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk3 ) @ ( sk1 @ ( sk12 @ sk2 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[67282]) ).
thf(67419,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk3 ) )
!= A )
| ( ( sk1 @ ( sk12 @ sk2 ) )
!= sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[67283]) ).
thf(67521,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= sk1 )
| ~ ( sk1 @ ( sk12 @ sk3 ) @ p4 ) ),
inference(simp,[status(thm)],[67419]) ).
thf(21746,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5840,2408]) ).
thf(21747,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21746]) ).
thf(21884,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= A )
| ( sk15 != sk12 )
| ( sk12 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21747]) ).
thf(21996,plain,
( ( sk15 != sk12 )
| ( sk12 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21884]) ).
thf(26455,plain,
( ( ( sk12 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[21996,991]) ).
thf(26456,plain,
( ( ( sk12 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[26455]) ).
thf(26510,plain,
( ( ( sk12 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[26456]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk17 @ ( A @ r1 ) )
| ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk17 @ ( A @ r1 ) )
| ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( B @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[36]) ).
thf(127,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( C )),bind(B,$thf( C ))]]) ).
thf(142,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(26773,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ ( sk12 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,2409]) ).
thf(26774,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ ( sk12 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26773]) ).
thf(26936,plain,
! [A: $i] :
( ( A != sk14 )
| ( sk15 != sk12 )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26774]) ).
thf(27000,plain,
( ( sk15 != sk12 )
| ( sk15 @ ( sk14 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26936]) ).
thf(28462,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27000,991]) ).
thf(28463,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28462]) ).
thf(28536,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28463]) ).
thf(33634,plain,
! [A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,2411]) ).
thf(33635,plain,
! [A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33634]) ).
thf(33818,plain,
! [A: $i] :
( ( sk14 != A )
| ( sk12 != sk1 )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33635]) ).
thf(33880,plain,
( ( sk12 != sk1 )
| ( sk1 @ ( sk14 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33818]) ).
thf(11893,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk13 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[11470,186]) ).
thf(11894,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[11893]) ).
thf(11917,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[11894]) ).
thf(2272,plain,
! [B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[29,45]) ).
thf(2273,plain,
! [B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[2272]) ).
thf(2274,plain,
( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[2273:[bind(A,$thf( sk12 )),bind(B,$thf( sk13 ))]]) ).
thf(2445,plain,
( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
| ~ $true ),
inference(rewrite,[status(thm)],[2274,24]) ).
thf(2446,plain,
sk12 @ ( sk13 @ sk2 ) @ p2,
inference(simp,[status(thm)],[2445]) ).
thf(2452,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) )
| ( ( sk15 @ sk16 )
!= sk15 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2446,1106]) ).
thf(2453,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) )
| ( ( sk15 @ sk16 )
!= sk15 ) ),
inference(simp,[status(thm)],[2452]) ).
thf(2476,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 @ sk16 ) )
| ( ( sk15 @ sk16 )
!= sk15 ) ),
inference(simp,[status(thm)],[2453]) ).
thf(26810,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,2409]) ).
thf(26811,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26810]) ).
thf(26939,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= A )
| ( sk15 != sk1 )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26811]) ).
thf(27003,plain,
( ( sk15 != sk1 )
| ( sk15 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26939]) ).
thf(31743,plain,
( ( ( sk15 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[27003,186]) ).
thf(31744,plain,
( ( ( sk15 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[31743]) ).
thf(31806,plain,
( ( ( sk15 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[31744]) ).
thf(294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk10 @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ( B @ ( C @ ( D @ sk6 ) ) @ ( D @ r1 ) )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( B @ r1 ) )
| ~ $true
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[49,36]) ).
thf(295,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk10 @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ( B @ ( C @ ( D @ sk6 ) ) @ ( D @ r1 ) )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( B @ r1 ) )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[294]) ).
thf(296,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk10 @ ( A @ ( B @ sk6 ) ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk7 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[295:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk10 )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk10 @ ( A @ ( B @ sk6 ) ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk7 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(83059,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk10 @ ( A @ ( B @ sk6 ) ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk7 )
| ~ $true ),
inference(rewrite,[status(thm)],[341,59]) ).
thf(83060,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk10 @ ( A @ ( B @ sk6 ) ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[83059]) ).
thf(323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk10 @ ( A @ r1 ) )
!= ( D @ ( C @ r1 ) ) )
| ~ ( C @ sk4 )
| ~ ( B @ ( C @ ( D @ sk5 ) ) @ p3 )
| ~ $true
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[49,38]) ).
thf(324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk10 @ ( A @ r1 ) )
!= ( D @ ( C @ r1 ) ) )
| ~ ( C @ sk4 )
| ~ ( B @ ( C @ ( D @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[323]) ).
thf(325,plain,
! [B: $i,A: $i] :
( ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( B @ sk10 @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ( B @ sk7 )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[324:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( E @ sk10 ))]]) ).
thf(340,plain,
! [B: $i,A: $i] :
( ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( B @ sk10 @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ( B @ sk7 )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[325]) ).
thf(96201,plain,
( ( ( sk14 @ ( sk1 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[24,2245]) ).
thf(96202,plain,
( ( ( sk14 @ ( sk1 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[96201]) ).
thf(96598,plain,
( ( sk14 != sk12 )
| ( sk1 != sk1 )
| ( sk15 != sk12 )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[96202]) ).
thf(96719,plain,
( ( sk14 != sk12 )
| ( sk15 != sk12 )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[96598]) ).
thf(21750,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( B @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,2408]) ).
thf(21751,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( B @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21750]) ).
thf(21752,plain,
sk12 @ ( sk12 @ sk2 ) @ p2,
inference(pattern_uni,[status(thm)],[21751:[bind(A,$thf( sk12 )),bind(B,$thf( sk12 ))]]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[28,36]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(96,plain,
! [A: $i] :
( ( sk1 @ ( sk15 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk15 @ r1 ) )
| ~ ( sk15 @ p2 )
| ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( sk1 )),bind(B,$thf( sk15 ))]]) ).
thf(128,plain,
! [A: $i] :
( ( sk1 @ ( sk15 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk15 @ r1 ) )
| ~ ( sk15 @ p2 )
| ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(13127,plain,
! [A: $i] :
( ( sk1 @ ( sk15 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk15 @ r1 ) )
| ~ ( sk15 @ p2 )
| ( sk15 @ sk4 )
| ~ $true ),
inference(rewrite,[status(thm)],[128,59]) ).
thf(13128,plain,
! [A: $i] :
( ( sk1 @ ( sk15 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk15 @ r1 ) )
| ~ ( sk15 @ p2 )
| ( sk15 @ sk4 ) ),
inference(simp,[status(thm)],[13127]) ).
thf(13201,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk1 @ ( sk15 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ $true
| ~ ( sk15 @ p2 )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[316,13128]) ).
thf(13202,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk1 @ ( sk15 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( sk15 @ p2 )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[13201]) ).
thf(13203,plain,
( ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ~ ( sk15 @ p2 )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[13202:[bind(A,$thf( sk15 @ sk10 ))]]) ).
thf(22052,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ~ $true
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[21752,13203]) ).
thf(22053,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[22052]) ).
thf(22101,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) )
!= sk15 )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[22053]) ).
thf(13875,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,2077]) ).
thf(13876,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13875]) ).
thf(13982,plain,
! [A: $i] :
( ( A != sk12 )
| ( sk15 != sk1 )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13876]) ).
thf(14014,plain,
( ( sk15 != sk1 )
| ~ ( sk15 @ ( sk12 @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13982]) ).
thf(33601,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,2411]) ).
thf(33602,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[33601]) ).
thf(33603,plain,
( ( sk1 @ ( sk1 @ sk10 @ sk2 ) @ p2 )
| ( sk1 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[33602:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(35391,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ~ $true
| ( sk15 @ sk4 )
| ( sk15 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[33603,13203]) ).
thf(35392,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[35391]) ).
thf(35456,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) )
!= sk15 )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[35392]) ).
thf(518,plain,
! [A: $i] :
( ( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[308,8]) ).
thf(519,plain,
! [A: $i] :
( ( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[518]) ).
thf(525,plain,
! [A: $i] :
( ( ( sk12 @ sk10 )
!= A )
| ( sk12 != sk1 )
| ~ ( A @ p4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[519]) ).
thf(533,plain,
( ( sk12 != sk1 )
| ~ ( sk12 @ sk10 @ p4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[525]) ).
thf(26709,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[316,2409]) ).
thf(26710,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[26709]) ).
thf(26711,plain,
( ( sk15 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
| ( sk15 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[26710:[bind(A,$thf( sk15 @ sk10 ))]]) ).
thf(31083,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ~ $true
| ( sk1 @ sk4 )
| ( sk1 @ sk7 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[26711,25889]) ).
thf(31084,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[31083]) ).
thf(31369,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) )
!= sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[31084]) ).
thf(6357,plain,
! [B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk3 ) @ ( A @ ( B @ sk2 ) @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[12,54]) ).
thf(6358,plain,
! [B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk3 ) @ ( A @ ( B @ sk2 ) @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[6357]) ).
thf(6359,plain,
( ( sk12 @ ( sk14 @ sk3 ) @ ( sk12 @ ( sk14 @ sk2 ) @ r1 ) )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[6358:[bind(A,$thf( sk12 )),bind(B,$thf( sk14 ))]]) ).
thf(74470,plain,
( ( sk12 @ ( sk14 @ sk3 ) @ ( sk12 @ ( sk14 @ sk2 ) @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[6359,24]) ).
thf(74471,plain,
sk12 @ ( sk14 @ sk3 ) @ ( sk12 @ ( sk14 @ sk2 ) @ r1 ),
inference(simp,[status(thm)],[74470]) ).
thf(74760,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk3 ) @ ( sk12 @ ( sk14 @ sk2 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74471,8]) ).
thf(74761,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk3 ) @ ( sk12 @ ( sk14 @ sk2 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[74760]) ).
thf(74860,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk3 ) )
!= A )
| ( ( sk12 @ ( sk14 @ sk2 ) )
!= sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[74761]) ).
thf(74978,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= sk1 )
| ~ ( sk12 @ ( sk14 @ sk3 ) @ p4 ) ),
inference(simp,[status(thm)],[74860]) ).
thf(28091,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26772,200]) ).
thf(28092,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28091]) ).
thf(28101,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28092]) ).
thf(13893,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,2077]) ).
thf(13894,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[13893]) ).
thf(13992,plain,
! [A: $i] :
( ( A
!= ( sk1 @ sk10 ) )
| ( sk15 != sk1 )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[13894]) ).
thf(14025,plain,
( ( sk15 != sk1 )
| ~ ( sk15 @ ( sk1 @ sk10 @ sk3 ) @ p3 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[13992]) ).
thf(5846,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5840,37]) ).
thf(5847,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[5846]) ).
thf(5848,plain,
~ ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ),
inference(pattern_uni,[status(thm)],[5847:[bind(A,$thf( sk1 @ ( sk15 @ sk2 ) ))]]) ).
thf(28029,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26772,5848]) ).
thf(28030,plain,
( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[28029]) ).
thf(28118,plain,
( ( sk15 @ ( sk15 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) ),
inference(simp,[status(thm)],[28030]) ).
thf(33563,plain,
! [A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,2411]) ).
thf(33564,plain,
! [A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33563]) ).
thf(33794,plain,
! [A: $i] :
( ( sk13 != A )
| ( sk12 != sk1 )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33564]) ).
thf(33865,plain,
( ( sk12 != sk1 )
| ( sk1 @ ( sk13 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33794]) ).
thf(35218,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33865,991]) ).
thf(35219,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35218]) ).
thf(35282,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35219]) ).
thf(33678,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,2411]) ).
thf(33679,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33678]) ).
thf(33680,plain,
sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2,
inference(pattern_uni,[status(thm)],[33679:[bind(A,$thf( sk1 @ ( sk1 @ sk2 ) ))]]) ).
thf(187,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ ( sk12 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,37]) ).
thf(188,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ ( sk12 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[187]) ).
thf(194,plain,
! [A: $i] :
( ( A != sk14 )
| ( sk15 != sk12 )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[188]) ).
thf(198,plain,
( ( sk15 != sk12 )
| ~ ( sk14 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[194]) ).
thf(33969,plain,
( ( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33680,198]) ).
thf(33970,plain,
( ( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[33969]) ).
thf(34039,plain,
( ( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[33970]) ).
thf(7290,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,37]) ).
thf(7291,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[7290]) ).
thf(7436,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= A )
| ( sk15 != sk1 )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[7291]) ).
thf(7447,plain,
( ( sk15 != sk1 )
| ~ ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[7436]) ).
thf(7489,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2446,7447]) ).
thf(7490,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[7489]) ).
thf(7499,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[7490]) ).
thf(26690,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5348,2409]) ).
thf(26691,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26690]) ).
thf(26945,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= A )
| ( sk15 != sk13 )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26691]) ).
thf(27006,plain,
( ( sk15 != sk13 )
| ( sk15 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26945]) ).
thf(17556,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,6674]) ).
thf(17557,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17556]) ).
thf(17773,plain,
( ( sk15 != sk14 )
| ( sk1 != sk1 )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17557]) ).
thf(17798,plain,
( ( sk15 != sk14 )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17773]) ).
thf(192,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,37]) ).
thf(193,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[192]) ).
thf(195,plain,
! [A: $i] :
( ( A != sk12 )
| ( sk15 != sk1 )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[193]) ).
thf(199,plain,
( ( sk15 != sk1 )
| ~ ( sk12 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[195]) ).
thf(22038,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21752,199]) ).
thf(22039,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[22038]) ).
thf(22086,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[22039]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk7 )
| ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk7 )
| ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(28208,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[26711,186]) ).
thf(28209,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[28208]) ).
thf(28270,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[28209]) ).
thf(2296,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[921,45]) ).
thf(2297,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[2296]) ).
thf(2298,plain,
( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
| ~ ( sk15 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[2297:[bind(A,$thf( sk15 )),bind(B,$thf( sk15 @ sk16 ))]]) ).
thf(8376,plain,
( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
| ~ $true ),
inference(rewrite,[status(thm)],[2298,28]) ).
thf(8377,plain,
sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2,
inference(simp,[status(thm)],[8376]) ).
thf(8395,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8377,7447]) ).
thf(8396,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[8395]) ).
thf(8426,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[8396]) ).
thf(672,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[616,43]) ).
thf(673,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[672]) ).
thf(710,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 )
!= A )
| ( ( sk1 @ sk10 )
!= sk13 )
| ( A @ p1 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[673]) ).
thf(719,plain,
( ( ( sk1 @ sk10 )
!= sk13 )
| ( sk1 @ sk10 @ sk10 @ p1 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[710]) ).
thf(11286,plain,
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,5396]) ).
thf(11287,plain,
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[11286]) ).
thf(11454,plain,
( ( sk13 != sk13 )
| ( sk12 != sk1 )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[11287]) ).
thf(11476,plain,
( ( sk12 != sk1 )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[11454]) ).
thf(12671,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[11476,991]) ).
thf(12672,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[12671]) ).
thf(12718,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[12672]) ).
thf(33786,plain,
! [A: $i] :
( ( ( sk13 @ sk16 @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[972,2411]) ).
thf(33787,plain,
! [A: $i] :
( ( ( sk13 @ sk16 @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[33786]) ).
thf(33814,plain,
! [A: $i] :
( ( ( sk13 @ sk16 )
!= A )
| ( sk13 != sk1 )
| ( sk15 != sk12 )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33787]) ).
thf(33876,plain,
( ( sk13 != sk1 )
| ( sk15 != sk12 )
| ( sk1 @ ( sk13 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33814]) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[38]) ).
thf(264,plain,
! [A: $i] :
( ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(271,plain,
! [A: $i] :
( ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(50461,plain,
! [A: $i] :
( ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[271,59]) ).
thf(50462,plain,
! [A: $i] :
( ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[50461]) ).
thf(50584,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,50462]) ).
thf(50585,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[50584]) ).
thf(50586,plain,
( ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[50585:[bind(A,$thf( sk1 @ ( sk1 @ sk2 ) ))]]) ).
thf(21803,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6622,2408]) ).
thf(21804,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21803]) ).
thf(21944,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= A )
| ( sk14 != sk12 )
| ( sk12 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21804]) ).
thf(21985,plain,
( ( sk14 != sk12 )
| ( sk12 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21944]) ).
thf(617,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,8]) ).
thf(618,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[617]) ).
thf(619,plain,
( ~ ( sk1 @ sk10 @ p4 )
| ( sk1 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[618:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(35512,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33880,198]) ).
thf(35513,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35512]) ).
thf(35584,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35513]) ).
thf(303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( D @ ( sk1 @ r1 ) ) )
| ( D @ sk10 @ ( D @ r1 ) )
| ( D @ sk7 )
| ~ $true
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[36,49]) ).
thf(304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( D @ ( sk1 @ r1 ) ) )
| ( D @ sk10 @ ( D @ r1 ) )
| ( D @ sk7 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[303]) ).
thf(305,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( sk1 @ sk6 ) ) @ sk10 @ ( B @ ( A @ ( sk1 @ sk6 ) ) @ r1 ) )
| ( B @ ( A @ ( sk1 @ sk6 ) ) @ sk7 )
| ~ ( sk1 @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[304:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( sk1 )),bind(D,$thf( G @ ( F @ ( sk1 @ sk6 ) ) ))]]) ).
thf(344,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( sk1 @ sk6 ) ) @ sk10 @ ( B @ ( A @ ( sk1 @ sk6 ) ) @ r1 ) )
| ( B @ ( A @ ( sk1 @ sk6 ) ) @ sk7 )
| ~ ( sk1 @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[305]) ).
thf(33986,plain,
( ( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33680,991]) ).
thf(33987,plain,
( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[33986]) ).
thf(34062,plain,
( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) ),
inference(simp,[status(thm)],[33987]) ).
thf(21677,plain,
! [A: $i] :
( ( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[308,2408]) ).
thf(21678,plain,
! [A: $i] :
( ( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[21677]) ).
thf(21679,plain,
( ( sk12 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
| ( sk12 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[21678:[bind(A,$thf( sk12 @ sk10 ))]]) ).
thf(23805,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ~ $true
| ( sk15 @ sk4 )
| ( sk15 @ sk7 )
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[21679,13203]) ).
thf(23806,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[23805]) ).
thf(23864,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) )
!= sk15 )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[23806]) ).
thf(2307,plain,
! [B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[12,45]) ).
thf(2308,plain,
! [B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[2307]) ).
thf(2309,plain,
( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[2308:[bind(A,$thf( sk12 )),bind(B,$thf( sk14 ))]]) ).
thf(3005,plain,
( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
| ~ $true ),
inference(rewrite,[status(thm)],[2309,24]) ).
thf(3006,plain,
sk12 @ ( sk14 @ sk2 ) @ p2,
inference(simp,[status(thm)],[3005]) ).
thf(7491,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3006,7447]) ).
thf(7492,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[7491]) ).
thf(7496,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[7492]) ).
thf(35213,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33865,199]) ).
thf(35214,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35213]) ).
thf(35271,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35214]) ).
thf(2015,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( B @ ( C @ sk3 ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,44]) ).
thf(2016,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( B @ ( C @ sk3 ) @ p3 )
| ~ ( C @ ( B @ r1 ) ) ),
inference(simp,[status(thm)],[2015]) ).
thf(2017,plain,
! [A: $i] :
( ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[2016:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(2091,plain,
! [A: $i] :
( ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[2017]) ).
thf(15920,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,2091]) ).
thf(15921,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[15920]) ).
thf(15922,plain,
( ~ ( sk1 @ ( sk1 @ sk10 @ sk3 ) @ p3 )
| ( sk1 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[15921:[bind(A,$thf( sk1 @ sk10 ))]]) ).
thf(9955,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9929,199]) ).
thf(9956,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[9955]) ).
thf(9989,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[9956]) ).
thf(28064,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26772,186]) ).
thf(28065,plain,
( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[28064]) ).
thf(28106,plain,
( ( sk15 @ ( sk15 @ sk2 ) )
!= ( sk15 @ sk16 ) ),
inference(simp,[status(thm)],[28065]) ).
thf(3016,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3006,199]) ).
thf(3017,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[3016]) ).
thf(3029,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[3017]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,36]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(79,plain,
! [A: $i] :
( ( sk1 @ ( sk12 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk12 @ r1 ) )
| ~ ( sk12 @ p2 )
| ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( sk1 )),bind(B,$thf( sk12 ))]]) ).
thf(132,plain,
! [A: $i] :
( ( sk1 @ ( sk12 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk12 @ r1 ) )
| ~ ( sk12 @ p2 )
| ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(16987,plain,
! [A: $i] :
( ( sk1 @ ( sk12 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk12 @ r1 ) )
| ~ ( sk12 @ p2 )
| ( sk12 @ sk4 )
| ~ $true ),
inference(rewrite,[status(thm)],[132,59]) ).
thf(16988,plain,
! [A: $i] :
( ( sk1 @ ( sk12 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk12 @ r1 ) )
| ~ ( sk12 @ p2 )
| ( sk12 @ sk4 ) ),
inference(simp,[status(thm)],[16987]) ).
thf(16998,plain,
! [A: $i] :
( ( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk1 @ ( sk12 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ $true
| ~ ( sk12 @ p2 )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[308,16988]) ).
thf(16999,plain,
! [A: $i] :
( ( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk1 @ ( sk12 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( sk12 @ p2 )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[16998]) ).
thf(17000,plain,
( ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ~ ( sk12 @ p2 )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[16999:[bind(A,$thf( sk12 @ sk10 ))]]) ).
thf(28006,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ~ $true
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[26772,17000]) ).
thf(28007,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[28006]) ).
thf(28121,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) )
!= sk12 )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[28007]) ).
thf(50506,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,50462]) ).
thf(50507,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[50506]) ).
thf(50508,plain,
( ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( sk15 @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[50507:[bind(A,$thf( sk15 ))]]) ).
thf(21712,plain,
! [A: $i] :
( ( ( A @ ( sk12 @ r1 ) )
!= ( sk15 @ ( sk1 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,2408]) ).
thf(21713,plain,
! [A: $i] :
( ( ( A @ ( sk12 @ r1 ) )
!= ( sk15 @ ( sk1 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21712]) ).
thf(21934,plain,
! [A: $i] :
( ( A != sk15 )
| ( sk12 != sk1 )
| ( sk12 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21713]) ).
thf(21975,plain,
( ( sk12 != sk1 )
| ( sk12 @ ( sk15 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21934]) ).
thf(9943,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9929,198]) ).
thf(9944,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[9943]) ).
thf(9988,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[9944]) ).
thf(19038,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[316,2100]) ).
thf(19039,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[19038]) ).
thf(19145,plain,
! [A: $i] :
( ( ( sk15 @ sk10 )
!= A )
| ( sk15 != sk12 )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[19039]) ).
thf(19184,plain,
( ( sk15 != sk12 )
| ~ ( sk12 @ ( sk15 @ sk10 @ sk3 ) @ p3 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[19145]) ).
thf(6285,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk3 ) @ ( A @ ( B @ sk2 ) @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[28,54]) ).
thf(6286,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk3 ) @ ( A @ ( B @ sk2 ) @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[6285]) ).
thf(6287,plain,
( ( sk1 @ ( sk15 @ sk3 ) @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ) )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[6286:[bind(A,$thf( sk1 )),bind(B,$thf( sk15 ))]]) ).
thf(72339,plain,
( ( sk1 @ ( sk15 @ sk3 ) @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[6287,59]) ).
thf(72340,plain,
sk1 @ ( sk15 @ sk3 ) @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ),
inference(simp,[status(thm)],[72339]) ).
thf(21800,plain,
! [A: $i] :
( ( ( sk12 @ sk16 @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[978,2408]) ).
thf(21801,plain,
! [A: $i] :
( ( ( sk12 @ sk16 @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[21800]) ).
thf(21802,plain,
( ( sk12 @ ( sk12 @ sk16 @ sk2 ) @ p2 )
| ( sk15 != sk1 ) ),
inference(pattern_uni,[status(thm)],[21801:[bind(A,$thf( sk12 @ sk16 ))]]) ).
thf(24037,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21802,199]) ).
thf(24038,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[24037]) ).
thf(24095,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[24038]) ).
thf(33623,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[921,2411]) ).
thf(33624,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33623]) ).
thf(33856,plain,
! [A: $i] :
( ( ( sk15 @ sk16 )
!= A )
| ( sk15 != sk1 )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33624]) ).
thf(33908,plain,
( ( sk15 != sk1 )
| ( sk1 @ ( sk15 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33856]) ).
thf(13861,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ sk16 @ ( sk14 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[962,2077]) ).
thf(13862,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ sk16 @ ( sk14 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[13861]) ).
thf(13991,plain,
! [A: $i] :
( ( A
!= ( sk14 @ sk16 ) )
| ( sk15 != sk14 )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[13862]) ).
thf(14024,plain,
( ( sk15 != sk14 )
| ~ ( sk15 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[13991]) ).
thf(31246,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ~ $true
| ( sk1 @ sk4 )
| ( sk1 @ sk7 )
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[21679,25889]) ).
thf(31247,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[31246]) ).
thf(31385,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) )
!= sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[31247]) ).
thf(26743,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,2409]) ).
thf(26744,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[26743]) ).
thf(26981,plain,
! [A: $i] :
( ( A
!= ( sk1 @ sk10 ) )
| ( sk15 != sk1 )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[26744]) ).
thf(27028,plain,
( ( sk15 != sk1 )
| ( sk15 @ ( sk1 @ sk10 @ sk2 ) @ p2 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[26981]) ).
thf(15889,plain,
! [A: $i] :
( ( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[308,2091]) ).
thf(15890,plain,
! [A: $i] :
( ( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[15889]) ).
thf(16004,plain,
! [A: $i] :
( ( ( sk12 @ sk10 )
!= A )
| ( sk12 != sk1 )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[15890]) ).
thf(16035,plain,
( ( sk12 != sk1 )
| ~ ( sk1 @ ( sk12 @ sk10 @ sk3 ) @ p3 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[16004]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk11 @ ( A @ r1 ) )
| ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk11 @ ( A @ r1 ) )
| ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(26438,plain,
( ( ( sk12 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[21996,198]) ).
thf(26439,plain,
( ( ( sk12 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[26438]) ).
thf(26517,plain,
( ( ( sk12 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[26439]) ).
thf(4583,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4527,48]) ).
thf(4584,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[4583]) ).
thf(4650,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= A )
| ( sk15 != sk12 )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[4584]) ).
thf(4675,plain,
( ( sk15 != sk12 )
| ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ ( sk1 @ ( sk12 @ sk2 ) @ r1 ) ) ),
inference(simp,[status(thm)],[4650]) ).
thf(157,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,43]) ).
thf(158,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[157]) ).
thf(173,plain,
! [A: $i] :
( ( A != sk12 )
| ( sk13 != sk1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[158]) ).
thf(178,plain,
( ( sk13 != sk1 )
| ( sk12 @ p1 ) ),
inference(simp,[status(thm)],[173]) ).
thf(287,plain,
( ( ( sk14 @ p1 )
!= ( sk12 @ p1 ) )
| ~ $true
| ( sk13 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[178,18]) ).
thf(288,plain,
( ( ( sk14 @ p1 )
!= ( sk12 @ p1 ) )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[287]) ).
thf(289,plain,
( ( sk14 != sk12 )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[288]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk7 )
| ( A @ ( B @ ( C @ sk8 ) ) @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk7 )
| ( A @ ( B @ ( C @ sk8 ) ) @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(17540,plain,
( ( ( sk14 @ ( sk1 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,6674]) ).
thf(17541,plain,
( ( ( sk14 @ ( sk1 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17540]) ).
thf(17752,plain,
( ( sk14 != sk12 )
| ( sk1 != sk1 )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17541]) ).
thf(17792,plain,
( ( sk14 != sk12 )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17752]) ).
thf(17847,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk14 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[17792,186]) ).
thf(17848,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk14 != sk12 ) ),
inference(simp,[status(thm)],[17847]) ).
thf(17884,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk14 != sk12 ) ),
inference(simp,[status(thm)],[17848]) ).
thf(28191,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[26711,991]) ).
thf(28192,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[28191]) ).
thf(28249,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[28192]) ).
thf(6009,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3450,5848]) ).
thf(6010,plain,
( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[6009]) ).
thf(6025,plain,
( ( sk1 @ ( sk1 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) ),
inference(simp,[status(thm)],[6010]) ).
thf(4533,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4527,37]) ).
thf(4534,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[4533]) ).
thf(4645,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= A )
| ( sk15 != sk12 )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[4534]) ).
thf(4670,plain,
( ( sk15 != sk12 )
| ~ ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[4645]) ).
thf(4684,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2413,4670]) ).
thf(4685,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[4684]) ).
thf(4696,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ sk16 )
!= ( sk1 @ ( sk12 @ sk2 ) ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[4685]) ).
thf(15907,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[316,2091]) ).
thf(15908,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15907]) ).
thf(16019,plain,
! [A: $i] :
( ( ( sk15 @ sk10 )
!= A )
| ( sk15 != sk1 )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15908]) ).
thf(16050,plain,
( ( sk15 != sk1 )
| ~ ( sk1 @ ( sk15 @ sk10 @ sk3 ) @ p3 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[16019]) ).
thf(34000,plain,
( ( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33680,186]) ).
thf(34001,plain,
( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[34000]) ).
thf(34045,plain,
( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) ),
inference(simp,[status(thm)],[34001]) ).
thf(2985,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2973,991]) ).
thf(2986,plain,
( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[2985]) ).
thf(2996,plain,
( ( sk1 @ ( sk15 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) ),
inference(simp,[status(thm)],[2986]) ).
thf(2458,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2446,991]) ).
thf(2459,plain,
( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[2458]) ).
thf(2469,plain,
( ( sk12 @ ( sk13 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) ),
inference(simp,[status(thm)],[2459]) ).
thf(7310,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,293]) ).
thf(7311,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[7310]) ).
thf(7431,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= sk13 )
| ( sk1 != sk1 )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[7311]) ).
thf(7441,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= sk13 )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[7431]) ).
thf(26827,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6622,2409]) ).
thf(26828,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26827]) ).
thf(26915,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= A )
| ( sk15 != sk14 )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26828]) ).
thf(26988,plain,
( ( sk15 != sk14 )
| ( sk15 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26915]) ).
thf(31601,plain,
( ( ( sk15 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk14 ) ),
inference(paramod_ordered,[status(thm)],[26988,186]) ).
thf(31602,plain,
( ( ( sk15 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[31601]) ).
thf(31652,plain,
( ( ( sk15 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[31602]) ).
thf(1660,plain,
! [A: $i] :
( ( ( sk12 @ sk16 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[978,8]) ).
thf(1661,plain,
! [A: $i] :
( ( ( sk12 @ sk16 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[1660]) ).
thf(1672,plain,
! [A: $i] :
( ( ( sk12 @ sk16 )
!= A )
| ( sk12 != sk1 )
| ~ ( A @ p4 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[1661]) ).
thf(1682,plain,
( ( sk12 != sk1 )
| ~ ( sk12 @ sk16 @ p4 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[1672]) ).
thf(1467,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ sk16 @ ( sk13 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[972,37]) ).
thf(1468,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ sk16 @ ( sk13 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1467]) ).
thf(1513,plain,
! [A: $i] :
( ( A
!= ( sk13 @ sk16 ) )
| ( sk15 != sk13 )
| ~ ( A @ sk16 @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1468]) ).
thf(1524,plain,
( ( sk15 != sk13 )
| ~ ( sk13 @ sk16 @ sk16 @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1513]) ).
thf(5548,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[3006,1524]) ).
thf(5549,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[5548]) ).
thf(5558,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= ( sk13 @ sk16 @ sk16 ) )
| ( sk15 != sk13 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[5549]) ).
thf(5892,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[5840,45]) ).
thf(5893,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[5892]) ).
thf(5894,plain,
( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
| ~ ( sk15 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[5893:[bind(A,$thf( sk15 )),bind(B,$thf( sk1 @ ( sk15 @ sk2 ) ))]]) ).
thf(15482,plain,
( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
| ~ $true ),
inference(rewrite,[status(thm)],[5894,28]) ).
thf(15483,plain,
sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2,
inference(simp,[status(thm)],[15482]) ).
thf(15518,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15483,991]) ).
thf(15519,plain,
( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[15518]) ).
thf(15554,plain,
( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) ),
inference(simp,[status(thm)],[15519]) ).
thf(1648,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk16 @ ( sk12 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[978,48]) ).
thf(1649,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk16 @ ( sk12 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[1648]) ).
thf(1667,plain,
! [A: $i] :
( ( A
!= ( sk12 @ sk16 ) )
| ( sk15 != sk12 )
| ( sk15 != sk1 )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[1649]) ).
thf(1677,plain,
( ( sk15 != sk12 )
| ( sk15 != sk1 )
| ( sk12 @ sk16 @ sk16 @ ( sk12 @ sk16 @ r1 ) ) ),
inference(simp,[status(thm)],[1667]) ).
thf(23901,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21975,198]) ).
thf(23902,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[23901]) ).
thf(23983,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[23902]) ).
thf(18187,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ~ $true
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[3006,17000]) ).
thf(18188,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[18187]) ).
thf(18324,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= sk12 )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[18188]) ).
thf(67245,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk3 ) @ ( sk1 @ ( sk12 @ sk2 ) @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67007,43]) ).
thf(67246,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk3 ) @ ( sk1 @ ( sk12 @ sk2 ) @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[67245]) ).
thf(67472,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk3 ) )
!= A )
| ( ( sk1 @ ( sk12 @ sk2 ) )
!= sk13 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[67246]) ).
thf(67575,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= sk13 )
| ( sk1 @ ( sk12 @ sk3 ) @ p1 ) ),
inference(simp,[status(thm)],[67472]) ).
thf(1990,plain,
! [B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[29,44]) ).
thf(1991,plain,
! [B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[1990]) ).
thf(1992,plain,
( ~ ( sk12 @ ( sk13 @ sk3 ) @ p3 )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[1991:[bind(A,$thf( sk12 )),bind(B,$thf( sk13 ))]]) ).
thf(2104,plain,
( ~ ( sk12 @ ( sk13 @ sk3 ) @ p3 )
| ~ $true ),
inference(rewrite,[status(thm)],[1992,24]) ).
thf(2105,plain,
~ ( sk12 @ ( sk13 @ sk3 ) @ p3 ),
inference(simp,[status(thm)],[2104]) ).
thf(18656,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk14 ) ),
inference(paramod_ordered,[status(thm)],[17798,991]) ).
thf(18657,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[18656]) ).
thf(18700,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[18657]) ).
thf(21776,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,2408]) ).
thf(21777,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21776]) ).
thf(21893,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 )
!= A )
| ( ( sk15 @ sk16 )
!= sk12 )
| ( sk12 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21777]) ).
thf(21953,plain,
( ( ( sk15 @ sk16 )
!= sk12 )
| ( sk12 @ ( sk15 @ sk16 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21893]) ).
thf(3458,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3450,198]) ).
thf(3459,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[3458]) ).
thf(3473,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[3459]) ).
thf(6035,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5912,37]) ).
thf(6036,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[6035]) ).
thf(6166,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ sk16 )
!= A )
| ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk15 )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[6036]) ).
thf(6189,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk15 )
| ~ ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[6166]) ).
thf(2419,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) )
| ( ( sk15 @ sk16 )
!= sk15 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2413,1106]) ).
thf(2420,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) )
| ( ( sk15 @ sk16 )
!= sk15 ) ),
inference(simp,[status(thm)],[2419]) ).
thf(2437,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 @ sk16 ) )
| ( ( sk15 @ sk16 )
!= sk15 ) ),
inference(simp,[status(thm)],[2420]) ).
thf(35695,plain,
( ( ( sk1 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33908,186]) ).
thf(35696,plain,
( ( ( sk1 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[35695]) ).
thf(35731,plain,
( ( ( sk1 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[35696]) ).
thf(5399,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[5348,44]) ).
thf(5400,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[5399]) ).
thf(5401,plain,
( ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 )
| ~ ( sk13 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[5400:[bind(A,$thf( sk13 )),bind(B,$thf( sk12 @ ( sk13 @ sk2 ) ))]]) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[12,38]) ).
thf(228,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[227]) ).
thf(229,plain,
! [A: $i] :
( ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk14 @ r1 ) )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[228:[bind(A,$thf( sk12 )),bind(B,$thf( sk14 ))]]) ).
thf(269,plain,
! [A: $i] :
( ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk14 @ r1 ) )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(47759,plain,
! [A: $i] :
( ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk14 @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[269,24]) ).
thf(47760,plain,
! [A: $i] :
( ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk14 @ r1 ) ) ),
inference(simp,[status(thm)],[47759]) ).
thf(47841,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk14 @ r1 ) ) )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( B @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,47760]) ).
thf(47842,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk14 @ r1 ) ) )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( B @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[47841]) ).
thf(47843,plain,
( ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( sk14 @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[47842:[bind(A,$thf( sk14 )),bind(B,$thf( sk14 ))]]) ).
thf(3012,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) )
| ( ( sk15 @ sk16 )
!= sk15 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3006,1106]) ).
thf(3013,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) )
| ( ( sk15 @ sk16 )
!= sk15 ) ),
inference(simp,[status(thm)],[3012]) ).
thf(3036,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 @ sk16 ) )
| ( ( sk15 @ sk16 )
!= sk15 ) ),
inference(simp,[status(thm)],[3013]) ).
thf(15710,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ~ $true
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[8377,13203]) ).
thf(15711,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15710]) ).
thf(15831,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= sk15 )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15711]) ).
thf(96256,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[28,2245]) ).
thf(96257,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[96256]) ).
thf(96687,plain,
( ( sk15 != sk14 )
| ( sk1 != sk1 )
| ( sk15 != sk12 )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[96257]) ).
thf(96743,plain,
( ( sk15 != sk14 )
| ( sk15 != sk12 )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[96687]) ).
thf(72592,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk3 ) @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72340,43]) ).
thf(72593,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk3 ) @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[72592]) ).
thf(72802,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk3 ) )
!= A )
| ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk13 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[72593]) ).
thf(72904,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk13 )
| ( sk1 @ ( sk15 @ sk3 ) @ p1 ) ),
inference(simp,[status(thm)],[72802]) ).
thf(5435,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5348,8]) ).
thf(5436,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[5435]) ).
thf(5464,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= A )
| ( sk13 != sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[5436]) ).
thf(5489,plain,
( ( sk13 != sk1 )
| ~ ( sk12 @ ( sk13 @ sk2 ) @ p4 ) ),
inference(simp,[status(thm)],[5464]) ).
thf(74723,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk3 ) @ ( sk12 @ ( sk14 @ sk2 ) @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74471,43]) ).
thf(74724,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk3 ) @ ( sk12 @ ( sk14 @ sk2 ) @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[74723]) ).
thf(74938,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk3 ) )
!= A )
| ( ( sk12 @ ( sk14 @ sk2 ) )
!= sk13 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[74724]) ).
thf(75055,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= sk13 )
| ( sk12 @ ( sk14 @ sk3 ) @ p1 ) ),
inference(simp,[status(thm)],[74938]) ).
thf(75083,plain,
( ( ( sk12 @ ( sk14 @ sk3 ) @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( ( sk12 @ ( sk14 @ sk2 ) )
!= sk13 ) ),
inference(paramod_ordered,[status(thm)],[75055,18]) ).
thf(75084,plain,
( ( ( sk12 @ ( sk14 @ sk3 ) @ p1 )
!= ( sk14 @ p1 ) )
| ( ( sk12 @ ( sk14 @ sk2 ) )
!= sk13 ) ),
inference(simp,[status(thm)],[75083]) ).
thf(75090,plain,
( ( ( sk12 @ ( sk14 @ sk3 ) )
!= sk14 )
| ( ( sk12 @ ( sk14 @ sk2 ) )
!= sk13 ) ),
inference(simp,[status(thm)],[75084]) ).
thf(31199,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ~ $true
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[26772,25889]) ).
thf(31200,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31199]) ).
thf(31423,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) )
!= sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31200]) ).
thf(15956,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,2091]) ).
thf(15957,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15956]) ).
thf(15958,plain,
~ ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk3 ) @ p3 ),
inference(pattern_uni,[status(thm)],[15957:[bind(A,$thf( sk1 @ ( sk1 @ sk2 ) ))]]) ).
thf(50484,plain,
! [A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,50462]) ).
thf(50485,plain,
! [A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[50484]) ).
thf(50486,plain,
( ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( sk12 @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[50485:[bind(A,$thf( sk12 ))]]) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk7 )
| ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk7 )
| ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(395,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( A @ sk7 )
| ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ r1 ) )
| ~ $true
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[29,39]) ).
thf(396,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( A @ sk7 )
| ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[395]) ).
thf(397,plain,
! [A: $i] :
( ~ ( A @ sk7 )
| ( A @ ( sk12 @ ( sk13 @ sk8 ) ) @ ( sk13 @ r1 ) )
| ~ ( sk12 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[396:[bind(A,$thf( A )),bind(B,$thf( sk12 )),bind(C,$thf( sk13 ))]]) ).
thf(35681,plain,
( ( ( sk1 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33908,991]) ).
thf(35682,plain,
( ( ( sk1 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[35681]) ).
thf(35738,plain,
( ( ( sk1 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[35682]) ).
thf(1980,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,44]) ).
thf(1981,plain,
! [B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[1980]) ).
thf(1982,plain,
( ~ ( sk1 @ ( sk12 @ sk3 ) @ p3 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[1981:[bind(A,$thf( sk1 )),bind(B,$thf( sk12 ))]]) ).
thf(2102,plain,
( ~ ( sk1 @ ( sk12 @ sk3 ) @ p3 )
| ~ $true ),
inference(rewrite,[status(thm)],[1982,59]) ).
thf(2103,plain,
~ ( sk1 @ ( sk12 @ sk3 ) @ p3 ),
inference(simp,[status(thm)],[2102]) ).
thf(4682,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2973,4670]) ).
thf(4683,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[4682]) ).
thf(4700,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[4683]) ).
thf(28073,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26772,4670]) ).
thf(28074,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28073]) ).
thf(28098,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28074]) ).
thf(2456,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2446,199]) ).
thf(2457,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[2456]) ).
thf(2473,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[2457]) ).
thf(18206,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ~ $true
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[8377,17000]) ).
thf(18207,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[18206]) ).
thf(18312,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= sk12 )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[18207]) ).
thf(15951,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,2091]) ).
thf(15952,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15951]) ).
thf(16013,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 )
!= A )
| ( ( sk15 @ sk16 )
!= sk1 )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15952]) ).
thf(16044,plain,
( ( ( sk15 @ sk16 )
!= sk1 )
| ~ ( sk1 @ ( sk15 @ sk16 @ sk16 @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[16013]) ).
thf(28197,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 @ sk7 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[26711,556]) ).
thf(28198,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[28197]) ).
thf(28267,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) )
!= ( sk15 @ sk10 @ sk16 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[28198]) ).
thf(22040,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21752,991]) ).
thf(22041,plain,
( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[22040]) ).
thf(22097,plain,
( ( sk12 @ ( sk12 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) ),
inference(simp,[status(thm)],[22041]) ).
thf(6109,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5912,43]) ).
thf(6110,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6109]) ).
thf(6157,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ sk16 )
!= A )
| ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk13 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[6110]) ).
thf(6180,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk13 )
| ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p1 ) ),
inference(simp,[status(thm)],[6157]) ).
thf(17519,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk13 ) ),
inference(paramod_ordered,[status(thm)],[6180,18]) ).
thf(17520,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p1 )
!= ( sk14 @ p1 ) )
| ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk13 ) ),
inference(simp,[status(thm)],[17519]) ).
thf(17526,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ sk16 )
!= sk14 )
| ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk13 ) ),
inference(simp,[status(thm)],[17520]) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( B @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[38]) ).
thf(263,plain,
! [A: $i] :
( ~ ( sk1 @ sk4 )
| ~ ( A @ ( sk1 @ ( A @ sk5 ) ) @ p3 )
| ~ ( sk1 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( C )),bind(B,$thf( sk1 ))]]) ).
thf(270,plain,
! [A: $i] :
( ~ ( sk1 @ sk4 )
| ~ ( A @ ( sk1 @ ( A @ sk5 ) ) @ p3 )
| ~ ( sk1 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[263]) ).
thf(13922,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,2077]) ).
thf(13923,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13922]) ).
thf(13972,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 )
!= A )
| ( ( sk15 @ sk16 )
!= sk15 )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13923]) ).
thf(14004,plain,
( ( ( sk15 @ sk16 )
!= sk15 )
| ~ ( sk15 @ ( sk15 @ sk16 @ sk16 @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13972]) ).
thf(1410,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ sk16 @ ( sk14 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[962,48]) ).
thf(1411,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ sk16 @ ( sk14 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1410]) ).
thf(1424,plain,
! [A: $i] :
( ( A
!= ( sk14 @ sk16 ) )
| ( sk15 != sk14 )
| ( sk15 != sk12 )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[1411]) ).
thf(1438,plain,
( ( sk15 != sk14 )
| ( sk15 != sk12 )
| ( sk14 @ sk16 @ sk16 @ ( sk14 @ sk16 @ r1 ) ) ),
inference(simp,[status(thm)],[1424]) ).
thf(2012,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[921,44]) ).
thf(2013,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[2012]) ).
thf(2014,plain,
( ~ ( sk15 @ ( sk15 @ sk16 @ sk3 ) @ p3 )
| ~ ( sk15 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[2013:[bind(A,$thf( sk15 )),bind(B,$thf( sk15 @ sk16 ))]]) ).
thf(8374,plain,
( ~ ( sk15 @ ( sk15 @ sk16 @ sk3 ) @ p3 )
| ~ $true ),
inference(rewrite,[status(thm)],[2014,28]) ).
thf(8375,plain,
~ ( sk15 @ ( sk15 @ sk16 @ sk3 ) @ p3 ),
inference(simp,[status(thm)],[8374]) ).
thf(7355,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,49]) ).
thf(7356,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 ) ),
inference(simp,[status(thm)],[7355]) ).
thf(7357,plain,
( ( sk1 @ ( sk1 @ sk2 ) @ sk10 @ ( sk1 @ ( sk1 @ sk2 ) @ r1 ) )
| ( sk1 @ ( sk1 @ sk2 ) @ sk7 ) ),
inference(pattern_uni,[status(thm)],[7356:[bind(A,$thf( sk1 @ ( sk1 @ sk2 ) ))]]) ).
thf(28460,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27000,199]) ).
thf(28461,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28460]) ).
thf(28525,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28461]) ).
thf(5354,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5348,37]) ).
thf(5355,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[5354]) ).
thf(5462,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= A )
| ( sk15 != sk13 )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[5355]) ).
thf(5487,plain,
( ( sk15 != sk13 )
| ~ ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[5462]) ).
thf(1963,plain,
! [B: $i,A: $i] :
( ( ( sk14 @ sk16 @ ( sk14 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[962,44]) ).
thf(1964,plain,
! [B: $i,A: $i] :
( ( ( sk14 @ sk16 @ ( sk14 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1963]) ).
thf(1965,plain,
( ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ~ ( sk14 @ ( sk1 @ r1 ) )
| ( sk15 != sk12 ) ),
inference(pattern_uni,[status(thm)],[1964:[bind(A,$thf( sk14 )),bind(B,$thf( sk14 @ sk16 ))]]) ).
thf(70801,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[28,1965]) ).
thf(70802,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[70801]) ).
thf(70988,plain,
( ( sk15 != sk14 )
| ( sk1 != sk1 )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[70802]) ).
thf(71051,plain,
( ( sk15 != sk14 )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[70988]) ).
thf(74510,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk3 ) @ ( sk12 @ ( sk14 @ sk2 ) @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74471,37]) ).
thf(74511,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk3 ) @ ( sk12 @ ( sk14 @ sk2 ) @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[74510]) ).
thf(74904,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk3 ) )
!= A )
| ( ( sk12 @ ( sk14 @ sk2 ) )
!= sk15 )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[74511]) ).
thf(75020,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= sk15 )
| ~ ( sk12 @ ( sk14 @ sk3 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[74904]) ).
thf(15909,plain,
! [A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,2091]) ).
thf(15910,plain,
! [A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15909]) ).
thf(16026,plain,
! [A: $i] :
( ( sk13 != A )
| ( sk12 != sk1 )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15910]) ).
thf(16059,plain,
( ( sk12 != sk1 )
| ~ ( sk1 @ ( sk13 @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[16026]) ).
thf(19097,plain,
! [A: $i] :
( ( ( sk12 @ sk16 @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[978,2100]) ).
thf(19098,plain,
! [A: $i] :
( ( ( sk12 @ sk16 @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[19097]) ).
thf(19099,plain,
( ~ ( sk12 @ ( sk12 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk1 ) ),
inference(pattern_uni,[status(thm)],[19098:[bind(A,$thf( sk12 @ sk16 ))]]) ).
thf(2324,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[616,45]) ).
thf(2325,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ p2 )
| ~ ( A @ ( sk1 @ r1 ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[2324]) ).
thf(2326,plain,
( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
| ~ ( sk1 @ sk10 @ ( sk1 @ r1 ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[2325:[bind(A,$thf( sk1 @ sk10 )),bind(B,$thf( sk1 @ sk10 @ sk10 ))]]) ).
thf(4100,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
| ~ $true
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,2326]) ).
thf(4101,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[4100]) ).
thf(4102,plain,
( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[4101:[]]) ).
thf(18224,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ~ $true
| ( sk12 @ sk4 )
| ( sk12 @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[4102,17000]) ).
thf(18225,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[18224]) ).
thf(18325,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) )
!= sk12 )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[18225]) ).
thf(15516,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15483,199]) ).
thf(15517,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[15516]) ).
thf(15563,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[15517]) ).
thf(29565,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27023,991]) ).
thf(29566,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[29565]) ).
thf(29618,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[29566]) ).
thf(13931,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk16 @ ( sk12 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[978,2077]) ).
thf(13932,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk16 @ ( sk12 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[13931]) ).
thf(13968,plain,
! [A: $i] :
( ( A
!= ( sk12 @ sk16 ) )
| ( sk15 != sk12 )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[13932]) ).
thf(14000,plain,
( ( sk15 != sk12 )
| ~ ( sk15 @ ( sk12 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[13968]) ).
thf(7367,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,48]) ).
thf(7368,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[7367]) ).
thf(7430,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= A )
| ( sk15 != sk1 )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[7368]) ).
thf(7439,plain,
( ( sk15 != sk1 )
| ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ ( sk1 @ ( sk1 @ sk2 ) @ r1 ) ) ),
inference(simp,[status(thm)],[7430]) ).
thf(68263,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( B @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,68167]) ).
thf(68264,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( B @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[68263]) ).
thf(68265,plain,
( ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( sk12 @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[68264:[bind(A,$thf( sk12 )),bind(B,$thf( sk12 ))]]) ).
thf(35573,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33880,200]) ).
thf(35574,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35573]) ).
thf(35579,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35574]) ).
thf(28445,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27000,198]) ).
thf(28446,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28445]) ).
thf(28515,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28446]) ).
thf(11292,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,5396]) ).
thf(11293,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[11292]) ).
thf(11428,plain,
( ( sk15 != sk13 )
| ( sk1 != sk1 )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[11293]) ).
thf(11471,plain,
( ( sk15 != sk13 )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[11428]) ).
thf(21739,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[921,2408]) ).
thf(21740,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21739]) ).
thf(21925,plain,
! [A: $i] :
( ( ( sk15 @ sk16 )
!= A )
| ( sk15 != sk12 )
| ( sk12 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21740]) ).
thf(21971,plain,
( ( sk15 != sk12 )
| ( sk12 @ ( sk15 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[21925]) ).
thf(25079,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[21971,4670]) ).
thf(25080,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[25079]) ).
thf(25123,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[25080]) ).
thf(33695,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6622,2411]) ).
thf(33696,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33695]) ).
thf(33804,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= A )
| ( sk14 != sk1 )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33696]) ).
thf(33873,plain,
( ( sk14 != sk1 )
| ( sk1 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33804]) ).
thf(36971,plain,
( ( ( sk1 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk14 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33873,186]) ).
thf(36972,plain,
( ( ( sk1 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk14 != sk1 ) ),
inference(simp,[status(thm)],[36971]) ).
thf(37010,plain,
( ( ( sk1 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk14 != sk1 ) ),
inference(simp,[status(thm)],[36972]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,36]) ).
thf(101,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ( sk14 != A )
| ( sk12 != sk1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ( B @ sk4 ) ),
inference(simp,[status(thm)],[101]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( sk12 != sk1 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ~ ( A @ ( sk14 @ r1 ) )
| ( sk14 @ ( A @ ( B @ sk6 ) ) @ ( B @ r1 ) )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[123]) ).
thf(22054,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21752,186]) ).
thf(22055,plain,
( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[22054]) ).
thf(22082,plain,
( ( sk12 @ ( sk12 @ sk2 ) )
!= ( sk15 @ sk16 ) ),
inference(simp,[status(thm)],[22055]) ).
thf(225,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,38]) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[225]) ).
thf(267,plain,
! [C: $i,B: $i,A: $i] :
( ( sk14 != A )
| ( sk12 != sk1 )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[226]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( sk12 != sk1 )
| ~ ( A @ sk4 )
| ~ ( sk14 @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk14 @ r1 ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk13 @ r1 ) ) )
| ( B @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,43]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk13 @ r1 ) ) )
| ( B @ p1 ) ),
inference(simp,[status(thm)],[163]) ).
thf(165,plain,
sk13 @ p1,
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( sk13 )),bind(B,$thf( sk13 ))]]) ).
thf(603,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,37]) ).
thf(604,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[603]) ).
thf(621,plain,
! [A: $i] :
( ( A
!= ( sk1 @ sk10 ) )
| ( sk15 != sk1 )
| ~ ( A @ sk16 @ p2 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[604]) ).
thf(625,plain,
( ( sk15 != sk1 )
| ~ ( sk1 @ sk10 @ sk16 @ p2 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[621]) ).
thf(22030,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21752,7447]) ).
thf(22031,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[22030]) ).
thf(22104,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[22031]) ).
thf(19086,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,2100]) ).
thf(19087,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19086]) ).
thf(19172,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 )
!= A )
| ( ( sk15 @ sk16 )
!= sk12 )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19087]) ).
thf(19214,plain,
( ( ( sk15 @ sk16 )
!= sk12 )
| ~ ( sk12 @ ( sk15 @ sk16 @ sk16 @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19172]) ).
thf(28050,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26772,991]) ).
thf(28051,plain,
( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[28050]) ).
thf(28115,plain,
( ( sk15 @ ( sk15 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) ),
inference(simp,[status(thm)],[28051]) ).
thf(12601,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk13 ) ),
inference(paramod_ordered,[status(thm)],[11471,186]) ).
thf(12602,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[12601]) ).
thf(12618,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[12602]) ).
thf(13691,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ ( sk1 @ sk10 @ sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ~ $true
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[12812,49]) ).
thf(13692,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ ( sk1 @ sk10 @ sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[13691]) ).
thf(13787,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) )
!= A )
| ( ( sk1 @ sk10 @ sk10 )
!= sk1 )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[13692]) ).
thf(13835,plain,
( ( ( sk1 @ sk10 @ sk10 )
!= sk1 )
| ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ sk10 @ ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ r1 ) )
| ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[13787]) ).
thf(3020,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[3006,556]) ).
thf(3021,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[3020]) ).
thf(3028,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= ( sk15 @ sk10 @ sk16 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[3021]) ).
thf(544,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[316,43]) ).
thf(545,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[544]) ).
thf(571,plain,
! [A: $i] :
( ( ( sk15 @ sk10 )
!= A )
| ( sk15 != sk13 )
| ( A @ p1 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[545]) ).
thf(579,plain,
( ( sk15 != sk13 )
| ( sk15 @ sk10 @ p1 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[571]) ).
thf(2206,plain,
( ( ( sk15 @ sk10 @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( sk15 != sk13 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[579,18]) ).
thf(2207,plain,
( ( ( sk15 @ sk10 @ p1 )
!= ( sk14 @ p1 ) )
| ( sk15 != sk13 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[2206]) ).
thf(2211,plain,
( ( ( sk15 @ sk10 )
!= sk14 )
| ( sk15 != sk13 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[2207]) ).
thf(3018,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3006,991]) ).
thf(3019,plain,
( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[3018]) ).
thf(3033,plain,
( ( sk12 @ ( sk14 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) ),
inference(simp,[status(thm)],[3019]) ).
thf(23790,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[21679,991]) ).
thf(23791,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[23790]) ).
thf(23841,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[23791]) ).
thf(63,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,8]) ).
thf(64,plain,
! [A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[63]) ).
thf(65,plain,
~ ( sk15 @ p4 ),
inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( sk15 ))]]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[29,38]) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[210]) ).
thf(212,plain,
! [A: $i] :
( ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk13 @ r1 ) )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[211:[bind(A,$thf( sk12 )),bind(B,$thf( sk13 ))]]) ).
thf(278,plain,
! [A: $i] :
( ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk13 @ r1 ) )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[212]) ).
thf(64098,plain,
! [A: $i] :
( ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk13 @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[278,24]) ).
thf(64099,plain,
! [A: $i] :
( ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( sk13 @ r1 ) ) ),
inference(simp,[status(thm)],[64098]) ).
thf(64147,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk15 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,64099]) ).
thf(64148,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk15 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[64147]) ).
thf(64323,plain,
! [A: $i] :
( ( A != sk15 )
| ( sk13 != sk1 )
| ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[64148]) ).
thf(64391,plain,
( ( sk13 != sk1 )
| ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( sk15 @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[64323]) ).
thf(901,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[316,48]) ).
thf(902,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[901]) ).
thf(903,plain,
( ( sk15 @ sk10 @ sk16 @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[902:[bind(A,$thf( sk15 @ sk10 ))]]) ).
thf(1146,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ sk16 @ ( sk15 @ sk10 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[903,43]) ).
thf(1147,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ sk16 @ ( sk15 @ sk10 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[1146]) ).
thf(1166,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ sk16 )
!= A )
| ( ( sk15 @ sk10 )
!= sk13 )
| ( A @ p1 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[1147]) ).
thf(1178,plain,
( ( ( sk15 @ sk10 )
!= sk13 )
| ( sk15 @ sk10 @ sk16 @ p1 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[1166]) ).
thf(5424,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5348,43]) ).
thf(5425,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[5424]) ).
thf(5426,plain,
sk12 @ ( sk13 @ sk2 ) @ p1,
inference(pattern_uni,[status(thm)],[5425:[bind(A,$thf( sk12 @ ( sk13 @ sk2 ) ))]]) ).
thf(5511,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5426,18]) ).
thf(5512,plain,
( ( sk12 @ ( sk13 @ sk2 ) @ p1 )
!= ( sk14 @ p1 ) ),
inference(simp,[status(thm)],[5511]) ).
thf(5515,plain,
( ( sk12 @ ( sk13 @ sk2 ) )
!= sk14 ),
inference(simp,[status(thm)],[5512]) ).
thf(29548,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27023,198]) ).
thf(29549,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[29548]) ).
thf(29626,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[29549]) ).
thf(940,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[616,48]) ).
thf(941,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[940]) ).
thf(956,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 )
!= A )
| ( ( sk1 @ sk10 )
!= sk15 )
| ( A @ sk16 @ ( A @ r1 ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[941]) ).
thf(974,plain,
( ( ( sk1 @ sk10 )
!= sk15 )
| ( sk1 @ sk10 @ sk10 @ sk16 @ ( sk1 @ sk10 @ sk10 @ r1 ) )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[956]) ).
thf(222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( D @ ( C @ r1 ) ) )
| ~ ( C @ sk4 )
| ~ ( B @ ( C @ ( D @ sk5 ) ) @ p3 )
| ~ $true
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[59,38]) ).
thf(223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( D @ ( C @ r1 ) ) )
| ~ ( C @ sk4 )
| ~ ( B @ ( C @ ( D @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[222]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( B @ ( A @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[223:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(15689,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ~ $true
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[2446,13203]) ).
thf(15690,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15689]) ).
thf(15826,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= sk15 )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15690]) ).
thf(312,plain,
! [A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,49]) ).
thf(313,plain,
! [A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 ) ),
inference(simp,[status(thm)],[312]) ).
thf(337,plain,
! [A: $i] :
( ( sk13 != A )
| ( sk12 != sk1 )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 ) ),
inference(simp,[status(thm)],[313]) ).
thf(345,plain,
( ( sk12 != sk1 )
| ( sk13 @ sk10 @ ( sk13 @ r1 ) )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[337]) ).
thf(9073,plain,
! [A: $i] :
( ( ( sk13 @ sk10 @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk12 != sk1 )
| ( sk13 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[345,8]) ).
thf(9074,plain,
! [A: $i] :
( ( ( sk13 @ sk10 @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk12 != sk1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[9073]) ).
thf(9118,plain,
! [A: $i] :
( ( ( sk13 @ sk10 )
!= A )
| ( sk13 != sk1 )
| ~ ( A @ p4 )
| ( sk12 != sk1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[9074]) ).
thf(9145,plain,
( ( sk13 != sk1 )
| ~ ( sk13 @ sk10 @ p4 )
| ( sk12 != sk1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[9118]) ).
thf(149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( B @ ( C @ ( D @ sk6 ) ) @ ( D @ r1 ) )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ $true
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[59,36]) ).
thf(150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( B @ ( C @ ( D @ sk6 ) ) @ ( D @ r1 ) )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[149]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk6 ) ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[150:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk6 ) ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(22072,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21752,200]) ).
thf(22073,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[22072]) ).
thf(22085,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[22073]) ).
thf(6011,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2973,5848]) ).
thf(6012,plain,
( ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[6011]) ).
thf(6028,plain,
( ( sk1 @ ( sk15 @ sk2 ) @ sk16 )
!= ( sk1 @ ( sk15 @ sk2 ) ) ),
inference(simp,[status(thm)],[6012]) ).
thf(28441,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27000,5848]) ).
thf(28442,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28441]) ).
thf(28532,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28442]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( B @ p2 )
| ~ ( B @ ( A @ sk10 @ r1 ) )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( B @ p2 )
| ~ ( B @ ( A @ sk10 @ r1 ) )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(4765,plain,
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,293]) ).
thf(4766,plain,
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[4765]) ).
thf(4823,plain,
( ( sk13 != sk13 )
| ( sk12 != sk1 )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[4766]) ).
thf(4840,plain,
( ( sk12 != sk1 )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[4823]) ).
thf(8393,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8377,6783]) ).
thf(8394,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[8393]) ).
thf(8429,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[8394]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,36]) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ( sk13 != A )
| ( sk12 != sk1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ~ ( B @ ( A @ r1 ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ( B @ sk4 ) ),
inference(simp,[status(thm)],[84]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( sk12 != sk1 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ~ ( A @ ( sk13 @ r1 ) )
| ( sk13 @ ( A @ ( B @ sk6 ) ) @ ( B @ r1 ) )
| ( A @ sk4 ) ),
inference(simp,[status(thm)],[126]) ).
thf(64106,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5348,64099]) ).
thf(64107,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[64106]) ).
thf(64108,plain,
( ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[64107:[bind(A,$thf( sk12 @ ( sk13 @ sk2 ) ))]]) ).
thf(15965,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6622,2091]) ).
thf(15966,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15965]) ).
thf(16023,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= A )
| ( sk14 != sk1 )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15966]) ).
thf(16055,plain,
( ( sk14 != sk1 )
| ~ ( sk1 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[16023]) ).
thf(25671,plain,
( ( ( sk12 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk14 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[21985,186]) ).
thf(25672,plain,
( ( ( sk12 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk14 != sk12 ) ),
inference(simp,[status(thm)],[25671]) ).
thf(25721,plain,
( ( ( sk12 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk14 != sk12 ) ),
inference(simp,[status(thm)],[25672]) ).
thf(18119,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ~ $true
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[3450,17000]) ).
thf(18120,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[18119]) ).
thf(18303,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= sk12 )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[18120]) ).
thf(4779,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,293]) ).
thf(4780,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[4779]) ).
thf(4833,plain,
! [A: $i] :
( ( A != sk13 )
| ( A != sk1 )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[4780]) ).
thf(4845,plain,
( ( sk13 != sk1 )
| ( sk13 @ sk10 @ p1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[4833]) ).
thf(28313,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[26992,198]) ).
thf(28314,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28313]) ).
thf(28382,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28314]) ).
thf(2991,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2973,186]) ).
thf(2992,plain,
( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[2991]) ).
thf(3001,plain,
( ( sk1 @ ( sk15 @ sk2 ) )
!= ( sk15 @ sk16 ) ),
inference(simp,[status(thm)],[2992]) ).
thf(15691,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ~ $true
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[3006,13203]) ).
thf(15692,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15691]) ).
thf(15798,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= sk15 )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15692]) ).
thf(320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk10 @ ( A @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( C @ sk4 )
| ~ ( B @ ( C @ ( D @ sk5 ) ) @ p3 )
| ~ ( D @ ( C @ r1 ) )
| ~ $true
| ~ ( B @ ( sk1 @ r1 ) )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[49,38]) ).
thf(321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk10 @ ( A @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( C @ sk4 )
| ~ ( B @ ( C @ ( D @ sk5 ) ) @ p3 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[320]) ).
thf(322,plain,
! [B: $i,A: $i] :
( ~ ( B @ sk10 @ sk4 )
| ~ ( B @ ( B @ sk10 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( B @ sk10 @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) )
| ( B @ sk7 )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[321:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk10 ))]]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ~ ( B @ sk10 @ sk4 )
| ~ ( B @ ( B @ sk10 @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( B @ sk10 @ r1 ) )
| ( B @ sk7 )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[322]) ).
thf(653,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ ( sk12 @ r1 ) ) )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,630]) ).
thf(654,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ ( sk12 @ r1 ) ) )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[653]) ).
thf(662,plain,
! [A: $i] :
( ( A != sk14 )
| ( sk15 != sk12 )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[654]) ).
thf(669,plain,
( ( sk15 != sk12 )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( sk14 @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[662]) ).
thf(15963,plain,
! [A: $i] :
( ( ( sk12 @ sk16 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[978,2091]) ).
thf(15964,plain,
! [A: $i] :
( ( ( sk12 @ sk16 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[15963]) ).
thf(16005,plain,
! [A: $i] :
( ( ( sk12 @ sk16 )
!= A )
| ( sk12 != sk1 )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[15964]) ).
thf(16036,plain,
( ( sk12 != sk1 )
| ~ ( sk1 @ ( sk12 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[16005]) ).
thf(35506,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33880,5848]) ).
thf(35507,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35506]) ).
thf(35592,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35507]) ).
thf(19068,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( B @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,2100]) ).
thf(19069,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( B @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19068]) ).
thf(19070,plain,
~ ( sk12 @ ( sk12 @ sk3 ) @ p3 ),
inference(pattern_uni,[status(thm)],[19069:[bind(A,$thf( sk12 )),bind(B,$thf( sk12 ))]]) ).
thf(1491,plain,
! [A: $i] :
( ( ( sk13 @ sk16 @ ( sk13 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[972,43]) ).
thf(1492,plain,
! [A: $i] :
( ( ( sk13 @ sk16 @ ( sk13 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1491]) ).
thf(1493,plain,
( ( sk13 @ sk16 @ p1 )
| ( sk15 != sk12 ) ),
inference(pattern_uni,[status(thm)],[1492:[bind(A,$thf( sk13 @ sk16 ))]]) ).
thf(2993,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2973,200]) ).
thf(2994,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2993]) ).
thf(3000,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2994]) ).
thf(47796,plain,
! [A: $i] :
( ( ( A @ ( sk14 @ r1 ) )
!= ( sk13 @ ( sk12 @ r1 ) ) )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,47760]) ).
thf(47797,plain,
! [A: $i] :
( ( ( A @ ( sk14 @ r1 ) )
!= ( sk13 @ ( sk12 @ r1 ) ) )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[47796]) ).
thf(47984,plain,
! [A: $i] :
( ( A != sk13 )
| ( sk14 != sk12 )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[47797]) ).
thf(48045,plain,
( ( sk14 != sk12 )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( sk13 @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[47984]) ).
thf(15658,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ~ $true
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[2413,13203]) ).
thf(15659,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15658]) ).
thf(15793,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= sk15 )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15659]) ).
thf(22001,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ~ $true
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[21752,17000]) ).
thf(22002,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[22001]) ).
thf(22100,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) )
!= sk12 )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[22002]) ).
thf(4720,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[4102,556]) ).
thf(4721,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ( sk15 @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[4720]) ).
thf(4744,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) )
!= ( sk15 @ sk10 @ sk16 ) )
| ( sk15 @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[4721]) ).
thf(3026,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3006,200]) ).
thf(3027,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[3026]) ).
thf(3032,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[3027]) ).
thf(2464,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2446,186]) ).
thf(2465,plain,
( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[2464]) ).
thf(2472,plain,
( ( sk12 @ ( sk13 @ sk2 ) )
!= ( sk15 @ sk16 ) ),
inference(simp,[status(thm)],[2465]) ).
thf(19064,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5840,2100]) ).
thf(19065,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19064]) ).
thf(19155,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= A )
| ( sk15 != sk12 )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19065]) ).
thf(19195,plain,
( ( sk15 != sk12 )
| ~ ( sk12 @ ( sk1 @ ( sk15 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19155]) ).
thf(47804,plain,
! [A: $i] :
( ( ( A @ ( sk14 @ r1 ) )
!= ( sk15 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,47760]) ).
thf(47805,plain,
! [A: $i] :
( ( ( A @ ( sk14 @ r1 ) )
!= ( sk15 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[47804]) ).
thf(47945,plain,
! [A: $i] :
( ( A != sk15 )
| ( sk14 != sk1 )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[47805]) ).
thf(48004,plain,
( ( sk14 != sk1 )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( sk15 @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[47945]) ).
thf(1086,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,8]) ).
thf(1087,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[1086]) ).
thf(1089,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 )
!= A )
| ( ( sk15 @ sk16 )
!= sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[1087]) ).
thf(1099,plain,
( ( ( sk15 @ sk16 )
!= sk1 )
| ~ ( sk15 @ sk16 @ sk16 @ p4 ) ),
inference(simp,[status(thm)],[1089]) ).
thf(26493,plain,
( ( ( sk12 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[21996,200]) ).
thf(26494,plain,
( ( ( sk12 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[26493]) ).
thf(26524,plain,
( ( ( sk12 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[26494]) ).
thf(5897,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[5840,44]) ).
thf(5898,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[5897]) ).
thf(5899,plain,
( ~ ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk3 ) @ p3 )
| ~ ( sk15 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[5898:[bind(A,$thf( sk15 )),bind(B,$thf( sk1 @ ( sk15 @ sk2 ) ))]]) ).
thf(13606,plain,
( ~ ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk3 ) @ p3 )
| ~ $true ),
inference(rewrite,[status(thm)],[5899,28]) ).
thf(13607,plain,
~ ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk3 ) @ p3 ),
inference(simp,[status(thm)],[13606]) ).
thf(18553,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk14 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[17796,991]) ).
thf(18554,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk14 != sk1 ) ),
inference(simp,[status(thm)],[18553]) ).
thf(18608,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk14 != sk1 ) ),
inference(simp,[status(thm)],[18554]) ).
thf(33621,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5840,2411]) ).
thf(33622,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33621]) ).
thf(33817,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= A )
| ( sk15 != sk1 )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33622]) ).
thf(33879,plain,
( ( sk15 != sk1 )
| ( sk1 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33817]) ).
thf(37105,plain,
( ( ( sk1 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33879,199]) ).
thf(37106,plain,
( ( ( sk1 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[37105]) ).
thf(37174,plain,
( ( ( sk1 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[37106]) ).
thf(694,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ~ $true
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[616,49]) ).
thf(695,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[694]) ).
thf(712,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 )
!= A )
| ( ( sk1 @ sk10 )
!= sk1 )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[695]) ).
thf(721,plain,
( ( ( sk1 @ sk10 )
!= sk1 )
| ( sk1 @ sk10 @ sk10 @ sk10 @ ( sk1 @ sk10 @ sk10 @ r1 ) )
| ( sk1 @ sk10 @ sk10 @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[712]) ).
thf(35198,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33865,198]) ).
thf(35199,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35198]) ).
thf(35285,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35199]) ).
thf(11502,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,5401]) ).
thf(11503,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[11502]) ).
thf(11565,plain,
( ( sk15 != sk13 )
| ( sk1 != sk1 )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[11503]) ).
thf(11610,plain,
( ( sk15 != sk13 )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[11565]) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk4 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk4 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(79242,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[59,2062]) ).
thf(79243,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[79242]) ).
thf(79412,plain,
! [A: $i] :
( ( A != sk13 )
| ( A != sk1 )
| ~ ( sk13 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[79243]) ).
thf(79466,plain,
( ( sk13 != sk1 )
| ~ ( sk13 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[79412]) ).
thf(21725,plain,
! [A: $i] :
( ( ( A @ ( sk12 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,2408]) ).
thf(21726,plain,
! [A: $i] :
( ( ( A @ ( sk12 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[21725]) ).
thf(21936,plain,
! [A: $i] :
( ( A
!= ( sk1 @ sk10 ) )
| ( sk12 != sk1 )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[21726]) ).
thf(21976,plain,
( ( sk12 != sk1 )
| ( sk12 @ ( sk1 @ sk10 @ sk2 ) @ p2 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[21936]) ).
thf(64124,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,64099]) ).
thf(64125,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[64124]) ).
thf(64349,plain,
! [A: $i] :
( ( A != sk12 )
| ( sk13 != sk1 )
| ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[64125]) ).
thf(64419,plain,
( ( sk13 != sk1 )
| ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( sk12 @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[64349]) ).
thf(35192,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33865,5848]) ).
thf(35193,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35192]) ).
thf(35270,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35193]) ).
thf(25073,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[21971,186]) ).
thf(25074,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[25073]) ).
thf(25106,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[25074]) ).
thf(7483,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2973,7447]) ).
thf(7484,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[7483]) ).
thf(7495,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[7484]) ).
thf(17585,plain,
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,6674]) ).
thf(17586,plain,
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17585]) ).
thf(17754,plain,
( ( sk14 != sk14 )
| ( sk12 != sk1 )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17586]) ).
thf(17793,plain,
( ( sk12 != sk1 )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17754]) ).
thf(8380,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8377,5487]) ).
thf(8381,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[8380]) ).
thf(8425,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[8381]) ).
thf(114,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( E @ ( D @ r1 ) ) )
| ( D @ ( E @ ( F @ sk6 ) ) @ ( F @ r1 ) )
| ~ ( F @ ( E @ r1 ) )
| ~ ( E @ p2 )
| ( E @ sk4 )
| ~ $true
| ~ ( D @ ( sk1 @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[36,36]) ).
thf(115,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( E @ ( D @ r1 ) ) )
| ( D @ ( E @ ( F @ sk6 ) ) @ ( F @ r1 ) )
| ~ ( F @ ( E @ r1 ) )
| ~ ( E @ p2 )
| ( E @ sk4 )
| ~ ( D @ ( sk1 @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ ( B @ sk6 ) ) @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( D @ ( C @ ( B @ sk6 ) ) @ r1 ) )
| ~ ( D @ ( C @ ( B @ sk6 ) ) @ p2 )
| ( D @ ( C @ ( B @ sk6 ) ) @ sk4 )
| ~ ( B @ ( sk1 @ r1 ) )
| ~ ( B @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( G )),bind(E,$thf( I @ ( H @ ( G @ sk6 ) ) ))]]) ).
thf(134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ ( B @ sk6 ) ) @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( D @ ( C @ ( B @ sk6 ) ) @ r1 ) )
| ~ ( D @ ( C @ ( B @ sk6 ) ) @ p2 )
| ( D @ ( C @ ( B @ sk6 ) ) @ sk4 )
| ~ ( B @ ( sk1 @ r1 ) )
| ~ ( B @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(67046,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk3 ) @ ( sk1 @ ( sk12 @ sk2 ) @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67007,37]) ).
thf(67047,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk3 ) @ ( sk1 @ ( sk12 @ sk2 ) @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[67046]) ).
thf(67381,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk3 ) )
!= A )
| ( ( sk1 @ ( sk12 @ sk2 ) )
!= sk15 )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[67047]) ).
thf(67483,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= sk15 )
| ~ ( sk1 @ ( sk12 @ sk3 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[67381]) ).
thf(203,plain,
( ( ( sk14 @ p1 )
!= ( sk13 @ p1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[165,18]) ).
thf(204,plain,
( ( sk14 @ p1 )
!= ( sk13 @ p1 ) ),
inference(simp,[status(thm)],[203]) ).
thf(205,plain,
sk14 != sk13,
inference(simp,[status(thm)],[204]) ).
thf(8413,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8377,186]) ).
thf(8414,plain,
( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[8413]) ).
thf(8422,plain,
( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk15 @ sk16 ) ),
inference(simp,[status(thm)],[8414]) ).
thf(28503,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27000,200]) ).
thf(28504,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28503]) ).
thf(28519,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28504]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[12,36]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(104,plain,
! [A: $i] :
( ( sk12 @ ( sk14 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk14 @ r1 ) )
| ~ ( sk14 @ p2 )
| ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( sk12 )),bind(B,$thf( sk14 ))]]) ).
thf(129,plain,
! [A: $i] :
( ( sk12 @ ( sk14 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk14 @ r1 ) )
| ~ ( sk14 @ p2 )
| ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(14034,plain,
! [A: $i] :
( ( sk12 @ ( sk14 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk14 @ r1 ) )
| ~ ( sk14 @ p2 )
| ( sk14 @ sk4 )
| ~ $true ),
inference(rewrite,[status(thm)],[129,24]) ).
thf(14035,plain,
! [A: $i] :
( ( sk12 @ ( sk14 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk14 @ r1 ) )
| ~ ( sk14 @ p2 )
| ( sk14 @ sk4 ) ),
inference(simp,[status(thm)],[14034]) ).
thf(15885,plain,
! [A: $i] :
( ( ( sk14 @ sk16 @ ( sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[962,2091]) ).
thf(15886,plain,
! [A: $i] :
( ( ( sk14 @ sk16 @ ( sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[15885]) ).
thf(16017,plain,
! [A: $i] :
( ( ( sk14 @ sk16 )
!= A )
| ( sk14 != sk1 )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[15886]) ).
thf(16048,plain,
( ( sk14 != sk1 )
| ~ ( sk1 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[16017]) ).
thf(79186,plain,
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[29,2062]) ).
thf(79187,plain,
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[79186]) ).
thf(79384,plain,
( ( sk13 != sk13 )
| ( sk12 != sk1 )
| ~ ( sk13 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[79187]) ).
thf(79456,plain,
( ( sk12 != sk1 )
| ~ ( sk13 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[79384]) ).
thf(13933,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6622,2077]) ).
thf(13934,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13933]) ).
thf(13971,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= A )
| ( sk15 != sk14 )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13934]) ).
thf(14003,plain,
( ( sk15 != sk14 )
| ~ ( sk15 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13971]) ).
thf(70775,plain,
( ( ( sk14 @ ( sk1 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[24,1965]) ).
thf(70776,plain,
( ( ( sk14 @ ( sk1 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[70775]) ).
thf(70966,plain,
( ( sk14 != sk12 )
| ( sk1 != sk1 )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[70776]) ).
thf(71045,plain,
( ( sk14 != sk12 )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[70966]) ).
thf(70,plain,
! [A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,8]) ).
thf(71,plain,
! [A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[70]) ).
thf(72,plain,
! [A: $i] :
( ( sk13 != A )
| ( sk12 != sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[71]) ).
thf(73,plain,
( ( sk12 != sk1 )
| ~ ( sk13 @ p4 ) ),
inference(simp,[status(thm)],[72]) ).
thf(5542,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[2413,1524]) ).
thf(5543,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[5542]) ).
thf(5557,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= ( sk13 @ sk16 @ sk16 ) )
| ( sk15 != sk13 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[5543]) ).
thf(28344,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[26992,186]) ).
thf(28345,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28344]) ).
thf(28390,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28345]) ).
thf(300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk10 @ ( A @ r1 ) )
!= ( D @ ( C @ r1 ) ) )
| ( B @ ( C @ ( D @ sk6 ) ) @ ( D @ r1 ) )
| ~ $true
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[49,36]) ).
thf(301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk10 @ ( A @ r1 ) )
!= ( D @ ( C @ r1 ) ) )
| ( B @ ( C @ ( D @ sk6 ) ) @ ( D @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[300]) ).
thf(302,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ sk10 @ sk6 ) ) @ ( B @ sk10 @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ( B @ sk7 )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[301:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( E @ sk10 ))]]) ).
thf(343,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ sk10 @ sk6 ) ) @ ( B @ sk10 @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ( B @ sk7 )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[302]) ).
thf(29579,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27023,186]) ).
thf(29580,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[29579]) ).
thf(29627,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[29580]) ).
thf(15501,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15483,198]) ).
thf(15502,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[15501]) ).
thf(15552,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[15502]) ).
thf(2421,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2413,198]) ).
thf(2422,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2421]) ).
thf(2440,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2422]) ).
thf(1502,plain,
! [A: $i] :
( ( ( sk13 @ sk16 @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[972,8]) ).
thf(1503,plain,
! [A: $i] :
( ( ( sk13 @ sk16 @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1502]) ).
thf(1505,plain,
! [A: $i] :
( ( ( sk13 @ sk16 )
!= A )
| ( sk13 != sk1 )
| ~ ( A @ p4 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1503]) ).
thf(1515,plain,
( ( sk13 != sk1 )
| ~ ( sk13 @ sk16 @ p4 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1505]) ).
thf(28476,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27000,186]) ).
thf(28477,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28476]) ).
thf(28521,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28477]) ).
thf(28048,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26772,199]) ).
thf(28049,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28048]) ).
thf(28124,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28049]) ).
thf(2981,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2973,198]) ).
thf(2982,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2981]) ).
thf(2995,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2982]) ).
thf(23897,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21975,5848]) ).
thf(23898,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[23897]) ).
thf(23985,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[23898]) ).
thf(6019,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3006,5848]) ).
thf(6020,plain,
( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[6019]) ).
thf(6026,plain,
( ( sk12 @ ( sk14 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) ),
inference(simp,[status(thm)],[6020]) ).
thf(13905,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ ( B @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,2077]) ).
thf(13906,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ ( B @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13905]) ).
thf(13907,plain,
~ ( sk15 @ ( sk15 @ sk3 ) @ p3 ),
inference(pattern_uni,[status(thm)],[13906:[bind(A,$thf( sk15 )),bind(B,$thf( sk15 ))]]) ).
thf(1076,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,43]) ).
thf(1077,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[1076]) ).
thf(1096,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 )
!= A )
| ( ( sk15 @ sk16 )
!= sk13 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[1077]) ).
thf(1107,plain,
( ( ( sk15 @ sk16 )
!= sk13 )
| ( sk15 @ sk16 @ sk16 @ p1 ) ),
inference(simp,[status(thm)],[1096]) ).
thf(1925,plain,
( ( ( sk15 @ sk16 @ sk16 @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( ( sk15 @ sk16 )
!= sk13 ) ),
inference(paramod_ordered,[status(thm)],[1107,18]) ).
thf(1926,plain,
( ( ( sk15 @ sk16 @ sk16 @ p1 )
!= ( sk14 @ p1 ) )
| ( ( sk15 @ sk16 )
!= sk13 ) ),
inference(simp,[status(thm)],[1925]) ).
thf(1927,plain,
( ( ( sk15 @ sk16 @ sk16 )
!= sk14 )
| ( ( sk15 @ sk16 )
!= sk13 ) ),
inference(simp,[status(thm)],[1926]) ).
thf(18670,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk14 ) ),
inference(paramod_ordered,[status(thm)],[17798,186]) ).
thf(18671,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[18670]) ).
thf(18704,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[18671]) ).
thf(33533,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5348,2411]) ).
thf(33534,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33533]) ).
thf(33832,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= A )
| ( sk13 != sk1 )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33534]) ).
thf(33891,plain,
( ( sk13 != sk1 )
| ( sk1 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33832]) ).
thf(37277,plain,
( ( ( sk1 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk13 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33891,186]) ).
thf(37278,plain,
( ( ( sk1 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[37277]) ).
thf(37332,plain,
( ( ( sk1 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[37278]) ).
thf(31221,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ~ $true
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[2446,25889]) ).
thf(31222,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31221]) ).
thf(31424,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31222]) ).
thf(35232,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33865,186]) ).
thf(35233,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35232]) ).
thf(35290,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35233]) ).
thf(33561,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[316,2411]) ).
thf(33562,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[33561]) ).
thf(33822,plain,
! [A: $i] :
( ( ( sk15 @ sk10 )
!= A )
| ( sk15 != sk1 )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[33562]) ).
thf(33884,plain,
( ( sk15 != sk1 )
| ( sk1 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[33822]) ).
thf(242,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,38]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[242]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( sk12 @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk12 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( sk12 ))]]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( sk12 @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk12 @ r1 ) ) ),
inference(simp,[status(thm)],[244]) ).
thf(35393,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[33603,186]) ).
thf(35394,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[35393]) ).
thf(35451,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[35394]) ).
thf(11532,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,5401]) ).
thf(11533,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[11532]) ).
thf(11578,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= sk13 )
| ( sk1 != sk1 )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[11533]) ).
thf(11615,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= sk13 )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[11578]) ).
thf(1784,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[921,42]) ).
thf(1785,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ sk2 ) @ ( B @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[1784]) ).
thf(1786,plain,
( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ ( sk15 @ sk16 @ r1 ) )
| ~ ( sk15 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[1785:[bind(A,$thf( sk15 )),bind(B,$thf( sk15 @ sk16 ))]]) ).
thf(60262,plain,
( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ ( sk15 @ sk16 @ r1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1786,28]) ).
thf(60263,plain,
sk15 @ ( sk15 @ sk16 @ sk2 ) @ ( sk15 @ sk16 @ r1 ),
inference(simp,[status(thm)],[60262]) ).
thf(60531,plain,
! [A: $i] :
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[60263,8]) ).
thf(60532,plain,
! [A: $i] :
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[60531]) ).
thf(60660,plain,
! [A: $i] :
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= A )
| ( ( sk15 @ sk16 )
!= sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[60532]) ).
thf(60805,plain,
( ( ( sk15 @ sk16 )
!= sk1 )
| ~ ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p4 ) ),
inference(simp,[status(thm)],[60660]) ).
thf(3462,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3450,991]) ).
thf(3463,plain,
( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[3462]) ).
thf(3472,plain,
( ( sk1 @ ( sk1 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) ),
inference(simp,[status(thm)],[3463]) ).
thf(68266,plain,
! [A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,68167]) ).
thf(68267,plain,
! [A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[68266]) ).
thf(68268,plain,
( ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( sk14 @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[68267:[bind(A,$thf( sk14 ))]]) ).
thf(565,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[316,49]) ).
thf(566,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[565]) ).
thf(569,plain,
! [A: $i] :
( ( ( sk15 @ sk10 )
!= A )
| ( sk15 != sk1 )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[566]) ).
thf(577,plain,
( ( sk15 != sk1 )
| ( sk15 @ sk10 @ sk10 @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk10 @ sk7 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[569]) ).
thf(33733,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4527,2411]) ).
thf(33734,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33733]) ).
thf(33833,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= A )
| ( sk12 != sk1 )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33734]) ).
thf(33892,plain,
( ( sk12 != sk1 )
| ( sk1 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33833]) ).
thf(37836,plain,
( ( ( sk1 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33892,186]) ).
thf(37837,plain,
( ( ( sk1 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[37836]) ).
thf(37895,plain,
( ( ( sk1 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[37837]) ).
thf(216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( C @ sk4 )
| ~ ( B @ ( C @ ( D @ sk5 ) ) @ p3 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,38]) ).
thf(217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( C @ sk4 )
| ~ ( B @ ( C @ ( D @ sk5 ) ) @ p3 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) ) ),
inference(simp,[status(thm)],[216]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( sk1 @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[217:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( sk1 @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[218]) ).
thf(35259,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33865,200]) ).
thf(35260,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35259]) ).
thf(35295,plain,
( ( ( sk1 @ ( sk13 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35260]) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ $true
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[28,38]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(259,plain,
! [A: $i] :
( ~ ( sk1 @ sk4 )
| ~ ( A @ ( sk1 @ ( sk15 @ sk5 ) ) @ p3 )
| ~ ( sk1 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk15 ))]]) ).
thf(5519,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2973,5487]) ).
thf(5520,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[5519]) ).
thf(5535,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[5520]) ).
thf(7485,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2413,7447]) ).
thf(7486,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[7485]) ).
thf(7497,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[7486]) ).
thf(161,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk15 @ ( sk1 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,43]) ).
thf(162,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk15 @ ( sk1 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[161]) ).
thf(172,plain,
! [A: $i] :
( ( A != sk15 )
| ( sk13 != sk1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[162]) ).
thf(177,plain,
( ( sk13 != sk1 )
| ( sk15 @ p1 ) ),
inference(simp,[status(thm)],[172]) ).
thf(284,plain,
( ( ( sk15 @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( sk13 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[177,18]) ).
thf(285,plain,
( ( ( sk15 @ p1 )
!= ( sk14 @ p1 ) )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[284]) ).
thf(286,plain,
( ( sk15 != sk14 )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[285]) ).
thf(32919,plain,
( ( ( sk15 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk13 ) ),
inference(paramod_ordered,[status(thm)],[27006,186]) ).
thf(32920,plain,
( ( ( sk15 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[32919]) ).
thf(32970,plain,
( ( ( sk15 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[32920]) ).
thf(13118,plain,
( ( ( sk15 @ sk10 @ sk16 @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( ( sk15 @ sk10 )
!= sk13 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[1178,18]) ).
thf(13119,plain,
( ( ( sk15 @ sk10 @ sk16 @ p1 )
!= ( sk14 @ p1 ) )
| ( ( sk15 @ sk10 )
!= sk13 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[13118]) ).
thf(13125,plain,
( ( ( sk15 @ sk10 @ sk16 )
!= sk14 )
| ( ( sk15 @ sk10 )
!= sk13 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[13119]) ).
thf(9957,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9929,991]) ).
thf(9958,plain,
( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[9957]) ).
thf(9984,plain,
( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) ),
inference(simp,[status(thm)],[9958]) ).
thf(79200,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[28,2062]) ).
thf(79201,plain,
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[79200]) ).
thf(79449,plain,
( ( sk15 != sk13 )
| ( sk1 != sk1 )
| ~ ( sk13 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[79201]) ).
thf(79475,plain,
( ( sk15 != sk13 )
| ~ ( sk13 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[79449]) ).
thf(28144,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ~ $true
| ( sk12 @ sk4 )
| ( sk12 @ sk7 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[26711,17000]) ).
thf(28145,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[28144]) ).
thf(28246,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) )
!= sk12 )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[28145]) ).
thf(5933,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5840,8]) ).
thf(5934,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[5933]) ).
thf(5976,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= A )
| ( sk15 != sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[5934]) ).
thf(5997,plain,
( ( sk15 != sk1 )
| ~ ( sk1 @ ( sk15 @ sk2 ) @ p4 ) ),
inference(simp,[status(thm)],[5976]) ).
thf(2460,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[2446,556]) ).
thf(2461,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[2460]) ).
thf(2474,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= ( sk15 @ sk10 @ sk16 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[2461]) ).
thf(5538,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[3450,1524]) ).
thf(5539,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[5538]) ).
thf(5556,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= ( sk13 @ sk16 @ sk16 ) )
| ( sk15 != sk13 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[5539]) ).
thf(8405,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8377,991]) ).
thf(8406,plain,
( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[8405]) ).
thf(8432,plain,
( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) ),
inference(simp,[status(thm)],[8406]) ).
thf(13867,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5348,2077]) ).
thf(13868,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13867]) ).
thf(13978,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= A )
| ( sk15 != sk13 )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13868]) ).
thf(14010,plain,
( ( sk15 != sk13 )
| ~ ( sk15 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13978]) ).
thf(22003,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21752,5487]) ).
thf(22004,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[22003]) ).
thf(22081,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[22004]) ).
thf(4605,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4527,8]) ).
thf(4606,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[4605]) ).
thf(4647,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= A )
| ( sk12 != sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[4606]) ).
thf(4672,plain,
( ( sk12 != sk1 )
| ~ ( sk1 @ ( sk12 @ sk2 ) @ p4 ) ),
inference(simp,[status(thm)],[4647]) ).
thf(2987,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[2973,556]) ).
thf(2988,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[2987]) ).
thf(3002,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= ( sk15 @ sk10 @ sk16 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[2988]) ).
thf(2425,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2413,991]) ).
thf(2426,plain,
( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[2425]) ).
thf(2442,plain,
( ( sk1 @ ( sk12 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) ),
inference(simp,[status(thm)],[2426]) ).
thf(24018,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21802,5848]) ).
thf(24019,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[24018]) ).
thf(24110,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[24019]) ).
thf(13865,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk10 @ ( sk12 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[308,2077]) ).
thf(13866,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk10 @ ( sk12 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[13865]) ).
thf(13994,plain,
! [A: $i] :
( ( A
!= ( sk12 @ sk10 ) )
| ( sk15 != sk12 )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[13866]) ).
thf(14027,plain,
( ( sk15 != sk12 )
| ~ ( sk15 @ ( sk12 @ sk10 @ sk3 ) @ p3 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[13994]) ).
thf(12591,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk13 ) ),
inference(paramod_ordered,[status(thm)],[11471,991]) ).
thf(12592,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[12591]) ).
thf(12624,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[12592]) ).
thf(5571,plain,
( ( ( sk13 @ sk10 @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( sk12 != sk1 )
| ( sk13 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[4840,18]) ).
thf(5572,plain,
( ( ( sk13 @ sk10 @ p1 )
!= ( sk14 @ p1 ) )
| ( sk12 != sk1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[5571]) ).
thf(5578,plain,
( ( ( sk13 @ sk10 )
!= sk14 )
| ( sk12 != sk1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[5572]) ).
thf(17943,plain,
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,6679]) ).
thf(17944,plain,
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[17943]) ).
thf(18045,plain,
( ( sk14 != sk14 )
| ( sk12 != sk1 )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[17944]) ).
thf(18067,plain,
( ( sk12 != sk1 )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[18045]) ).
thf(23766,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[21679,5848]) ).
thf(23767,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[23766]) ).
thf(23838,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[23767]) ).
thf(233,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( D @ ( sk1 @ r1 ) ) )
| ~ ( E @ sk4 )
| ~ ( D @ ( E @ ( F @ sk5 ) ) @ p3 )
| ~ ( F @ ( E @ r1 ) )
| ~ ( E @ ( D @ r1 ) )
| ~ $true
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[36,38]) ).
thf(234,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( D @ ( sk1 @ r1 ) ) )
| ~ ( E @ sk4 )
| ~ ( D @ ( E @ ( F @ sk5 ) ) @ p3 )
| ~ ( F @ ( E @ r1 ) )
| ~ ( E @ ( D @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[233]) ).
thf(235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( D @ ( C @ ( sk1 @ sk6 ) ) @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( D @ ( C @ ( sk1 @ sk6 ) ) @ r1 ) )
| ~ ( sk1 @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[234:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( sk1 )),bind(D,$thf( I @ ( H @ ( sk1 @ sk6 ) ) )),bind(E,$thf( E )),bind(F,$thf( F ))]]) ).
thf(274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( D @ ( C @ ( sk1 @ sk6 ) ) @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( D @ ( C @ ( sk1 @ sk6 ) ) @ r1 ) )
| ~ ( sk1 @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk10 @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( C @ sk4 )
| ~ ( B @ ( C @ ( D @ sk5 ) ) @ p3 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ $true
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[49,38]) ).
thf(318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk10 @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( C @ sk4 )
| ~ ( B @ ( C @ ( D @ sk5 ) ) @ p3 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[317]) ).
thf(319,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( sk1 @ sk10 @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk7 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk10 )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(347,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( sk1 @ sk10 @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk7 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[319]) ).
thf(96970,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( sk1 @ sk10 @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk7 )
| ~ $true ),
inference(rewrite,[status(thm)],[347,59]) ).
thf(96971,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( sk1 @ sk10 @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[96970]) ).
thf(21765,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[616,2408]) ).
thf(21766,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[21765]) ).
thf(21890,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 )
!= A )
| ( ( sk1 @ sk10 )
!= sk12 )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[21766]) ).
thf(21950,plain,
( ( ( sk1 @ sk10 )
!= sk12 )
| ( sk12 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[21890]) ).
thf(4680,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3450,4670]) ).
thf(4681,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[4680]) ).
thf(4699,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[4681]) ).
thf(17654,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ~ ( sk14 @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[6674,186]) ).
thf(17655,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ ( sk14 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[17654]) ).
thf(17725,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ~ ( sk14 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[17655]) ).
thf(8407,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[8377,556]) ).
thf(8408,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[8407]) ).
thf(8436,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk15 @ sk10 @ sk16 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[8408]) ).
thf(5517,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3450,5487]) ).
thf(5518,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[5517]) ).
thf(5531,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[5518]) ).
thf(17833,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk14 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[17792,991]) ).
thf(17834,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk14 != sk12 ) ),
inference(simp,[status(thm)],[17833]) ).
thf(17886,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk14 != sk12 ) ),
inference(simp,[status(thm)],[17834]) ).
thf(25059,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[21971,991]) ).
thf(25060,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[25059]) ).
thf(25111,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[25060]) ).
thf(2063,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[44]) ).
thf(2074,plain,
( ~ ( sk1 @ ( sk1 @ sk3 ) @ p3 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[2063:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(2110,plain,
( ~ ( sk1 @ ( sk1 @ sk3 ) @ p3 )
| ~ $true ),
inference(rewrite,[status(thm)],[2074,59]) ).
thf(2111,plain,
~ ( sk1 @ ( sk1 @ sk3 ) @ p3 ),
inference(simp,[status(thm)],[2110]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( B @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[36]) ).
thf(125,plain,
! [A: $i] :
( ( A @ ( sk1 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( sk1 @ p2 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( C )),bind(B,$thf( sk1 ))]]) ).
thf(140,plain,
! [A: $i] :
( ( A @ ( sk1 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( sk1 @ p2 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(19091,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,2100]) ).
thf(19092,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19091]) ).
thf(19146,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= A )
| ( sk12 != sk1 )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19092]) ).
thf(19185,plain,
( ( sk12 != sk1 )
| ~ ( sk12 @ ( sk1 @ ( sk1 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19146]) ).
thf(3014,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3006,198]) ).
thf(3015,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[3014]) ).
thf(3034,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[3015]) ).
thf(26913,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ sk16 @ ( sk13 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[972,2409]) ).
thf(26914,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ sk16 @ ( sk13 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[26913]) ).
thf(26960,plain,
! [A: $i] :
( ( A
!= ( sk13 @ sk16 ) )
| ( sk15 != sk13 )
| ( sk15 != sk12 )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26914]) ).
thf(27018,plain,
( ( sk15 != sk13 )
| ( sk15 != sk12 )
| ( sk15 @ ( sk13 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26960]) ).
thf(6811,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ p2 ) )
| ( sk15 != sk14 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3006,6783]) ).
thf(6812,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ p2 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[6811]) ).
thf(6817,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ sk16 )
!= ( sk12 @ ( sk14 @ sk2 ) ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[6812]) ).
thf(28206,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ~ $true
| ( sk15 @ sk4 )
| ( sk15 @ sk7 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[26711,13203]) ).
thf(28207,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[28206]) ).
thf(28261,plain,
( ( ( sk15 @ ( sk15 @ sk10 @ sk2 ) )
!= sk15 )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[28207]) ).
thf(5540,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[2973,1524]) ).
thf(5541,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[5540]) ).
thf(5552,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= ( sk13 @ sk16 @ sk16 ) )
| ( sk15 != sk13 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[5541]) ).
thf(4692,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3006,4670]) ).
thf(4693,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[4692]) ).
thf(4694,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[4693]) ).
thf(28320,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[26992,7447]) ).
thf(28321,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28320]) ).
thf(28400,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28321]) ).
thf(646,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ ( sk12 @ r1 ) ) )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,630]) ).
thf(647,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ ( sk12 @ r1 ) ) )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[646]) ).
thf(661,plain,
! [A: $i] :
( ( A != sk13 )
| ( sk15 != sk12 )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[647]) ).
thf(668,plain,
( ( sk15 != sk12 )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( sk13 @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[661]) ).
thf(146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ( B @ ( C @ ( D @ sk6 ) ) @ ( D @ r1 ) )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( B @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,36]) ).
thf(147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ( B @ ( C @ ( D @ sk6 ) ) @ ( D @ r1 ) )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( B @ r1 ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( A @ ( B @ sk6 ) ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( A @ ( B @ sk6 ) ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(1156,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ sk16 @ ( sk15 @ sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[903,8]) ).
thf(1157,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ sk16 @ ( sk15 @ sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[1156]) ).
thf(1165,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ sk16 )
!= A )
| ( ( sk15 @ sk10 )
!= sk1 )
| ~ ( A @ p4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[1157]) ).
thf(1177,plain,
( ( ( sk15 @ sk10 )
!= sk1 )
| ~ ( sk15 @ sk10 @ sk16 @ p4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[1165]) ).
thf(23932,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21975,186]) ).
thf(23933,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[23932]) ).
thf(23971,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[23933]) ).
thf(68157,plain,
( ( ( sk1 @ ( sk12 @ sk3 ) @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( ( sk1 @ ( sk12 @ sk2 ) )
!= sk13 ) ),
inference(paramod_ordered,[status(thm)],[67575,18]) ).
thf(68158,plain,
( ( ( sk1 @ ( sk12 @ sk3 ) @ p1 )
!= ( sk14 @ p1 ) )
| ( ( sk1 @ ( sk12 @ sk2 ) )
!= sk13 ) ),
inference(simp,[status(thm)],[68157]) ).
thf(68164,plain,
( ( ( sk1 @ ( sk12 @ sk3 ) )
!= sk14 )
| ( ( sk1 @ ( sk12 @ sk2 ) )
!= sk13 ) ),
inference(simp,[status(thm)],[68158]) ).
thf(17614,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,6674]) ).
thf(17615,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17614]) ).
thf(17755,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= sk14 )
| ( sk1 != sk1 )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17615]) ).
thf(17794,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= sk14 )
| ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[17755]) ).
thf(15976,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4527,2091]) ).
thf(15977,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15976]) ).
thf(16029,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= A )
| ( sk12 != sk1 )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15977]) ).
thf(16062,plain,
( ( sk12 != sk1 )
| ~ ( sk1 @ ( sk1 @ ( sk12 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[16029]) ).
thf(19100,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6622,2100]) ).
thf(19101,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19100]) ).
thf(19140,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= A )
| ( sk14 != sk12 )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19101]) ).
thf(19179,plain,
( ( sk14 != sk12 )
| ~ ( sk12 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19140]) ).
thf(72379,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk3 ) @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72340,37]) ).
thf(72380,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk3 ) @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[72379]) ).
thf(72765,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk3 ) )
!= A )
| ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk15 )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[72380]) ).
thf(72866,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk15 )
| ~ ( sk1 @ ( sk15 @ sk3 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[72765]) ).
thf(15528,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15483,186]) ).
thf(15529,plain,
( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[15528]) ).
thf(15566,plain,
( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) ),
inference(simp,[status(thm)],[15529]) ).
thf(31107,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ~ $true
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[3450,25889]) ).
thf(31108,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31107]) ).
thf(31400,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31108]) ).
thf(13882,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[316,2077]) ).
thf(13883,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[13882]) ).
thf(13884,plain,
( ~ ( sk15 @ ( sk15 @ sk10 @ sk3 ) @ p3 )
| ( sk15 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[13883:[bind(A,$thf( sk15 @ sk10 ))]]) ).
thf(2983,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2973,199]) ).
thf(2984,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[2983]) ).
thf(2999,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[2984]) ).
thf(3460,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3450,199]) ).
thf(3461,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[3460]) ).
thf(3480,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[3461]) ).
thf(1122,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ sk16 @ ( sk15 @ sk10 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[903,37]) ).
thf(1123,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ sk16 @ ( sk15 @ sk10 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[1122]) ).
thf(1160,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ sk16 )
!= A )
| ( ( sk15 @ sk10 )
!= sk15 )
| ~ ( A @ sk16 @ p2 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[1123]) ).
thf(1171,plain,
( ( ( sk15 @ sk10 )
!= sk15 )
| ~ ( sk15 @ sk10 @ sk16 @ sk16 @ p2 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[1160]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,36]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( sk12 @ ( A @ ( B @ sk6 ) ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( sk12 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( sk12 ))]]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( sk12 @ ( A @ ( B @ sk6 ) ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( sk12 @ r1 ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(2427,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[2413,556]) ).
thf(2428,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[2427]) ).
thf(2439,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= ( sk15 @ sk10 @ sk16 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[2428]) ).
thf(15996,plain,
! [A: $i] :
( ( ( sk13 @ sk16 @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[972,2091]) ).
thf(15997,plain,
! [A: $i] :
( ( ( sk13 @ sk16 @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[15996]) ).
thf(16025,plain,
! [A: $i] :
( ( ( sk13 @ sk16 )
!= A )
| ( sk13 != sk1 )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[15997]) ).
thf(16057,plain,
( ( sk13 != sk1 )
| ~ ( sk1 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[16025]) ).
thf(7380,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,43]) ).
thf(7381,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[7380]) ).
thf(7432,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= A )
| ( sk13 != sk1 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[7381]) ).
thf(7442,plain,
( ( sk13 != sk1 )
| ( sk1 @ ( sk1 @ sk2 ) @ p1 ) ),
inference(simp,[status(thm)],[7432]) ).
thf(7472,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( sk13 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[7442,18]) ).
thf(7473,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p1 )
!= ( sk14 @ p1 ) )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[7472]) ).
thf(7479,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= sk14 )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[7473]) ).
thf(6803,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2973,6783]) ).
thf(6804,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[6803]) ).
thf(6816,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[6804]) ).
thf(21697,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[316,2408]) ).
thf(21698,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[21697]) ).
thf(21941,plain,
! [A: $i] :
( ( ( sk15 @ sk10 )
!= A )
| ( sk15 != sk12 )
| ( sk12 @ ( A @ sk2 ) @ p2 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[21698]) ).
thf(21982,plain,
( ( sk15 != sk12 )
| ( sk12 @ ( sk15 @ sk10 @ sk2 ) @ p2 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[21941]) ).
thf(22023,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21752,198]) ).
thf(22024,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[22023]) ).
thf(22084,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[22024]) ).
thf(26800,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,2409]) ).
thf(26801,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26800]) ).
thf(26940,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 )
!= A )
| ( ( sk15 @ sk16 )
!= sk15 )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26801]) ).
thf(27004,plain,
( ( ( sk15 @ sk16 )
!= sk15 )
| ( sk15 @ ( sk15 @ sk16 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26940]) ).
thf(6017,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2446,5848]) ).
thf(6018,plain,
( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[6017]) ).
thf(6029,plain,
( ( sk12 @ ( sk13 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) ),
inference(simp,[status(thm)],[6018]) ).
thf(23916,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21975,199]) ).
thf(23917,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[23916]) ).
thf(23975,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[23917]) ).
thf(12681,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[11476,186]) ).
thf(12682,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[12681]) ).
thf(12708,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[12682]) ).
thf(1996,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[28,44]) ).
thf(1997,plain,
! [B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[1996]) ).
thf(1998,plain,
( ~ ( sk1 @ ( sk15 @ sk3 ) @ p3 )
| ~ ( sk1 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[1997:[bind(A,$thf( sk1 )),bind(B,$thf( sk15 ))]]) ).
thf(2106,plain,
( ~ ( sk1 @ ( sk15 @ sk3 ) @ p3 )
| ~ $true ),
inference(rewrite,[status(thm)],[1998,59]) ).
thf(2107,plain,
~ ( sk1 @ ( sk15 @ sk3 ) @ p3 ),
inference(simp,[status(thm)],[2106]) ).
thf(297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk10 @ ( A @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( B @ ( C @ ( D @ sk6 ) ) @ ( D @ r1 ) )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ $true
| ~ ( B @ ( sk1 @ r1 ) )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[49,36]) ).
thf(298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk10 @ ( A @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( B @ ( C @ ( D @ sk6 ) ) @ ( D @ r1 ) )
| ~ ( D @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( B @ ( sk1 @ r1 ) )
| ( A @ sk7 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[297]) ).
thf(299,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ sk10 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( B @ sk10 @ r1 ) )
| ~ ( B @ sk10 @ p2 )
| ( B @ sk10 @ sk4 )
| ~ ( B @ ( sk1 @ r1 ) )
| ( B @ sk7 )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[298:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk10 ))]]) ).
thf(342,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ sk10 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( B @ sk10 @ r1 ) )
| ~ ( B @ sk10 @ p2 )
| ( B @ sk10 @ sk4 )
| ( B @ sk7 )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[299]) ).
thf(19016,plain,
! [A: $i] :
( ( ( sk14 @ sk16 @ ( sk14 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[962,2100]) ).
thf(19017,plain,
! [A: $i] :
( ( ( sk14 @ sk16 @ ( sk14 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[19016]) ).
thf(19143,plain,
! [A: $i] :
( ( ( sk14 @ sk16 )
!= A )
| ( sk14 != sk12 )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[19017]) ).
thf(19182,plain,
( ( sk14 != sk12 )
| ~ ( sk12 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[19143]) ).
thf(6809,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2446,6783]) ).
thf(6810,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[6809]) ).
thf(6821,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[6810]) ).
thf(60302,plain,
! [A: $i] :
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[60263,37]) ).
thf(60303,plain,
! [A: $i] :
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[60302]) ).
thf(60680,plain,
! [A: $i] :
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= A )
| ( ( sk15 @ sk16 )
!= sk15 )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[60303]) ).
thf(60713,plain,
( ( ( sk15 @ sk16 )
!= sk15 )
| ~ ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[60680]) ).
thf(33531,plain,
! [A: $i] :
( ( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[308,2411]) ).
thf(33532,plain,
! [A: $i] :
( ( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[33531]) ).
thf(33792,plain,
! [A: $i] :
( ( ( sk12 @ sk10 )
!= A )
| ( sk12 != sk1 )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[33532]) ).
thf(33862,plain,
( ( sk12 != sk1 )
| ( sk1 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[33792]) ).
thf(25038,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[21971,5848]) ).
thf(25039,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[25038]) ).
thf(25104,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[25039]) ).
thf(31223,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ~ $true
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[3006,25889]) ).
thf(31224,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31223]) ).
thf(31370,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31224]) ).
thf(1024,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[921,8]) ).
thf(1025,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[1024]) ).
thf(1027,plain,
! [A: $i] :
( ( ( sk15 @ sk16 )
!= A )
| ( sk15 != sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[1025]) ).
thf(1034,plain,
( ( sk15 != sk1 )
| ~ ( sk15 @ sk16 @ p4 ) ),
inference(simp,[status(thm)],[1027]) ).
thf(15623,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ~ $true
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[3450,13203]) ).
thf(15624,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15623]) ).
thf(15804,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= sk15 )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15624]) ).
thf(1388,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ sk16 @ ( sk14 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[962,37]) ).
thf(1389,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ sk16 @ ( sk14 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1388]) ).
thf(1433,plain,
! [A: $i] :
( ( A
!= ( sk14 @ sk16 ) )
| ( sk15 != sk14 )
| ~ ( A @ sk16 @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1389]) ).
thf(1448,plain,
( ( sk15 != sk14 )
| ~ ( sk14 @ sk16 @ sk16 @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1433]) ).
thf(3022,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[3006,1448]) ).
thf(3023,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[3022]) ).
thf(3031,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= ( sk14 @ sk16 @ sk16 ) )
| ( sk15 != sk14 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[3023]) ).
thf(2454,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2446,198]) ).
thf(2455,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2454]) ).
thf(2471,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2455]) ).
thf(22046,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[21752,556]) ).
thf(22047,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[22046]) ).
thf(22078,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) )
!= ( sk15 @ sk10 @ sk16 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[22047]) ).
thf(35527,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33880,199]) ).
thf(35528,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35527]) ).
thf(35594,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35528]) ).
thf(33984,plain,
( ( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33680,199]) ).
thf(33985,plain,
( ( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[33984]) ).
thf(34064,plain,
( ( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[33985]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( B @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,8]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( B @ p4 ) ),
inference(simp,[status(thm)],[143]) ).
thf(145,plain,
~ ( sk1 @ p4 ),
inference(pattern_uni,[status(thm)],[144:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(26688,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk10 @ ( sk12 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[308,2409]) ).
thf(26689,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk10 @ ( sk12 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[26688]) ).
thf(26977,plain,
! [A: $i] :
( ( A
!= ( sk12 @ sk10 ) )
| ( sk15 != sk12 )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[26689]) ).
thf(27026,plain,
( ( sk15 != sk12 )
| ( sk15 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[26977]) ).
thf(1529,plain,
( ( ( sk13 @ sk16 @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[1493,18]) ).
thf(1530,plain,
( ( ( sk13 @ sk16 @ p1 )
!= ( sk14 @ p1 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1529]) ).
thf(1531,plain,
( ( ( sk13 @ sk16 )
!= sk14 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1530]) ).
thf(17941,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,6679]) ).
thf(17942,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[17941]) ).
thf(18028,plain,
! [A: $i] :
( ( A != sk14 )
| ( A != sk1 )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[17942]) ).
thf(18060,plain,
( ( sk14 != sk1 )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[18028]) ).
thf(28328,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[26992,199]) ).
thf(28329,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28328]) ).
thf(28406,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28329]) ).
thf(22019,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21752,5848]) ).
thf(22020,plain,
( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[22019]) ).
thf(22093,plain,
( ( sk12 @ ( sk12 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) ),
inference(simp,[status(thm)],[22020]) ).
thf(567,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[316,8]) ).
thf(568,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[567]) ).
thf(572,plain,
! [A: $i] :
( ( ( sk15 @ sk10 )
!= A )
| ( sk15 != sk1 )
| ~ ( A @ p4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[568]) ).
thf(580,plain,
( ( sk15 != sk1 )
| ~ ( sk15 @ sk10 @ p4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[572]) ).
thf(15522,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[15483,556]) ).
thf(15523,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15522]) ).
thf(15551,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk10 @ sk16 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15523]) ).
thf(50552,plain,
! [A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,50462]) ).
thf(50553,plain,
! [A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[50552]) ).
thf(50648,plain,
! [A: $i] :
( ( sk14 != A )
| ( sk12 != sk1 )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[50553]) ).
thf(50709,plain,
( ( sk12 != sk1 )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( sk14 @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[50648]) ).
thf(15541,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15483,200]) ).
thf(15542,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[15541]) ).
thf(15549,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[15542]) ).
thf(219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( C @ sk4 )
| ~ ( B @ ( C @ ( D @ sk5 ) ) @ p3 )
| ~ ( D @ ( C @ r1 ) )
| ~ $true
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[59,38]) ).
thf(220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( C @ sk4 )
| ~ ( B @ ( C @ ( D @ sk5 ) ) @ p3 )
| ~ ( D @ ( C @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( A @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(282,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( A @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(70843,plain,
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[12,1965]) ).
thf(70844,plain,
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[70843]) ).
thf(70947,plain,
( ( sk14 != sk14 )
| ( sk12 != sk1 )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[70844]) ).
thf(71040,plain,
( ( sk12 != sk1 )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[70947]) ).
thf(13943,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4527,2077]) ).
thf(13944,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13943]) ).
thf(13984,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= A )
| ( sk15 != sk12 )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13944]) ).
thf(14017,plain,
( ( sk15 != sk12 )
| ~ ( sk15 @ ( sk1 @ ( sk12 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13984]) ).
thf(22,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( A @ ( B @ ( C @ sk6 ) ) @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(50,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ p2 )
| ~ ( D @ ( A @ ( B @ ( C @ sk6 ) ) @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(15891,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5348,2091]) ).
thf(15892,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15891]) ).
thf(16016,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= A )
| ( sk13 != sk1 )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15892]) ).
thf(16047,plain,
( ( sk13 != sk1 )
| ~ ( sk1 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[16016]) ).
thf(47783,plain,
! [A: $i] :
( ( ( A @ ( sk14 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,47760]) ).
thf(47784,plain,
! [A: $i] :
( ( ( A @ ( sk14 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[47783]) ).
thf(47961,plain,
! [A: $i] :
( ( A != sk12 )
| ( sk14 != sk1 )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[47784]) ).
thf(48022,plain,
( ( sk14 != sk1 )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( sk12 @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[47961]) ).
thf(19020,plain,
! [A: $i] :
( ( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[308,2100]) ).
thf(19021,plain,
! [A: $i] :
( ( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[19020]) ).
thf(19022,plain,
( ~ ( sk12 @ ( sk12 @ sk10 @ sk3 ) @ p3 )
| ( sk12 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[19021:[bind(A,$thf( sk12 @ sk10 ))]]) ).
thf(18450,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[17793,991]) ).
thf(18451,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[18450]) ).
thf(18488,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[18451]) ).
thf(50549,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( B @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,50462]) ).
thf(50550,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( B @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[50549]) ).
thf(50551,plain,
( ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( sk1 @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[50550:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(31244,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ~ $true
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[8377,25889]) ).
thf(31245,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31244]) ).
thf(31428,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31245]) ).
thf(23956,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21975,200]) ).
thf(23957,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[23956]) ).
thf(23979,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[23957]) ).
thf(35376,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[33603,991]) ).
thf(35377,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[35376]) ).
thf(35435,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[35377]) ).
thf(2462,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[2446,1448]) ).
thf(2463,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2462]) ).
thf(2468,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= ( sk14 @ sk16 @ sk16 ) )
| ( sk15 != sk14 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2463]) ).
thf(9959,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[9929,556]) ).
thf(9960,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[9959]) ).
thf(9991,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk10 @ sk16 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[9960]) ).
thf(28008,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26772,5487]) ).
thf(28009,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[28008]) ).
thf(28108,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[28009]) ).
thf(28485,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27000,4670]) ).
thf(28486,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28485]) ).
thf(28524,plain,
( ( ( sk15 @ ( sk14 @ sk2 ) )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28486]) ).
thf(28035,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26772,6783]) ).
thf(28036,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[28035]) ).
thf(28123,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[28036]) ).
thf(9965,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9929,186]) ).
thf(9966,plain,
( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[9965]) ).
thf(9986,plain,
( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) ),
inference(simp,[status(thm)],[9966]) ).
thf(18137,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ~ $true
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[2973,17000]) ).
thf(18138,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[18137]) ).
thf(18346,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk12 )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[18138]) ).
thf(5546,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[2446,1524]) ).
thf(5547,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[5546]) ).
thf(5555,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= ( sk13 @ sk16 @ sk16 ) )
| ( sk15 != sk13 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[5547]) ).
thf(72629,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk3 ) @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72340,8]) ).
thf(72630,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk3 ) @ ( sk1 @ ( sk15 @ sk2 ) @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[72629]) ).
thf(72807,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk3 ) )
!= A )
| ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[72630]) ).
thf(72907,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk1 )
| ~ ( sk1 @ ( sk15 @ sk3 ) @ p4 ) ),
inference(simp,[status(thm)],[72807]) ).
thf(3466,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[3450,1448]) ).
thf(3467,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[3466]) ).
thf(3475,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= ( sk14 @ sk16 @ sk16 ) )
| ( sk15 != sk14 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[3467]) ).
thf(29588,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27023,4670]) ).
thf(29589,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[29588]) ).
thf(29613,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[29589]) ).
thf(25184,plain,
( ( ( sk12 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21951,991]) ).
thf(25185,plain,
( ( ( sk12 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[25184]) ).
thf(25230,plain,
( ( ( sk12 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[25185]) ).
thf(152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( D @ ( C @ r1 ) ) )
| ( B @ ( C @ ( D @ sk6 ) ) @ ( D @ r1 ) )
| ~ $true
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[59,36]) ).
thf(153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( D @ ( C @ r1 ) ) )
| ( B @ ( C @ ( D @ sk6 ) ) @ ( D @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(25042,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[21971,198]) ).
thf(25043,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[25042]) ).
thf(25112,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[25043]) ).
thf(8420,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8377,200]) ).
thf(8421,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[8420]) ).
thf(8433,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[8421]) ).
thf(68344,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4527,68167]) ).
thf(68345,plain,
! [A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( A @ ( sk12 @ r1 ) ) )
| ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[68344]) ).
thf(68346,plain,
( ~ ( sk12 @ sk4 )
| ~ ( sk1 @ ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[68345:[bind(A,$thf( sk1 @ ( sk12 @ sk2 ) ))]]) ).
thf(7481,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3450,7447]) ).
thf(7482,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[7481]) ).
thf(7498,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ sk16 )
!= ( sk1 @ ( sk1 @ sk2 ) ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[7482]) ).
thf(9974,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9929,200]) ).
thf(9975,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[9974]) ).
thf(9983,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[9975]) ).
thf(26825,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk16 @ ( sk12 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[978,2409]) ).
thf(26826,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk16 @ ( sk12 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[26825]) ).
thf(26969,plain,
! [A: $i] :
( ( A
!= ( sk12 @ sk16 ) )
| ( sk15 != sk12 )
| ( sk15 != sk1 )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26826]) ).
thf(27024,plain,
( ( sk15 != sk12 )
| ( sk15 != sk1 )
| ( sk15 @ ( sk12 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26969]) ).
thf(168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( D @ ( sk13 @ r1 ) ) )
| ( D @ p1 )
| ~ $true
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[36,43]) ).
thf(169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( D @ ( sk13 @ r1 ) ) )
| ( D @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( sk13 @ sk6 ) ) @ p1 )
| ~ ( sk13 @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( sk13 )),bind(D,$thf( G @ ( F @ ( sk13 @ sk6 ) ) ))]]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( sk13 @ sk6 ) ) @ p1 )
| ~ ( sk13 @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[170]) ).
thf(384,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( A @ sk7 )
| ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ r1 ) )
| ~ $true
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,39]) ).
thf(385,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( A @ sk7 )
| ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[384]) ).
thf(386,plain,
! [A: $i] :
( ~ ( A @ sk7 )
| ( A @ ( sk1 @ ( sk12 @ sk8 ) ) @ ( sk12 @ r1 ) )
| ~ ( sk1 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[385:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk12 ))]]) ).
thf(33693,plain,
! [A: $i] :
( ( ( sk12 @ sk16 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[978,2411]) ).
thf(33694,plain,
! [A: $i] :
( ( ( sk12 @ sk16 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[33693]) ).
thf(33846,plain,
! [A: $i] :
( ( ( sk12 @ sk16 )
!= A )
| ( sk12 != sk1 )
| ( sk15 != sk1 )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33694]) ).
thf(33899,plain,
( ( sk12 != sk1 )
| ( sk15 != sk1 )
| ( sk1 @ ( sk12 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33846]) ).
thf(17959,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,6679]) ).
thf(17960,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[17959]) ).
thf(18044,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= sk14 )
| ( sk1 != sk1 )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[17960]) ).
thf(18066,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= sk14 )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[18044]) ).
thf(60487,plain,
! [A: $i] :
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[60263,43]) ).
thf(60488,plain,
! [A: $i] :
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[60487]) ).
thf(60689,plain,
! [A: $i] :
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= A )
| ( ( sk15 @ sk16 )
!= sk13 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[60488]) ).
thf(60722,plain,
( ( ( sk15 @ sk16 )
!= sk13 )
| ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p1 ) ),
inference(simp,[status(thm)],[60689]) ).
thf(64190,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk13 @ r1 ) ) )
| ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( B @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,64099]) ).
thf(64191,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk13 @ r1 ) ) )
| ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( B @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[64190]) ).
thf(64192,plain,
( ~ ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk13 @ ( sk13 @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[64191:[bind(A,$thf( sk13 )),bind(B,$thf( sk13 ))]]) ).
thf(592,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,43]) ).
thf(593,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ( A @ p1 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[592]) ).
thf(620,plain,
! [A: $i] :
( ( A
!= ( sk1 @ sk10 ) )
| ( sk13 != sk1 )
| ( A @ p1 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[593]) ).
thf(624,plain,
( ( sk13 != sk1 )
| ( sk1 @ sk10 @ p1 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[620]) ).
thf(2579,plain,
( ( ( sk1 @ sk10 @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( sk13 != sk1 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[624,18]) ).
thf(2580,plain,
( ( ( sk1 @ sk10 @ p1 )
!= ( sk14 @ p1 ) )
| ( sk13 != sk1 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[2579]) ).
thf(2584,plain,
( ( ( sk1 @ sk10 )
!= sk14 )
| ( sk13 != sk1 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[2580]) ).
thf(8415,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8377,4670]) ).
thf(8416,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[8415]) ).
thf(8431,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[8416]) ).
thf(22060,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21752,4670]) ).
thf(22061,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[22060]) ).
thf(22102,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[22061]) ).
thf(28033,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26772,198]) ).
thf(28034,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28033]) ).
thf(28113,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[28034]) ).
thf(5527,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3006,5487]) ).
thf(5528,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[5527]) ).
thf(5536,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[5528]) ).
thf(17911,plain,
( ( ( sk14 @ ( sk1 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,6679]) ).
thf(17912,plain,
( ( ( sk14 @ ( sk1 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[17911]) ).
thf(18029,plain,
( ( sk14 != sk12 )
| ( sk1 != sk1 )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[17912]) ).
thf(18061,plain,
( ( sk14 != sk12 )
| ~ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[18029]) ).
thf(18185,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ~ $true
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[2446,17000]) ).
thf(18186,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[18185]) ).
thf(18355,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= sk12 )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[18186]) ).
thf(24039,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21802,991]) ).
thf(24040,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[24039]) ).
thf(24092,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[24040]) ).
thf(13963,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ sk16 @ ( sk13 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[972,2077]) ).
thf(13964,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ sk16 @ ( sk13 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[13963]) ).
thf(13977,plain,
! [A: $i] :
( ( A
!= ( sk13 @ sk16 ) )
| ( sk15 != sk13 )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[13964]) ).
thf(14009,plain,
( ( sk15 != sk13 )
| ~ ( sk15 @ ( sk13 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[13977]) ).
thf(35319,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ~ $true
| ( sk12 @ sk4 )
| ( sk12 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[33603,17000]) ).
thf(35320,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[35319]) ).
thf(35431,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) )
!= sk12 )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[35320]) ).
thf(37124,plain,
( ( ( sk1 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33879,186]) ).
thf(37125,plain,
( ( ( sk1 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[37124]) ).
thf(37175,plain,
( ( ( sk1 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[37125]) ).
thf(2433,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2413,200]) ).
thf(2434,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2433]) ).
thf(2435,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2434]) ).
thf(15930,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5840,2091]) ).
thf(15931,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15930]) ).
thf(15999,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= A )
| ( sk15 != sk1 )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15931]) ).
thf(16070,plain,
( ( sk15 != sk1 )
| ~ ( sk1 @ ( sk1 @ ( sk15 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15999]) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ $true
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,38]) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[248]) ).
thf(250,plain,
! [A: $i] :
( ~ ( sk1 @ sk4 )
| ~ ( A @ ( sk1 @ ( sk12 @ sk5 ) ) @ p3 )
| ~ ( sk1 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[249:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk12 ))]]) ).
thf(3464,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[3450,556]) ).
thf(3465,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk15 @ sk10 @ sk16 @ p2 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[3464]) ).
thf(3478,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= ( sk15 @ sk10 @ sk16 ) )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[3465]) ).
thf(29542,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27023,5848]) ).
thf(29543,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[29542]) ).
thf(29639,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[29543]) ).
thf(4690,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2446,4670]) ).
thf(4691,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[4690]) ).
thf(4698,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= ( sk1 @ ( sk12 @ sk2 ) @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[4691]) ).
thf(28309,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[26992,5848]) ).
thf(28310,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28309]) ).
thf(28388,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28310]) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ $true
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[28,36]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(99,plain,
! [A: $i] :
( ( A @ ( sk1 @ ( sk15 @ sk6 ) ) @ ( sk15 @ r1 ) )
| ~ ( sk1 @ p2 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[98:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk15 ))]]) ).
thf(879,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk10 @ ( sk12 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[308,48]) ).
thf(880,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk10 @ ( sk12 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[879]) ).
thf(958,plain,
! [A: $i] :
( ( A
!= ( sk12 @ sk10 ) )
| ( sk15 != sk12 )
| ( A @ sk16 @ ( A @ r1 ) )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[880]) ).
thf(976,plain,
( ( sk15 != sk12 )
| ( sk12 @ sk10 @ sk16 @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[958]) ).
thf(2989,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[2973,1448]) ).
thf(2990,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2989]) ).
thf(2997,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= ( sk14 @ sk16 @ sk16 ) )
| ( sk15 != sk14 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2990]) ).
thf(26469,plain,
( ( ( sk12 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[21996,186]) ).
thf(26470,plain,
( ( ( sk12 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[26469]) ).
thf(26514,plain,
( ( ( sk12 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[26470]) ).
thf(15641,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ~ $true
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[2973,13203]) ).
thf(15642,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15641]) ).
thf(15796,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk15 )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[15642]) ).
thf(11371,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ~ ( sk13 @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[5396,186]) ).
thf(11372,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ ( sk13 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[11371]) ).
thf(11412,plain,
( ( ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ~ ( sk13 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[11372]) ).
thf(33668,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,2411]) ).
thf(33669,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 @ ( sk15 @ sk16 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33668]) ).
thf(33854,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ sk16 )
!= A )
| ( ( sk15 @ sk16 )
!= sk1 )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33669]) ).
thf(33906,plain,
( ( ( sk15 @ sk16 )
!= sk1 )
| ( sk1 @ ( sk15 @ sk16 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33854]) ).
thf(2429,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[2413,1448]) ).
thf(2430,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2429]) ).
thf(2443,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= ( sk14 @ sk16 @ sk16 ) )
| ( sk15 != sk14 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2430]) ).
thf(881,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,48]) ).
thf(882,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[881]) ).
thf(961,plain,
! [A: $i] :
( ( A
!= ( sk1 @ sk10 ) )
| ( sk15 != sk1 )
| ( A @ sk16 @ ( A @ r1 ) )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[882]) ).
thf(963,plain,
( ( sk15 != sk1 )
| ( sk1 @ sk10 @ sk16 @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[961]) ).
thf(6801,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3450,6783]) ).
thf(6802,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[6801]) ).
thf(6818,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[6802]) ).
thf(34027,plain,
( ( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33680,200]) ).
thf(34028,plain,
( ( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[34027]) ).
thf(34038,plain,
( ( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[34028]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk7 )
| ~ ( A @ ( B @ ( C @ sk9 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk7 )
| ~ ( A @ ( B @ ( C @ sk9 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(13908,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ ( sk12 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,2077]) ).
thf(13909,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ ( sk12 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13908]) ).
thf(13993,plain,
! [A: $i] :
( ( A != sk14 )
| ( sk15 != sk12 )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13909]) ).
thf(14026,plain,
( ( sk15 != sk12 )
| ~ ( sk15 @ ( sk14 @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13993]) ).
thf(650,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( B @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,630]) ).
thf(651,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( B @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( B @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[650]) ).
thf(652,plain,
( ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( sk15 @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[651:[bind(A,$thf( sk15 )),bind(B,$thf( sk15 ))]]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk17 @ p1 )
| ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk17 @ p1 )
| ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(11339,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,5396]) ).
thf(11340,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[11339]) ).
thf(11422,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= sk13 )
| ( sk1 != sk1 )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[11340]) ).
thf(11469,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= sk13 )
| ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[11422]) ).
thf(15497,plain,
( ( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15483,5848]) ).
thf(15498,plain,
( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[15497]) ).
thf(15561,plain,
( ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) ),
inference(simp,[status(thm)],[15498]) ).
thf(5412,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5348,48]) ).
thf(5413,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) @ ( sk13 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[5412]) ).
thf(5480,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= A )
| ( sk15 != sk13 )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[5413]) ).
thf(5505,plain,
( ( sk15 != sk13 )
| ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ ( sk12 @ ( sk13 @ sk2 ) @ r1 ) ) ),
inference(simp,[status(thm)],[5480]) ).
thf(33527,plain,
! [A: $i] :
( ( ( sk14 @ sk16 @ ( sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[962,2411]) ).
thf(33528,plain,
! [A: $i] :
( ( ( sk14 @ sk16 @ ( sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( sk1 @ ( A @ sk2 ) @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[33527]) ).
thf(33828,plain,
! [A: $i] :
( ( ( sk14 @ sk16 )
!= A )
| ( sk14 != sk1 )
| ( sk15 != sk12 )
| ( sk1 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33528]) ).
thf(33889,plain,
( ( sk14 != sk1 )
| ( sk15 != sk12 )
| ( sk1 @ ( sk14 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[33828]) ).
thf(23918,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21975,991]) ).
thf(23919,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[23918]) ).
thf(23962,plain,
( ( ( sk12 @ ( sk15 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[23919]) ).
thf(50498,plain,
! [A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,50462]) ).
thf(50499,plain,
! [A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[50498]) ).
thf(50655,plain,
! [A: $i] :
( ( sk13 != A )
| ( sk12 != sk1 )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[50499]) ).
thf(50717,plain,
( ( sk12 != sk1 )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ ( sk1 @ ( sk13 @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[50655]) ).
thf(6013,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2413,5848]) ).
thf(6014,plain,
( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[6013]) ).
thf(6023,plain,
( ( sk1 @ ( sk12 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) ),
inference(simp,[status(thm)],[6014]) ).
thf(24029,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21802,7447]) ).
thf(24030,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[24029]) ).
thf(24086,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[24030]) ).
thf(18154,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ~ $true
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[2413,17000]) ).
thf(18155,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[18154]) ).
thf(18305,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= sk12 )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[18155]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,36]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( sk15 @ ( A @ ( B @ sk6 ) ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( sk15 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( sk15 ))]]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ( sk15 @ ( A @ ( B @ sk6 ) ) @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( sk15 @ r1 ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(2979,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) )
| ( ( sk15 @ sk16 )
!= sk15 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2973,1106]) ).
thf(2980,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) )
| ( ( sk15 @ sk16 )
!= sk15 ) ),
inference(simp,[status(thm)],[2979]) ).
thf(3003,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 @ sk16 ) )
| ( ( sk15 @ sk16 )
!= sk15 ) ),
inference(simp,[status(thm)],[2980]) ).
thf(1489,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ sk16 @ ( sk13 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[972,48]) ).
thf(1490,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ sk16 @ ( sk13 @ r1 ) ) )
| ( A @ sk16 @ ( A @ r1 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1489]) ).
thf(1512,plain,
! [A: $i] :
( ( A
!= ( sk13 @ sk16 ) )
| ( sk15 != sk13 )
| ( sk15 != sk12 )
| ( A @ sk16 @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[1490]) ).
thf(1523,plain,
( ( sk15 != sk13 )
| ( sk15 != sk12 )
| ( sk13 @ sk16 @ sk16 @ ( sk13 @ sk16 @ r1 ) ) ),
inference(simp,[status(thm)],[1512]) ).
thf(13885,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ ( sk12 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,2077]) ).
thf(13886,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk13 @ ( sk12 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13885]) ).
thf(13966,plain,
! [A: $i] :
( ( A != sk13 )
| ( sk15 != sk12 )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13886]) ).
thf(13998,plain,
( ( sk15 != sk12 )
| ~ ( sk15 @ ( sk13 @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13966]) ).
thf(33033,plain,
( ( ( sk15 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27017,198]) ).
thf(33034,plain,
( ( ( sk15 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[33033]) ).
thf(33117,plain,
( ( ( sk15 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[33034]) ).
thf(29563,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27023,199]) ).
thf(29564,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[29563]) ).
thf(29620,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[29564]) ).
thf(25657,plain,
( ( ( sk12 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk14 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[21985,991]) ).
thf(25658,plain,
( ( ( sk12 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk14 != sk12 ) ),
inference(simp,[status(thm)],[25657]) ).
thf(25718,plain,
( ( ( sk12 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk14 != sk12 ) ),
inference(simp,[status(thm)],[25658]) ).
thf(28040,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26772,7447]) ).
thf(28041,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28040]) ).
thf(28100,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) )
!= ( sk1 @ ( sk1 @ sk2 ) @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28041]) ).
thf(2466,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2446,200]) ).
thf(2467,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2466]) ).
thf(2475,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[2467]) ).
thf(6846,plain,
( ( ( sk13 @ sk10 @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( sk13 != sk1 )
| ( sk13 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[4845,18]) ).
thf(6847,plain,
( ( ( sk13 @ sk10 @ p1 )
!= ( sk14 @ p1 ) )
| ( sk13 != sk1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[6846]) ).
thf(6854,plain,
( ( ( sk13 @ sk10 )
!= sk14 )
| ( sk13 != sk1 )
| ( sk13 @ sk7 ) ),
inference(simp,[status(thm)],[6847]) ).
thf(5525,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ p2 ) )
| ( sk15 != sk13 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2446,5487]) ).
thf(5526,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ p2 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[5525]) ).
thf(5532,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) @ sk16 )
!= ( sk12 @ ( sk13 @ sk2 ) ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[5526]) ).
thf(33963,plain,
( ( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33680,5848]) ).
thf(33964,plain,
( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[33963]) ).
thf(34049,plain,
( ( sk1 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) ),
inference(simp,[status(thm)],[33964]) ).
thf(19055,plain,
! [A: $i] :
( ( ( A @ ( sk12 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ~ $true
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[328,2100]) ).
thf(19056,plain,
! [A: $i] :
( ( ( A @ ( sk12 @ r1 ) )
!= ( sk1 @ sk10 @ ( sk1 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[19055]) ).
thf(19156,plain,
! [A: $i] :
( ( A
!= ( sk1 @ sk10 ) )
| ( sk12 != sk1 )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[19056]) ).
thf(19196,plain,
( ( sk12 != sk1 )
| ~ ( sk12 @ ( sk1 @ sk10 @ sk3 ) @ p3 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[19156]) ).
thf(166,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk14 @ ( sk12 @ r1 ) ) )
| ( A @ p1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,43]) ).
thf(167,plain,
! [A: $i] :
( ( ( A @ ( sk13 @ r1 ) )
!= ( sk14 @ ( sk12 @ r1 ) ) )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[166]) ).
thf(171,plain,
! [A: $i] :
( ( A != sk14 )
| ( sk13 != sk12 )
| ( A @ p1 ) ),
inference(simp,[status(thm)],[167]) ).
thf(176,plain,
( ( sk13 != sk12 )
| ( sk14 @ p1 ) ),
inference(simp,[status(thm)],[171]) ).
thf(206,plain,
( ( sk13 != sk12 )
| $false ),
inference(rewrite,[status(thm)],[176,18]) ).
thf(207,plain,
sk13 != sk12,
inference(simp,[status(thm)],[206]) ).
thf(641,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,630]) ).
thf(642,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ ( sk1 @ r1 ) ) )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[641]) ).
thf(660,plain,
! [A: $i] :
( ( A != sk12 )
| ( sk15 != sk1 )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[642]) ).
thf(667,plain,
( ( sk15 != sk1 )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( sk12 @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[660]) ).
thf(1422,plain,
! [A: $i] :
( ( ( sk14 @ sk16 @ ( sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[962,8]) ).
thf(1423,plain,
! [A: $i] :
( ( ( sk14 @ sk16 @ ( sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1422]) ).
thf(1426,plain,
! [A: $i] :
( ( ( sk14 @ sk16 )
!= A )
| ( sk14 != sk1 )
| ~ ( A @ p4 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1423]) ).
thf(1440,plain,
( ( sk14 != sk1 )
| ~ ( sk14 @ sk16 @ p4 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[1426]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,38]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(265,plain,
! [C: $i,B: $i,A: $i] :
( ( sk13 != A )
| ( sk12 != sk1 )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(272,plain,
! [B: $i,A: $i] :
( ( sk12 != sk1 )
| ~ ( A @ sk4 )
| ~ ( sk13 @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk13 @ r1 ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(5867,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5840,630]) ).
thf(5868,plain,
! [A: $i] :
( ( ( sk1 @ ( sk15 @ sk2 ) @ ( sk15 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[5867]) ).
thf(5869,plain,
( ~ ( sk15 @ sk4 )
| ~ ( sk1 @ ( sk15 @ ( sk1 @ ( sk15 @ sk2 ) @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[5868:[bind(A,$thf( sk1 @ ( sk15 @ sk2 ) ))]]) ).
thf(329,plain,
! [A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,49]) ).
thf(330,plain,
! [A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 ) ),
inference(simp,[status(thm)],[329]) ).
thf(338,plain,
! [A: $i] :
( ( sk14 != A )
| ( sk12 != sk1 )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 ) ),
inference(simp,[status(thm)],[330]) ).
thf(346,plain,
( ( sk12 != sk1 )
| ( sk14 @ sk10 @ ( sk14 @ r1 ) )
| ( sk14 @ sk7 ) ),
inference(simp,[status(thm)],[338]) ).
thf(26684,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ sk16 @ ( sk14 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[962,2409]) ).
thf(26685,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk14 @ sk16 @ ( sk14 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[26684]) ).
thf(26978,plain,
! [A: $i] :
( ( A
!= ( sk14 @ sk16 ) )
| ( sk15 != sk14 )
| ( sk15 != sk12 )
| ( sk15 @ ( A @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26685]) ).
thf(27027,plain,
( ( sk15 != sk14 )
| ( sk15 != sk12 )
| ( sk15 @ ( sk14 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[26978]) ).
thf(22025,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk14 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21752,6783]) ).
thf(22026,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[22025]) ).
thf(22099,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) )
!= ( sk12 @ ( sk14 @ sk2 ) @ sk16 ) )
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[22026]) ).
thf(15937,plain,
! [A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,2091]) ).
thf(15938,plain,
! [A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15937]) ).
thf(16007,plain,
! [A: $i] :
( ( sk14 != A )
| ( sk12 != sk1 )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15938]) ).
thf(16038,plain,
( ( sk12 != sk1 )
| ~ ( sk1 @ ( sk14 @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[16007]) ).
thf(28330,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[26992,991]) ).
thf(28331,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28330]) ).
thf(28393,plain,
( ( ( sk15 @ ( sk12 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[28331]) ).
thf(23748,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ~ $true
| ( sk12 @ sk4 )
| ( sk12 @ sk7 )
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[21679,17000]) ).
thf(23749,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
!= ( sk12 @ p2 ) )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[23748]) ).
thf(23847,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) )
!= sk12 )
| ( sk1 @ ( sk12 @ ( sk12 @ sk10 @ sk6 ) ) @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk4 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[23749]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ $true
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,36]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(82,plain,
! [A: $i] :
( ( A @ ( sk1 @ ( sk12 @ sk6 ) ) @ ( sk12 @ r1 ) )
| ~ ( sk1 @ p2 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk12 ))]]) ).
thf(31266,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ~ $true
| ( sk1 @ sk4 )
| ( sk1 @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[4102,25889]) ).
thf(31267,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31266]) ).
thf(31363,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) )
!= sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31267]) ).
thf(18464,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[17793,186]) ).
thf(18465,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[18464]) ).
thf(18491,plain,
( ( ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[18465]) ).
thf(9278,plain,
! [A: $i] :
( ( ( sk14 @ sk10 @ ( sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true
| ( sk12 != sk1 )
| ( sk14 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[346,8]) ).
thf(9279,plain,
! [A: $i] :
( ( ( sk14 @ sk10 @ ( sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ( sk12 != sk1 )
| ( sk14 @ sk7 ) ),
inference(simp,[status(thm)],[9278]) ).
thf(9326,plain,
! [A: $i] :
( ( ( sk14 @ sk10 )
!= A )
| ( sk14 != sk1 )
| ~ ( A @ p4 )
| ( sk12 != sk1 )
| ( sk14 @ sk7 ) ),
inference(simp,[status(thm)],[9279]) ).
thf(9361,plain,
( ( sk14 != sk1 )
| ~ ( sk14 @ sk10 @ p4 )
| ( sk12 != sk1 )
| ( sk14 @ sk7 ) ),
inference(simp,[status(thm)],[9326]) ).
thf(15925,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[921,2091]) ).
thf(15926,plain,
! [A: $i] :
( ( ( sk15 @ sk16 @ ( sk15 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15925]) ).
thf(16010,plain,
! [A: $i] :
( ( ( sk15 @ sk16 )
!= A )
| ( sk15 != sk1 )
| ~ ( sk1 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[15926]) ).
thf(16041,plain,
( ( sk15 != sk1 )
| ~ ( sk1 @ ( sk15 @ sk16 @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[16010]) ).
thf(31136,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ~ $true
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[2973,25889]) ).
thf(31137,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31136]) ).
thf(31427,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31137]) ).
thf(70841,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[59,1965]) ).
thf(70842,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[70841]) ).
thf(70956,plain,
! [A: $i] :
( ( A != sk14 )
| ( A != sk1 )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[70842]) ).
thf(71042,plain,
( ( sk14 != sk1 )
| ~ ( sk14 @ ( sk14 @ sk16 @ sk3 ) @ p3 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[70956]) ).
thf(23807,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[21679,186]) ).
thf(23808,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[23807]) ).
thf(23863,plain,
( ( ( sk12 @ ( sk12 @ sk10 @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[23808]) ).
thf(96332,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[59,2245]) ).
thf(96333,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk14 @ ( sk1 @ r1 ) ) )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[96332]) ).
thf(96612,plain,
! [A: $i] :
( ( A != sk14 )
| ( A != sk1 )
| ( sk15 != sk12 )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[96333]) ).
thf(96723,plain,
( ( sk14 != sk1 )
| ( sk15 != sk12 )
| ( sk14 @ ( sk14 @ sk16 @ sk2 ) @ p2 ) ),
inference(simp,[status(thm)],[96612]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk11 @ p1 )
| ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ sk11 @ p1 )
| ( C @ p1 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(5521,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk13 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2413,5487]) ).
thf(5522,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 @ p2 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[5521]) ).
thf(5537,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= ( sk12 @ ( sk13 @ sk2 ) @ sk16 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[5522]) ).
thf(35676,plain,
( ( ( sk1 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33908,199]) ).
thf(35677,plain,
( ( ( sk1 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[35676]) ).
thf(35758,plain,
( ( ( sk1 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[35677]) ).
thf(19049,plain,
! [A: $i] :
( ( ( A @ ( sk12 @ r1 ) )
!= ( sk15 @ ( sk1 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,2100]) ).
thf(19050,plain,
! [A: $i] :
( ( ( A @ ( sk12 @ r1 ) )
!= ( sk15 @ ( sk1 @ r1 ) ) )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19049]) ).
thf(19165,plain,
! [A: $i] :
( ( A != sk15 )
| ( sk12 != sk1 )
| ~ ( sk12 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19050]) ).
thf(19207,plain,
( ( sk12 != sk1 )
| ~ ( sk12 @ ( sk15 @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[19165]) ).
thf(262,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( B @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[38]) ).
thf(266,plain,
! [A: $i] :
( ~ ( A @ sk4 )
| ~ ( A @ ( A @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[262:[bind(A,$thf( C )),bind(B,$thf( C ))]]) ).
thf(273,plain,
! [A: $i] :
( ~ ( A @ sk4 )
| ~ ( A @ ( A @ ( A @ sk5 ) ) @ p3 )
| ~ ( A @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(11516,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,5401]) ).
thf(11517,plain,
! [A: $i] :
( ( ( A @ ( A @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[11516]) ).
thf(11571,plain,
! [A: $i] :
( ( A != sk13 )
| ( A != sk1 )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[11517]) ).
thf(11612,plain,
( ( sk13 != sk1 )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[11571]) ).
thf(31727,plain,
( ( ( sk15 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[27003,199]) ).
thf(31728,plain,
( ( ( sk15 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[31727]) ).
thf(31786,plain,
( ( ( sk15 @ ( sk1 @ ( sk1 @ sk2 ) @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[31728]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ $true
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[12,36]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(107,plain,
! [A: $i] :
( ( A @ ( sk12 @ ( sk14 @ sk6 ) ) @ ( sk14 @ r1 ) )
| ~ ( sk12 @ p2 )
| ( sk12 @ sk4 )
| ~ ( sk12 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[106:[bind(A,$thf( A )),bind(B,$thf( sk12 )),bind(C,$thf( sk14 ))]]) ).
thf(117,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( F @ ( E @ r1 ) ) )
| ( D @ ( E @ ( F @ sk6 ) ) @ ( F @ r1 ) )
| ~ $true
| ~ ( E @ p2 )
| ( E @ sk4 )
| ~ ( E @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[36,36]) ).
thf(118,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( F @ ( E @ r1 ) ) )
| ( D @ ( E @ ( F @ sk6 ) ) @ ( F @ r1 ) )
| ~ ( E @ p2 )
| ( E @ sk4 )
| ~ ( E @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ ( B @ sk6 ) ) @ sk6 ) ) @ ( D @ ( C @ ( B @ sk6 ) ) @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ~ ( B @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( G )),bind(F,$thf( I @ ( H @ ( G @ sk6 ) ) ))]]) ).
thf(136,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ ( B @ sk6 ) ) @ sk6 ) ) @ ( D @ ( C @ ( B @ sk6 ) ) @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ~ ( B @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(29606,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27023,200]) ).
thf(29607,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[29606]) ).
thf(29642,plain,
( ( ( sk15 @ ( sk13 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[29607]) ).
thf(8403,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8377,199]) ).
thf(8404,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[8403]) ).
thf(8424,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[8404]) ).
thf(13713,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ ( sk1 @ sk10 @ sk10 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ~ $true
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[12812,43]) ).
thf(13714,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ ( sk1 @ sk10 @ sk10 @ r1 ) )
!= ( A @ ( sk13 @ r1 ) ) )
| ( A @ p1 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[13713]) ).
thf(13794,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) )
!= A )
| ( ( sk1 @ sk10 @ sk10 )
!= sk13 )
| ( A @ p1 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[13714]) ).
thf(13842,plain,
( ( ( sk1 @ sk10 @ sk10 )
!= sk13 )
| ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p1 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[13794]) ).
thf(7400,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,8]) ).
thf(7401,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[7400]) ).
thf(7402,plain,
~ ( sk1 @ ( sk1 @ sk2 ) @ p4 ),
inference(pattern_uni,[status(thm)],[7401:[bind(A,$thf( sk1 @ ( sk1 @ sk2 ) ))]]) ).
thf(24053,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk15 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21802,186]) ).
thf(24054,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[24053]) ).
thf(24102,plain,
( ( ( sk12 @ ( sk12 @ sk16 @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[24054]) ).
thf(92920,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,2020]) ).
thf(92921,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[92920]) ).
thf(92922,plain,
~ ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ ( sk1 @ sk2 ) @ sk3 ) @ p3 ),
inference(pattern_uni,[status(thm)],[92921:[bind(A,$thf( sk1 @ ( sk1 @ sk2 ) ))]]) ).
thf(251,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,38]) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk15 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) ) ),
inference(simp,[status(thm)],[251]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( sk15 @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk15 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[252:[bind(A,$thf( sk15 ))]]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk4 )
| ~ ( sk15 @ ( A @ ( B @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk15 @ r1 ) ) ),
inference(simp,[status(thm)],[253]) ).
thf(69986,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk3 ) @ ( sk12 @ ( sk13 @ sk2 ) @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69947,37]) ).
thf(69987,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk3 ) @ ( sk12 @ ( sk13 @ sk2 ) @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[69986]) ).
thf(70389,plain,
! [A: $i] :
( ( ( sk12 @ ( sk13 @ sk3 ) )
!= A )
| ( ( sk12 @ ( sk13 @ sk2 ) )
!= sk15 )
| ~ ( A @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[69987]) ).
thf(70526,plain,
( ( ( sk12 @ ( sk13 @ sk2 ) )
!= sk15 )
| ~ ( sk12 @ ( sk13 @ sk3 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[70389]) ).
thf(1134,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ sk16 @ ( sk15 @ sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ~ $true
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[903,49]) ).
thf(1135,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ sk16 @ ( sk15 @ sk10 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[1134]) ).
thf(1161,plain,
! [A: $i] :
( ( ( sk15 @ sk10 @ sk16 )
!= A )
| ( ( sk15 @ sk10 )
!= sk1 )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[1135]) ).
thf(1172,plain,
( ( ( sk15 @ sk10 )
!= sk1 )
| ( sk15 @ sk10 @ sk16 @ sk10 @ ( sk15 @ sk10 @ sk16 @ r1 ) )
| ( sk15 @ sk10 @ sk16 @ sk7 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[1161]) ).
thf(26789,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ~ $true
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[616,2409]) ).
thf(26790,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 @ ( sk1 @ sk10 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[26789]) ).
thf(26952,plain,
! [A: $i] :
( ( ( sk1 @ sk10 @ sk10 )
!= A )
| ( ( sk1 @ sk10 )
!= sk15 )
| ( sk15 @ ( A @ sk2 ) @ p2 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[26790]) ).
thf(27014,plain,
( ( ( sk1 @ sk10 )
!= sk15 )
| ( sk15 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[26952]) ).
thf(3468,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3450,186]) ).
thf(3469,plain,
( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[3468]) ).
thf(3479,plain,
( ( sk1 @ ( sk1 @ sk2 ) )
!= ( sk15 @ sk16 ) ),
inference(simp,[status(thm)],[3469]) ).
thf(25097,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[21971,200]) ).
thf(25098,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[25097]) ).
thf(25103,plain,
( ( ( sk12 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[25098]) ).
thf(72945,plain,
( ( ( sk1 @ ( sk15 @ sk3 ) @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk13 ) ),
inference(paramod_ordered,[status(thm)],[72904,18]) ).
thf(72946,plain,
( ( ( sk1 @ ( sk15 @ sk3 ) @ p1 )
!= ( sk14 @ p1 ) )
| ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk13 ) ),
inference(simp,[status(thm)],[72945]) ).
thf(72952,plain,
( ( ( sk1 @ ( sk15 @ sk3 ) )
!= sk14 )
| ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk13 ) ),
inference(simp,[status(thm)],[72946]) ).
thf(33091,plain,
( ( ( sk15 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true
| ( sk15 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[27017,200]) ).
thf(33092,plain,
( ( ( sk15 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[33091]) ).
thf(33128,plain,
( ( ( sk15 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[33092]) ).
thf(516,plain,
! [A: $i] :
( ( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ~ $true
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[308,49]) ).
thf(517,plain,
! [A: $i] :
( ( ( sk12 @ sk10 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[516]) ).
thf(524,plain,
! [A: $i] :
( ( ( sk12 @ sk10 )
!= A )
| ( sk12 != sk1 )
| ( A @ sk10 @ ( A @ r1 ) )
| ( A @ sk7 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[517]) ).
thf(532,plain,
( ( sk12 != sk1 )
| ( sk12 @ sk10 @ sk10 @ ( sk12 @ sk10 @ r1 ) )
| ( sk12 @ sk10 @ sk7 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[524]) ).
thf(92879,plain,
! [A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,2020]) ).
thf(92880,plain,
! [A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[92879]) ).
thf(93037,plain,
! [A: $i] :
( ( sk14 != A )
| ( sk12 != sk1 )
| ~ ( A @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[92880]) ).
thf(93127,plain,
( ( sk12 != sk1 )
| ~ ( sk14 @ ( sk14 @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[93037]) ).
thf(31069,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ~ $true
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[21752,25889]) ).
thf(31070,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31069]) ).
thf(31403,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) )
!= sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[31070]) ).
thf(61365,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( ( sk15 @ sk16 )
!= sk13 ) ),
inference(paramod_ordered,[status(thm)],[60722,18]) ).
thf(61366,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p1 )
!= ( sk14 @ p1 ) )
| ( ( sk15 @ sk16 )
!= sk13 ) ),
inference(simp,[status(thm)],[61365]) ).
thf(61372,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= sk14 )
| ( ( sk15 @ sk16 )
!= sk13 ) ),
inference(simp,[status(thm)],[61366]) ).
thf(22007,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) )
| ( ( sk15 @ sk16 )
!= sk15 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21752,1106]) ).
thf(22008,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ sk16 @ p2 ) )
| ( ( sk15 @ sk16 )
!= sk15 ) ),
inference(simp,[status(thm)],[22007]) ).
thf(22094,plain,
( ( ( sk12 @ ( sk12 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 @ sk16 ) )
| ( ( sk15 @ sk16 )
!= sk15 ) ),
inference(simp,[status(thm)],[22008]) ).
thf(60,plain,
! [A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,8]) ).
thf(61,plain,
! [A: $i] :
( ( ( sk12 @ ( sk1 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[60]) ).
thf(62,plain,
~ ( sk12 @ p4 ),
inference(pattern_uni,[status(thm)],[61:[bind(A,$thf( sk12 ))]]) ).
thf(239,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( F @ ( E @ r1 ) ) )
| ~ ( E @ sk4 )
| ~ ( D @ ( E @ ( F @ sk5 ) ) @ p3 )
| ~ $true
| ~ ( E @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[36,38]) ).
thf(240,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( F @ ( E @ r1 ) ) )
| ~ ( E @ sk4 )
| ~ ( D @ ( E @ ( F @ sk5 ) ) @ p3 )
| ~ ( E @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[239]) ).
thf(241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( D @ ( C @ ( B @ sk6 ) ) @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ~ ( B @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( G )),bind(F,$thf( I @ ( H @ ( G @ sk6 ) ) ))]]) ).
thf(277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( D @ ( C @ ( B @ sk6 ) ) @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) )
| ~ ( B @ ( C @ r1 ) )
| ~ ( C @ p2 )
| ( C @ sk4 )
| ~ ( C @ ( D @ r1 ) )
| ~ ( D @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[241]) ).
thf(8391,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8377,198]) ).
thf(8392,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk14 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[8391]) ).
thf(8427,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk14 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[8392]) ).
thf(13924,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7283,2077]) ).
thf(13925,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) @ ( sk1 @ r1 ) )
!= ( A @ ( sk15 @ r1 ) ) )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13924]) ).
thf(13985,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= A )
| ( sk15 != sk1 )
| ~ ( sk15 @ ( A @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13925]) ).
thf(14018,plain,
( ( sk15 != sk1 )
| ~ ( sk15 @ ( sk1 @ ( sk1 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[13985]) ).
thf(35546,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33880,186]) ).
thf(35547,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35546]) ).
thf(35581,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) )
!= ( sk15 @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35547]) ).
thf(35532,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ~ $true
| ( sk12 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33880,991]) ).
thf(35533,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ sk16 @ p2 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35532]) ).
thf(35580,plain,
( ( ( sk1 @ ( sk14 @ sk2 ) )
!= ( sk15 @ sk16 @ sk16 ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[35533]) ).
thf(506,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk10 @ ( sk12 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ~ $true
| ( sk12 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[308,37]) ).
thf(507,plain,
! [A: $i] :
( ( ( A @ ( sk15 @ r1 ) )
!= ( sk12 @ sk10 @ ( sk12 @ r1 ) ) )
| ~ ( A @ sk16 @ p2 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[506]) ).
thf(520,plain,
! [A: $i] :
( ( A
!= ( sk12 @ sk10 ) )
| ( sk15 != sk12 )
| ~ ( A @ sk16 @ p2 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[507]) ).
thf(528,plain,
( ( sk15 != sk12 )
| ~ ( sk12 @ sk10 @ sk16 @ p2 )
| ( sk12 @ sk7 ) ),
inference(simp,[status(thm)],[520]) ).
thf(6201,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( sk15 != sk13 ) ),
inference(paramod_ordered,[status(thm)],[5982,18]) ).
thf(6202,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) @ p1 )
!= ( sk14 @ p1 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[6201]) ).
thf(6205,plain,
( ( ( sk1 @ ( sk15 @ sk2 ) )
!= sk14 )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[6202]) ).
thf(28062,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ~ $true
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[26772,13203]) ).
thf(28063,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[28062]) ).
thf(28110,plain,
( ( ( sk15 @ ( sk15 @ sk2 ) )
!= sk15 )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 ) ),
inference(simp,[status(thm)],[28063]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk4 )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk4 )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( D @ ( sk1 @ r1 ) ) )
| ~ ( D @ p4 )
| ~ $true
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[36,8]) ).
thf(109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
!= ( D @ ( sk1 @ r1 ) ) )
| ~ ( D @ p4 )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( sk1 @ sk6 ) ) @ p4 )
| ~ ( sk1 @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[109:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( sk1 )),bind(D,$thf( G @ ( F @ ( sk1 @ sk6 ) ) ))]]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( sk1 @ sk6 ) ) @ p4 )
| ~ ( sk1 @ ( A @ r1 ) )
| ~ ( A @ p2 )
| ( A @ sk4 )
| ~ ( A @ ( B @ r1 ) )
| ~ ( B @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(8387,plain,
( ( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8377,5848]) ).
thf(8388,plain,
( ( sk15 @ ( sk15 @ sk16 @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[8387]) ).
thf(8437,plain,
( ( sk15 @ ( sk15 @ sk16 @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) ),
inference(simp,[status(thm)],[8388]) ).
thf(9939,plain,
( ( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9929,5848]) ).
thf(9940,plain,
( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) @ p2 )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[9939]) ).
thf(9992,plain,
( ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk2 ) )
!= ( sk1 @ ( sk15 @ sk2 ) @ sk16 ) ),
inference(simp,[status(thm)],[9940]) ).
thf(35343,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ~ $true
| ( sk1 @ sk4 )
| ( sk1 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[33603,25889]) ).
thf(35344,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) @ p2 )
!= ( sk1 @ p2 ) )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[35343]) ).
thf(35449,plain,
( ( ( sk1 @ ( sk1 @ sk10 @ sk2 ) )
!= sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ sk10 @ sk6 ) ) @ ( sk1 @ sk10 @ r1 ) )
| ( sk1 @ sk4 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[35344]) ).
thf(15720,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ~ $true
| ( sk15 @ sk4 )
| ( sk15 @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[4102,13203]) ).
thf(15721,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) @ p2 )
!= ( sk15 @ p2 ) )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[15720]) ).
thf(15818,plain,
( ( ( sk1 @ sk10 @ ( sk1 @ sk10 @ sk10 @ sk2 ) )
!= sk15 )
| ( sk1 @ ( sk15 @ ( sk15 @ sk10 @ sk6 ) ) @ ( sk15 @ sk10 @ r1 ) )
| ( sk15 @ sk4 )
| ( sk15 @ sk7 )
| ( sk1 @ sk10 @ sk7 )
| ( sk1 @ sk7 ) ),
inference(simp,[status(thm)],[15721]) ).
thf(11498,plain,
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,5401]) ).
thf(11499,plain,
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( sk13 @ ( sk1 @ r1 ) ) )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[11498]) ).
thf(11580,plain,
( ( sk13 != sk13 )
| ( sk12 != sk1 )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[11499]) ).
thf(11616,plain,
( ( sk12 != sk1 )
| ~ ( sk13 @ ( sk12 @ ( sk13 @ sk2 ) @ sk3 ) @ p3 ) ),
inference(simp,[status(thm)],[11580]) ).
thf(6717,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6622,8]) ).
thf(6718,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk1 @ r1 ) ) )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[6717]) ).
thf(6765,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) )
!= A )
| ( sk14 != sk1 )
| ~ ( A @ p4 ) ),
inference(simp,[status(thm)],[6718]) ).
thf(6797,plain,
( ( sk14 != sk1 )
| ~ ( sk12 @ ( sk14 @ sk2 ) @ p4 ) ),
inference(simp,[status(thm)],[6765]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ $true
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[29,36]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(90,plain,
! [A: $i] :
( ( A @ ( sk12 @ ( sk13 @ sk6 ) ) @ ( sk13 @ r1 ) )
| ~ ( sk12 @ p2 )
| ( sk12 @ sk4 )
| ~ ( sk12 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( A )),bind(B,$thf( sk12 )),bind(C,$thf( sk13 ))]]) ).
thf(3470,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3450,200]) ).
thf(3471,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) @ p2 )
!= ( sk13 @ sk16 @ p2 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[3470]) ).
thf(3474,plain,
( ( ( sk1 @ ( sk1 @ sk2 ) )
!= ( sk13 @ sk16 ) )
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[3471]) ).
thf(47887,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk14 @ r1 ) ) )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6622,47760]) ).
thf(47888,plain,
! [A: $i] :
( ( ( sk12 @ ( sk14 @ sk2 ) @ ( sk14 @ r1 ) )
!= ( A @ ( sk14 @ r1 ) ) )
| ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( A @ sk5 ) ) @ p3 ) ),
inference(simp,[status(thm)],[47887]) ).
thf(47889,plain,
( ~ ( sk14 @ sk4 )
| ~ ( sk12 @ ( sk14 @ ( sk12 @ ( sk14 @ sk2 ) @ sk5 ) ) @ p3 ) ),
inference(pattern_uni,[status(thm)],[47888:[bind(A,$thf( sk12 @ ( sk14 @ sk2 ) ))]]) ).
thf(1182,plain,
( ( ( sk15 @ sk16 @ p1 )
!= ( sk14 @ p1 ) )
| ~ $true
| ( sk15 != sk13 ) ),
inference(paramod_ordered,[status(thm)],[1036,18]) ).
thf(1183,plain,
( ( ( sk15 @ sk16 @ p1 )
!= ( sk14 @ p1 ) )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[1182]) ).
thf(1184,plain,
( ( ( sk15 @ sk16 )
!= sk14 )
| ( sk15 != sk13 ) ),
inference(simp,[status(thm)],[1183]) ).
thf(2431,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2413,186]) ).
thf(2432,plain,
( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[2431]) ).
thf(2436,plain,
( ( sk1 @ ( sk12 @ sk2 ) )
!= ( sk15 @ sk16 ) ),
inference(simp,[status(thm)],[2432]) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ $true
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[29,38]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[213]) ).
thf(215,plain,
! [A: $i] :
( ~ ( sk12 @ sk4 )
| ~ ( A @ ( sk12 @ ( sk13 @ sk5 ) ) @ p3 )
| ~ ( sk12 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[214:[bind(A,$thf( A )),bind(B,$thf( sk12 )),bind(C,$thf( sk13 ))]]) ).
thf(2423,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2413,199]) ).
thf(2424,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) @ p2 )
!= ( sk12 @ sk16 @ p2 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[2423]) ).
thf(2438,plain,
( ( ( sk1 @ ( sk12 @ sk2 ) )
!= ( sk12 @ sk16 ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[2424]) ).
thf(4568,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[4527,44]) ).
thf(4569,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk12 @ sk2 ) @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ~ ( A @ ( B @ sk3 ) @ p3 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[4568]) ).
thf(4570,plain,
( ~ ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk3 ) @ p3 )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[4569:[bind(A,$thf( sk12 )),bind(B,$thf( sk1 @ ( sk12 @ sk2 ) ))]]) ).
thf(10668,plain,
( ~ ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk3 ) @ p3 )
| ~ $true ),
inference(rewrite,[status(thm)],[4570,24]) ).
thf(10669,plain,
~ ( sk12 @ ( sk1 @ ( sk12 @ sk2 ) @ sk3 ) @ p3 ),
inference(simp,[status(thm)],[10668]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ $true
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[29,36]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk13 @ ( sk12 @ r1 ) )
!= ( B @ ( A @ r1 ) ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ r1 ) )
| ~ ( C @ ( B @ r1 ) )
| ~ ( B @ p2 )
| ( B @ sk4 )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(87,plain,
! [A: $i] :
( ( sk12 @ ( sk13 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk13 @ r1 ) )
| ~ ( sk13 @ p2 )
| ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( sk12 )),bind(B,$thf( sk13 ))]]) ).
thf(135,plain,
! [A: $i] :
( ( sk12 @ ( sk13 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk13 @ r1 ) )
| ~ ( sk13 @ p2 )
| ( sk13 @ sk4 )
| ~ ( sk12 @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(20758,plain,
! [A: $i] :
( ( sk12 @ ( sk13 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk13 @ r1 ) )
| ~ ( sk13 @ p2 )
| ( sk13 @ sk4 )
| ~ $true ),
inference(rewrite,[status(thm)],[135,24]) ).
thf(20759,plain,
! [A: $i] :
( ( sk12 @ ( sk13 @ ( A @ sk6 ) ) @ ( A @ r1 ) )
| ~ ( A @ ( sk13 @ r1 ) )
| ~ ( sk13 @ p2 )
| ( sk13 @ sk4 ) ),
inference(simp,[status(thm)],[20758]) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ $true
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(paramod_ordered,[status(thm)],[12,38]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk14 @ ( sk12 @ r1 ) )
!= ( C @ ( B @ r1 ) ) )
| ~ ( B @ sk4 )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ p3 )
| ~ ( B @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(232,plain,
! [A: $i] :
( ~ ( sk12 @ sk4 )
| ~ ( A @ ( sk12 @ ( sk14 @ sk5 ) ) @ p3 )
| ~ ( sk12 @ ( A @ r1 ) )
| ~ ( A @ ( sk1 @ r1 ) ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( A )),bind(B,$thf( sk12 )),bind(C,$thf( sk14 ))]]) ).
thf(3024,plain,
( ( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3006,186]) ).
thf(3025,plain,
( ( sk12 @ ( sk14 @ sk2 ) @ p2 )
!= ( sk15 @ sk16 @ p2 ) ),
inference(simp,[status(thm)],[3024]) ).
thf(3035,plain,
( ( sk12 @ ( sk14 @ sk2 ) )
!= ( sk15 @ sk16 ) ),
inference(simp,[status(thm)],[3025]) ).
thf(123260,plain,
$false,
inference(e,[status(thm)],[9929,1036,6836,4835,70549,2109,28394,92847,3477,28097,962,31408,645,69,11922,70502,6172,6819,33103,12812,28114,93141,2077,68211,7517,276,994,308,6776,18052,5348,202,18603,27023,33885,93180,2062,25228,68440,21967,5982,19213,96748,67521,26510,56,142,28536,33880,11917,2476,31806,83060,340,96719,22101,14014,35456,533,31369,74978,28101,14025,28118,35282,34039,42,7499,27006,2020,17798,24,37,21752,22086,52,28270,8426,719,12718,33876,50586,21985,619,35584,344,34062,23864,7496,35271,15922,9989,28106,3029,28121,50508,21975,9988,19184,72340,24095,33908,14024,31385,27028,26711,16035,46,26517,4675,289,57,316,17884,29,28249,6025,4696,16050,34045,2996,2469,7441,31652,1682,5558,15554,1677,23983,18324,67575,2105,18700,21953,3473,6189,2437,35731,5401,47843,293,3036,15831,96743,72904,5489,75090,31423,15958,50486,397,35738,2103,4700,17000,28098,3450,2473,18312,16044,50462,28267,22097,17526,270,14004,1438,8375,7357,28525,5487,71051,75020,16059,19099,18325,33603,630,15563,29618,14000,7439,68265,35579,2409,28,28515,38,11471,25123,37010,137,22082,275,165,5396,625,22104,19214,28115,12618,13835,3028,2211,3033,23841,65,64391,1178,5515,29626,974,224,1106,2245,15826,2100,9145,47760,156,22085,6028,2973,28532,74471,53,4840,8429,141,64108,16055,25721,18303,4845,28382,21951,3001,328,15798,339,69947,669,16036,35592,19070,1493,3000,48045,15793,22100,4744,3032,2472,19195,48004,1099,26524,13607,18608,37174,721,35285,11610,41,79466,21976,64419,35270,33680,25106,7495,17793,8425,134,67483,205,8422,28519,14035,16048,2408,79456,5840,14003,71045,73,5557,28390,343,29627,921,15552,2440,1515,28521,28124,2995,23985,6026,13907,1927,45,18704,25889,37332,2413,31424,35290,33884,33865,279,35451,11615,60805,3472,68268,577,59,1965,37895,281,35295,259,5535,44,7497,286,32970,13125,579,12,9984,54,79475,28246,1107,5997,2474,5556,26772,8432,14010,22081,4672,3002,49,2442,24110,21802,75055,14027,12624,5578,18067,23838,274,96971,21950,5848,1524,4699,17725,8436,25739,39,5531,17886,616,25111,11470,345,2111,140,2446,19185,3034,27018,6817,28261,33873,5552,4694,28400,3006,668,155,198,1177,23971,68164,17794,16062,6783,1015,19179,72866,15566,31400,13884,2999,33891,3480,1171,130,2439,16057,7479,6816,21982,6180,22084,27004,6029,23975,12708,2107,68167,7447,342,19182,6821,60713,33862,25104,31370,1034,15804,3031,67007,2471,22078,35594,34064,145,7283,48,17796,27026,1531,18060,28406,22093,580,15551,18,50709,15549,282,71040,64099,14017,50,16047,48022,19022,18488,50551,31428,23979,35435,2468,199,9991,28108,8377,28524,177,28123,9986,5912,18346,5555,72907,3475,21679,29613,2411,6679,25230,154,25112,15483,8433,68346,7498,70507,991,9983,27024,175,978,386,33899,18066,60722,43,64192,2584,33879,8431,6622,16988,556,22102,28113,5536,18061,18355,24092,14009,35431,21996,37175,2435,16070,250,3478,29639,4698,28388,99,976,903,6674,2997,26514,1448,4102,15796,11412,33906,2443,963,6818,34038,40,27017,14026,13203,652,5426,186,55,11469,15561,5505,33889,27000,23962,1674,50717,6023,24086,18305,139,3003,1523,13128,13998,4527,33117,29620,17792,25718,8,28100,2475,58,6854,5532,34049,19196,207,667,1440,272,5869,346,27027,22099,16038,28393,23847,82,31363,18491,9361,16041,31427,4670,27003,71042,36,23863,96723,51,5537,35758,19207,273,11612,4843,31786,107,136,29642,33892,8424,13842,2091,7402,24102,92922,283,70526,4,1172,27014,3479,26992,25103,72952,33128,532,624,93127,31403,61372,22094,62,178,277,8427,14018,35581,60263,35580,528,21971,11476,6205,28110,47,131,8437,9992,35449,15818,200,11616,6797,90,3474,47889,1184,2436,215,2438,26988,10669,20759,232,3035,972,7442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL670+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.37 % Computer : n012.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 23:11:05 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.76/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.93/0.96 % [INFO] Parsing done (149ms).
% 0.93/0.97 % [INFO] Running in sequential loop mode.
% 1.49/1.29 % [INFO] eprover registered as external prover.
% 1.68/1.30 % [INFO] Scanning for conjecture ...
% 1.89/1.40 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.89/1.44 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.89/1.44 % [INFO] Problem is first-order (TPTP FOF).
% 1.89/1.45 % [INFO] Type checking passed.
% 1.89/1.46 % [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 ...
% 135.99/36.22 % External prover 'e' found a proof!
% 135.99/36.22 % [INFO] Killing All external provers ...
% 135.99/36.22 % Time passed: 35740ms (effective reasoning time: 35242ms)
% 135.99/36.22 % 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)>
% 135.99/36.22 % Axioms used in derivation (1): reflexivity
% 135.99/36.22 % No. of inferences in proof: 2285
% 135.99/36.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 35740 ms resp. 35242 ms w/o parsing
% 134.73/36.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 134.73/36.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------