TSTP Solution File: LCL642+1.001 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL642+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:30:52 EDT 2023
% Result : Theorem 119.32s 21.77s
% Output : Refutation 120.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 41
% Syntax : Number of formulae : 1653 ( 35 unt; 40 typ; 0 def)
% Number of atoms : 8613 (2173 equ; 0 cnn)
% Maximal formula atoms : 107 ( 5 avg)
% Number of connectives : 21071 (4894 ~;5661 |; 25 &;10491 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 15 con; 0-4 aty)
% Number of variables : 867 ( 0 ^; 863 !; 4 ?; 867 :)
% Comments :
%------------------------------------------------------------------------------
thf(r1_type,type,
r1: $i > $i > $o ).
thf(p3_type,type,
p3: $i > $o ).
thf(p2_type,type,
p2: $i > $o ).
thf(p1_type,type,
p1: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > $i ).
thf(sk4_type,type,
sk4: $i > $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i > $i ).
thf(sk10_type,type,
sk10: $i > $i ).
thf(sk11_type,type,
sk11: $o ).
thf(sk12_type,type,
sk12: $o ).
thf(sk13_type,type,
sk13: $i > $i > $i ).
thf(sk14_type,type,
sk14: $i > $i > $i ).
thf(sk15_type,type,
sk15: $i ).
thf(sk16_type,type,
sk16: $i ).
thf(sk17_type,type,
sk17: $i ).
thf(sk18_type,type,
sk18: $i ).
thf(sk19_type,type,
sk19: $o ).
thf(sk20_type,type,
sk20: $i ).
thf(sk21_type,type,
sk21: $i ).
thf(sk22_type,type,
sk22: $i > $i ).
thf(sk23_type,type,
sk23: $i > $i ).
thf(sk24_type,type,
sk24: $i > $o ).
thf(sk25_type,type,
sk25: $i > $o ).
thf(sk26_type,type,
sk26: $i > $i > $i > $i > $i ).
thf(sk27_type,type,
sk27: $i > $i > $i > $i > $i ).
thf(sk28_type,type,
sk28: $i > $i > $i ).
thf(sk29_type,type,
sk29: $i > $i > $i ).
thf(sk30_type,type,
sk30: $i > $i > $i ).
thf(sk31_type,type,
sk31: $i > $o ).
thf(sk32_type,type,
sk32: $i > $i ).
thf(sk33_type,type,
sk33: $i > $i ).
thf(sk34_type,type,
sk34: $i > $i > $i ).
thf(sk35_type,type,
sk35: $i > $i > $i ).
thf(sk36_type,type,
sk36: $i > $i ).
thf(1,conjecture,
~ ? [A: $i] :
~ ( ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p3 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p3 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p3 @ D ) )
| ~ ( p3 @ C ) ) )
| ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) )
| ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p1 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p1 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p1 @ D ) )
| ~ ( p1 @ C ) ) )
| ~ ( ( ( ( ! [B: $i] :
( ~ ( r1 @ A @ B )
| ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) ) )
& ( ( p2 @ A )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C ) )
| ~ ( p2 @ B ) ) ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( ( ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) )
& ( ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) ) )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( ( ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F )
| ~ ! [G: $i] :
( ~ ( r1 @ F @ G )
| ! [H: $i] :
( ~ ( r1 @ G @ H )
| ( p2 @ H ) )
| ~ ( p2 @ G ) ) ) )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E )
| ~ ! [F: $i] :
( ~ ( r1 @ E @ F )
| ! [G: $i] :
( ~ ( r1 @ F @ G )
| ( p2 @ G ) )
| ~ ( p2 @ F ) ) ) )
& ( ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) ) )
| ~ ( ( ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E )
| ~ ! [F: $i] :
( ~ ( r1 @ E @ F )
| ! [G: $i] :
( ~ ( r1 @ F @ G )
| ( p2 @ G ) )
| ~ ( p2 @ F ) ) ) )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) )
& ( ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) ) ) ) )
& ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
thf(2,negated_conjecture,
~ ~ ? [A: $i] :
~ ( ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p3 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p3 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p3 @ D ) )
| ~ ( p3 @ C ) ) )
| ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) )
| ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p1 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p1 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p1 @ D ) )
| ~ ( p1 @ C ) ) )
| ~ ( ( ( ( ! [B: $i] :
( ~ ( r1 @ A @ B )
| ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) ) )
& ( ( p2 @ A )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C ) )
| ~ ( p2 @ B ) ) ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( ( ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) )
& ( ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) ) )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( ( ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F )
| ~ ! [G: $i] :
( ~ ( r1 @ F @ G )
| ! [H: $i] :
( ~ ( r1 @ G @ H )
| ( p2 @ H ) )
| ~ ( p2 @ G ) ) ) )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E )
| ~ ! [F: $i] :
( ~ ( r1 @ E @ F )
| ! [G: $i] :
( ~ ( r1 @ F @ G )
| ( p2 @ G ) )
| ~ ( p2 @ F ) ) ) )
& ( ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) ) )
| ~ ( ( ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E )
| ~ ! [F: $i] :
( ~ ( r1 @ E @ F )
| ! [G: $i] :
( ~ ( r1 @ F @ G )
| ( p2 @ G ) )
| ~ ( p2 @ F ) ) ) )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) )
& ( ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) ) ) ) )
& ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ? [A: $i] :
~ ( ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p3 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p3 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p3 @ D ) )
| ~ ( p3 @ C ) ) )
| ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) )
| ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p1 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p1 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p1 @ D ) )
| ~ ( p1 @ C ) ) )
| ~ ( ( ( ( ! [B: $i] :
( ~ ( r1 @ A @ B )
| ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) ) )
& ( ( p2 @ A )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C ) )
| ~ ( p2 @ B ) ) ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( ( ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) )
& ( ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) ) )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( ( ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F )
| ~ ! [G: $i] :
( ~ ( r1 @ F @ G )
| ! [H: $i] :
( ~ ( r1 @ G @ H )
| ( p2 @ H ) )
| ~ ( p2 @ G ) ) ) )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E )
| ~ ! [F: $i] :
( ~ ( r1 @ E @ F )
| ! [G: $i] :
( ~ ( r1 @ F @ G )
| ( p2 @ G ) )
| ~ ( p2 @ F ) ) ) )
& ( ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) ) )
| ~ ( ( ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E )
| ~ ! [F: $i] :
( ~ ( r1 @ E @ F )
| ! [G: $i] :
( ~ ( r1 @ F @ G )
| ( p2 @ G ) )
| ~ ( p2 @ F ) ) ) )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) )
& ( ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) ) ) ) )
& ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
? [A: $i] :
~ ( ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p3 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p3 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p3 @ D ) )
| ~ ( p3 @ C ) ) )
| ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) )
| ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p1 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p1 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p1 @ D ) )
| ~ ( p1 @ C ) ) )
| ~ ( ( ( ( ! [B: $i] :
( ~ ( r1 @ A @ B )
| ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) ) )
& ( ( p2 @ A )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C ) )
| ~ ( p2 @ B ) ) ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( ( ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) )
& ( ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) ) )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( ( ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F )
| ~ ! [G: $i] :
( ~ ( r1 @ F @ G )
| ! [H: $i] :
( ~ ( r1 @ G @ H )
| ( p2 @ H ) )
| ~ ( p2 @ G ) ) ) )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E )
| ~ ! [F: $i] :
( ~ ( r1 @ E @ F )
| ! [G: $i] :
( ~ ( r1 @ F @ G )
| ( p2 @ G ) )
| ~ ( p2 @ F ) ) ) )
& ( ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) ) )
| ~ ( ( ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E )
| ~ ! [F: $i] :
( ~ ( r1 @ E @ F )
| ! [G: $i] :
( ~ ( r1 @ F @ G )
| ( p2 @ G ) )
| ~ ( p2 @ F ) ) ) )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) )
& ( ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) ) ) ) )
& ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) ) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
~ ! [A: $i] :
( ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p3 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p3 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p3 @ D ) )
| ~ ( p3 @ C ) ) )
| ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) )
| ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p1 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p1 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p1 @ D ) )
| ~ ( p1 @ C ) ) )
| ~ ( ( ( ( ! [B: $i] :
( ~ ( r1 @ A @ B )
| ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) ) )
& ( ( p2 @ A )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C ) )
| ~ ( p2 @ B ) ) ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( ( ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) )
& ( ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D ) )
| ~ ( p2 @ C ) ) ) )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( ( ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F )
| ~ ! [G: $i] :
( ~ ( r1 @ F @ G )
| ! [H: $i] :
( ~ ( r1 @ G @ H )
| ( p2 @ H ) )
| ~ ( p2 @ G ) ) ) )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E )
| ~ ! [F: $i] :
( ~ ( r1 @ E @ F )
| ! [G: $i] :
( ~ ( r1 @ F @ G )
| ( p2 @ G ) )
| ~ ( p2 @ F ) ) ) )
& ( ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) ) )
| ~ ( ( ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E )
| ~ ! [F: $i] :
( ~ ( r1 @ E @ F )
| ! [G: $i] :
( ~ ( r1 @ F @ G )
| ( p2 @ G ) )
| ~ ( p2 @ F ) ) ) )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ! [E: $i] :
( ~ ( r1 @ D @ E )
| ! [F: $i] :
( ~ ( r1 @ E @ F )
| ( p2 @ F ) )
| ~ ( p2 @ E ) ) ) )
& ( ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) ) ) ) )
& ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ! [D: $i] :
( ~ ( r1 @ C @ D )
| ! [E: $i] :
( ~ ( r1 @ D @ E )
| ( p2 @ E ) )
| ~ ( p2 @ D ) ) ) ) ) ),
inference(miniscope,[status(thm)],[4]) ).
thf(69,plain,
( ( p2 @ sk1 )
| ~ ( p2 @ sk17 )
| sk11 ),
inference(cnf,[status(esa)],[5]) ).
thf(57,plain,
( ~ sk11
| ( r1 @ sk1 @ sk18 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(41,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(88,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(5809,plain,
! [A: $i] :
( ~ sk11
| ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ sk18 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,88]) ).
thf(5810,plain,
( ~ sk11
| ( p1 @ sk18 )
| ( r1 @ sk18 @ ( sk9 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[5809:[bind(A,$thf( sk18 ))]]) ).
thf(47,plain,
r1 @ sk1 @ sk5,
inference(cnf,[status(esa)],[5]) ).
thf(49,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( p2 @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(97,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( p2 @ ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(11292,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,97]) ).
thf(11293,plain,
( ( p2 @ sk5 )
| ( p2 @ ( sk6 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[11292:[bind(A,$thf( sk5 ))]]) ).
thf(39,plain,
~ ( p2 @ sk5 ),
inference(cnf,[status(esa)],[5]) ).
thf(11656,plain,
( $false
| ( p2 @ ( sk6 @ sk5 ) ) ),
inference(rewrite,[status(thm)],[11293,39]) ).
thf(11657,plain,
p2 @ ( sk6 @ sk5 ),
inference(simp,[status(thm)],[11656]) ).
thf(51,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(109,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(19319,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,109]) ).
thf(19320,plain,
( ( p2 @ sk5 )
| ~ ( p2 @ ( sk7 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[19319:[bind(A,$thf( sk5 ))]]) ).
thf(19566,plain,
( $false
| ~ ( p2 @ ( sk7 @ sk5 ) ) ),
inference(rewrite,[status(thm)],[19320,39]) ).
thf(19567,plain,
~ ( p2 @ ( sk7 @ sk5 ) ),
inference(simp,[status(thm)],[19566]) ).
thf(19582,plain,
( ( p2 @ ( sk7 @ sk5 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[11657,19567]) ).
thf(19594,plain,
( ( sk7 @ sk5 )
!= ( sk6 @ sk5 ) ),
inference(simp,[status(thm)],[19582]) ).
thf(6,plain,
( ( p2 @ sk1 )
| ( p2 @ sk16 )
| sk11 ),
inference(cnf,[status(esa)],[5]) ).
thf(125,plain,
( ( p2 @ sk1 )
| sk11
| ( ( p2 @ sk16 )
!= ( p2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[6,39]) ).
thf(127,plain,
( ( p2 @ sk1 )
| sk11
| ( sk16 != sk5 ) ),
inference(simp,[status(thm)],[125]) ).
thf(7,plain,
r1 @ sk1 @ sk2,
inference(cnf,[status(esa)],[5]) ).
thf(17,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(91,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(8134,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,91]) ).
thf(8135,plain,
( ( p2 @ sk2 )
| ~ ( p2 @ ( sk36 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8134:[bind(A,$thf( sk2 ))]]) ).
thf(8272,plain,
( sk11
| ( sk16 != sk5 )
| ( p2 @ sk2 )
| ( ( p2 @ ( sk36 @ sk2 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[127,8135]) ).
thf(8283,plain,
( sk11
| ( p2 @ sk2 )
| ( sk16 != sk5 )
| ( ( sk36 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[8272]) ).
thf(18,plain,
r1 @ sk1 @ sk8,
inference(cnf,[status(esa)],[5]) ).
thf(60,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(517,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( r1 @ sk1 @ sk8 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,60]) ).
thf(518,plain,
( ( p3 @ sk8 )
| ( r1 @ sk8 @ ( sk3 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[517:[bind(A,$thf( sk8 ))]]) ).
thf(19,plain,
( ~ sk11
| ( r1 @ sk20 @ sk21 )
| ~ sk19 ),
inference(cnf,[status(esa)],[5]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ B )
| ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ( p2 @ B )
| ~ ( sk31 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ B )
| ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ( p2 @ B )
| ~ ( sk31 @ A ) ),
inference(simp,[status(thm)],[37]) ).
thf(415,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk11
| ~ sk19
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ B )
| ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ( p2 @ B )
| ~ ( sk31 @ A )
| ( ( r1 @ sk20 @ sk21 )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19,77]) ).
thf(444,plain,
! [C: $i,B: $i,A: $i] :
( ( p2 @ C )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ B )
| ~ ( r1 @ B @ C )
| ~ ( p2 @ B )
| ~ ( sk31 @ A )
| ( sk20 != sk18 )
| ( sk21 != A ) ),
inference(simp,[status(thm)],[415]) ).
thf(468,plain,
! [B: $i,A: $i] :
( ( p2 @ B )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( r1 @ ( sk33 @ sk21 ) @ A )
| ~ ( r1 @ A @ B )
| ~ ( p2 @ A )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 ) ),
inference(simp,[status(thm)],[444]) ).
thf(20,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ( p2 @ A )
| ( p2 @ ( sk22 @ A ) )
| ~ sk19 ),
inference(cnf,[status(esa)],[5]) ).
thf(81,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ( p2 @ A )
| ( p2 @ ( sk22 @ A ) )
| ~ sk19 ),
inference(simp,[status(thm)],[20]) ).
thf(2978,plain,
! [A: $i] :
( ~ sk11
| ( p2 @ A )
| ( p2 @ ( sk22 @ A ) )
| ~ sk19
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk1 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[47,81]) ).
thf(2983,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk22 @ A ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[2978]) ).
thf(2998,plain,
( ( p2 @ sk5 )
| ( p2 @ ( sk22 @ sk5 ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[2983]) ).
thf(33337,plain,
( $false
| ( p2 @ ( sk22 @ sk5 ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 ) ),
inference(rewrite,[status(thm)],[2998,39]) ).
thf(33338,plain,
( ( p2 @ ( sk22 @ sk5 ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[33337]) ).
thf(48,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(98,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(11967,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,98]) ).
thf(11968,plain,
( ( p2 @ sk5 )
| ( r1 @ sk5 @ ( sk36 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[11967:[bind(A,$thf( sk5 ))]]) ).
thf(13678,plain,
( $false
| ( r1 @ sk5 @ ( sk36 @ sk5 ) ) ),
inference(rewrite,[status(thm)],[11968,39]) ).
thf(13679,plain,
r1 @ sk5 @ ( sk36 @ sk5 ),
inference(simp,[status(thm)],[13678]) ).
thf(19231,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( ( r1 @ sk5 @ ( sk36 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13679,109]) ).
thf(19352,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( sk5 != sk1 )
| ( ( sk36 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[19231]) ).
thf(19420,plain,
( ( p2 @ ( sk36 @ sk5 ) )
| ~ ( p2 @ ( sk7 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[19352]) ).
thf(8160,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,91]) ).
thf(8161,plain,
( ( p2 @ sk5 )
| ~ ( p2 @ ( sk36 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[8160:[bind(A,$thf( sk5 ))]]) ).
thf(8305,plain,
( $false
| ~ ( p2 @ ( sk36 @ sk5 ) ) ),
inference(rewrite,[status(thm)],[8161,39]) ).
thf(8306,plain,
~ ( p2 @ ( sk36 @ sk5 ) ),
inference(simp,[status(thm)],[8305]) ).
thf(22479,plain,
( $false
| ~ ( p2 @ ( sk7 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(rewrite,[status(thm)],[19420,8306]) ).
thf(22480,plain,
( ~ ( p2 @ ( sk7 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[22479]) ).
thf(33344,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( sk5 != sk1 )
| ( ( p2 @ ( sk22 @ sk5 ) )
!= ( p2 @ ( sk7 @ ( sk36 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[33338,22480]) ).
thf(33526,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( sk5 != sk1 )
| ( ( sk22 @ sk5 )
!= ( sk7 @ ( sk36 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[33344]) ).
thf(11274,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk8 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,97]) ).
thf(11275,plain,
( ( p2 @ sk8 )
| ( p2 @ ( sk6 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[11274:[bind(A,$thf( sk8 ))]]) ).
thf(19585,plain,
( ( p2 @ sk8 )
| ( ( p2 @ ( sk7 @ sk5 ) )
!= ( p2 @ ( sk6 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11275,19567]) ).
thf(19611,plain,
( ( p2 @ sk8 )
| ( ( sk7 @ sk5 )
!= ( sk6 @ sk8 ) ) ),
inference(simp,[status(thm)],[19585]) ).
thf(15,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(110,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(20011,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,110]) ).
thf(20012,plain,
( ( p2 @ sk5 )
| ( r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[20011:[bind(A,$thf( sk5 ))]]) ).
thf(21154,plain,
( $false
| ( r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ) ) ),
inference(rewrite,[status(thm)],[20012,39]) ).
thf(21155,plain,
r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ),
inference(simp,[status(thm)],[21154]) ).
thf(21195,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( ( r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21155,97]) ).
thf(21324,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk7 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[21195]) ).
thf(21381,plain,
( ( p2 @ ( sk7 @ sk5 ) )
| ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) )
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[21324]) ).
thf(27145,plain,
( $false
| ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) )
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[21381,19567]) ).
thf(27146,plain,
( ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) )
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[27145]) ).
thf(10,plain,
( ~ sk11
| ( r1 @ sk18 @ sk20 )
| ~ sk19 ),
inference(cnf,[status(esa)],[5]) ).
thf(25,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(78,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A ) ),
inference(simp,[status(thm)],[25]) ).
thf(135,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,78]) ).
thf(136,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ ( sk33 @ sk20 ) )
| ~ ( sk31 @ sk20 ) ),
inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( sk20 ))]]) ).
thf(27246,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ( ( p2 @ ( sk33 @ sk20 ) )
!= ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27146,136]) ).
thf(27315,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ( ( sk33 @ sk20 )
!= ( sk6 @ ( sk7 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[27246]) ).
thf(119,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk1 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[47,78]) ).
thf(120,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( sk18 != sk1 )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[119]) ).
thf(121,plain,
( ~ sk11
| ~ ( sk24 @ sk5 )
| ~ ( p2 @ ( sk33 @ sk5 ) )
| ~ ( sk31 @ sk5 )
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[120]) ).
thf(33363,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk5 )
| ~ ( sk31 @ sk5 )
| ( ( p2 @ ( sk33 @ sk5 ) )
!= ( p2 @ ( sk22 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33338,121]) ).
thf(33472,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk5 )
| ~ ( sk31 @ sk5 )
| ( ( sk33 @ sk5 )
!= ( sk22 @ sk5 ) ) ),
inference(simp,[status(thm)],[33363]) ).
thf(14,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ( p1 @ ( sk9 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(80,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ( p1 @ ( sk9 @ A ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(2807,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ sk8 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,80]) ).
thf(2808,plain,
( ( p1 @ sk8 )
| ( p1 @ ( sk9 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[2807:[bind(A,$thf( sk8 ))]]) ).
thf(50,plain,
~ ( p1 @ sk8 ),
inference(cnf,[status(esa)],[5]) ).
thf(2897,plain,
( $false
| ( p1 @ ( sk9 @ sk8 ) ) ),
inference(rewrite,[status(thm)],[2808,50]) ).
thf(2898,plain,
p1 @ ( sk9 @ sk8 ),
inference(simp,[status(thm)],[2897]) ).
thf(9,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(86,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(4411,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,86]) ).
thf(4412,plain,
( ( p2 @ sk5 )
| ( r1 @ sk5 @ ( sk6 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[4411:[bind(A,$thf( sk5 ))]]) ).
thf(4718,plain,
( $false
| ( r1 @ sk5 @ ( sk6 @ sk5 ) ) ),
inference(rewrite,[status(thm)],[4412,39]) ).
thf(4719,plain,
r1 @ sk5 @ ( sk6 @ sk5 ),
inference(simp,[status(thm)],[4718]) ).
thf(42,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(75,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(4764,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( r1 @ sk5 @ ( sk6 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4719,75]) ).
thf(4780,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[4764]) ).
thf(4813,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ~ ( p1 @ ( sk10 @ ( sk6 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[4780]) ).
thf(5463,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p1 @ ( sk10 @ ( sk6 @ sk5 ) ) )
!= ( p1 @ ( sk9 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2898,4813]) ).
thf(5469,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk10 @ ( sk6 @ sk5 ) )
!= ( sk9 @ sk8 ) ) ),
inference(simp,[status(thm)],[5463]) ).
thf(514,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,60]) ).
thf(515,plain,
( ( p3 @ sk2 )
| ( r1 @ sk2 @ ( sk3 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[514:[bind(A,$thf( sk2 ))]]) ).
thf(31,plain,
~ ( p3 @ sk2 ),
inference(cnf,[status(esa)],[5]) ).
thf(820,plain,
( $false
| ( r1 @ sk2 @ ( sk3 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[515,31]) ).
thf(821,plain,
r1 @ sk2 @ ( sk3 @ sk2 ),
inference(simp,[status(thm)],[820]) ).
thf(2793,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ sk2 @ ( sk3 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,80]) ).
thf(2827,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( sk2 != sk1 )
| ( ( sk3 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[2793]) ).
thf(2846,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ( p1 @ ( sk9 @ ( sk3 @ sk2 ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[2827]) ).
thf(4001,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p1 @ ( sk9 @ ( sk3 @ sk2 ) ) )
!= ( p1 @ ( sk3 @ sk2 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2846]) ).
thf(4005,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( sk9 @ ( sk3 @ sk2 ) )
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[4001]) ).
thf(16,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(156,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,16]) ).
thf(157,plain,
( ( p3 @ sk2 )
| ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[156:[bind(A,$thf( sk2 ))]]) ).
thf(183,plain,
( $false
| ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[157,31]) ).
thf(184,plain,
r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ),
inference(simp,[status(thm)],[183]) ).
thf(38,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(236,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[184,38]) ).
thf(255,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[236]) ).
thf(267,plain,
( ( p3 @ ( sk4 @ sk2 ) )
| ( p3 @ ( sk3 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[255]) ).
thf(40,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(325,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,40]) ).
thf(326,plain,
( ( p3 @ sk2 )
| ~ ( p3 @ ( sk4 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[325:[bind(A,$thf( sk2 ))]]) ).
thf(546,plain,
( $false
| ~ ( p3 @ ( sk4 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[326,31]) ).
thf(547,plain,
~ ( p3 @ ( sk4 @ sk2 ) ),
inference(simp,[status(thm)],[546]) ).
thf(2340,plain,
( $false
| ( p3 @ ( sk3 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[267,547]) ).
thf(2341,plain,
( ( p3 @ ( sk3 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[2340]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( p2 @ ( sk13 @ B @ A ) )
| sk12
| sk11 ),
inference(cnf,[status(esa)],[5]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( p2 @ ( sk13 @ B @ A ) )
| sk12
| sk11 ),
inference(simp,[status(thm)],[11]) ).
thf(2085,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( r1 @ sk20 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19,75]) ).
thf(2094,plain,
! [A: $i] :
( ( p1 @ A )
| ~ sk11
| ~ sk19
| ~ ( p1 @ ( sk10 @ A ) )
| ( sk20 != sk1 )
| ( sk21 != A ) ),
inference(simp,[status(thm)],[2085]) ).
thf(2109,plain,
( ( p1 @ sk21 )
| ~ sk11
| ~ sk19
| ~ ( p1 @ ( sk10 @ sk21 ) )
| ( sk20 != sk1 ) ),
inference(simp,[status(thm)],[2094]) ).
thf(131,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk1 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[57,78]) ).
thf(132,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( sk18 != sk1 )
| ( A != sk18 ) ),
inference(simp,[status(thm)],[131]) ).
thf(133,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( p2 @ ( sk33 @ sk18 ) )
| ~ ( sk31 @ sk18 )
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[132]) ).
thf(33369,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ( ( p2 @ ( sk33 @ sk18 ) )
!= ( p2 @ ( sk22 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33338,133]) ).
thf(33543,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ( ( sk33 @ sk18 )
!= ( sk22 @ sk5 ) ) ),
inference(simp,[status(thm)],[33369]) ).
thf(332,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ sk20 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19,40]) ).
thf(339,plain,
! [A: $i] :
( ( p3 @ A )
| ~ sk11
| ~ sk19
| ~ ( p3 @ ( sk4 @ A ) )
| ( sk20 != sk1 )
| ( sk21 != A ) ),
inference(simp,[status(thm)],[332]) ).
thf(347,plain,
( ( p3 @ sk21 )
| ~ sk11
| ~ sk19
| ~ ( p3 @ ( sk4 @ sk21 ) )
| ( sk20 != sk1 ) ),
inference(simp,[status(thm)],[339]) ).
thf(11264,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,97]) ).
thf(11265,plain,
( ( p2 @ sk2 )
| ( p2 @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[11264:[bind(A,$thf( sk2 ))]]) ).
thf(11438,plain,
( ( p2 @ sk2 )
| ( ( p2 @ ( sk6 @ sk2 ) )
!= ( p2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[11265,39]) ).
thf(11504,plain,
( ( p2 @ sk2 )
| ( ( sk6 @ sk2 )
!= sk5 ) ),
inference(simp,[status(thm)],[11438]) ).
thf(13706,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( ( r1 @ sk5 @ ( sk36 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13679,97]) ).
thf(13808,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( sk5 != sk1 )
| ( ( sk36 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[13706]) ).
thf(13855,plain,
( ( p2 @ ( sk36 @ sk5 ) )
| ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[13808]) ).
thf(16315,plain,
( $false
| ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(rewrite,[status(thm)],[13855,8306]) ).
thf(16316,plain,
( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[16315]) ).
thf(16338,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ( sk18 != sk1 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk33 @ sk18 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,133]) ).
thf(16427,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ( sk18 != sk1 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk33 @ sk18 ) ) ),
inference(simp,[status(thm)],[16338]) ).
thf(237,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,38]) ).
thf(238,plain,
( ( p3 @ sk5 )
| ( p3 @ ( sk3 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[237:[bind(A,$thf( sk5 ))]]) ).
thf(320,plain,
! [A: $i] :
( ( p3 @ sk5 )
| ~ ( r1 @ sk1 @ A )
| ( p3 @ A )
| ( ( p3 @ ( sk4 @ A ) )
!= ( p3 @ ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[238,40]) ).
thf(333,plain,
! [A: $i] :
( ( p3 @ sk5 )
| ( p3 @ A )
| ~ ( r1 @ sk1 @ A )
| ( ( sk4 @ A )
!= ( sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[320]) ).
thf(248,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ sk1 @ sk8 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,38]) ).
thf(249,plain,
( ( p3 @ sk8 )
| ( p3 @ ( sk3 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( sk8 ))]]) ).
thf(19295,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk8 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,109]) ).
thf(19296,plain,
( ( p2 @ sk8 )
| ~ ( p2 @ ( sk7 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[19295:[bind(A,$thf( sk8 ))]]) ).
thf(19521,plain,
( ( p2 @ sk2 )
| ( p2 @ sk8 )
| ( ( p2 @ ( sk7 @ sk8 ) )
!= ( p2 @ ( sk6 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11265,19296]) ).
thf(19543,plain,
( ( p2 @ sk2 )
| ( p2 @ sk8 )
| ( ( sk7 @ sk8 )
!= ( sk6 @ sk2 ) ) ),
inference(simp,[status(thm)],[19521]) ).
thf(34,plain,
( ( p2 @ sk1 )
| ( r1 @ sk1 @ sk16 )
| sk11 ),
inference(cnf,[status(esa)],[5]) ).
thf(511,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( r1 @ sk1 @ sk16 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,60]) ).
thf(512,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( r1 @ sk16 @ ( sk3 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[511:[bind(A,$thf( sk16 ))]]) ).
thf(14070,plain,
! [B: $i,A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ B )
| ( p2 @ ( sk13 @ B @ A ) )
| sk12
| ( ( r1 @ sk16 @ ( sk3 @ sk16 ) )
!= ( r1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[512,101]) ).
thf(14071,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ~ ( r1 @ sk1 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| ( p2 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
| sk12 ),
inference(pattern_uni,[status(thm)],[14070:[bind(A,$thf( sk16 )),bind(B,$thf( sk3 @ sk16 ))]]) ).
thf(25991,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| ( p2 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
| sk12
| ( ( r1 @ sk1 @ sk16 )
!= ( r1 @ sk1 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[34,14071]) ).
thf(25992,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| ( p2 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
| sk12 ),
inference(pattern_uni,[status(thm)],[25991:[]]) ).
thf(26400,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p2 @ sk2 )
| ( ( p2 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
!= ( p2 @ ( sk36 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[25992,8135]) ).
thf(26461,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p2 @ sk2 )
| ( ( sk13 @ ( sk3 @ sk16 ) @ sk16 )
!= ( sk36 @ sk2 ) ) ),
inference(simp,[status(thm)],[26400]) ).
thf(24,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ( r1 @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ~ ( sk31 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(76,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ( r1 @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ~ ( sk31 @ A ) ),
inference(simp,[status(thm)],[24]) ).
thf(2219,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ B )
| ~ ( p2 @ ( sk33 @ B ) )
| ~ ( sk31 @ B )
| ( ( r1 @ ( sk32 @ A ) @ ( sk33 @ A ) )
!= ( r1 @ sk18 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[76,78]) ).
thf(2293,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ B )
| ~ ( p2 @ ( sk33 @ B ) )
| ~ ( sk31 @ B )
| ( ( sk32 @ A )
!= sk18 )
| ( ( sk33 @ A )
!= B ) ),
inference(simp,[status(thm)],[2219]) ).
thf(2331,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ ( sk33 @ A ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ A ) ) )
| ~ ( sk31 @ ( sk33 @ A ) )
| ( ( sk32 @ A )
!= sk18 ) ),
inference(simp,[status(thm)],[2293]) ).
thf(44,plain,
( ~ sk11
| sk19
| ~ ( p2 @ sk18 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(11559,plain,
( ( p2 @ sk8 )
| ~ sk11
| sk19
| ( ( p2 @ ( sk6 @ sk8 ) )
!= ( p2 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[11275,44]) ).
thf(11620,plain,
( ( p2 @ sk8 )
| sk19
| ~ sk11
| ( ( sk6 @ sk8 )
!= sk18 ) ),
inference(simp,[status(thm)],[11559]) ).
thf(8142,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( r1 @ sk1 @ sk8 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,91]) ).
thf(8143,plain,
( ( p2 @ sk8 )
| ~ ( p2 @ ( sk36 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[8142:[bind(A,$thf( sk8 ))]]) ).
thf(26419,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p2 @ sk8 )
| ( ( p2 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
!= ( p2 @ ( sk36 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[25992,8143]) ).
thf(26451,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p2 @ sk8 )
| ( ( sk13 @ ( sk3 @ sk16 ) @ sk16 )
!= ( sk36 @ sk8 ) ) ),
inference(simp,[status(thm)],[26419]) ).
thf(11241,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( ( r1 @ sk2 @ ( sk3 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,97]) ).
thf(11345,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( sk2 != sk1 )
| ( ( sk3 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[11241]) ).
thf(11394,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( p2 @ ( sk6 @ ( sk3 @ sk2 ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[11345]) ).
thf(246,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,38]) ).
thf(247,plain,
( ( p3 @ sk2 )
| ( p3 @ ( sk3 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[246:[bind(A,$thf( sk2 ))]]) ).
thf(273,plain,
( $false
| ( p3 @ ( sk3 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[247,31]) ).
thf(274,plain,
p3 @ ( sk3 @ sk2 ),
inference(simp,[status(thm)],[273]) ).
thf(551,plain,
( ( p3 @ ( sk4 @ sk2 ) )
!= ( p3 @ ( sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[274,547]) ).
thf(555,plain,
( ( sk4 @ sk2 )
!= ( sk3 @ sk2 ) ),
inference(simp,[status(thm)],[551]) ).
thf(146,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,16]) ).
thf(165,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( sk20 != A ) ),
inference(simp,[status(thm)],[146]) ).
thf(170,plain,
( ( p3 @ sk20 )
| ( r1 @ ( sk3 @ sk20 ) @ ( sk4 @ sk20 ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[165]) ).
thf(2075,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,75]) ).
thf(2076,plain,
( ( p1 @ sk2 )
| ~ ( p1 @ ( sk10 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[2075:[bind(A,$thf( sk2 ))]]) ).
thf(2901,plain,
( ( p1 @ sk2 )
| ( ( p1 @ ( sk10 @ sk2 ) )
!= ( p1 @ ( sk9 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2898,2076]) ).
thf(2908,plain,
( ( p1 @ sk2 )
| ( ( sk10 @ sk2 )
!= ( sk9 @ sk8 ) ) ),
inference(simp,[status(thm)],[2901]) ).
thf(11235,plain,
! [A: $i] :
( ~ sk11
| ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk18 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,97]) ).
thf(11236,plain,
( ~ sk11
| ( p2 @ sk18 )
| ( p2 @ ( sk6 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[11235:[bind(A,$thf( sk18 ))]]) ).
thf(13006,plain,
( ~ sk11
| ( p2 @ sk18 )
| ( ( p2 @ ( sk6 @ sk18 ) )
!= ( p2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[11236,39]) ).
thf(13062,plain,
( ( p2 @ sk18 )
| ~ sk11
| ( ( sk6 @ sk18 )
!= sk5 ) ),
inference(simp,[status(thm)],[13006]) ).
thf(22,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ( sk31 @ A )
| ~ ( p2 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(93,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ( sk31 @ A )
| ~ ( p2 @ A ) ),
inference(simp,[status(thm)],[22]) ).
thf(8851,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ~ ( sk24 @ A )
| ( sk31 @ A )
| ~ ( p2 @ A )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,93]) ).
thf(8852,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( sk31 @ sk20 )
| ~ ( p2 @ sk20 ) ),
inference(pattern_uni,[status(thm)],[8851:[bind(A,$thf( sk20 ))]]) ).
thf(11715,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ( ( p2 @ ( sk33 @ sk20 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,136]) ).
thf(11725,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ( ( sk33 @ sk20 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11715]) ).
thf(23823,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ( ( sk33 @ sk20 )
!= ( sk6 @ sk5 ) )
| ( ( sk31 @ sk20 )
!= ( sk31 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[8852,11725]) ).
thf(23824,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ( ( sk33 @ sk20 )
!= ( sk6 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[23823:[]]) ).
thf(25255,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( ( sk33 @ sk20 )
!= ( sk6 @ sk5 ) )
| ( ( p2 @ ( sk6 @ sk5 ) )
!= ( p2 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[11657,23824]) ).
thf(25272,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( ( sk33 @ sk20 )
!= ( sk6 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk20 ) ),
inference(simp,[status(thm)],[25255]) ).
thf(33428,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk20 )
| ( ( sk33 @ sk20 )
!= ( sk6 @ sk5 ) )
| ( ( p2 @ ( sk22 @ sk5 ) )
!= ( p2 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[33338,23824]) ).
thf(33500,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk20 )
| ( ( sk33 @ sk20 )
!= ( sk6 @ sk5 ) )
| ( ( sk22 @ sk5 )
!= sk20 ) ),
inference(simp,[status(thm)],[33428]) ).
thf(32,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ( r1 @ A @ ( sk32 @ A ) )
| ~ ( sk31 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(92,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ( r1 @ A @ ( sk32 @ A ) )
| ~ ( sk31 @ A ) ),
inference(simp,[status(thm)],[32]) ).
thf(8482,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ B )
| ~ ( p2 @ ( sk33 @ B ) )
| ~ ( sk31 @ B )
| ( ( r1 @ A @ ( sk32 @ A ) )
!= ( r1 @ sk18 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[92,78]) ).
thf(8483,plain,
( ~ sk11
| ~ ( r1 @ sk18 @ sk18 )
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( sk24 @ ( sk32 @ sk18 ) )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ~ ( sk31 @ ( sk32 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[8482:[bind(A,$thf( sk18 )),bind(B,$thf( sk32 @ sk18 ))]]) ).
thf(8706,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( sk24 @ ( sk32 @ sk18 ) )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ~ ( sk31 @ ( sk32 @ sk18 ) )
| ( ( r1 @ sk18 @ sk18 )
!= ( r1 @ sk1 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[57,8483]) ).
thf(8775,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( sk24 @ ( sk32 @ sk18 ) )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ~ ( sk31 @ ( sk32 @ sk18 ) )
| ( sk18 != sk1 )
| ( sk18 != sk18 ) ),
inference(simp,[status(thm)],[8706]) ).
thf(8805,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( sk24 @ ( sk32 @ sk18 ) )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ~ ( sk31 @ ( sk32 @ sk18 ) )
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[8775]) ).
thf(8824,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( sk24 @ ( sk32 @ sk18 ) )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ( sk18 != sk1 )
| ( ( sk31 @ ( sk32 @ sk18 ) )
!= ( sk31 @ sk18 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8805]) ).
thf(8828,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( sk24 @ ( sk32 @ sk18 ) )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ( sk18 != sk1 )
| ( ( sk32 @ sk18 )
!= sk18 ) ),
inference(simp,[status(thm)],[8824]) ).
thf(9061,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ( sk18 != sk1 )
| ( ( sk32 @ sk18 )
!= sk18 )
| ( ( sk24 @ ( sk32 @ sk18 ) )
!= ( sk24 @ sk18 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8828]) ).
thf(9064,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ( sk18 != sk1 )
| ( ( sk32 @ sk18 )
!= sk18 )
| ( ( sk32 @ sk18 )
!= sk18 ) ),
inference(simp,[status(thm)],[9061]) ).
thf(9066,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ( sk18 != sk1 )
| ( ( sk32 @ sk18 )
!= sk18 ) ),
inference(simp,[status(thm)],[9064]) ).
thf(11719,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ( sk18 != sk1 )
| ( ( sk32 @ sk18 )
!= sk18 )
| ( ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,9066]) ).
thf(11724,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ( sk18 != sk1 )
| ( ( sk32 @ sk18 )
!= sk18 )
| ( ( sk33 @ ( sk32 @ sk18 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11719]) ).
thf(13725,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( r1 @ sk5 @ ( sk36 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13679,91]) ).
thf(13791,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( sk5 != sk1 )
| ( ( sk36 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[13725]) ).
thf(13840,plain,
( ( p2 @ ( sk36 @ sk5 ) )
| ~ ( p2 @ ( sk36 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[13791]) ).
thf(16273,plain,
( $false
| ~ ( p2 @ ( sk36 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(rewrite,[status(thm)],[13840,8306]) ).
thf(16274,plain,
( ~ ( p2 @ ( sk36 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[16273]) ).
thf(16342,plain,
( ( sk5 != sk1 )
| ( ( p2 @ ( sk36 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,16274]) ).
thf(16402,plain,
( ( sk5 != sk1 )
| ( ( sk36 @ ( sk36 @ sk5 ) )
!= ( sk6 @ ( sk36 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[16342]) ).
thf(113,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[7,78]) ).
thf(114,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( sk18 != sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[113]) ).
thf(115,plain,
( ~ sk11
| ~ ( sk24 @ sk2 )
| ~ ( p2 @ ( sk33 @ sk2 ) )
| ~ ( sk31 @ sk2 )
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[114]) ).
thf(45,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(89,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(6720,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( ( r1 @ sk1 @ sk8 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,89]) ).
thf(6721,plain,
( ( p1 @ sk8 )
| ( r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[6720:[bind(A,$thf( sk8 ))]]) ).
thf(7045,plain,
( $false
| ( r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ) ) ),
inference(rewrite,[status(thm)],[6721,50]) ).
thf(7046,plain,
r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ),
inference(simp,[status(thm)],[7045]) ).
thf(7084,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7046,80]) ).
thf(7118,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[7084]) ).
thf(7154,plain,
( ( p1 @ ( sk10 @ sk8 ) )
| ( p1 @ ( sk9 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[7118]) ).
thf(2078,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( r1 @ sk1 @ sk8 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,75]) ).
thf(2079,plain,
( ( p1 @ sk8 )
| ~ ( p1 @ ( sk10 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[2078:[bind(A,$thf( sk8 ))]]) ).
thf(2117,plain,
( $false
| ~ ( p1 @ ( sk10 @ sk8 ) ) ),
inference(rewrite,[status(thm)],[2079,50]) ).
thf(2118,plain,
~ ( p1 @ ( sk10 @ sk8 ) ),
inference(simp,[status(thm)],[2117]) ).
thf(18492,plain,
( $false
| ( p1 @ ( sk9 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[7154,2118]) ).
thf(18493,plain,
( ( p1 @ ( sk9 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[18492]) ).
thf(18498,plain,
( ( ( sk9 @ sk8 )
!= sk1 )
| ( p1 @ sk2 )
| ( ( p1 @ ( sk9 @ ( sk10 @ sk8 ) ) )
!= ( p1 @ ( sk10 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[18493,2076]) ).
thf(18514,plain,
( ( p1 @ sk2 )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk9 @ ( sk10 @ sk8 ) )
!= ( sk10 @ sk2 ) ) ),
inference(simp,[status(thm)],[18498]) ).
thf(19279,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,109]) ).
thf(19280,plain,
( ( p2 @ sk2 )
| ~ ( p2 @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[19279:[bind(A,$thf( sk2 ))]]) ).
thf(19471,plain,
( ( p2 @ sk2 )
| ( ( p2 @ ( sk7 @ sk2 ) )
!= ( p2 @ ( sk6 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11265,19280]) ).
thf(19508,plain,
( ( p2 @ sk2 )
| ( ( sk7 @ sk2 )
!= ( sk6 @ sk2 ) ) ),
inference(simp,[status(thm)],[19471]) ).
thf(275,plain,
( ( p3 @ ( sk3 @ sk2 ) )
!= ( p3 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[274,31]) ).
thf(276,plain,
( ( sk3 @ sk2 )
!= sk2 ),
inference(simp,[status(thm)],[275]) ).
thf(243,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ sk1 @ sk16 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,38]) ).
thf(244,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p3 @ ( sk3 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( sk16 ))]]) ).
thf(27,plain,
( ~ sk12
| ~ ( p2 @ sk15 )
| sk11 ),
inference(cnf,[status(esa)],[5]) ).
thf(300,plain,
( sk11
| ( p3 @ sk16 )
| ( p3 @ ( sk3 @ sk16 ) )
| ~ sk12
| ( ( p2 @ sk15 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[244,27]) ).
thf(308,plain,
( sk11
| ( p3 @ sk16 )
| ( p3 @ ( sk3 @ sk16 ) )
| ~ sk12
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[300]) ).
thf(6669,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( ( r1 @ sk2 @ ( sk3 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,89]) ).
thf(6771,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( sk2 != sk1 )
| ( ( sk3 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[6669]) ).
thf(6900,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ( r1 @ ( sk9 @ ( sk3 @ sk2 ) ) @ ( sk10 @ ( sk3 @ sk2 ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[6771]) ).
thf(2786,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[184,80]) ).
thf(2830,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[2786]) ).
thf(2849,plain,
( ( p1 @ ( sk4 @ sk2 ) )
| ( p1 @ ( sk9 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[2830]) ).
thf(9452,plain,
( ( p1 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p1 @ ( sk10 @ sk8 ) )
!= ( p1 @ ( sk9 @ ( sk4 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2849,2118]) ).
thf(9469,plain,
( ( p1 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk10 @ sk8 )
!= ( sk9 @ ( sk4 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[9452]) ).
thf(2949,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p2 @ A )
| ( p2 @ ( sk22 @ A ) )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,81]) ).
thf(2950,plain,
( ~ sk11
| ~ sk19
| ( p2 @ sk20 )
| ( p2 @ ( sk22 @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[2949:[bind(A,$thf( sk20 ))]]) ).
thf(3736,plain,
( ~ sk11
| ~ sk19
| ( p2 @ sk20 )
| ( ( p2 @ ( sk22 @ sk20 ) )
!= ( p2 @ sk20 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2950]) ).
thf(3745,plain,
( ( p2 @ sk20 )
| ~ sk11
| ~ sk19
| ( ( sk22 @ sk20 )
!= sk20 ) ),
inference(simp,[status(thm)],[3736]) ).
thf(2657,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ ( sk33 @ A ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ A ) ) )
| ~ ( sk31 @ ( sk33 @ A ) )
| ( ( sk32 @ A )
!= sk18 )
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[18,2331]) ).
thf(2671,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ ( sk33 @ A ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ A ) ) )
| ~ ( sk31 @ ( sk33 @ A ) )
| ( ( sk32 @ A )
!= sk18 )
| ( sk18 != sk1 )
| ( A != sk8 ) ),
inference(simp,[status(thm)],[2657]) ).
thf(2686,plain,
( ~ sk11
| ~ ( sk24 @ sk8 )
| ~ ( sk31 @ sk8 )
| ~ ( sk24 @ ( sk33 @ sk8 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk8 ) ) )
| ~ ( sk31 @ ( sk33 @ sk8 ) )
| ( ( sk32 @ sk8 )
!= sk18 )
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[2671]) ).
thf(137,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ sk20 @ sk21 )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19,78]) ).
thf(138,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( sk20 != sk18 )
| ( sk21 != A ) ),
inference(simp,[status(thm)],[137]) ).
thf(139,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ ( sk33 @ sk21 ) )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 ) ),
inference(simp,[status(thm)],[138]) ).
thf(16379,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk33 @ sk21 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,139]) ).
thf(16413,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk33 @ sk21 ) ) ),
inference(simp,[status(thm)],[16379]) ).
thf(11797,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[184,98]) ).
thf(12003,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[11797]) ).
thf(12097,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( r1 @ ( sk4 @ sk2 ) @ ( sk36 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[12003]) ).
thf(27151,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( sk5 != sk1 )
| ( ( p2 @ ( sk7 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27146,22480]) ).
thf(27259,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( sk5 != sk1 )
| ( ( sk7 @ ( sk36 @ sk5 ) )
!= ( sk6 @ ( sk7 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[27151]) ).
thf(8287,plain,
( ( p2 @ sk1 )
| sk11
| ( p2 @ sk8 )
| ( ( p2 @ ( sk36 @ sk8 ) )
!= ( p2 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[6,8143]) ).
thf(8298,plain,
( ( p2 @ sk1 )
| sk11
| ( p2 @ sk8 )
| ( ( sk36 @ sk8 )
!= sk16 ) ),
inference(simp,[status(thm)],[8287]) ).
thf(23884,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ~ ( p2 @ ( sk33 @ sk20 ) )
| ( ( sk31 @ sk20 )
!= ( sk31 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[8852,136]) ).
thf(23885,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ~ ( p2 @ ( sk33 @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[23884:[]]) ).
thf(3315,plain,
( ~ sk11
| ~ ( sk24 @ sk8 )
| ~ ( sk31 @ sk8 )
| ~ ( sk24 @ ( sk33 @ sk8 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk8 ) ) )
| ( ( sk32 @ sk8 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk31 @ ( sk33 @ sk8 ) )
!= ( sk31 @ sk8 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2686]) ).
thf(3317,plain,
( ~ sk11
| ~ ( sk24 @ sk8 )
| ~ ( sk31 @ sk8 )
| ~ ( sk24 @ ( sk33 @ sk8 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk8 ) ) )
| ( ( sk32 @ sk8 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk8 )
!= sk8 ) ),
inference(simp,[status(thm)],[3315]) ).
thf(4289,plain,
( ~ sk11
| ~ ( sk24 @ sk8 )
| ~ ( sk31 @ sk8 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk8 ) ) )
| ( ( sk32 @ sk8 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk8 )
!= sk8 )
| ( ( sk24 @ ( sk33 @ sk8 ) )
!= ( sk24 @ sk8 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3317]) ).
thf(4293,plain,
( ~ sk11
| ~ ( sk24 @ sk8 )
| ~ ( sk31 @ sk8 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk8 ) ) )
| ( ( sk32 @ sk8 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk8 )
!= sk8 )
| ( ( sk33 @ sk8 )
!= sk8 ) ),
inference(simp,[status(thm)],[4289]) ).
thf(4294,plain,
( ~ sk11
| ~ ( sk24 @ sk8 )
| ~ ( sk31 @ sk8 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk8 ) ) )
| ( ( sk32 @ sk8 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk8 )
!= sk8 ) ),
inference(simp,[status(thm)],[4293]) ).
thf(6750,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( ( r1 @ sk5 @ ( sk6 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4719,89]) ).
thf(6824,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[6750]) ).
thf(6877,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ( r1 @ ( sk9 @ ( sk6 @ sk5 ) ) @ ( sk10 @ ( sk6 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[6824]) ).
thf(11232,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[184,97]) ).
thf(11316,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[11232]) ).
thf(11365,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( p2 @ ( sk6 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[11316]) ).
thf(24743,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p2 @ ( sk6 @ ( sk4 @ sk2 ) ) )
!= ( p2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[11365,39]) ).
thf(24819,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk6 @ ( sk4 @ sk2 ) )
!= sk5 ) ),
inference(simp,[status(thm)],[24743]) ).
thf(5883,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ sk8 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,88]) ).
thf(5884,plain,
( ( p1 @ sk8 )
| ( r1 @ sk8 @ ( sk9 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[5883:[bind(A,$thf( sk8 ))]]) ).
thf(6157,plain,
( $false
| ( r1 @ sk8 @ ( sk9 @ sk8 ) ) ),
inference(rewrite,[status(thm)],[5884,50]) ).
thf(6158,plain,
r1 @ sk8 @ ( sk9 @ sk8 ),
inference(simp,[status(thm)],[6157]) ).
thf(6196,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ sk8 @ ( sk9 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6158,16]) ).
thf(6247,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( sk8 != sk1 )
| ( ( sk9 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[6196]) ).
thf(6278,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ( r1 @ ( sk3 @ ( sk9 @ sk8 ) ) @ ( sk4 @ ( sk9 @ sk8 ) ) )
| ( sk8 != sk1 ) ),
inference(simp,[status(thm)],[6247]) ).
thf(29,plain,
( ~ sk12
| ( r1 @ sk1 @ sk15 )
| sk11 ),
inference(cnf,[status(esa)],[5]) ).
thf(5813,plain,
! [A: $i] :
( ~ sk12
| sk11
| ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ sk15 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,88]) ).
thf(5814,plain,
( ~ sk12
| sk11
| ( p1 @ sk15 )
| ( r1 @ sk15 @ ( sk9 @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[5813:[bind(A,$thf( sk15 ))]]) ).
thf(16334,plain,
( ( sk5 != sk1 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk36 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,8306]) ).
thf(16424,plain,
( ( sk5 != sk1 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk36 @ sk5 ) ) ),
inference(simp,[status(thm)],[16334]) ).
thf(5860,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ sk16 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,88]) ).
thf(5861,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( r1 @ sk16 @ ( sk9 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[5860:[bind(A,$thf( sk16 ))]]) ).
thf(14047,plain,
! [B: $i,A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ B )
| ( p2 @ ( sk13 @ B @ A ) )
| sk12
| ( ( r1 @ sk16 @ ( sk9 @ sk16 ) )
!= ( r1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5861,101]) ).
thf(14048,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ~ ( r1 @ sk1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| ( p2 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
| sk12 ),
inference(pattern_uni,[status(thm)],[14047:[bind(A,$thf( sk16 )),bind(B,$thf( sk9 @ sk16 ))]]) ).
thf(23386,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| ( p2 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
| sk12
| ( ( r1 @ sk1 @ sk16 )
!= ( r1 @ sk1 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[34,14048]) ).
thf(23387,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| ( p2 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
| sk12 ),
inference(pattern_uni,[status(thm)],[23386:[]]) ).
thf(23677,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p2 @ sk2 )
| ( ( p2 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
!= ( p2 @ ( sk36 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[23387,8135]) ).
thf(23745,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p2 @ sk2 )
| ( ( sk13 @ ( sk9 @ sk16 ) @ sk16 )
!= ( sk36 @ sk2 ) ) ),
inference(simp,[status(thm)],[23677]) ).
thf(19526,plain,
( ( sk5 != sk1 )
| ( p2 @ sk8 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk7 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,19296]) ).
thf(19565,plain,
( ( p2 @ sk8 )
| ( sk5 != sk1 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk7 @ sk8 ) ) ),
inference(simp,[status(thm)],[19526]) ).
thf(11432,plain,
( ( p2 @ sk2 )
| ~ sk12
| sk11
| ( ( p2 @ ( sk6 @ sk2 ) )
!= ( p2 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[11265,27]) ).
thf(11468,plain,
( ( p2 @ sk2 )
| sk11
| ~ sk12
| ( ( sk6 @ sk2 )
!= sk15 ) ),
inference(simp,[status(thm)],[11432]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ B @ ( sk13 @ B @ A ) )
| sk12
| sk11 ),
inference(cnf,[status(esa)],[5]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ B @ ( sk13 @ B @ A ) )
| sk12
| sk11 ),
inference(simp,[status(thm)],[35]) ).
thf(1366,plain,
! [B: $i,A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ B )
| ( r1 @ B @ ( sk13 @ B @ A ) )
| sk12
| ( ( r1 @ sk16 @ ( sk3 @ sk16 ) )
!= ( r1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[512,73]) ).
thf(1367,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ~ ( r1 @ sk1 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| ( r1 @ ( sk3 @ sk16 ) @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
| sk12 ),
inference(pattern_uni,[status(thm)],[1366:[bind(A,$thf( sk16 )),bind(B,$thf( sk3 @ sk16 ))]]) ).
thf(1606,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| ( r1 @ ( sk3 @ sk16 ) @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
| sk12
| ( ( r1 @ sk1 @ sk16 )
!= ( r1 @ sk1 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[34,1367]) ).
thf(1607,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| ( r1 @ ( sk3 @ sk16 ) @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
| sk12 ),
inference(pattern_uni,[status(thm)],[1606:[]]) ).
thf(2006,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( r1 @ ( sk3 @ sk16 ) @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1607,60]) ).
thf(2029,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( sk3 @ sk16 )
!= sk1 )
| ( ( sk13 @ ( sk3 @ sk16 ) @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[2006]) ).
thf(2035,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p3 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
| ( r1 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) @ ( sk3 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) ) )
| ( ( sk3 @ sk16 )
!= sk1 ) ),
inference(simp,[status(thm)],[2029]) ).
thf(21167,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ) )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21155,78]) ).
thf(21331,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( sk6 @ sk5 )
!= sk18 )
| ( ( sk7 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[21167]) ).
thf(21387,plain,
( ~ sk11
| ~ ( sk24 @ ( sk7 @ sk5 ) )
| ~ ( p2 @ ( sk33 @ ( sk7 @ sk5 ) ) )
| ~ ( sk31 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk18 ) ),
inference(simp,[status(thm)],[21331]) ).
thf(21419,plain,
( ~ sk11
| ~ ( sk24 @ ( sk7 @ sk5 ) )
| ~ ( sk31 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk18 )
| ( ( p2 @ ( sk33 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,21387]) ).
thf(21435,plain,
( ~ sk11
| ~ ( sk24 @ ( sk7 @ sk5 ) )
| ~ ( sk31 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk18 )
| ( ( sk33 @ ( sk7 @ sk5 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[21419]) ).
thf(239,plain,
! [A: $i] :
( ~ sk11
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ sk1 @ sk18 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,38]) ).
thf(240,plain,
( ~ sk11
| ( p3 @ sk18 )
| ( p3 @ ( sk3 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[239:[bind(A,$thf( sk18 ))]]) ).
thf(316,plain,
! [A: $i] :
( ~ sk11
| ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk18 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,40]) ).
thf(317,plain,
( ~ sk11
| ( p3 @ sk18 )
| ~ ( p3 @ ( sk4 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[316:[bind(A,$thf( sk18 ))]]) ).
thf(1059,plain,
( ~ sk11
| ( p3 @ sk18 )
| ( ( p3 @ ( sk4 @ sk18 ) )
!= ( p3 @ ( sk3 @ sk18 ) ) ) ),
inference(paramod_ordered,[status(thm)],[240,317]) ).
thf(1063,plain,
( ( p3 @ sk18 )
| ~ sk11
| ( ( sk4 @ sk18 )
!= ( sk3 @ sk18 ) ) ),
inference(simp,[status(thm)],[1059]) ).
thf(321,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk16 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,40]) ).
thf(322,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ~ ( p3 @ ( sk4 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[321:[bind(A,$thf( sk16 ))]]) ).
thf(5675,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( ( p3 @ ( sk4 @ sk16 ) )
!= ( p3 @ ( sk3 @ sk16 ) ) ) ),
inference(paramod_ordered,[status(thm)],[244,322]) ).
thf(5708,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( ( sk4 @ sk16 )
!= ( sk3 @ sk16 ) ) ),
inference(simp,[status(thm)],[5675]) ).
thf(149,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,16]) ).
thf(150,plain,
( ( p3 @ sk5 )
| ( r1 @ ( sk3 @ sk5 ) @ ( sk4 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( sk5 ))]]) ).
thf(403,plain,
! [C: $i,B: $i,A: $i] :
( ( p3 @ sk5 )
| ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ B )
| ( p2 @ C )
| ~ ( p2 @ B )
| ~ ( sk31 @ A )
| ( ( r1 @ ( sk3 @ sk5 ) @ ( sk4 @ sk5 ) )
!= ( r1 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[150,77]) ).
thf(404,plain,
! [A: $i] :
( ( p3 @ sk5 )
| ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ ( sk3 @ sk5 ) )
| ( p2 @ ( sk4 @ sk5 ) )
| ~ ( p2 @ ( sk3 @ sk5 ) )
| ~ ( sk31 @ A ) ),
inference(pattern_uni,[status(thm)],[403:[bind(A,$thf( A )),bind(B,$thf( sk3 @ sk5 )),bind(C,$thf( sk4 @ sk5 ))]]) ).
thf(11299,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( ( r1 @ sk8 @ ( sk9 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6158,97]) ).
thf(11315,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( sk8 != sk1 )
| ( ( sk9 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[11299]) ).
thf(11364,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( p2 @ ( sk6 @ ( sk9 @ sk8 ) ) )
| ( sk8 != sk1 ) ),
inference(simp,[status(thm)],[11315]) ).
thf(15671,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p2 @ ( sk6 @ ( sk9 @ sk8 ) ) )
!= ( p2 @ ( sk9 @ sk8 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11364]) ).
thf(15683,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p2 @ ( sk6 @ ( sk9 @ sk8 ) ) )
!= ( p2 @ ( sk9 @ sk8 ) ) ) ),
inference(simp,[status(thm)],[15671]) ).
thf(11592,plain,
( ( p2 @ sk8 )
| ( ( p2 @ ( sk6 @ sk8 ) )
!= ( p2 @ sk8 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11275]) ).
thf(11613,plain,
( ( p2 @ sk8 )
| ( ( sk6 @ sk8 )
!= sk8 ) ),
inference(simp,[status(thm)],[11592]) ).
thf(8098,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,91]) ).
thf(8216,plain,
! [A: $i] :
( ( p2 @ A )
| ~ sk11
| ~ sk19
| ~ ( p2 @ ( sk36 @ A ) )
| ( sk18 != sk1 )
| ( sk20 != A ) ),
inference(simp,[status(thm)],[8098]) ).
thf(8239,plain,
( ( p2 @ sk20 )
| ~ sk11
| ~ sk19
| ~ ( p2 @ ( sk36 @ sk20 ) )
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[8216]) ).
thf(2804,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,80]) ).
thf(2805,plain,
( ( p1 @ sk2 )
| ( p1 @ ( sk9 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[2804:[bind(A,$thf( sk2 ))]]) ).
thf(2876,plain,
( ( p1 @ sk2 )
| ( ( p1 @ ( sk10 @ sk8 ) )
!= ( p1 @ ( sk9 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2805,2118]) ).
thf(2886,plain,
( ( p1 @ sk2 )
| ( ( sk10 @ sk8 )
!= ( sk9 @ sk2 ) ) ),
inference(simp,[status(thm)],[2876]) ).
thf(13724,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( ( r1 @ sk5 @ ( sk36 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13679,98]) ).
thf(13805,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( sk5 != sk1 )
| ( ( sk36 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[13724]) ).
thf(13853,plain,
( ( p2 @ ( sk36 @ sk5 ) )
| ( r1 @ ( sk36 @ sk5 ) @ ( sk36 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[13805]) ).
thf(31906,plain,
( $false
| ( r1 @ ( sk36 @ sk5 ) @ ( sk36 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(rewrite,[status(thm)],[13853,8306]) ).
thf(31907,plain,
( ( r1 @ ( sk36 @ sk5 ) @ ( sk36 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[31906]) ).
thf(27208,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( p2 @ sk2 )
| ( ( p2 @ ( sk36 @ sk2 ) )
!= ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27146,8135]) ).
thf(27298,plain,
( ( p2 @ sk2 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk36 @ sk2 )
!= ( sk6 @ ( sk7 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[27208]) ).
thf(7052,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ) )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7046,78]) ).
thf(7132,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( sk9 @ sk8 )
!= sk18 )
| ( ( sk10 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[7052]) ).
thf(7168,plain,
( ~ sk11
| ~ ( sk24 @ ( sk10 @ sk8 ) )
| ~ ( p2 @ ( sk33 @ ( sk10 @ sk8 ) ) )
| ~ ( sk31 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk18 ) ),
inference(simp,[status(thm)],[7132]) ).
thf(24927,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ( ( p2 @ ( sk33 @ sk20 ) )
!= ( p2 @ sk20 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[23885]) ).
thf(24953,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ( ( p2 @ ( sk33 @ sk20 ) )
!= ( p2 @ sk20 ) ) ),
inference(simp,[status(thm)],[24927]) ).
thf(33391,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ( ( p2 @ ( sk33 @ sk20 ) )
!= ( p2 @ ( sk22 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33338,24953]) ).
thf(33511,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ( ( sk33 @ sk20 )
!= ( sk22 @ sk5 ) ) ),
inference(simp,[status(thm)],[33391]) ).
thf(13701,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ sk5 @ ( sk36 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13679,38]) ).
thf(13815,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( sk5 != sk1 )
| ( ( sk36 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[13701]) ).
thf(13862,plain,
( ( p3 @ ( sk36 @ sk5 ) )
| ( p3 @ ( sk3 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[13815]) ).
thf(13751,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ sk5 @ ( sk36 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13679,40]) ).
thf(13786,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( sk5 != sk1 )
| ( ( sk36 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[13751]) ).
thf(13835,plain,
( ( p3 @ ( sk36 @ sk5 ) )
| ~ ( p3 @ ( sk4 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[13786]) ).
thf(17419,plain,
( ( p3 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p3 @ ( sk4 @ ( sk36 @ sk5 ) ) )
!= ( p3 @ ( sk3 @ ( sk36 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13862,13835]) ).
thf(17446,plain,
( ( p3 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk4 @ ( sk36 @ sk5 ) )
!= ( sk3 @ ( sk36 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[17419]) ).
thf(9459,plain,
( ( p1 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p1 @ ( sk9 @ ( sk4 @ sk2 ) ) )
!= ( p1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[2849,50]) ).
thf(9476,plain,
( ( p1 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk9 @ ( sk4 @ sk2 ) )
!= sk8 ) ),
inference(simp,[status(thm)],[9459]) ).
thf(4737,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ sk5 @ ( sk6 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4719,38]) ).
thf(4797,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[4737]) ).
thf(4831,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ( p3 @ ( sk3 @ ( sk6 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[4797]) ).
thf(5505,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p3 @ ( sk3 @ ( sk6 @ sk5 ) ) )
!= ( p3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[4831,31]) ).
thf(5518,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk3 @ ( sk6 @ sk5 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[5505]) ).
thf(4370,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,86]) ).
thf(4371,plain,
( ( p2 @ sk2 )
| ( r1 @ sk2 @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[4370:[bind(A,$thf( sk2 ))]]) ).
thf(2791,plain,
! [A: $i] :
( ~ sk12
| sk11
| ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ sk15 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,80]) ).
thf(2792,plain,
( ~ sk12
| sk11
| ( p1 @ sk15 )
| ( p1 @ ( sk9 @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[2791:[bind(A,$thf( sk15 ))]]) ).
thf(3676,plain,
( ~ sk12
| sk11
| ( p1 @ sk15 )
| ( ( p1 @ ( sk10 @ sk8 ) )
!= ( p1 @ ( sk9 @ sk15 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2792,2118]) ).
thf(3688,plain,
( sk11
| ( p1 @ sk15 )
| ~ sk12
| ( ( sk10 @ sk8 )
!= ( sk9 @ sk15 ) ) ),
inference(simp,[status(thm)],[3676]) ).
thf(2781,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,80]) ).
thf(2782,plain,
( ( p1 @ sk5 )
| ( p1 @ ( sk9 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[2781:[bind(A,$thf( sk5 ))]]) ).
thf(2859,plain,
( ( p1 @ sk5 )
| ( ( p1 @ ( sk9 @ sk5 ) )
!= ( p1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[2782,50]) ).
thf(2869,plain,
( ( p1 @ sk5 )
| ( ( sk9 @ sk5 )
!= sk8 ) ),
inference(simp,[status(thm)],[2859]) ).
thf(21227,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21155,80]) ).
thf(21322,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk7 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[21227]) ).
thf(21379,plain,
( ( p1 @ ( sk7 @ sk5 ) )
| ( p1 @ ( sk9 @ ( sk7 @ sk5 ) ) )
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[21322]) ).
thf(26797,plain,
( ( p1 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p1 @ ( sk9 @ ( sk7 @ sk5 ) ) )
!= ( p1 @ ( sk7 @ sk5 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21379]) ).
thf(26802,plain,
( ( p1 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk9 @ ( sk7 @ sk5 ) )
!= ( sk7 @ sk5 ) ) ),
inference(simp,[status(thm)],[26797]) ).
thf(6177,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ sk8 @ ( sk9 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6158,38]) ).
thf(6229,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( sk8 != sk1 )
| ( ( sk9 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[6177]) ).
thf(6259,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ( p3 @ ( sk3 @ ( sk9 @ sk8 ) ) )
| ( sk8 != sk1 ) ),
inference(simp,[status(thm)],[6229]) ).
thf(7983,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p3 @ ( sk3 @ ( sk9 @ sk8 ) ) )
!= ( p3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[6259,31]) ).
thf(7993,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( sk3 @ ( sk9 @ sk8 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[7983]) ).
thf(2064,plain,
! [A: $i] :
( ~ sk12
| sk11
| ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( r1 @ sk1 @ sk15 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,75]) ).
thf(2065,plain,
( ~ sk12
| sk11
| ( p1 @ sk15 )
| ~ ( p1 @ ( sk10 @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[2064:[bind(A,$thf( sk15 ))]]) ).
thf(2902,plain,
( ~ sk12
| sk11
| ( p1 @ sk15 )
| ( ( p1 @ ( sk10 @ sk15 ) )
!= ( p1 @ ( sk9 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2898,2065]) ).
thf(2916,plain,
( sk11
| ( p1 @ sk15 )
| ~ sk12
| ( ( sk10 @ sk15 )
!= ( sk9 @ sk8 ) ) ),
inference(simp,[status(thm)],[2902]) ).
thf(19328,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( ( r1 @ sk8 @ ( sk9 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6158,109]) ).
thf(19382,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( sk8 != sk1 )
| ( ( sk9 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[19328]) ).
thf(19443,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ~ ( p2 @ ( sk7 @ ( sk9 @ sk8 ) ) )
| ( sk8 != sk1 ) ),
inference(simp,[status(thm)],[19382]) ).
thf(3679,plain,
( ~ sk12
| sk11
| ( p1 @ sk15 )
| ( ( p1 @ ( sk10 @ sk15 ) )
!= ( p1 @ ( sk9 @ sk15 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2792,2065]) ).
thf(3689,plain,
( sk11
| ( p1 @ sk15 )
| ~ sk12
| ( ( sk10 @ sk15 )
!= ( sk9 @ sk15 ) ) ),
inference(simp,[status(thm)],[3679]) ).
thf(11912,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( ( r1 @ sk1 @ sk8 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,98]) ).
thf(11913,plain,
( ( p2 @ sk8 )
| ( r1 @ sk8 @ ( sk36 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[11912:[bind(A,$thf( sk8 ))]]) ).
thf(503,plain,
! [A: $i] :
( ~ sk11
| ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( r1 @ sk1 @ sk18 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,60]) ).
thf(504,plain,
( ~ sk11
| ( p3 @ sk18 )
| ( r1 @ sk18 @ ( sk3 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[503:[bind(A,$thf( sk18 ))]]) ).
thf(27195,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ( ( p2 @ ( sk33 @ sk20 ) )
!= ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27146,24953]) ).
thf(27263,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ( ( sk33 @ sk20 )
!= ( sk6 @ ( sk7 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[27195]) ).
thf(24760,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p2 @ ( sk7 @ sk5 ) )
!= ( p2 @ ( sk6 @ ( sk4 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11365,19567]) ).
thf(24842,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk7 @ sk5 )
!= ( sk6 @ ( sk4 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[24760]) ).
thf(3744,plain,
( ( p2 @ sk20 )
| ~ sk11
| ~ sk19
| ( ( p2 @ ( sk22 @ sk20 ) )
!= ( p2 @ sk20 ) ) ),
inference(simp,[status(thm)],[3736]) ).
thf(5683,plain,
( sk11
| ( p3 @ sk16 )
| ~ ( p3 @ ( sk4 @ sk16 ) )
| ( ( p2 @ sk5 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[322,39]) ).
thf(5706,plain,
( sk11
| ( p3 @ sk16 )
| ~ ( p3 @ ( sk4 @ sk16 ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[5683]) ).
thf(27172,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27146,8306]) ).
thf(27308,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk36 @ sk5 )
!= ( sk6 @ ( sk7 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[27172]) ).
thf(11697,plain,
( ( p2 @ ( sk6 @ sk5 ) )
!= ( p2 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[11657,39]) ).
thf(11760,plain,
( ( sk6 @ sk5 )
!= sk5 ),
inference(simp,[status(thm)],[11697]) ).
thf(8126,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7046,91]) ).
thf(8182,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[8126]) ).
thf(8257,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ~ ( p2 @ ( sk36 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[8182]) ).
thf(5920,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ sk5 @ ( sk6 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4719,88]) ).
thf(5957,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[5920]) ).
thf(6010,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ( r1 @ ( sk6 @ sk5 ) @ ( sk9 @ ( sk6 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[5957]) ).
thf(13726,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ sk5 @ ( sk36 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13679,80]) ).
thf(13777,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( sk5 != sk1 )
| ( ( sk36 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[13726]) ).
thf(13826,plain,
( ( p1 @ ( sk36 @ sk5 ) )
| ( p1 @ ( sk9 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[13777]) ).
thf(21225,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21155,91]) ).
thf(21326,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk7 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[21225]) ).
thf(21382,plain,
( ( p2 @ ( sk7 @ sk5 ) )
| ~ ( p2 @ ( sk36 @ ( sk7 @ sk5 ) ) )
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[21326]) ).
thf(27392,plain,
( $false
| ~ ( p2 @ ( sk36 @ ( sk7 @ sk5 ) ) )
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[21382,19567]) ).
thf(27393,plain,
( ~ ( p2 @ ( sk36 @ ( sk7 @ sk5 ) ) )
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[27392]) ).
thf(185,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[184,78]) ).
thf(187,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( sk3 @ sk2 )
!= sk18 )
| ( ( sk4 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[185]) ).
thf(189,plain,
( ~ sk11
| ~ ( sk24 @ ( sk4 @ sk2 ) )
| ~ ( p2 @ ( sk33 @ ( sk4 @ sk2 ) ) )
| ~ ( sk31 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk18 ) ),
inference(simp,[status(thm)],[187]) ).
thf(11658,plain,
( ( p2 @ sk1 )
| sk11
| ( ( p2 @ ( sk6 @ sk5 ) )
!= ( p2 @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[11657,69]) ).
thf(11773,plain,
( ( p2 @ sk1 )
| sk11
| ( ( sk6 @ sk5 )
!= sk17 ) ),
inference(simp,[status(thm)],[11658]) ).
thf(241,plain,
! [A: $i] :
( ~ sk12
| sk11
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ sk1 @ sk15 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,38]) ).
thf(242,plain,
( ~ sk12
| sk11
| ( p3 @ sk15 )
| ( p3 @ ( sk3 @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[241:[bind(A,$thf( sk15 ))]]) ).
thf(2047,plain,
( ~ sk12
| sk11
| ( p3 @ sk15 )
| ( ( p3 @ ( sk3 @ sk15 ) )
!= ( p3 @ sk15 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[242]) ).
thf(2049,plain,
( sk11
| ( p3 @ sk15 )
| ~ sk12
| ( ( p3 @ ( sk3 @ sk15 ) )
!= ( p3 @ sk15 ) ) ),
inference(simp,[status(thm)],[2047]) ).
thf(19590,plain,
( ~ sk11
| ( p2 @ sk18 )
| ( ( p2 @ ( sk7 @ sk5 ) )
!= ( p2 @ ( sk6 @ sk18 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11236,19567]) ).
thf(19604,plain,
( ( p2 @ sk18 )
| ~ sk11
| ( ( sk7 @ sk5 )
!= ( sk6 @ sk18 ) ) ),
inference(simp,[status(thm)],[19590]) ).
thf(11527,plain,
( ( p2 @ sk8 )
| ( p2 @ sk1 )
| sk11
| ( ( p2 @ ( sk6 @ sk8 ) )
!= ( p2 @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[11275,69]) ).
thf(11600,plain,
( ( p2 @ sk8 )
| ( p2 @ sk1 )
| sk11
| ( ( sk6 @ sk8 )
!= sk17 ) ),
inference(simp,[status(thm)],[11527]) ).
thf(15684,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( sk6 @ ( sk9 @ sk8 ) )
!= ( sk9 @ sk8 ) ) ),
inference(simp,[status(thm)],[15671]) ).
thf(3996,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p1 @ ( sk9 @ ( sk3 @ sk2 ) ) )
!= ( p1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[2846,50]) ).
thf(4008,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( sk9 @ ( sk3 @ sk2 ) )
!= sk8 ) ),
inference(simp,[status(thm)],[3996]) ).
thf(6164,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk8 @ ( sk9 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6158,78]) ).
thf(6241,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( sk18 != sk8 )
| ( A
!= ( sk9 @ sk8 ) ) ),
inference(simp,[status(thm)],[6164]) ).
thf(6272,plain,
( ~ sk11
| ~ ( sk24 @ ( sk9 @ sk8 ) )
| ~ ( p2 @ ( sk33 @ ( sk9 @ sk8 ) ) )
| ~ ( sk31 @ ( sk9 @ sk8 ) )
| ( sk18 != sk8 ) ),
inference(simp,[status(thm)],[6241]) ).
thf(24784,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p2 @ ( sk6 @ ( sk4 @ sk2 ) ) )
!= ( p2 @ ( sk4 @ sk2 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11365]) ).
thf(24811,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk6 @ ( sk4 @ sk2 ) )
!= ( sk4 @ sk2 ) ) ),
inference(simp,[status(thm)],[24784]) ).
thf(151,plain,
! [A: $i] :
( ~ sk11
| ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk18 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,16]) ).
thf(152,plain,
( ~ sk11
| ( p3 @ sk18 )
| ( r1 @ ( sk3 @ sk18 ) @ ( sk4 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[151:[bind(A,$thf( sk18 ))]]) ).
thf(16353,plain,
( ( sk5 != sk1 )
| ~ sk12
| sk11
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[16316,27]) ).
thf(16394,plain,
( sk11
| ( sk5 != sk1 )
| ~ sk12
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= sk15 ) ),
inference(simp,[status(thm)],[16353]) ).
thf(7100,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7046,75]) ).
thf(7112,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[7100]) ).
thf(7148,plain,
( ( p1 @ ( sk10 @ sk8 ) )
| ~ ( p1 @ ( sk10 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[7112]) ).
thf(10933,plain,
( $false
| ~ ( p1 @ ( sk10 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[7148,2118]) ).
thf(10934,plain,
( ~ ( p1 @ ( sk10 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[10933]) ).
thf(10944,plain,
( ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p1 @ ( sk10 @ ( sk10 @ sk8 ) ) )
!= ( p1 @ ( sk9 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2898,10934]) ).
thf(10945,plain,
( ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ ( sk10 @ sk8 ) )
!= ( sk9 @ sk8 ) ) ),
inference(simp,[status(thm)],[10944]) ).
thf(15755,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ ( sk6 @ ( sk3 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11394,8306]) ).
thf(15824,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( sk36 @ sk5 )
!= ( sk6 @ ( sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[15755]) ).
thf(19955,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk8 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,110]) ).
thf(19956,plain,
( ( p2 @ sk8 )
| ( r1 @ ( sk6 @ sk8 ) @ ( sk7 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[19955:[bind(A,$thf( sk8 ))]]) ).
thf(4304,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[184,86]) ).
thf(4433,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[4304]) ).
thf(4471,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( r1 @ ( sk4 @ sk2 ) @ ( sk6 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[4433]) ).
thf(4755,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ sk5 @ ( sk6 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4719,80]) ).
thf(4782,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[4755]) ).
thf(4815,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ( p1 @ ( sk9 @ ( sk6 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[4782]) ).
thf(5485,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p1 @ ( sk9 @ ( sk6 @ sk5 ) ) )
!= ( p1 @ ( sk6 @ sk5 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4815]) ).
thf(5493,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p1 @ ( sk9 @ ( sk6 @ sk5 ) ) )
!= ( p1 @ ( sk6 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[5485]) ).
thf(2059,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[184,75]) ).
thf(2100,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[2059]) ).
thf(2115,plain,
( ( p1 @ ( sk4 @ sk2 ) )
| ~ ( p1 @ ( sk10 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[2100]) ).
thf(9453,plain,
( ( p1 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p1 @ ( sk10 @ ( sk4 @ sk2 ) ) )
!= ( p1 @ ( sk9 @ ( sk4 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2849,2115]) ).
thf(9475,plain,
( ( p1 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk10 @ ( sk4 @ sk2 ) )
!= ( sk9 @ ( sk4 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[9453]) ).
thf(147,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk8 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,16]) ).
thf(148,plain,
( ( p3 @ sk8 )
| ( r1 @ ( sk3 @ sk8 ) @ ( sk4 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( sk8 ))]]) ).
thf(245,plain,
! [A: $i] :
( ( p3 @ sk8 )
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ ( sk3 @ sk8 ) @ ( sk4 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[148,38]) ).
thf(256,plain,
! [A: $i] :
( ( p3 @ sk8 )
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( sk3 @ sk8 )
!= sk1 )
| ( ( sk4 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[245]) ).
thf(261,plain,
( ( p3 @ sk8 )
| ( p3 @ ( sk4 @ sk8 ) )
| ( p3 @ ( sk3 @ ( sk4 @ sk8 ) ) )
| ( ( sk3 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[256]) ).
thf(8267,plain,
( ( p2 @ sk1 )
| sk11
| ( p2 @ sk2 )
| ( ( p2 @ ( sk36 @ sk2 ) )
!= ( p2 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[6,8135]) ).
thf(8284,plain,
( ( p2 @ sk1 )
| sk11
| ( p2 @ sk2 )
| ( ( sk36 @ sk2 )
!= sk16 ) ),
inference(simp,[status(thm)],[8267]) ).
thf(597,plain,
! [B: $i,A: $i] :
( ( p2 @ B )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( r1 @ A @ B )
| ~ ( p2 @ A )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( r1 @ ( sk33 @ sk21 ) @ A )
!= ( r1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[7,468]) ).
thf(621,plain,
! [B: $i,A: $i] :
( ( p2 @ B )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( r1 @ A @ B )
| ~ ( p2 @ A )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[597]) ).
thf(635,plain,
! [A: $i] :
( ( p2 @ A )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( r1 @ sk2 @ A )
| ~ ( p2 @ sk2 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 ) ),
inference(simp,[status(thm)],[621]) ).
thf(650,plain,
! [A: $i] :
( ( p2 @ A )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk2 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( ( r1 @ sk2 @ A )
!= ( r1 @ sk1 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[47,635]) ).
thf(672,plain,
! [A: $i] :
( ( p2 @ A )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk2 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk2 != sk1 )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[650]) ).
thf(676,plain,
( ( p2 @ sk5 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk2 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[672]) ).
thf(899,plain,
( $false
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk2 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk2 != sk1 ) ),
inference(rewrite,[status(thm)],[676,39]) ).
thf(900,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk2 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[899]) ).
thf(11695,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk2 != sk1 )
| ( ( p2 @ ( sk6 @ sk5 ) )
!= ( p2 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[11657,900]) ).
thf(11778,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk2 != sk1 )
| ( ( sk6 @ sk5 )
!= sk2 ) ),
inference(simp,[status(thm)],[11695]) ).
thf(8112,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( r1 @ sk2 @ ( sk3 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,91]) ).
thf(8202,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( sk2 != sk1 )
| ( ( sk3 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[8112]) ).
thf(8229,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ~ ( p2 @ ( sk36 @ ( sk3 @ sk2 ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[8202]) ).
thf(6587,plain,
! [B: $i,A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ B )
| ( r1 @ B @ ( sk13 @ B @ A ) )
| sk12
| ( ( r1 @ sk16 @ ( sk9 @ sk16 ) )
!= ( r1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5861,73]) ).
thf(6588,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ~ ( r1 @ sk1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| ( r1 @ ( sk9 @ sk16 ) @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
| sk12 ),
inference(pattern_uni,[status(thm)],[6587:[bind(A,$thf( sk16 )),bind(B,$thf( sk9 @ sk16 ))]]) ).
thf(34004,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| ( r1 @ ( sk9 @ sk16 ) @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
| sk12
| ( ( r1 @ sk1 @ sk16 )
!= ( r1 @ sk1 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[34,6588]) ).
thf(34005,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| ( r1 @ ( sk9 @ sk16 ) @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
| sk12 ),
inference(pattern_uni,[status(thm)],[34004:[]]) ).
thf(35170,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ ( sk9 @ sk16 ) @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34005,38]) ).
thf(35294,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( sk9 @ sk16 )
!= sk1 )
| ( ( sk13 @ ( sk9 @ sk16 ) @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[35170]) ).
thf(35321,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p3 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
| ( p3 @ ( sk3 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) ) )
| ( ( sk9 @ sk16 )
!= sk1 ) ),
inference(simp,[status(thm)],[35294]) ).
thf(2885,plain,
( ( p1 @ sk2 )
| ( ( p1 @ ( sk9 @ sk2 ) )
!= ( p1 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2805]) ).
thf(2893,plain,
( ( p1 @ sk2 )
| ( ( p1 @ ( sk9 @ sk2 ) )
!= ( p1 @ sk2 ) ) ),
inference(simp,[status(thm)],[2885]) ).
thf(21199,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( ( r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21155,109]) ).
thf(21333,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk7 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[21199]) ).
thf(21389,plain,
( ( p2 @ ( sk7 @ sk5 ) )
| ~ ( p2 @ ( sk7 @ ( sk7 @ sk5 ) ) )
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[21333]) ).
thf(27446,plain,
( $false
| ~ ( p2 @ ( sk7 @ ( sk7 @ sk5 ) ) )
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[21389,19567]) ).
thf(27447,plain,
( ~ ( p2 @ ( sk7 @ ( sk7 @ sk5 ) ) )
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[27446]) ).
thf(27459,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk7 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27146,27447]) ).
thf(27483,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk7 @ ( sk7 @ sk5 ) )
!= ( sk6 @ ( sk7 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[27459]) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ( sk31 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ( p2 @ B ) ),
inference(cnf,[status(esa)],[5]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ( sk31 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ( p2 @ B ) ),
inference(simp,[status(thm)],[8]) ).
thf(2007,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ ( sk3 @ sk16 ) @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1607,38]) ).
thf(2028,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( sk3 @ sk16 )
!= sk1 )
| ( ( sk13 @ ( sk3 @ sk16 ) @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[2007]) ).
thf(2034,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p3 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
| ( p3 @ ( sk3 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) ) )
| ( ( sk3 @ sk16 )
!= sk1 ) ),
inference(simp,[status(thm)],[2028]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ ( sk13 @ B @ A ) @ ( sk14 @ B @ A ) )
| sk12
| sk11 ),
inference(cnf,[status(esa)],[5]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ ( sk13 @ B @ A ) @ ( sk14 @ B @ A ) )
| sk12
| sk11 ),
inference(simp,[status(thm)],[33]) ).
thf(16374,plain,
( ( sk5 != sk1 )
| ( p2 @ sk8 )
| ( ( p2 @ ( sk36 @ sk8 ) )
!= ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,8143]) ).
thf(16431,plain,
( ( p2 @ sk8 )
| ( sk5 != sk1 )
| ( ( sk36 @ sk8 )
!= ( sk6 @ ( sk36 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[16374]) ).
thf(11430,plain,
( ( p2 @ sk2 )
| ~ sk11
| sk19
| ( ( p2 @ ( sk6 @ sk2 ) )
!= ( p2 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[11265,44]) ).
thf(11523,plain,
( ( p2 @ sk2 )
| sk19
| ~ sk11
| ( ( sk6 @ sk2 )
!= sk18 ) ),
inference(simp,[status(thm)],[11430]) ).
thf(116,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[18,78]) ).
thf(117,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( sk18 != sk1 )
| ( A != sk8 ) ),
inference(simp,[status(thm)],[116]) ).
thf(118,plain,
( ~ sk11
| ~ ( sk24 @ sk8 )
| ~ ( p2 @ ( sk33 @ sk8 ) )
| ~ ( sk31 @ sk8 )
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[117]) ).
thf(33399,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk8 )
| ~ ( sk31 @ sk8 )
| ( ( p2 @ ( sk33 @ sk8 ) )
!= ( p2 @ ( sk22 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33338,118]) ).
thf(33468,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk8 )
| ~ ( sk31 @ sk8 )
| ( ( sk33 @ sk8 )
!= ( sk22 @ sk5 ) ) ),
inference(simp,[status(thm)],[33399]) ).
thf(22495,plain,
( ( sk5 != sk1 )
| ( ( p2 @ ( sk7 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,22480]) ).
thf(22529,plain,
( ( sk5 != sk1 )
| ( ( sk7 @ ( sk36 @ sk5 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[22495]) ).
thf(35161,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( r1 @ ( sk9 @ sk16 ) @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34005,60]) ).
thf(35279,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( sk9 @ sk16 )
!= sk1 )
| ( ( sk13 @ ( sk9 @ sk16 ) @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[35161]) ).
thf(35306,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p3 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
| ( r1 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) @ ( sk3 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) ) )
| ( ( sk9 @ sk16 )
!= sk1 ) ),
inference(simp,[status(thm)],[35279]) ).
thf(11237,plain,
! [A: $i] :
( ~ sk12
| sk11
| ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk15 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,97]) ).
thf(11238,plain,
( ~ sk12
| sk11
| ( p2 @ sk15 )
| ( p2 @ ( sk6 @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[11237:[bind(A,$thf( sk15 ))]]) ).
thf(13947,plain,
( ~ sk12
| sk11
| ( p2 @ sk15 )
| ( ( p2 @ ( sk6 @ sk15 ) )
!= ( p2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[11238,39]) ).
thf(13987,plain,
( sk11
| ( p2 @ sk15 )
| ~ sk12
| ( ( sk6 @ sk15 )
!= sk5 ) ),
inference(simp,[status(thm)],[13947]) ).
thf(19483,plain,
( ( p2 @ sk8 )
| ( p2 @ sk2 )
| ( ( p2 @ ( sk7 @ sk2 ) )
!= ( p2 @ ( sk6 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11275,19280]) ).
thf(19495,plain,
( ( p2 @ sk8 )
| ( p2 @ sk2 )
| ( ( sk7 @ sk2 )
!= ( sk6 @ sk8 ) ) ),
inference(simp,[status(thm)],[19483]) ).
thf(124,plain,
( ( p2 @ sk1 )
| sk11
| ~ sk12
| ( ( p2 @ sk16 )
!= ( p2 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[6,27]) ).
thf(128,plain,
( ( p2 @ sk1 )
| sk11
| ~ sk12
| ( sk16 != sk15 ) ),
inference(simp,[status(thm)],[124]) ).
thf(19579,plain,
( sk11
| ~ sk12
| ( sk16 != sk15 )
| ( ( p2 @ ( sk7 @ sk5 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[128,19567]) ).
thf(19598,plain,
( sk11
| ~ sk12
| ( sk16 != sk15 )
| ( ( sk7 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[19579]) ).
thf(11979,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( ( r1 @ sk8 @ ( sk9 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6158,98]) ).
thf(12011,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( sk8 != sk1 )
| ( ( sk9 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[11979]) ).
thf(12105,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( r1 @ ( sk9 @ sk8 ) @ ( sk36 @ ( sk9 @ sk8 ) ) )
| ( sk8 != sk1 ) ),
inference(simp,[status(thm)],[12011]) ).
thf(11256,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( ( r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7046,97]) ).
thf(11307,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk6 @ A ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[11256]) ).
thf(11356,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( p2 @ ( sk6 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[11307]) ).
thf(24559,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p2 @ ( sk6 @ ( sk10 @ sk8 ) ) )
!= ( p2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[11356,39]) ).
thf(24676,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk6 @ ( sk10 @ sk8 ) )
!= sk5 ) ),
inference(simp,[status(thm)],[24559]) ).
thf(329,plain,
! [A: $i] :
( ( p3 @ sk5 )
| ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ ( sk3 @ sk5 ) @ ( sk4 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[150,40]) ).
thf(340,plain,
! [A: $i] :
( ( p3 @ sk5 )
| ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( sk3 @ sk5 )
!= sk1 )
| ( ( sk4 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[329]) ).
thf(348,plain,
( ( p3 @ sk5 )
| ( p3 @ ( sk4 @ sk5 ) )
| ~ ( p3 @ ( sk4 @ ( sk4 @ sk5 ) ) )
| ( ( sk3 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[340]) ).
thf(33368,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk22 @ sk5 ) )
!= ( p2 @ ( sk7 @ ( sk7 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[33338,27447]) ).
thf(33485,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk22 @ sk5 )
!= ( sk7 @ ( sk7 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[33368]) ).
thf(24954,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ( ( sk33 @ sk20 )
!= sk20 ) ),
inference(simp,[status(thm)],[24927]) ).
thf(2072,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( r1 @ sk1 @ sk16 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,75]) ).
thf(2073,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ~ ( p1 @ ( sk10 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[2072:[bind(A,$thf( sk16 ))]]) ).
thf(1047,plain,
( ~ sk11
| ( p3 @ sk18 )
| ( ( p3 @ ( sk3 @ sk18 ) )
!= ( p3 @ sk18 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[240]) ).
thf(1051,plain,
( ( p3 @ sk18 )
| ~ sk11
| ( ( sk3 @ sk18 )
!= sk18 ) ),
inference(simp,[status(thm)],[1047]) ).
thf(4724,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk5 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4719,78]) ).
thf(4777,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( sk18 != sk5 )
| ( A
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[4724]) ).
thf(4810,plain,
( ~ sk11
| ~ ( sk24 @ ( sk6 @ sk5 ) )
| ~ ( p2 @ ( sk33 @ ( sk6 @ sk5 ) ) )
| ~ ( sk31 @ ( sk6 @ sk5 ) )
| ( sk18 != sk5 ) ),
inference(simp,[status(thm)],[4777]) ).
thf(11870,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( ( r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7046,98]) ).
thf(11996,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[11870]) ).
thf(12090,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( r1 @ ( sk10 @ sk8 ) @ ( sk36 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[11996]) ).
thf(278,plain,
( ( p3 @ sk8 )
| ( ( p3 @ ( sk3 @ sk8 ) )
!= ( p3 @ sk8 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[249]) ).
thf(280,plain,
( ( p3 @ sk8 )
| ( ( p3 @ ( sk3 @ sk8 ) )
!= ( p3 @ sk8 ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(3720,plain,
( ~ sk11
| ~ sk19
| ( p2 @ sk20 )
| ( ( p2 @ ( sk22 @ sk20 ) )
!= ( p2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[2950,39]) ).
thf(3739,plain,
( ( p2 @ sk20 )
| ~ sk11
| ~ sk19
| ( ( sk22 @ sk20 )
!= sk5 ) ),
inference(simp,[status(thm)],[3720]) ).
thf(126,plain,
( ( p2 @ sk1 )
| sk11
| ( ( p2 @ sk16 )
!= ( p2 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6]) ).
thf(130,plain,
( ( p2 @ sk1 )
| sk11
| ( sk16 != sk1 ) ),
inference(simp,[status(thm)],[126]) ).
thf(218,plain,
( sk11
| ( sk16 != sk1 )
| ( ( p2 @ sk5 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[130,39]) ).
thf(221,plain,
( sk11
| ( sk16 != sk1 )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[218]) ).
thf(11805,plain,
! [A: $i] :
( ~ sk12
| sk11
| ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( ( r1 @ sk1 @ sk15 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,98]) ).
thf(11806,plain,
( ~ sk12
| sk11
| ( p2 @ sk15 )
| ( r1 @ sk15 @ ( sk36 @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[11805:[bind(A,$thf( sk15 ))]]) ).
thf(301,plain,
( sk11
| ( p3 @ sk16 )
| ( p3 @ ( sk3 @ sk16 ) )
| ( ( p2 @ sk5 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[244,39]) ).
thf(304,plain,
( sk11
| ( p3 @ sk16 )
| ( p3 @ ( sk3 @ sk16 ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[301]) ).
thf(2763,plain,
( sk11
| ( p3 @ sk16 )
| ( sk5 != sk1 )
| ( ( p3 @ ( sk4 @ sk2 ) )
!= ( p3 @ ( sk3 @ sk16 ) ) ) ),
inference(paramod_ordered,[status(thm)],[304,547]) ).
thf(2772,plain,
( sk11
| ( p3 @ sk16 )
| ( sk5 != sk1 )
| ( ( sk4 @ sk2 )
!= ( sk3 @ sk16 ) ) ),
inference(simp,[status(thm)],[2763]) ).
thf(23700,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p2 @ sk8 )
| ( ( p2 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
!= ( p2 @ ( sk36 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[23387,8143]) ).
thf(23736,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p2 @ sk8 )
| ( ( sk13 @ ( sk9 @ sk16 ) @ sk16 )
!= ( sk36 @ sk8 ) ) ),
inference(simp,[status(thm)],[23700]) ).
thf(4735,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( r1 @ sk5 @ ( sk6 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4719,60]) ).
thf(4793,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[4735]) ).
thf(4825,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ( r1 @ ( sk6 @ sk5 ) @ ( sk3 @ ( sk6 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[4793]) ).
thf(2638,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ ( sk33 @ A ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ A ) ) )
| ~ ( sk31 @ ( sk33 @ A ) )
| ( ( sk32 @ A )
!= sk18 )
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk1 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[57,2331]) ).
thf(2669,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ ( sk33 @ A ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ A ) ) )
| ~ ( sk31 @ ( sk33 @ A ) )
| ( ( sk32 @ A )
!= sk18 )
| ( sk18 != sk1 )
| ( A != sk18 ) ),
inference(simp,[status(thm)],[2638]) ).
thf(2684,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( sk24 @ ( sk33 @ sk18 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk18 ) ) )
| ~ ( sk31 @ ( sk33 @ sk18 ) )
| ( ( sk32 @ sk18 )
!= sk18 )
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[2669]) ).
thf(3305,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( sk24 @ ( sk33 @ sk18 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk18 ) ) )
| ( ( sk32 @ sk18 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk31 @ ( sk33 @ sk18 ) )
!= ( sk31 @ sk18 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2684]) ).
thf(3307,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( sk24 @ ( sk33 @ sk18 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk18 ) ) )
| ( ( sk32 @ sk18 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk18 )
!= sk18 ) ),
inference(simp,[status(thm)],[3305]) ).
thf(4033,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk18 ) ) )
| ( ( sk32 @ sk18 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk18 )
!= sk18 )
| ( ( sk24 @ ( sk33 @ sk18 ) )
!= ( sk24 @ sk18 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3307]) ).
thf(4035,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk18 ) ) )
| ( ( sk32 @ sk18 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk18 )
!= sk18 )
| ( ( sk33 @ sk18 )
!= sk18 ) ),
inference(simp,[status(thm)],[4033]) ).
thf(4038,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk18 ) ) )
| ( ( sk32 @ sk18 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk18 )
!= sk18 ) ),
inference(simp,[status(thm)],[4035]) ).
thf(2058,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,75]) ).
thf(2088,plain,
! [A: $i] :
( ( p1 @ A )
| ~ sk11
| ~ sk19
| ~ ( p1 @ ( sk10 @ A ) )
| ( sk18 != sk1 )
| ( sk20 != A ) ),
inference(simp,[status(thm)],[2058]) ).
thf(2103,plain,
( ( p1 @ sk20 )
| ~ sk11
| ~ sk19
| ~ ( p1 @ ( sk10 @ sk20 ) )
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[2088]) ).
thf(186,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[184,16]) ).
thf(188,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[186]) ).
thf(190,plain,
( ( p3 @ ( sk4 @ sk2 ) )
| ( r1 @ ( sk3 @ ( sk4 @ sk2 ) ) @ ( sk4 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[188]) ).
thf(26855,plain,
( $false
| ( r1 @ ( sk3 @ ( sk4 @ sk2 ) ) @ ( sk4 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[190,547]) ).
thf(26856,plain,
( ( r1 @ ( sk3 @ ( sk4 @ sk2 ) ) @ ( sk4 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[26855]) ).
thf(11566,plain,
( ( p2 @ sk8 )
| ( p2 @ sk2 )
| ( ( p2 @ ( sk36 @ sk2 ) )
!= ( p2 @ ( sk6 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11275,8135]) ).
thf(11596,plain,
( ( p2 @ sk8 )
| ( p2 @ sk2 )
| ( ( sk36 @ sk2 )
!= ( sk6 @ sk8 ) ) ),
inference(simp,[status(thm)],[11566]) ).
thf(33343,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk2 )
| ~ ( sk31 @ sk2 )
| ( ( p2 @ ( sk33 @ sk2 ) )
!= ( p2 @ ( sk22 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33338,115]) ).
thf(33504,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk2 )
| ~ ( sk31 @ sk2 )
| ( ( sk33 @ sk2 )
!= ( sk22 @ sk5 ) ) ),
inference(simp,[status(thm)],[33343]) ).
thf(33353,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk36 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ ( sk22 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33338,27393]) ).
thf(33475,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk36 @ ( sk7 @ sk5 ) )
!= ( sk22 @ sk5 ) ) ),
inference(simp,[status(thm)],[33353]) ).
thf(26791,plain,
( ( p1 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p1 @ ( sk9 @ ( sk7 @ sk5 ) ) )
!= ( p1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[21379,50]) ).
thf(26799,plain,
( ( p1 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk9 @ ( sk7 @ sk5 ) )
!= sk8 ) ),
inference(simp,[status(thm)],[26791]) ).
thf(19480,plain,
( ( p2 @ sk2 )
| ( ( p2 @ ( sk7 @ sk2 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,19280]) ).
thf(19497,plain,
( ( p2 @ sk2 )
| ( ( sk7 @ sk2 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[19480]) ).
thf(17433,plain,
( ( p3 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p3 @ ( sk3 @ ( sk36 @ sk5 ) ) )
!= ( p3 @ ( sk36 @ sk5 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[13862]) ).
thf(17442,plain,
( ( p3 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk3 @ ( sk36 @ sk5 ) )
!= ( sk36 @ sk5 ) ) ),
inference(simp,[status(thm)],[17433]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p3 @ A )
| ( p3 @ B )
| ( p3 @ ( sk3 @ B ) )
| ( ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,38]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( p3 @ A )
| ( p3 @ B )
| ( p3 @ ( sk3 @ B ) )
| ~ ( r1 @ sk1 @ A )
| ( ( sk3 @ A )
!= sk1 )
| ( ( sk4 @ A )
!= B ) ),
inference(simp,[status(thm)],[251]) ).
thf(265,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk4 @ A ) )
| ( p3 @ ( sk3 @ ( sk4 @ A ) ) )
| ~ ( r1 @ sk1 @ A )
| ( ( sk3 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[260]) ).
thf(56,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ( p2 @ ( sk27 @ D @ C @ B @ A ) )
| ( sk25 @ B )
| ( sk24 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(74,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ( p2 @ ( sk27 @ D @ C @ B @ A ) )
| ( sk25 @ B )
| ( sk24 @ A ) ),
inference(simp,[status(thm)],[56]) ).
thf(21193,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21155,38]) ).
thf(21323,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk7 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[21193]) ).
thf(21380,plain,
( ( p3 @ ( sk7 @ sk5 ) )
| ( p3 @ ( sk3 @ ( sk7 @ sk5 ) ) )
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[21323]) ).
thf(27121,plain,
( ( p3 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p3 @ ( sk3 @ ( sk7 @ sk5 ) ) )
!= ( p3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[21380,31]) ).
thf(27142,plain,
( ( p3 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk3 @ ( sk7 @ sk5 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[27121]) ).
thf(33376,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( sk5 != sk1 )
| ( ( p2 @ ( sk36 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk22 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33338,16274]) ).
thf(33473,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( sk5 != sk1 )
| ( ( sk36 @ ( sk36 @ sk5 ) )
!= ( sk22 @ sk5 ) ) ),
inference(simp,[status(thm)],[33376]) ).
thf(579,plain,
! [B: $i,A: $i] :
( ~ sk11
| ( p2 @ B )
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( r1 @ A @ B )
| ~ ( p2 @ A )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( r1 @ ( sk33 @ sk21 ) @ A )
!= ( r1 @ sk1 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[57,468]) ).
thf(623,plain,
! [B: $i,A: $i] :
( ( p2 @ B )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( r1 @ A @ B )
| ~ ( p2 @ A )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( A != sk18 ) ),
inference(simp,[status(thm)],[579]) ).
thf(637,plain,
! [A: $i] :
( ( p2 @ A )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( r1 @ sk18 @ A )
| ~ ( p2 @ sk18 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 ) ),
inference(simp,[status(thm)],[623]) ).
thf(1529,plain,
! [A: $i] :
( ( p2 @ A )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk18 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk2 @ ( sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[821,637]) ).
thf(1552,plain,
! [A: $i] :
( ( p2 @ A )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk18 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk18 != sk2 )
| ( A
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[1529]) ).
thf(1564,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk18 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk18 != sk2 ) ),
inference(simp,[status(thm)],[1552]) ).
thf(19236,plain,
! [A: $i] :
( ~ sk11
| ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk18 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,109]) ).
thf(19237,plain,
( ~ sk11
| ( p2 @ sk18 )
| ~ ( p2 @ ( sk7 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[19236:[bind(A,$thf( sk18 ))]]) ).
thf(19796,plain,
( ~ sk11
| ( p2 @ sk18 )
| ( ( p2 @ ( sk7 @ sk18 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,19237]) ).
thf(19812,plain,
( ( p2 @ sk18 )
| ~ sk11
| ( ( sk7 @ sk18 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[19796]) ).
thf(303,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( ( p3 @ ( sk3 @ sk16 ) )
!= ( p3 @ sk16 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[244]) ).
thf(307,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( ( sk3 @ sk16 )
!= sk16 ) ),
inference(simp,[status(thm)],[303]) ).
thf(144,plain,
( ( p2 @ sk1 )
| sk11
| ( ( p2 @ sk17 )
!= ( p2 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[6,69]) ).
thf(145,plain,
( ( p2 @ sk1 )
| sk11
| ( sk17 != sk16 ) ),
inference(simp,[status(thm)],[144]) ).
thf(8291,plain,
( sk11
| ( sk17 != sk16 )
| ( p2 @ sk8 )
| ( ( p2 @ ( sk36 @ sk8 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[145,8143]) ).
thf(8302,plain,
( sk11
| ( p2 @ sk8 )
| ( sk17 != sk16 )
| ( ( sk36 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[8291]) ).
thf(5480,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p1 @ ( sk9 @ ( sk6 @ sk5 ) ) )
!= ( p1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[4815,50]) ).
thf(5487,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk9 @ ( sk6 @ sk5 ) )
!= sk8 ) ),
inference(simp,[status(thm)],[5480]) ).
thf(10935,plain,
( ( p1 @ sk5 )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p1 @ ( sk10 @ ( sk10 @ sk8 ) ) )
!= ( p1 @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2782,10934]) ).
thf(10947,plain,
( ( p1 @ sk5 )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ ( sk10 @ sk8 ) )
!= ( sk9 @ sk5 ) ) ),
inference(simp,[status(thm)],[10935]) ).
thf(231,plain,
( sk11
| ( sk17 != sk16 )
| ( ( p2 @ sk5 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[145,39]) ).
thf(233,plain,
( sk11
| ( sk17 != sk16 )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[231]) ).
thf(2900,plain,
( ( p1 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p1 @ ( sk10 @ ( sk4 @ sk2 ) ) )
!= ( p1 @ ( sk9 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2898,2115]) ).
thf(2910,plain,
( ( p1 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk10 @ ( sk4 @ sk2 ) )
!= ( sk9 @ sk8 ) ) ),
inference(simp,[status(thm)],[2900]) ).
thf(16359,plain,
( ( sk5 != sk1 )
| ( p2 @ sk2 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk36 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,8135]) ).
thf(16401,plain,
( ( p2 @ sk2 )
| ( sk5 != sk1 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk36 @ sk2 ) ) ),
inference(simp,[status(thm)],[16359]) ).
thf(268,plain,
( ( p3 @ sk5 )
| ( ( p3 @ ( sk3 @ sk5 ) )
!= ( p3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[238,31]) ).
thf(270,plain,
( ( p3 @ sk5 )
| ( ( sk3 @ sk5 )
!= sk2 ) ),
inference(simp,[status(thm)],[268]) ).
thf(24903,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ ( sk33 @ sk20 ) )
| ( ( p2 @ ( sk6 @ sk5 ) )
!= ( p2 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[11657,23885]) ).
thf(24938,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ ( sk33 @ sk20 ) )
| ( ( sk6 @ sk5 )
!= sk20 ) ),
inference(simp,[status(thm)],[24903]) ).
thf(25292,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( ( sk6 @ sk5 )
!= sk20 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk33 @ sk20 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,24938]) ).
thf(25316,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( ( sk6 @ sk5 )
!= sk20 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk33 @ sk20 ) ) ),
inference(simp,[status(thm)],[25292]) ).
thf(28,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ( p2 @ A )
| ( r1 @ A @ ( sk22 @ A ) )
| ~ sk19 ),
inference(cnf,[status(esa)],[5]) ).
thf(85,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ( p2 @ A )
| ( r1 @ A @ ( sk22 @ A ) )
| ~ sk19 ),
inference(simp,[status(thm)],[28]) ).
thf(198,plain,
( sk11
| ( sk16 != sk5 )
| ( ( p2 @ sk5 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[127,39]) ).
thf(201,plain,
( sk11
| ( sk16 != sk5 )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[198]) ).
thf(27227,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( p2 @ sk8 )
| ( ( p2 @ ( sk36 @ sk8 ) )
!= ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27146,8143]) ).
thf(27265,plain,
( ( p2 @ sk8 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk36 @ sk8 )
!= ( sk6 @ ( sk7 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[27227]) ).
thf(23582,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p2 @ ( sk36 @ ( sk10 @ sk8 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,8257]) ).
thf(23594,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk36 @ ( sk10 @ sk8 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[23582]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk21 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ A )
| ~ sk19 ),
inference(cnf,[status(esa)],[5]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk21 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ A )
| ~ sk19 ),
inference(simp,[status(thm)],[43]) ).
thf(27453,plain,
( ( p2 @ sk2 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk7 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11265,27447]) ).
thf(27479,plain,
( ( p2 @ sk2 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk7 @ ( sk7 @ sk5 ) )
!= ( sk6 @ sk2 ) ) ),
inference(simp,[status(thm)],[27453]) ).
thf(311,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[184,40]) ).
thf(335,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[311]) ).
thf(344,plain,
( ( p3 @ ( sk4 @ sk2 ) )
| ~ ( p3 @ ( sk4 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[335]) ).
thf(2609,plain,
( $false
| ~ ( p3 @ ( sk4 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[344,547]) ).
thf(2610,plain,
( ~ ( p3 @ ( sk4 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[2609]) ).
thf(2616,plain,
( ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p3 @ ( sk4 @ ( sk4 @ sk2 ) ) )
!= ( p3 @ ( sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[274,2610]) ).
thf(2621,plain,
( ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ ( sk4 @ sk2 ) )
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[2616]) ).
thf(4311,plain,
! [A: $i] :
( ~ sk12
| sk11
| ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk15 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,86]) ).
thf(4312,plain,
( ~ sk12
| sk11
| ( p2 @ sk15 )
| ( r1 @ sk15 @ ( sk6 @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[4311:[bind(A,$thf( sk15 ))]]) ).
thf(2789,plain,
! [A: $i] :
( ~ sk11
| ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ sk18 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,80]) ).
thf(2790,plain,
( ~ sk11
| ( p1 @ sk18 )
| ( p1 @ ( sk9 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[2789:[bind(A,$thf( sk18 ))]]) ).
thf(36,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk23 @ A ) )
| ~ sk19 ),
inference(cnf,[status(esa)],[5]) ).
thf(108,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk23 @ A ) )
| ~ sk19 ),
inference(simp,[status(thm)],[36]) ).
thf(18782,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p2 @ A )
| ~ ( p2 @ ( sk23 @ A ) )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,108]) ).
thf(18783,plain,
( ~ sk11
| ~ sk19
| ( p2 @ sk20 )
| ~ ( p2 @ ( sk23 @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[18782:[bind(A,$thf( sk20 ))]]) ).
thf(19188,plain,
( ~ sk11
| ~ sk19
| ( p2 @ sk20 )
| ( ( p2 @ ( sk23 @ sk20 ) )
!= ( p2 @ ( sk22 @ sk20 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2950,18783]) ).
thf(19218,plain,
( ( p2 @ sk20 )
| ~ sk11
| ~ sk19
| ( ( sk23 @ sk20 )
!= ( sk22 @ sk20 ) ) ),
inference(simp,[status(thm)],[19188]) ).
thf(2767,plain,
( sk11
| ( p3 @ sk16 )
| ( sk5 != sk1 )
| ( ( p3 @ ( sk3 @ sk16 ) )
!= ( p3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[304,31]) ).
thf(2773,plain,
( sk11
| ( p3 @ sk16 )
| ( sk5 != sk1 )
| ( ( sk3 @ sk16 )
!= sk2 ) ),
inference(simp,[status(thm)],[2767]) ).
thf(7989,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p3 @ ( sk3 @ ( sk9 @ sk8 ) ) )
!= ( p3 @ ( sk9 @ sk8 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6259]) ).
thf(7999,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( sk3 @ ( sk9 @ sk8 ) )
!= ( sk9 @ sk8 ) ) ),
inference(simp,[status(thm)],[7989]) ).
thf(8101,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[184,91]) ).
thf(8176,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[8101]) ).
thf(8253,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ~ ( p2 @ ( sk36 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[8176]) ).
thf(23271,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p2 @ ( sk36 @ ( sk4 @ sk2 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,8253]) ).
thf(23295,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk36 @ ( sk4 @ sk2 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[23271]) ).
thf(8106,plain,
! [A: $i] :
( ~ sk12
| sk11
| ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( r1 @ sk1 @ sk15 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,91]) ).
thf(8107,plain,
( ~ sk12
| sk11
| ( p2 @ sk15 )
| ~ ( p2 @ ( sk36 @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[8106:[bind(A,$thf( sk15 ))]]) ).
thf(11692,plain,
( ~ sk12
| sk11
| ( p2 @ sk15 )
| ( ( p2 @ ( sk36 @ sk15 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,8107]) ).
thf(11751,plain,
( sk11
| ( p2 @ sk15 )
| ~ sk12
| ( ( sk36 @ sk15 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11692]) ).
thf(11689,plain,
( ~ sk11
| sk19
| ( ( p2 @ ( sk6 @ sk5 ) )
!= ( p2 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[11657,44]) ).
thf(11766,plain,
( sk19
| ~ sk11
| ( ( sk6 @ sk5 )
!= sk18 ) ),
inference(simp,[status(thm)],[11689]) ).
thf(11544,plain,
( ( p2 @ sk8 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ ( sk6 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11275,8306]) ).
thf(11619,plain,
( ( p2 @ sk8 )
| ( ( sk36 @ sk5 )
!= ( sk6 @ sk8 ) ) ),
inference(simp,[status(thm)],[11544]) ).
thf(11463,plain,
( ( p2 @ sk2 )
| ( ( p2 @ ( sk6 @ sk2 ) )
!= ( p2 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11265]) ).
thf(11484,plain,
( ( p2 @ sk2 )
| ( ( sk6 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[11463]) ).
thf(327,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk8 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,40]) ).
thf(328,plain,
( ( p3 @ sk8 )
| ~ ( p3 @ ( sk4 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[327:[bind(A,$thf( sk8 ))]]) ).
thf(557,plain,
( ( p3 @ sk8 )
| ( ( p3 @ ( sk4 @ sk8 ) )
!= ( p3 @ ( sk3 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[249,328]) ).
thf(561,plain,
( ( p3 @ sk8 )
| ( ( sk4 @ sk8 )
!= ( sk3 @ sk8 ) ) ),
inference(simp,[status(thm)],[557]) ).
thf(391,plain,
! [C: $i,B: $i,A: $i] :
( ( p3 @ sk8 )
| ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ B )
| ( p2 @ C )
| ~ ( p2 @ B )
| ~ ( sk31 @ A )
| ( ( r1 @ ( sk3 @ sk8 ) @ ( sk4 @ sk8 ) )
!= ( r1 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[148,77]) ).
thf(392,plain,
! [A: $i] :
( ( p3 @ sk8 )
| ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ ( sk3 @ sk8 ) )
| ( p2 @ ( sk4 @ sk8 ) )
| ~ ( p2 @ ( sk3 @ sk8 ) )
| ~ ( sk31 @ A ) ),
inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( A )),bind(B,$thf( sk3 @ sk8 )),bind(C,$thf( sk4 @ sk8 ))]]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk30 @ B @ A ) )
| ( sk24 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk30 @ B @ A ) )
| ( sk24 @ A ) ),
inference(simp,[status(thm)],[61]) ).
thf(33346,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ ( sk33 @ sk20 ) )
| ( ( p2 @ ( sk22 @ sk5 ) )
!= ( p2 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[33338,23885]) ).
thf(33516,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ ( sk33 @ sk20 ) )
| ( ( sk22 @ sk5 )
!= sk20 ) ),
inference(simp,[status(thm)],[33346]) ).
thf(19575,plain,
( ~ sk12
| sk11
| ( p2 @ sk15 )
| ( ( p2 @ ( sk7 @ sk5 ) )
!= ( p2 @ ( sk6 @ sk15 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11238,19567]) ).
thf(19595,plain,
( sk11
| ( p2 @ sk15 )
| ~ sk12
| ( ( sk7 @ sk5 )
!= ( sk6 @ sk15 ) ) ),
inference(simp,[status(thm)],[19575]) ).
thf(312,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ~ ( r1 @ sk1 @ A )
| ( p3 @ A )
| ( ( p3 @ ( sk4 @ A ) )
!= ( p3 @ ( sk3 @ sk16 ) ) ) ),
inference(paramod_ordered,[status(thm)],[244,40]) ).
thf(334,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p3 @ A )
| ~ ( r1 @ sk1 @ A )
| ( ( sk4 @ A )
!= ( sk3 @ sk16 ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(11415,plain,
( ( p2 @ sk2 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ ( sk6 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11265,8306]) ).
thf(11520,plain,
( ( p2 @ sk2 )
| ( ( sk36 @ sk5 )
!= ( sk6 @ sk2 ) ) ),
inference(simp,[status(thm)],[11415]) ).
thf(33364,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk20 )
| ( ( sk33 @ sk20 )
!= sk20 )
| ( ( p2 @ ( sk22 @ sk5 ) )
!= ( p2 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[33338,24954]) ).
thf(33459,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk20 )
| ( ( sk33 @ sk20 )
!= sk20 )
| ( ( sk22 @ sk5 )
!= sk20 ) ),
inference(simp,[status(thm)],[33364]) ).
thf(19841,plain,
! [A: $i] :
( ~ sk11
| ( p2 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk18 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,110]) ).
thf(19842,plain,
( ~ sk11
| ( p2 @ sk18 )
| ( r1 @ ( sk6 @ sk18 ) @ ( sk7 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[19841:[bind(A,$thf( sk18 ))]]) ).
thf(11679,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ( sk18 != sk1 )
| ( ( p2 @ ( sk33 @ sk18 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,133]) ).
thf(11768,plain,
( ~ sk11
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk18 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11679]) ).
thf(323,plain,
! [A: $i] :
( ( p3 @ sk8 )
| ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ ( sk3 @ sk8 ) @ ( sk4 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[148,40]) ).
thf(342,plain,
! [A: $i] :
( ( p3 @ sk8 )
| ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( sk3 @ sk8 )
!= sk1 )
| ( ( sk4 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[323]) ).
thf(349,plain,
( ( p3 @ sk8 )
| ( p3 @ ( sk4 @ sk8 ) )
| ~ ( p3 @ ( sk4 @ ( sk4 @ sk8 ) ) )
| ( ( sk3 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[342]) ).
thf(5501,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p3 @ ( sk3 @ ( sk6 @ sk5 ) ) )
!= ( p3 @ ( sk4 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4831,547]) ).
thf(5512,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk3 @ ( sk6 @ sk5 ) )
!= ( sk4 @ sk2 ) ) ),
inference(simp,[status(thm)],[5501]) ).
thf(7978,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p3 @ ( sk3 @ ( sk9 @ sk8 ) ) )
!= ( p3 @ ( sk4 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6259,547]) ).
thf(7994,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( sk3 @ ( sk9 @ sk8 ) )
!= ( sk4 @ sk2 ) ) ),
inference(simp,[status(thm)],[7978]) ).
thf(2855,plain,
( ( p1 @ sk5 )
| ( ( p1 @ ( sk10 @ sk8 ) )
!= ( p1 @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2782,2118]) ).
thf(2873,plain,
( ( p1 @ sk5 )
| ( ( sk10 @ sk8 )
!= ( sk9 @ sk5 ) ) ),
inference(simp,[status(thm)],[2855]) ).
thf(2055,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,75]) ).
thf(2056,plain,
( ( p1 @ sk5 )
| ~ ( p1 @ ( sk10 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[2055:[bind(A,$thf( sk5 ))]]) ).
thf(2860,plain,
( ( p1 @ sk5 )
| ( ( p1 @ ( sk10 @ sk5 ) )
!= ( p1 @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2782,2056]) ).
thf(2872,plain,
( ( p1 @ sk5 )
| ( ( sk10 @ sk5 )
!= ( sk9 @ sk5 ) ) ),
inference(simp,[status(thm)],[2860]) ).
thf(4763,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ sk5 @ ( sk6 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4719,40]) ).
thf(4798,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[4763]) ).
thf(4832,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ~ ( p3 @ ( sk4 @ ( sk6 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[4798]) ).
thf(5530,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p3 @ ( sk4 @ ( sk6 @ sk5 ) ) )
!= ( p3 @ ( sk3 @ ( sk6 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4831,4832]) ).
thf(5534,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk4 @ ( sk6 @ sk5 ) )
!= ( sk3 @ ( sk6 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[5530]) ).
thf(5820,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ sk2 @ ( sk3 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,88]) ).
thf(5941,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( sk2 != sk1 )
| ( ( sk3 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[5820]) ).
thf(5988,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ( r1 @ ( sk3 @ sk2 ) @ ( sk9 @ ( sk3 @ sk2 ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[5941]) ).
thf(318,plain,
! [A: $i] :
( ~ sk12
| sk11
| ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk15 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,40]) ).
thf(319,plain,
( ~ sk12
| sk11
| ( p3 @ sk15 )
| ~ ( p3 @ ( sk4 @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( sk15 ))]]) ).
thf(2197,plain,
( ~ sk12
| sk11
| ( p3 @ sk15 )
| ( ( p3 @ ( sk4 @ sk15 ) )
!= ( p3 @ ( sk3 @ sk15 ) ) ) ),
inference(paramod_ordered,[status(thm)],[242,319]) ).
thf(2200,plain,
( sk11
| ( p3 @ sk15 )
| ~ sk12
| ( ( sk4 @ sk15 )
!= ( sk3 @ sk15 ) ) ),
inference(simp,[status(thm)],[2197]) ).
thf(19238,plain,
! [A: $i] :
( ~ sk12
| sk11
| ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk15 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,109]) ).
thf(19239,plain,
( ~ sk12
| sk11
| ( p2 @ sk15 )
| ~ ( p2 @ ( sk7 @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[19238:[bind(A,$thf( sk15 ))]]) ).
thf(21448,plain,
( ~ sk12
| sk11
| ( p2 @ sk15 )
| ( ( p2 @ ( sk7 @ sk15 ) )
!= ( p2 @ ( sk6 @ sk15 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11238,19239]) ).
thf(21470,plain,
( sk11
| ( p2 @ sk15 )
| ~ sk12
| ( ( sk7 @ sk15 )
!= ( sk6 @ sk15 ) ) ),
inference(simp,[status(thm)],[21448]) ).
thf(11561,plain,
( ( p2 @ sk8 )
| ~ sk12
| sk11
| ( ( p2 @ ( sk6 @ sk8 ) )
!= ( p2 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[11275,27]) ).
thf(11624,plain,
( ( p2 @ sk8 )
| sk11
| ~ sk12
| ( ( sk6 @ sk8 )
!= sk15 ) ),
inference(simp,[status(thm)],[11561]) ).
thf(13031,plain,
( ~ sk11
| ( p2 @ sk18 )
| ( ( p2 @ ( sk6 @ sk18 ) )
!= ( p2 @ sk18 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11236]) ).
thf(13070,plain,
( ( p2 @ sk18 )
| ~ sk11
| ( ( sk6 @ sk18 )
!= sk18 ) ),
inference(simp,[status(thm)],[13031]) ).
thf(53,plain,
( ~ sk11
| ~ ( p2 @ sk21 )
| ~ sk19 ),
inference(cnf,[status(esa)],[5]) ).
thf(11552,plain,
( ( p2 @ sk8 )
| ~ sk11
| ~ sk19
| ( ( p2 @ ( sk6 @ sk8 ) )
!= ( p2 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[11275,53]) ).
thf(11646,plain,
( ( p2 @ sk8 )
| ~ sk11
| ~ sk19
| ( ( sk6 @ sk8 )
!= sk21 ) ),
inference(simp,[status(thm)],[11552]) ).
thf(2800,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ sk16 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,80]) ).
thf(2801,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p1 @ ( sk9 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[2800:[bind(A,$thf( sk16 ))]]) ).
thf(35134,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ ( sk9 @ sk16 ) @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34005,88]) ).
thf(35280,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( sk9 @ sk16 )
!= sk1 )
| ( ( sk13 @ ( sk9 @ sk16 ) @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[35134]) ).
thf(35307,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p1 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
| ( r1 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) @ ( sk9 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) ) )
| ( ( sk9 @ sk16 )
!= sk1 ) ),
inference(simp,[status(thm)],[35280]) ).
thf(11711,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( p2 @ ( sk33 @ sk21 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,139]) ).
thf(11762,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11711]) ).
thf(15881,plain,
( ( p1 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p1 @ ( sk9 @ ( sk36 @ sk5 ) ) )
!= ( p1 @ ( sk10 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[13826,2118]) ).
thf(15896,plain,
( ( p1 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk9 @ ( sk36 @ sk5 ) )
!= ( sk10 @ sk8 ) ) ),
inference(simp,[status(thm)],[15881]) ).
thf(8314,plain,
( sk11
| ( sk16 != sk5 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[127,8306]) ).
thf(8319,plain,
( sk11
| ( sk16 != sk5 )
| ( ( sk36 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[8314]) ).
thf(13718,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk5 @ ( sk36 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13679,86]) ).
thf(13795,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( sk5 != sk1 )
| ( ( sk36 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[13718]) ).
thf(13844,plain,
( ( p2 @ ( sk36 @ sk5 ) )
| ( r1 @ ( sk36 @ sk5 ) @ ( sk6 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[13795]) ).
thf(31079,plain,
( $false
| ( r1 @ ( sk36 @ sk5 ) @ ( sk6 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(rewrite,[status(thm)],[13844,8306]) ).
thf(31080,plain,
( ( r1 @ ( sk36 @ sk5 ) @ ( sk6 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[31079]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p3 @ A )
| ( p3 @ B )
| ( r1 @ ( sk3 @ B ) @ ( sk4 @ B ) )
| ( ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,16]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( p3 @ A )
| ( p3 @ B )
| ( r1 @ ( sk3 @ B ) @ ( sk4 @ B ) )
| ~ ( r1 @ sk1 @ A )
| ( ( sk3 @ A )
!= sk1 )
| ( ( sk4 @ A )
!= B ) ),
inference(simp,[status(thm)],[158]) ).
thf(169,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk4 @ A ) )
| ( r1 @ ( sk3 @ ( sk4 @ A ) ) @ ( sk4 @ ( sk4 @ A ) ) )
| ~ ( r1 @ sk1 @ A )
| ( ( sk3 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[164]) ).
thf(2664,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ ( sk33 @ A ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ A ) ) )
| ~ ( sk31 @ ( sk33 @ A ) )
| ( ( sk32 @ A )
!= sk18 )
| ( ( r1 @ sk20 @ sk21 )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19,2331]) ).
thf(2675,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ ( sk33 @ A ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ A ) ) )
| ~ ( sk31 @ ( sk33 @ A ) )
| ( ( sk32 @ A )
!= sk18 )
| ( sk20 != sk18 )
| ( sk21 != A ) ),
inference(simp,[status(thm)],[2664]) ).
thf(2690,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( sk31 @ sk21 )
| ~ ( sk24 @ ( sk33 @ sk21 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk21 ) ) )
| ~ ( sk31 @ ( sk33 @ sk21 ) )
| ( ( sk32 @ sk21 )
!= sk18 )
| ( sk20 != sk18 ) ),
inference(simp,[status(thm)],[2675]) ).
thf(6554,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( sk31 @ sk21 )
| ~ ( sk24 @ ( sk33 @ sk21 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk21 ) ) )
| ( ( sk32 @ sk21 )
!= sk18 )
| ( sk20 != sk18 )
| ( ( sk31 @ ( sk33 @ sk21 ) )
!= ( sk31 @ sk21 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2690]) ).
thf(6558,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( sk31 @ sk21 )
| ~ ( sk24 @ ( sk33 @ sk21 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk21 ) ) )
| ( ( sk32 @ sk21 )
!= sk18 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk21 ) ),
inference(simp,[status(thm)],[6554]) ).
thf(8349,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( sk31 @ sk21 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk21 ) ) )
| ( ( sk32 @ sk21 )
!= sk18 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk21 )
| ( ( sk24 @ ( sk33 @ sk21 ) )
!= ( sk24 @ sk21 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6558]) ).
thf(8351,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( sk31 @ sk21 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk21 ) ) )
| ( ( sk32 @ sk21 )
!= sk18 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk21 )
| ( ( sk33 @ sk21 )
!= sk21 ) ),
inference(simp,[status(thm)],[8349]) ).
thf(8354,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( sk31 @ sk21 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk21 ) ) )
| ( ( sk32 @ sk21 )
!= sk18 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk21 ) ),
inference(simp,[status(thm)],[8351]) ).
thf(19270,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( ( r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7046,109]) ).
thf(19369,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[19270]) ).
thf(19433,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ~ ( p2 @ ( sk7 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[19369]) ).
thf(8700,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( sk24 @ ( sk32 @ sk18 ) )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ~ ( sk31 @ ( sk32 @ sk18 ) )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk18 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[10,8483]) ).
thf(8767,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( sk24 @ ( sk32 @ sk18 ) )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ~ ( sk31 @ ( sk32 @ sk18 ) )
| ( sk18 != sk18 )
| ( sk20 != sk18 ) ),
inference(simp,[status(thm)],[8700]) ).
thf(8813,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( sk24 @ ( sk32 @ sk18 ) )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ~ ( sk31 @ ( sk32 @ sk18 ) )
| ( sk20 != sk18 ) ),
inference(simp,[status(thm)],[8767]) ).
thf(9488,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( sk24 @ ( sk32 @ sk18 ) )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ( sk20 != sk18 )
| ( ( sk31 @ ( sk32 @ sk18 ) )
!= ( sk31 @ sk18 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8813]) ).
thf(9490,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( sk24 @ ( sk32 @ sk18 ) )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ( sk20 != sk18 )
| ( ( sk32 @ sk18 )
!= sk18 ) ),
inference(simp,[status(thm)],[9488]) ).
thf(9503,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ( sk20 != sk18 )
| ( ( sk32 @ sk18 )
!= sk18 )
| ( ( sk24 @ ( sk32 @ sk18 ) )
!= ( sk24 @ sk18 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9490]) ).
thf(9507,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ( sk20 != sk18 )
| ( ( sk32 @ sk18 )
!= sk18 )
| ( ( sk32 @ sk18 )
!= sk18 ) ),
inference(simp,[status(thm)],[9503]) ).
thf(9508,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ~ ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
| ( sk20 != sk18 )
| ( ( sk32 @ sk18 )
!= sk18 ) ),
inference(simp,[status(thm)],[9507]) ).
thf(11684,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ( sk20 != sk18 )
| ( ( sk32 @ sk18 )
!= sk18 )
| ( ( p2 @ ( sk33 @ ( sk32 @ sk18 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,9508]) ).
thf(11734,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk18 )
| ~ ( sk31 @ sk18 )
| ( sk20 != sk18 )
| ( ( sk32 @ sk18 )
!= sk18 )
| ( ( sk33 @ ( sk32 @ sk18 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11684]) ).
thf(2784,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,80]) ).
thf(2821,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( sk20 != A ) ),
inference(simp,[status(thm)],[2784]) ).
thf(2840,plain,
( ( p1 @ sk20 )
| ( p1 @ ( sk9 @ sk20 ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[2821]) ).
thf(7066,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7046,38]) ).
thf(7136,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[7066]) ).
thf(7172,plain,
( ( p3 @ ( sk10 @ sk8 ) )
| ( p3 @ ( sk3 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[7136]) ).
thf(18973,plain,
( ( p3 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p3 @ ( sk3 @ ( sk10 @ sk8 ) ) )
!= ( p3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[7172,31]) ).
thf(18994,plain,
( ( p3 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk3 @ ( sk10 @ sk8 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[18973]) ).
thf(16344,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ sk19
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[16316,53]) ).
thf(16414,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ sk19
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= sk21 ) ),
inference(simp,[status(thm)],[16344]) ).
thf(3050,plain,
( ~ sk11
| ( p1 @ sk18 )
| ( p1 @ sk5 )
| ( ( p1 @ ( sk10 @ sk5 ) )
!= ( p1 @ ( sk9 @ sk18 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2790,2056]) ).
thf(3060,plain,
( ( p1 @ sk18 )
| ( p1 @ sk5 )
| ~ sk11
| ( ( sk10 @ sk5 )
!= ( sk9 @ sk18 ) ) ),
inference(simp,[status(thm)],[3050]) ).
thf(26394,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p2 @ sk8 )
| ( ( p2 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
!= ( p2 @ ( sk7 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[25992,19296]) ).
thf(26470,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p2 @ sk8 )
| ( ( sk13 @ ( sk3 @ sk16 ) @ sk16 )
!= ( sk7 @ sk8 ) ) ),
inference(simp,[status(thm)],[26394]) ).
thf(19476,plain,
( ( sk5 != sk1 )
| ( p2 @ sk2 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk7 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,19280]) ).
thf(19515,plain,
( ( p2 @ sk2 )
| ( sk5 != sk1 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk7 @ sk2 ) ) ),
inference(simp,[status(thm)],[19476]) ).
thf(313,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,40]) ).
thf(314,plain,
( ( p3 @ sk5 )
| ~ ( p3 @ ( sk4 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[313:[bind(A,$thf( sk5 ))]]) ).
thf(484,plain,
( ( p3 @ sk8 )
| ( p3 @ sk5 )
| ( ( p3 @ ( sk4 @ sk5 ) )
!= ( p3 @ ( sk3 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[249,314]) ).
thf(488,plain,
( ( p3 @ sk8 )
| ( p3 @ sk5 )
| ( ( sk4 @ sk5 )
!= ( sk3 @ sk8 ) ) ),
inference(simp,[status(thm)],[484]) ).
thf(8104,plain,
! [A: $i] :
( ~ sk11
| ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( r1 @ sk1 @ sk18 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,91]) ).
thf(8105,plain,
( ~ sk11
| ( p2 @ sk18 )
| ~ ( p2 @ ( sk36 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[8104:[bind(A,$thf( sk18 ))]]) ).
thf(2970,plain,
! [A: $i] :
( ~ sk11
| ( p2 @ A )
| ( p2 @ ( sk22 @ A ) )
| ~ sk19
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[18,81]) ).
thf(2985,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk22 @ A ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( A != sk8 ) ),
inference(simp,[status(thm)],[2970]) ).
thf(3000,plain,
( ( p2 @ sk8 )
| ( p2 @ ( sk22 @ sk8 ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[2985]) ).
thf(27413,plain,
( ( p2 @ sk8 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk36 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11275,27393]) ).
thf(27440,plain,
( ( p2 @ sk8 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk36 @ ( sk7 @ sk5 ) )
!= ( sk6 @ sk8 ) ) ),
inference(simp,[status(thm)],[27413]) ).
thf(8158,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( r1 @ sk20 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19,91]) ).
thf(8184,plain,
! [A: $i] :
( ( p2 @ A )
| ~ sk11
| ~ sk19
| ~ ( p2 @ ( sk36 @ A ) )
| ( sk20 != sk1 )
| ( sk21 != A ) ),
inference(simp,[status(thm)],[8158]) ).
thf(8258,plain,
( ( p2 @ sk21 )
| ~ sk11
| ~ sk19
| ~ ( p2 @ ( sk36 @ sk21 ) )
| ( sk20 != sk1 ) ),
inference(simp,[status(thm)],[8184]) ).
thf(2041,plain,
( ~ sk12
| sk11
| ( p3 @ sk15 )
| ( ( p3 @ ( sk4 @ sk2 ) )
!= ( p3 @ ( sk3 @ sk15 ) ) ) ),
inference(paramod_ordered,[status(thm)],[242,547]) ).
thf(2053,plain,
( sk11
| ( p3 @ sk15 )
| ~ sk12
| ( ( sk4 @ sk2 )
!= ( sk3 @ sk15 ) ) ),
inference(simp,[status(thm)],[2041]) ).
thf(485,plain,
( ( p3 @ sk5 )
| ( ( p3 @ ( sk4 @ sk5 ) )
!= ( p3 @ ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[238,314]) ).
thf(489,plain,
( ( p3 @ sk5 )
| ( ( sk4 @ sk5 )
!= ( sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[485]) ).
thf(21255,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21155,40]) ).
thf(21312,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk7 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[21255]) ).
thf(21370,plain,
( ( p3 @ ( sk7 @ sk5 ) )
| ~ ( p3 @ ( sk4 @ ( sk7 @ sk5 ) ) )
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[21312]) ).
thf(825,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk2 @ ( sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[821,78]) ).
thf(839,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( sk18 != sk2 )
| ( A
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[825]) ).
thf(848,plain,
( ~ sk11
| ~ ( sk24 @ ( sk3 @ sk2 ) )
| ~ ( p2 @ ( sk33 @ ( sk3 @ sk2 ) ) )
| ~ ( sk31 @ ( sk3 @ sk2 ) )
| ( sk18 != sk2 ) ),
inference(simp,[status(thm)],[839]) ).
thf(11700,plain,
( ~ sk11
| ~ ( sk24 @ ( sk3 @ sk2 ) )
| ~ ( sk31 @ ( sk3 @ sk2 ) )
| ( sk18 != sk2 )
| ( ( p2 @ ( sk33 @ ( sk3 @ sk2 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,848]) ).
thf(11774,plain,
( ~ sk11
| ~ ( sk24 @ ( sk3 @ sk2 ) )
| ~ ( sk31 @ ( sk3 @ sk2 ) )
| ( sk18 != sk2 )
| ( ( sk33 @ ( sk3 @ sk2 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11700]) ).
thf(6192,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk8 @ ( sk9 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6158,86]) ).
thf(6244,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( sk8 != sk1 )
| ( ( sk9 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[6192]) ).
thf(6275,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( r1 @ ( sk9 @ sk8 ) @ ( sk6 @ ( sk9 @ sk8 ) ) )
| ( sk8 != sk1 ) ),
inference(simp,[status(thm)],[6244]) ).
thf(19927,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,110]) ).
thf(19928,plain,
( ( p2 @ sk2 )
| ( r1 @ ( sk6 @ sk2 ) @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[19927:[bind(A,$thf( sk2 ))]]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ B @ ( sk29 @ B @ A ) )
| ( sk24 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ B @ ( sk29 @ B @ A ) )
| ( sk24 @ A ) ),
inference(simp,[status(thm)],[54]) ).
thf(11800,plain,
! [A: $i] :
( ~ sk11
| ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( ( r1 @ sk1 @ sk18 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,98]) ).
thf(11801,plain,
( ~ sk11
| ( p2 @ sk18 )
| ( r1 @ sk18 @ ( sk36 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[11800:[bind(A,$thf( sk18 ))]]) ).
thf(16352,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ sk8 )
| ~ ( sk31 @ sk8 )
| ( sk18 != sk1 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk33 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,118]) ).
thf(16436,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ sk8 )
| ~ ( sk31 @ sk8 )
| ( sk18 != sk1 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk33 @ sk8 ) ) ),
inference(simp,[status(thm)],[16352]) ).
thf(5478,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p1 @ ( sk10 @ ( sk6 @ sk5 ) ) )
!= ( p1 @ ( sk9 @ ( sk6 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4815,4813]) ).
thf(5496,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk10 @ ( sk6 @ sk5 ) )
!= ( sk9 @ ( sk6 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[5478]) ).
thf(550,plain,
( ( p3 @ sk5 )
| ( ( p3 @ ( sk4 @ sk2 ) )
!= ( p3 @ ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[238,547]) ).
thf(554,plain,
( ( p3 @ sk5 )
| ( ( sk4 @ sk2 )
!= ( sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[550]) ).
thf(18496,plain,
( ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p1 @ ( sk9 @ ( sk10 @ sk8 ) ) )
!= ( p1 @ ( sk10 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[18493,2118]) ).
thf(18512,plain,
( ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk9 @ ( sk10 @ sk8 ) )
!= ( sk10 @ sk8 ) ) ),
inference(simp,[status(thm)],[18496]) ).
thf(11671,plain,
( ~ sk11
| ~ ( sk24 @ ( sk9 @ sk8 ) )
| ~ ( sk31 @ ( sk9 @ sk8 ) )
| ( sk18 != sk8 )
| ( ( p2 @ ( sk33 @ ( sk9 @ sk8 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,6272]) ).
thf(11757,plain,
( ~ sk11
| ~ ( sk24 @ ( sk9 @ sk8 ) )
| ~ ( sk31 @ ( sk9 @ sk8 ) )
| ( sk18 != sk8 )
| ( ( sk33 @ ( sk9 @ sk8 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11671]) ).
thf(27458,plain,
( ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk7 @ ( sk7 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,27447]) ).
thf(27493,plain,
( ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk7 @ ( sk7 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[27458]) ).
thf(7998,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p3 @ ( sk3 @ ( sk9 @ sk8 ) ) )
!= ( p3 @ ( sk9 @ sk8 ) ) ) ),
inference(simp,[status(thm)],[7989]) ).
thf(16360,plain,
( ( sk5 != sk1 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[16316,39]) ).
thf(16419,plain,
( ( sk5 != sk1 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= sk5 ) ),
inference(simp,[status(thm)],[16360]) ).
thf(6175,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( r1 @ sk8 @ ( sk9 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6158,60]) ).
thf(6240,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( sk8 != sk1 )
| ( ( sk9 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[6175]) ).
thf(6271,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ( r1 @ ( sk9 @ sk8 ) @ ( sk3 @ ( sk9 @ sk8 ) ) )
| ( sk8 != sk1 ) ),
inference(simp,[status(thm)],[6240]) ).
thf(11691,plain,
( ~ sk12
| sk11
| ( ( p2 @ ( sk6 @ sk5 ) )
!= ( p2 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[11657,27]) ).
thf(11742,plain,
( sk11
| ~ sk12
| ( ( sk6 @ sk5 )
!= sk15 ) ),
inference(simp,[status(thm)],[11691]) ).
thf(8309,plain,
( ( p2 @ sk1 )
| sk11
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[6,8306]) ).
thf(8326,plain,
( ( p2 @ sk1 )
| sk11
| ( ( sk36 @ sk5 )
!= sk16 ) ),
inference(simp,[status(thm)],[8309]) ).
thf(3054,plain,
( ~ sk11
| ( p1 @ sk18 )
| ( ( p1 @ ( sk9 @ sk18 ) )
!= ( p1 @ sk18 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2790]) ).
thf(3059,plain,
( ( p1 @ sk18 )
| ~ sk11
| ( ( sk9 @ sk18 )
!= sk18 ) ),
inference(simp,[status(thm)],[3054]) ).
thf(129,plain,
( ( p2 @ sk1 )
| sk11
| ( ( p2 @ sk16 )
!= ( p2 @ sk1 ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(3686,plain,
( ~ sk12
| sk11
| ( p1 @ sk15 )
| ( ( p1 @ ( sk9 @ sk15 ) )
!= ( p1 @ sk15 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2792]) ).
thf(3692,plain,
( sk11
| ( p1 @ sk15 )
| ~ sk12
| ( ( sk9 @ sk15 )
!= sk15 ) ),
inference(simp,[status(thm)],[3686]) ).
thf(35209,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ ( sk9 @ sk16 ) @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34005,80]) ).
thf(35275,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( sk9 @ sk16 )
!= sk1 )
| ( ( sk13 @ ( sk9 @ sk16 ) @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[35209]) ).
thf(35302,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p1 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
| ( p1 @ ( sk9 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) ) )
| ( ( sk9 @ sk16 )
!= sk1 ) ),
inference(simp,[status(thm)],[35275]) ).
thf(3047,plain,
( ~ sk11
| ( p1 @ sk18 )
| ( p1 @ sk2 )
| ( ( p1 @ ( sk10 @ sk2 ) )
!= ( p1 @ ( sk9 @ sk18 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2790,2076]) ).
thf(3064,plain,
( ( p1 @ sk18 )
| ( p1 @ sk2 )
| ~ sk11
| ( ( sk10 @ sk2 )
!= ( sk9 @ sk18 ) ) ),
inference(simp,[status(thm)],[3047]) ).
thf(7099,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7046,40]) ).
thf(7138,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[7099]) ).
thf(7174,plain,
( ( p3 @ ( sk10 @ sk8 ) )
| ~ ( p3 @ ( sk4 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[7138]) ).
thf(16386,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk33 @ sk20 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,136]) ).
thf(16396,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk33 @ sk20 ) ) ),
inference(simp,[status(thm)],[16386]) ).
thf(23856,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ( sk5 != sk1 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk33 @ sk20 ) )
| ( ( sk31 @ sk20 )
!= ( sk31 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[8852,16396]) ).
thf(23857,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ( sk5 != sk1 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk33 @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[23856:[]]) ).
thf(2814,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ sk20 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19,80]) ).
thf(2817,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ~ sk11
| ~ sk19
| ( sk20 != sk1 )
| ( sk21 != A ) ),
inference(simp,[status(thm)],[2814]) ).
thf(2836,plain,
( ( p1 @ sk21 )
| ( p1 @ ( sk9 @ sk21 ) )
| ~ sk11
| ~ sk19
| ( sk20 != sk1 ) ),
inference(simp,[status(thm)],[2817]) ).
thf(19244,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( ( r1 @ sk2 @ ( sk3 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,109]) ).
thf(19378,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( sk2 != sk1 )
| ( ( sk3 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[19244]) ).
thf(19440,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ~ ( p2 @ ( sk7 @ ( sk3 @ sk2 ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[19378]) ).
thf(22919,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p2 @ ( sk7 @ ( sk3 @ sk2 ) ) )
!= ( p2 @ ( sk6 @ ( sk3 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11394,19440]) ).
thf(22954,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( sk7 @ ( sk3 @ sk2 ) )
!= ( sk6 @ ( sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[22919]) ).
thf(27409,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk36 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,27393]) ).
thf(27428,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk36 @ ( sk7 @ sk5 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[27409]) ).
thf(1058,plain,
( ~ sk11
| ( p3 @ sk18 )
| ( ( p3 @ ( sk4 @ sk18 ) )
!= ( p3 @ ( sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[274,317]) ).
thf(1060,plain,
( ( p3 @ sk18 )
| ~ sk11
| ( ( sk4 @ sk18 )
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[1058]) ).
thf(1050,plain,
( ( p3 @ sk18 )
| ~ sk11
| ( ( p3 @ ( sk3 @ sk18 ) )
!= ( p3 @ sk18 ) ) ),
inference(simp,[status(thm)],[1047]) ).
thf(19482,plain,
( sk11
| ( sk17 != sk16 )
| ( p2 @ sk2 )
| ( ( p2 @ ( sk7 @ sk2 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[145,19280]) ).
thf(19498,plain,
( sk11
| ( p2 @ sk2 )
| ( sk17 != sk16 )
| ( ( sk7 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[19482]) ).
thf(19481,plain,
( sk11
| ( sk16 != sk1 )
| ( p2 @ sk2 )
| ( ( p2 @ ( sk7 @ sk2 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[130,19280]) ).
thf(19491,plain,
( sk11
| ( p2 @ sk2 )
| ( sk16 != sk1 )
| ( ( sk7 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[19481]) ).
thf(507,plain,
! [A: $i] :
( ~ sk12
| sk11
| ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( r1 @ sk1 @ sk15 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,60]) ).
thf(508,plain,
( ~ sk12
| sk11
| ( p3 @ sk15 )
| ( r1 @ sk15 @ ( sk3 @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[507:[bind(A,$thf( sk15 ))]]) ).
thf(2062,plain,
! [A: $i] :
( ~ sk11
| ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( r1 @ sk1 @ sk18 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,75]) ).
thf(2063,plain,
( ~ sk11
| ( p1 @ sk18 )
| ~ ( p1 @ ( sk10 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[2062:[bind(A,$thf( sk18 ))]]) ).
thf(2907,plain,
( ~ sk11
| ( p1 @ sk18 )
| ( ( p1 @ ( sk10 @ sk18 ) )
!= ( p1 @ ( sk9 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2898,2063]) ).
thf(2915,plain,
( ( p1 @ sk18 )
| ~ sk11
| ( ( sk10 @ sk18 )
!= ( sk9 @ sk8 ) ) ),
inference(simp,[status(thm)],[2907]) ).
thf(11674,plain,
( ~ sk11
| ~ ( sk24 @ ( sk6 @ sk5 ) )
| ~ ( sk31 @ ( sk6 @ sk5 ) )
| ( sk18 != sk5 )
| ( ( p2 @ ( sk33 @ ( sk6 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,4810]) ).
thf(11769,plain,
( ~ sk11
| ~ ( sk24 @ ( sk6 @ sk5 ) )
| ~ ( sk31 @ ( sk6 @ sk5 ) )
| ( sk18 != sk5 )
| ( ( sk33 @ ( sk6 @ sk5 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11674]) ).
thf(2066,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( r1 @ sk2 @ ( sk3 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,75]) ).
thf(2098,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( sk2 != sk1 )
| ( ( sk3 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[2066]) ).
thf(2113,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ~ ( p1 @ ( sk10 @ ( sk3 @ sk2 ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[2098]) ).
thf(2905,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p1 @ ( sk10 @ ( sk3 @ sk2 ) ) )
!= ( p1 @ ( sk9 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2898,2113]) ).
thf(2909,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( sk10 @ ( sk3 @ sk2 ) )
!= ( sk9 @ sk8 ) ) ),
inference(simp,[status(thm)],[2905]) ).
thf(7064,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7046,60]) ).
thf(7114,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[7064]) ).
thf(7150,plain,
( ( p3 @ ( sk10 @ sk8 ) )
| ( r1 @ ( sk10 @ sk8 ) @ ( sk3 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[7114]) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ( p2 @ ( sk26 @ D @ C @ B @ A ) )
| ( sk25 @ B )
| ( sk24 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ( p2 @ ( sk26 @ D @ C @ B @ A ) )
| ( sk25 @ B )
| ( sk24 @ A ) ),
inference(simp,[status(thm)],[23]) ).
thf(24967,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( ( sk33 @ sk20 )
!= sk20 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[16316,24954]) ).
thf(24985,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( ( sk33 @ sk20 )
!= sk20 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= sk20 ) ),
inference(simp,[status(thm)],[24967]) ).
thf(359,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk11
| ~ sk19
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ B )
| ( p2 @ C )
| ~ ( p2 @ B )
| ~ ( sk31 @ A )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10,77]) ).
thf(360,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ sk18 )
| ( p2 @ sk20 )
| ~ ( p2 @ sk18 )
| ~ ( sk31 @ A ) ),
inference(pattern_uni,[status(thm)],[359:[bind(A,$thf( A )),bind(B,$thf( sk18 )),bind(C,$thf( sk20 ))]]) ).
thf(13686,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk5 @ ( sk36 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[13679,78]) ).
thf(13793,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( sk18 != sk5 )
| ( A
!= ( sk36 @ sk5 ) ) ),
inference(simp,[status(thm)],[13686]) ).
thf(13842,plain,
( ~ sk11
| ~ ( sk24 @ ( sk36 @ sk5 ) )
| ~ ( p2 @ ( sk33 @ ( sk36 @ sk5 ) ) )
| ~ ( sk31 @ ( sk36 @ sk5 ) )
| ( sk18 != sk5 ) ),
inference(simp,[status(thm)],[13793]) ).
thf(16387,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ ( sk36 @ sk5 ) )
| ~ ( sk31 @ ( sk36 @ sk5 ) )
| ( sk18 != sk5 )
| ( ( p2 @ ( sk33 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,13842]) ).
thf(16405,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ ( sk36 @ sk5 ) )
| ~ ( sk31 @ ( sk36 @ sk5 ) )
| ( sk18 != sk5 )
| ( ( sk33 @ ( sk36 @ sk5 ) )
!= ( sk6 @ ( sk36 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[16387]) ).
thf(25251,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( ( sk33 @ sk20 )
!= ( sk6 @ sk5 ) )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[16316,23824]) ).
thf(25276,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( ( sk33 @ sk20 )
!= ( sk6 @ sk5 ) )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= sk20 ) ),
inference(simp,[status(thm)],[25251]) ).
thf(8270,plain,
( sk11
| ( sk16 != sk1 )
| ( p2 @ sk2 )
| ( ( p2 @ ( sk36 @ sk2 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[130,8135]) ).
thf(8279,plain,
( sk11
| ( p2 @ sk2 )
| ( sk16 != sk1 )
| ( ( sk36 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[8270]) ).
thf(1045,plain,
( ~ sk11
| ( p3 @ sk18 )
| ( ( p3 @ ( sk3 @ sk18 ) )
!= ( p3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[240,31]) ).
thf(1054,plain,
( ( p3 @ sk18 )
| ~ sk11
| ( ( sk3 @ sk18 )
!= sk2 ) ),
inference(simp,[status(thm)],[1045]) ).
thf(10938,plain,
( ( p1 @ sk2 )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p1 @ ( sk10 @ ( sk10 @ sk8 ) ) )
!= ( p1 @ ( sk9 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2805,10934]) ).
thf(10951,plain,
( ( p1 @ sk2 )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ ( sk10 @ sk8 ) )
!= ( sk9 @ sk2 ) ) ),
inference(simp,[status(thm)],[10938]) ).
thf(5929,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,88]) ).
thf(5930,plain,
( ( p1 @ sk5 )
| ( r1 @ sk5 @ ( sk9 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[5929:[bind(A,$thf( sk5 ))]]) ).
thf(19530,plain,
( ( p2 @ sk8 )
| ( ( p2 @ ( sk7 @ sk8 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,19296]) ).
thf(19547,plain,
( ( p2 @ sk8 )
| ( ( sk7 @ sk8 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[19530]) ).
thf(15888,plain,
( ( p1 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p1 @ ( sk9 @ ( sk36 @ sk5 ) ) )
!= ( p1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[13826,50]) ).
thf(15908,plain,
( ( p1 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk9 @ ( sk36 @ sk5 ) )
!= sk8 ) ),
inference(simp,[status(thm)],[15888]) ).
thf(4004,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p1 @ ( sk9 @ ( sk3 @ sk2 ) ) )
!= ( p1 @ ( sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[4001]) ).
thf(4307,plain,
! [A: $i] :
( ~ sk11
| ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk18 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,86]) ).
thf(4308,plain,
( ~ sk11
| ( p2 @ sk18 )
| ( r1 @ sk18 @ ( sk6 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[4307:[bind(A,$thf( sk18 ))]]) ).
thf(7081,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7046,86]) ).
thf(7124,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[7081]) ).
thf(7160,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( r1 @ ( sk10 @ sk8 ) @ ( sk6 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[7124]) ).
thf(8313,plain,
( sk11
| ( sk17 != sk16 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[145,8306]) ).
thf(8322,plain,
( sk11
| ( sk17 != sk16 )
| ( ( sk36 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[8313]) ).
thf(2631,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ ( sk33 @ A ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ A ) ) )
| ~ ( sk31 @ ( sk33 @ A ) )
| ( ( sk32 @ A )
!= sk18 )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,2331]) ).
thf(2632,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ~ ( sk24 @ ( sk33 @ sk20 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk20 ) ) )
| ~ ( sk31 @ ( sk33 @ sk20 ) )
| ( ( sk32 @ sk20 )
!= sk18 ) ),
inference(pattern_uni,[status(thm)],[2631:[bind(A,$thf( sk20 ))]]) ).
thf(2703,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ~ ( sk24 @ ( sk33 @ sk20 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk20 ) ) )
| ( ( sk32 @ sk20 )
!= sk18 )
| ( ( sk31 @ ( sk33 @ sk20 ) )
!= ( sk31 @ sk20 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2632]) ).
thf(2705,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ~ ( sk24 @ ( sk33 @ sk20 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk20 ) ) )
| ( ( sk32 @ sk20 )
!= sk18 )
| ( ( sk33 @ sk20 )
!= sk20 ) ),
inference(simp,[status(thm)],[2703]) ).
thf(2924,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk20 ) ) )
| ( ( sk32 @ sk20 )
!= sk18 )
| ( ( sk33 @ sk20 )
!= sk20 )
| ( ( sk24 @ ( sk33 @ sk20 ) )
!= ( sk24 @ sk20 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2705]) ).
thf(2926,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk20 ) ) )
| ( ( sk32 @ sk20 )
!= sk18 )
| ( ( sk33 @ sk20 )
!= sk20 )
| ( ( sk33 @ sk20 )
!= sk20 ) ),
inference(simp,[status(thm)],[2924]) ).
thf(2927,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk20 ) ) )
| ( ( sk32 @ sk20 )
!= sk18 )
| ( ( sk33 @ sk20 )
!= sk20 ) ),
inference(simp,[status(thm)],[2926]) ).
thf(11704,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ( ( sk32 @ sk20 )
!= sk18 )
| ( ( sk33 @ sk20 )
!= sk20 )
| ( ( p2 @ ( sk33 @ ( sk33 @ sk20 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,2927]) ).
thf(11747,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ( ( sk32 @ sk20 )
!= sk18 )
| ( ( sk33 @ sk20 )
!= sk20 )
| ( ( sk33 @ ( sk33 @ sk20 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11704]) ).
thf(2019,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ ( sk3 @ sk16 ) @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1607,16]) ).
thf(2032,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( sk3 @ sk16 )
!= sk1 )
| ( ( sk13 @ ( sk3 @ sk16 ) @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[2019]) ).
thf(2033,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p3 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
| ( r1 @ ( sk3 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) ) @ ( sk4 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) ) )
| ( ( sk3 @ sk16 )
!= sk1 ) ),
inference(simp,[status(thm)],[2032]) ).
thf(15639,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p2 @ ( sk6 @ ( sk9 @ sk8 ) ) )
!= ( p2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[11364,39]) ).
thf(15707,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( sk6 @ ( sk9 @ sk8 ) )
!= sk5 ) ),
inference(simp,[status(thm)],[15639]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p3 @ A )
| ~ sk11
| ~ ( sk24 @ B )
| ~ ( p2 @ ( sk33 @ B ) )
| ~ ( sk31 @ B )
| ( ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
!= ( r1 @ sk18 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,78]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( p3 @ A )
| ~ ( r1 @ sk1 @ A )
| ~ sk11
| ~ ( sk24 @ B )
| ~ ( p2 @ ( sk33 @ B ) )
| ~ ( sk31 @ B )
| ( ( sk3 @ A )
!= sk18 )
| ( ( sk4 @ A )
!= B ) ),
inference(simp,[status(thm)],[153]) ).
thf(166,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( r1 @ sk1 @ A )
| ~ sk11
| ~ ( sk24 @ ( sk4 @ A ) )
| ~ ( p2 @ ( sk33 @ ( sk4 @ A ) ) )
| ~ ( sk31 @ ( sk4 @ A ) )
| ( ( sk3 @ A )
!= sk18 ) ),
inference(simp,[status(thm)],[161]) ).
thf(33378,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( ( p2 @ ( sk22 @ sk5 ) )
!= ( p2 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[33338,53]) ).
thf(33520,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( ( sk22 @ sk5 )
!= sk21 ) ),
inference(simp,[status(thm)],[33378]) ).
thf(13734,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ sk5 @ ( sk36 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13679,16]) ).
thf(13801,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( sk5 != sk1 )
| ( ( sk36 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[13734]) ).
thf(13849,plain,
( ( p3 @ ( sk36 @ sk5 ) )
| ( r1 @ ( sk3 @ ( sk36 @ sk5 ) ) @ ( sk4 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[13801]) ).
thf(5678,plain,
( sk11
| ( p3 @ sk16 )
| ~ ( p3 @ ( sk4 @ sk16 ) )
| ~ sk12
| ( ( p2 @ sk15 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[322,27]) ).
thf(5715,plain,
( sk11
| ( p3 @ sk16 )
| ~ ( p3 @ ( sk4 @ sk16 ) )
| ~ sk12
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[5678]) ).
thf(2894,plain,
( ( p1 @ sk2 )
| ( ( sk9 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[2885]) ).
thf(7559,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( ( p1 @ ( sk10 @ sk16 ) )
!= ( p1 @ ( sk9 @ sk16 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2801,2073]) ).
thf(7567,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( ( sk10 @ sk16 )
!= ( sk9 @ sk16 ) ) ),
inference(simp,[status(thm)],[7559]) ).
thf(19804,plain,
( ~ sk11
| ( p2 @ sk18 )
| ( ( p2 @ ( sk7 @ sk18 ) )
!= ( p2 @ ( sk6 @ sk18 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11236,19237]) ).
thf(19807,plain,
( ( p2 @ sk18 )
| ~ sk11
| ( ( sk7 @ sk18 )
!= ( sk6 @ sk18 ) ) ),
inference(simp,[status(thm)],[19804]) ).
thf(21455,plain,
( ~ sk12
| sk11
| ( p2 @ sk15 )
| ( ( p2 @ ( sk7 @ sk15 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,19239]) ).
thf(21473,plain,
( sk11
| ( p2 @ sk15 )
| ~ sk12
| ( ( sk7 @ sk15 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[21455]) ).
thf(27114,plain,
( ( p3 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p3 @ ( sk3 @ ( sk7 @ sk5 ) ) )
!= ( p3 @ ( sk4 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21380,547]) ).
thf(27133,plain,
( ( p3 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk3 @ ( sk7 @ sk5 ) )
!= ( sk4 @ sk2 ) ) ),
inference(simp,[status(thm)],[27114]) ).
thf(11696,plain,
( ( p2 @ sk2 )
| ( ( p2 @ ( sk36 @ sk2 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,8135]) ).
thf(11737,plain,
( ( p2 @ sk2 )
| ( ( sk36 @ sk2 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11696]) ).
thf(2937,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( ( p1 @ ( sk9 @ sk16 ) )
!= ( p1 @ sk16 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2801]) ).
thf(2941,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( ( sk9 @ sk16 )
!= sk16 ) ),
inference(simp,[status(thm)],[2937]) ).
thf(253,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ sk20 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19,38]) ).
thf(259,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ~ sk11
| ~ sk19
| ( sk20 != sk1 )
| ( sk21 != A ) ),
inference(simp,[status(thm)],[253]) ).
thf(264,plain,
( ( p3 @ sk21 )
| ( p3 @ ( sk3 @ sk21 ) )
| ~ sk11
| ~ sk19
| ( sk20 != sk1 ) ),
inference(simp,[status(thm)],[259]) ).
thf(11815,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( ( r1 @ sk2 @ ( sk3 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,98]) ).
thf(12025,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( sk2 != sk1 )
| ( ( sk3 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[11815]) ).
thf(12119,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( r1 @ ( sk3 @ sk2 ) @ ( sk36 @ ( sk3 @ sk2 ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[12025]) ).
thf(277,plain,
( ( p3 @ sk8 )
| ( ( p3 @ ( sk3 @ sk8 ) )
!= ( p3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[249,31]) ).
thf(279,plain,
( ( p3 @ sk8 )
| ( ( sk3 @ sk8 )
!= sk2 ) ),
inference(simp,[status(thm)],[277]) ).
thf(22486,plain,
( ( p2 @ sk2 )
| ( sk5 != sk1 )
| ( ( p2 @ ( sk7 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11265,22480]) ).
thf(22530,plain,
( ( p2 @ sk2 )
| ( sk5 != sk1 )
| ( ( sk7 @ ( sk36 @ sk5 ) )
!= ( sk6 @ sk2 ) ) ),
inference(simp,[status(thm)],[22486]) ).
thf(172,plain,
! [A: $i] :
( ( p3 @ sk8 )
| ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ ( sk3 @ sk8 ) @ ( sk4 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[148,16]) ).
thf(174,plain,
! [A: $i] :
( ( p3 @ sk8 )
| ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( sk3 @ sk8 )
!= sk1 )
| ( ( sk4 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[172]) ).
thf(176,plain,
( ( p3 @ sk8 )
| ( p3 @ ( sk4 @ sk8 ) )
| ( r1 @ ( sk3 @ ( sk4 @ sk8 ) ) @ ( sk4 @ ( sk4 @ sk8 ) ) )
| ( ( sk3 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[174]) ).
thf(22931,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p2 @ ( sk7 @ ( sk3 @ sk2 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,19440]) ).
thf(22945,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( sk7 @ ( sk3 @ sk2 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[22931]) ).
thf(15894,plain,
( ( p1 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p1 @ ( sk9 @ ( sk36 @ sk5 ) ) )
!= ( p1 @ ( sk36 @ sk5 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[13826]) ).
thf(15904,plain,
( ( p1 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk9 @ ( sk36 @ sk5 ) )
!= ( sk36 @ sk5 ) ) ),
inference(simp,[status(thm)],[15894]) ).
thf(17427,plain,
( ( p3 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p3 @ ( sk3 @ ( sk36 @ sk5 ) ) )
!= ( p3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[13862,31]) ).
thf(17439,plain,
( ( p3 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk3 @ ( sk36 @ sk5 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[17427]) ).
thf(12991,plain,
( ~ sk11
| ( p2 @ sk18 )
| ~ sk19
| ( ( p2 @ ( sk6 @ sk18 ) )
!= ( p2 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[11236,53]) ).
thf(13060,plain,
( ( p2 @ sk18 )
| ~ sk11
| ~ sk19
| ( ( sk6 @ sk18 )
!= sk21 ) ),
inference(simp,[status(thm)],[12991]) ).
thf(1520,plain,
! [A: $i] :
( ( p2 @ A )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk18 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk1 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[47,637]) ).
thf(1556,plain,
! [A: $i] :
( ( p2 @ A )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk18 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk18 != sk1 )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[1520]) ).
thf(1568,plain,
( ( p2 @ sk5 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk18 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[1556]) ).
thf(2119,plain,
( $false
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk18 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk18 != sk1 ) ),
inference(rewrite,[status(thm)],[1568,39]) ).
thf(2120,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk18 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[2119]) ).
thf(11713,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk18 != sk1 )
| ( ( p2 @ ( sk6 @ sk5 ) )
!= ( p2 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[11657,2120]) ).
thf(11729,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk18 != sk1 )
| ( ( sk6 @ sk5 )
!= sk18 ) ),
inference(simp,[status(thm)],[11713]) ).
thf(5806,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[184,88]) ).
thf(5966,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[5806]) ).
thf(6019,plain,
( ( p1 @ ( sk4 @ sk2 ) )
| ( r1 @ ( sk4 @ sk2 ) @ ( sk9 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[5966]) ).
thf(33388,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk20 )
| ( ( sk6 @ sk5 )
!= sk20 )
| ( ( p2 @ ( sk33 @ sk20 ) )
!= ( p2 @ ( sk22 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33338,24938]) ).
thf(33498,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk20 )
| ( ( sk6 @ sk5 )
!= sk20 )
| ( ( sk33 @ sk20 )
!= ( sk22 @ sk5 ) ) ),
inference(simp,[status(thm)],[33388]) ).
thf(281,plain,
( ( p3 @ sk8 )
| ( ( sk3 @ sk8 )
!= sk8 ) ),
inference(simp,[status(thm)],[278]) ).
thf(11483,plain,
( ( p2 @ sk2 )
| ( ( p2 @ ( sk6 @ sk2 ) )
!= ( p2 @ sk2 ) ) ),
inference(simp,[status(thm)],[11463]) ).
thf(558,plain,
( ( p3 @ sk5 )
| ( p3 @ sk8 )
| ( ( p3 @ ( sk4 @ sk8 ) )
!= ( p3 @ ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[238,328]) ).
thf(562,plain,
( ( p3 @ sk5 )
| ( p3 @ sk8 )
| ( ( sk4 @ sk8 )
!= ( sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[558]) ).
thf(23829,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ~ ( sk24 @ sk8 )
| ~ ( p2 @ ( sk33 @ sk8 ) )
| ( sk18 != sk1 )
| ( ( sk31 @ sk20 )
!= ( sk31 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[8852,118]) ).
thf(23899,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ~ ( sk24 @ sk8 )
| ~ ( p2 @ ( sk33 @ sk8 ) )
| ( sk18 != sk1 )
| ( sk20 != sk8 ) ),
inference(simp,[status(thm)],[23829]) ).
thf(32868,plain,
( ~ sk11
| ~ sk19
| ~ ( p2 @ sk20 )
| ~ ( sk24 @ sk8 )
| ~ ( p2 @ ( sk33 @ sk8 ) )
| ( sk18 != sk1 )
| ( sk20 != sk8 )
| ( ( sk24 @ sk20 )
!= ( sk24 @ sk8 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[23899]) ).
thf(32888,plain,
( ~ sk11
| ~ sk19
| ~ ( p2 @ sk20 )
| ~ ( sk24 @ sk8 )
| ~ ( p2 @ ( sk33 @ sk8 ) )
| ( sk18 != sk1 )
| ( sk20 != sk8 )
| ( sk20 != sk8 ) ),
inference(simp,[status(thm)],[32868]) ).
thf(32901,plain,
( ~ sk11
| ~ sk19
| ~ ( p2 @ sk20 )
| ~ ( sk24 @ sk8 )
| ~ ( p2 @ ( sk33 @ sk8 ) )
| ( sk18 != sk1 )
| ( sk20 != sk8 ) ),
inference(simp,[status(thm)],[32888]) ).
thf(16289,plain,
( ( p2 @ sk8 )
| ( sk5 != sk1 )
| ( ( p2 @ ( sk36 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11275,16274]) ).
thf(16313,plain,
( ( p2 @ sk8 )
| ( sk5 != sk1 )
| ( ( sk36 @ ( sk36 @ sk5 ) )
!= ( sk6 @ sk8 ) ) ),
inference(simp,[status(thm)],[16289]) ).
thf(2878,plain,
( ( p1 @ sk2 )
| ( ( p1 @ ( sk10 @ sk2 ) )
!= ( p1 @ ( sk9 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2805,2076]) ).
thf(2891,plain,
( ( p1 @ sk2 )
| ( ( sk10 @ sk2 )
!= ( sk9 @ sk2 ) ) ),
inference(simp,[status(thm)],[2878]) ).
thf(8290,plain,
( sk11
| ( sk16 != sk1 )
| ( p2 @ sk8 )
| ( ( p2 @ ( sk36 @ sk8 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[130,8143]) ).
thf(8300,plain,
( sk11
| ( p2 @ sk8 )
| ( sk16 != sk1 )
| ( ( sk36 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[8290]) ).
thf(5525,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p3 @ ( sk4 @ ( sk6 @ sk5 ) ) )
!= ( p3 @ ( sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[274,4832]) ).
thf(5539,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk4 @ ( sk6 @ sk5 ) )
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[5525]) ).
thf(11665,plain,
( ~ sk11
| ~ ( sk24 @ ( sk10 @ sk8 ) )
| ~ ( sk31 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk18 )
| ( ( p2 @ ( sk33 @ ( sk10 @ sk8 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,7168]) ).
thf(11765,plain,
( ~ sk11
| ~ ( sk24 @ ( sk10 @ sk8 ) )
| ~ ( sk31 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk18 )
| ( ( sk33 @ ( sk10 @ sk8 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11665]) ).
thf(2629,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ ( sk33 @ A ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ A ) ) )
| ~ ( sk31 @ ( sk33 @ A ) )
| ( ( sk32 @ A )
!= sk18 )
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk1 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[47,2331]) ).
thf(2678,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ ( sk33 @ A ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ A ) ) )
| ~ ( sk31 @ ( sk33 @ A ) )
| ( ( sk32 @ A )
!= sk18 )
| ( sk18 != sk1 )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[2629]) ).
thf(2693,plain,
( ~ sk11
| ~ ( sk24 @ sk5 )
| ~ ( sk31 @ sk5 )
| ~ ( sk24 @ ( sk33 @ sk5 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk5 ) ) )
| ~ ( sk31 @ ( sk33 @ sk5 ) )
| ( ( sk32 @ sk5 )
!= sk18 )
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[2678]) ).
thf(3658,plain,
( ~ sk11
| ~ ( sk24 @ sk5 )
| ~ ( sk31 @ sk5 )
| ~ ( sk24 @ ( sk33 @ sk5 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk5 ) ) )
| ( ( sk32 @ sk5 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk31 @ ( sk33 @ sk5 ) )
!= ( sk31 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2693]) ).
thf(3661,plain,
( ~ sk11
| ~ ( sk24 @ sk5 )
| ~ ( sk31 @ sk5 )
| ~ ( sk24 @ ( sk33 @ sk5 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk5 ) ) )
| ( ( sk32 @ sk5 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk5 )
!= sk5 ) ),
inference(simp,[status(thm)],[3658]) ).
thf(5551,plain,
( ~ sk11
| ~ ( sk24 @ sk5 )
| ~ ( sk31 @ sk5 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk5 ) ) )
| ( ( sk32 @ sk5 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk5 )
!= sk5 )
| ( ( sk24 @ ( sk33 @ sk5 ) )
!= ( sk24 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3661]) ).
thf(5554,plain,
( ~ sk11
| ~ ( sk24 @ sk5 )
| ~ ( sk31 @ sk5 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk5 ) ) )
| ( ( sk32 @ sk5 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk5 )
!= sk5 )
| ( ( sk33 @ sk5 )
!= sk5 ) ),
inference(simp,[status(thm)],[5551]) ).
thf(5556,plain,
( ~ sk11
| ~ ( sk24 @ sk5 )
| ~ ( sk31 @ sk5 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk5 ) ) )
| ( ( sk32 @ sk5 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk5 )
!= sk5 ) ),
inference(simp,[status(thm)],[5554]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ~ ( sk25 @ B )
| ~ ( p2 @ ( sk28 @ B @ A ) )
| ( sk24 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ~ ( sk25 @ B )
| ~ ( p2 @ ( sk28 @ B @ A ) )
| ( sk24 @ A ) ),
inference(simp,[status(thm)],[65]) ).
thf(8310,plain,
( sk11
| ~ sk12
| ( sk16 != sk15 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[128,8306]) ).
thf(8318,plain,
( sk11
| ~ sk12
| ( sk16 != sk15 )
| ( ( sk36 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[8310]) ).
thf(177,plain,
! [A: $i] :
( ( p3 @ sk5 )
| ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ ( sk3 @ sk5 ) @ ( sk4 @ sk5 ) )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[150,78]) ).
thf(179,plain,
! [A: $i] :
( ( p3 @ sk5 )
| ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( sk3 @ sk5 )
!= sk18 )
| ( ( sk4 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[177]) ).
thf(181,plain,
( ( p3 @ sk5 )
| ~ sk11
| ~ ( sk24 @ ( sk4 @ sk5 ) )
| ~ ( p2 @ ( sk33 @ ( sk4 @ sk5 ) ) )
| ~ ( sk31 @ ( sk4 @ sk5 ) )
| ( ( sk3 @ sk5 )
!= sk18 ) ),
inference(simp,[status(thm)],[179]) ).
thf(18509,plain,
( ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p1 @ ( sk10 @ ( sk10 @ sk8 ) ) )
!= ( p1 @ ( sk9 @ ( sk10 @ sk8 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[18493,10934]) ).
thf(18519,plain,
( ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ ( sk10 @ sk8 ) )
!= ( sk9 @ ( sk10 @ sk8 ) ) ) ),
inference(simp,[status(thm)],[18509]) ).
thf(19578,plain,
( ( sk5 != sk1 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk7 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,19567]) ).
thf(19609,plain,
( ( sk5 != sk1 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk7 @ sk5 ) ) ),
inference(simp,[status(thm)],[19578]) ).
thf(2344,plain,
( ( ( sk3 @ sk2 )
!= sk1 )
| ( p3 @ sk8 )
| ( ( p3 @ ( sk4 @ sk8 ) )
!= ( p3 @ ( sk3 @ ( sk4 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2341,328]) ).
thf(2358,plain,
( ( p3 @ sk8 )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ sk8 )
!= ( sk3 @ ( sk4 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[2344]) ).
thf(23650,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p2 @ sk2 )
| ( ( p2 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
!= ( p2 @ ( sk7 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[23387,19280]) ).
thf(23751,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p2 @ sk2 )
| ( ( sk13 @ ( sk9 @ sk16 ) @ sk16 )
!= ( sk7 @ sk2 ) ) ),
inference(simp,[status(thm)],[23650]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p3 @ A )
| ( p3 @ B )
| ~ ( p3 @ ( sk4 @ B ) )
| ( ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,40]) ).
thf(343,plain,
! [B: $i,A: $i] :
( ( p3 @ A )
| ( p3 @ B )
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ ( sk4 @ B ) )
| ( ( sk3 @ A )
!= sk1 )
| ( ( sk4 @ A )
!= B ) ),
inference(simp,[status(thm)],[330]) ).
thf(350,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk4 @ A ) )
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ ( sk4 @ ( sk4 @ A ) ) )
| ( ( sk3 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[343]) ).
thf(217,plain,
( sk11
| ( sk16 != sk1 )
| ~ sk12
| ( ( p2 @ sk15 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[130,27]) ).
thf(219,plain,
( sk11
| ( sk16 != sk1 )
| ~ sk12
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[217]) ).
thf(19586,plain,
( sk11
| ( sk16 != sk5 )
| ( ( p2 @ ( sk7 @ sk5 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[127,19567]) ).
thf(19606,plain,
( sk11
| ( sk16 != sk5 )
| ( ( sk7 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[19586]) ).
thf(3710,plain,
( ~ sk11
| ~ sk19
| ( p2 @ sk20 )
| ( ( p2 @ ( sk22 @ sk20 ) )
!= ( p2 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[2950,53]) ).
thf(3764,plain,
( ( p2 @ sk20 )
| ~ sk11
| ~ sk19
| ( ( sk22 @ sk20 )
!= sk21 ) ),
inference(simp,[status(thm)],[3710]) ).
thf(1041,plain,
( ~ sk11
| ( p3 @ sk18 )
| ( p3 @ sk5 )
| ( ( p3 @ ( sk4 @ sk5 ) )
!= ( p3 @ ( sk3 @ sk18 ) ) ) ),
inference(paramod_ordered,[status(thm)],[240,314]) ).
thf(1048,plain,
( ( p3 @ sk18 )
| ( p3 @ sk5 )
| ~ sk11
| ( ( sk4 @ sk5 )
!= ( sk3 @ sk18 ) ) ),
inference(simp,[status(thm)],[1041]) ).
thf(24895,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ ( sk33 @ sk20 ) )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[16316,23885]) ).
thf(24951,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ ( sk33 @ sk20 ) )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= sk20 ) ),
inference(simp,[status(thm)],[24895]) ).
thf(11675,plain,
( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[11657,8306]) ).
thf(11733,plain,
( ( sk36 @ sk5 )
!= ( sk6 @ sk5 ) ),
inference(simp,[status(thm)],[11675]) ).
thf(731,plain,
( sk11
| ~ sk12
| ( sk16 != sk15 )
| ( ( p2 @ sk5 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[128,39]) ).
thf(737,plain,
( sk11
| ~ sk12
| ( sk16 != sk15 )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[731]) ).
thf(2863,plain,
( ( p1 @ sk5 )
| ~ sk11
| ( p1 @ sk18 )
| ( ( p1 @ ( sk10 @ sk18 ) )
!= ( p1 @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2782,2063]) ).
thf(2871,plain,
( ( p1 @ sk5 )
| ( p1 @ sk18 )
| ~ sk11
| ( ( sk10 @ sk18 )
!= ( sk9 @ sk5 ) ) ),
inference(simp,[status(thm)],[2863]) ).
thf(8271,plain,
( sk11
| ( sk17 != sk16 )
| ( p2 @ sk2 )
| ( ( p2 @ ( sk36 @ sk2 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[145,8135]) ).
thf(8276,plain,
( sk11
| ( p2 @ sk2 )
| ( sk17 != sk16 )
| ( ( sk36 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[8271]) ).
thf(11398,plain,
( ( p2 @ sk2 )
| ( p2 @ sk1 )
| sk11
| ( ( p2 @ ( sk6 @ sk2 ) )
!= ( p2 @ sk17 ) ) ),
inference(paramod_ordered,[status(thm)],[11265,69]) ).
thf(11487,plain,
( ( p2 @ sk2 )
| ( p2 @ sk1 )
| sk11
| ( ( sk6 @ sk2 )
!= sk17 ) ),
inference(simp,[status(thm)],[11398]) ).
thf(269,plain,
( ( p3 @ sk5 )
| ( ( p3 @ ( sk3 @ sk5 ) )
!= ( p3 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[238]) ).
thf(271,plain,
( ( p3 @ sk5 )
| ( ( p3 @ ( sk3 @ sk5 ) )
!= ( p3 @ sk5 ) ) ),
inference(simp,[status(thm)],[269]) ).
thf(8167,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( ( r1 @ sk8 @ ( sk9 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6158,91]) ).
thf(8205,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk36 @ A ) )
| ( sk8 != sk1 )
| ( ( sk9 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[8167]) ).
thf(8232,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ~ ( p2 @ ( sk36 @ ( sk9 @ sk8 ) ) )
| ( sk8 != sk1 ) ),
inference(simp,[status(thm)],[8205]) ).
thf(15668,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p2 @ ( sk36 @ ( sk9 @ sk8 ) ) )
!= ( p2 @ ( sk6 @ ( sk9 @ sk8 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11364,8232]) ).
thf(15713,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( sk36 @ ( sk9 @ sk8 ) )
!= ( sk6 @ ( sk9 @ sk8 ) ) ) ),
inference(simp,[status(thm)],[15668]) ).
thf(2881,plain,
( ( p1 @ sk2 )
| ( p1 @ sk5 )
| ( ( p1 @ ( sk10 @ sk5 ) )
!= ( p1 @ ( sk9 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2805,2056]) ).
thf(2896,plain,
( ( p1 @ sk2 )
| ( p1 @ sk5 )
| ( ( sk10 @ sk5 )
!= ( sk9 @ sk2 ) ) ),
inference(simp,[status(thm)],[2881]) ).
thf(207,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk16 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,16]) ).
thf(208,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( r1 @ ( sk3 @ sk16 ) @ ( sk4 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( sk16 ))]]) ).
thf(5509,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p3 @ ( sk3 @ ( sk6 @ sk5 ) ) )
!= ( p3 @ ( sk6 @ sk5 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4831]) ).
thf(5511,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk3 @ ( sk6 @ sk5 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[5509]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ sk11
| sk19
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ~ sk11
| sk19
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ A ) ),
inference(simp,[status(thm)],[26]) ).
thf(13752,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( r1 @ sk5 @ ( sk36 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13679,75]) ).
thf(13809,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( sk5 != sk1 )
| ( ( sk36 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[13752]) ).
thf(13856,plain,
( ( p1 @ ( sk36 @ sk5 ) )
| ~ ( p1 @ ( sk10 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[13809]) ).
thf(2771,plain,
( sk11
| ( p3 @ sk16 )
| ( sk5 != sk1 )
| ( ( p3 @ ( sk3 @ sk16 ) )
!= ( p3 @ sk16 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[304]) ).
thf(2780,plain,
( sk11
| ( p3 @ sk16 )
| ( sk5 != sk1 )
| ( ( sk3 @ sk16 )
!= sk16 ) ),
inference(simp,[status(thm)],[2771]) ).
thf(22981,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p2 @ ( sk7 @ ( sk9 @ sk8 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,19443]) ).
thf(23004,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( sk7 @ ( sk9 @ sk8 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[22981]) ).
thf(2864,plain,
( ( p1 @ sk5 )
| ( ( p1 @ ( sk9 @ sk5 ) )
!= ( p1 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2782]) ).
thf(2874,plain,
( ( p1 @ sk5 )
| ( ( p1 @ ( sk9 @ sk5 ) )
!= ( p1 @ sk5 ) ) ),
inference(simp,[status(thm)],[2864]) ).
thf(27404,plain,
( ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk36 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,27393]) ).
thf(27424,plain,
( ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk36 @ ( sk7 @ sk5 ) )
!= ( sk6 @ ( sk36 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[27404]) ).
thf(154,plain,
! [A: $i] :
( ~ sk12
| sk11
| ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk15 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,16]) ).
thf(155,plain,
( ~ sk12
| sk11
| ( p3 @ sk15 )
| ( r1 @ ( sk3 @ sk15 ) @ ( sk4 @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[154:[bind(A,$thf( sk15 ))]]) ).
thf(19573,plain,
( ( p2 @ sk2 )
| ( ( p2 @ ( sk7 @ sk5 ) )
!= ( p2 @ ( sk6 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11265,19567]) ).
thf(19616,plain,
( ( p2 @ sk2 )
| ( ( sk7 @ sk5 )
!= ( sk6 @ sk2 ) ) ),
inference(simp,[status(thm)],[19573]) ).
thf(19583,plain,
( sk11
| ( sk16 != sk1 )
| ( ( p2 @ ( sk7 @ sk5 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[130,19567]) ).
thf(19599,plain,
( sk11
| ( sk16 != sk1 )
| ( ( sk7 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[19583]) ).
thf(310,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,40]) ).
thf(336,plain,
! [A: $i] :
( ( p3 @ A )
| ~ sk11
| ~ sk19
| ~ ( p3 @ ( sk4 @ A ) )
| ( sk18 != sk1 )
| ( sk20 != A ) ),
inference(simp,[status(thm)],[310]) ).
thf(345,plain,
( ( p3 @ sk20 )
| ~ sk11
| ~ sk19
| ~ ( p3 @ ( sk4 @ sk20 ) )
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[336]) ).
thf(33447,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ( ( p2 @ ( sk33 @ sk20 ) )
!= ( p2 @ ( sk22 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33338,136]) ).
thf(33528,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ( ( sk33 @ sk20 )
!= ( sk22 @ sk5 ) ) ),
inference(simp,[status(thm)],[33447]) ).
thf(3053,plain,
( ~ sk11
| ( p1 @ sk18 )
| ( ( p1 @ ( sk10 @ sk18 ) )
!= ( p1 @ ( sk9 @ sk18 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2790,2063]) ).
thf(3055,plain,
( ( p1 @ sk18 )
| ~ sk11
| ( ( sk10 @ sk18 )
!= ( sk9 @ sk18 ) ) ),
inference(simp,[status(thm)],[3053]) ).
thf(548,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( ( p3 @ ( sk4 @ sk2 ) )
!= ( p3 @ ( sk3 @ sk16 ) ) ) ),
inference(paramod_ordered,[status(thm)],[244,547]) ).
thf(552,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( ( sk4 @ sk2 )
!= ( sk3 @ sk16 ) ) ),
inference(simp,[status(thm)],[548]) ).
thf(13924,plain,
( ~ sk12
| sk11
| ( p2 @ sk15 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ ( sk6 @ sk15 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11238,8306]) ).
thf(13980,plain,
( sk11
| ( p2 @ sk15 )
| ~ sk12
| ( ( sk36 @ sk5 )
!= ( sk6 @ sk15 ) ) ),
inference(simp,[status(thm)],[13924]) ).
thf(4756,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ sk5 @ ( sk6 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4719,16]) ).
thf(4786,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[4756]) ).
thf(4818,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ( r1 @ ( sk3 @ ( sk6 @ sk5 ) ) @ ( sk4 @ ( sk6 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[4786]) ).
thf(8268,plain,
( sk11
| ~ sk12
| ( sk16 != sk15 )
| ( p2 @ sk2 )
| ( ( p2 @ ( sk36 @ sk2 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[128,8135]) ).
thf(8281,plain,
( sk11
| ( p2 @ sk2 )
| ~ sk12
| ( sk16 != sk15 )
| ( ( sk36 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[8268]) ).
thf(13069,plain,
( ( p2 @ sk18 )
| ~ sk11
| ( ( p2 @ ( sk6 @ sk18 ) )
!= ( p2 @ sk18 ) ) ),
inference(simp,[status(thm)],[13031]) ).
thf(1056,plain,
( ( p3 @ sk5 )
| ~ sk11
| ( p3 @ sk18 )
| ( ( p3 @ ( sk4 @ sk18 ) )
!= ( p3 @ ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[238,317]) ).
thf(1061,plain,
( ( p3 @ sk5 )
| ( p3 @ sk18 )
| ~ sk11
| ( ( sk4 @ sk18 )
!= ( sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[1056]) ).
thf(2904,plain,
( ( p1 @ sk5 )
| ( ( p1 @ ( sk10 @ sk5 ) )
!= ( p1 @ ( sk9 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2898,2056]) ).
thf(2911,plain,
( ( p1 @ sk5 )
| ( ( sk10 @ sk5 )
!= ( sk9 @ sk8 ) ) ),
inference(simp,[status(thm)],[2904]) ).
thf(6659,plain,
! [A: $i] :
( ~ sk11
| ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( ( r1 @ sk1 @ sk18 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,89]) ).
thf(6660,plain,
( ~ sk11
| ( p1 @ sk18 )
| ( r1 @ ( sk9 @ sk18 ) @ ( sk10 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[6659:[bind(A,$thf( sk18 ))]]) ).
thf(665,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p2 @ A )
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk2 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( ( r1 @ sk20 @ sk21 )
!= ( r1 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19,635]) ).
thf(671,plain,
! [A: $i] :
( ( p2 @ A )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk2 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk20 != sk2 )
| ( sk21 != A ) ),
inference(simp,[status(thm)],[665]) ).
thf(685,plain,
( ( p2 @ sk21 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk2 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk20 != sk2 ) ),
inference(simp,[status(thm)],[671]) ).
thf(2044,plain,
( ~ sk12
| sk11
| ( p3 @ sk15 )
| ( ( p3 @ ( sk3 @ sk15 ) )
!= ( p3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[242,31]) ).
thf(2051,plain,
( sk11
| ( p3 @ sk15 )
| ~ sk12
| ( ( sk3 @ sk15 )
!= sk2 ) ),
inference(simp,[status(thm)],[2044]) ).
thf(2612,plain,
( ( p3 @ sk8 )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p3 @ ( sk4 @ ( sk4 @ sk2 ) ) )
!= ( p3 @ ( sk3 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[249,2610]) ).
thf(2620,plain,
( ( p3 @ sk8 )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ ( sk4 @ sk2 ) )
!= ( sk3 @ sk8 ) ) ),
inference(simp,[status(thm)],[2612]) ).
thf(19574,plain,
( ( p2 @ sk1 )
| sk11
| ( ( p2 @ ( sk7 @ sk5 ) )
!= ( p2 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[6,19567]) ).
thf(19602,plain,
( ( p2 @ sk1 )
| sk11
| ( ( sk7 @ sk5 )
!= sk16 ) ),
inference(simp,[status(thm)],[19574]) ).
thf(11690,plain,
( ~ sk11
| ~ ( sk24 @ sk8 )
| ~ ( sk31 @ sk8 )
| ( sk18 != sk1 )
| ( ( p2 @ ( sk33 @ sk8 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,118]) ).
thf(11775,plain,
( ~ sk11
| ~ ( sk24 @ sk8 )
| ~ ( sk31 @ sk8 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk8 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11690]) ).
thf(2653,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ ( sk33 @ A ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ A ) ) )
| ~ ( sk31 @ ( sk33 @ A ) )
| ( ( sk32 @ A )
!= sk18 )
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[7,2331]) ).
thf(2668,plain,
! [A: $i] :
( ~ sk11
| ~ ( sk24 @ A )
| ~ ( sk31 @ A )
| ~ ( sk24 @ ( sk33 @ A ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ A ) ) )
| ~ ( sk31 @ ( sk33 @ A ) )
| ( ( sk32 @ A )
!= sk18 )
| ( sk18 != sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[2653]) ).
thf(2683,plain,
( ~ sk11
| ~ ( sk24 @ sk2 )
| ~ ( sk31 @ sk2 )
| ~ ( sk24 @ ( sk33 @ sk2 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk2 ) ) )
| ~ ( sk31 @ ( sk33 @ sk2 ) )
| ( ( sk32 @ sk2 )
!= sk18 )
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[2668]) ).
thf(3023,plain,
( ~ sk11
| ~ ( sk24 @ sk2 )
| ~ ( sk31 @ sk2 )
| ~ ( sk24 @ ( sk33 @ sk2 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk2 ) ) )
| ( ( sk32 @ sk2 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk31 @ ( sk33 @ sk2 ) )
!= ( sk31 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2683]) ).
thf(3025,plain,
( ~ sk11
| ~ ( sk24 @ sk2 )
| ~ ( sk31 @ sk2 )
| ~ ( sk24 @ ( sk33 @ sk2 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk2 ) ) )
| ( ( sk32 @ sk2 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[3023]) ).
thf(3670,plain,
( ~ sk11
| ~ ( sk24 @ sk2 )
| ~ ( sk31 @ sk2 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk2 ) ) )
| ( ( sk32 @ sk2 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk2 )
!= sk2 )
| ( ( sk24 @ ( sk33 @ sk2 ) )
!= ( sk24 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3025]) ).
thf(3672,plain,
( ~ sk11
| ~ ( sk24 @ sk2 )
| ~ ( sk31 @ sk2 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk2 ) ) )
| ( ( sk32 @ sk2 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk2 )
!= sk2 )
| ( ( sk33 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[3670]) ).
thf(3674,plain,
( ~ sk11
| ~ ( sk24 @ sk2 )
| ~ ( sk31 @ sk2 )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk2 ) ) )
| ( ( sk32 @ sk2 )
!= sk18 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[3672]) ).
thf(306,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( ( p3 @ ( sk3 @ sk16 ) )
!= ( p3 @ sk16 ) ) ),
inference(simp,[status(thm)],[303]) ).
thf(559,plain,
( ( p3 @ sk8 )
| ( ( p3 @ ( sk4 @ sk8 ) )
!= ( p3 @ ( sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[274,328]) ).
thf(563,plain,
( ( p3 @ sk8 )
| ( ( sk4 @ sk8 )
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[559]) ).
thf(5473,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p1 @ ( sk10 @ sk8 ) )
!= ( p1 @ ( sk9 @ ( sk6 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4815,2118]) ).
thf(5495,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk10 @ sk8 )
!= ( sk9 @ ( sk6 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[5473]) ).
thf(19232,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[184,109]) ).
thf(19331,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk7 @ A ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[19232]) ).
thf(19409,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ~ ( p2 @ ( sk7 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[19331]) ).
thf(12984,plain,
( ~ sk11
| ( p2 @ sk18 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ ( sk6 @ sk18 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11236,8306]) ).
thf(13085,plain,
( ( p2 @ sk18 )
| ~ sk11
| ( ( sk36 @ sk5 )
!= ( sk6 @ sk18 ) ) ),
inference(simp,[status(thm)],[12984]) ).
thf(15812,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p2 @ ( sk6 @ ( sk3 @ sk2 ) ) )
!= ( p2 @ ( sk3 @ sk2 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11394]) ).
thf(15829,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( sk6 @ ( sk3 @ sk2 ) )
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[15812]) ).
thf(3681,plain,
( ~ sk12
| sk11
| ( p1 @ sk15 )
| ( ( p1 @ ( sk9 @ sk15 ) )
!= ( p1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[2792,50]) ).
thf(3687,plain,
( sk11
| ( p1 @ sk15 )
| ~ sk12
| ( ( sk9 @ sk15 )
!= sk8 ) ),
inference(simp,[status(thm)],[3681]) ).
thf(2968,plain,
! [A: $i] :
( ~ sk11
| ( p2 @ A )
| ( p2 @ ( sk22 @ A ) )
| ~ sk19
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[7,81]) ).
thf(2984,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk22 @ A ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[2968]) ).
thf(2999,plain,
( ( p2 @ sk2 )
| ( p2 @ ( sk22 @ sk2 ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[2984]) ).
thf(16332,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ sk5 )
| ~ ( sk31 @ sk5 )
| ( sk18 != sk1 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk33 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,121]) ).
thf(16408,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ sk5 )
| ~ ( sk31 @ sk5 )
| ( sk18 != sk1 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk33 @ sk5 ) ) ),
inference(simp,[status(thm)],[16332]) ).
thf(160,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ sk20 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19,16]) ).
thf(162,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ~ sk11
| ~ sk19
| ( sk20 != sk1 )
| ( sk21 != A ) ),
inference(simp,[status(thm)],[160]) ).
thf(167,plain,
( ( p3 @ sk21 )
| ( r1 @ ( sk3 @ sk21 ) @ ( sk4 @ sk21 ) )
| ~ sk11
| ~ sk19
| ( sk20 != sk1 ) ),
inference(simp,[status(thm)],[162]) ).
thf(19533,plain,
( ( p2 @ sk8 )
| ( ( p2 @ ( sk7 @ sk8 ) )
!= ( p2 @ ( sk6 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11275,19296]) ).
thf(19542,plain,
( ( p2 @ sk8 )
| ( ( sk7 @ sk8 )
!= ( sk6 @ sk8 ) ) ),
inference(simp,[status(thm)],[19533]) ).
thf(62,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ( p2 @ A )
| ( r1 @ ( sk22 @ A ) @ ( sk23 @ A ) )
| ~ sk19 ),
inference(cnf,[status(esa)],[5]) ).
thf(112,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ( p2 @ A )
| ( r1 @ ( sk22 @ A ) @ ( sk23 @ A ) )
| ~ sk19 ),
inference(simp,[status(thm)],[62]) ).
thf(5682,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( ( p3 @ ( sk4 @ sk16 ) )
!= ( p3 @ ( sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[274,322]) ).
thf(5710,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( ( sk4 @ sk16 )
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[5682]) ).
thf(549,plain,
( ( p3 @ sk8 )
| ( ( p3 @ ( sk4 @ sk2 ) )
!= ( p3 @ ( sk3 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[249,547]) ).
thf(553,plain,
( ( p3 @ sk8 )
| ( ( sk4 @ sk2 )
!= ( sk3 @ sk8 ) ) ),
inference(simp,[status(thm)],[549]) ).
thf(11662,plain,
( ~ sk11
| ~ ( sk24 @ sk2 )
| ~ ( sk31 @ sk2 )
| ( sk18 != sk1 )
| ( ( p2 @ ( sk33 @ sk2 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,115]) ).
thf(11758,plain,
( ~ sk11
| ~ ( sk24 @ sk2 )
| ~ ( sk31 @ sk2 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk2 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11662]) ).
thf(11888,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk36 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,98]) ).
thf(11889,plain,
( ( p2 @ sk2 )
| ( r1 @ sk2 @ ( sk36 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[11888:[bind(A,$thf( sk2 ))]]) ).
thf(19522,plain,
( ( p2 @ sk1 )
| sk11
| ( p2 @ sk8 )
| ( ( p2 @ ( sk7 @ sk8 ) )
!= ( p2 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[6,19296]) ).
thf(19563,plain,
( ( p2 @ sk1 )
| sk11
| ( p2 @ sk8 )
| ( ( sk7 @ sk8 )
!= sk16 ) ),
inference(simp,[status(thm)],[19522]) ).
thf(486,plain,
( ( p3 @ sk5 )
| ( ( p3 @ ( sk4 @ sk5 ) )
!= ( p3 @ ( sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[274,314]) ).
thf(490,plain,
( ( p3 @ sk5 )
| ( ( sk4 @ sk5 )
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[486]) ).
thf(2903,plain,
( ( p1 @ ( sk9 @ sk8 ) )
!= ( p1 @ sk8 ) ),
inference(paramod_ordered,[status(thm)],[2898,50]) ).
thf(2914,plain,
( ( sk9 @ sk8 )
!= sk8 ),
inference(simp,[status(thm)],[2903]) ).
thf(7563,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( ( p1 @ ( sk10 @ sk16 ) )
!= ( p1 @ ( sk9 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2898,2073]) ).
thf(7571,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( ( sk10 @ sk16 )
!= ( sk9 @ sk8 ) ) ),
inference(simp,[status(thm)],[7563]) ).
thf(2976,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p2 @ A )
| ( p2 @ ( sk22 @ A ) )
| ( ( r1 @ sk20 @ sk21 )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19,81]) ).
thf(2979,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk22 @ A ) )
| ~ sk11
| ~ sk19
| ( sk20 != sk18 )
| ( sk21 != A ) ),
inference(simp,[status(thm)],[2976]) ).
thf(2994,plain,
( ( p2 @ sk21 )
| ( p2 @ ( sk22 @ sk21 ) )
| ~ sk11
| ~ sk19
| ( sk20 != sk18 ) ),
inference(simp,[status(thm)],[2979]) ).
thf(13698,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( ( r1 @ sk5 @ ( sk36 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13679,89]) ).
thf(13804,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( sk5 != sk1 )
| ( ( sk36 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[13698]) ).
thf(13852,plain,
( ( p1 @ ( sk36 @ sk5 ) )
| ( r1 @ ( sk9 @ ( sk36 @ sk5 ) ) @ ( sk10 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[13804]) ).
thf(645,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p2 @ A )
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk2 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,635]) ).
thf(666,plain,
! [A: $i] :
( ( p2 @ A )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk2 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk18 != sk2 )
| ( sk20 != A ) ),
inference(simp,[status(thm)],[645]) ).
thf(680,plain,
( ( p2 @ sk20 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk21 )
| ~ ( p2 @ sk2 )
| ~ ( sk31 @ sk21 )
| ( sk20 != sk18 )
| ( ( sk33 @ sk21 )
!= sk1 )
| ( sk18 != sk2 ) ),
inference(simp,[status(thm)],[666]) ).
thf(8308,plain,
( ~ sk11
| ~ sk19
| ( p2 @ sk20 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ ( sk22 @ sk20 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2950,8306]) ).
thf(8323,plain,
( ( p2 @ sk20 )
| ~ sk11
| ~ sk19
| ( ( sk36 @ sk5 )
!= ( sk22 @ sk20 ) ) ),
inference(simp,[status(thm)],[8308]) ).
thf(2932,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( ( p1 @ ( sk9 @ sk16 ) )
!= ( p1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[2801,50]) ).
thf(2942,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( ( sk9 @ sk16 )
!= sk8 ) ),
inference(simp,[status(thm)],[2932]) ).
thf(22491,plain,
( ( sk5 != sk1 )
| ( ( p2 @ ( sk7 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,22480]) ).
thf(22515,plain,
( ( sk5 != sk1 )
| ( ( sk7 @ ( sk36 @ sk5 ) )
!= ( sk6 @ ( sk36 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[22491]) ).
thf(12,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ( r1 @ D @ ( sk26 @ D @ C @ B @ A ) )
| ( sk25 @ B )
| ( sk24 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(95,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ( r1 @ D @ ( sk26 @ D @ C @ B @ A ) )
| ( sk25 @ B )
| ( sk24 @ A ) ),
inference(simp,[status(thm)],[12]) ).
thf(11708,plain,
( ( p2 @ sk8 )
| ( ( p2 @ ( sk36 @ sk8 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,8143]) ).
thf(11743,plain,
( ( p2 @ sk8 )
| ( ( sk36 @ sk8 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11708]) ).
thf(27202,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( p2 @ sk8 )
| ( ( p2 @ ( sk7 @ sk8 ) )
!= ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27146,19296]) ).
thf(27338,plain,
( ( p2 @ sk8 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk7 @ sk8 )
!= ( sk6 @ ( sk7 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[27202]) ).
thf(3058,plain,
( ( p1 @ sk18 )
| ~ sk11
| ( ( p1 @ ( sk9 @ sk18 ) )
!= ( p1 @ sk18 ) ) ),
inference(simp,[status(thm)],[3054]) ).
thf(27228,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ ( sk7 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[27146,19567]) ).
thf(27285,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk6 @ ( sk7 @ sk5 ) )
!= ( sk7 @ sk5 ) ) ),
inference(simp,[status(thm)],[27228]) ).
thf(11666,plain,
( ~ sk11
| ~ ( sk24 @ ( sk4 @ sk2 ) )
| ~ ( sk31 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk18 )
| ( ( p2 @ ( sk33 @ ( sk4 @ sk2 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,189]) ).
thf(11726,plain,
( ~ sk11
| ~ ( sk24 @ ( sk4 @ sk2 ) )
| ~ ( sk31 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk18 )
| ( ( sk33 @ ( sk4 @ sk2 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11666]) ).
thf(9464,plain,
( ( p1 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p1 @ ( sk9 @ ( sk4 @ sk2 ) ) )
!= ( p1 @ ( sk4 @ sk2 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2849]) ).
thf(9467,plain,
( ( p1 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk9 @ ( sk4 @ sk2 ) )
!= ( sk4 @ sk2 ) ) ),
inference(simp,[status(thm)],[9464]) ).
thf(15915,plain,
( ( p3 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p3 @ ( sk4 @ ( sk36 @ sk5 ) ) )
!= ( p3 @ ( sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[274,13835]) ).
thf(15924,plain,
( ( p3 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk4 @ ( sk36 @ sk5 ) )
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[15915]) ).
thf(19198,plain,
( ~ sk11
| ~ sk19
| ( p2 @ sk20 )
| ( ( p2 @ ( sk23 @ sk20 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,18783]) ).
thf(19211,plain,
( ( p2 @ sk20 )
| ~ sk11
| ~ sk19
| ( ( sk23 @ sk20 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[19198]) ).
thf(4376,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk8 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,86]) ).
thf(4377,plain,
( ( p2 @ sk8 )
| ( r1 @ sk8 @ ( sk6 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[4376:[bind(A,$thf( sk8 ))]]) ).
thf(8288,plain,
( sk11
| ~ sk12
| ( sk16 != sk15 )
| ( p2 @ sk8 )
| ( ( p2 @ ( sk36 @ sk8 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[128,8143]) ).
thf(8295,plain,
( sk11
| ( p2 @ sk8 )
| ~ sk12
| ( sk16 != sk15 )
| ( ( sk36 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[8288]) ).
thf(235,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,38]) ).
thf(258,plain,
! [A: $i] :
( ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( sk20 != A ) ),
inference(simp,[status(thm)],[235]) ).
thf(263,plain,
( ( p3 @ sk20 )
| ( p3 @ ( sk3 @ sk20 ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[258]) ).
thf(2884,plain,
( ( p1 @ sk2 )
| ~ sk11
| ( p1 @ sk18 )
| ( ( p1 @ ( sk10 @ sk18 ) )
!= ( p1 @ ( sk9 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2805,2063]) ).
thf(2888,plain,
( ( p1 @ sk2 )
| ( p1 @ sk18 )
| ~ sk11
| ( ( sk10 @ sk18 )
!= ( sk9 @ sk2 ) ) ),
inference(simp,[status(thm)],[2884]) ).
thf(3691,plain,
( sk11
| ( p1 @ sk15 )
| ~ sk12
| ( ( p1 @ ( sk9 @ sk15 ) )
!= ( p1 @ sk15 ) ) ),
inference(simp,[status(thm)],[3686]) ).
thf(178,plain,
! [A: $i] :
( ( p3 @ sk5 )
| ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( r1 @ ( sk3 @ sk5 ) @ ( sk4 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[150,16]) ).
thf(180,plain,
! [A: $i] :
( ( p3 @ sk5 )
| ( p3 @ A )
| ( r1 @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( sk3 @ sk5 )
!= sk1 )
| ( ( sk4 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[178]) ).
thf(182,plain,
( ( p3 @ sk5 )
| ( p3 @ ( sk4 @ sk5 ) )
| ( r1 @ ( sk3 @ ( sk4 @ sk5 ) ) @ ( sk4 @ ( sk4 @ sk5 ) ) )
| ( ( sk3 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[180]) ).
thf(3998,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p1 @ ( sk10 @ ( sk3 @ sk2 ) ) )
!= ( p1 @ ( sk9 @ ( sk3 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2846,2113]) ).
thf(4003,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( sk10 @ ( sk3 @ sk2 ) )
!= ( sk9 @ ( sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[3998]) ).
thf(27170,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( ( sk33 @ sk20 )
!= sk20 )
| ( ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[27146,24954]) ).
thf(27261,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( ( sk33 @ sk20 )
!= sk20 )
| ( ( sk6 @ ( sk7 @ sk5 ) )
!= sk20 ) ),
inference(simp,[status(thm)],[27170]) ).
thf(13942,plain,
( ~ sk12
| sk11
| ( p2 @ sk15 )
| ( ( p2 @ ( sk36 @ sk15 ) )
!= ( p2 @ ( sk6 @ sk15 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11238,8107]) ).
thf(13978,plain,
( sk11
| ( p2 @ sk15 )
| ~ sk12
| ( ( sk36 @ sk15 )
!= ( sk6 @ sk15 ) ) ),
inference(simp,[status(thm)],[13942]) ).
thf(24527,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ ( sk6 @ ( sk10 @ sk8 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11356,8306]) ).
thf(24678,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk36 @ sk5 )
!= ( sk6 @ ( sk10 @ sk8 ) ) ) ),
inference(simp,[status(thm)],[24527]) ).
thf(15614,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ ( sk6 @ ( sk9 @ sk8 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11364,8306]) ).
thf(15676,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( sk36 @ sk5 )
!= ( sk6 @ ( sk9 @ sk8 ) ) ) ),
inference(simp,[status(thm)],[15614]) ).
thf(27210,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[27146,39]) ).
thf(27306,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk6 @ ( sk7 @ sk5 ) )
!= sk5 ) ),
inference(simp,[status(thm)],[27210]) ).
thf(6714,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,89]) ).
thf(6715,plain,
( ( p1 @ sk2 )
| ( r1 @ ( sk9 @ sk2 ) @ ( sk10 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[6714:[bind(A,$thf( sk2 ))]]) ).
thf(1043,plain,
( ~ sk11
| ( p3 @ sk18 )
| ( ( p3 @ ( sk4 @ sk2 ) )
!= ( p3 @ ( sk3 @ sk18 ) ) ) ),
inference(paramod_ordered,[status(thm)],[240,547]) ).
thf(1053,plain,
( ( p3 @ sk18 )
| ~ sk11
| ( ( sk4 @ sk2 )
!= ( sk3 @ sk18 ) ) ),
inference(simp,[status(thm)],[1043]) ).
thf(197,plain,
( sk11
| ( sk16 != sk5 )
| ~ sk12
| ( ( p2 @ sk15 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[127,27]) ).
thf(199,plain,
( sk11
| ( sk16 != sk5 )
| ~ sk12
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[197]) ).
thf(33409,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( ( p2 @ ( sk22 @ sk5 ) )
!= ( p2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[33338,39]) ).
thf(33466,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( ( sk22 @ sk5 )
!= sk5 ) ),
inference(simp,[status(thm)],[33409]) ).
thf(16333,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ ( sk6 @ sk5 ) )
| ~ ( sk31 @ ( sk6 @ sk5 ) )
| ( sk18 != sk5 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk33 @ ( sk6 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,4810]) ).
thf(16416,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ ( sk6 @ sk5 ) )
| ~ ( sk31 @ ( sk6 @ sk5 ) )
| ( sk18 != sk5 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk33 @ ( sk6 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[16333]) ).
thf(16280,plain,
( ( p2 @ sk2 )
| ( sk5 != sk1 )
| ( ( p2 @ ( sk36 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11265,16274]) ).
thf(16295,plain,
( ( p2 @ sk2 )
| ( sk5 != sk1 )
| ( ( sk36 @ ( sk36 @ sk5 ) )
!= ( sk6 @ sk2 ) ) ),
inference(simp,[status(thm)],[16280]) ).
thf(501,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,60]) ).
thf(502,plain,
( ( p3 @ sk5 )
| ( r1 @ sk5 @ ( sk3 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[501:[bind(A,$thf( sk5 ))]]) ).
thf(21256,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21155,75]) ).
thf(21300,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk10 @ A ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk7 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[21256]) ).
thf(21356,plain,
( ( p1 @ ( sk7 @ sk5 ) )
| ~ ( p1 @ ( sk10 @ ( sk7 @ sk5 ) ) )
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[21300]) ).
thf(32933,plain,
( ~ sk11
| ~ sk19
| ~ ( p2 @ sk20 )
| ~ ( sk24 @ sk8 )
| ( sk18 != sk1 )
| ( sk20 != sk8 )
| ( ( p2 @ ( sk33 @ sk8 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,32901]) ).
thf(32965,plain,
( ~ sk11
| ~ sk19
| ~ ( p2 @ sk20 )
| ~ ( sk24 @ sk8 )
| ( sk18 != sk1 )
| ( sk20 != sk8 )
| ( ( sk33 @ sk8 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[32933]) ).
thf(11578,plain,
( ( p2 @ sk8 )
| ( ( p2 @ ( sk36 @ sk8 ) )
!= ( p2 @ ( sk6 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11275,8143]) ).
thf(11622,plain,
( ( p2 @ sk8 )
| ( ( sk36 @ sk8 )
!= ( sk6 @ sk8 ) ) ),
inference(simp,[status(thm)],[11578]) ).
thf(315,plain,
! [A: $i] :
( ( p3 @ sk8 )
| ~ ( r1 @ sk1 @ A )
| ( p3 @ A )
| ( ( p3 @ ( sk4 @ A ) )
!= ( p3 @ ( sk3 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[249,40]) ).
thf(338,plain,
! [A: $i] :
( ( p3 @ sk8 )
| ( p3 @ A )
| ~ ( r1 @ sk1 @ A )
| ( ( sk4 @ A )
!= ( sk3 @ sk8 ) ) ),
inference(simp,[status(thm)],[315]) ).
thf(26369,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p2 @ sk2 )
| ( ( p2 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
!= ( p2 @ ( sk7 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[25992,19280]) ).
thf(26455,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p2 @ sk2 )
| ( ( sk13 @ ( sk3 @ sk16 ) @ sk16 )
!= ( sk7 @ sk2 ) ) ),
inference(simp,[status(thm)],[26369]) ).
thf(26758,plain,
( ( p3 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p3 @ ( sk4 @ ( sk7 @ sk5 ) ) )
!= ( p3 @ ( sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[274,21370]) ).
thf(26771,plain,
( ( p3 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk4 @ ( sk7 @ sk5 ) )
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[26758]) ).
thf(11449,plain,
( ( p2 @ sk2 )
| ( p2 @ sk8 )
| ( ( p2 @ ( sk36 @ sk8 ) )
!= ( p2 @ ( sk6 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11265,8143]) ).
thf(11475,plain,
( ( p2 @ sk2 )
| ( p2 @ sk8 )
| ( ( sk36 @ sk8 )
!= ( sk6 @ sk2 ) ) ),
inference(simp,[status(thm)],[11449]) ).
thf(15828,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p2 @ ( sk6 @ ( sk3 @ sk2 ) ) )
!= ( p2 @ ( sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[15812]) ).
thf(11683,plain,
( ~ sk11
| ( p2 @ sk18 )
| ( ( p2 @ ( sk36 @ sk18 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,8105]) ).
thf(11749,plain,
( ( p2 @ sk18 )
| ~ sk11
| ( ( sk36 @ sk18 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11683]) ).
thf(19531,plain,
( sk11
| ( sk16 != sk1 )
| ( p2 @ sk8 )
| ( ( p2 @ ( sk7 @ sk8 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[130,19296]) ).
thf(19549,plain,
( sk11
| ( p2 @ sk8 )
| ( sk16 != sk1 )
| ( ( sk7 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[19531]) ).
thf(2345,plain,
( ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p3 @ ( sk3 @ ( sk4 @ sk2 ) ) )
!= ( p3 @ ( sk4 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2341,547]) ).
thf(2357,plain,
( ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk3 @ ( sk4 @ sk2 ) )
!= ( sk4 @ sk2 ) ) ),
inference(simp,[status(thm)],[2345]) ).
thf(1042,plain,
( ~ sk11
| ( p3 @ sk18 )
| ( p3 @ sk8 )
| ( ( p3 @ ( sk4 @ sk8 ) )
!= ( p3 @ ( sk3 @ sk18 ) ) ) ),
inference(paramod_ordered,[status(thm)],[240,328]) ).
thf(1052,plain,
( ( p3 @ sk18 )
| ( p3 @ sk8 )
| ~ sk11
| ( ( sk4 @ sk8 )
!= ( sk3 @ sk18 ) ) ),
inference(simp,[status(thm)],[1042]) ).
thf(22498,plain,
( ( p2 @ sk8 )
| ( sk5 != sk1 )
| ( ( p2 @ ( sk7 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11275,22480]) ).
thf(22526,plain,
( ( p2 @ sk8 )
| ( sk5 != sk1 )
| ( ( sk7 @ ( sk36 @ sk5 ) )
!= ( sk6 @ sk8 ) ) ),
inference(simp,[status(thm)],[22498]) ).
thf(171,plain,
! [A: $i] :
( ( p3 @ sk8 )
| ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( r1 @ ( sk3 @ sk8 ) @ ( sk4 @ sk8 ) )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[148,78]) ).
thf(173,plain,
! [A: $i] :
( ( p3 @ sk8 )
| ~ sk11
| ~ ( sk24 @ A )
| ~ ( p2 @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( ( sk3 @ sk8 )
!= sk18 )
| ( ( sk4 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[171]) ).
thf(175,plain,
( ( p3 @ sk8 )
| ~ sk11
| ~ ( sk24 @ ( sk4 @ sk8 ) )
| ~ ( p2 @ ( sk33 @ ( sk4 @ sk8 ) ) )
| ~ ( sk31 @ ( sk4 @ sk8 ) )
| ( ( sk3 @ sk8 )
!= sk18 ) ),
inference(simp,[status(thm)],[173]) ).
thf(15752,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p2 @ ( sk36 @ ( sk3 @ sk2 ) ) )
!= ( p2 @ ( sk6 @ ( sk3 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11394,8229]) ).
thf(15822,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( sk36 @ ( sk3 @ sk2 ) )
!= ( sk6 @ ( sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[15752]) ).
thf(17421,plain,
( ( p3 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p3 @ ( sk3 @ ( sk36 @ sk5 ) ) )
!= ( p3 @ ( sk4 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[13862,547]) ).
thf(17438,plain,
( ( p3 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk3 @ ( sk36 @ sk5 ) )
!= ( sk4 @ sk2 ) ) ),
inference(simp,[status(thm)],[17421]) ).
thf(2956,plain,
! [A: $i] :
( ~ sk11
| ( p2 @ A )
| ( p2 @ ( sk22 @ A ) )
| ~ sk19
| ( ( r1 @ sk18 @ A )
!= ( r1 @ sk1 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[57,81]) ).
thf(2992,plain,
! [A: $i] :
( ( p2 @ A )
| ( p2 @ ( sk22 @ A ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( A != sk18 ) ),
inference(simp,[status(thm)],[2956]) ).
thf(3007,plain,
( ( p2 @ sk18 )
| ( p2 @ ( sk22 @ sk18 ) )
| ~ sk11
| ~ sk19
| ( sk18 != sk1 ) ),
inference(simp,[status(thm)],[2992]) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ~ ( sk25 @ B )
| ~ ( r1 @ ( sk28 @ B @ A ) @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ( p2 @ C )
| ( sk24 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(72,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ~ ( sk25 @ B )
| ~ ( r1 @ ( sk28 @ B @ A ) @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ( p2 @ C )
| ( sk24 @ A ) ),
inference(simp,[status(thm)],[66]) ).
thf(24601,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p2 @ ( sk6 @ ( sk10 @ sk8 ) ) )
!= ( p2 @ ( sk10 @ sk8 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11356]) ).
thf(24665,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk6 @ ( sk10 @ sk8 ) )
!= ( sk10 @ sk8 ) ) ),
inference(simp,[status(thm)],[24601]) ).
thf(13,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ( r1 @ ( sk26 @ D @ C @ B @ A ) @ ( sk27 @ D @ C @ B @ A ) )
| ( sk25 @ B )
| ( sk24 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(87,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ( r1 @ ( sk26 @ D @ C @ B @ A ) @ ( sk27 @ D @ C @ B @ A ) )
| ( sk25 @ B )
| ( sk24 @ A ) ),
inference(simp,[status(thm)],[13]) ).
thf(469,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ ( sk3 @ sk16 ) @ ( sk4 @ sk16 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[208,38]) ).
thf(479,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( sk3 @ sk16 )
!= sk1 )
| ( ( sk4 @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[469]) ).
thf(482,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p3 @ ( sk4 @ sk16 ) )
| ( p3 @ ( sk3 @ ( sk4 @ sk16 ) ) )
| ( ( sk3 @ sk16 )
!= sk1 ) ),
inference(simp,[status(thm)],[479]) ).
thf(27467,plain,
( ( p2 @ sk8 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk7 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11275,27447]) ).
thf(27491,plain,
( ( p2 @ sk8 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk7 @ ( sk7 @ sk5 ) )
!= ( sk6 @ sk8 ) ) ),
inference(simp,[status(thm)],[27467]) ).
thf(5510,plain,
( ( p3 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p3 @ ( sk3 @ ( sk6 @ sk5 ) ) )
!= ( p3 @ ( sk6 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[5509]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ sk12
| ~ ( r1 @ sk15 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ A )
| sk11 ),
inference(cnf,[status(esa)],[5]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ~ sk12
| ~ ( r1 @ sk15 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ A )
| sk11 ),
inference(simp,[status(thm)],[55]) ).
thf(2857,plain,
( ( p1 @ sk5 )
| ( p1 @ sk2 )
| ( ( p1 @ ( sk10 @ sk2 ) )
!= ( p1 @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2782,2076]) ).
thf(2865,plain,
( ( p1 @ sk5 )
| ( p1 @ sk2 )
| ( ( sk10 @ sk2 )
!= ( sk9 @ sk5 ) ) ),
inference(simp,[status(thm)],[2857]) ).
thf(2875,plain,
( ( p1 @ sk5 )
| ( ( sk9 @ sk5 )
!= sk5 ) ),
inference(simp,[status(thm)],[2864]) ).
thf(2611,plain,
( ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p3 @ ( sk4 @ ( sk4 @ sk2 ) ) )
!= ( p3 @ ( sk3 @ ( sk4 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2341,2610]) ).
thf(2626,plain,
( ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ ( sk4 @ sk2 ) )
!= ( sk3 @ ( sk4 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[2611]) ).
thf(2348,plain,
( ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p3 @ ( sk3 @ ( sk4 @ sk2 ) ) )
!= ( p3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2341,31]) ).
thf(2352,plain,
( ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk3 @ ( sk4 @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[2348]) ).
thf(6757,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,89]) ).
thf(6758,plain,
( ( p1 @ sk5 )
| ( r1 @ ( sk9 @ sk5 ) @ ( sk10 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[6757:[bind(A,$thf( sk5 ))]]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ~ ( sk25 @ B )
| ( r1 @ B @ ( sk28 @ B @ A ) )
| ( sk24 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ~ ( sk25 @ B )
| ( r1 @ B @ ( sk28 @ B @ A ) )
| ( sk24 @ A ) ),
inference(simp,[status(thm)],[63]) ).
thf(19484,plain,
( sk11
| ( sk16 != sk5 )
| ( p2 @ sk2 )
| ( ( p2 @ ( sk7 @ sk2 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[127,19280]) ).
thf(19493,plain,
( sk11
| ( p2 @ sk2 )
| ( sk16 != sk5 )
| ( ( sk7 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[19484]) ).
thf(33366,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ ( sk22 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33338,8306]) ).
thf(33521,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( ( sk36 @ sk5 )
!= ( sk22 @ sk5 ) ) ),
inference(simp,[status(thm)],[33366]) ).
thf(3049,plain,
( ~ sk11
| ( p1 @ sk18 )
| ( ( p1 @ ( sk9 @ sk18 ) )
!= ( p1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[2790,50]) ).
thf(3056,plain,
( ( p1 @ sk18 )
| ~ sk11
| ( ( sk9 @ sk18 )
!= sk8 ) ),
inference(simp,[status(thm)],[3049]) ).
thf(19572,plain,
( ~ sk11
| ~ sk19
| ( p2 @ sk20 )
| ( ( p2 @ ( sk22 @ sk20 ) )
!= ( p2 @ ( sk7 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2950,19567]) ).
thf(19593,plain,
( ( p2 @ sk20 )
| ~ sk11
| ~ sk19
| ( ( sk22 @ sk20 )
!= ( sk7 @ sk5 ) ) ),
inference(simp,[status(thm)],[19572]) ).
thf(27183,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ~ sk11
| ~ sk19
| ( ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[27146,53]) ).
thf(27258,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ~ sk11
| ~ sk19
| ( ( sk6 @ ( sk7 @ sk5 ) )
!= sk21 ) ),
inference(simp,[status(thm)],[27183]) ).
thf(16365,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ ( sk3 @ sk2 ) )
| ~ ( sk31 @ ( sk3 @ sk2 ) )
| ( sk18 != sk2 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk33 @ ( sk3 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,848]) ).
thf(16397,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ ( sk3 @ sk2 ) )
| ~ ( sk31 @ ( sk3 @ sk2 ) )
| ( sk18 != sk2 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk33 @ ( sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[16365]) ).
thf(11672,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p2 @ ( sk36 @ ( sk3 @ sk2 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,8229]) ).
thf(11745,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( sk36 @ ( sk3 @ sk2 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11672]) ).
thf(11437,plain,
( ( p2 @ sk2 )
| ( ( p2 @ ( sk36 @ sk2 ) )
!= ( p2 @ ( sk6 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11265,8135]) ).
thf(11514,plain,
( ( p2 @ sk2 )
| ( ( sk36 @ sk2 )
!= ( sk6 @ sk2 ) ) ),
inference(simp,[status(thm)],[11437]) ).
thf(1055,plain,
( ( p3 @ sk8 )
| ~ sk11
| ( p3 @ sk18 )
| ( ( p3 @ ( sk4 @ sk18 ) )
!= ( p3 @ ( sk3 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[249,317]) ).
thf(1062,plain,
( ( p3 @ sk8 )
| ( p3 @ sk18 )
| ~ sk11
| ( ( sk4 @ sk18 )
!= ( sk3 @ sk8 ) ) ),
inference(simp,[status(thm)],[1055]) ).
thf(6210,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( ( r1 @ sk8 @ ( sk9 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6158,40]) ).
thf(6224,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( p3 @ ( sk4 @ A ) )
| ( sk8 != sk1 )
| ( ( sk9 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[6210]) ).
thf(6254,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ~ ( p3 @ ( sk4 @ ( sk9 @ sk8 ) ) )
| ( sk8 != sk1 ) ),
inference(simp,[status(thm)],[6224]) ).
thf(7988,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p3 @ ( sk4 @ ( sk9 @ sk8 ) ) )
!= ( p3 @ ( sk3 @ ( sk9 @ sk8 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6259,6254]) ).
thf(7996,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( sk4 @ ( sk9 @ sk8 ) )
!= ( sk3 @ ( sk9 @ sk8 ) ) ) ),
inference(simp,[status(thm)],[7988]) ).
thf(27399,plain,
( ( p2 @ sk2 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk36 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11265,27393]) ).
thf(27430,plain,
( ( p2 @ sk2 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk36 @ ( sk7 @ sk5 ) )
!= ( sk6 @ sk2 ) ) ),
inference(simp,[status(thm)],[27399]) ).
thf(11423,plain,
( ( p2 @ sk2 )
| ~ sk11
| ~ sk19
| ( ( p2 @ ( sk6 @ sk2 ) )
!= ( p2 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[11265,53]) ).
thf(11469,plain,
( ( p2 @ sk2 )
| ~ sk11
| ~ sk19
| ( ( sk6 @ sk2 )
!= sk21 ) ),
inference(simp,[status(thm)],[11423]) ).
thf(7958,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p3 @ ( sk4 @ ( sk9 @ sk8 ) ) )
!= ( p3 @ ( sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[274,6254]) ).
thf(7964,plain,
( ( p3 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( sk4 @ ( sk9 @ sk8 ) )
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[7958]) ).
thf(19534,plain,
( sk11
| ( sk16 != sk5 )
| ( p2 @ sk8 )
| ( ( p2 @ ( sk7 @ sk8 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[127,19296]) ).
thf(19554,plain,
( sk11
| ( p2 @ sk8 )
| ( sk16 != sk5 )
| ( ( sk7 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[19534]) ).
thf(2928,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( ( p1 @ ( sk10 @ sk8 ) )
!= ( p1 @ ( sk9 @ sk16 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2801,2118]) ).
thf(2944,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( ( sk10 @ sk8 )
!= ( sk9 @ sk16 ) ) ),
inference(simp,[status(thm)],[2928]) ).
thf(18505,plain,
( ( ( sk9 @ sk8 )
!= sk1 )
| ( p1 @ sk5 )
| ( ( p1 @ ( sk9 @ ( sk10 @ sk8 ) ) )
!= ( p1 @ ( sk10 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[18493,2056]) ).
thf(18518,plain,
( ( p1 @ sk5 )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk9 @ ( sk10 @ sk8 ) )
!= ( sk10 @ sk5 ) ) ),
inference(simp,[status(thm)],[18505]) ).
thf(13699,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( r1 @ sk5 @ ( sk36 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13679,60]) ).
thf(13797,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( sk5 != sk1 )
| ( ( sk36 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[13699]) ).
thf(13846,plain,
( ( p3 @ ( sk36 @ sk5 ) )
| ( r1 @ ( sk36 @ sk5 ) @ ( sk3 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[13797]) ).
thf(24971,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( ( sk33 @ sk20 )
!= sk20 )
| ( ( p2 @ ( sk6 @ sk5 ) )
!= ( p2 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[11657,24954]) ).
thf(24984,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( ( sk33 @ sk20 )
!= sk20 )
| ( ( sk6 @ sk5 )
!= sk20 ) ),
inference(simp,[status(thm)],[24971]) ).
thf(8292,plain,
( sk11
| ( sk16 != sk5 )
| ( p2 @ sk8 )
| ( ( p2 @ ( sk36 @ sk8 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[127,8143]) ).
thf(8304,plain,
( sk11
| ( p2 @ sk8 )
| ( sk16 != sk5 )
| ( ( sk36 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[8292]) ).
thf(2195,plain,
( ~ sk12
| sk11
| ( p3 @ sk15 )
| ( ( p3 @ ( sk4 @ sk15 ) )
!= ( p3 @ ( sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[274,319]) ).
thf(2198,plain,
( sk11
| ( p3 @ sk15 )
| ~ sk12
| ( ( sk4 @ sk15 )
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[2195]) ).
thf(4318,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk2 @ ( sk3 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,86]) ).
thf(4440,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( sk2 != sk1 )
| ( ( sk3 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[4318]) ).
thf(4478,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( r1 @ ( sk3 @ sk2 ) @ ( sk6 @ ( sk3 @ sk2 ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[4440]) ).
thf(32960,plain,
( ~ sk11
| ~ sk19
| ~ ( p2 @ sk20 )
| ~ ( sk24 @ sk8 )
| ( sk18 != sk1 )
| ( sk20 != sk8 )
| ( ( p2 @ ( sk33 @ sk8 ) )
!= ( p2 @ sk20 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[32901]) ).
thf(32984,plain,
( ~ sk11
| ~ sk19
| ~ ( p2 @ sk20 )
| ~ ( sk24 @ sk8 )
| ( sk18 != sk1 )
| ( sk20 != sk8 )
| ( ( sk33 @ sk8 )
!= sk20 ) ),
inference(simp,[status(thm)],[32960]) ).
thf(19570,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p2 @ ( sk7 @ sk5 ) )
!= ( p2 @ ( sk6 @ ( sk3 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11394,19567]) ).
thf(19600,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( sk7 @ sk5 )
!= ( sk6 @ ( sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[19570]) ).
thf(492,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[184,60]) ).
thf(527,plain,
! [A: $i] :
( ( p3 @ A )
| ( r1 @ A @ ( sk3 @ A ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[492]) ).
thf(535,plain,
( ( p3 @ ( sk4 @ sk2 ) )
| ( r1 @ ( sk4 @ sk2 ) @ ( sk3 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[527]) ).
thf(36522,plain,
( $false
| ( r1 @ ( sk4 @ sk2 ) @ ( sk3 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[535,547]) ).
thf(36523,plain,
( ( r1 @ ( sk4 @ sk2 ) @ ( sk3 @ ( sk4 @ sk2 ) ) )
| ( ( sk3 @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[36522]) ).
thf(19577,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p2 @ ( sk6 @ ( sk9 @ sk8 ) ) )
!= ( p2 @ ( sk7 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11364,19567]) ).
thf(19605,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( sk6 @ ( sk9 @ sk8 ) )
!= ( sk7 @ sk5 ) ) ),
inference(simp,[status(thm)],[19577]) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ B )
| ( p2 @ C )
| ~ ( p2 @ B )
| ~ ( sk31 @ A )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[47,77]) ).
thf(374,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ sk1 )
| ( p2 @ sk5 )
| ~ ( p2 @ sk1 )
| ~ ( sk31 @ A ) ),
inference(pattern_uni,[status(thm)],[373:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk5 ))]]) ).
thf(36056,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ sk1 )
| $false
| ~ ( p2 @ sk1 )
| ~ ( sk31 @ A ) ),
inference(rewrite,[status(thm)],[374,39]) ).
thf(36057,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ sk1 )
| ~ ( p2 @ sk1 )
| ~ ( sk31 @ A ) ),
inference(simp,[status(thm)],[36056]) ).
thf(36070,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ sk1 )
| ~ ( p2 @ sk1 )
| ~ ( sk31 @ A )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,36057]) ).
thf(36071,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( r1 @ ( sk33 @ sk20 ) @ sk1 )
| ~ ( p2 @ sk1 )
| ~ ( sk31 @ sk20 ) ),
inference(pattern_uni,[status(thm)],[36070:[bind(A,$thf( sk20 ))]]) ).
thf(24710,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ ( sk6 @ ( sk4 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11365,8306]) ).
thf(24829,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk36 @ sk5 )
!= ( sk6 @ ( sk4 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[24710]) ).
thf(14563,plain,
( ~ sk11
| ~ ( sk24 @ ( sk36 @ sk5 ) )
| ~ ( sk31 @ ( sk36 @ sk5 ) )
| ( sk18 != sk5 )
| ( ( p2 @ ( sk33 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,13842]) ).
thf(14575,plain,
( ~ sk11
| ~ ( sk24 @ ( sk36 @ sk5 ) )
| ~ ( sk31 @ ( sk36 @ sk5 ) )
| ( sk18 != sk5 )
| ( ( sk33 @ ( sk36 @ sk5 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[14563]) ).
thf(19472,plain,
( ( p2 @ sk1 )
| sk11
| ( p2 @ sk2 )
| ( ( p2 @ ( sk7 @ sk2 ) )
!= ( p2 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[6,19280]) ).
thf(19505,plain,
( ( p2 @ sk1 )
| sk11
| ( p2 @ sk2 )
| ( ( sk7 @ sk2 )
!= sk16 ) ),
inference(simp,[status(thm)],[19472]) ).
thf(272,plain,
( ( p3 @ sk5 )
| ( ( sk3 @ sk5 )
!= sk5 ) ),
inference(simp,[status(thm)],[269]) ).
thf(7051,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ ( sk9 @ sk8 ) @ ( sk10 @ sk8 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7046,88]) ).
thf(7116,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk10 @ sk8 )
!= A ) ),
inference(simp,[status(thm)],[7051]) ).
thf(7152,plain,
( ( p1 @ ( sk10 @ sk8 ) )
| ( r1 @ ( sk10 @ sk8 ) @ ( sk9 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[7116]) ).
thf(39946,plain,
( $false
| ( r1 @ ( sk10 @ sk8 ) @ ( sk9 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(rewrite,[status(thm)],[7152,2118]) ).
thf(39947,plain,
( ( r1 @ ( sk10 @ sk8 ) @ ( sk9 @ ( sk10 @ sk8 ) ) )
| ( ( sk9 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[39946]) ).
thf(2613,plain,
( ( p3 @ sk5 )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p3 @ ( sk4 @ ( sk4 @ sk2 ) ) )
!= ( p3 @ ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[238,2610]) ).
thf(2623,plain,
( ( p3 @ sk5 )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ ( sk4 @ sk2 ) )
!= ( sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[2613]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ B @ ( sk34 @ B @ A ) )
| ~ ( sk31 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ B @ ( sk34 @ B @ A ) )
| ~ ( sk31 @ A ) ),
inference(simp,[status(thm)],[46]) ).
thf(18979,plain,
( ( p3 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p3 @ ( sk3 @ ( sk10 @ sk8 ) ) )
!= ( p3 @ ( sk10 @ sk8 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[7172]) ).
thf(18991,plain,
( ( p3 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk3 @ ( sk10 @ sk8 ) )
!= ( sk10 @ sk8 ) ) ),
inference(simp,[status(thm)],[18979]) ).
thf(6702,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( ( r1 @ sk1 @ sk16 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,89]) ).
thf(6703,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( r1 @ ( sk9 @ sk16 ) @ ( sk10 @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[6702:[bind(A,$thf( sk16 ))]]) ).
thf(15780,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p2 @ ( sk6 @ ( sk3 @ sk2 ) ) )
!= ( p2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[11394,39]) ).
thf(15813,plain,
( ( p2 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( sk6 @ ( sk3 @ sk2 ) )
!= sk5 ) ),
inference(simp,[status(thm)],[15780]) ).
thf(8312,plain,
( sk11
| ( sk16 != sk1 )
| ( ( p2 @ ( sk36 @ sk5 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[130,8306]) ).
thf(8324,plain,
( sk11
| ( sk16 != sk1 )
| ( ( sk36 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[8312]) ).
thf(30,plain,
( ( p2 @ sk1 )
| ( r1 @ sk16 @ sk17 )
| sk11 ),
inference(cnf,[status(esa)],[5]) ).
thf(19532,plain,
( sk11
| ( sk17 != sk16 )
| ( p2 @ sk8 )
| ( ( p2 @ ( sk7 @ sk8 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[145,19296]) ).
thf(19564,plain,
( sk11
| ( p2 @ sk8 )
| ( sk17 != sk16 )
| ( ( sk7 @ sk8 )
!= sk1 ) ),
inference(simp,[status(thm)],[19532]) ).
thf(17396,plain,
( ( p1 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p1 @ ( sk10 @ ( sk36 @ sk5 ) ) )
!= ( p1 @ ( sk9 @ ( sk36 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13826,13856]) ).
thf(17414,plain,
( ( p1 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk10 @ ( sk36 @ sk5 ) )
!= ( sk9 @ ( sk36 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[17396]) ).
thf(26240,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( p2 @ ( sk7 @ ( sk4 @ sk2 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,19409]) ).
thf(26253,plain,
( ( p2 @ ( sk4 @ sk2 ) )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk7 @ ( sk4 @ sk2 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[26240]) ).
thf(11612,plain,
( ( p2 @ sk8 )
| ( ( p2 @ ( sk6 @ sk8 ) )
!= ( p2 @ sk8 ) ) ),
inference(simp,[status(thm)],[11592]) ).
thf(3045,plain,
( ~ sk11
| ( p1 @ sk18 )
| ( ( p1 @ ( sk10 @ sk8 ) )
!= ( p1 @ ( sk9 @ sk18 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2790,2118]) ).
thf(3062,plain,
( ( p1 @ sk18 )
| ~ sk11
| ( ( sk10 @ sk8 )
!= ( sk9 @ sk18 ) ) ),
inference(simp,[status(thm)],[3045]) ).
thf(730,plain,
( sk11
| ~ sk12
| ( sk16 != sk15 )
| ( ( p2 @ sk15 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[128,27]) ).
thf(735,plain,
( sk11
| ~ sk12
| ( sk16 != sk15 )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[730]) ).
thf(27181,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( sk5 != sk1 )
| ( ( p2 @ ( sk36 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27146,16274]) ).
thf(27307,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( sk5 != sk1 )
| ( ( sk36 @ ( sk36 @ sk5 ) )
!= ( sk6 @ ( sk7 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[27181]) ).
thf(250,plain,
! [A: $i] :
( ( p3 @ sk5 )
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( r1 @ ( sk3 @ sk5 ) @ ( sk4 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[150,38]) ).
thf(257,plain,
! [A: $i] :
( ( p3 @ sk5 )
| ( p3 @ A )
| ( p3 @ ( sk3 @ A ) )
| ( ( sk3 @ sk5 )
!= sk1 )
| ( ( sk4 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[250]) ).
thf(262,plain,
( ( p3 @ sk5 )
| ( p3 @ ( sk4 @ sk5 ) )
| ( p3 @ ( sk3 @ ( sk4 @ sk5 ) ) )
| ( ( sk3 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[257]) ).
thf(23672,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p2 @ sk8 )
| ( ( p2 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
!= ( p2 @ ( sk7 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[23387,19296]) ).
thf(23750,plain,
( ( p2 @ sk1 )
| sk11
| ( p1 @ sk16 )
| ( p2 @ ( sk9 @ sk16 ) )
| sk12
| ( p2 @ sk8 )
| ( ( sk13 @ ( sk9 @ sk16 ) @ sk16 )
!= ( sk7 @ sk8 ) ) ),
inference(simp,[status(thm)],[23672]) ).
thf(33427,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( ( p2 @ ( sk22 @ sk5 ) )
!= ( p2 @ ( sk7 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33338,19567]) ).
thf(33481,plain,
( ~ sk11
| ~ sk19
| ( sk18 != sk1 )
| ( ( sk22 @ sk5 )
!= ( sk7 @ sk5 ) ) ),
inference(simp,[status(thm)],[33427]) ).
thf(2050,plain,
( sk11
| ( p3 @ sk15 )
| ~ sk12
| ( ( sk3 @ sk15 )
!= sk15 ) ),
inference(simp,[status(thm)],[2047]) ).
thf(41239,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ~ ( r1 @ ( sk33 @ sk20 ) @ sk1 )
| ~ ( p2 @ sk1 )
| ( ( sk31 @ sk20 )
!= ( sk31 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[8852,36071]) ).
thf(41240,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ sk20 )
| ~ ( r1 @ ( sk33 @ sk20 ) @ sk1 )
| ~ ( p2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[41239:[]]) ).
thf(25825,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( ( p2 @ ( sk33 @ sk20 ) )
!= ( p2 @ sk20 ) )
| ( ( p2 @ ( sk6 @ sk5 ) )
!= ( p2 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[11657,24953]) ).
thf(25877,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ( ( p2 @ ( sk33 @ sk20 ) )
!= ( p2 @ sk20 ) )
| ( ( sk6 @ sk5 )
!= sk20 ) ),
inference(simp,[status(thm)],[25825]) ).
thf(302,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( ( p3 @ ( sk3 @ sk16 ) )
!= ( p3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[244,31]) ).
thf(305,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( ( sk3 @ sk16 )
!= sk2 ) ),
inference(simp,[status(thm)],[302]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( p2 @ ( sk34 @ B @ A ) )
| ~ ( sk31 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( p2 @ ( sk34 @ B @ A ) )
| ~ ( sk31 @ A ) ),
inference(simp,[status(thm)],[58]) ).
thf(324,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p3 @ A )
| ( ( p3 @ ( sk4 @ A ) )
!= ( p3 @ ( sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[274,40]) ).
thf(341,plain,
! [A: $i] :
( ( p3 @ A )
| ~ ( r1 @ sk1 @ A )
| ( ( sk4 @ A )
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[324]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ ( sk34 @ B @ A ) @ ( sk35 @ B @ A ) )
| ~ ( sk31 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ ( sk34 @ B @ A ) @ ( sk35 @ B @ A ) )
| ~ ( sk31 @ A ) ),
inference(simp,[status(thm)],[52]) ).
thf(16351,plain,
( ( sk5 != sk1 )
| ~ sk11
| sk19
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[16316,44]) ).
thf(16407,plain,
( sk19
| ( sk5 != sk1 )
| ~ sk11
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= sk18 ) ),
inference(simp,[status(thm)],[16351]) ).
thf(22976,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p2 @ ( sk7 @ ( sk9 @ sk8 ) ) )
!= ( p2 @ ( sk6 @ ( sk9 @ sk8 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11364,19443]) ).
thf(23000,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( sk7 @ ( sk9 @ sk8 ) )
!= ( sk6 @ ( sk9 @ sk8 ) ) ) ),
inference(simp,[status(thm)],[22976]) ).
thf(2899,plain,
( ( p1 @ ( sk10 @ sk8 ) )
!= ( p1 @ ( sk9 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[2898,2118]) ).
thf(2913,plain,
( ( sk10 @ sk8 )
!= ( sk9 @ sk8 ) ),
inference(simp,[status(thm)],[2899]) ).
thf(26298,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p2 @ ( sk7 @ ( sk10 @ sk8 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,19433]) ).
thf(26332,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk7 @ ( sk10 @ sk8 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[26298]) ).
thf(23665,plain,
( ( p2 @ sk1 )
| sk11
| ( p2 @ ( sk9 @ sk16 ) )
| ( p2 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
| sk12
| ( p1 @ sk2 )
| ( ( p1 @ ( sk10 @ sk2 ) )
!= ( p1 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[23387,2076]) ).
thf(23733,plain,
( ( p2 @ sk1 )
| sk11
| ( p2 @ ( sk9 @ sk16 ) )
| ( p2 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
| sk12
| ( p1 @ sk2 )
| ( ( sk10 @ sk2 )
!= sk16 ) ),
inference(simp,[status(thm)],[23665]) ).
thf(19584,plain,
( sk11
| ( sk17 != sk16 )
| ( ( p2 @ ( sk7 @ sk5 ) )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[145,19567]) ).
thf(19601,plain,
( sk11
| ( sk17 != sk16 )
| ( ( sk7 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[19584]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk35 @ B @ A ) )
| ~ ( sk31 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk35 @ B @ A ) )
| ~ ( sk31 @ A ) ),
inference(simp,[status(thm)],[59]) ).
thf(18967,plain,
( ( p3 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p3 @ ( sk3 @ ( sk10 @ sk8 ) ) )
!= ( p3 @ ( sk4 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[7172,547]) ).
thf(18987,plain,
( ( p3 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk3 @ ( sk10 @ sk8 ) )
!= ( sk4 @ sk2 ) ) ),
inference(simp,[status(thm)],[18967]) ).
thf(11673,plain,
( ~ sk11
| ~ ( sk24 @ sk5 )
| ~ ( sk31 @ sk5 )
| ( sk18 != sk1 )
| ( ( p2 @ ( sk33 @ sk5 ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,121]) ).
thf(11727,plain,
( ~ sk11
| ~ ( sk24 @ sk5 )
| ~ ( sk31 @ sk5 )
| ( sk18 != sk1 )
| ( ( sk33 @ sk5 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11673]) ).
thf(2704,plain,
( ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( sk31 @ sk20 )
| ~ ( sk24 @ ( sk33 @ sk20 ) )
| ~ ( p2 @ ( sk33 @ ( sk33 @ sk20 ) ) )
| ( ( sk32 @ sk20 )
!= sk18 )
| ( ( sk31 @ ( sk33 @ sk20 ) )
!= ( sk31 @ sk20 ) ) ),
inference(simp,[status(thm)],[2703]) ).
thf(11567,plain,
( ( p2 @ sk8 )
| ( ( p2 @ ( sk6 @ sk8 ) )
!= ( p2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[11275,39]) ).
thf(11644,plain,
( ( p2 @ sk8 )
| ( ( sk6 @ sk8 )
!= sk5 ) ),
inference(simp,[status(thm)],[11567]) ).
thf(26782,plain,
( ( p1 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p1 @ ( sk10 @ sk8 ) )
!= ( p1 @ ( sk9 @ ( sk7 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[21379,2118]) ).
thf(26808,plain,
( ( p1 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk10 @ sk8 )
!= ( sk9 @ ( sk7 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[26782]) ).
thf(27154,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ ( sk33 @ sk20 ) )
| ( ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[27146,23885]) ).
thf(27331,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ~ sk11
| ~ sk19
| ~ ( sk24 @ sk20 )
| ~ ( p2 @ ( sk33 @ sk20 ) )
| ( ( sk6 @ ( sk7 @ sk5 ) )
!= sk20 ) ),
inference(simp,[status(thm)],[27154]) ).
thf(16286,plain,
( ( sk5 != sk1 )
| ( ( p2 @ ( sk36 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,16274]) ).
thf(16314,plain,
( ( sk5 != sk1 )
| ( ( sk36 @ ( sk36 @ sk5 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[16286]) ).
thf(2812,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( r1 @ ( sk3 @ sk16 ) @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1607,80]) ).
thf(2828,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p1 @ A )
| ( p1 @ ( sk9 @ A ) )
| ( ( sk3 @ sk16 )
!= sk1 )
| ( ( sk13 @ ( sk3 @ sk16 ) @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[2812]) ).
thf(2847,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p1 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
| ( p1 @ ( sk9 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) ) )
| ( ( sk3 @ sk16 )
!= sk1 ) ),
inference(simp,[status(thm)],[2828]) ).
thf(4117,plain,
! [A: $i] :
( ~ sk11
| ~ sk19
| ( p2 @ A )
| ( r1 @ A @ ( sk22 @ A ) )
| ( ( r1 @ sk18 @ sk20 )
!= ( r1 @ sk18 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,85]) ).
thf(4118,plain,
( ~ sk11
| ~ sk19
| ( p2 @ sk20 )
| ( r1 @ sk20 @ ( sk22 @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[4117:[bind(A,$thf( sk20 ))]]) ).
thf(27177,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( p2 @ sk2 )
| ( ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ ( sk7 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[27146,19280]) ).
thf(27311,plain,
( ( p2 @ sk2 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk6 @ ( sk7 @ sk5 ) )
!= ( sk7 @ sk2 ) ) ),
inference(simp,[status(thm)],[27177]) ).
thf(27463,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk7 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,27447]) ).
thf(27497,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk7 @ ( sk7 @ sk5 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[27463]) ).
thf(13684,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ sk5 @ ( sk36 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13679,88]) ).
thf(13819,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( sk5 != sk1 )
| ( ( sk36 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[13684]) ).
thf(13866,plain,
( ( p1 @ ( sk36 @ sk5 ) )
| ( r1 @ ( sk36 @ sk5 ) @ ( sk9 @ ( sk36 @ sk5 ) ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[13819]) ).
thf(19001,plain,
( ( p3 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p3 @ ( sk4 @ ( sk10 @ sk8 ) ) )
!= ( p3 @ ( sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[274,7174]) ).
thf(19019,plain,
( ( p3 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk4 @ ( sk10 @ sk8 ) )
!= ( sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[19001]) ).
thf(26738,plain,
( ( p1 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p1 @ ( sk10 @ ( sk7 @ sk5 ) ) )
!= ( p1 @ ( sk9 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2898,21356]) ).
thf(26749,plain,
( ( p1 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk10 @ ( sk7 @ sk5 ) )
!= ( sk9 @ sk8 ) ) ),
inference(simp,[status(thm)],[26738]) ).
thf(2349,plain,
( ( ( sk3 @ sk2 )
!= sk1 )
| ( p3 @ sk5 )
| ( ( p3 @ ( sk4 @ sk5 ) )
!= ( p3 @ ( sk3 @ ( sk4 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2341,314]) ).
thf(2353,plain,
( ( p3 @ sk5 )
| ( ( sk3 @ sk2 )
!= sk1 )
| ( ( sk4 @ sk5 )
!= ( sk3 @ ( sk4 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[2349]) ).
thf(17406,plain,
( ( p1 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( p1 @ ( sk10 @ ( sk36 @ sk5 ) ) )
!= ( p1 @ ( sk9 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2898,13856]) ).
thf(17409,plain,
( ( p1 @ ( sk36 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk10 @ ( sk36 @ sk5 ) )
!= ( sk9 @ sk8 ) ) ),
inference(simp,[status(thm)],[17406]) ).
thf(13975,plain,
( ~ sk12
| sk11
| ( p2 @ sk15 )
| ( ( p2 @ ( sk6 @ sk15 ) )
!= ( p2 @ sk15 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11238]) ).
thf(13977,plain,
( sk11
| ( p2 @ sk15 )
| ~ sk12
| ( ( sk6 @ sk15 )
!= sk15 ) ),
inference(simp,[status(thm)],[13975]) ).
thf(24577,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p2 @ ( sk6 @ ( sk10 @ sk8 ) ) )
!= ( p2 @ ( sk7 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11356,19567]) ).
thf(24615,plain,
( ( p2 @ ( sk10 @ sk8 ) )
| ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk6 @ ( sk10 @ sk8 ) )
!= ( sk7 @ sk5 ) ) ),
inference(simp,[status(thm)],[24577]) ).
thf(27405,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p2 @ ( sk36 @ ( sk7 @ sk5 ) ) )
!= ( p2 @ ( sk6 @ ( sk7 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27146,27393]) ).
thf(27443,plain,
( ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk36 @ ( sk7 @ sk5 ) )
!= ( sk6 @ ( sk7 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[27405]) ).
thf(11721,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( p2 @ ( sk36 @ ( sk9 @ sk8 ) ) )
!= ( p2 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11657,8232]) ).
thf(11764,plain,
( ( p2 @ ( sk9 @ sk8 ) )
| ( sk8 != sk1 )
| ( ( sk36 @ ( sk9 @ sk8 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[11721]) ).
thf(5876,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,88]) ).
thf(5877,plain,
( ( p1 @ sk2 )
| ( r1 @ sk2 @ ( sk9 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[5876:[bind(A,$thf( sk2 ))]]) ).
thf(18504,plain,
( ( ( sk9 @ sk8 )
!= sk1 )
| ( ( p1 @ ( sk9 @ ( sk10 @ sk8 ) ) )
!= ( p1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[18493,50]) ).
thf(18510,plain,
( ( ( sk9 @ sk8 )
!= sk1 )
| ( ( sk9 @ ( sk10 @ sk8 ) )
!= sk8 ) ),
inference(simp,[status(thm)],[18504]) ).
thf(16330,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ ( sk9 @ sk8 ) )
| ~ ( sk31 @ ( sk9 @ sk8 ) )
| ( sk18 != sk8 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk33 @ ( sk9 @ sk8 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,6272]) ).
thf(16430,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ ( sk9 @ sk8 ) )
| ~ ( sk31 @ ( sk9 @ sk8 ) )
| ( sk18 != sk8 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk33 @ ( sk9 @ sk8 ) ) ) ),
inference(simp,[status(thm)],[16330]) ).
thf(2880,plain,
( ( p1 @ sk2 )
| ( ( p1 @ ( sk9 @ sk2 ) )
!= ( p1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[2805,50]) ).
thf(2887,plain,
( ( p1 @ sk2 )
| ( ( sk9 @ sk2 )
!= sk8 ) ),
inference(simp,[status(thm)],[2880]) ).
thf(11682,plain,
( ~ sk11
| ~ sk19
| ( ( p2 @ ( sk6 @ sk5 ) )
!= ( p2 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[11657,53]) ).
thf(11754,plain,
( ~ sk11
| ~ sk19
| ( ( sk6 @ sk5 )
!= sk21 ) ),
inference(simp,[status(thm)],[11682]) ).
thf(23703,plain,
( ( p2 @ sk1 )
| sk11
| ( p2 @ ( sk9 @ sk16 ) )
| ( p2 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
| sk12
| ( p1 @ sk5 )
| ( ( p1 @ ( sk10 @ sk5 ) )
!= ( p1 @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[23387,2056]) ).
thf(23755,plain,
( ( p2 @ sk1 )
| sk11
| ( p2 @ ( sk9 @ sk16 ) )
| ( p2 @ ( sk13 @ ( sk9 @ sk16 ) @ sk16 ) )
| sk12
| ( p1 @ sk5 )
| ( ( sk10 @ sk5 )
!= sk16 ) ),
inference(simp,[status(thm)],[23703]) ).
thf(6748,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( ( r1 @ ( sk3 @ sk16 ) @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1607,89]) ).
thf(6793,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( ( sk3 @ sk16 )
!= sk1 )
| ( ( sk13 @ ( sk3 @ sk16 ) @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[6748]) ).
thf(6839,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p1 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
| ( r1 @ ( sk9 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) ) @ ( sk10 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) ) )
| ( ( sk3 @ sk16 )
!= sk1 ) ),
inference(simp,[status(thm)],[6793]) ).
thf(12992,plain,
( ~ sk11
| ( p2 @ sk18 )
| ( ( p2 @ ( sk36 @ sk18 ) )
!= ( p2 @ ( sk6 @ sk18 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11236,8105]) ).
thf(13048,plain,
( ( p2 @ sk18 )
| ~ sk11
| ( ( sk36 @ sk18 )
!= ( sk6 @ sk18 ) ) ),
inference(simp,[status(thm)],[12992]) ).
thf(230,plain,
( sk11
| ( sk17 != sk16 )
| ~ sk12
| ( ( p2 @ sk15 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[145,27]) ).
thf(232,plain,
( sk11
| ( sk17 != sk16 )
| ~ sk12
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[230]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ ( sk29 @ B @ A ) @ ( sk30 @ B @ A ) )
| ( sk24 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ ( sk29 @ B @ A ) @ ( sk30 @ B @ A ) )
| ( sk24 @ A ) ),
inference(simp,[status(thm)],[64]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk14 @ B @ A ) )
| sk12
| sk11 ),
inference(cnf,[status(esa)],[5]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk14 @ B @ A ) )
| sk12
| sk11 ),
inference(simp,[status(thm)],[68]) ).
thf(5918,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ ( sk3 @ sk16 ) @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1607,88]) ).
thf(5939,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( sk3 @ sk16 )
!= sk1 )
| ( ( sk13 @ ( sk3 @ sk16 ) @ sk16 )
!= A ) ),
inference(simp,[status(thm)],[5918]) ).
thf(5986,plain,
( ( p2 @ sk1 )
| sk11
| ( p3 @ sk16 )
| ( p2 @ ( sk3 @ sk16 ) )
| sk12
| ( p1 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) )
| ( r1 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) @ ( sk9 @ ( sk13 @ ( sk3 @ sk16 ) @ sk16 ) ) )
| ( ( sk3 @ sk16 )
!= sk1 ) ),
inference(simp,[status(thm)],[5939]) ).
thf(5494,plain,
( ( p1 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 )
| ( ( sk9 @ ( sk6 @ sk5 ) )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[5485]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( p2 @ ( sk29 @ B @ A ) )
| ( sk24 @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( p2 @ ( sk29 @ B @ A ) )
| ( sk24 @ A ) ),
inference(simp,[status(thm)],[21]) ).
thf(6662,plain,
! [A: $i] :
( ~ sk12
| sk11
| ( p1 @ A )
| ( r1 @ ( sk9 @ A ) @ ( sk10 @ A ) )
| ( ( r1 @ sk1 @ sk15 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,89]) ).
thf(6663,plain,
( ~ sk12
| sk11
| ( p1 @ sk15 )
| ( r1 @ ( sk9 @ sk15 ) @ ( sk10 @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[6662:[bind(A,$thf( sk15 ))]]) ).
thf(27127,plain,
( ( p3 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( p3 @ ( sk3 @ ( sk7 @ sk5 ) ) )
!= ( p3 @ ( sk7 @ sk5 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21380]) ).
thf(27141,plain,
( ( p3 @ ( sk7 @ sk5 ) )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk3 @ ( sk7 @ sk5 ) )
!= ( sk7 @ sk5 ) ) ),
inference(simp,[status(thm)],[27127]) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ B )
| ( p2 @ C )
| ~ ( p2 @ B )
| ~ ( sk31 @ A )
| ( ( r1 @ ( sk3 @ sk2 ) @ ( sk4 @ sk2 ) )
!= ( r1 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[184,77]) ).
thf(364,plain,
! [A: $i] :
( ~ sk11
| ~ ( r1 @ sk18 @ A )
| ~ ( sk24 @ A )
| ~ ( r1 @ ( sk33 @ A ) @ ( sk3 @ sk2 ) )
| ( p2 @ ( sk4 @ sk2 ) )
| ~ ( p2 @ ( sk3 @ sk2 ) )
| ~ ( sk31 @ A ) ),
inference(pattern_uni,[status(thm)],[363:[bind(A,$thf( A )),bind(B,$thf( sk3 @ sk2 )),bind(C,$thf( sk4 @ sk2 ))]]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( r1 @ ( sk36 @ A ) @ B )
| ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ( p2 @ B ) ),
inference(cnf,[status(esa)],[5]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( r1 @ ( sk36 @ A ) @ B )
| ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ( p2 @ B ) ),
inference(simp,[status(thm)],[67]) ).
thf(16321,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ sk2 )
| ~ ( sk31 @ sk2 )
| ( sk18 != sk1 )
| ( ( p2 @ ( sk6 @ ( sk36 @ sk5 ) ) )
!= ( p2 @ ( sk33 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16316,115]) ).
thf(16447,plain,
( ( sk5 != sk1 )
| ~ sk11
| ~ ( sk24 @ sk2 )
| ~ ( sk31 @ sk2 )
| ( sk18 != sk1 )
| ( ( sk6 @ ( sk36 @ sk5 ) )
!= ( sk33 @ sk2 ) ) ),
inference(simp,[status(thm)],[16321]) ).
thf(3990,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( p1 @ ( sk10 @ sk8 ) )
!= ( p1 @ ( sk9 @ ( sk3 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2846,2118]) ).
thf(4002,plain,
( ( p1 @ ( sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( ( sk10 @ sk8 )
!= ( sk9 @ ( sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[3990]) ).
thf(55409,plain,
$false,
inference(e,[status(thm)],[69,5810,19594,8283,518,468,33526,19611,88,27315,33472,5469,4005,2341,101,2109,33543,347,11504,16427,333,249,19543,26461,2331,11620,26451,11394,555,170,2908,13062,25272,33500,11724,16402,115,18514,19508,276,308,6900,22480,9469,10,3745,2686,16413,12097,27259,8298,23885,4294,6877,24819,6278,5814,16424,23745,19565,11468,2035,21435,1063,5708,404,15683,11613,8239,2886,31907,27298,7168,33511,17446,9476,5518,4371,3688,2869,26802,7993,2916,13679,19443,184,3689,11913,504,110,27263,24842,3744,5706,27308,23387,11760,8257,6010,13826,27393,189,11773,2049,19604,11600,15684,4008,29,93,6272,24811,152,16394,10945,15824,19956,57,8483,4471,78,5493,9475,261,8284,11778,8229,5861,35321,2782,2893,27483,106,2034,84,16431,11523,6259,2950,33468,22529,35306,13987,19495,19598,4815,12105,238,24676,121,348,33485,24954,2073,1051,821,4810,12090,280,3739,11265,221,8306,11806,2772,23736,4825,4038,2103,26856,11596,33504,33475,26799,27447,89,133,19497,17442,265,74,27142,33473,1564,19812,307,60,8302,2118,5487,10947,233,6,512,2910,16401,270,25316,85,201,27265,19280,23594,102,27479,2621,4312,2790,19218,2773,7999,23295,11751,11766,11619,11484,561,392,70,33516,19595,334,18493,11520,11238,2805,33459,19842,11768,349,5512,7994,38,92,2873,97,2872,5534,5988,2200,21470,16274,11624,8852,13070,13835,11646,317,2801,35307,11762,15896,8319,31080,53,169,8354,19433,11356,11734,2840,2115,18994,16414,3060,26470,19515,488,8105,3000,27440,8258,2053,489,21370,11774,6275,19928,96,11801,109,328,9508,16436,5496,11364,77,554,18512,11757,27493,7998,637,16419,6271,547,11742,16316,8326,3059,33338,129,24938,3692,35302,3064,7174,21155,27146,23857,2836,22954,27428,1060,1050,19498,128,19491,508,24953,2076,2915,11769,2909,73,7150,105,244,11725,24985,360,16405,25276,8279,1054,10951,5930,19547,15908,4004,4308,7160,8322,11747,2033,15707,166,34,148,33520,13849,5715,2894,7567,19807,21473,7046,21380,27133,11737,2941,264,12119,279,22530,176,22945,15904,17439,44,2849,13060,19440,11729,6019,33498,281,27,11483,562,32901,16313,118,19296,18783,8107,2891,8300,5539,11765,5556,86,71,8318,181,18519,11657,19609,2358,23751,350,219,19606,274,3764,8135,81,1048,24951,11733,76,7,737,98,2871,2065,8276,900,11365,39,11487,271,15713,2896,208,5511,2610,103,13856,2780,23004,848,240,2874,27424,155,34005,19616,19599,2632,345,33528,3055,552,13980,4818,19239,91,108,8281,13069,1061,2911,6660,685,4832,130,2051,2620,19602,11775,3674,306,563,3,5495,80,19409,7172,13085,15829,3687,2999,16408,167,2693,19542,112,2684,2846,5710,553,11758,145,11889,19563,490,2914,7571,4813,2994,13852,680,8323,2927,2942,22515,150,11275,95,11743,27338,3058,18,8143,27285,11726,9467,16396,15924,19211,4377,8295,8813,263,2888,19567,3691,182,16,4003,27261,13978,127,24678,15676,27306,6715,50,1053,199,33466,16416,16295,23824,502,21356,32965,11622,338,26455,26771,11475,31,2056,15828,11749,2113,19549,2357,1052,22526,175,15822,314,17438,3007,72,21379,24665,87,482,27491,5510,104,2792,2865,2875,2626,2352,6758,99,19493,33521,3056,19593,27258,16397,11745,319,11514,304,1062,7996,27430,11469,8805,40,7964,139,19554,2944,18518,75,8253,13846,24984,8304,2198,4478,32984,19600,36523,2120,19605,36071,24829,14575,19505,1607,272,39947,2623,82,18991,6703,15813,8324,2683,30,19564,17414,4719,26253,19,11612,3062,735,27307,262,23750,33481,2050,41240,13862,25877,305,107,242,341,79,16407,23000,21387,2913,26332,635,23733,19237,19601,94,18987,11727,136,13842,2704,11644,25992,26808,2063,27331,36057,16314,2847,4118,27311,4831,47,27497,13866,19019,9066,26749,2353,17409,13977,11236,24615,2898,27443,11764,322,5877,18510,16430,2887,2690,11754,23755,6839,13048,232,90,111,5986,5494,10934,83,6663,6158,6254,27141,364,8232,100,16447,4002]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL642+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n014.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 15:40:59 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.83/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.98 % [INFO] Parsing done (118ms).
% 1.19/0.98 % [INFO] Running in sequential loop mode.
% 1.58/1.17 % [INFO] eprover registered as external prover.
% 1.58/1.18 % [INFO] cvc4 registered as external prover.
% 1.78/1.18 % [INFO] Scanning for conjecture ...
% 2.01/1.27 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 2.01/1.30 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.01/1.30 % [INFO] Problem is first-order (TPTP FOF).
% 2.01/1.31 % [INFO] Type checking passed.
% 2.01/1.31 % [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 ...
% 119.32/21.76 % External prover 'e' found a proof!
% 119.32/21.76 % [INFO] Killing All external provers ...
% 119.32/21.77 % Time passed: 21234ms (effective reasoning time: 20779ms)
% 119.32/21.77 % 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)>
% 119.32/21.77 % Axioms used in derivation (0):
% 119.32/21.77 % No. of inferences in proof: 1613
% 119.32/21.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21234 ms resp. 20779 ms w/o parsing
% 120.07/22.01 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 120.07/22.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------