TSTP Solution File: LCL660+1.001 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : LCL660+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 : Tue May 7 07:55:38 EDT 2024
% Result : Theorem 131.23s 23.55s
% Output : Refutation 131.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 48
% Syntax : Number of formulae : 1034 ( 24 unt; 46 typ; 0 def)
% Number of atoms : 5097 ( 700 equ; 0 cnn)
% Maximal formula atoms : 120 ( 5 avg)
% Number of connectives : 11919 (2613 ~;3252 |; 35 &;6019 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 17 con; 0-4 aty)
% Number of variables : 846 ( 0 ^ 842 !; 4 ?; 846 :)
% Comments :
%------------------------------------------------------------------------------
thf(r1_type,type,
r1: $i > $i > $o ).
thf(p3_type,type,
p3: $i > $o ).
thf(p2_type,type,
p2: $i > $o ).
thf(p4_type,type,
p4: $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: $o ).
thf(sk9_type,type,
sk9: $i > $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk11_type,type,
sk11: $i > $i ).
thf(sk12_type,type,
sk12: $i > $i ).
thf(sk13_type,type,
sk13: $i ).
thf(sk14_type,type,
sk14: $i > $i ).
thf(sk15_type,type,
sk15: $i > $i ).
thf(sk16_type,type,
sk16: $o ).
thf(sk17_type,type,
sk17: $o ).
thf(sk18_type,type,
sk18: $i > $i > $i ).
thf(sk19_type,type,
sk19: $i > $i > $i ).
thf(sk20_type,type,
sk20: $i ).
thf(sk21_type,type,
sk21: $i ).
thf(sk22_type,type,
sk22: $i ).
thf(sk23_type,type,
sk23: $i ).
thf(sk24_type,type,
sk24: $o ).
thf(sk25_type,type,
sk25: $i ).
thf(sk26_type,type,
sk26: $i ).
thf(sk27_type,type,
sk27: $i > $i ).
thf(sk28_type,type,
sk28: $i > $i ).
thf(sk29_type,type,
sk29: $i > $o ).
thf(sk30_type,type,
sk30: $i > $o ).
thf(sk31_type,type,
sk31: $i > $i > $i > $i > $i ).
thf(sk32_type,type,
sk32: $i > $i > $i > $i > $i ).
thf(sk33_type,type,
sk33: $i > $i > $i ).
thf(sk34_type,type,
sk34: $i > $i > $i ).
thf(sk35_type,type,
sk35: $i > $i > $i ).
thf(sk36_type,type,
sk36: $i > $o ).
thf(sk37_type,type,
sk37: $i > $i ).
thf(sk38_type,type,
sk38: $i > $i ).
thf(sk39_type,type,
sk39: $i > $i > $i ).
thf(sk40_type,type,
sk40: $i > $i > $i ).
thf(sk41_type,type,
sk41: $i > $i ).
thf(1,conjecture,
~ ? [A: $i] :
~ ( ( ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ~ ( p3 @ B ) )
& ( ! [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 )
| ( p4 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p4 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p4 @ D ) )
| ~ ( p4 @ C ) ) )
| ( ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ~ ( 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 )
| ( 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 )
| ( p4 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p4 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p4 @ D ) )
| ~ ( p4 @ C ) ) )
| ( ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ~ ( 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(4,plain,
~ ~ ? [A: $i] :
~ ( ( ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ~ ( p3 @ B ) )
& ( ! [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 )
| ( p4 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p4 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p4 @ D ) )
| ~ ( p4 @ C ) ) )
| ( ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ~ ( 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(5,plain,
? [A: $i] :
~ ( ( ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ~ ( p3 @ B ) )
& ( ! [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 )
| ( p4 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p4 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p4 @ D ) )
| ~ ( p4 @ C ) ) )
| ( ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ~ ( 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)],[4]) ).
thf(6,plain,
~ ! [A: $i] :
( ( ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ~ ( p3 @ B ) )
& ( ! [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 )
| ( p4 @ B ) )
| ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ( p4 @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ! [D: $i] :
( ~ ( r1 @ C @ D )
| ( p4 @ D ) )
| ~ ( p4 @ C ) ) )
| ( ~ ! [B: $i] :
( ~ ( r1 @ A @ B )
| ~ ! [C: $i] :
( ~ ( r1 @ B @ C )
| ~ ( 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)],[5]) ).
thf(69,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( r1 @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(44,plain,
( ( p2 @ sk1 )
| ( r1 @ sk1 @ sk21 )
| sk16 ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ( p1 @ ( sk14 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(121,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ( p1 @ ( sk14 @ A ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(29598,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk16
| ( p1 @ A )
| ( p1 @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44,121]) ).
thf(29599,plain,
( ( p2 @ sk1 )
| sk16
| ( p1 @ sk21 )
| ( p1 @ ( sk14 @ sk21 ) ) ),
inference(pattern_uni,[status(thm)],[29598:[bind(A,$thf( sk21 ))]]) ).
thf(30,plain,
r1 @ sk1 @ sk5,
inference(cnf,[status(esa)],[6]) ).
thf(3,axiom,
! [A: $i] : ( r1 @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(128,plain,
! [A: $i] : ( r1 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(129,plain,
! [A: $i] : ( r1 @ A @ A ),
inference(cnf,[status(esa)],[128]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(164,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1 @ sk1 @ B )
| ~ ( p3 @ B )
| ( p2 @ C )
| ~ ( p2 @ ( sk4 @ C ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[129,14]) ).
thf(165,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ sk1 )
| ~ ( p2 @ ( sk4 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(191,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ sk1 )
| ~ ( p2 @ ( sk4 @ sk1 ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(40017,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ( p2 @ sk1 )
| ~ ( p2 @ ( sk4 @ sk1 ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,191]) ).
thf(40018,plain,
( ~ ( p3 @ sk5 )
| ( p2 @ sk1 )
| ~ ( p2 @ ( sk4 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[40017:[bind(A,$thf( sk5 ))]]) ).
thf(17,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ~ ( p2 @ ( sk38 @ A ) )
| ~ ( sk36 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(101,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ~ ( p2 @ ( sk38 @ A ) )
| ~ ( sk36 @ A ) ),
inference(simp,[status(thm)],[17]) ).
thf(62,plain,
( ( p2 @ sk1 )
| ( p2 @ sk21 )
| sk16 ),
inference(cnf,[status(esa)],[6]) ).
thf(9,plain,
( sk8
| ~ ( p2 @ sk10 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(147,plain,
( ( p2 @ sk1 )
| sk16
| sk8
| ( ( p2 @ sk21 )
!= ( p2 @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[62,9]) ).
thf(152,plain,
( ( p2 @ sk1 )
| sk16
| sk8
| ( sk21 != sk10 ) ),
inference(simp,[status(thm)],[147]) ).
thf(26,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ~ ( p2 @ sk2 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(132,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,26]) ).
thf(133,plain,
( ~ ( p3 @ sk5 )
| ~ ( p2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( sk5 ))]]) ).
thf(455,plain,
( sk16
| sk8
| ( sk21 != sk10 )
| ~ ( p3 @ sk5 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[152,133]) ).
thf(468,plain,
( sk16
| sk8
| ( sk21 != sk10 )
| ~ ( p3 @ sk5 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[455]) ).
thf(27,plain,
( ~ sk16
| ( r1 @ sk1 @ sk23 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(22,plain,
! [A: $i] :
( sk8
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk12 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(103,plain,
! [A: $i] :
( sk8
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk12 @ A ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(16123,plain,
! [A: $i] :
( ~ sk16
| sk8
| ( p2 @ A )
| ~ ( p2 @ ( sk12 @ A ) )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,103]) ).
thf(16124,plain,
( ~ sk16
| sk8
| ( p2 @ sk23 )
| ~ ( p2 @ ( sk12 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[16123:[bind(A,$thf( sk23 ))]]) ).
thf(46,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ( r1 @ A @ ( sk14 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(87,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ( r1 @ A @ ( sk14 @ A ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(4864,plain,
! [B: $i,A: $i] :
( ( p1 @ B )
| ( r1 @ B @ ( sk14 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,87]) ).
thf(4865,plain,
( ( p1 @ sk1 )
| ( r1 @ sk1 @ ( sk14 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[4864:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(25,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( r1 @ A @ ( sk41 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(85,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( r1 @ A @ ( sk41 @ A ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(5027,plain,
! [A: $i] :
( ( p1 @ sk1 )
| ( p2 @ A )
| ( r1 @ A @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ ( sk14 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4865,85]) ).
thf(5028,plain,
( ( p1 @ sk1 )
| ( p2 @ ( sk14 @ sk1 ) )
| ( r1 @ ( sk14 @ sk1 ) @ ( sk41 @ ( sk14 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[5027:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ ( sk34 @ B @ A ) @ ( sk35 @ B @ A ) )
| ( sk29 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ ( sk34 @ B @ A ) @ ( sk35 @ B @ A ) )
| ( sk29 @ A ) ),
inference(simp,[status(thm)],[78]) ).
thf(1018,plain,
! [B: $i,A: $i] :
( ~ ( p3 @ B )
| ( r1 @ sk1 @ sk2 )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,69]) ).
thf(1019,plain,
( ~ ( p3 @ sk1 )
| ( r1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1018:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(51,plain,
! [A: $i] :
( sk8
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( p2 @ ( sk11 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(124,plain,
! [A: $i] :
( sk8
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( p2 @ ( sk11 @ A ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(1109,plain,
! [A: $i] :
( ~ ( p3 @ sk1 )
| sk8
| ( p2 @ A )
| ( p2 @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1019,124]) ).
thf(1110,plain,
( ~ ( p3 @ sk1 )
| sk8
| ( p2 @ sk2 )
| ( p2 @ ( sk11 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1109:[bind(A,$thf( sk2 ))]]) ).
thf(1004,plain,
! [A: $i] :
( ~ sk16
| sk8
| ( p2 @ A )
| ( p2 @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,124]) ).
thf(1005,plain,
( ~ sk16
| sk8
| ( p2 @ sk23 )
| ( p2 @ ( sk11 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[1004:[bind(A,$thf( sk23 ))]]) ).
thf(63,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ( sk36 @ A )
| ~ ( p2 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(110,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ( sk36 @ A )
| ~ ( p2 @ A ) ),
inference(simp,[status(thm)],[63]) ).
thf(20257,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( sk29 @ B )
| ( sk36 @ B )
| ~ ( p2 @ B )
| ( ( r1 @ A @ A )
!= ( r1 @ sk23 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,110]) ).
thf(20258,plain,
( ~ sk16
| ~ ( sk29 @ sk23 )
| ( sk36 @ sk23 )
| ~ ( p2 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[20257:[bind(A,$thf( sk23 )),bind(B,$thf( sk23 ))]]) ).
thf(49,plain,
r1 @ sk1 @ sk13,
inference(cnf,[status(esa)],[6]) ).
thf(1055,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ( r1 @ sk1 @ sk2 )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,69]) ).
thf(1056,plain,
( ~ ( p3 @ sk13 )
| ( r1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1055:[bind(A,$thf( sk13 ))]]) ).
thf(50,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p4 @ A )
| ( p4 @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(112,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p4 @ A )
| ( p4 @ ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(21393,plain,
! [A: $i] :
( ~ ( p3 @ sk13 )
| ( p4 @ A )
| ( p4 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1056,112]) ).
thf(21394,plain,
( ~ ( p3 @ sk13 )
| ( p4 @ sk2 )
| ( p4 @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[21393:[bind(A,$thf( sk2 ))]]) ).
thf(75,plain,
~ ( p4 @ sk5 ),
inference(cnf,[status(esa)],[6]) ).
thf(25489,plain,
( ~ ( p3 @ sk13 )
| ( p4 @ sk2 )
| ( ( p4 @ ( sk6 @ sk2 ) )
!= ( p4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21394,75]) ).
thf(25508,plain,
( ( p4 @ sk2 )
| ~ ( p3 @ sk13 )
| ( ( sk6 @ sk2 )
!= sk5 ) ),
inference(simp,[status(thm)],[25489]) ).
thf(56,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ~ sk8 ),
inference(cnf,[status(esa)],[6]) ).
thf(82,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( r1 @ A @ ( sk9 @ A ) )
| ~ sk8 ),
inference(simp,[status(thm)],[56]) ).
thf(2726,plain,
! [A: $i] :
( ( r1 @ A @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,82]) ).
thf(2727,plain,
( ( r1 @ sk5 @ ( sk9 @ sk5 ) )
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[2726:[bind(A,$thf( sk5 ))]]) ).
thf(48,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p3 @ ( sk9 @ A ) )
| ~ sk8 ),
inference(cnf,[status(esa)],[6]) ).
thf(109,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p3 @ ( sk9 @ A ) )
| ~ sk8 ),
inference(simp,[status(thm)],[48]) ).
thf(2909,plain,
! [A: $i] :
( ~ sk8
| ( p3 @ ( sk9 @ A ) )
| ( ( r1 @ sk5 @ ( sk9 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2727,109]) ).
thf(2936,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( sk5 != sk1 )
| ( ( sk9 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[2909]) ).
thf(2953,plain,
( ( p3 @ ( sk9 @ ( sk9 @ sk5 ) ) )
| ~ sk8
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[2936]) ).
thf(57,plain,
( ~ sk17
| ( r1 @ sk1 @ sk20 )
| sk16 ),
inference(cnf,[status(esa)],[6]) ).
thf(2675,plain,
! [A: $i] :
( ~ sk17
| sk16
| ( r1 @ A @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk1 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,82]) ).
thf(2676,plain,
( ~ sk17
| sk16
| ( r1 @ sk20 @ ( sk9 @ sk20 ) )
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[2675:[bind(A,$thf( sk20 ))]]) ).
thf(1069,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ( r1 @ sk1 @ sk2 )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,69]) ).
thf(1070,plain,
( ~ ( p3 @ sk5 )
| ( r1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1069:[bind(A,$thf( sk5 ))]]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,14]) ).
thf(175,plain,
! [A: $i] :
( ~ ( p3 @ sk5 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) ) ),
inference(pattern_uni,[status(thm)],[174:[bind(A,$thf( sk5 ))]]) ).
thf(194,plain,
! [A: $i] :
( ~ ( p3 @ sk5 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(43045,plain,
! [A: $i] :
( ~ ( p3 @ sk5 )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1070,194]) ).
thf(43046,plain,
( ~ ( p3 @ sk5 )
| ( p2 @ sk2 )
| ~ ( p2 @ ( sk4 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[43045:[bind(A,$thf( sk2 ))]]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk19 @ B @ A ) )
| sk17
| sk16 ),
inference(cnf,[status(esa)],[6]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk19 @ B @ A ) )
| sk17
| sk16 ),
inference(simp,[status(thm)],[23]) ).
thf(4877,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,87]) ).
thf(4878,plain,
( ( p1 @ sk13 )
| ( r1 @ sk13 @ ( sk14 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[4877:[bind(A,$thf( sk13 ))]]) ).
thf(16,plain,
~ ( p1 @ sk13 ),
inference(cnf,[status(esa)],[6]) ).
thf(5075,plain,
( $false
| ( r1 @ sk13 @ ( sk14 @ sk13 ) ) ),
inference(rewrite,[status(thm)],[4878,16]) ).
thf(5076,plain,
r1 @ sk13 @ ( sk14 @ sk13 ),
inference(simp,[status(thm)],[5075]) ).
thf(5095,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ sk13 @ ( sk14 @ sk13 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5076,26]) ).
thf(5109,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( sk13 != sk1 )
| ( ( sk14 @ sk13 )
!= A ) ),
inference(simp,[status(thm)],[5095]) ).
thf(5141,plain,
( ~ ( p3 @ ( sk14 @ sk13 ) )
| ~ ( p2 @ sk2 )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[5109]) ).
thf(11,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ( p2 @ A )
| ( p2 @ ( sk27 @ A ) )
| ~ sk24 ),
inference(cnf,[status(esa)],[6]) ).
thf(115,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ( p2 @ A )
| ( p2 @ ( sk27 @ A ) )
| ~ sk24 ),
inference(simp,[status(thm)],[11]) ).
thf(388,plain,
! [B: $i,A: $i] :
( ( p3 @ ( sk9 @ B ) )
| ~ sk8
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,109]) ).
thf(389,plain,
( ( p3 @ ( sk9 @ sk1 ) )
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[388:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(2687,plain,
! [B: $i,A: $i] :
( ( r1 @ B @ ( sk9 @ B ) )
| ~ sk8
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,82]) ).
thf(2688,plain,
( ( r1 @ sk1 @ ( sk9 @ sk1 ) )
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[2687:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(2781,plain,
! [A: $i] :
( ~ sk8
| ~ ( p3 @ A )
| ( r1 @ sk1 @ sk2 )
| ( ( r1 @ sk1 @ ( sk9 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2688,69]) ).
thf(2782,plain,
( ~ sk8
| ~ ( p3 @ ( sk9 @ sk1 ) )
| ( r1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2781:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(8325,plain,
( ~ sk8
| ( r1 @ sk1 @ sk2 )
| ( ( p3 @ ( sk9 @ sk1 ) )
!= ( p3 @ ( sk9 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[389,2782]) ).
thf(8326,plain,
( ~ sk8
| ( r1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[8325:[]]) ).
thf(21329,plain,
! [A: $i] :
( ~ sk8
| ( p4 @ A )
| ( p4 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8326,112]) ).
thf(21330,plain,
( ~ sk8
| ( p4 @ sk2 )
| ( p4 @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[21329:[bind(A,$thf( sk2 ))]]) ).
thf(22751,plain,
( ~ sk8
| ( p4 @ sk2 )
| ( ( p4 @ ( sk6 @ sk2 ) )
!= ( p4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21330,75]) ).
thf(22759,plain,
( ( p4 @ sk2 )
| ~ sk8
| ( ( sk6 @ sk2 )
!= sk5 ) ),
inference(simp,[status(thm)],[22751]) ).
thf(21391,plain,
! [A: $i] :
( ( p4 @ A )
| ( p4 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,112]) ).
thf(21392,plain,
( ( p4 @ sk5 )
| ( p4 @ ( sk6 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[21391:[bind(A,$thf( sk5 ))]]) ).
thf(21557,plain,
( $false
| ( p4 @ ( sk6 @ sk5 ) ) ),
inference(rewrite,[status(thm)],[21392,75]) ).
thf(21558,plain,
p4 @ ( sk6 @ sk5 ),
inference(simp,[status(thm)],[21557]) ).
thf(18,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p4 @ A )
| ~ ( p4 @ ( sk7 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(111,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p4 @ A )
| ~ ( p4 @ ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(20886,plain,
! [B: $i,A: $i] :
( ( p4 @ B )
| ~ ( p4 @ ( sk7 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,111]) ).
thf(20887,plain,
( ( p4 @ sk1 )
| ~ ( p4 @ ( sk7 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[20886:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(21563,plain,
( ( p4 @ sk1 )
| ( ( p4 @ ( sk7 @ sk1 ) )
!= ( p4 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21558,20887]) ).
thf(21573,plain,
( ( p4 @ sk1 )
| ( ( sk7 @ sk1 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[21563]) ).
thf(20921,plain,
! [A: $i] :
( ~ sk8
| ( p4 @ A )
| ~ ( p4 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ ( sk9 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2688,111]) ).
thf(20922,plain,
( ~ sk8
| ( p4 @ ( sk9 @ sk1 ) )
| ~ ( p4 @ ( sk7 @ ( sk9 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[20921:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(20946,plain,
! [A: $i] :
( ( p4 @ A )
| ~ ( p4 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,111]) ).
thf(20947,plain,
( ( p4 @ sk5 )
| ~ ( p4 @ ( sk7 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[20946:[bind(A,$thf( sk5 ))]]) ).
thf(21088,plain,
( $false
| ~ ( p4 @ ( sk7 @ sk5 ) ) ),
inference(rewrite,[status(thm)],[20947,75]) ).
thf(21089,plain,
~ ( p4 @ ( sk7 @ sk5 ) ),
inference(simp,[status(thm)],[21088]) ).
thf(1007,plain,
! [A: $i] :
( sk8
| ( p2 @ A )
| ( p2 @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,124]) ).
thf(1008,plain,
( sk8
| ( p2 @ sk13 )
| ( p2 @ ( sk11 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[1007:[bind(A,$thf( sk13 ))]]) ).
thf(1561,plain,
( sk8
| ( p2 @ sk13 )
| ( ( p2 @ ( sk11 @ sk13 ) )
!= ( p2 @ sk13 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1008]) ).
thf(1569,plain,
( sk8
| ( p2 @ sk13 )
| ( ( p2 @ ( sk11 @ sk13 ) )
!= ( p2 @ sk13 ) ) ),
inference(simp,[status(thm)],[1561]) ).
thf(21565,plain,
( ( p4 @ ( sk6 @ sk5 ) )
!= ( p4 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[21558,75]) ).
thf(21570,plain,
( ( sk6 @ sk5 )
!= sk5 ),
inference(simp,[status(thm)],[21565]) ).
thf(151,plain,
( ( p2 @ sk1 )
| sk16
| ( ( p2 @ sk21 )
!= ( p2 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[62]) ).
thf(158,plain,
( ( p2 @ sk1 )
| sk16
| ( sk21 != sk1 ) ),
inference(simp,[status(thm)],[151]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ~ ( p3 @ B )
| ~ ( p2 @ sk2 )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,26]) ).
thf(142,plain,
( ~ ( p3 @ sk1 )
| ~ ( p2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[141:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(252,plain,
( sk16
| ( sk21 != sk1 )
| ~ ( p3 @ sk1 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[158,142]) ).
thf(269,plain,
( sk16
| ( sk21 != sk1 )
| ~ ( p3 @ sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[252]) ).
thf(10,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p4 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(81,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p4 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(5036,plain,
! [A: $i] :
( ( p1 @ sk1 )
| ( p4 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ ( sk14 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4865,81]) ).
thf(5037,plain,
( ( p1 @ sk1 )
| ( p4 @ ( sk14 @ sk1 ) )
| ( r1 @ ( sk6 @ ( sk14 @ sk1 ) ) @ ( sk7 @ ( sk14 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[5036:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(8550,plain,
! [A: $i] :
( ~ sk8
| ( p2 @ A )
| ( r1 @ A @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8326,85]) ).
thf(8551,plain,
( ~ sk8
| ( p2 @ sk2 )
| ( r1 @ sk2 @ ( sk41 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8550:[bind(A,$thf( sk2 ))]]) ).
thf(29618,plain,
! [A: $i] :
( ~ ( p3 @ sk5 )
| ( p1 @ A )
| ( p1 @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1070,121]) ).
thf(29619,plain,
( ~ ( p3 @ sk5 )
| ( p1 @ sk2 )
| ( p1 @ ( sk14 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[29618:[bind(A,$thf( sk2 ))]]) ).
thf(32348,plain,
( ~ ( p3 @ sk5 )
| ( p1 @ sk2 )
| ( ( p1 @ ( sk14 @ sk2 ) )
!= ( p1 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29619]) ).
thf(32366,plain,
( ( p1 @ sk2 )
| ~ ( p3 @ sk5 )
| ( ( sk14 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[32348]) ).
thf(39,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk28 @ A ) )
| ~ sk24 ),
inference(cnf,[status(esa)],[6]) ).
thf(108,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk28 @ A ) )
| ~ sk24 ),
inference(simp,[status(thm)],[39]) ).
thf(19766,plain,
! [B: $i,A: $i] :
( ~ sk16
| ( p2 @ B )
| ~ ( p2 @ ( sk28 @ B ) )
| ~ sk24
| ( ( r1 @ A @ A )
!= ( r1 @ sk23 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,108]) ).
thf(19767,plain,
( ~ sk16
| ( p2 @ sk23 )
| ~ ( p2 @ ( sk28 @ sk23 ) )
| ~ sk24 ),
inference(pattern_uni,[status(thm)],[19766:[bind(A,$thf( sk23 )),bind(B,$thf( sk23 ))]]) ).
thf(76,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk41 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(106,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk41 @ A ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(18239,plain,
! [A: $i] :
( ~ ( p3 @ sk5 )
| ( p2 @ A )
| ~ ( p2 @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1070,106]) ).
thf(18240,plain,
( ~ ( p3 @ sk5 )
| ( p2 @ sk2 )
| ~ ( p2 @ ( sk41 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[18239:[bind(A,$thf( sk2 ))]]) ).
thf(422,plain,
! [A: $i] :
( ~ sk8
| ~ ( r1 @ sk1 @ A )
| ~ ( p2 @ sk2 )
| ( ( p3 @ ( sk9 @ sk1 ) )
!= ( p3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[389,26]) ).
thf(423,plain,
( ~ sk8
| ~ ( r1 @ sk1 @ ( sk9 @ sk1 ) )
| ~ ( p2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[422:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(2797,plain,
( ~ sk8
| ~ ( p2 @ sk2 )
| ( ( r1 @ sk1 @ ( sk9 @ sk1 ) )
!= ( r1 @ sk1 @ ( sk9 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2688,423]) ).
thf(2798,plain,
( ~ sk8
| ~ ( p2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2797:[]]) ).
thf(2841,plain,
( sk16
| ( sk21 != sk1 )
| ~ sk8
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[158,2798]) ).
thf(2844,plain,
( sk16
| ( sk21 != sk1 )
| ~ sk8
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[2841]) ).
thf(149,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk16
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( ( p2 @ sk21 )
!= ( p2 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[62,26]) ).
thf(153,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk16
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( sk21 != sk2 ) ),
inference(simp,[status(thm)],[149]) ).
thf(21333,plain,
! [B: $i,A: $i] :
( ( p4 @ B )
| ( p4 @ ( sk6 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,112]) ).
thf(21334,plain,
( ( p4 @ sk1 )
| ( p4 @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[21333:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(21525,plain,
( ( p4 @ sk1 )
| ( ( p4 @ ( sk6 @ sk1 ) )
!= ( p4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21334,75]) ).
thf(21534,plain,
( ( p4 @ sk1 )
| ( ( sk6 @ sk1 )
!= sk5 ) ),
inference(simp,[status(thm)],[21525]) ).
thf(64,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ~ ( p1 @ ( sk15 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(100,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ~ ( p1 @ ( sk15 @ A ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(14904,plain,
! [A: $i] :
( ~ ( p3 @ sk1 )
| ( p1 @ A )
| ~ ( p1 @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1019,100]) ).
thf(14905,plain,
( ~ ( p3 @ sk1 )
| ( p1 @ sk2 )
| ~ ( p1 @ ( sk15 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[14904:[bind(A,$thf( sk2 ))]]) ).
thf(29652,plain,
! [A: $i] :
( ~ ( p3 @ sk13 )
| ( p1 @ A )
| ( p1 @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1056,121]) ).
thf(29653,plain,
( ~ ( p3 @ sk13 )
| ( p1 @ sk2 )
| ( p1 @ ( sk14 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[29652:[bind(A,$thf( sk2 ))]]) ).
thf(32405,plain,
( ~ ( p3 @ sk13 )
| ( p1 @ sk2 )
| ( ( p1 @ ( sk14 @ sk2 ) )
!= ( p1 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[29653,16]) ).
thf(32420,plain,
( ( p1 @ sk2 )
| ~ ( p3 @ sk13 )
| ( ( sk14 @ sk2 )
!= sk13 ) ),
inference(simp,[status(thm)],[32405]) ).
thf(3825,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,85]) ).
thf(3826,plain,
( ( p2 @ sk5 )
| ( r1 @ sk5 @ ( sk41 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[3825:[bind(A,$thf( sk5 ))]]) ).
thf(3779,plain,
! [B: $i,A: $i] :
( ( p2 @ B )
| ( r1 @ B @ ( sk41 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,85]) ).
thf(3780,plain,
( ( p2 @ sk1 )
| ( r1 @ sk1 @ ( sk41 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[3779:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(37,plain,
! [A: $i] :
( sk8
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( r1 @ ( sk11 @ A ) @ ( sk12 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(84,plain,
! [A: $i] :
( sk8
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( r1 @ ( sk11 @ A ) @ ( sk12 @ A ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(3914,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk8
| ( p2 @ A )
| ( r1 @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( ( r1 @ sk1 @ ( sk41 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3780,84]) ).
thf(3915,plain,
( ( p2 @ sk1 )
| sk8
| ( p2 @ ( sk41 @ sk1 ) )
| ( r1 @ ( sk11 @ ( sk41 @ sk1 ) ) @ ( sk12 @ ( sk41 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[3914:[bind(A,$thf( sk41 @ sk1 ))]]) ).
thf(54,plain,
( ~ sk17
| ~ ( p2 @ sk20 )
| sk16 ),
inference(cnf,[status(esa)],[6]) ).
thf(160,plain,
( ( p2 @ sk1 )
| sk16
| ~ sk17
| ( ( p2 @ sk21 )
!= ( p2 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[62,54]) ).
thf(161,plain,
( ( p2 @ sk1 )
| sk16
| ~ sk17
| ( sk21 != sk20 ) ),
inference(simp,[status(thm)],[160]) ).
thf(212,plain,
! [A: $i] :
( ~ sk17
| sk16
| ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ sk1 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,26]) ).
thf(213,plain,
( ~ sk17
| sk16
| ~ ( p3 @ sk20 )
| ~ ( p2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[212:[bind(A,$thf( sk20 ))]]) ).
thf(774,plain,
( sk16
| ~ sk17
| ( sk21 != sk20 )
| ~ ( p3 @ sk20 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[161,213]) ).
thf(782,plain,
( sk16
| ~ sk17
| ( sk21 != sk20 )
| ~ ( p3 @ sk20 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[774]) ).
thf(5046,plain,
! [A: $i] :
( ( p1 @ sk1 )
| ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ sk1 @ ( sk14 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4865,26]) ).
thf(5047,plain,
( ( p1 @ sk1 )
| ~ ( p3 @ ( sk14 @ sk1 ) )
| ~ ( p2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5046:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(13047,plain,
( ~ ( p3 @ ( sk14 @ sk1 ) )
| ~ ( p2 @ sk2 )
| ( ( p1 @ sk13 )
!= ( p1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[5047,16]) ).
thf(13083,plain,
( ~ ( p3 @ ( sk14 @ sk1 ) )
| ~ ( p2 @ sk2 )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[13047]) ).
thf(61,plain,
! [A: $i] :
( sk8
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( r1 @ A @ ( sk11 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(90,plain,
! [A: $i] :
( sk8
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ( r1 @ A @ ( sk11 @ A ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(6904,plain,
! [B: $i,A: $i] :
( sk8
| ( p2 @ B )
| ( r1 @ B @ ( sk11 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,90]) ).
thf(6905,plain,
( sk8
| ( p2 @ sk1 )
| ( r1 @ sk1 @ ( sk11 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[6904:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(29556,plain,
! [A: $i] :
( sk8
| ( p2 @ sk1 )
| ( p1 @ A )
| ( p1 @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ ( sk11 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6905,121]) ).
thf(29557,plain,
( sk8
| ( p2 @ sk1 )
| ( p1 @ ( sk11 @ sk1 ) )
| ( p1 @ ( sk14 @ ( sk11 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[29556:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(39933,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ( p2 @ sk1 )
| ~ ( p2 @ ( sk4 @ sk1 ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,191]) ).
thf(39934,plain,
( ~ ( p3 @ sk13 )
| ( p2 @ sk1 )
| ~ ( p2 @ ( sk4 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[39933:[bind(A,$thf( sk13 ))]]) ).
thf(35,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ( r1 @ ( sk14 @ A ) @ ( sk15 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(80,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p1 @ A )
| ( r1 @ ( sk14 @ A ) @ ( sk15 @ A ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(1802,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk16
| ( p1 @ A )
| ( r1 @ ( sk14 @ A ) @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44,80]) ).
thf(1803,plain,
( ( p2 @ sk1 )
| sk16
| ( p1 @ sk21 )
| ( r1 @ ( sk14 @ sk21 ) @ ( sk15 @ sk21 ) ) ),
inference(pattern_uni,[status(thm)],[1802:[bind(A,$thf( sk21 ))]]) ).
thf(143,plain,
( ( p2 @ sk1 )
| sk16
| ~ ( p3 @ sk1 )
| ( ( p2 @ sk21 )
!= ( p2 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[62,142]) ).
thf(156,plain,
( ( p2 @ sk1 )
| sk16
| ~ ( p3 @ sk1 )
| ( sk21 != sk2 ) ),
inference(simp,[status(thm)],[143]) ).
thf(5299,plain,
( sk16
| ~ ( p3 @ sk1 )
| ( sk21 != sk2 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[156,142]) ).
thf(5342,plain,
( sk16
| ~ ( p3 @ sk1 )
| ( sk21 != sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[5299]) ).
thf(73,plain,
( sk8
| ( r1 @ sk1 @ sk10 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(21335,plain,
! [A: $i] :
( sk8
| ( p4 @ A )
| ( p4 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,112]) ).
thf(21336,plain,
( sk8
| ( p4 @ sk10 )
| ( p4 @ ( sk6 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[21335:[bind(A,$thf( sk10 ))]]) ).
thf(21581,plain,
( sk8
| ( p4 @ sk10 )
| ( ( p4 @ ( sk6 @ sk10 ) )
!= ( p4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21336,75]) ).
thf(21592,plain,
( sk8
| ( p4 @ sk10 )
| ( ( sk6 @ sk10 )
!= sk5 ) ),
inference(simp,[status(thm)],[21581]) ).
thf(18246,plain,
! [A: $i] :
( ~ sk8
| ( p2 @ A )
| ~ ( p2 @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ ( sk9 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2688,106]) ).
thf(18247,plain,
( ~ sk8
| ( p2 @ ( sk9 @ sk1 ) )
| ~ ( p2 @ ( sk41 @ ( sk9 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[18246:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(42,plain,
( ~ sk16
| sk24
| ~ ( p2 @ sk23 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(16126,plain,
! [A: $i] :
( sk8
| ( p2 @ A )
| ~ ( p2 @ ( sk12 @ A ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,103]) ).
thf(16127,plain,
( sk8
| ( p2 @ sk13 )
| ~ ( p2 @ ( sk12 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[16126:[bind(A,$thf( sk13 ))]]) ).
thf(16385,plain,
( sk8
| ( p2 @ sk13 )
| ( ( p2 @ ( sk12 @ sk13 ) )
!= ( p2 @ ( sk11 @ sk13 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1008,16127]) ).
thf(16398,plain,
( sk8
| ( p2 @ sk13 )
| ( ( sk12 @ sk13 )
!= ( sk11 @ sk13 ) ) ),
inference(simp,[status(thm)],[16385]) ).
thf(999,plain,
! [A: $i] :
( sk8
| ( p2 @ A )
| ( p2 @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,124]) ).
thf(1000,plain,
( sk8
| ( p2 @ sk10 )
| ( p2 @ ( sk11 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[999:[bind(A,$thf( sk10 ))]]) ).
thf(1509,plain,
( sk8
| ( p2 @ sk10 )
| ( ( p2 @ ( sk11 @ sk10 ) )
!= ( p2 @ sk10 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1000]) ).
thf(1518,plain,
( sk8
| ( p2 @ sk10 )
| ( ( p2 @ ( sk11 @ sk10 ) )
!= ( p2 @ sk10 ) ) ),
inference(simp,[status(thm)],[1509]) ).
thf(990,plain,
! [B: $i,A: $i] :
( sk8
| ( p2 @ B )
| ( p2 @ ( sk11 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,124]) ).
thf(991,plain,
( sk8
| ( p2 @ sk1 )
| ( p2 @ ( sk11 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[990:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(60,plain,
( ~ sk16
| ~ ( p2 @ sk26 )
| ~ sk24 ),
inference(cnf,[status(esa)],[6]) ).
thf(1237,plain,
( sk8
| ( p2 @ sk1 )
| ~ sk16
| ~ sk24
| ( ( p2 @ ( sk11 @ sk1 ) )
!= ( p2 @ sk26 ) ) ),
inference(paramod_ordered,[status(thm)],[991,60]) ).
thf(1265,plain,
( sk8
| ( p2 @ sk1 )
| ~ sk16
| ~ sk24
| ( ( sk11 @ sk1 )
!= sk26 ) ),
inference(simp,[status(thm)],[1237]) ).
thf(29588,plain,
! [B: $i,A: $i] :
( ( p1 @ B )
| ( p1 @ ( sk14 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,121]) ).
thf(29589,plain,
( ( p1 @ sk1 )
| ( p1 @ ( sk14 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[29588:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(1807,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ ( sk14 @ A ) @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,80]) ).
thf(1808,plain,
( ( p1 @ sk13 )
| ( r1 @ ( sk14 @ sk13 ) @ ( sk15 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[1807:[bind(A,$thf( sk13 ))]]) ).
thf(1931,plain,
( $false
| ( r1 @ ( sk14 @ sk13 ) @ ( sk15 @ sk13 ) ) ),
inference(rewrite,[status(thm)],[1808,16]) ).
thf(1932,plain,
r1 @ ( sk14 @ sk13 ) @ ( sk15 @ sk13 ),
inference(simp,[status(thm)],[1931]) ).
thf(1940,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ ( sk14 @ sk13 ) @ ( sk15 @ sk13 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1932,109]) ).
thf(1969,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( sk14 @ sk13 )
!= sk1 )
| ( ( sk15 @ sk13 )
!= A ) ),
inference(simp,[status(thm)],[1940]) ).
thf(1985,plain,
( ( p3 @ ( sk9 @ ( sk15 @ sk13 ) ) )
| ~ sk8
| ( ( sk14 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[1969]) ).
thf(2697,plain,
! [A: $i] :
( ~ sk16
| ( r1 @ A @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,82]) ).
thf(2698,plain,
( ~ sk16
| ( r1 @ sk23 @ ( sk9 @ sk23 ) )
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[2697:[bind(A,$thf( sk23 ))]]) ).
thf(1489,plain,
( sk8
| ( p2 @ sk10 )
| ( ( p2 @ ( sk11 @ sk10 ) )
!= ( p2 @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[1000,9]) ).
thf(1511,plain,
( sk8
| ( p2 @ sk10 )
| ( ( sk11 @ sk10 )
!= sk10 ) ),
inference(simp,[status(thm)],[1489]) ).
thf(21523,plain,
( ( p4 @ sk1 )
| ( ( p4 @ ( sk7 @ sk1 ) )
!= ( p4 @ ( sk6 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21334,20887]) ).
thf(21530,plain,
( ( p4 @ sk1 )
| ( ( sk7 @ sk1 )
!= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[21523]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk1 @ B )
!= ( r1 @ sk1 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[14]) ).
thf(186,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) ) ),
inference(pattern_uni,[status(thm)],[185:[bind(A,$thf( B ))]]) ).
thf(196,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(21345,plain,
! [A: $i] :
( ~ sk16
| ( p4 @ A )
| ( p4 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,112]) ).
thf(21346,plain,
( ~ sk16
| ( p4 @ sk23 )
| ( p4 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[21345:[bind(A,$thf( sk23 ))]]) ).
thf(20898,plain,
! [A: $i] :
( ~ sk16
| ( p4 @ A )
| ~ ( p4 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,111]) ).
thf(20899,plain,
( ~ sk16
| ( p4 @ sk23 )
| ~ ( p4 @ ( sk7 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[20898:[bind(A,$thf( sk23 ))]]) ).
thf(22766,plain,
( ~ sk16
| ( p4 @ sk23 )
| ( ( p4 @ ( sk7 @ sk23 ) )
!= ( p4 @ ( sk6 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21346,20899]) ).
thf(22777,plain,
( ( p4 @ sk23 )
| ~ sk16
| ( ( sk7 @ sk23 )
!= ( sk6 @ sk23 ) ) ),
inference(simp,[status(thm)],[22766]) ).
thf(16175,plain,
! [A: $i] :
( sk8
| ( p2 @ A )
| ~ ( p2 @ ( sk12 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,103]) ).
thf(16176,plain,
( sk8
| ( p2 @ sk5 )
| ~ ( p2 @ ( sk12 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[16175:[bind(A,$thf( sk5 ))]]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk26 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ A )
| ~ sk24 ),
inference(cnf,[status(esa)],[6]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk26 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ A )
| ~ sk24 ),
inference(simp,[status(thm)],[19]) ).
thf(157,plain,
( ( p2 @ sk1 )
| sk16
| ( ( p2 @ sk21 )
!= ( p2 @ sk1 ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(38,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p4 @ A )
| ( r1 @ A @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(95,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p4 @ A )
| ( r1 @ A @ ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(11039,plain,
! [A: $i] :
( ( p1 @ sk1 )
| ( p4 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ ( sk14 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4865,95]) ).
thf(11040,plain,
( ( p1 @ sk1 )
| ( p4 @ ( sk14 @ sk1 ) )
| ( r1 @ ( sk14 @ sk1 ) @ ( sk6 @ ( sk14 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[11039:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(29605,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,121]) ).
thf(29606,plain,
( ( p1 @ sk13 )
| ( p1 @ ( sk14 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[29605:[bind(A,$thf( sk13 ))]]) ).
thf(29814,plain,
( $false
| ( p1 @ ( sk14 @ sk13 ) ) ),
inference(rewrite,[status(thm)],[29606,16]) ).
thf(29815,plain,
p1 @ ( sk14 @ sk13 ),
inference(simp,[status(thm)],[29814]) ).
thf(14897,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,100]) ).
thf(14898,plain,
( ( p1 @ sk5 )
| ~ ( p1 @ ( sk15 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[14897:[bind(A,$thf( sk5 ))]]) ).
thf(29823,plain,
( ( p1 @ sk5 )
| ( ( p1 @ ( sk15 @ sk5 ) )
!= ( p1 @ ( sk14 @ sk13 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29815,14898]) ).
thf(29837,plain,
( ( p1 @ sk5 )
| ( ( sk15 @ sk5 )
!= ( sk14 @ sk13 ) ) ),
inference(simp,[status(thm)],[29823]) ).
thf(18206,plain,
! [B: $i,A: $i] :
( ( p2 @ B )
| ~ ( p2 @ ( sk41 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,106]) ).
thf(18207,plain,
( ( p2 @ sk1 )
| ~ ( p2 @ ( sk41 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[18206:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(18439,plain,
( ( p2 @ sk1 )
| sk16
| ( ( p2 @ ( sk41 @ sk1 ) )
!= ( p2 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[62,18207]) ).
thf(18451,plain,
( ( p2 @ sk1 )
| sk16
| ( ( sk41 @ sk1 )
!= sk21 ) ),
inference(simp,[status(thm)],[18439]) ).
thf(29584,plain,
! [A: $i] :
( ~ sk8
| ( p1 @ A )
| ( p1 @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8326,121]) ).
thf(29585,plain,
( ~ sk8
| ( p1 @ sk2 )
| ( p1 @ ( sk14 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[29584:[bind(A,$thf( sk2 ))]]) ).
thf(30548,plain,
( ~ sk8
| ( p1 @ sk2 )
| ( ( p1 @ ( sk14 @ sk2 ) )
!= ( p1 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[29585,16]) ).
thf(30558,plain,
( ( p1 @ sk2 )
| ~ sk8
| ( ( sk14 @ sk2 )
!= sk13 ) ),
inference(simp,[status(thm)],[30548]) ).
thf(16113,plain,
! [A: $i] :
( sk8
| ( p2 @ A )
| ~ ( p2 @ ( sk12 @ A ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,103]) ).
thf(16114,plain,
( sk8
| ( p2 @ sk10 )
| ~ ( p2 @ ( sk12 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[16113:[bind(A,$thf( sk10 ))]]) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( p3 @ B )
| ~ ( r1 @ sk1 @ C )
| ( p2 @ C )
| ~ ( p2 @ ( sk4 @ C ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,14]) ).
thf(163,plain,
! [A: $i] :
( ~ ( p3 @ sk1 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) ) ),
inference(pattern_uni,[status(thm)],[162:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(190,plain,
! [A: $i] :
( ~ ( p3 @ sk1 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(38967,plain,
! [A: $i] :
( ~ ( p3 @ sk1 )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1019,190]) ).
thf(38968,plain,
( ~ ( p3 @ sk1 )
| ( p2 @ sk2 )
| ~ ( p2 @ ( sk4 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[38967:[bind(A,$thf( sk2 ))]]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ( p2 @ B )
| ( r1 @ B @ ( sk3 @ B ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( r1 @ ( sk41 @ A ) @ B )
| ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ( p2 @ B ) ),
inference(cnf,[status(esa)],[6]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( r1 @ ( sk41 @ A ) @ B )
| ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ( p2 @ B ) ),
inference(simp,[status(thm)],[33]) ).
thf(3918,plain,
! [A: $i] :
( ( p2 @ sk1 )
| ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk1 @ ( sk41 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3780,109]) ).
thf(3919,plain,
( ( p2 @ sk1 )
| ( p3 @ ( sk9 @ ( sk41 @ sk1 ) ) )
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[3918:[bind(A,$thf( sk41 @ sk1 ))]]) ).
thf(29650,plain,
! [A: $i] :
( ( p1 @ A )
| ( p1 @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,121]) ).
thf(29651,plain,
( ( p1 @ sk5 )
| ( p1 @ ( sk14 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[29650:[bind(A,$thf( sk5 ))]]) ).
thf(29852,plain,
( ( p1 @ sk5 )
| ( ( p1 @ ( sk14 @ sk5 ) )
!= ( p1 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29651]) ).
thf(29856,plain,
( ( p1 @ sk5 )
| ( ( sk14 @ sk5 )
!= sk5 ) ),
inference(simp,[status(thm)],[29852]) ).
thf(21348,plain,
! [A: $i] :
( ( p4 @ A )
| ( p4 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,112]) ).
thf(21349,plain,
( ( p4 @ sk13 )
| ( p4 @ ( sk6 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[21348:[bind(A,$thf( sk13 ))]]) ).
thf(21544,plain,
( ( p4 @ sk13 )
| ( ( p4 @ ( sk6 @ sk13 ) )
!= ( p4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21349,75]) ).
thf(21556,plain,
( ( p4 @ sk13 )
| ( ( sk6 @ sk13 )
!= sk5 ) ),
inference(simp,[status(thm)],[21544]) ).
thf(11029,plain,
! [A: $i] :
( ( p4 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,95]) ).
thf(11030,plain,
( ( p4 @ sk5 )
| ( r1 @ sk5 @ ( sk6 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[11029:[bind(A,$thf( sk5 ))]]) ).
thf(11396,plain,
( $false
| ( r1 @ sk5 @ ( sk6 @ sk5 ) ) ),
inference(rewrite,[status(thm)],[11030,75]) ).
thf(11397,plain,
r1 @ sk5 @ ( sk6 @ sk5 ),
inference(simp,[status(thm)],[11396]) ).
thf(11398,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ( r1 @ sk1 @ sk2 )
| ( ( r1 @ sk5 @ ( sk6 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11397,69]) ).
thf(11470,plain,
! [A: $i] :
( ( r1 @ sk1 @ sk2 )
| ~ ( p3 @ A )
| ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[11398]) ).
thf(11500,plain,
( ( r1 @ sk1 @ sk2 )
| ~ ( p3 @ ( sk6 @ sk5 ) )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[11470]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ~ sk17
| sk16
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk1 @ sk20 )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57,14]) ).
thf(211,plain,
! [A: $i] :
( ~ sk17
| sk16
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ sk20 )
| ~ ( p2 @ ( sk4 @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( A )),bind(B,$thf( sk20 ))]]) ).
thf(22745,plain,
( ~ sk8
| ( p4 @ sk2 )
| ( ( p4 @ ( sk7 @ sk5 ) )
!= ( p4 @ ( sk6 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21330,21089]) ).
thf(22762,plain,
( ( p4 @ sk2 )
| ~ sk8
| ( ( sk7 @ sk5 )
!= ( sk6 @ sk2 ) ) ),
inference(simp,[status(thm)],[22745]) ).
thf(24013,plain,
! [B: $i,A: $i] :
( ~ sk16
| ( p2 @ B )
| ( p2 @ ( sk27 @ B ) )
| ~ sk24
| ( ( r1 @ A @ A )
!= ( r1 @ sk23 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,115]) ).
thf(24014,plain,
( ~ sk16
| ( p2 @ sk23 )
| ( p2 @ ( sk27 @ sk23 ) )
| ~ sk24 ),
inference(pattern_uni,[status(thm)],[24013:[bind(A,$thf( sk23 )),bind(B,$thf( sk23 ))]]) ).
thf(27118,plain,
( ~ sk16
| ( p2 @ sk23 )
| ~ sk24
| ( ( p2 @ ( sk27 @ sk23 ) )
!= ( p2 @ sk23 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[24014]) ).
thf(27147,plain,
( ( p2 @ sk23 )
| ~ sk16
| ~ sk24
| ( ( sk27 @ sk23 )
!= sk23 ) ),
inference(simp,[status(thm)],[27118]) ).
thf(14838,plain,
! [A: $i] :
( ~ sk8
| ( p1 @ A )
| ~ ( p1 @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8326,100]) ).
thf(14839,plain,
( ~ sk8
| ( p1 @ sk2 )
| ~ ( p1 @ ( sk15 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[14838:[bind(A,$thf( sk2 ))]]) ).
thf(29822,plain,
( ~ sk8
| ( p1 @ sk2 )
| ( ( p1 @ ( sk15 @ sk2 ) )
!= ( p1 @ ( sk14 @ sk13 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29815,14839]) ).
thf(29833,plain,
( ( p1 @ sk2 )
| ~ sk8
| ( ( sk15 @ sk2 )
!= ( sk14 @ sk13 ) ) ),
inference(simp,[status(thm)],[29822]) ).
thf(14811,plain,
! [A: $i] :
( ~ sk17
| sk16
| ( p1 @ A )
| ~ ( p1 @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,100]) ).
thf(14812,plain,
( ~ sk17
| sk16
| ( p1 @ sk20 )
| ~ ( p1 @ ( sk15 @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[14811:[bind(A,$thf( sk20 ))]]) ).
thf(77,plain,
( ( p2 @ sk1 )
| ~ ( p2 @ sk22 )
| sk16 ),
inference(cnf,[status(esa)],[6]) ).
thf(215,plain,
( ( p2 @ sk1 )
| sk16
| ( ( p2 @ sk22 )
!= ( p2 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[62,77]) ).
thf(216,plain,
( ( p2 @ sk1 )
| sk16
| ( sk22 != sk21 ) ),
inference(simp,[status(thm)],[215]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[30,14]) ).
thf(177,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ sk5 )
| ~ ( p2 @ ( sk4 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( A )),bind(B,$thf( sk5 ))]]) ).
thf(35864,plain,
! [B: $i,A: $i] :
( ~ ( p3 @ B )
| ( p2 @ sk5 )
| ~ ( p2 @ ( sk4 @ sk5 ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,177]) ).
thf(35865,plain,
( ~ ( p3 @ sk1 )
| ( p2 @ sk5 )
| ~ ( p2 @ ( sk4 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[35864:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(738,plain,
( sk16
| ~ sk17
| ( sk21 != sk20 )
| ~ ( p3 @ sk5 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[161,133]) ).
thf(756,plain,
( sk16
| ~ sk17
| ( sk21 != sk20 )
| ~ ( p3 @ sk5 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[738]) ).
thf(2793,plain,
! [A: $i] :
( ~ sk8
| ( p3 @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ ( sk9 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2688,109]) ).
thf(2794,plain,
( ~ sk8
| ( p3 @ ( sk9 @ ( sk9 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[2793:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(5031,plain,
! [A: $i] :
( ( p1 @ sk1 )
| sk8
| ( p2 @ A )
| ( p2 @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ ( sk14 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4865,124]) ).
thf(5032,plain,
( ( p1 @ sk1 )
| sk8
| ( p2 @ ( sk14 @ sk1 ) )
| ( p2 @ ( sk11 @ ( sk14 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[5031:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(3922,plain,
! [A: $i] :
( ( p2 @ sk1 )
| ( p4 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ ( sk41 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3780,81]) ).
thf(3923,plain,
( ( p2 @ sk1 )
| ( p4 @ ( sk41 @ sk1 ) )
| ( r1 @ ( sk6 @ ( sk41 @ sk1 ) ) @ ( sk7 @ ( sk41 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[3922:[bind(A,$thf( sk41 @ sk1 ))]]) ).
thf(1050,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk16
| ~ ( p3 @ A )
| ( r1 @ sk1 @ sk2 )
| ( ( r1 @ sk1 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44,69]) ).
thf(1051,plain,
( ( p2 @ sk1 )
| sk16
| ~ ( p3 @ sk21 )
| ( r1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1050:[bind(A,$thf( sk21 ))]]) ).
thf(18208,plain,
! [A: $i] :
( sk8
| ( p2 @ A )
| ~ ( p2 @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,106]) ).
thf(18209,plain,
( sk8
| ( p2 @ sk10 )
| ~ ( p2 @ ( sk41 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[18208:[bind(A,$thf( sk10 ))]]) ).
thf(18758,plain,
( sk8
| ( p2 @ sk10 )
| ( ( p2 @ ( sk41 @ sk10 ) )
!= ( p2 @ ( sk11 @ sk10 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1000,18209]) ).
thf(18786,plain,
( sk8
| ( p2 @ sk10 )
| ( ( sk41 @ sk10 )
!= ( sk11 @ sk10 ) ) ),
inference(simp,[status(thm)],[18758]) ).
thf(130,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,26]) ).
thf(131,plain,
( ~ ( p3 @ sk13 )
| ~ ( p2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( sk13 ))]]) ).
thf(150,plain,
( ( p2 @ sk1 )
| sk16
| ~ ( p3 @ sk13 )
| ( ( p2 @ sk21 )
!= ( p2 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[62,131]) ).
thf(155,plain,
( ( p2 @ sk1 )
| sk16
| ~ ( p3 @ sk13 )
| ( sk21 != sk2 ) ),
inference(simp,[status(thm)],[150]) ).
thf(4798,plain,
( sk16
| ~ ( p3 @ sk13 )
| ( sk21 != sk2 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[155,131]) ).
thf(4810,plain,
( sk16
| ~ ( p3 @ sk13 )
| ( sk21 != sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[4798]) ).
thf(20888,plain,
! [A: $i] :
( sk8
| ( p4 @ A )
| ~ ( p4 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,111]) ).
thf(20889,plain,
( sk8
| ( p4 @ sk10 )
| ~ ( p4 @ ( sk7 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[20888:[bind(A,$thf( sk10 ))]]) ).
thf(21561,plain,
( sk8
| ( p4 @ sk10 )
| ( ( p4 @ ( sk7 @ sk10 ) )
!= ( p4 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21558,20889]) ).
thf(21569,plain,
( sk8
| ( p4 @ sk10 )
| ( ( sk7 @ sk10 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[21561]) ).
thf(8574,plain,
! [A: $i] :
( ~ sk8
| ( p1 @ A )
| ( r1 @ A @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8326,87]) ).
thf(8575,plain,
( ~ sk8
| ( p1 @ sk2 )
| ( r1 @ sk2 @ ( sk14 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8574:[bind(A,$thf( sk2 ))]]) ).
thf(34,plain,
( ~ sk16
| ( r1 @ sk23 @ sk25 )
| ~ sk24 ),
inference(cnf,[status(esa)],[6]) ).
thf(392,plain,
! [A: $i] :
( ~ sk16
| ~ sk24
| ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk23 @ sk25 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,109]) ).
thf(408,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk16
| ~ sk24
| ~ sk8
| ( sk23 != sk1 )
| ( sk25 != A ) ),
inference(simp,[status(thm)],[392]) ).
thf(411,plain,
( ( p3 @ ( sk9 @ sk25 ) )
| ~ sk16
| ~ sk24
| ~ sk8
| ( sk23 != sk1 ) ),
inference(simp,[status(thm)],[408]) ).
thf(72,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ( p2 @ A )
| ( r1 @ ( sk27 @ A ) @ ( sk28 @ A ) )
| ~ sk24 ),
inference(cnf,[status(esa)],[6]) ).
thf(116,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ( p2 @ A )
| ( r1 @ ( sk27 @ A ) @ ( sk28 @ A ) )
| ~ sk24 ),
inference(simp,[status(thm)],[72]) ).
thf(22769,plain,
( ~ sk16
| ( p4 @ sk23 )
| ( ( p4 @ ( sk6 @ sk23 ) )
!= ( p4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21346,75]) ).
thf(22774,plain,
( ( p4 @ sk23 )
| ~ sk16
| ( ( sk6 @ sk23 )
!= sk5 ) ),
inference(simp,[status(thm)],[22769]) ).
thf(14899,plain,
! [A: $i] :
( ~ ( p3 @ sk13 )
| ( p1 @ A )
| ~ ( p1 @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1056,100]) ).
thf(14900,plain,
( ~ ( p3 @ sk13 )
| ( p1 @ sk2 )
| ~ ( p1 @ ( sk15 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[14899:[bind(A,$thf( sk2 ))]]) ).
thf(3405,plain,
! [A: $i] :
( sk8
| ( p2 @ A )
| ( r1 @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,84]) ).
thf(3406,plain,
( sk8
| ( p2 @ sk5 )
| ( r1 @ ( sk11 @ sk5 ) @ ( sk12 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[3405:[bind(A,$thf( sk5 ))]]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ sk24
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk23 @ sk25 )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[34,14]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( p2 @ B )
| ~ sk16
| ~ sk24
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ~ ( p2 @ ( sk4 @ B ) )
| ( sk23 != sk1 )
| ( sk25 != B ) ),
inference(simp,[status(thm)],[200]) ).
thf(206,plain,
! [A: $i] :
( ( p2 @ sk25 )
| ~ sk16
| ~ sk24
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ~ ( p2 @ ( sk4 @ sk25 ) )
| ( sk23 != sk1 ) ),
inference(simp,[status(thm)],[203]) ).
thf(24020,plain,
! [A: $i] :
( ~ sk16
| ~ sk24
| ( p2 @ A )
| ( p2 @ ( sk27 @ A ) )
| ( ( r1 @ sk23 @ sk25 )
!= ( r1 @ sk23 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,115]) ).
thf(24021,plain,
( ~ sk16
| ~ sk24
| ( p2 @ sk25 )
| ( p2 @ ( sk27 @ sk25 ) ) ),
inference(pattern_uni,[status(thm)],[24020:[bind(A,$thf( sk25 ))]]) ).
thf(28571,plain,
( ~ sk16
| ~ sk24
| ( p2 @ sk25 )
| ( ( p2 @ ( sk27 @ sk25 ) )
!= ( p2 @ sk26 ) ) ),
inference(paramod_ordered,[status(thm)],[24021,60]) ).
thf(28666,plain,
( ( p2 @ sk25 )
| ~ sk16
| ~ sk24
| ( ( sk27 @ sk25 )
!= sk26 ) ),
inference(simp,[status(thm)],[28571]) ).
thf(14856,plain,
! [A: $i] :
( ( p1 @ A )
| ~ ( p1 @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,100]) ).
thf(14857,plain,
( ( p1 @ sk13 )
| ~ ( p1 @ ( sk15 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[14856:[bind(A,$thf( sk13 ))]]) ).
thf(15017,plain,
( $false
| ~ ( p1 @ ( sk15 @ sk13 ) ) ),
inference(rewrite,[status(thm)],[14857,16]) ).
thf(15018,plain,
~ ( p1 @ ( sk15 @ sk13 ) ),
inference(simp,[status(thm)],[15017]) ).
thf(15020,plain,
( ~ ( p3 @ ( sk14 @ sk1 ) )
| ~ ( p2 @ sk2 )
| ( ( p1 @ ( sk15 @ sk13 ) )
!= ( p1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[5047,15018]) ).
thf(15023,plain,
( ~ ( p3 @ ( sk14 @ sk1 ) )
| ~ ( p2 @ sk2 )
| ( ( sk15 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[15020]) ).
thf(731,plain,
( sk16
| ~ sk17
| ( sk21 != sk20 )
| ~ ( p3 @ sk1 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[161,142]) ).
thf(766,plain,
( sk16
| ~ sk17
| ( sk21 != sk20 )
| ~ ( p3 @ sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[731]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ( sk36 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ( p2 @ B ) ),
inference(cnf,[status(esa)],[6]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ( sk36 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ( p2 @ B ) ),
inference(simp,[status(thm)],[29]) ).
thf(4923,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ A @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,87]) ).
thf(4924,plain,
( ( p1 @ sk5 )
| ( r1 @ sk5 @ ( sk14 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[4923:[bind(A,$thf( sk5 ))]]) ).
thf(20902,plain,
! [A: $i] :
( ( p4 @ A )
| ~ ( p4 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,111]) ).
thf(20903,plain,
( ( p4 @ sk13 )
| ~ ( p4 @ ( sk7 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[20902:[bind(A,$thf( sk13 ))]]) ).
thf(144,plain,
( ( p2 @ sk1 )
| sk16
| ~ ( p3 @ sk5 )
| ( ( p2 @ sk21 )
!= ( p2 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[62,133]) ).
thf(154,plain,
( ( p2 @ sk1 )
| sk16
| ~ ( p3 @ sk5 )
| ( sk21 != sk2 ) ),
inference(simp,[status(thm)],[144]) ).
thf(4713,plain,
( sk16
| ~ ( p3 @ sk5 )
| ( sk21 != sk2 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[154,133]) ).
thf(4753,plain,
( sk16
| ~ ( p3 @ sk5 )
| ( sk21 != sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[4713]) ).
thf(21398,plain,
! [A: $i] :
( ~ ( p3 @ sk1 )
| ( p4 @ A )
| ( p4 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1019,112]) ).
thf(21399,plain,
( ~ ( p3 @ sk1 )
| ( p4 @ sk2 )
| ( p4 @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[21398:[bind(A,$thf( sk2 ))]]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ~ ( sk30 @ B )
| ~ ( p2 @ ( sk33 @ B @ A ) )
| ( sk29 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ~ ( sk30 @ B )
| ~ ( p2 @ ( sk33 @ B @ A ) )
| ( sk29 @ A ) ),
inference(simp,[status(thm)],[32]) ).
thf(1046,plain,
! [A: $i] :
( sk8
| ~ ( p3 @ A )
| ( r1 @ sk1 @ sk2 )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,69]) ).
thf(1047,plain,
( sk8
| ~ ( p3 @ sk10 )
| ( r1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1046:[bind(A,$thf( sk10 ))]]) ).
thf(43,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ( r1 @ A @ ( sk37 @ A ) )
| ~ ( sk36 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(117,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ( r1 @ A @ ( sk37 @ A ) )
| ~ ( sk36 @ A ) ),
inference(simp,[status(thm)],[43]) ).
thf(255,plain,
( sk16
| ( sk21 != sk1 )
| ~ ( p3 @ sk5 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[158,133]) ).
thf(270,plain,
( sk16
| ( sk21 != sk1 )
| ~ ( p3 @ sk5 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[255]) ).
thf(10953,plain,
! [A: $i] :
( ~ sk8
| ( p4 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8326,95]) ).
thf(10954,plain,
( ~ sk8
| ( p4 @ sk2 )
| ( r1 @ sk2 @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[10953:[bind(A,$thf( sk2 ))]]) ).
thf(10957,plain,
! [B: $i,A: $i] :
( ( p4 @ B )
| ( r1 @ B @ ( sk6 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,95]) ).
thf(10958,plain,
( ( p4 @ sk1 )
| ( r1 @ sk1 @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[10957:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(11198,plain,
! [A: $i] :
( ( p4 @ sk1 )
| ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk1 @ ( sk6 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10958,109]) ).
thf(11199,plain,
( ( p4 @ sk1 )
| ( p3 @ ( sk9 @ ( sk6 @ sk1 ) ) )
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[11198:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(15926,plain,
( ( p3 @ ( sk9 @ ( sk6 @ sk1 ) ) )
| ~ sk8
| ( ( p4 @ sk5 )
!= ( p4 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[11199,75]) ).
thf(15935,plain,
( ( p3 @ ( sk9 @ ( sk6 @ sk1 ) ) )
| ~ sk8
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[15926]) ).
thf(18223,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,106]) ).
thf(18224,plain,
( ( p2 @ sk13 )
| ~ ( p2 @ ( sk41 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[18223:[bind(A,$thf( sk13 ))]]) ).
thf(18477,plain,
( sk8
| ( p2 @ sk13 )
| ( ( p2 @ ( sk41 @ sk13 ) )
!= ( p2 @ ( sk11 @ sk13 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1008,18224]) ).
thf(18493,plain,
( sk8
| ( p2 @ sk13 )
| ( ( sk41 @ sk13 )
!= ( sk11 @ sk13 ) ) ),
inference(simp,[status(thm)],[18477]) ).
thf(20882,plain,
! [A: $i] :
( ~ sk8
| ( p4 @ A )
| ~ ( p4 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8326,111]) ).
thf(20883,plain,
( ~ sk8
| ( p4 @ sk2 )
| ~ ( p4 @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[20882:[bind(A,$thf( sk2 ))]]) ).
thf(21564,plain,
( ~ sk8
| ( p4 @ sk2 )
| ( ( p4 @ ( sk7 @ sk2 ) )
!= ( p4 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21558,20883]) ).
thf(21567,plain,
( ( p4 @ sk2 )
| ~ sk8
| ( ( sk7 @ sk2 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[21564]) ).
thf(2248,plain,
! [B: $i,A: $i] :
( ( p4 @ B )
| ( r1 @ ( sk6 @ B ) @ ( sk7 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,81]) ).
thf(2249,plain,
( ( p4 @ sk1 )
| ( r1 @ ( sk6 @ sk1 ) @ ( sk7 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[2248:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(1570,plain,
( sk8
| ( p2 @ sk13 )
| ( ( sk11 @ sk13 )
!= sk13 ) ),
inference(simp,[status(thm)],[1561]) ).
thf(11222,plain,
! [A: $i] :
( ( p4 @ sk1 )
| ( p1 @ A )
| ( r1 @ A @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ ( sk6 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10958,87]) ).
thf(11223,plain,
( ( p4 @ sk1 )
| ( p1 @ ( sk6 @ sk1 ) )
| ( r1 @ ( sk6 @ sk1 ) @ ( sk14 @ ( sk6 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[11222:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(29843,plain,
( ( p1 @ sk5 )
| ( ( p1 @ ( sk15 @ sk13 ) )
!= ( p1 @ ( sk14 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29651,15018]) ).
thf(29861,plain,
( ( p1 @ sk5 )
| ( ( sk15 @ sk13 )
!= ( sk14 @ sk5 ) ) ),
inference(simp,[status(thm)],[29843]) ).
thf(2700,plain,
! [A: $i] :
( ( r1 @ A @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,82]) ).
thf(2701,plain,
( ( r1 @ sk13 @ ( sk9 @ sk13 ) )
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[2700:[bind(A,$thf( sk13 ))]]) ).
thf(2855,plain,
! [A: $i] :
( ~ sk8
| ( p3 @ ( sk9 @ A ) )
| ( ( r1 @ sk13 @ ( sk9 @ sk13 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2701,109]) ).
thf(2884,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( sk13 != sk1 )
| ( ( sk9 @ sk13 )
!= A ) ),
inference(simp,[status(thm)],[2855]) ).
thf(2890,plain,
( ( p3 @ ( sk9 @ ( sk9 @ sk13 ) ) )
| ~ sk8
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[2884]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,14]) ).
thf(181,plain,
! [A: $i] :
( ~ ( p3 @ sk13 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) ) ),
inference(pattern_uni,[status(thm)],[180:[bind(A,$thf( sk13 ))]]) ).
thf(195,plain,
! [A: $i] :
( ~ ( p3 @ sk13 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(45206,plain,
! [A: $i] :
( ~ ( p3 @ sk13 )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1056,195]) ).
thf(45207,plain,
( ~ ( p3 @ sk13 )
| ( p2 @ sk2 )
| ~ ( p2 @ ( sk4 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[45206:[bind(A,$thf( sk2 ))]]) ).
thf(286,plain,
( sk16
| ( sk22 != sk21 )
| ~ sk17
| ( ( p2 @ sk20 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[216,54]) ).
thf(297,plain,
( sk16
| ( sk22 != sk21 )
| ~ sk17
| ( sk20 != sk1 ) ),
inference(simp,[status(thm)],[286]) ).
thf(166,plain,
! [B: $i,A: $i] :
( sk8
| ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,14]) ).
thf(167,plain,
! [A: $i] :
( sk8
| ~ ( p3 @ sk10 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) ) ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( sk10 ))]]) ).
thf(192,plain,
! [A: $i] :
( sk8
| ~ ( p3 @ sk10 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(3370,plain,
! [A: $i] :
( sk8
| ( p2 @ A )
| ( r1 @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,84]) ).
thf(3371,plain,
( sk8
| ( p2 @ sk10 )
| ( r1 @ ( sk11 @ sk10 ) @ ( sk12 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[3370:[bind(A,$thf( sk10 ))]]) ).
thf(21,plain,
( ( p2 @ sk1 )
| ( r1 @ sk21 @ sk22 )
| sk16 ),
inference(cnf,[status(esa)],[6]) ).
thf(136,plain,
! [A: $i] :
( ~ sk16
| ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,26]) ).
thf(137,plain,
( ~ sk16
| ~ ( p3 @ sk23 )
| ~ ( p2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[136:[bind(A,$thf( sk23 ))]]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ ( sk18 @ B @ A ) @ ( sk19 @ B @ A ) )
| sk17
| sk16 ),
inference(cnf,[status(esa)],[6]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ ( sk18 @ B @ A ) @ ( sk19 @ B @ A ) )
| sk17
| sk16 ),
inference(simp,[status(thm)],[70]) ).
thf(12,plain,
( ~ sk16
| ( r1 @ sk25 @ sk26 )
| ~ sk24 ),
inference(cnf,[status(esa)],[6]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ sk24
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk25 @ sk26 )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,14]) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( p2 @ B )
| ~ sk16
| ~ sk24
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ~ ( p2 @ ( sk4 @ B ) )
| ( sk25 != sk1 )
| ( sk26 != B ) ),
inference(simp,[status(thm)],[179]) ).
thf(197,plain,
! [A: $i] :
( ( p2 @ sk26 )
| ~ sk16
| ~ sk24
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ~ ( p2 @ ( sk4 @ sk26 ) )
| ( sk25 != sk1 ) ),
inference(simp,[status(thm)],[188]) ).
thf(29602,plain,
! [A: $i] :
( ~ sk16
| ( p1 @ A )
| ( p1 @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,121]) ).
thf(29603,plain,
( ~ sk16
| ( p1 @ sk23 )
| ( p1 @ ( sk14 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[29602:[bind(A,$thf( sk23 ))]]) ).
thf(30574,plain,
( ~ sk16
| ( p1 @ sk23 )
| ( ( p1 @ ( sk14 @ sk23 ) )
!= ( p1 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[29603,16]) ).
thf(30584,plain,
( ( p1 @ sk23 )
| ~ sk16
| ( ( sk14 @ sk23 )
!= sk13 ) ),
inference(simp,[status(thm)],[30574]) ).
thf(21299,plain,
! [A: $i] :
( ~ sk17
| sk16
| ( p4 @ A )
| ( p4 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,112]) ).
thf(21300,plain,
( ~ sk17
| sk16
| ( p4 @ sk20 )
| ( p4 @ ( sk6 @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[21299:[bind(A,$thf( sk20 ))]]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ B @ ( sk34 @ B @ A ) )
| ( sk29 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ B @ ( sk34 @ B @ A ) )
| ( sk29 @ A ) ),
inference(simp,[status(thm)],[13]) ).
thf(14842,plain,
! [B: $i,A: $i] :
( ( p1 @ B )
| ~ ( p1 @ ( sk15 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,100]) ).
thf(14843,plain,
( ( p1 @ sk1 )
| ~ ( p1 @ ( sk15 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[14842:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(29797,plain,
( ( p1 @ sk1 )
| ( ( p1 @ ( sk15 @ sk1 ) )
!= ( p1 @ ( sk14 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29589,14843]) ).
thf(29806,plain,
( ( p1 @ sk1 )
| ( ( sk15 @ sk1 )
!= ( sk14 @ sk1 ) ) ),
inference(simp,[status(thm)],[29797]) ).
thf(3930,plain,
! [A: $i] :
( ( p2 @ sk1 )
| ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ sk1 @ ( sk41 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3780,26]) ).
thf(3931,plain,
( ( p2 @ sk1 )
| ~ ( p3 @ ( sk41 @ sk1 ) )
| ~ ( p2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3930:[bind(A,$thf( sk41 @ sk1 ))]]) ).
thf(743,plain,
( sk16
| ~ sk17
| ( sk21 != sk20 )
| sk8
| ( ( p2 @ sk10 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[161,9]) ).
thf(757,plain,
( sk16
| sk8
| ~ sk17
| ( sk21 != sk20 )
| ( sk10 != sk1 ) ),
inference(simp,[status(thm)],[743]) ).
thf(3781,plain,
! [A: $i] :
( sk8
| ( p2 @ A )
| ( r1 @ A @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,85]) ).
thf(3782,plain,
( sk8
| ( p2 @ sk10 )
| ( r1 @ sk10 @ ( sk41 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[3781:[bind(A,$thf( sk10 ))]]) ).
thf(3380,plain,
! [A: $i] :
( sk8
| ( p2 @ A )
| ( r1 @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,84]) ).
thf(3381,plain,
( sk8
| ( p2 @ sk13 )
| ( r1 @ ( sk11 @ sk13 ) @ ( sk12 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[3380:[bind(A,$thf( sk13 ))]]) ).
thf(168,plain,
! [B: $i,A: $i] :
( sk8
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[73,14]) ).
thf(169,plain,
! [A: $i] :
( sk8
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ sk10 )
| ~ ( p2 @ ( sk4 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[168:[bind(A,$thf( A )),bind(B,$thf( sk10 ))]]) ).
thf(10754,plain,
( ~ sk16
| sk8
| ( p2 @ sk23 )
| ( ( p2 @ ( sk11 @ sk23 ) )
!= ( p2 @ sk23 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1005]) ).
thf(10771,plain,
( sk8
| ( p2 @ sk23 )
| ~ sk16
| ( ( sk11 @ sk23 )
!= sk23 ) ),
inference(simp,[status(thm)],[10754]) ).
thf(10736,plain,
( ~ sk16
| sk8
| ( p2 @ sk23 )
| ( ( p2 @ ( sk11 @ sk23 ) )
!= ( p2 @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[1005,9]) ).
thf(10760,plain,
( sk8
| ( p2 @ sk23 )
| ~ sk16
| ( ( sk11 @ sk23 )
!= sk10 ) ),
inference(simp,[status(thm)],[10736]) ).
thf(21538,plain,
( ( p4 @ sk13 )
| ( ( p4 @ ( sk7 @ sk5 ) )
!= ( p4 @ ( sk6 @ sk13 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21349,21089]) ).
thf(21547,plain,
( ( p4 @ sk13 )
| ( ( sk7 @ sk5 )
!= ( sk6 @ sk13 ) ) ),
inference(simp,[status(thm)],[21538]) ).
thf(992,plain,
! [A: $i] :
( sk8
| ( p2 @ A )
| ( p2 @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,124]) ).
thf(993,plain,
( sk8
| ( p2 @ sk5 )
| ( p2 @ ( sk11 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[992:[bind(A,$thf( sk5 ))]]) ).
thf(16422,plain,
( sk8
| ( p2 @ sk5 )
| ( ( p2 @ ( sk12 @ sk5 ) )
!= ( p2 @ ( sk11 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[993,16176]) ).
thf(16441,plain,
( sk8
| ( p2 @ sk5 )
| ( ( sk12 @ sk5 )
!= ( sk11 @ sk5 ) ) ),
inference(simp,[status(thm)],[16422]) ).
thf(1246,plain,
( sk8
| ( p2 @ sk1 )
| ( ( p2 @ ( sk11 @ sk1 ) )
!= ( p2 @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[991,9]) ).
thf(1270,plain,
( sk8
| ( p2 @ sk1 )
| ( ( sk11 @ sk1 )
!= sk10 ) ),
inference(simp,[status(thm)],[1246]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[49,14]) ).
thf(183,plain,
! [A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ sk13 )
| ~ ( p2 @ ( sk4 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[182:[bind(A,$thf( A )),bind(B,$thf( sk13 ))]]) ).
thf(37268,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ( p2 @ sk13 )
| ~ ( p2 @ ( sk4 @ sk13 ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,183]) ).
thf(37269,plain,
( ~ ( p3 @ sk13 )
| ( p2 @ sk13 )
| ~ ( p2 @ ( sk4 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[37268:[bind(A,$thf( sk13 ))]]) ).
thf(402,plain,
! [A: $i] :
( ~ sk16
| ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,109]) ).
thf(403,plain,
( ~ sk16
| ( p3 @ ( sk9 @ sk23 ) )
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[402:[bind(A,$thf( sk23 ))]]) ).
thf(28620,plain,
( ~ sk16
| ~ sk24
| ( p2 @ sk25 )
| ( ( p2 @ ( sk27 @ sk25 ) )
!= ( p2 @ sk25 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[24021]) ).
thf(28675,plain,
( ( p2 @ sk25 )
| ~ sk16
| ~ sk24
| ( ( sk27 @ sk25 )
!= sk25 ) ),
inference(simp,[status(thm)],[28620]) ).
thf(10913,plain,
! [A: $i] :
( sk8
| ( p2 @ sk1 )
| ( p4 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ ( sk11 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6905,95]) ).
thf(10914,plain,
( sk8
| ( p2 @ sk1 )
| ( p4 @ ( sk11 @ sk1 ) )
| ( r1 @ ( sk11 @ sk1 ) @ ( sk6 @ ( sk11 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[10913:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(4937,plain,
! [A: $i] :
( ~ ( p3 @ sk1 )
| ( p1 @ A )
| ( r1 @ A @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1019,87]) ).
thf(4938,plain,
( ~ ( p3 @ sk1 )
| ( p1 @ sk2 )
| ( r1 @ sk2 @ ( sk14 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[4937:[bind(A,$thf( sk2 ))]]) ).
thf(11045,plain,
! [A: $i] :
( ~ ( p3 @ sk1 )
| ( p4 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1019,95]) ).
thf(11046,plain,
( ~ ( p3 @ sk1 )
| ( p4 @ sk2 )
| ( r1 @ sk2 @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[11045:[bind(A,$thf( sk2 ))]]) ).
thf(22750,plain,
( ~ sk8
| ( p4 @ sk2 )
| ( ( p4 @ ( sk7 @ sk2 ) )
!= ( p4 @ ( sk6 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21330,20883]) ).
thf(22758,plain,
( ( p4 @ sk2 )
| ~ sk8
| ( ( sk7 @ sk2 )
!= ( sk6 @ sk2 ) ) ),
inference(simp,[status(thm)],[22750]) ).
thf(4866,plain,
! [A: $i] :
( sk8
| ( p1 @ A )
| ( r1 @ A @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,87]) ).
thf(4867,plain,
( sk8
| ( p1 @ sk10 )
| ( r1 @ sk10 @ ( sk14 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[4866:[bind(A,$thf( sk10 ))]]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( p2 @ ( sk39 @ B @ A ) )
| ~ ( sk36 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( p2 @ ( sk39 @ B @ A ) )
| ~ ( sk36 @ A ) ),
inference(simp,[status(thm)],[53]) ).
thf(447,plain,
( sk16
| sk8
| ( sk21 != sk10 )
| ~ ( p3 @ sk1 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[152,142]) ).
thf(471,plain,
( sk16
| sk8
| ( sk21 != sk10 )
| ~ ( p3 @ sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[447]) ).
thf(224,plain,
! [A: $i] :
( ~ sk16
| ~ sk24
| ~ ( sk29 @ A )
| ~ ( p2 @ ( sk38 @ A ) )
| ~ ( sk36 @ A )
| ( ( r1 @ sk23 @ sk25 )
!= ( r1 @ sk23 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,101]) ).
thf(225,plain,
( ~ sk16
| ~ sk24
| ~ ( sk29 @ sk25 )
| ~ ( p2 @ ( sk38 @ sk25 ) )
| ~ ( sk36 @ sk25 ) ),
inference(pattern_uni,[status(thm)],[224:[bind(A,$thf( sk25 ))]]) ).
thf(38861,plain,
! [B: $i,A: $i] :
( ~ ( p3 @ sk1 )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,190]) ).
thf(38862,plain,
( ~ ( p3 @ sk1 )
| ( p2 @ sk1 )
| ~ ( p2 @ ( sk4 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[38861:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(21577,plain,
( sk8
| ( p4 @ sk10 )
| ( ( p4 @ ( sk7 @ sk10 ) )
!= ( p4 @ ( sk6 @ sk10 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21336,20889]) ).
thf(21587,plain,
( sk8
| ( p4 @ sk10 )
| ( ( sk7 @ sk10 )
!= ( sk6 @ sk10 ) ) ),
inference(simp,[status(thm)],[21577]) ).
thf(11421,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk5 @ ( sk6 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11397,109]) ).
thf(11466,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[11421]) ).
thf(11496,plain,
( ( p3 @ ( sk9 @ ( sk6 @ sk5 ) ) )
| ~ sk8
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[11466]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,14]) ).
thf(171,plain,
! [A: $i] :
( ~ sk16
| ~ ( p3 @ sk23 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( sk23 ))]]) ).
thf(193,plain,
! [A: $i] :
( ~ sk16
| ~ ( p3 @ sk23 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[171]) ).
thf(10967,plain,
! [A: $i] :
( ~ sk16
| ( p4 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,95]) ).
thf(10968,plain,
( ~ sk16
| ( p4 @ sk23 )
| ( r1 @ sk23 @ ( sk6 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[10967:[bind(A,$thf( sk23 ))]]) ).
thf(2836,plain,
( sk16
| ~ sk17
| ( sk21 != sk20 )
| ~ sk8
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[161,2798]) ).
thf(2845,plain,
( sk16
| ~ sk17
| ( sk21 != sk20 )
| ~ sk8
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[2836]) ).
thf(22771,plain,
( ~ sk16
| ( p4 @ sk23 )
| ( ( p4 @ ( sk6 @ sk23 ) )
!= ( p4 @ sk23 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21346]) ).
thf(22781,plain,
( ( p4 @ sk23 )
| ~ sk16
| ( ( sk6 @ sk23 )
!= sk23 ) ),
inference(simp,[status(thm)],[22771]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27,14]) ).
thf(173,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ( p2 @ sk23 )
| ~ ( p2 @ ( sk4 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( A )),bind(B,$thf( sk23 ))]]) ).
thf(4933,plain,
! [A: $i] :
( ~ ( p3 @ sk13 )
| ( p1 @ A )
| ( r1 @ A @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1056,87]) ).
thf(4934,plain,
( ~ ( p3 @ sk13 )
| ( p1 @ sk2 )
| ( r1 @ sk2 @ ( sk14 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[4933:[bind(A,$thf( sk2 ))]]) ).
thf(1798,plain,
! [A: $i] :
( sk8
| ( p1 @ A )
| ( r1 @ ( sk14 @ A ) @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,80]) ).
thf(1799,plain,
( sk8
| ( p1 @ sk10 )
| ( r1 @ ( sk14 @ sk10 ) @ ( sk15 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[1798:[bind(A,$thf( sk10 ))]]) ).
thf(14874,plain,
! [A: $i] :
( ~ sk8
| ( p1 @ A )
| ~ ( p1 @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ ( sk9 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2688,100]) ).
thf(14875,plain,
( ~ sk8
| ( p1 @ ( sk9 @ sk1 ) )
| ~ ( p1 @ ( sk15 @ ( sk9 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[14874:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(5025,plain,
! [A: $i] :
( ( p1 @ sk1 )
| sk8
| ( p2 @ A )
| ( r1 @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( ( r1 @ sk1 @ ( sk14 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4865,84]) ).
thf(5026,plain,
( ( p1 @ sk1 )
| sk8
| ( p2 @ ( sk14 @ sk1 ) )
| ( r1 @ ( sk11 @ ( sk14 @ sk1 ) ) @ ( sk12 @ ( sk14 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[5025:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(18275,plain,
! [A: $i] :
( ( p2 @ A )
| ~ ( p2 @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,106]) ).
thf(18276,plain,
( ( p2 @ sk5 )
| ~ ( p2 @ ( sk41 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[18275:[bind(A,$thf( sk5 ))]]) ).
thf(10999,plain,
! [A: $i] :
( ~ ( p3 @ sk5 )
| ( p4 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1070,95]) ).
thf(11000,plain,
( ~ ( p3 @ sk5 )
| ( p4 @ sk2 )
| ( r1 @ sk2 @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[10999:[bind(A,$thf( sk2 ))]]) ).
thf(11022,plain,
! [A: $i] :
( ( p2 @ sk1 )
| ( p4 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ ( sk41 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3780,95]) ).
thf(11023,plain,
( ( p2 @ sk1 )
| ( p4 @ ( sk41 @ sk1 ) )
| ( r1 @ ( sk41 @ sk1 ) @ ( sk6 @ ( sk41 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[11022:[bind(A,$thf( sk41 @ sk1 ))]]) ).
thf(996,plain,
! [A: $i] :
( ~ sk17
| sk16
| sk8
| ( p2 @ A )
| ( p2 @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,124]) ).
thf(997,plain,
( ~ sk17
| sk16
| sk8
| ( p2 @ sk20 )
| ( p2 @ ( sk11 @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[996:[bind(A,$thf( sk20 ))]]) ).
thf(5077,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ( r1 @ sk1 @ sk2 )
| ( ( r1 @ sk13 @ ( sk14 @ sk13 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5076,69]) ).
thf(5117,plain,
! [A: $i] :
( ( r1 @ sk1 @ sk2 )
| ~ ( p3 @ A )
| ( sk13 != sk1 )
| ( ( sk14 @ sk13 )
!= A ) ),
inference(simp,[status(thm)],[5077]) ).
thf(5149,plain,
( ( r1 @ sk1 @ sk2 )
| ~ ( p3 @ ( sk14 @ sk13 ) )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[5117]) ).
thf(7168,plain,
! [A: $i] :
( sk8
| ( p2 @ sk1 )
| ( p1 @ A )
| ( r1 @ ( sk14 @ A ) @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ ( sk11 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6905,80]) ).
thf(7169,plain,
( sk8
| ( p2 @ sk1 )
| ( p1 @ ( sk11 @ sk1 ) )
| ( r1 @ ( sk14 @ ( sk11 @ sk1 ) ) @ ( sk15 @ ( sk11 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7168:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(16111,plain,
! [B: $i,A: $i] :
( sk8
| ( p2 @ B )
| ~ ( p2 @ ( sk12 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,103]) ).
thf(16112,plain,
( sk8
| ( p2 @ sk1 )
| ~ ( p2 @ ( sk12 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[16111:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(71,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ( p2 @ A )
| ( r1 @ A @ ( sk27 @ A ) )
| ~ sk24 ),
inference(cnf,[status(esa)],[6]) ).
thf(105,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ( p2 @ A )
| ( r1 @ A @ ( sk27 @ A ) )
| ~ sk24 ),
inference(simp,[status(thm)],[71]) ).
thf(6962,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk8
| ( p2 @ A )
| ( r1 @ A @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ ( sk41 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3780,90]) ).
thf(6963,plain,
( ( p2 @ sk1 )
| sk8
| ( p2 @ ( sk41 @ sk1 ) )
| ( r1 @ ( sk41 @ sk1 ) @ ( sk11 @ ( sk41 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[6962:[bind(A,$thf( sk41 @ sk1 ))]]) ).
thf(257,plain,
( sk16
| ( sk21 != sk1 )
| sk8
| ( ( p2 @ sk10 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[158,9]) ).
thf(266,plain,
( sk16
| sk8
| ( sk21 != sk1 )
| ( sk10 != sk1 ) ),
inference(simp,[status(thm)],[257]) ).
thf(1778,plain,
! [B: $i,A: $i] :
( ( p1 @ B )
| ( r1 @ ( sk14 @ B ) @ ( sk15 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,80]) ).
thf(1779,plain,
( ( p1 @ sk1 )
| ( r1 @ ( sk14 @ sk1 ) @ ( sk15 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1778:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ sk24
| ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk23 @ sk25 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,14]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( p2 @ B )
| ~ sk16
| ~ sk24
| ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( sk23 != sk1 )
| ( sk25 != A ) ),
inference(simp,[status(thm)],[199]) ).
thf(205,plain,
! [A: $i] :
( ( p2 @ A )
| ~ sk16
| ~ sk24
| ~ ( p3 @ sk25 )
| ~ ( r1 @ sk1 @ A )
| ~ ( p2 @ ( sk4 @ A ) )
| ( sk23 != sk1 ) ),
inference(simp,[status(thm)],[202]) ).
thf(14844,plain,
! [A: $i] :
( sk8
| ( p1 @ A )
| ~ ( p1 @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,100]) ).
thf(14845,plain,
( sk8
| ( p1 @ sk10 )
| ~ ( p1 @ ( sk15 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[14844:[bind(A,$thf( sk10 ))]]) ).
thf(29825,plain,
( sk8
| ( p1 @ sk10 )
| ( ( p1 @ ( sk15 @ sk10 ) )
!= ( p1 @ ( sk14 @ sk13 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29815,14845]) ).
thf(29834,plain,
( sk8
| ( p1 @ sk10 )
| ( ( sk15 @ sk10 )
!= ( sk14 @ sk13 ) ) ),
inference(simp,[status(thm)],[29825]) ).
thf(397,plain,
! [A: $i] :
( ~ sk17
| sk16
| ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk1 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,109]) ).
thf(398,plain,
( ~ sk17
| sk16
| ( p3 @ ( sk9 @ sk20 ) )
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[397:[bind(A,$thf( sk20 ))]]) ).
thf(30552,plain,
( ~ sk8
| ( p1 @ sk2 )
| ( ( p1 @ ( sk14 @ sk2 ) )
!= ( p1 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29585]) ).
thf(30557,plain,
( ( p1 @ sk2 )
| ~ sk8
| ( ( sk14 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[30552]) ).
thf(29551,plain,
! [A: $i] :
( ~ sk17
| sk16
| ( p1 @ A )
| ( p1 @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,121]) ).
thf(29552,plain,
( ~ sk17
| sk16
| ( p1 @ sk20 )
| ( p1 @ ( sk14 @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[29551:[bind(A,$thf( sk20 ))]]) ).
thf(3806,plain,
! [A: $i] :
( ~ ( p3 @ sk5 )
| ( p2 @ A )
| ( r1 @ A @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1070,85]) ).
thf(3807,plain,
( ~ ( p3 @ sk5 )
| ( p2 @ sk2 )
| ( r1 @ sk2 @ ( sk41 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[3806:[bind(A,$thf( sk2 ))]]) ).
thf(3833,plain,
! [A: $i] :
( ~ ( p3 @ sk13 )
| ( p2 @ A )
| ( r1 @ A @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1056,85]) ).
thf(3834,plain,
( ~ ( p3 @ sk13 )
| ( p2 @ sk2 )
| ( r1 @ sk2 @ ( sk41 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[3833:[bind(A,$thf( sk2 ))]]) ).
thf(25070,plain,
( ~ sk17
| sk16
| ( p4 @ sk20 )
| ( ( p4 @ ( sk6 @ sk20 ) )
!= ( p4 @ sk20 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21300]) ).
thf(25075,plain,
( sk16
| ( p4 @ sk20 )
| ~ sk17
| ( ( sk6 @ sk20 )
!= sk20 ) ),
inference(simp,[status(thm)],[25070]) ).
thf(6981,plain,
! [A: $i] :
( ( p1 @ sk1 )
| sk8
| ( p2 @ A )
| ( r1 @ A @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ ( sk14 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4865,90]) ).
thf(6982,plain,
( ( p1 @ sk1 )
| sk8
| ( p2 @ ( sk14 @ sk1 ) )
| ( r1 @ ( sk14 @ sk1 ) @ ( sk11 @ ( sk14 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[6981:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(10970,plain,
! [A: $i] :
( ( p4 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,95]) ).
thf(10971,plain,
( ( p4 @ sk13 )
| ( r1 @ sk13 @ ( sk6 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[10970:[bind(A,$thf( sk13 ))]]) ).
thf(20949,plain,
! [A: $i] :
( ~ ( p3 @ sk13 )
| ( p4 @ A )
| ~ ( p4 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1056,111]) ).
thf(20950,plain,
( ~ ( p3 @ sk13 )
| ( p4 @ sk2 )
| ~ ( p4 @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[20949:[bind(A,$thf( sk2 ))]]) ).
thf(21559,plain,
( ( p4 @ ( sk7 @ sk5 ) )
!= ( p4 @ ( sk6 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21558,21089]) ).
thf(21568,plain,
( ( sk7 @ sk5 )
!= ( sk6 @ sk5 ) ),
inference(simp,[status(thm)],[21559]) ).
thf(3791,plain,
! [A: $i] :
( ( p2 @ A )
| ( r1 @ A @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,85]) ).
thf(3792,plain,
( ( p2 @ sk13 )
| ( r1 @ sk13 @ ( sk41 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[3791:[bind(A,$thf( sk13 ))]]) ).
thf(289,plain,
( sk16
| ( sk22 != sk21 )
| ~ ( p3 @ sk13 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[216,131]) ).
thf(296,plain,
( sk16
| ( sk22 != sk21 )
| ~ ( p3 @ sk13 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[289]) ).
thf(21519,plain,
( ( p4 @ sk1 )
| ( ( p4 @ ( sk7 @ sk5 ) )
!= ( p4 @ ( sk6 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21334,21089]) ).
thf(21536,plain,
( ( p4 @ sk1 )
| ( ( sk7 @ sk5 )
!= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[21519]) ).
thf(1248,plain,
( sk8
| ( p2 @ sk1 )
| sk16
| ( ( p2 @ ( sk11 @ sk1 ) )
!= ( p2 @ sk22 ) ) ),
inference(paramod_ordered,[status(thm)],[991,77]) ).
thf(1278,plain,
( sk8
| ( p2 @ sk1 )
| sk16
| ( ( sk11 @ sk1 )
!= sk22 ) ),
inference(simp,[status(thm)],[1248]) ).
thf(281,plain,
( sk16
| ( sk22 != sk21 )
| sk8
| ( ( p2 @ sk10 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[216,9]) ).
thf(298,plain,
( sk16
| sk8
| ( sk22 != sk21 )
| ( sk10 != sk1 ) ),
inference(simp,[status(thm)],[281]) ).
thf(2843,plain,
( ( p2 @ sk1 )
| sk16
| ~ sk8
| ( ( p2 @ sk21 )
!= ( p2 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[62,2798]) ).
thf(2847,plain,
( ( p2 @ sk1 )
| sk16
| ~ sk8
| ( sk21 != sk2 ) ),
inference(simp,[status(thm)],[2843]) ).
thf(3722,plain,
( sk16
| ~ sk8
| ( sk21 != sk2 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[2847,2798]) ).
thf(3741,plain,
( sk16
| ~ sk8
| ( sk21 != sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[3722]) ).
thf(3724,plain,
( sk16
| ~ sk8
| ( sk21 != sk2 )
| ~ sk17
| ( ( p2 @ sk20 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[2847,54]) ).
thf(3736,plain,
( sk16
| ~ sk8
| ( sk21 != sk2 )
| ~ sk17
| ( sk20 != sk1 ) ),
inference(simp,[status(thm)],[3724]) ).
thf(279,plain,
( sk16
| ( sk22 != sk21 )
| ~ ( p3 @ sk5 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[216,133]) ).
thf(291,plain,
( sk16
| ( sk22 != sk21 )
| ~ ( p3 @ sk5 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[279]) ).
thf(40,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ( r1 @ D @ ( sk31 @ D @ C @ B @ A ) )
| ( sk30 @ B )
| ( sk29 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ( r1 @ D @ ( sk31 @ D @ C @ B @ A ) )
| ( sk30 @ B )
| ( sk29 @ A ) ),
inference(simp,[status(thm)],[40]) ).
thf(14868,plain,
! [A: $i] :
( ~ ( p3 @ sk5 )
| ( p1 @ A )
| ~ ( p1 @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1070,100]) ).
thf(14869,plain,
( ~ ( p3 @ sk5 )
| ( p1 @ sk2 )
| ~ ( p1 @ ( sk15 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[14868:[bind(A,$thf( sk2 ))]]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( sk29 @ B )
| ~ ( p2 @ ( sk38 @ B ) )
| ~ ( sk36 @ B )
| ( ( r1 @ A @ A )
!= ( r1 @ sk23 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,101]) ).
thf(222,plain,
( ~ sk16
| ~ ( sk29 @ sk23 )
| ~ ( p2 @ ( sk38 @ sk23 ) )
| ~ ( sk36 @ sk23 ) ),
inference(pattern_uni,[status(thm)],[221:[bind(A,$thf( sk23 )),bind(B,$thf( sk23 ))]]) ).
thf(20704,plain,
( ~ sk16
| ~ ( sk29 @ sk23 )
| ~ ( p2 @ sk23 )
| ~ ( p2 @ ( sk38 @ sk23 ) )
| ( ( sk36 @ sk23 )
!= ( sk36 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[20258,222]) ).
thf(20705,plain,
( ~ sk16
| ~ ( sk29 @ sk23 )
| ~ ( p2 @ sk23 )
| ~ ( p2 @ ( sk38 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[20704:[]]) ).
thf(29848,plain,
( ( p1 @ sk5 )
| ( ( p1 @ ( sk14 @ sk5 ) )
!= ( p1 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[29651,16]) ).
thf(29864,plain,
( ( p1 @ sk5 )
| ( ( sk14 @ sk5 )
!= sk13 ) ),
inference(simp,[status(thm)],[29848]) ).
thf(1241,plain,
( sk8
| ( p2 @ sk1 )
| ~ ( p3 @ sk5 )
| ( ( p2 @ ( sk11 @ sk1 ) )
!= ( p2 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[991,133]) ).
thf(1271,plain,
( sk8
| ( p2 @ sk1 )
| ~ ( p3 @ sk5 )
| ( ( sk11 @ sk1 )
!= sk2 ) ),
inference(simp,[status(thm)],[1241]) ).
thf(11200,plain,
! [A: $i] :
( ( p4 @ sk1 )
| sk8
| ( p2 @ A )
| ( p2 @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ ( sk6 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10958,124]) ).
thf(11201,plain,
( ( p4 @ sk1 )
| sk8
| ( p2 @ ( sk6 @ sk1 ) )
| ( p2 @ ( sk11 @ ( sk6 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[11200:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(29590,plain,
! [A: $i] :
( sk8
| ( p1 @ A )
| ( p1 @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,121]) ).
thf(29591,plain,
( sk8
| ( p1 @ sk10 )
| ( p1 @ ( sk14 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[29590:[bind(A,$thf( sk10 ))]]) ).
thf(30526,plain,
( sk8
| ( p1 @ sk10 )
| ( ( p1 @ ( sk14 @ sk10 ) )
!= ( p1 @ sk10 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29591]) ).
thf(30529,plain,
( sk8
| ( p1 @ sk10 )
| ( ( sk14 @ sk10 )
!= sk10 ) ),
inference(simp,[status(thm)],[30526]) ).
thf(134,plain,
! [A: $i] :
( sk8
| ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,26]) ).
thf(135,plain,
( sk8
| ~ ( p3 @ sk10 )
| ~ ( p2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( sk10 ))]]) ).
thf(452,plain,
( sk16
| sk8
| ( sk21 != sk10 )
| ~ ( p3 @ sk10 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[152,135]) ).
thf(466,plain,
( sk16
| sk8
| ( sk21 != sk10 )
| ~ ( p3 @ sk10 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[452]) ).
thf(228,plain,
! [A: $i] :
( ~ sk16
| ~ sk24
| ~ ( sk29 @ A )
| ~ ( p2 @ ( sk38 @ A ) )
| ~ ( sk36 @ A )
| ( ( r1 @ sk25 @ sk26 )
!= ( r1 @ sk23 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12,101]) ).
thf(231,plain,
! [A: $i] :
( ~ sk16
| ~ sk24
| ~ ( sk29 @ A )
| ~ ( p2 @ ( sk38 @ A ) )
| ~ ( sk36 @ A )
| ( sk25 != sk23 )
| ( sk26 != A ) ),
inference(simp,[status(thm)],[228]) ).
thf(236,plain,
( ~ sk16
| ~ sk24
| ~ ( sk29 @ sk26 )
| ~ ( p2 @ ( sk38 @ sk26 ) )
| ~ ( sk36 @ sk26 )
| ( sk25 != sk23 ) ),
inference(simp,[status(thm)],[231]) ).
thf(20914,plain,
! [A: $i] :
( ~ ( p3 @ sk5 )
| ( p4 @ A )
| ~ ( p4 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1070,111]) ).
thf(20915,plain,
( ~ ( p3 @ sk5 )
| ( p4 @ sk2 )
| ~ ( p4 @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[20914:[bind(A,$thf( sk2 ))]]) ).
thf(11037,plain,
! [A: $i] :
( ~ ( p3 @ sk13 )
| ( p4 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1056,95]) ).
thf(11038,plain,
( ~ ( p3 @ sk13 )
| ( p4 @ sk2 )
| ( r1 @ sk2 @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[11037:[bind(A,$thf( sk2 ))]]) ).
thf(11224,plain,
! [A: $i] :
( ( p4 @ sk1 )
| ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ sk1 @ ( sk6 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10958,26]) ).
thf(11225,plain,
( ( p4 @ sk1 )
| ~ ( p3 @ ( sk6 @ sk1 ) )
| ~ ( p2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[11224:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(21091,plain,
( ~ ( p3 @ ( sk6 @ sk1 ) )
| ~ ( p2 @ sk2 )
| ( ( p4 @ ( sk7 @ sk5 ) )
!= ( p4 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[11225,21089]) ).
thf(21094,plain,
( ~ ( p3 @ ( sk6 @ sk1 ) )
| ~ ( p2 @ sk2 )
| ( ( sk7 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[21091]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ sk17
| ~ ( r1 @ sk20 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ A )
| sk16 ),
inference(cnf,[status(esa)],[6]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ~ sk17
| ~ ( r1 @ sk20 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ A )
| sk16 ),
inference(simp,[status(thm)],[52]) ).
thf(21360,plain,
! [A: $i] :
( ~ ( p3 @ sk5 )
| ( p4 @ A )
| ( p4 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1070,112]) ).
thf(21361,plain,
( ~ ( p3 @ sk5 )
| ( p4 @ sk2 )
| ( p4 @ ( sk6 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[21360:[bind(A,$thf( sk2 ))]]) ).
thf(24946,plain,
( ~ ( p3 @ sk5 )
| ( p4 @ sk2 )
| ( ( p4 @ ( sk6 @ sk2 ) )
!= ( p4 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21361]) ).
thf(24948,plain,
( ( p4 @ sk2 )
| ~ ( p3 @ sk5 )
| ( ( sk6 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[24946]) ).
thf(14853,plain,
! [A: $i] :
( ~ sk16
| ( p1 @ A )
| ~ ( p1 @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,100]) ).
thf(14854,plain,
( ~ sk16
| ( p1 @ sk23 )
| ~ ( p1 @ ( sk15 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[14853:[bind(A,$thf( sk23 ))]]) ).
thf(776,plain,
( sk16
| ( sk21 != sk1 )
| ~ sk17
| ~ ( p3 @ sk20 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[158,213]) ).
thf(787,plain,
( sk16
| ( sk21 != sk1 )
| ~ sk17
| ~ ( p3 @ sk20 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[776]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( p2 @ sk1 )
| sk16
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ( p2 @ B )
| ( ( p2 @ ( sk4 @ B ) )
!= ( p2 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[62,14]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( p2 @ sk1 )
| sk16
| ( p2 @ B )
| ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ( ( sk4 @ B )
!= sk21 ) ),
inference(simp,[status(thm)],[184]) ).
thf(22753,plain,
( ~ sk8
| ( p4 @ sk2 )
| ( ( p4 @ ( sk6 @ sk2 ) )
!= ( p4 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21330]) ).
thf(22757,plain,
( ( p4 @ sk2 )
| ~ sk8
| ( ( sk6 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[22753]) ).
thf(405,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,109]) ).
thf(406,plain,
( ( p3 @ ( sk9 @ sk13 ) )
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[405:[bind(A,$thf( sk13 ))]]) ).
thf(67,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ~ ( sk30 @ B )
| ~ ( r1 @ ( sk33 @ B @ A ) @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ( p2 @ C )
| ( sk29 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ~ ( sk30 @ B )
| ~ ( r1 @ ( sk33 @ B @ A ) @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ( p2 @ C )
| ( sk29 @ A ) ),
inference(simp,[status(thm)],[67]) ).
thf(6919,plain,
! [A: $i] :
( sk8
| ( p2 @ A )
| ( r1 @ A @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,90]) ).
thf(6920,plain,
( sk8
| ( p2 @ sk13 )
| ( r1 @ sk13 @ ( sk11 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[6919:[bind(A,$thf( sk13 ))]]) ).
thf(30543,plain,
( ~ sk8
| ( p1 @ sk2 )
| ( ( p1 @ ( sk15 @ sk13 ) )
!= ( p1 @ ( sk14 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29585,15018]) ).
thf(30554,plain,
( ( p1 @ sk2 )
| ~ sk8
| ( ( sk15 @ sk13 )
!= ( sk14 @ sk2 ) ) ),
inference(simp,[status(thm)],[30543]) ).
thf(779,plain,
( ( p2 @ sk1 )
| sk16
| ~ sk17
| ~ ( p3 @ sk20 )
| ( ( p2 @ sk21 )
!= ( p2 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[62,213]) ).
thf(784,plain,
( ( p2 @ sk1 )
| sk16
| ~ sk17
| ~ ( p3 @ sk20 )
| ( sk21 != sk2 ) ),
inference(simp,[status(thm)],[779]) ).
thf(376,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk16
| ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ sk1 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44,26]) ).
thf(377,plain,
( ( p2 @ sk1 )
| sk16
| ~ ( p3 @ sk21 )
| ~ ( p2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[376:[bind(A,$thf( sk21 ))]]) ).
thf(1541,plain,
( sk8
| ( p2 @ sk13 )
| ( ( p2 @ ( sk11 @ sk13 ) )
!= ( p2 @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[1008,9]) ).
thf(1571,plain,
( sk8
| ( p2 @ sk13 )
| ( ( sk11 @ sk13 )
!= sk10 ) ),
inference(simp,[status(thm)],[1541]) ).
thf(21575,plain,
( sk8
| ( p4 @ sk10 )
| ( ( p4 @ ( sk7 @ sk5 ) )
!= ( p4 @ ( sk6 @ sk10 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21336,21089]) ).
thf(21590,plain,
( sk8
| ( p4 @ sk10 )
| ( ( sk7 @ sk5 )
!= ( sk6 @ sk10 ) ) ),
inference(simp,[status(thm)],[21575]) ).
thf(30522,plain,
( sk8
| ( p1 @ sk10 )
| ( ( p1 @ ( sk14 @ sk10 ) )
!= ( p1 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[29591,16]) ).
thf(30536,plain,
( sk8
| ( p1 @ sk10 )
| ( ( sk14 @ sk10 )
!= sk13 ) ),
inference(simp,[status(thm)],[30522]) ).
thf(11439,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ sk5 @ ( sk6 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11397,26]) ).
thf(11457,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( sk5 != sk1 )
| ( ( sk6 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[11439]) ).
thf(11487,plain,
( ~ ( p3 @ ( sk6 @ sk5 ) )
| ~ ( p2 @ sk2 )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[11457]) ).
thf(22763,plain,
( ~ sk16
| ( p4 @ sk23 )
| ( ( p4 @ ( sk7 @ sk5 ) )
!= ( p4 @ ( sk6 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21346,21089]) ).
thf(22776,plain,
( ( p4 @ sk23 )
| ~ sk16
| ( ( sk7 @ sk5 )
!= ( sk6 @ sk23 ) ) ),
inference(simp,[status(thm)],[22763]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ ( sk39 @ B @ A ) @ ( sk40 @ B @ A ) )
| ~ ( sk36 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ ( sk39 @ B @ A ) @ ( sk40 @ B @ A ) )
| ~ ( sk36 @ A ) ),
inference(simp,[status(thm)],[41]) ).
thf(30569,plain,
( ~ sk16
| ( p1 @ sk23 )
| ( ( p1 @ ( sk15 @ sk13 ) )
!= ( p1 @ ( sk14 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29603,15018]) ).
thf(30586,plain,
( ( p1 @ sk23 )
| ~ sk16
| ( ( sk15 @ sk13 )
!= ( sk14 @ sk23 ) ) ),
inference(simp,[status(thm)],[30569]) ).
thf(30571,plain,
( ~ sk16
| ( p1 @ sk23 )
| ( ( p1 @ ( sk15 @ sk23 ) )
!= ( p1 @ ( sk14 @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29603,14854]) ).
thf(30581,plain,
( ( p1 @ sk23 )
| ~ sk16
| ( ( sk15 @ sk23 )
!= ( sk14 @ sk23 ) ) ),
inference(simp,[status(thm)],[30571]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ( p2 @ B )
| ( r1 @ ( sk3 @ B ) @ ( sk4 @ B ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(1313,plain,
( sk8
| ( p2 @ sk5 )
| ( ( p2 @ ( sk11 @ sk5 ) )
!= ( p2 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[993]) ).
thf(1325,plain,
( sk8
| ( p2 @ sk5 )
| ( ( p2 @ ( sk11 @ sk5 ) )
!= ( p2 @ sk5 ) ) ),
inference(simp,[status(thm)],[1313]) ).
thf(25499,plain,
( ~ ( p3 @ sk13 )
| ( p4 @ sk2 )
| ( ( p4 @ ( sk6 @ sk2 ) )
!= ( p4 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21394]) ).
thf(25501,plain,
( ( p4 @ sk2 )
| ~ ( p3 @ sk13 )
| ( ( sk6 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[25499]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ sk24
| ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk25 @ sk26 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12,14]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( p2 @ B )
| ~ sk16
| ~ sk24
| ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( sk25 != sk1 )
| ( sk26 != A ) ),
inference(simp,[status(thm)],[178]) ).
thf(198,plain,
! [A: $i] :
( ( p2 @ A )
| ~ sk16
| ~ sk24
| ~ ( p3 @ sk26 )
| ~ ( r1 @ sk1 @ A )
| ~ ( p2 @ ( sk4 @ A ) )
| ( sk25 != sk1 ) ),
inference(simp,[status(thm)],[189]) ).
thf(1819,plain,
! [A: $i] :
( ( p1 @ A )
| ( r1 @ ( sk14 @ A ) @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,80]) ).
thf(1820,plain,
( ( p1 @ sk5 )
| ( r1 @ ( sk14 @ sk5 ) @ ( sk15 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[1819:[bind(A,$thf( sk5 ))]]) ).
thf(2260,plain,
! [A: $i] :
( ( p4 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,81]) ).
thf(2261,plain,
( ( p4 @ sk13 )
| ( r1 @ ( sk6 @ sk13 ) @ ( sk7 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[2260:[bind(A,$thf( sk13 ))]]) ).
thf(138,plain,
! [A: $i] :
( ~ sk16
| ~ sk24
| ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ sk25 @ sk26 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12,26]) ).
thf(139,plain,
! [A: $i] :
( ~ sk16
| ~ sk24
| ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( sk25 != sk1 )
| ( sk26 != A ) ),
inference(simp,[status(thm)],[138]) ).
thf(140,plain,
( ~ sk16
| ~ sk24
| ~ ( p3 @ sk26 )
| ~ ( p2 @ sk2 )
| ( sk25 != sk1 ) ),
inference(simp,[status(thm)],[139]) ).
thf(29821,plain,
( ~ sk16
| ( p1 @ sk23 )
| ( ( p1 @ ( sk15 @ sk23 ) )
!= ( p1 @ ( sk14 @ sk13 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29815,14854]) ).
thf(29832,plain,
( ( p1 @ sk23 )
| ~ sk16
| ( ( sk15 @ sk23 )
!= ( sk14 @ sk13 ) ) ),
inference(simp,[status(thm)],[29821]) ).
thf(400,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk16
| ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk1 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44,109]) ).
thf(401,plain,
( ( p2 @ sk1 )
| sk16
| ( p3 @ ( sk9 @ sk21 ) )
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[400:[bind(A,$thf( sk21 ))]]) ).
thf(695,plain,
( sk16
| ( p3 @ ( sk9 @ sk21 ) )
| ~ sk8
| ~ sk17
| ( ( p2 @ sk20 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[401,54]) ).
thf(726,plain,
( sk16
| ( p3 @ ( sk9 @ sk21 ) )
| ~ sk8
| ~ sk17
| ( sk20 != sk1 ) ),
inference(simp,[status(thm)],[695]) ).
thf(74,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ( p2 @ ( sk32 @ D @ C @ B @ A ) )
| ( sk30 @ B )
| ( sk29 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(91,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ~ ( p2 @ ( sk32 @ D @ C @ B @ A ) )
| ( sk30 @ B )
| ( sk29 @ A ) ),
inference(simp,[status(thm)],[74]) ).
thf(27069,plain,
( ~ sk16
| ( p2 @ sk23 )
| ~ sk24
| ( ( p2 @ ( sk27 @ sk23 ) )
!= ( p2 @ sk26 ) ) ),
inference(paramod_ordered,[status(thm)],[24014,60]) ).
thf(27149,plain,
( ( p2 @ sk23 )
| ~ sk16
| ~ sk24
| ( ( sk27 @ sk23 )
!= sk26 ) ),
inference(simp,[status(thm)],[27069]) ).
thf(30546,plain,
( ~ sk8
| ( p1 @ sk2 )
| ( ( p1 @ ( sk15 @ sk2 ) )
!= ( p1 @ ( sk14 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29585,14839]) ).
thf(30564,plain,
( ( p1 @ sk2 )
| ~ sk8
| ( ( sk15 @ sk2 )
!= ( sk14 @ sk2 ) ) ),
inference(simp,[status(thm)],[30546]) ).
thf(29657,plain,
! [A: $i] :
( ~ ( p3 @ sk1 )
| ( p1 @ A )
| ( p1 @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1019,121]) ).
thf(29658,plain,
( ~ ( p3 @ sk1 )
| ( p1 @ sk2 )
| ( p1 @ ( sk14 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[29657:[bind(A,$thf( sk2 ))]]) ).
thf(3837,plain,
! [A: $i] :
( ~ ( p3 @ sk1 )
| ( p2 @ A )
| ( r1 @ A @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1019,85]) ).
thf(3838,plain,
( ~ ( p3 @ sk1 )
| ( p2 @ sk2 )
| ( r1 @ sk2 @ ( sk41 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[3837:[bind(A,$thf( sk2 ))]]) ).
thf(21562,plain,
( ~ sk16
| ( p4 @ sk23 )
| ( ( p4 @ ( sk7 @ sk23 ) )
!= ( p4 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21558,20899]) ).
thf(21571,plain,
( ( p4 @ sk23 )
| ~ sk16
| ( ( sk7 @ sk23 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[21562]) ).
thf(3916,plain,
! [A: $i] :
( ( p2 @ sk1 )
| ( p2 @ A )
| ( r1 @ A @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ ( sk41 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3780,85]) ).
thf(3917,plain,
( ( p2 @ sk1 )
| ( p2 @ ( sk41 @ sk1 ) )
| ( r1 @ ( sk41 @ sk1 ) @ ( sk41 @ ( sk41 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[3916:[bind(A,$thf( sk41 @ sk1 ))]]) ).
thf(33303,plain,
( ~ sk17
| sk16
| ( p1 @ sk20 )
| ( ( p1 @ ( sk14 @ sk20 ) )
!= ( p1 @ sk20 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29552]) ).
thf(33316,plain,
( sk16
| ( p1 @ sk20 )
| ~ sk17
| ( ( sk14 @ sk20 )
!= sk20 ) ),
inference(simp,[status(thm)],[33303]) ).
thf(393,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,109]) ).
thf(394,plain,
( ( p3 @ ( sk9 @ sk5 ) )
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[393:[bind(A,$thf( sk5 ))]]) ).
thf(33298,plain,
( ~ sk17
| sk16
| ( p1 @ sk20 )
| ( ( p1 @ ( sk14 @ sk20 ) )
!= ( p1 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[29552,16]) ).
thf(33304,plain,
( sk16
| ( p1 @ sk20 )
| ~ sk17
| ( ( sk14 @ sk20 )
!= sk13 ) ),
inference(simp,[status(thm)],[33298]) ).
thf(265,plain,
( sk16
| ( sk21 != sk1 )
| ~ ( p3 @ sk13 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[158,131]) ).
thf(267,plain,
( sk16
| ( sk21 != sk1 )
| ~ ( p3 @ sk13 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[265]) ).
thf(1804,plain,
! [A: $i] :
( ~ sk16
| ( p1 @ A )
| ( r1 @ ( sk14 @ A ) @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,80]) ).
thf(1805,plain,
( ~ sk16
| ( p1 @ sk23 )
| ( r1 @ ( sk14 @ sk23 ) @ ( sk15 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[1804:[bind(A,$thf( sk23 ))]]) ).
thf(2275,plain,
! [A: $i] :
( ( p4 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,81]) ).
thf(2276,plain,
( ( p4 @ sk5 )
| ( r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[2275:[bind(A,$thf( sk5 ))]]) ).
thf(2461,plain,
( $false
| ( r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ) ) ),
inference(rewrite,[status(thm)],[2276,75]) ).
thf(2462,plain,
r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ),
inference(simp,[status(thm)],[2461]) ).
thf(2470,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2462,109]) ).
thf(2497,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk7 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[2470]) ).
thf(2506,plain,
( ( p3 @ ( sk9 @ ( sk7 @ sk5 ) ) )
| ~ sk8
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[2497]) ).
thf(6906,plain,
! [A: $i] :
( sk8
| ( p2 @ A )
| ( r1 @ A @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,90]) ).
thf(6907,plain,
( sk8
| ( p2 @ sk10 )
| ( r1 @ sk10 @ ( sk11 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[6906:[bind(A,$thf( sk10 ))]]) ).
thf(8572,plain,
! [A: $i] :
( ~ sk8
| ( p1 @ A )
| ( r1 @ ( sk14 @ A ) @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8326,80]) ).
thf(8573,plain,
( ~ sk8
| ( p1 @ sk2 )
| ( r1 @ ( sk14 @ sk2 ) @ ( sk15 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8572:[bind(A,$thf( sk2 ))]]) ).
thf(11192,plain,
! [A: $i] :
( ( p4 @ sk1 )
| ( p2 @ A )
| ( r1 @ A @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ ( sk6 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10958,85]) ).
thf(11193,plain,
( ( p4 @ sk1 )
| ( p2 @ ( sk6 @ sk1 ) )
| ( r1 @ ( sk6 @ sk1 ) @ ( sk41 @ ( sk6 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[11192:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(8559,plain,
! [A: $i] :
( ~ sk8
| ( p4 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8326,81]) ).
thf(8560,plain,
( ~ sk8
| ( p4 @ sk2 )
| ( r1 @ ( sk6 @ sk2 ) @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8559:[bind(A,$thf( sk2 ))]]) ).
thf(29577,plain,
! [A: $i] :
( ( p4 @ sk1 )
| ( p1 @ A )
| ( p1 @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ ( sk6 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10958,121]) ).
thf(29578,plain,
( ( p4 @ sk1 )
| ( p1 @ ( sk6 @ sk1 ) )
| ( p1 @ ( sk14 @ ( sk6 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[29577:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(29847,plain,
( ( p1 @ sk5 )
| ( ( p1 @ ( sk15 @ sk5 ) )
!= ( p1 @ ( sk14 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29651,14898]) ).
thf(29854,plain,
( ( p1 @ sk5 )
| ( ( sk15 @ sk5 )
!= ( sk14 @ sk5 ) ) ),
inference(simp,[status(thm)],[29847]) ).
thf(37350,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ( p2 @ sk13 )
| ~ ( p2 @ ( sk4 @ sk13 ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,183]) ).
thf(37351,plain,
( ~ ( p3 @ sk5 )
| ( p2 @ sk13 )
| ~ ( p2 @ ( sk4 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[37350:[bind(A,$thf( sk5 ))]]) ).
thf(3920,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk8
| ( p2 @ A )
| ( p2 @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ ( sk41 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3780,124]) ).
thf(3921,plain,
( ( p2 @ sk1 )
| sk8
| ( p2 @ ( sk41 @ sk1 ) )
| ( p2 @ ( sk11 @ ( sk41 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[3920:[bind(A,$thf( sk41 @ sk1 ))]]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( p2 @ ( sk34 @ B @ A ) )
| ( sk29 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( p2 @ ( sk34 @ B @ A ) )
| ( sk29 @ A ) ),
inference(simp,[status(thm)],[36]) ).
thf(25558,plain,
( ~ ( p3 @ sk1 )
| ( p4 @ sk2 )
| ( ( p4 @ ( sk6 @ sk2 ) )
!= ( p4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21399,75]) ).
thf(25582,plain,
( ( p4 @ sk2 )
| ~ ( p3 @ sk1 )
| ( ( sk6 @ sk2 )
!= sk5 ) ),
inference(simp,[status(thm)],[25558]) ).
thf(21527,plain,
( ( p4 @ sk1 )
| ( ( p4 @ ( sk6 @ sk1 ) )
!= ( p4 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21334]) ).
thf(21532,plain,
( ( p4 @ sk1 )
| ( ( sk6 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[21527]) ).
thf(9301,plain,
( ( p2 @ sk1 )
| sk16
| ~ ( p3 @ sk21 )
| ( ( p2 @ sk21 )
!= ( p2 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[62,377]) ).
thf(9317,plain,
( ( p2 @ sk1 )
| sk16
| ~ ( p3 @ sk21 )
| ( sk21 != sk2 ) ),
inference(simp,[status(thm)],[9301]) ).
thf(30517,plain,
( sk8
| ( p1 @ sk10 )
| ( ( p1 @ ( sk15 @ sk13 ) )
!= ( p1 @ ( sk14 @ sk10 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29591,15018]) ).
thf(30537,plain,
( sk8
| ( p1 @ sk10 )
| ( ( sk15 @ sk13 )
!= ( sk14 @ sk10 ) ) ),
inference(simp,[status(thm)],[30517]) ).
thf(4900,plain,
! [A: $i] :
( ~ ( p3 @ sk5 )
| ( p1 @ A )
| ( r1 @ A @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1070,87]) ).
thf(4901,plain,
( ~ ( p3 @ sk5 )
| ( p1 @ sk2 )
| ( r1 @ sk2 @ ( sk14 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[4900:[bind(A,$thf( sk2 ))]]) ).
thf(2842,plain,
( sk16
| ( p3 @ ( sk9 @ sk21 ) )
| ~ sk8
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[401,2798]) ).
thf(2846,plain,
( sk16
| ( p3 @ ( sk9 @ sk21 ) )
| ~ sk8
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[2842]) ).
thf(2255,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk16
| ( p4 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44,81]) ).
thf(2256,plain,
( ( p2 @ sk1 )
| sk16
| ( p4 @ sk21 )
| ( r1 @ ( sk6 @ sk21 ) @ ( sk7 @ sk21 ) ) ),
inference(pattern_uni,[status(thm)],[2255:[bind(A,$thf( sk21 ))]]) ).
thf(29799,plain,
( ( p1 @ sk1 )
| ( ( p1 @ ( sk14 @ sk1 ) )
!= ( p1 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29589]) ).
thf(29803,plain,
( ( p1 @ sk1 )
| ( ( p1 @ ( sk14 @ sk1 ) )
!= ( p1 @ sk1 ) ) ),
inference(simp,[status(thm)],[29799]) ).
thf(29819,plain,
( ( p1 @ ( sk15 @ sk13 ) )
!= ( p1 @ ( sk14 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[29815,15018]) ).
thf(29839,plain,
( ( sk15 @ sk13 )
!= ( sk14 @ sk13 ) ),
inference(simp,[status(thm)],[29819]) ).
thf(21395,plain,
! [A: $i] :
( ( p1 @ sk1 )
| ( p4 @ A )
| ( p4 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ ( sk14 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4865,112]) ).
thf(21396,plain,
( ( p1 @ sk1 )
| ( p4 @ ( sk14 @ sk1 ) )
| ( p4 @ ( sk6 @ ( sk14 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[21395:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(18434,plain,
( sk8
| ( p2 @ sk1 )
| ( ( p2 @ ( sk41 @ sk1 ) )
!= ( p2 @ ( sk11 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[991,18207]) ).
thf(18449,plain,
( sk8
| ( p2 @ sk1 )
| ( ( sk41 @ sk1 )
!= ( sk11 @ sk1 ) ) ),
inference(simp,[status(thm)],[18434]) ).
thf(284,plain,
( sk16
| ( sk22 != sk21 )
| sk8
| ~ ( p3 @ sk10 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[216,135]) ).
thf(295,plain,
( sk16
| sk8
| ( sk22 != sk21 )
| ~ ( p3 @ sk10 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[284]) ).
thf(3903,plain,
! [A: $i] :
( ( p2 @ sk1 )
| ~ ( p3 @ A )
| ( r1 @ sk1 @ sk2 )
| ( ( r1 @ sk1 @ ( sk41 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3780,69]) ).
thf(3904,plain,
( ( p2 @ sk1 )
| ~ ( p3 @ ( sk41 @ sk1 ) )
| ( r1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3903:[bind(A,$thf( sk41 @ sk1 ))]]) ).
thf(2478,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ ( sk6 @ sk5 ) @ ( sk7 @ sk5 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2462,26]) ).
thf(2492,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( sk6 @ sk5 )
!= sk1 )
| ( ( sk7 @ sk5 )
!= A ) ),
inference(simp,[status(thm)],[2478]) ).
thf(2518,plain,
( ~ ( p3 @ ( sk7 @ sk5 ) )
| ~ ( p2 @ sk2 )
| ( ( sk6 @ sk5 )
!= sk1 ) ),
inference(simp,[status(thm)],[2492]) ).
thf(29642,plain,
! [A: $i] :
( ( p2 @ sk1 )
| ( p1 @ A )
| ( p1 @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ ( sk41 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3780,121]) ).
thf(29643,plain,
( ( p2 @ sk1 )
| ( p1 @ ( sk41 @ sk1 ) )
| ( p1 @ ( sk14 @ ( sk41 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[29642:[bind(A,$thf( sk41 @ sk1 ))]]) ).
thf(1264,plain,
( sk8
| ( p2 @ sk1 )
| ( ( p2 @ ( sk11 @ sk1 ) )
!= ( p2 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[991]) ).
thf(1267,plain,
( sk8
| ( p2 @ sk1 )
| ( ( p2 @ ( sk11 @ sk1 ) )
!= ( p2 @ sk1 ) ) ),
inference(simp,[status(thm)],[1264]) ).
thf(32417,plain,
( ~ ( p3 @ sk13 )
| ( p1 @ sk2 )
| ( ( p1 @ ( sk14 @ sk2 ) )
!= ( p1 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29653]) ).
thf(32450,plain,
( ( p1 @ sk2 )
| ~ ( p3 @ sk13 )
| ( ( sk14 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[32417]) ).
thf(1052,plain,
! [A: $i] :
( ~ sk16
| ~ ( p3 @ A )
| ( r1 @ sk1 @ sk2 )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,69]) ).
thf(1053,plain,
( ~ sk16
| ~ ( p3 @ sk23 )
| ( r1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1052:[bind(A,$thf( sk23 ))]]) ).
thf(21304,plain,
! [A: $i] :
( sk8
| ( p2 @ sk1 )
| ( p4 @ A )
| ( p4 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ ( sk11 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6905,112]) ).
thf(21305,plain,
( sk8
| ( p2 @ sk1 )
| ( p4 @ ( sk11 @ sk1 ) )
| ( p4 @ ( sk6 @ ( sk11 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[21304:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(1037,plain,
! [A: $i] :
( ~ sk17
| sk16
| ~ ( p3 @ A )
| ( r1 @ sk1 @ sk2 )
| ( ( r1 @ sk1 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,69]) ).
thf(1038,plain,
( ~ sk17
| sk16
| ~ ( p3 @ sk20 )
| ( r1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1037:[bind(A,$thf( sk20 ))]]) ).
thf(450,plain,
( sk16
| sk8
| ( sk21 != sk10 )
| ( ( p2 @ sk10 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[152,9]) ).
thf(470,plain,
( sk16
| sk8
| ( sk21 != sk10 )
| ( sk10 != sk1 ) ),
inference(simp,[status(thm)],[450]) ).
thf(4874,plain,
! [A: $i] :
( ~ sk16
| ( p1 @ A )
| ( r1 @ A @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,87]) ).
thf(4875,plain,
( ~ sk16
| ( p1 @ sk23 )
| ( r1 @ sk23 @ ( sk14 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[4874:[bind(A,$thf( sk23 ))]]) ).
thf(19773,plain,
! [A: $i] :
( ~ sk16
| ~ sk24
| ( p2 @ A )
| ~ ( p2 @ ( sk28 @ A ) )
| ( ( r1 @ sk23 @ sk25 )
!= ( r1 @ sk23 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,108]) ).
thf(19774,plain,
( ~ sk16
| ~ sk24
| ( p2 @ sk25 )
| ~ ( p2 @ ( sk28 @ sk25 ) ) ),
inference(pattern_uni,[status(thm)],[19773:[bind(A,$thf( sk25 ))]]) ).
thf(5014,plain,
! [A: $i] :
( ( p1 @ sk1 )
| ~ ( p3 @ A )
| ( r1 @ sk1 @ sk2 )
| ( ( r1 @ sk1 @ ( sk14 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4865,69]) ).
thf(5015,plain,
( ( p1 @ sk1 )
| ~ ( p3 @ ( sk14 @ sk1 ) )
| ( r1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5014:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(21546,plain,
( ( p4 @ sk13 )
| ( ( p4 @ ( sk6 @ sk13 ) )
!= ( p4 @ sk13 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21349]) ).
thf(21554,plain,
( ( p4 @ sk13 )
| ( ( sk6 @ sk13 )
!= sk13 ) ),
inference(simp,[status(thm)],[21546]) ).
thf(5029,plain,
! [A: $i] :
( ( p1 @ sk1 )
| ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk1 @ ( sk14 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4865,109]) ).
thf(5030,plain,
( ( p1 @ sk1 )
| ( p3 @ ( sk9 @ ( sk14 @ sk1 ) ) )
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[5029:[bind(A,$thf( sk14 @ sk1 ))]]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ B @ ( sk39 @ B @ A ) )
| ~ ( sk36 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ B @ ( sk39 @ B @ A ) )
| ~ ( sk36 @ A ) ),
inference(simp,[status(thm)],[15]) ).
thf(18169,plain,
! [A: $i] :
( ~ sk17
| sk16
| ( p2 @ A )
| ~ ( p2 @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,106]) ).
thf(18170,plain,
( ~ sk17
| sk16
| ( p2 @ sk20 )
| ~ ( p2 @ ( sk41 @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[18169:[bind(A,$thf( sk20 ))]]) ).
thf(8578,plain,
! [A: $i] :
( ~ sk8
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8326,82]) ).
thf(8579,plain,
( ~ sk8
| ( r1 @ sk2 @ ( sk9 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8578:[bind(A,$thf( sk2 ))]]) ).
thf(9081,plain,
! [A: $i] :
( ~ sk8
| ( p3 @ ( sk9 @ A ) )
| ( ( r1 @ sk2 @ ( sk9 @ sk2 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8579,109]) ).
thf(9124,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( sk2 != sk1 )
| ( ( sk9 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[9081]) ).
thf(9151,plain,
( ( p3 @ ( sk9 @ ( sk9 @ sk2 ) ) )
| ~ sk8
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[9124]) ).
thf(16341,plain,
( sk8
| ( p2 @ sk10 )
| ( ( p2 @ ( sk12 @ sk10 ) )
!= ( p2 @ ( sk11 @ sk10 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1000,16114]) ).
thf(16367,plain,
( sk8
| ( p2 @ sk10 )
| ( ( sk12 @ sk10 )
!= ( sk11 @ sk10 ) ) ),
inference(simp,[status(thm)],[16341]) ).
thf(7162,plain,
! [A: $i] :
( sk8
| ( p2 @ sk1 )
| ( p4 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ ( sk11 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6905,81]) ).
thf(7163,plain,
( sk8
| ( p2 @ sk1 )
| ( p4 @ ( sk11 @ sk1 ) )
| ( r1 @ ( sk6 @ ( sk11 @ sk1 ) ) @ ( sk7 @ ( sk11 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7162:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(1251,plain,
( sk8
| ( p2 @ sk1 )
| ~ sk17
| sk16
| ( ( p2 @ ( sk11 @ sk1 ) )
!= ( p2 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[991,54]) ).
thf(1272,plain,
( sk8
| ( p2 @ sk1 )
| sk16
| ~ sk17
| ( ( sk11 @ sk1 )
!= sk20 ) ),
inference(simp,[status(thm)],[1251]) ).
thf(2834,plain,
( sk16
| ( sk22 != sk21 )
| ~ sk8
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[216,2798]) ).
thf(2848,plain,
( sk16
| ( sk22 != sk21 )
| ~ sk8
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[2834]) ).
thf(18519,plain,
( sk8
| ( p2 @ sk5 )
| ( ( p2 @ ( sk41 @ sk5 ) )
!= ( p2 @ ( sk11 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[993,18276]) ).
thf(18533,plain,
( sk8
| ( p2 @ sk5 )
| ( ( sk41 @ sk5 )
!= ( sk11 @ sk5 ) ) ),
inference(simp,[status(thm)],[18519]) ).
thf(35965,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ( p2 @ sk5 )
| ~ ( p2 @ ( sk4 @ sk5 ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,177]) ).
thf(35966,plain,
( ~ ( p3 @ sk5 )
| ( p2 @ sk5 )
| ~ ( p2 @ ( sk4 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[35965:[bind(A,$thf( sk5 ))]]) ).
thf(45,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ( r1 @ ( sk37 @ A ) @ ( sk38 @ A ) )
| ~ ( sk36 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(99,plain,
! [A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ( r1 @ ( sk37 @ A ) @ ( sk38 @ A ) )
| ~ ( sk36 @ A ) ),
inference(simp,[status(thm)],[45]) ).
thf(29824,plain,
( ( p1 @ ( sk14 @ sk13 ) )
!= ( p1 @ sk13 ) ),
inference(paramod_ordered,[status(thm)],[29815,16]) ).
thf(29828,plain,
( ( sk14 @ sk13 )
!= sk13 ),
inference(simp,[status(thm)],[29824]) ).
thf(6969,plain,
! [A: $i] :
( sk8
| ( p2 @ A )
| ( r1 @ A @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ sk5 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30,90]) ).
thf(6970,plain,
( sk8
| ( p2 @ sk5 )
| ( r1 @ sk5 @ ( sk11 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[6969:[bind(A,$thf( sk5 ))]]) ).
thf(32336,plain,
( ~ ( p3 @ sk5 )
| ( p1 @ sk2 )
| ( ( p1 @ ( sk14 @ sk2 ) )
!= ( p1 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[29619,16]) ).
thf(32357,plain,
( ( p1 @ sk2 )
| ~ ( p3 @ sk5 )
| ( ( sk14 @ sk2 )
!= sk13 ) ),
inference(simp,[status(thm)],[32336]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ~ ( sk30 @ B )
| ( r1 @ B @ ( sk33 @ B @ A ) )
| ( sk29 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ~ ( sk30 @ B )
| ( r1 @ B @ ( sk33 @ B @ A ) )
| ( sk29 @ A ) ),
inference(simp,[status(thm)],[59]) ).
thf(22705,plain,
( ~ sk16
| ~ ( sk29 @ sk23 )
| ~ ( p2 @ sk23 )
| ( ( p2 @ ( sk38 @ sk23 ) )
!= ( p2 @ sk23 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[20705]) ).
thf(22711,plain,
( ~ sk16
| ~ ( sk29 @ sk23 )
| ~ ( p2 @ sk23 )
| ( ( sk38 @ sk23 )
!= sk23 ) ),
inference(simp,[status(thm)],[22705]) ).
thf(1156,plain,
! [A: $i] :
( ~ ( p3 @ sk13 )
| sk8
| ( p2 @ A )
| ( p2 @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1056,124]) ).
thf(1157,plain,
( ~ ( p3 @ sk13 )
| sk8
| ( p2 @ sk2 )
| ( p2 @ ( sk11 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1156:[bind(A,$thf( sk2 ))]]) ).
thf(4872,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk16
| ( p1 @ A )
| ( r1 @ A @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44,87]) ).
thf(4873,plain,
( ( p2 @ sk1 )
| sk16
| ( p1 @ sk21 )
| ( r1 @ sk21 @ ( sk14 @ sk21 ) ) ),
inference(pattern_uni,[status(thm)],[4872:[bind(A,$thf( sk21 ))]]) ).
thf(217,plain,
( ( p2 @ sk1 )
| sk16
| sk8
| ~ ( p3 @ sk10 )
| ( ( p2 @ sk21 )
!= ( p2 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[62,135]) ).
thf(218,plain,
( ( p2 @ sk1 )
| sk16
| sk8
| ~ ( p3 @ sk10 )
| ( sk21 != sk2 ) ),
inference(simp,[status(thm)],[217]) ).
thf(29826,plain,
( ( p1 @ sk1 )
| ( ( p1 @ ( sk15 @ sk1 ) )
!= ( p1 @ ( sk14 @ sk13 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29815,14843]) ).
thf(29831,plain,
( ( p1 @ sk1 )
| ( ( sk15 @ sk1 )
!= ( sk14 @ sk13 ) ) ),
inference(simp,[status(thm)],[29826]) ).
thf(3928,plain,
! [A: $i] :
( ( p2 @ sk1 )
| ( p1 @ A )
| ( r1 @ ( sk14 @ A ) @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ ( sk41 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3780,80]) ).
thf(3929,plain,
( ( p2 @ sk1 )
| ( p1 @ ( sk41 @ sk1 ) )
| ( r1 @ ( sk14 @ ( sk41 @ sk1 ) ) @ ( sk15 @ ( sk41 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[3928:[bind(A,$thf( sk41 @ sk1 ))]]) ).
thf(16566,plain,
( ~ ( p3 @ ( sk6 @ sk1 ) )
| ~ ( p2 @ sk2 )
| ( ( p4 @ sk5 )
!= ( p4 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[11225,75]) ).
thf(16575,plain,
( ~ ( p3 @ ( sk6 @ sk1 ) )
| ~ ( p2 @ sk2 )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[16566]) ).
thf(30523,plain,
( sk8
| ( p1 @ sk10 )
| ( ( p1 @ ( sk15 @ sk10 ) )
!= ( p1 @ ( sk14 @ sk10 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29591,14845]) ).
thf(30530,plain,
( sk8
| ( p1 @ sk10 )
| ( ( sk15 @ sk10 )
!= ( sk14 @ sk10 ) ) ),
inference(simp,[status(thm)],[30523]) ).
thf(32486,plain,
( ~ ( p3 @ sk1 )
| ( p1 @ sk2 )
| ( ( p1 @ ( sk14 @ sk2 ) )
!= ( p1 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29658]) ).
thf(32512,plain,
( ( p1 @ sk2 )
| ~ ( p3 @ sk1 )
| ( ( sk14 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[32486]) ).
thf(1326,plain,
( sk8
| ( p2 @ sk5 )
| ( ( sk11 @ sk5 )
!= sk5 ) ),
inference(simp,[status(thm)],[1313]) ).
thf(3788,plain,
! [A: $i] :
( ~ sk16
| ( p2 @ A )
| ( r1 @ A @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,85]) ).
thf(3789,plain,
( ~ sk16
| ( p2 @ sk23 )
| ( r1 @ sk23 @ ( sk41 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[3788:[bind(A,$thf( sk23 ))]]) ).
thf(2250,plain,
! [A: $i] :
( sk8
| ( p4 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,81]) ).
thf(2251,plain,
( sk8
| ( p4 @ sk10 )
| ( r1 @ ( sk6 @ sk10 ) @ ( sk7 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[2250:[bind(A,$thf( sk10 ))]]) ).
thf(3368,plain,
! [B: $i,A: $i] :
( sk8
| ( p2 @ B )
| ( r1 @ ( sk11 @ B ) @ ( sk12 @ B ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,84]) ).
thf(3369,plain,
( sk8
| ( p2 @ sk1 )
| ( r1 @ ( sk11 @ sk1 ) @ ( sk12 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[3368:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(2810,plain,
! [A: $i] :
( ~ sk8
| ( r1 @ A @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ ( sk9 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2688,82]) ).
thf(2811,plain,
( ~ sk8
| ( r1 @ ( sk9 @ sk1 ) @ ( sk9 @ ( sk9 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[2810:[bind(A,$thf( sk9 @ sk1 ))]]) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ( p2 @ ( sk31 @ D @ C @ B @ A ) )
| ( sk30 @ B )
| ( sk29 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ( p2 @ ( sk31 @ D @ C @ B @ A ) )
| ( sk30 @ B )
| ( sk29 @ A ) ),
inference(simp,[status(thm)],[31]) ).
thf(769,plain,
( sk16
| ( sk22 != sk21 )
| ~ sk17
| ~ ( p3 @ sk20 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[216,213]) ).
thf(786,plain,
( sk16
| ( sk22 != sk21 )
| ~ sk17
| ~ ( p3 @ sk20 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[769]) ).
thf(25568,plain,
( ~ ( p3 @ sk1 )
| ( p4 @ sk2 )
| ( ( p4 @ ( sk6 @ sk2 ) )
!= ( p4 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21399]) ).
thf(25600,plain,
( ( p4 @ sk2 )
| ~ ( p3 @ sk1 )
| ( ( sk6 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[25568]) ).
thf(12238,plain,
( ( p3 @ ( sk9 @ ( sk14 @ sk1 ) ) )
| ~ sk8
| ( ( p1 @ sk13 )
!= ( p1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[5030,16]) ).
thf(12268,plain,
( ( p3 @ ( sk9 @ ( sk14 @ sk1 ) ) )
| ~ sk8
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[12238]) ).
thf(201,plain,
! [A: $i] :
( ~ sk16
| ~ sk24
| ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ sk23 @ sk25 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,26]) ).
thf(204,plain,
! [A: $i] :
( ~ sk16
| ~ sk24
| ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( sk23 != sk1 )
| ( sk25 != A ) ),
inference(simp,[status(thm)],[201]) ).
thf(207,plain,
( ~ sk16
| ~ sk24
| ~ ( p3 @ sk25 )
| ~ ( p2 @ sk2 )
| ( sk23 != sk1 ) ),
inference(simp,[status(thm)],[204]) ).
thf(21583,plain,
( sk8
| ( p4 @ sk10 )
| ( ( p4 @ ( sk6 @ sk10 ) )
!= ( p4 @ sk10 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21336]) ).
thf(21589,plain,
( sk8
| ( p4 @ sk10 )
| ( ( sk6 @ sk10 )
!= sk10 ) ),
inference(simp,[status(thm)],[21583]) ).
thf(24937,plain,
( ~ ( p3 @ sk5 )
| ( p4 @ sk2 )
| ( ( p4 @ ( sk6 @ sk2 ) )
!= ( p4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21361,75]) ).
thf(24955,plain,
( ( p4 @ sk2 )
| ~ ( p3 @ sk5 )
| ( ( sk6 @ sk2 )
!= sk5 ) ),
inference(simp,[status(thm)],[24937]) ).
thf(10959,plain,
! [A: $i] :
( sk8
| ( p4 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk10 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[73,95]) ).
thf(10960,plain,
( sk8
| ( p4 @ sk10 )
| ( r1 @ sk10 @ ( sk6 @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[10959:[bind(A,$thf( sk10 ))]]) ).
thf(21560,plain,
( ( p4 @ sk13 )
| ( ( p4 @ ( sk7 @ sk13 ) )
!= ( p4 @ ( sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21558,20903]) ).
thf(21574,plain,
( ( p4 @ sk13 )
| ( ( sk7 @ sk13 )
!= ( sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[21560]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ~ sk17
| sk16
| ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk4 @ B ) )
| ( ( r1 @ sk1 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,14]) ).
thf(209,plain,
! [A: $i] :
( ~ sk17
| sk16
| ~ ( p3 @ sk20 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) ) ),
inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( sk20 ))]]) ).
thf(214,plain,
! [A: $i] :
( ~ sk17
| sk16
| ~ ( p3 @ sk20 )
| ~ ( r1 @ sk1 @ A )
| ( p2 @ A )
| ~ ( p2 @ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(276,plain,
( sk16
| ( sk22 != sk21 )
| ~ ( p3 @ sk1 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[216,142]) ).
thf(290,plain,
( sk16
| ( sk22 != sk21 )
| ~ ( p3 @ sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[276]) ).
thf(55,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ( r1 @ ( sk31 @ D @ C @ B @ A ) @ ( sk32 @ D @ C @ B @ A ) )
| ( sk30 @ B )
| ( sk29 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ~ ( r1 @ B @ C )
| ~ ( r1 @ C @ D )
| ( p2 @ D )
| ( r1 @ ( sk31 @ D @ C @ B @ A ) @ ( sk32 @ D @ C @ B @ A ) )
| ( sk30 @ B )
| ( sk29 @ A ) ),
inference(simp,[status(thm)],[55]) ).
thf(37247,plain,
! [B: $i,A: $i] :
( ~ ( p3 @ B )
| ( p2 @ sk13 )
| ~ ( p2 @ ( sk4 @ sk13 ) )
| ( ( r1 @ A @ A )
!= ( r1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,183]) ).
thf(37248,plain,
( ~ ( p3 @ sk1 )
| ( p2 @ sk13 )
| ~ ( p2 @ ( sk4 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[37247:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(11166,plain,
! [A: $i] :
( ( p4 @ sk1 )
| ~ ( p3 @ A )
| ( r1 @ sk1 @ sk2 )
| ( ( r1 @ sk1 @ ( sk6 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10958,69]) ).
thf(11167,plain,
( ( p4 @ sk1 )
| ~ ( p3 @ ( sk6 @ sk1 ) )
| ( r1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[11166:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(2257,plain,
! [A: $i] :
( ~ sk16
| ( p4 @ A )
| ( r1 @ ( sk6 @ A ) @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,81]) ).
thf(2258,plain,
( ~ sk16
| ( p4 @ sk23 )
| ( r1 @ ( sk6 @ sk23 ) @ ( sk7 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[2257:[bind(A,$thf( sk23 ))]]) ).
thf(20954,plain,
! [A: $i] :
( ~ ( p3 @ sk1 )
| ( p4 @ A )
| ~ ( p4 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1019,111]) ).
thf(20955,plain,
( ~ ( p3 @ sk1 )
| ( p4 @ sk2 )
| ~ ( p4 @ ( sk7 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[20954:[bind(A,$thf( sk2 ))]]) ).
thf(4916,plain,
! [A: $i] :
( ( p2 @ sk1 )
| ( p1 @ A )
| ( r1 @ A @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ ( sk41 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3780,87]) ).
thf(4917,plain,
( ( p2 @ sk1 )
| ( p1 @ ( sk41 @ sk1 ) )
| ( r1 @ ( sk41 @ sk1 ) @ ( sk14 @ ( sk41 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[4916:[bind(A,$thf( sk41 @ sk1 ))]]) ).
thf(5085,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk13 @ ( sk14 @ sk13 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5076,109]) ).
thf(5120,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( sk13 != sk1 )
| ( ( sk14 @ sk13 )
!= A ) ),
inference(simp,[status(thm)],[5085]) ).
thf(5129,plain,
( ( p3 @ ( sk9 @ ( sk14 @ sk13 ) ) )
| ~ sk8
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[5120]) ).
thf(18219,plain,
! [A: $i] :
( ~ sk16
| ( p2 @ A )
| ~ ( p2 @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk23 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,106]) ).
thf(18220,plain,
( ~ sk16
| ( p2 @ sk23 )
| ~ ( p2 @ ( sk41 @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[18219:[bind(A,$thf( sk23 ))]]) ).
thf(18277,plain,
! [A: $i] :
( ~ ( p3 @ sk13 )
| ( p2 @ A )
| ~ ( p2 @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1056,106]) ).
thf(18278,plain,
( ~ ( p3 @ sk13 )
| ( p2 @ sk2 )
| ~ ( p2 @ ( sk41 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[18277:[bind(A,$thf( sk2 ))]]) ).
thf(29790,plain,
( ( p1 @ sk1 )
| ( ( p1 @ ( sk15 @ sk13 ) )
!= ( p1 @ ( sk14 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29589,15018]) ).
thf(29813,plain,
( ( p1 @ sk1 )
| ( ( sk15 @ sk13 )
!= ( sk14 @ sk1 ) ) ),
inference(simp,[status(thm)],[29790]) ).
thf(35885,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ( p2 @ sk5 )
| ~ ( p2 @ ( sk4 @ sk5 ) )
| ( ( r1 @ sk1 @ sk13 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,177]) ).
thf(35886,plain,
( ~ ( p3 @ sk13 )
| ( p2 @ sk5 )
| ~ ( p2 @ ( sk4 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[35885:[bind(A,$thf( sk13 ))]]) ).
thf(11218,plain,
! [A: $i] :
( ( p4 @ sk1 )
| ( p1 @ A )
| ( r1 @ ( sk14 @ A ) @ ( sk15 @ A ) )
| ( ( r1 @ sk1 @ ( sk6 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10958,80]) ).
thf(11219,plain,
( ( p4 @ sk1 )
| ( p1 @ ( sk6 @ sk1 ) )
| ( r1 @ ( sk14 @ ( sk6 @ sk1 ) ) @ ( sk15 @ ( sk6 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[11218:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(262,plain,
( sk16
| ( sk21 != sk1 )
| ~ sk17
| ( ( p2 @ sk20 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[158,54]) ).
thf(273,plain,
( sk16
| ( sk21 != sk1 )
| ~ sk17
| ( sk20 != sk1 ) ),
inference(simp,[status(thm)],[262]) ).
thf(21539,plain,
( ( p4 @ sk13 )
| ( ( p4 @ ( sk7 @ sk13 ) )
!= ( p4 @ ( sk6 @ sk13 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21349,20903]) ).
thf(21549,plain,
( ( p4 @ sk13 )
| ( ( sk7 @ sk13 )
!= ( sk6 @ sk13 ) ) ),
inference(simp,[status(thm)],[21539]) ).
thf(404,plain,
! [A: $i] :
( ~ sk16
| ~ sk24
| ( p3 @ ( sk9 @ A ) )
| ~ sk8
| ( ( r1 @ sk25 @ sk26 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12,109]) ).
thf(407,plain,
! [A: $i] :
( ( p3 @ ( sk9 @ A ) )
| ~ sk16
| ~ sk24
| ~ sk8
| ( sk25 != sk1 )
| ( sk26 != A ) ),
inference(simp,[status(thm)],[404]) ).
thf(410,plain,
( ( p3 @ ( sk9 @ sk26 ) )
| ~ sk16
| ~ sk24
| ~ sk8
| ( sk25 != sk1 ) ),
inference(simp,[status(thm)],[407]) ).
thf(21531,plain,
( ( p4 @ sk1 )
| ( ( p4 @ ( sk6 @ sk1 ) )
!= ( p4 @ sk1 ) ) ),
inference(simp,[status(thm)],[21527]) ).
thf(18202,plain,
! [A: $i] :
( ~ sk8
| ( p2 @ A )
| ~ ( p2 @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8326,106]) ).
thf(18203,plain,
( ~ sk8
| ( p2 @ sk2 )
| ~ ( p2 @ ( sk41 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[18202:[bind(A,$thf( sk2 ))]]) ).
thf(7170,plain,
! [A: $i] :
( sk8
| ( p2 @ sk1 )
| ( p1 @ A )
| ( r1 @ A @ ( sk14 @ A ) )
| ( ( r1 @ sk1 @ ( sk11 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6905,87]) ).
thf(7171,plain,
( sk8
| ( p2 @ sk1 )
| ( p1 @ ( sk11 @ sk1 ) )
| ( r1 @ ( sk11 @ sk1 ) @ ( sk14 @ ( sk11 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[7170:[bind(A,$thf( sk11 @ sk1 ))]]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk40 @ B @ A ) )
| ~ ( sk36 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk40 @ B @ A ) )
| ~ ( sk36 @ A ) ),
inference(simp,[status(thm)],[7]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ~ sk16
| sk24
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ~ sk16
| sk24
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ A ) ),
inference(simp,[status(thm)],[47]) ).
thf(1295,plain,
( sk8
| ( p2 @ sk5 )
| ( ( p2 @ ( sk11 @ sk5 ) )
!= ( p2 @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[993,9]) ).
thf(1314,plain,
( sk8
| ( p2 @ sk5 )
| ( ( sk11 @ sk5 )
!= sk10 ) ),
inference(simp,[status(thm)],[1295]) ).
thf(29804,plain,
( ( p1 @ sk1 )
| ( ( sk14 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[29799]) ).
thf(260,plain,
( sk16
| ( sk21 != sk1 )
| sk8
| ~ ( p3 @ sk10 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[158,135]) ).
thf(268,plain,
( sk16
| sk8
| ( sk21 != sk1 )
| ~ ( p3 @ sk10 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[260]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ~ ( r1 @ ( sk38 @ A ) @ B )
| ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ( p2 @ B )
| ~ ( sk36 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( sk29 @ A )
| ~ ( r1 @ ( sk38 @ A ) @ B )
| ~ ( r1 @ B @ C )
| ( p2 @ C )
| ~ ( p2 @ B )
| ~ ( sk36 @ A ) ),
inference(simp,[status(thm)],[65]) ).
thf(752,plain,
( sk16
| ~ sk17
| ( sk21 != sk20 )
| ~ ( p3 @ sk13 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[161,131]) ).
thf(767,plain,
( sk16
| ~ sk17
| ( sk21 != sk20 )
| ~ ( p3 @ sk13 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[752]) ).
thf(30578,plain,
( ~ sk16
| ( p1 @ sk23 )
| ( ( p1 @ ( sk14 @ sk23 ) )
!= ( p1 @ sk23 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29603]) ).
thf(30591,plain,
( ( p1 @ sk23 )
| ~ sk16
| ( ( sk14 @ sk23 )
!= sk23 ) ),
inference(simp,[status(thm)],[30578]) ).
thf(16313,plain,
( ( p2 @ sk1 )
| sk16
| sk8
| ( ( p2 @ ( sk12 @ sk1 ) )
!= ( p2 @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[62,16112]) ).
thf(16331,plain,
( ( p2 @ sk1 )
| sk16
| sk8
| ( ( sk12 @ sk1 )
!= sk21 ) ),
inference(simp,[status(thm)],[16313]) ).
thf(10579,plain,
( ( p3 @ ( sk9 @ ( sk41 @ sk1 ) ) )
| ~ sk8
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[3919,2798]) ).
thf(10622,plain,
( ( p3 @ ( sk9 @ ( sk41 @ sk1 ) ) )
| ~ sk8
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[10579]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( p2 @ ( sk18 @ B @ A ) )
| sk17
| sk16 ),
inference(cnf,[status(esa)],[6]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( p2 @ ( sk18 @ B @ A ) )
| sk17
| sk16 ),
inference(simp,[status(thm)],[28]) ).
thf(21343,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk16
| ( p4 @ A )
| ( p4 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44,112]) ).
thf(21344,plain,
( ( p2 @ sk1 )
| sk16
| ( p4 @ sk21 )
| ( p4 @ ( sk6 @ sk21 ) ) ),
inference(pattern_uni,[status(thm)],[21343:[bind(A,$thf( sk21 ))]]) ).
thf(10965,plain,
! [A: $i] :
( ( p2 @ sk1 )
| sk16
| ( p4 @ A )
| ( r1 @ A @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ sk21 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44,95]) ).
thf(10966,plain,
( ( p2 @ sk1 )
| sk16
| ( p4 @ sk21 )
| ( r1 @ sk21 @ ( sk6 @ sk21 ) ) ),
inference(pattern_uni,[status(thm)],[10965:[bind(A,$thf( sk21 ))]]) ).
thf(460,plain,
( sk16
| sk8
| ( sk21 != sk10 )
| ~ sk17
| ( ( p2 @ sk20 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[152,54]) ).
thf(464,plain,
( sk16
| sk8
| ( sk21 != sk10 )
| ~ sk17
| ( sk20 != sk1 ) ),
inference(simp,[status(thm)],[460]) ).
thf(1268,plain,
( sk8
| ( p2 @ sk1 )
| ( ( sk11 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[1264]) ).
thf(16308,plain,
( sk8
| ( p2 @ sk1 )
| ( ( p2 @ ( sk12 @ sk1 ) )
!= ( p2 @ ( sk11 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[991,16112]) ).
thf(16314,plain,
( sk8
| ( p2 @ sk1 )
| ( ( sk12 @ sk1 )
!= ( sk11 @ sk1 ) ) ),
inference(simp,[status(thm)],[16308]) ).
thf(32474,plain,
( ~ ( p3 @ sk1 )
| ( p1 @ sk2 )
| ( ( p1 @ ( sk14 @ sk2 ) )
!= ( p1 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[29658,16]) ).
thf(32520,plain,
( ( p1 @ sk2 )
| ~ ( p3 @ sk1 )
| ( ( sk14 @ sk2 )
!= sk13 ) ),
inference(simp,[status(thm)],[32474]) ).
thf(1947,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( r1 @ ( sk14 @ sk13 ) @ ( sk15 @ sk13 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1932,26]) ).
thf(1958,plain,
! [A: $i] :
( ~ ( p3 @ A )
| ~ ( p2 @ sk2 )
| ( ( sk14 @ sk13 )
!= sk1 )
| ( ( sk15 @ sk13 )
!= A ) ),
inference(simp,[status(thm)],[1947]) ).
thf(1976,plain,
( ~ ( p3 @ ( sk15 @ sk13 ) )
| ~ ( p2 @ sk2 )
| ( ( sk14 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[1958]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( p3 @ A )
| ~ ( r1 @ sk1 @ B )
| ( p2 @ B )
| ( p2 @ ( sk3 @ B ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(21553,plain,
( ( p4 @ sk13 )
| ( ( p4 @ ( sk6 @ sk13 ) )
!= ( p4 @ sk13 ) ) ),
inference(simp,[status(thm)],[21546]) ).
thf(25064,plain,
( ~ sk17
| sk16
| ( p4 @ sk20 )
| ( ( p4 @ ( sk6 @ sk20 ) )
!= ( p4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[21300,75]) ).
thf(25072,plain,
( sk16
| ( p4 @ sk20 )
| ~ sk17
| ( ( sk6 @ sk20 )
!= sk5 ) ),
inference(simp,[status(thm)],[25064]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ B @ ( sk18 @ B @ A ) )
| sk17
| sk16 ),
inference(cnf,[status(esa)],[6]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ~ ( r1 @ sk1 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ( r1 @ B @ ( sk18 @ B @ A ) )
| sk17
| sk16 ),
inference(simp,[status(thm)],[58]) ).
thf(463,plain,
( sk16
| sk8
| ( sk21 != sk10 )
| ~ ( p3 @ sk13 )
| ( ( p2 @ sk2 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[152,131]) ).
thf(469,plain,
( sk16
| sk8
| ( sk21 != sk10 )
| ~ ( p3 @ sk13 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[463]) ).
thf(8552,plain,
! [A: $i] :
( ~ sk8
| ( p3 @ ( sk9 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8326,109]) ).
thf(8553,plain,
( ~ sk8
| ( p3 @ ( sk9 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[8552:[bind(A,$thf( sk2 ))]]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk35 @ B @ A ) )
| ( sk29 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ~ sk16
| ~ ( r1 @ sk23 @ A )
| ~ ( r1 @ A @ B )
| ( p2 @ B )
| ~ ( p2 @ ( sk35 @ B @ A ) )
| ( sk29 @ A ) ),
inference(simp,[status(thm)],[24]) ).
thf(29795,plain,
( ( p1 @ sk1 )
| ( ( p1 @ ( sk14 @ sk1 ) )
!= ( p1 @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[29589,16]) ).
thf(29800,plain,
( ( p1 @ sk1 )
| ( ( sk14 @ sk1 )
!= sk13 ) ),
inference(simp,[status(thm)],[29795]) ).
thf(18284,plain,
! [A: $i] :
( ~ ( p3 @ sk1 )
| ( p2 @ A )
| ~ ( p2 @ ( sk41 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1019,106]) ).
thf(18285,plain,
( ~ ( p3 @ sk1 )
| ( p2 @ sk2 )
| ~ ( p2 @ ( sk41 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[18284:[bind(A,$thf( sk2 ))]]) ).
thf(11240,plain,
! [A: $i] :
( ( p4 @ sk1 )
| sk8
| ( p2 @ A )
| ( r1 @ A @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ ( sk6 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10958,90]) ).
thf(11241,plain,
( ( p4 @ sk1 )
| sk8
| ( p2 @ ( sk6 @ sk1 ) )
| ( r1 @ ( sk6 @ sk1 ) @ ( sk11 @ ( sk6 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[11240:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(1203,plain,
! [A: $i] :
( ~ ( p3 @ sk5 )
| sk8
| ( p2 @ A )
| ( p2 @ ( sk11 @ A ) )
| ( ( r1 @ sk1 @ sk2 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1070,124]) ).
thf(1204,plain,
( ~ ( p3 @ sk5 )
| sk8
| ( p2 @ sk2 )
| ( p2 @ ( sk11 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1203:[bind(A,$thf( sk2 ))]]) ).
thf(20852,plain,
! [A: $i] :
( ~ sk17
| sk16
| ( p4 @ A )
| ~ ( p4 @ ( sk7 @ A ) )
| ( ( r1 @ sk1 @ sk20 )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,111]) ).
thf(20853,plain,
( ~ sk17
| sk16
| ( p4 @ sk20 )
| ~ ( p4 @ ( sk7 @ sk20 ) ) ),
inference(pattern_uni,[status(thm)],[20852:[bind(A,$thf( sk20 ))]]) ).
thf(21384,plain,
! [A: $i] :
( ( p2 @ sk1 )
| ( p4 @ A )
| ( p4 @ ( sk6 @ A ) )
| ( ( r1 @ sk1 @ ( sk41 @ sk1 ) )
!= ( r1 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3780,112]) ).
thf(21385,plain,
( ( p2 @ sk1 )
| ( p4 @ ( sk41 @ sk1 ) )
| ( p4 @ ( sk6 @ ( sk41 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[21384:[bind(A,$thf( sk41 @ sk1 ))]]) ).
thf(15021,plain,
( ( p3 @ ( sk9 @ ( sk14 @ sk1 ) ) )
| ~ sk8
| ( ( p1 @ ( sk15 @ sk13 ) )
!= ( p1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[5030,15018]) ).
thf(15024,plain,
( ( p3 @ ( sk9 @ ( sk14 @ sk1 ) ) )
| ~ sk8
| ( ( sk15 @ sk13 )
!= sk1 ) ),
inference(simp,[status(thm)],[15021]) ).
thf(29855,plain,
( ( p1 @ sk5 )
| ( ( p1 @ ( sk14 @ sk5 ) )
!= ( p1 @ sk5 ) ) ),
inference(simp,[status(thm)],[29852]) ).
thf(746,plain,
( sk16
| ~ sk17
| ( sk21 != sk20 )
| ( ( p2 @ sk20 )
!= ( p2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[161,54]) ).
thf(755,plain,
( sk16
| ~ sk17
| ( sk21 != sk20 )
| ( sk20 != sk1 ) ),
inference(simp,[status(thm)],[746]) ).
thf(69823,plain,
$false,
inference(e,[status(thm)],[69,29599,40018,101,468,16124,5028,88,1110,1005,20258,25508,2953,2676,43046,120,5141,115,22759,21573,20922,21089,1569,21570,269,5037,8551,32366,19767,18240,2844,153,21534,14905,142,32420,3826,3915,782,13083,29557,39934,1803,5342,21592,18247,42,16398,29653,1518,1265,389,14,29589,1985,2698,1511,21530,196,22777,110,16176,125,157,11040,29837,21394,18451,30558,152,16114,38968,57,5076,20,6905,93,3919,29856,21556,11500,211,22762,27147,29833,14812,29585,216,35865,756,2794,18207,106,5032,121,3923,84,1051,18786,4810,21569,8575,411,116,22774,14900,3406,206,28666,15023,766,89,4924,133,24021,20903,4753,85,21399,20889,102,1047,60,117,270,10954,15935,18493,21567,2249,1570,11223,29861,18209,2890,45207,297,192,3371,21,137,92,197,30584,21300,97,29806,15018,3931,757,10958,3782,156,3381,169,10771,10760,21547,16441,1270,37269,403,9,2798,16127,77,28675,10914,4938,11046,22758,4867,96,109,471,124,225,38862,21587,11496,193,10968,2845,1932,22781,173,4934,1799,129,14875,5026,18276,11000,11023,997,5149,8326,7169,16112,73,105,6963,266,1779,205,29834,398,30557,29552,3807,128,3834,25075,6982,21349,10971,34,20950,161,21568,3792,296,21536,1278,298,29815,20899,3741,2727,191,44,3736,291,118,14869,27,20705,29864,1271,11201,30529,466,236,20915,11038,21094,86,24948,12,54,14854,21336,787,21558,49,20887,187,22757,406,113,6920,30554,784,81,377,1571,21590,30536,11487,22776,98,29651,14839,103,30586,30581,66,1325,25501,155,198,108,1820,2261,140,29832,213,726,21346,91,27149,30564,29658,3838,21571,3917,33316,394,135,1000,33304,267,80,1805,2506,6907,8573,14898,11193,8560,29578,29854,29591,37351,29619,112,3921,123,25582,21532,9317,30537,4901,2846,2256,29803,194,29839,5047,21396,18449,295,1070,21361,95,3904,2518,29643,1267,32450,11225,993,1053,21305,2688,177,1038,20883,470,2701,4875,19774,5015,21554,16,5030,127,18170,9151,154,16367,7163,1008,1272,2848,991,18533,35966,99,87,29828,6970,32357,104,22711,1157,4873,218,29831,3929,8579,16575,30530,32512,1326,3789,2251,158,3369,2811,21330,114,401,786,26,25600,18224,12268,3780,75,14845,207,2462,21589,24955,10960,21574,214,290,119,82,37248,11167,2258,20955,24014,4917,5129,18220,30,18278,29813,35886,21334,11219,190,183,273,21549,410,21531,18203,7171,107,126,1314,11199,29804,268,79,767,1056,30591,16331,4865,10622,94,29603,14843,4,21344,195,10966,464,1268,16314,2847,32520,1019,1976,131,68,62,21553,25072,122,469,8553,11397,83,29800,18285,11241,1204,222,100,90,111,20853,21385,15024,29855,755]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL660+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n008.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 : Mon May 6 12:02:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.97/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.99 % [INFO] Parsing done (129ms).
% 1.25/1.00 % [INFO] Running in sequential loop mode.
% 1.82/1.22 % [INFO] eprover registered as external prover.
% 1.82/1.22 % [INFO] cvc4 registered as external prover.
% 1.82/1.23 % [INFO] Scanning for conjecture ...
% 2.14/1.34 % [INFO] Found a conjecture and 1 axioms. Running axiom selection ...
% 2.30/1.37 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.30/1.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.30/1.38 % [INFO] Type checking passed.
% 2.30/1.39 % [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 ...
% 131.23/23.55 % External prover 'e' found a proof!
% 131.23/23.55 % [INFO] Killing All external provers ...
% 131.23/23.55 % Time passed: 23022ms (effective reasoning time: 22551ms)
% 131.23/23.55 % 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)>
% 131.23/23.55 % Axioms used in derivation (1): reflexivity
% 131.23/23.55 % No. of inferences in proof: 988
% 131.23/23.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23022 ms resp. 22551 ms w/o parsing
% 131.58/23.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 131.96/23.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------