TSTP Solution File: SEV155^5 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV155^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n022.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 : Mon Jun 24 15:58:21 EDT 2024
% Result : Theorem 82.18s 18.63s
% Output : Refutation 82.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 1
% Syntax : Number of formulae : 479 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 2789 ( 293 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 6388 (1416 ~;1382 |; 54 &;3452 @)
% ( 0 <=>; 84 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 172 ( 172 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 63 usr; 47 con; 0-2 aty)
% Number of variables : 1030 ( 290 ^ 740 !; 0 ?;1030 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_type,type,
sk1: a > a > $o ).
thf(sk2_type,type,
sk2: a > a > $o ).
thf(sk3_type,type,
sk3: a ).
thf(sk4_type,type,
sk4: a ).
thf(sk5_type,type,
sk5: $o ).
thf(sk6_type,type,
sk6: $o ).
thf(sk7_type,type,
sk7: a ).
thf(sk8_type,type,
sk8: a ).
thf(sk9_type,type,
sk9: $o ).
thf(sk10_type,type,
sk10: ( a > a > $o ) > a ).
thf(sk11_type,type,
sk11: ( a > a > $o ) > a ).
thf(sk15_type,type,
sk15: ( a > a > $o ) > a ).
thf(sk16_type,type,
sk16: ( a > a > $o ) > a ).
thf(sk20_type,type,
sk20: a > a > $o ).
thf(sk21_type,type,
sk21: a ).
thf(sk23_type,type,
sk23: a ).
thf(sk24_type,type,
sk24: ( a > a > $o ) > $o ).
thf(sk25_type,type,
sk25: ( a > a > $o ) > a ).
thf(sk26_type,type,
sk26: ( a > a > $o ) > a ).
thf(sk30_type,type,
sk30: ( a > a > $o ) > $o ).
thf(sk31_type,type,
sk31: ( a > a > $o ) > a ).
thf(sk32_type,type,
sk32: ( a > a > $o ) > a ).
thf(sk36_type,type,
sk36: a > a > $o ).
thf(sk37_type,type,
sk37: ( a > a > $o ) > $o ).
thf(sk38_type,type,
sk38: ( a > a > $o ) > a ).
thf(sk39_type,type,
sk39: ( a > a > $o ) > a ).
thf(sk43_type,type,
sk43: a > a > $o ).
thf(sk44_type,type,
sk44: a ).
thf(sk45_type,type,
sk45: a ).
thf(sk46_type,type,
sk46: a ).
thf(sk47_type,type,
sk47: a ).
thf(sk48_type,type,
sk48: a ).
thf(sk49_type,type,
sk49: a ).
thf(sk50_type,type,
sk50: a ).
thf(sk51_type,type,
sk51: a ).
thf(sk52_type,type,
sk52: a ).
thf(sk53_type,type,
sk53: a ).
thf(sk54_type,type,
sk54: a ).
thf(sk55_type,type,
sk55: a ).
thf(sk56_type,type,
sk56: a ).
thf(sk57_type,type,
sk57: a ).
thf(sk58_type,type,
sk58: a ).
thf(sk59_type,type,
sk59: a ).
thf(sk60_type,type,
sk60: a ).
thf(sk61_type,type,
sk61: a ).
thf(sk62_type,type,
sk62: a ).
thf(sk63_type,type,
sk63: a ).
thf(1,conjecture,
! [A: a > a > $o,B: a > a > $o,C: a,D: a] :
( ( ( ! [E: a,F: a] :
( ( ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( A @ H @ I )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) )
| ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( B @ H @ I )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) ) )
=> ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( ( A @ H @ I )
| ( B @ H @ I ) )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) ) )
& ! [E: a,F: a,G: a] :
( ( ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ E @ F ) )
& ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ F @ G ) ) )
=> ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ E @ G ) ) ) )
=> ! [E: a > a > $o] :
( ( ! [F: a,G: a] :
( ( ( A @ F @ G )
| ( B @ F @ G ) )
=> ( E @ F @ G ) )
& ! [F: a,G: a,H: a] :
( ( ( E @ F @ G )
& ( E @ G @ H ) )
=> ( E @ F @ H ) ) )
=> ( E @ C @ D ) ) )
=> ! [E: a > a > $o] :
( ( ! [F: a,G: a] :
( ( ( A @ F @ G )
| ( B @ F @ G ) )
=> ( E @ F @ G ) )
& ! [F: a,G: a,H: a] :
( ( ( E @ F @ G )
& ( E @ G @ H ) )
=> ( E @ F @ H ) ) )
=> ( E @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM250D_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > a > $o,B: a > a > $o,C: a,D: a] :
( ( ( ! [E: a,F: a] :
( ( ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( A @ H @ I )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) )
| ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( B @ H @ I )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) ) )
=> ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( ( A @ H @ I )
| ( B @ H @ I ) )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) ) )
& ! [E: a,F: a,G: a] :
( ( ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ E @ F ) )
& ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ F @ G ) ) )
=> ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ E @ G ) ) ) )
=> ! [E: a > a > $o] :
( ( ! [F: a,G: a] :
( ( ( A @ F @ G )
| ( B @ F @ G ) )
=> ( E @ F @ G ) )
& ! [F: a,G: a,H: a] :
( ( ( E @ F @ G )
& ( E @ G @ H ) )
=> ( E @ F @ H ) ) )
=> ( E @ C @ D ) ) )
=> ! [E: a > a > $o] :
( ( ! [F: a,G: a] :
( ( ( A @ F @ G )
| ( B @ F @ G ) )
=> ( E @ F @ G ) )
& ! [F: a,G: a,H: a] :
( ( ( E @ F @ G )
& ( E @ G @ H ) )
=> ( E @ F @ H ) ) )
=> ( E @ C @ D ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > a > $o,B: a > a > $o,C: a,D: a] :
( ( ( ! [E: a,F: a] :
( ( ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( A @ H @ I )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) )
| ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( B @ H @ I )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) ) )
=> ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( ( A @ H @ I )
| ( B @ H @ I ) )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) ) )
& ! [E: a,F: a,G: a] :
( ( ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ E @ F ) )
& ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ F @ G ) ) )
=> ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ E @ G ) ) ) )
=> ! [E: a > a > $o] :
( ( ! [F: a,G: a] :
( ( ( A @ F @ G )
| ( B @ F @ G ) )
=> ( E @ F @ G ) )
& ! [F: a,G: a,H: a] :
( ( ( E @ F @ G )
& ( E @ G @ H ) )
=> ( E @ F @ H ) ) )
=> ( E @ C @ D ) ) )
=> ! [E: a > a > $o] :
( ( ! [F: a,G: a] :
( ( ( A @ F @ G )
| ( B @ F @ G ) )
=> ( E @ F @ G ) )
& ! [F: a,G: a,H: a] :
( ( ( E @ F @ G )
& ( E @ G @ H ) )
=> ( E @ F @ H ) ) )
=> ( E @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk43 @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(72,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk43 @ A @ B ) ),
inference(simp,[status(thm)],[19]) ).
thf(24,plain,
! [C: a,B: a,A: a] :
( ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ C )
| ( sk43 @ A @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(53,plain,
! [C: a,B: a,A: a] :
( ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ C )
| ( sk43 @ A @ C ) ),
inference(simp,[status(thm)],[24]) ).
thf(11,plain,
~ ( sk43 @ sk3 @ sk4 ),
inference(cnf,[status(esa)],[3]) ).
thf(445,plain,
! [C: a,B: a,A: a] :
( ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ C )
| ( ( sk43 @ A @ C )
!= ( sk43 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[53,11]) ).
thf(446,plain,
! [A: a] :
( ~ ( sk43 @ sk3 @ A )
| ~ ( sk43 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[445:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(477,plain,
! [A: a] :
( ~ ( sk43 @ sk3 @ A )
| ~ ( sk43 @ A @ sk4 ) ),
inference(simp,[status(thm)],[446]) ).
thf(488,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[72,477]) ).
thf(489,plain,
! [A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk43 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[488:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(692,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ sk4 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,489]) ).
thf(693,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[692:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(704,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ sk4 ) ),
inference(simp,[status(thm)],[693]) ).
thf(806,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( ( sk1 @ A @ sk4 )
!= ( sk1 @ sk3 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[704]) ).
thf(809,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( ( sk1 @ A @ sk4 )
!= ( sk1 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[806]) ).
thf(16,plain,
! [A: a > a > $o] :
( ~ sk5
| ~ ( A @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ~ ( sk37 @ A )
| ( A @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(68,plain,
! [A: a > a > $o] :
( ~ sk5
| ~ ( A @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ~ ( sk37 @ A )
| ( A @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[16]) ).
thf(85,plain,
( ~ sk5
| ~ ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk37 @ sk43 )
| ( sk43 @ sk3 @ sk4 ) ),
inference(prim_subst,[status(thm)],[68:[bind(A,$thf( sk43 ))]]) ).
thf(277,plain,
( ~ sk5
| ~ ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk37 @ sk43 )
| $false ),
inference(rewrite,[status(thm)],[85,11]) ).
thf(278,plain,
( ~ sk5
| ~ ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk37 @ sk43 ) ),
inference(simp,[status(thm)],[277]) ).
thf(443,plain,
! [C: a,B: a,A: a] :
( ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ C )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk43 @ A @ C )
!= ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,278]) ).
thf(444,plain,
! [A: a] :
( ~ ( sk43 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk43 @ A @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(pattern_uni,[status(thm)],[443:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( B )),bind(C,$thf( sk39 @ sk43 ))]]) ).
thf(476,plain,
! [A: a] :
( ~ ( sk43 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk43 @ A @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(simp,[status(thm)],[444]) ).
thf(3020,plain,
! [A: a] :
( ~ ( sk43 @ ( sk38 @ sk43 ) @ A )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk43 @ A @ ( sk39 @ sk43 ) )
!= ( sk43 @ ( sk38 @ sk43 ) @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[476]) ).
thf(3025,plain,
! [A: a] :
( ~ ( sk43 @ ( sk38 @ sk43 ) @ A )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( A
!= ( sk38 @ sk43 ) )
| ( ( sk39 @ sk43 )
!= A ) ),
inference(simp,[status(thm)],[3020]) ).
thf(3031,plain,
( ~ ( sk43 @ ( sk38 @ sk43 ) @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(simp,[status(thm)],[3025]) ).
thf(3043,plain,
! [C: a,B: a,A: a] :
( ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ C )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) )
| ( ( sk43 @ A @ C )
!= ( sk43 @ ( sk38 @ sk43 ) @ ( sk38 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,3031]) ).
thf(3044,plain,
! [A: a] :
( ~ ( sk43 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk43 @ A @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(pattern_uni,[status(thm)],[3043:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( B )),bind(C,$thf( sk38 @ sk43 ))]]) ).
thf(3065,plain,
! [A: a] :
( ~ ( sk43 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk43 @ A @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(simp,[status(thm)],[3044]) ).
thf(8783,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ ( sk38 @ sk43 ) @ C )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ ( sk38 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[72,3065]) ).
thf(8784,plain,
! [A: a] :
( ~ ( sk1 @ A @ ( sk38 @ sk43 ) )
| ~ ( sk43 @ ( sk38 @ sk43 ) @ A )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(pattern_uni,[status(thm)],[8783:[bind(A,$thf( A )),bind(B,$thf( sk38 @ sk43 )),bind(C,$thf( A ))]]) ).
thf(30,plain,
! [A: a > a > $o] :
( ( sk1 @ ( sk10 @ A ) @ ( sk11 @ A ) )
| ( A @ ( sk13 @ A ) @ ( sk14 @ A ) )
| ( A @ sk7 @ sk8 )
| sk9
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(583,plain,
( ( sk1
@ ( sk10
@ ^ [A: a,B: a] : sk9 )
@ ( sk11
@ ^ [A: a,B: a] : sk9 ) )
| sk9
| sk9
| sk9
| ~ sk6
| sk5 ),
inference(prim_subst,[status(thm)],[30:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk9 ))]]) ).
thf(648,plain,
( ( sk1
@ ( sk10
@ ^ [A: a,B: a] : sk9 )
@ ( sk11
@ ^ [A: a,B: a] : sk9 ) )
| sk9
| ~ sk6
| sk5 ),
inference(simp,[status(thm)],[583]) ).
thf(75,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[72,11]) ).
thf(76,plain,
~ ( sk1 @ sk3 @ sk4 ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(867,plain,
( sk9
| ~ sk6
| sk5
| ( ( sk1
@ ( sk10
@ ^ [A: a,B: a] : sk9 )
@ ( sk11
@ ^ [A: a,B: a] : sk9 ) )
!= ( sk1 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[648,76]) ).
thf(892,plain,
( sk9
| sk5
| ~ sk6
| ( ( sk10
@ ^ [A: a,B: a] : sk9 )
!= sk3 )
| ( ( sk11
@ ^ [A: a,B: a] : sk9 )
!= sk4 ) ),
inference(simp,[status(thm)],[867]) ).
thf(31,plain,
! [A: a > a > $o] :
( ~ sk9
| ( sk2 @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ( A @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( A @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(69,plain,
! [A: a > a > $o] :
( ~ sk9
| ( sk2 @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ( A @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( A @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(simp,[status(thm)],[31]) ).
thf(34,plain,
! [A: a > a > $o] :
( ~ sk5
| ( sk37 @ A )
| ( A @ ( sk40 @ A ) @ ( sk41 @ A ) )
| ( A @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(63,plain,
! [A: a > a > $o] :
( ~ sk5
| ( sk37 @ A )
| ( A @ ( sk40 @ A ) @ ( sk41 @ A ) )
| ( A @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[34]) ).
thf(13010,plain,
! [A: a > a > $o] :
( ~ sk5
| ( sk37 @ A )
| ( A @ sk3 @ sk4 )
| ( ( A @ ( sk40 @ A ) @ ( sk41 @ A ) )
!= ~ sk5 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[63]) ).
thf(13204,plain,
( ~ sk5
| ( sk37
@ ^ [A: a,B: a] : ~ sk5 )
| ~ sk5 ),
inference(pre_uni,[status(thm)],[13010:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ~ ( sk5 ) ))]]) ).
thf(13462,plain,
( ~ sk5
| ( sk37
@ ^ [A: a,B: a] : ~ sk5 )
| ~ sk5 ),
inference(cnf,[status(esa)],[13204]) ).
thf(13463,plain,
( ~ sk5
| ( sk37
@ ^ [A: a,B: a] : ~ sk5 ) ),
inference(simp,[status(thm)],[13462]) ).
thf(101,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk2 ) @ ( sk39 @ sk2 ) )
| ~ ( sk37 @ sk2 )
| ( sk2 @ sk3 @ sk4 ) ),
inference(prim_subst,[status(thm)],[68:[bind(A,$thf( sk2 ))]]) ).
thf(5,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk43 @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(43,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk43 @ A @ B ) ),
inference(simp,[status(thm)],[5]) ).
thf(73,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[43,11]) ).
thf(74,plain,
~ ( sk2 @ sk3 @ sk4 ),
inference(pattern_uni,[status(thm)],[73:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(24424,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk2 ) @ ( sk39 @ sk2 ) )
| ~ ( sk37 @ sk2 )
| $false ),
inference(rewrite,[status(thm)],[101,74]) ).
thf(24425,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk2 ) @ ( sk39 @ sk2 ) )
| ~ ( sk37 @ sk2 ) ),
inference(simp,[status(thm)],[24424]) ).
thf(24454,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk2 ) @ ( sk39 @ sk2 ) )
| ( ( sk37 @ sk2 )
!= ( sk37
@ ^ [A: a,B: a] : ~ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[13463,24425]) ).
thf(24485,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk2 ) @ ( sk39 @ sk2 ) )
| ( sk2
!= ( ^ [A: a,B: a] : ~ sk5 ) ) ),
inference(simp,[status(thm)],[24454]) ).
thf(24585,plain,
( ( ( sk2 @ sk62 @ sk63 )
!= ~ sk5 )
| ~ sk5
| ~ ( sk2 @ ( sk38 @ sk2 ) @ ( sk39 @ sk2 ) ) ),
inference(func_ext,[status(esa)],[24485]) ).
thf(14,plain,
! [A: a > a > $o] :
( sk6
| ( sk30 @ A )
| ( A @ ( sk34 @ A ) @ ( sk35 @ A ) )
| ( A @ sk22 @ sk23 )
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(45,plain,
! [A: a > a > $o] :
( sk6
| ( sk30 @ A )
| ( A @ ( sk34 @ A ) @ ( sk35 @ A ) )
| ( A @ sk22 @ sk23 )
| sk5 ),
inference(simp,[status(thm)],[14]) ).
thf(18,plain,
( sk6
| ~ ( sk36 @ sk21 @ sk23 )
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(275,plain,
! [A: a > a > $o] :
( sk6
| ( sk30 @ A )
| ( A @ sk22 @ sk23 )
| sk5
| ( ( A @ ( sk34 @ A ) @ ( sk35 @ A ) )
!= ( sk36 @ sk21 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[45,18]) ).
thf(276,plain,
( sk6
| ( sk30
@ ^ [A: a,B: a] : ( sk36 @ sk21 @ sk23 ) )
| ( sk36 @ sk21 @ sk23 )
| sk5 ),
inference(pre_uni,[status(thm)],[275:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk36 @ sk21 @ sk23 ) ))]]) ).
thf(492,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[43,477]) ).
thf(493,plain,
! [A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk43 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[492:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(717,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ C )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk43 @ A @ C )
!= ( sk43 @ sk3 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[53,493]) ).
thf(718,plain,
! [B: a,A: a] :
( ~ ( sk43 @ sk3 @ A )
| ~ ( sk43 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[717:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(741,plain,
! [B: a,A: a] :
( ~ ( sk43 @ sk3 @ A )
| ~ ( sk43 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[718]) ).
thf(93,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk1 ) @ ( sk39 @ sk1 ) )
| ~ ( sk37 @ sk1 )
| ( sk1 @ sk3 @ sk4 ) ),
inference(prim_subst,[status(thm)],[68:[bind(A,$thf( sk1 ))]]) ).
thf(23405,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk1 ) @ ( sk39 @ sk1 ) )
| ~ ( sk37 @ sk1 )
| $false ),
inference(rewrite,[status(thm)],[93,76]) ).
thf(23406,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk1 ) @ ( sk39 @ sk1 ) )
| ~ ( sk37 @ sk1 ) ),
inference(simp,[status(thm)],[23405]) ).
thf(482,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ C )
| ~ ( sk43 @ sk3 @ D )
| ( ( sk43 @ A @ C )
!= ( sk43 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[53,477]) ).
thf(483,plain,
! [B: a,A: a] :
( ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ sk4 )
| ~ ( sk43 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[482:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( A ))]]) ).
thf(4268,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ D @ sk4 )
| ~ ( sk43 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[72,483]) ).
thf(4269,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ B @ sk4 )
| ~ ( sk43 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[4268:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(6688,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk43 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[72,4269]) ).
thf(6689,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk43 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[6688:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(6776,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk43 @ sk3 @ B ) ),
inference(simp,[status(thm)],[6689]) ).
thf(685,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ C )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk43 @ A @ C )
!= ( sk43 @ sk3 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[53,489]) ).
thf(686,plain,
! [B: a,A: a] :
( ~ ( sk43 @ sk3 @ A )
| ~ ( sk43 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[685:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(712,plain,
! [B: a,A: a] :
( ~ ( sk43 @ sk3 @ A )
| ~ ( sk43 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[686]) ).
thf(4523,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ C @ D )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,712]) ).
thf(4524,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk43 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4523:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(4603,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk43 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[4524]) ).
thf(33,plain,
! [A: a > a > $o] :
( sk6
| ~ ( A @ ( sk31 @ A ) @ ( sk32 @ A ) )
| ~ ( sk30 @ A )
| ( A @ sk22 @ sk23 )
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(56,plain,
! [A: a > a > $o] :
( sk6
| ~ ( A @ ( sk31 @ A ) @ ( sk32 @ A ) )
| ~ ( sk30 @ A )
| ( A @ sk22 @ sk23 )
| sk5 ),
inference(simp,[status(thm)],[33]) ).
thf(3048,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ ( sk38 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[72,3031]) ).
thf(3049,plain,
( ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(pattern_uni,[status(thm)],[3048:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( sk38 @ sk43 ))]]) ).
thf(13016,plain,
( ~ sk5
| ( sk37
@ ^ [A: a,B: a] : $false )
| $false
| $false ),
inference(prim_subst,[status(thm)],[63:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(13295,plain,
( ~ sk5
| ( sk37
@ ^ [A: a,B: a] : $false ) ),
inference(simp,[status(thm)],[13016]) ).
thf(284,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[43,278]) ).
thf(285,plain,
( ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(pattern_uni,[status(thm)],[284:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( sk39 @ sk43 ))]]) ).
thf(13559,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( ( sk37 @ sk43 )
!= ( sk37
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[13295,285]) ).
thf(13623,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk43
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[13559]) ).
thf(13694,plain,
( ~ sk5
| ~ ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( ( sk37 @ sk43 )
!= ( sk37
@ ^ [A: a,B: a] : ~ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[13463,278]) ).
thf(13753,plain,
( ~ sk5
| ~ ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk43
!= ( ^ [A: a,B: a] : ~ sk5 ) ) ),
inference(simp,[status(thm)],[13694]) ).
thf(14764,plain,
( ( ( sk43 @ sk54 @ sk55 )
!= ~ sk5 )
| ~ sk5
| ~ ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ),
inference(func_ext,[status(esa)],[13753]) ).
thf(18596,plain,
( ~ sk5
| ~ ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk43 @ sk54 @ sk55 )
| ~ sk5 ),
inference(bool_ext,[status(thm)],[14764]) ).
thf(18682,plain,
( ~ sk5
| ( sk43 @ sk54 @ sk55 )
| ~ ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5 ),
inference(cnf,[status(esa)],[18596]) ).
thf(18683,plain,
( ~ sk5
| ( sk43 @ sk54 @ sk55 )
| ~ ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ),
inference(simp,[status(thm)],[18682]) ).
thf(18721,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ sk5
| ( sk43 @ sk54 @ sk55 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[72,18683]) ).
thf(18722,plain,
( ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5
| ( sk43 @ sk54 @ sk55 ) ),
inference(pattern_uni,[status(thm)],[18721:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( sk39 @ sk43 ))]]) ).
thf(21303,plain,
( ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5
| ( ( sk43 @ sk54 @ sk55 )
!= ( sk43 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18722,11]) ).
thf(21358,plain,
( ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5
| ( sk54 != sk3 )
| ( sk55 != sk4 ) ),
inference(simp,[status(thm)],[21303]) ).
thf(14039,plain,
( ( sk43 @ sk46 @ sk47 )
| ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ),
inference(func_ext,[status(esa)],[13623]) ).
thf(15359,plain,
! [A: a] :
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk1 @ A @ sk4 )
| ( ( sk43 @ sk46 @ sk47 )
!= ( sk43 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14039,489]) ).
thf(15445,plain,
! [A: a] :
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk1 @ A @ sk4 )
| ( sk46 != sk3 )
| ( sk47 != A ) ),
inference(simp,[status(thm)],[15359]) ).
thf(15541,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk1 @ sk47 @ sk4 )
| ( sk46 != sk3 ) ),
inference(simp,[status(thm)],[15445]) ).
thf(494,plain,
! [A: a] :
( ~ ( sk43 @ sk3 @ A )
| ( ( sk43 @ A @ sk4 )
!= ( sk43 @ sk3 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[477]) ).
thf(500,plain,
! [A: a] :
( ~ ( sk43 @ sk3 @ A )
| ( A != sk3 )
| ( sk4 != A ) ),
inference(simp,[status(thm)],[494]) ).
thf(508,plain,
( ~ ( sk43 @ sk3 @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[500]) ).
thf(510,plain,
! [C: a,B: a,A: a] :
( ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ C )
| ( sk4 != sk3 )
| ( ( sk43 @ A @ C )
!= ( sk43 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[53,508]) ).
thf(511,plain,
! [A: a] :
( ~ ( sk43 @ sk3 @ A )
| ~ ( sk43 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[510:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(519,plain,
! [A: a] :
( ~ ( sk43 @ sk3 @ A )
| ~ ( sk43 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[511]) ).
thf(1953,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ sk3 @ C )
| ( sk4 != sk3 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[72,519]) ).
thf(1954,plain,
! [A: a] :
( ~ ( sk1 @ A @ sk3 )
| ~ ( sk43 @ sk3 @ A )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[1953:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(694,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ sk4 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,489]) ).
thf(695,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[694:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(705,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ sk4 ) ),
inference(simp,[status(thm)],[695]) ).
thf(873,plain,
! [A: a] :
( sk9
| ~ sk6
| sk5
| ~ ( sk2 @ sk3 @ A )
| ( ( sk1
@ ( sk10
@ ^ [B: a,C: a] : sk9 )
@ ( sk11
@ ^ [B: a,C: a] : sk9 ) )
!= ( sk1 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[648,705]) ).
thf(885,plain,
! [A: a] :
( sk9
| sk5
| ~ sk6
| ~ ( sk2 @ sk3 @ A )
| ( ( sk10
@ ^ [B: a,C: a] : sk9 )
!= A )
| ( ( sk11
@ ^ [B: a,C: a] : sk9 )
!= sk4 ) ),
inference(simp,[status(thm)],[873]) ).
thf(898,plain,
( sk9
| sk5
| ~ sk6
| ~ ( sk2 @ sk3
@ ( sk10
@ ^ [A: a,B: a] : sk9 ) )
| ( ( sk11
@ ^ [A: a,B: a] : sk9 )
!= sk4 ) ),
inference(simp,[status(thm)],[885]) ).
thf(17,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk1 @ A @ B )
| ( sk36 @ A @ B )
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(61,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk1 @ A @ B )
| ( sk36 @ A @ B )
| sk5 ),
inference(simp,[status(thm)],[17]) ).
thf(11644,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk1 @ A @ B )
| sk5
| ( ( sk36 @ A @ B )
!= ( sk36 @ sk21 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[61,18]) ).
thf(11645,plain,
( sk6
| ~ ( sk1 @ sk21 @ sk23 )
| sk5 ),
inference(pattern_uni,[status(thm)],[11644:[bind(A,$thf( sk21 )),bind(B,$thf( sk23 ))]]) ).
thf(37,plain,
! [A: a > a > $o] :
( ~ ( A @ ( sk10 @ A ) @ ( sk11 @ A ) )
| ( A @ ( sk12 @ A ) @ ( sk13 @ A ) )
| ( A @ sk7 @ sk8 )
| sk9
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(25,plain,
( ~ ( sk20 @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(42,plain,
! [A: a > a > $o] :
( sk6
| ( sk24 @ A )
| ( A @ ( sk28 @ A ) @ ( sk29 @ A ) )
| ( A @ sk21 @ sk22 )
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(52,plain,
! [A: a > a > $o] :
( sk6
| ( sk24 @ A )
| ( A @ ( sk28 @ A ) @ ( sk29 @ A ) )
| ( A @ sk21 @ sk22 )
| sk5 ),
inference(simp,[status(thm)],[42]) ).
thf(490,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ C @ sk4 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,477]) ).
thf(491,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk43 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[490:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(503,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk43 @ A @ sk4 ) ),
inference(simp,[status(thm)],[491]) ).
thf(774,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ C )
| ~ ( sk2 @ sk3 @ D )
| ( ( sk43 @ A @ C )
!= ( sk43 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[53,503]) ).
thf(775,plain,
! [B: a,A: a] :
( ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ sk4 )
| ~ ( sk2 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[774:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( A ))]]) ).
thf(5149,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ D @ sk4 )
| ~ ( sk2 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[72,775]) ).
thf(5150,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ B @ sk4 )
| ~ ( sk2 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[5149:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4274,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ D @ sk4 )
| ~ ( sk43 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[43,483]) ).
thf(4275,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ B @ sk4 )
| ~ ( sk43 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[4274:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(282,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[72,278]) ).
thf(283,plain,
( ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( sk39 @ sk43 ))]]) ).
thf(13591,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( ( sk37 @ sk43 )
!= ( sk37
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[13295,283]) ).
thf(13607,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk43
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[13591]) ).
thf(13988,plain,
( ( sk43 @ sk44 @ sk45 )
| ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ),
inference(func_ext,[status(esa)],[13607]) ).
thf(15078,plain,
! [A: a] :
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk2 @ sk3 @ A )
| ( ( sk43 @ sk44 @ sk45 )
!= ( sk43 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[13988,503]) ).
thf(15190,plain,
! [A: a] :
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk2 @ sk3 @ A )
| ( sk44 != A )
| ( sk45 != sk4 ) ),
inference(simp,[status(thm)],[15078]) ).
thf(15264,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk2 @ sk3 @ sk44 )
| ( sk45 != sk4 ) ),
inference(simp,[status(thm)],[15190]) ).
thf(4270,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ C @ D )
| ~ ( sk43 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[72,483]) ).
thf(4271,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk43 @ B @ A )
| ~ ( sk43 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[4270:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(4353,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk43 @ B @ A )
| ~ ( sk43 @ sk3 @ B ) ),
inference(simp,[status(thm)],[4271]) ).
thf(20,plain,
! [A: a > a > $o] :
( ~ ( A @ ( sk10 @ A ) @ ( sk11 @ A ) )
| ( A @ ( sk13 @ A ) @ ( sk14 @ A ) )
| ( A @ sk7 @ sk8 )
| sk9
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ ( sk25 @ A ) @ ( sk26 @ A ) )
| ( sk2 @ ( sk25 @ A ) @ ( sk26 @ A ) )
| ~ ( sk24 @ A )
| ( A @ sk21 @ sk22 )
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(46,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ ( sk25 @ A ) @ ( sk26 @ A ) )
| ( sk2 @ ( sk25 @ A ) @ ( sk26 @ A ) )
| ~ ( sk24 @ A )
| ( A @ sk21 @ sk22 )
| sk5 ),
inference(simp,[status(thm)],[9]) ).
thf(28,plain,
! [A: a > a > $o] :
( ~ sk9
| ( sk2 @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ( A @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ( A @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(57,plain,
! [A: a > a > $o] :
( ~ sk9
| ( sk2 @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ( A @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ( A @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(simp,[status(thm)],[28]) ).
thf(5641,plain,
( sk6
| ( sk24
@ ^ [A: a,B: a] : sk6 )
| sk6
| sk6
| sk5 ),
inference(prim_subst,[status(thm)],[52:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk6 ))]]) ).
thf(5792,plain,
( sk6
| ( sk24
@ ^ [A: a,B: a] : sk6 )
| sk5 ),
inference(simp,[status(thm)],[5641]) ).
thf(151,plain,
( sk6
| ( sk30
@ ^ [A: a,B: a] : sk9 )
| sk9
| sk9
| sk5 ),
inference(prim_subst,[status(thm)],[45:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk9 ))]]) ).
thf(179,plain,
( sk6
| ( sk30
@ ^ [A: a,B: a] : sk9 )
| sk9
| sk5 ),
inference(simp,[status(thm)],[151]) ).
thf(15097,plain,
! [A: a] :
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk43 @ A @ sk4 )
| ( ( sk43 @ sk44 @ sk45 )
!= ( sk43 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13988,477]) ).
thf(15187,plain,
! [A: a] :
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk43 @ A @ sk4 )
| ( sk44 != sk3 )
| ( sk45 != A ) ),
inference(simp,[status(thm)],[15097]) ).
thf(15261,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk43 @ sk45 @ sk4 )
| ( sk44 != sk3 ) ),
inference(simp,[status(thm)],[15187]) ).
thf(513,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk4 != sk3 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[72,508]) ).
thf(514,plain,
( ~ ( sk1 @ sk3 @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[513:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(13030,plain,
( ~ sk5
| ( sk37
@ ^ [A: a,B: a] : sk9 )
| sk9
| sk9 ),
inference(prim_subst,[status(thm)],[63:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk9 ))]]) ).
thf(13305,plain,
( ~ sk5
| ( sk37
@ ^ [A: a,B: a] : sk9 )
| sk9 ),
inference(simp,[status(thm)],[13030]) ).
thf(725,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ sk4 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,493]) ).
thf(726,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[725:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(734,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ sk4 ) ),
inference(simp,[status(thm)],[726]) ).
thf(8781,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ C @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,3065]) ).
thf(8782,plain,
! [A: a] :
( ~ ( sk1 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk43 @ A @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(pattern_uni,[status(thm)],[8781:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(8823,plain,
! [A: a] :
( ~ ( sk1 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk43 @ A @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(simp,[status(thm)],[8782]) ).
thf(3006,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ C @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,476]) ).
thf(3007,plain,
! [A: a] :
( ~ ( sk2 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk43 @ A @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(pattern_uni,[status(thm)],[3006:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3036,plain,
! [A: a] :
( ~ ( sk2 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk43 @ A @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(simp,[status(thm)],[3007]) ).
thf(39,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk20 @ A @ B )
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(67,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk20 @ A @ B )
| ~ sk6
| sk5 ),
inference(simp,[status(thm)],[39]) ).
thf(16027,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ sk6
| sk5
| ( ( sk20 @ A @ B )
!= ( sk20 @ sk7 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[67,25]) ).
thf(16028,plain,
( ~ ( sk2 @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(pattern_uni,[status(thm)],[16027:[bind(A,$thf( sk7 )),bind(B,$thf( sk8 ))]]) ).
thf(1951,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,519]) ).
thf(1952,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk43 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[1951:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1975,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk43 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[1952]) ).
thf(6,plain,
! [A: a > a > $o] :
( ( sk1 @ ( sk10 @ A ) @ ( sk11 @ A ) )
| ~ ( A @ ( sk12 @ A ) @ ( sk14 @ A ) )
| ( A @ sk7 @ sk8 )
| sk9
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(41,plain,
! [A: a > a > $o] :
( sk6
| ( sk24 @ A )
| ( A @ ( sk27 @ A ) @ ( sk28 @ A ) )
| ( A @ sk21 @ sk22 )
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(60,plain,
! [A: a > a > $o] :
( sk6
| ( sk24 @ A )
| ( A @ ( sk27 @ A ) @ ( sk28 @ A ) )
| ( A @ sk21 @ sk22 )
| sk5 ),
inference(simp,[status(thm)],[41]) ).
thf(601,plain,
( ( sk1
@ ( sk10
@ ^ [A: a,B: a] : sk5 )
@ ( sk11
@ ^ [A: a,B: a] : sk5 ) )
| sk5
| sk5
| sk9
| ~ sk6
| sk5 ),
inference(prim_subst,[status(thm)],[30:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk5 ))]]) ).
thf(661,plain,
( ( sk1
@ ( sk10
@ ^ [A: a,B: a] : sk5 )
@ ( sk11
@ ^ [A: a,B: a] : sk5 ) )
| sk5
| sk9
| ~ sk6 ),
inference(simp,[status(thm)],[601]) ).
thf(3004,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ ( sk38 @ sk43 ) @ C )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ ( sk39 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[72,476]) ).
thf(3005,plain,
! [A: a] :
( ~ ( sk1 @ A @ ( sk39 @ sk43 ) )
| ~ ( sk43 @ ( sk38 @ sk43 ) @ A )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(pattern_uni,[status(thm)],[3004:[bind(A,$thf( A )),bind(B,$thf( sk39 @ sk43 )),bind(C,$thf( A ))]]) ).
thf(3969,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,3005]) ).
thf(3970,plain,
! [A: a] :
( ~ ( sk1 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk1 @ A @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(pattern_uni,[status(thm)],[3969:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3995,plain,
! [A: a] :
( ~ ( sk1 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk1 @ A @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(simp,[status(thm)],[3970]) ).
thf(24444,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk2 ) @ ( sk39 @ sk2 ) )
| ( ( sk37 @ sk2 )
!= ( sk37
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[13295,24425]) ).
thf(24502,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk2 ) @ ( sk39 @ sk2 ) )
| ( sk2
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[24444]) ).
thf(1957,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ sk3 @ C )
| ( sk4 != sk3 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[43,519]) ).
thf(1958,plain,
! [A: a] :
( ~ ( sk2 @ A @ sk3 )
| ~ ( sk43 @ sk3 @ A )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[1957:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(2287,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,1958]) ).
thf(2288,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[2287:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2307,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[2288]) ).
thf(80,plain,
! [A: a > a > $o] :
( ~ sk5
| ~ ( sk37 @ A )
| ( A @ sk3 @ sk4 )
| ( ( A @ ( sk38 @ A ) @ ( sk39 @ A ) )
!= ( ~ ( A @ sk3 @ sk4 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[68]) ).
thf(102,plain,
! [A: a > a > $o] :
( ( A @ sk3 @ sk4 )
| ~ sk5
| ~ ( sk37 @ A )
| ( ( A @ ( sk38 @ A ) @ ( sk39 @ A ) )
!= ( ~ ( A @ sk3 @ sk4 ) ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(15361,plain,
! [A: a] :
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk2 @ sk3 @ A )
| ( ( sk43 @ sk46 @ sk47 )
!= ( sk43 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[14039,503]) ).
thf(15446,plain,
! [A: a] :
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk2 @ sk3 @ A )
| ( sk46 != A )
| ( sk47 != sk4 ) ),
inference(simp,[status(thm)],[15361]) ).
thf(15542,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk2 @ sk3 @ sk46 )
| ( sk47 != sk4 ) ),
inference(simp,[status(thm)],[15446]) ).
thf(499,plain,
! [A: a] :
( ~ ( sk43 @ sk3 @ A )
| ( ( sk43 @ A @ sk4 )
!= ( sk43 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[494]) ).
thf(1607,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( ( sk43 @ C @ sk4 )
!= ( sk43 @ sk3 @ C ) )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,499]) ).
thf(1608,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( ( sk43 @ A @ sk4 )
!= ( sk43 @ sk3 @ A ) ) ),
inference(pattern_uni,[status(thm)],[1607:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1636,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( ( sk43 @ A @ sk4 )
!= ( sk43 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[1608]) ).
thf(18724,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ sk5
| ( sk43 @ sk54 @ sk55 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[43,18683]) ).
thf(18725,plain,
( ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5
| ( sk43 @ sk54 @ sk55 ) ),
inference(pattern_uni,[status(thm)],[18724:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( sk39 @ sk43 ))]]) ).
thf(486,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ C @ sk4 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,477]) ).
thf(487,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk43 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[486:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(502,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk43 @ A @ sk4 ) ),
inference(simp,[status(thm)],[487]) ).
thf(745,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ C )
| ~ ( sk1 @ sk3 @ D )
| ( ( sk43 @ A @ C )
!= ( sk43 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[53,502]) ).
thf(746,plain,
! [B: a,A: a] :
( ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ sk4 )
| ~ ( sk1 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[745:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( A ))]]) ).
thf(5644,plain,
( sk6
| ( sk24
@ ^ [A: a,B: a] : sk5 )
| sk5
| sk5
| sk5 ),
inference(prim_subst,[status(thm)],[52:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk5 ))]]) ).
thf(5794,plain,
( sk6
| ( sk24
@ ^ [A: a,B: a] : sk5 )
| sk5 ),
inference(simp,[status(thm)],[5644]) ).
thf(5043,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ D @ sk4 )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[72,746]) ).
thf(5044,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ B @ sk4 )
| ~ ( sk1 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[5043:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(26,plain,
! [A: a > a > $o] :
( ~ sk5
| ( sk37 @ A )
| ( A @ ( sk41 @ A ) @ ( sk42 @ A ) )
| ( A @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(70,plain,
! [A: a > a > $o] :
( ~ sk5
| ( sk37 @ A )
| ( A @ ( sk41 @ A ) @ ( sk42 @ A ) )
| ( A @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[26]) ).
thf(15076,plain,
! [A: a] :
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk1 @ A @ sk4 )
| ( ( sk43 @ sk44 @ sk45 )
!= ( sk43 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13988,489]) ).
thf(15228,plain,
! [A: a] :
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk1 @ A @ sk4 )
| ( sk44 != sk3 )
| ( sk45 != A ) ),
inference(simp,[status(thm)],[15076]) ).
thf(15298,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk1 @ sk45 @ sk4 )
| ( sk44 != sk3 ) ),
inference(simp,[status(thm)],[15228]) ).
thf(599,plain,
( ( sk1
@ ( sk10
@ ^ [A: a,B: a] : $false )
@ ( sk11
@ ^ [A: a,B: a] : $false ) )
| $false
| $false
| sk9
| ~ sk6
| sk5 ),
inference(prim_subst,[status(thm)],[30:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(659,plain,
( ( sk1
@ ( sk10
@ ^ [A: a,B: a] : $false )
@ ( sk11
@ ^ [A: a,B: a] : $false ) )
| sk9
| ~ sk6
| sk5 ),
inference(simp,[status(thm)],[599]) ).
thf(1197,plain,
( sk9
| ~ sk6
| sk5
| ( ( sk1
@ ( sk10
@ ^ [A: a,B: a] : $false )
@ ( sk11
@ ^ [A: a,B: a] : $false ) )
!= ( sk1 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[659,76]) ).
thf(1223,plain,
( sk9
| sk5
| ~ sk6
| ( ( sk10
@ ^ [A: a,B: a] : $false )
!= sk3 )
| ( ( sk11
@ ^ [A: a,B: a] : $false )
!= sk4 ) ),
inference(simp,[status(thm)],[1197]) ).
thf(866,plain,
! [A: a] :
( sk9
| ~ sk6
| sk5
| ~ ( sk1 @ sk3 @ A )
| ( ( sk1
@ ( sk10
@ ^ [B: a,C: a] : sk9 )
@ ( sk11
@ ^ [B: a,C: a] : sk9 ) )
!= ( sk1 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[648,704]) ).
thf(879,plain,
! [A: a] :
( sk9
| sk5
| ~ sk6
| ~ ( sk1 @ sk3 @ A )
| ( ( sk10
@ ^ [B: a,C: a] : sk9 )
!= A )
| ( ( sk11
@ ^ [B: a,C: a] : sk9 )
!= sk4 ) ),
inference(simp,[status(thm)],[866]) ).
thf(894,plain,
( sk9
| sk5
| ~ sk6
| ~ ( sk1 @ sk3
@ ( sk10
@ ^ [A: a,B: a] : sk9 ) )
| ( ( sk11
@ ^ [A: a,B: a] : sk9 )
!= sk4 ) ),
inference(simp,[status(thm)],[879]) ).
thf(92,plain,
( ~ sk5
| ~ ( sk20 @ ( sk38 @ sk20 ) @ ( sk39 @ sk20 ) )
| ~ ( sk37 @ sk20 )
| ( sk20 @ sk3 @ sk4 ) ),
inference(prim_subst,[status(thm)],[68:[bind(A,$thf( sk20 ))]]) ).
thf(97,plain,
( ~ sk5
| ~ ( sk36 @ ( sk38 @ sk36 ) @ ( sk39 @ sk36 ) )
| ~ ( sk37 @ sk36 )
| ( sk36 @ sk3 @ sk4 ) ),
inference(prim_subst,[status(thm)],[68:[bind(A,$thf( sk36 ))]]) ).
thf(15,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk2 @ A @ B )
| ( sk36 @ A @ B )
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(51,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk2 @ A @ B )
| ( sk36 @ A @ B )
| sk5 ),
inference(simp,[status(thm)],[15]) ).
thf(4994,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk2 @ A @ B )
| sk5
| ( ( sk36 @ A @ B )
!= ( sk36 @ sk21 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[51,18]) ).
thf(4995,plain,
( sk6
| ~ ( sk2 @ sk21 @ sk23 )
| sk5 ),
inference(pattern_uni,[status(thm)],[4994:[bind(A,$thf( sk21 )),bind(B,$thf( sk23 ))]]) ).
thf(5016,plain,
! [A: a > a > $o] :
( sk6
| ( sk30 @ A )
| ( A @ sk22 @ sk23 )
| sk5
| ( ( A @ ( sk34 @ A ) @ ( sk35 @ A ) )
!= ( sk2 @ sk21 @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[45,4995]) ).
thf(5021,plain,
( sk6
| ( sk30
@ ^ [A: a,B: a] : ( sk2 @ sk21 @ sk23 ) )
| ( sk2 @ sk21 @ sk23 )
| sk5 ),
inference(pre_uni,[status(thm)],[5016:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk2 @ sk21 @ sk23 ) ))]]) ).
thf(15353,plain,
! [A: a] :
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk43 @ sk3 @ A )
| ( ( sk43 @ sk46 @ sk47 )
!= ( sk43 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[14039,499]) ).
thf(15450,plain,
! [A: a] :
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk43 @ sk3 @ A )
| ( sk46 != A )
| ( sk47 != sk4 ) ),
inference(simp,[status(thm)],[15353]) ).
thf(15546,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk43 @ sk3 @ sk46 )
| ( sk47 != sk4 ) ),
inference(simp,[status(thm)],[15450]) ).
thf(1601,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( ( sk43 @ C @ sk4 )
!= ( sk43 @ sk3 @ C ) )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,499]) ).
thf(1602,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( ( sk43 @ A @ sk4 )
!= ( sk43 @ sk3 @ A ) ) ),
inference(pattern_uni,[status(thm)],[1601:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1634,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( ( sk43 @ A @ sk4 )
!= ( sk43 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[1602]) ).
thf(8787,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ ( sk38 @ sk43 ) @ C )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ ( sk38 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[43,3065]) ).
thf(8788,plain,
! [A: a] :
( ~ ( sk2 @ A @ ( sk38 @ sk43 ) )
| ~ ( sk43 @ ( sk38 @ sk43 ) @ A )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(pattern_uni,[status(thm)],[8787:[bind(A,$thf( A )),bind(B,$thf( sk38 @ sk43 )),bind(C,$thf( A ))]]) ).
thf(13574,plain,
( ~ sk5
| ~ ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( ( sk37 @ sk43 )
!= ( sk37
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[13295,278]) ).
thf(13638,plain,
( ~ sk5
| ~ ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk43
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[13574]) ).
thf(14265,plain,
( ( sk43 @ sk48 @ sk49 )
| ~ sk5
| ~ ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ),
inference(func_ext,[status(esa)],[13638]) ).
thf(15603,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk43 @ sk48 @ sk49 )
| ~ sk5
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[72,14265]) ).
thf(15604,plain,
( ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk43 @ sk48 @ sk49 )
| ~ sk5 ),
inference(pattern_uni,[status(thm)],[15603:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( sk39 @ sk43 ))]]) ).
thf(16290,plain,
( ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5
| ( ( sk43 @ sk48 @ sk49 )
!= ( sk43 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[15604,11]) ).
thf(16371,plain,
( ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5
| ( sk48 != sk3 )
| ( sk49 != sk4 ) ),
inference(simp,[status(thm)],[16290]) ).
thf(27,plain,
! [A: a > a > $o] :
( ~ sk9
| ( sk2 @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ~ ( A @ ( sk17 @ A ) @ ( sk19 @ A ) )
| ( A @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(65,plain,
! [A: a > a > $o] :
( ~ sk9
| ( sk2 @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ~ ( A @ ( sk17 @ A ) @ ( sk19 @ A ) )
| ( A @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(simp,[status(thm)],[27]) ).
thf(6816,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk43 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[43,4275]) ).
thf(6817,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk43 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[6816:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(6888,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk43 @ sk3 @ B ) ),
inference(simp,[status(thm)],[6817]) ).
thf(24519,plain,
( ( sk2 @ sk60 @ sk61 )
| ~ sk5
| ~ ( sk2 @ ( sk38 @ sk2 ) @ ( sk39 @ sk2 ) ) ),
inference(func_ext,[status(esa)],[24502]) ).
thf(15605,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk43 @ sk48 @ sk49 )
| ~ sk5
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[43,14265]) ).
thf(15606,plain,
( ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk43 @ sk48 @ sk49 )
| ~ sk5 ),
inference(pattern_uni,[status(thm)],[15605:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( sk39 @ sk43 ))]]) ).
thf(3008,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ ( sk38 @ sk43 ) @ C )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ ( sk39 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[43,476]) ).
thf(3009,plain,
! [A: a] :
( ~ ( sk2 @ A @ ( sk39 @ sk43 ) )
| ~ ( sk43 @ ( sk38 @ sk43 ) @ A )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(pattern_uni,[status(thm)],[3008:[bind(A,$thf( A )),bind(B,$thf( sk39 @ sk43 )),bind(C,$thf( A ))]]) ).
thf(4024,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,3009]) ).
thf(4025,plain,
! [A: a] :
( ~ ( sk2 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk2 @ A @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(pattern_uni,[status(thm)],[4024:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(4048,plain,
! [A: a] :
( ~ ( sk2 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk2 @ A @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(simp,[status(thm)],[4025]) ).
thf(15342,plain,
! [A: a] :
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk2 @ A @ sk4 )
| ( ( sk43 @ sk46 @ sk47 )
!= ( sk43 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14039,493]) ).
thf(15449,plain,
! [A: a] :
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk2 @ A @ sk4 )
| ( sk46 != sk3 )
| ( sk47 != A ) ),
inference(simp,[status(thm)],[15342]) ).
thf(15545,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk2 @ sk47 @ sk4 )
| ( sk46 != sk3 ) ),
inference(simp,[status(thm)],[15449]) ).
thf(5640,plain,
( sk6
| ( sk24
@ ^ [A: a,B: a] : sk9 )
| sk9
| sk9
| sk5 ),
inference(prim_subst,[status(thm)],[52:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk9 ))]]) ).
thf(5791,plain,
( sk6
| ( sk24
@ ^ [A: a,B: a] : sk9 )
| sk9
| sk5 ),
inference(simp,[status(thm)],[5640]) ).
thf(13714,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( ( sk37 @ sk43 )
!= ( sk37
@ ^ [A: a,B: a] : ~ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[13463,283]) ).
thf(13729,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk43
!= ( ^ [A: a,B: a] : ~ sk5 ) ) ),
inference(simp,[status(thm)],[13714]) ).
thf(14319,plain,
( ( ( sk43 @ sk50 @ sk51 )
!= ~ sk5 )
| ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ),
inference(func_ext,[status(esa)],[13729]) ).
thf(14819,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk43 @ sk50 @ sk51 )
| ~ sk5 ),
inference(bool_ext,[status(thm)],[14319]) ).
thf(14881,plain,
( ~ sk5
| ( sk43 @ sk50 @ sk51 )
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5 ),
inference(cnf,[status(esa)],[14819]) ).
thf(14882,plain,
( ~ sk5
| ( sk43 @ sk50 @ sk51 )
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ),
inference(simp,[status(thm)],[14881]) ).
thf(2002,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,1954]) ).
thf(2003,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[2002:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2038,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[2003]) ).
thf(1206,plain,
! [B: a,A: a] :
( sk9
| ~ sk6
| sk5
| ( sk43 @ A @ B )
| ( ( sk1
@ ( sk10
@ ^ [C: a,D: a] : $false )
@ ( sk11
@ ^ [C: a,D: a] : $false ) )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[659,72]) ).
thf(1207,plain,
( sk9
| ~ sk6
| sk5
| ( sk43
@ ( sk10
@ ^ [A: a,B: a] : $false )
@ ( sk11
@ ^ [A: a,B: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[1206:[bind(A,$thf( sk10 @ ^ [C: a] : ^ [D: a] : $false )),bind(B,$thf( sk11 @ ^ [C: a] : ^ [D: a] : $false ))]]) ).
thf(38,plain,
! [A: a > a > $o] :
( ~ sk5
| ( sk1 @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ( sk2 @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ~ ( sk37 @ A )
| ( A @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(58,plain,
! [A: a > a > $o] :
( ~ sk5
| ( sk1 @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ( sk2 @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ~ ( sk37 @ A )
| ( A @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[38]) ).
thf(13704,plain,
! [A: a > a > $o] :
( ~ sk5
| ( sk1 @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ( sk2 @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ( A @ sk3 @ sk4 )
| ( ( sk37
@ ^ [B: a,C: a] : ~ sk5 )
!= ( sk37 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13463,58]) ).
thf(13705,plain,
( ~ sk5
| ( sk1
@ ( sk38
@ ^ [A: a,B: a] : ~ sk5 )
@ ( sk39
@ ^ [A: a,B: a] : ~ sk5 ) )
| ( sk2
@ ( sk38
@ ^ [A: a,B: a] : ~ sk5 )
@ ( sk39
@ ^ [A: a,B: a] : ~ sk5 ) )
| ~ sk5 ),
inference(pattern_uni,[status(thm)],[13704:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ~ ( sk5 ) ))]]) ).
thf(13764,plain,
( ~ sk5
| ( sk2
@ ( sk38
@ ^ [A: a,B: a] : ~ sk5 )
@ ( sk39
@ ^ [A: a,B: a] : ~ sk5 ) )
| ( sk1
@ ( sk38
@ ^ [A: a,B: a] : ~ sk5 )
@ ( sk39
@ ^ [A: a,B: a] : ~ sk5 ) )
| ~ sk5 ),
inference(cnf,[status(esa)],[13705]) ).
thf(13765,plain,
( ~ sk5
| ( sk2
@ ( sk38
@ ^ [A: a,B: a] : ~ sk5 )
@ ( sk39
@ ^ [A: a,B: a] : ~ sk5 ) )
| ( sk1
@ ( sk38
@ ^ [A: a,B: a] : ~ sk5 )
@ ( sk39
@ ^ [A: a,B: a] : ~ sk5 ) ) ),
inference(simp,[status(thm)],[13764]) ).
thf(22657,plain,
! [B: a,A: a] :
( ~ sk5
| ( sk1
@ ( sk38
@ ^ [C: a,D: a] : ~ sk5 )
@ ( sk39
@ ^ [C: a,D: a] : ~ sk5 ) )
| ( sk43 @ A @ B )
| ( ( sk2
@ ( sk38
@ ^ [C: a,D: a] : ~ sk5 )
@ ( sk39
@ ^ [C: a,D: a] : ~ sk5 ) )
!= ( sk2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13765,43]) ).
thf(22658,plain,
( ~ sk5
| ( sk1
@ ( sk38
@ ^ [A: a,B: a] : ~ sk5 )
@ ( sk39
@ ^ [A: a,B: a] : ~ sk5 ) )
| ( sk43
@ ( sk38
@ ^ [A: a,B: a] : ~ sk5 )
@ ( sk39
@ ^ [A: a,B: a] : ~ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[22657:[bind(A,$thf( sk38 @ ^ [C: a] : ^ [D: a] : ~ ( sk5 ) )),bind(B,$thf( sk39 @ ^ [C: a] : ^ [D: a] : ~ ( sk5 ) ))]]) ).
thf(21,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk20 @ A @ B )
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(55,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk20 @ A @ B )
| ~ sk6
| sk5 ),
inference(simp,[status(thm)],[21]) ).
thf(6907,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ sk6
| sk5
| ( ( sk20 @ A @ B )
!= ( sk20 @ sk7 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[55,25]) ).
thf(6908,plain,
( ~ ( sk1 @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(pattern_uni,[status(thm)],[6907:[bind(A,$thf( sk7 )),bind(B,$thf( sk8 ))]]) ).
thf(23433,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk1 ) @ ( sk39 @ sk1 ) )
| ( ( sk37 @ sk1 )
!= ( sk37
@ ^ [A: a,B: a] : ~ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[13463,23406]) ).
thf(23476,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk1 ) @ ( sk39 @ sk1 ) )
| ( sk1
!= ( ^ [A: a,B: a] : ~ sk5 ) ) ),
inference(simp,[status(thm)],[23433]) ).
thf(15381,plain,
! [A: a] :
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk43 @ A @ sk4 )
| ( ( sk43 @ sk46 @ sk47 )
!= ( sk43 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14039,477]) ).
thf(15512,plain,
! [A: a] :
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk43 @ A @ sk4 )
| ( sk46 != sk3 )
| ( sk47 != A ) ),
inference(simp,[status(thm)],[15381]) ).
thf(15535,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk43 @ sk47 @ sk4 )
| ( sk46 != sk3 ) ),
inference(simp,[status(thm)],[15512]) ).
thf(18640,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( ( sk43 @ sk54 @ sk55 )
!= ~ sk5 )
| ~ sk5
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[72,14764]) ).
thf(18641,plain,
( ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( ( sk43 @ sk54 @ sk55 )
!= ~ sk5 )
| ~ sk5 ),
inference(pattern_uni,[status(thm)],[18640:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( sk39 @ sk43 ))]]) ).
thf(23422,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk1 ) @ ( sk39 @ sk1 ) )
| ( ( sk37 @ sk1 )
!= ( sk37
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[13295,23406]) ).
thf(23467,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk1 ) @ ( sk39 @ sk1 ) )
| ( sk1
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[23422]) ).
thf(5047,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ D @ sk4 )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[43,746]) ).
thf(5048,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ B @ sk4 )
| ~ ( sk1 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[5047:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(22,plain,
! [A: a > a > $o] :
( sk6
| ( sk30 @ A )
| ~ ( A @ ( sk33 @ A ) @ ( sk35 @ A ) )
| ( A @ sk22 @ sk23 )
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(64,plain,
! [A: a > a > $o] :
( sk6
| ( sk30 @ A )
| ~ ( A @ ( sk33 @ A ) @ ( sk35 @ A ) )
| ( A @ sk22 @ sk23 )
| sk5 ),
inference(simp,[status(thm)],[22]) ).
thf(723,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ sk4 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,493]) ).
thf(724,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[723:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(733,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ sk4 ) ),
inference(simp,[status(thm)],[724]) ).
thf(13677,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( ( sk37 @ sk43 )
!= ( sk37
@ ^ [A: a,B: a] : ~ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[13463,285]) ).
thf(13752,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk43
!= ( ^ [A: a,B: a] : ~ sk5 ) ) ),
inference(simp,[status(thm)],[13677]) ).
thf(14714,plain,
( ( ( sk43 @ sk52 @ sk53 )
!= ~ sk5 )
| ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ),
inference(func_ext,[status(esa)],[13752]) ).
thf(13,plain,
! [A: a > a > $o] :
( sk6
| ~ ( A @ ( sk25 @ A ) @ ( sk26 @ A ) )
| ~ ( sk24 @ A )
| ( A @ sk21 @ sk22 )
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(59,plain,
! [A: a > a > $o] :
( sk6
| ~ ( A @ ( sk25 @ A ) @ ( sk26 @ A ) )
| ~ ( sk24 @ A )
| ( A @ sk21 @ sk22 )
| sk5 ),
inference(simp,[status(thm)],[13]) ).
thf(21610,plain,
( ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5
| ( ( sk43 @ sk54 @ sk55 )
!= ( sk43 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18725,11]) ).
thf(21703,plain,
( ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5
| ( sk54 != sk3 )
| ( sk55 != sk4 ) ),
inference(simp,[status(thm)],[21610]) ).
thf(10,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ ( sk31 @ A ) @ ( sk32 @ A ) )
| ( sk2 @ ( sk31 @ A ) @ ( sk32 @ A ) )
| ~ ( sk30 @ A )
| ( A @ sk22 @ sk23 )
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(44,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ ( sk31 @ A ) @ ( sk32 @ A ) )
| ( sk2 @ ( sk31 @ A ) @ ( sk32 @ A ) )
| ~ ( sk30 @ A )
| ( A @ sk22 @ sk23 )
| sk5 ),
inference(simp,[status(thm)],[10]) ).
thf(8860,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,8784]) ).
thf(8861,plain,
! [A: a] :
( ~ ( sk1 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk1 @ A @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(pattern_uni,[status(thm)],[8860:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(8900,plain,
! [A: a] :
( ~ ( sk1 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk1 @ A @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(simp,[status(thm)],[8861]) ).
thf(29,plain,
! [A: a > a > $o] :
( sk6
| ( sk30 @ A )
| ( A @ ( sk33 @ A ) @ ( sk34 @ A ) )
| ( A @ sk22 @ sk23 )
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(54,plain,
! [A: a > a > $o] :
( sk6
| ( sk30 @ A )
| ( A @ ( sk33 @ A ) @ ( sk34 @ A ) )
| ( A @ sk22 @ sk23 )
| sk5 ),
inference(simp,[status(thm)],[29]) ).
thf(3050,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ ( sk38 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[43,3031]) ).
thf(3051,plain,
( ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(pattern_uni,[status(thm)],[3050:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( sk38 @ sk43 ))]]) ).
thf(2289,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,1958]) ).
thf(2290,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[2289:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2308,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[2290]) ).
thf(4623,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ C @ D )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,741]) ).
thf(4624,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk43 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4623:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(4672,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk43 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[4624]) ).
thf(8,plain,
! [A: a > a > $o] :
( ~ sk9
| ~ ( A @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ~ ( A @ ( sk17 @ A ) @ ( sk19 @ A ) )
| ( A @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(49,plain,
! [A: a > a > $o] :
( ~ sk9
| ~ ( A @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ~ ( A @ ( sk17 @ A ) @ ( sk19 @ A ) )
| ( A @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(simp,[status(thm)],[8]) ).
thf(18217,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk43 @ sk52 @ sk53 )
| ~ sk5 ),
inference(bool_ext,[status(thm)],[14714]) ).
thf(18294,plain,
( ~ sk5
| ( sk43 @ sk52 @ sk53 )
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5 ),
inference(cnf,[status(esa)],[18217]) ).
thf(18295,plain,
( ~ sk5
| ( sk43 @ sk52 @ sk53 )
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ),
inference(simp,[status(thm)],[18294]) ).
thf(18418,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( ( sk43 @ sk52 @ sk53 )
!= ( sk43 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18295,11]) ).
thf(18487,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk52 != sk3 )
| ( sk53 != sk4 ) ),
inference(simp,[status(thm)],[18418]) ).
thf(4525,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ sk3 @ C )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[43,712]) ).
thf(4526,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ sk3 @ A )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4525:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(23,plain,
! [A: a > a > $o] :
( ~ sk9
| ~ ( A @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ( A @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ( A @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(71,plain,
! [A: a > a > $o] :
( ~ sk9
| ~ ( A @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ( A @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ( A @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(simp,[status(thm)],[23]) ).
thf(15098,plain,
! [A: a] :
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk43 @ sk3 @ A )
| ( ( sk43 @ sk44 @ sk45 )
!= ( sk43 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[13988,477]) ).
thf(15167,plain,
! [A: a] :
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk43 @ sk3 @ A )
| ( sk44 != A )
| ( sk45 != sk4 ) ),
inference(simp,[status(thm)],[15098]) ).
thf(15244,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk43 @ sk3 @ sk44 )
| ( sk45 != sk4 ) ),
inference(simp,[status(thm)],[15167]) ).
thf(15749,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( ( sk43 @ sk50 @ sk51 )
!= ( sk43 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[14882,11]) ).
thf(15842,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk50 != sk3 )
| ( sk51 != sk4 ) ),
inference(simp,[status(thm)],[15749]) ).
thf(5155,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ C @ D )
| ~ ( sk2 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[43,775]) ).
thf(5156,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk43 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[5155:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(5212,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk43 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(simp,[status(thm)],[5156]) ).
thf(3971,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,3005]) ).
thf(3972,plain,
! [A: a] :
( ~ ( sk2 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk1 @ A @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(pattern_uni,[status(thm)],[3971:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3996,plain,
! [A: a] :
( ~ ( sk2 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk1 @ A @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(simp,[status(thm)],[3972]) ).
thf(15409,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( ( sk43 @ sk46 @ sk47 )
!= ( sk43 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[14039,11]) ).
thf(15455,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk46 != sk3 )
| ( sk47 != sk4 ) ),
inference(simp,[status(thm)],[15409]) ).
thf(8785,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ C @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,3065]) ).
thf(8786,plain,
! [A: a] :
( ~ ( sk2 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk43 @ A @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(pattern_uni,[status(thm)],[8785:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(8826,plain,
! [A: a] :
( ~ ( sk2 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk43 @ A @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(simp,[status(thm)],[8786]) ).
thf(15060,plain,
! [A: a] :
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk2 @ A @ sk4 )
| ( ( sk43 @ sk44 @ sk45 )
!= ( sk43 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13988,493]) ).
thf(15183,plain,
! [A: a] :
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk2 @ A @ sk4 )
| ( sk44 != sk3 )
| ( sk45 != A ) ),
inference(simp,[status(thm)],[15060]) ).
thf(15259,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk2 @ sk45 @ sk4 )
| ( sk44 != sk3 ) ),
inference(simp,[status(thm)],[15183]) ).
thf(7,plain,
! [C: a,B: a,A: a] :
( ~ ( sk20 @ A @ B )
| ~ ( sk20 @ B @ C )
| ( sk20 @ A @ C )
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(66,plain,
! [C: a,B: a,A: a] :
( ~ ( sk20 @ A @ B )
| ~ ( sk20 @ B @ C )
| ( sk20 @ A @ C )
| ~ sk6
| sk5 ),
inference(simp,[status(thm)],[7]) ).
thf(4625,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ sk3 @ C )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[72,741]) ).
thf(4626,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ sk3 @ A )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4625:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(581,plain,
! [A: a > a > $o] :
( ( sk1 @ ( sk10 @ A ) @ ( sk11 @ A ) )
| ( A @ sk7 @ sk8 )
| sk9
| ~ sk6
| sk5
| ( ( A @ ( sk13 @ A ) @ ( sk14 @ A ) )
!= ~ sk6 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[30]) ).
thf(636,plain,
( ( sk1
@ ( sk10
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk11
@ ^ [A: a,B: a] : ~ sk6 ) )
| ~ sk6
| sk9
| ~ sk6
| sk5 ),
inference(pre_uni,[status(thm)],[581:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ~ ( sk6 ) ))]]) ).
thf(679,plain,
( sk5
| ~ sk6
| sk9
| ~ sk6
| ( sk1
@ ( sk10
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk11
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(cnf,[status(esa)],[636]) ).
thf(680,plain,
( sk5
| ~ sk6
| sk9
| ( sk1
@ ( sk10
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk11
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[679]) ).
thf(515,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk4 != sk3 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[43,508]) ).
thf(516,plain,
( ~ ( sk2 @ sk3 @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[515:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(13583,plain,
! [A: a > a > $o] :
( ~ sk5
| ( sk1 @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ( sk2 @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ( A @ sk3 @ sk4 )
| ( ( sk37
@ ^ [B: a,C: a] : $false )
!= ( sk37 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13295,58]) ).
thf(13584,plain,
( ~ sk5
| ( sk1
@ ( sk38
@ ^ [A: a,B: a] : $false )
@ ( sk39
@ ^ [A: a,B: a] : $false ) )
| ( sk2
@ ( sk38
@ ^ [A: a,B: a] : $false )
@ ( sk39
@ ^ [A: a,B: a] : $false ) )
| $false ),
inference(pattern_uni,[status(thm)],[13583:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(13641,plain,
( ~ sk5
| ( sk1
@ ( sk38
@ ^ [A: a,B: a] : $false )
@ ( sk39
@ ^ [A: a,B: a] : $false ) )
| ( sk2
@ ( sk38
@ ^ [A: a,B: a] : $false )
@ ( sk39
@ ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[13584]) ).
thf(2000,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,1954]) ).
thf(2001,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[2000:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2037,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[2001]) ).
thf(15125,plain,
! [A: a] :
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk1 @ sk3 @ A )
| ( ( sk43 @ sk44 @ sk45 )
!= ( sk43 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[13988,502]) ).
thf(15176,plain,
! [A: a] :
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk1 @ sk3 @ A )
| ( sk44 != A )
| ( sk45 != sk4 ) ),
inference(simp,[status(thm)],[15125]) ).
thf(15252,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ ( sk1 @ sk3 @ sk44 )
| ( sk45 != sk4 ) ),
inference(simp,[status(thm)],[15176]) ).
thf(4276,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ C @ D )
| ~ ( sk43 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[43,483]) ).
thf(4277,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk43 @ B @ A )
| ~ ( sk43 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[4276:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(4355,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk43 @ B @ A )
| ~ ( sk43 @ sk3 @ B ) ),
inference(simp,[status(thm)],[4277]) ).
thf(35,plain,
! [A: a > a > $o] :
( ~ sk5
| ( sk37 @ A )
| ~ ( A @ ( sk40 @ A ) @ ( sk42 @ A ) )
| ( A @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(48,plain,
! [A: a > a > $o] :
( ~ sk5
| ( sk37 @ A )
| ~ ( A @ ( sk40 @ A ) @ ( sk42 @ A ) )
| ( A @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[35]) ).
thf(4627,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ C @ D )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,741]) ).
thf(4628,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk43 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4627:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(4673,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk43 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[4628]) ).
thf(4629,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ sk3 @ C )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[43,741]) ).
thf(4630,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ sk3 @ A )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4629:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4,plain,
! [C: a,B: a,A: a] :
( sk6
| ~ ( sk36 @ A @ B )
| ~ ( sk36 @ B @ C )
| ( sk36 @ A @ C )
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(50,plain,
! [C: a,B: a,A: a] :
( sk6
| ~ ( sk36 @ A @ B )
| ~ ( sk36 @ B @ C )
| ( sk36 @ A @ C )
| sk5 ),
inference(simp,[status(thm)],[4]) ).
thf(4521,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ sk3 @ C )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[72,712]) ).
thf(4522,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ sk3 @ A )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4521:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(148,plain,
( sk6
| ( sk30
@ ^ [A: a,B: a] : sk5 )
| sk5
| sk5
| sk5 ),
inference(prim_subst,[status(thm)],[45:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk5 ))]]) ).
thf(177,plain,
( sk6
| ( sk30
@ ^ [A: a,B: a] : sk5 )
| sk5 ),
inference(simp,[status(thm)],[148]) ).
thf(5153,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ D @ sk4 )
| ~ ( sk2 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[43,775]) ).
thf(5154,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ B @ sk4 )
| ~ ( sk2 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[5153:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(16838,plain,
! [B: a,A: a] :
( ~ sk5
| ( sk1
@ ( sk38
@ ^ [C: a,D: a] : $false )
@ ( sk39
@ ^ [C: a,D: a] : $false ) )
| ( sk43 @ A @ B )
| ( ( sk2
@ ( sk38
@ ^ [C: a,D: a] : $false )
@ ( sk39
@ ^ [C: a,D: a] : $false ) )
!= ( sk2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13641,43]) ).
thf(16839,plain,
( ~ sk5
| ( sk1
@ ( sk38
@ ^ [A: a,B: a] : $false )
@ ( sk39
@ ^ [A: a,B: a] : $false ) )
| ( sk43
@ ( sk38
@ ^ [A: a,B: a] : $false )
@ ( sk39
@ ^ [A: a,B: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[16838:[bind(A,$thf( sk38 @ ^ [C: a] : ^ [D: a] : $false )),bind(B,$thf( sk39 @ ^ [C: a] : ^ [D: a] : $false ))]]) ).
thf(4022,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,3009]) ).
thf(4023,plain,
! [A: a] :
( ~ ( sk1 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk2 @ A @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(pattern_uni,[status(thm)],[4022:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(4046,plain,
! [A: a] :
( ~ ( sk1 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk2 @ A @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(simp,[status(thm)],[4023]) ).
thf(875,plain,
! [B: a,A: a] :
( sk9
| ~ sk6
| sk5
| ( sk43 @ A @ B )
| ( ( sk1
@ ( sk10
@ ^ [C: a,D: a] : sk9 )
@ ( sk11
@ ^ [C: a,D: a] : sk9 ) )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[648,72]) ).
thf(876,plain,
( sk9
| ~ sk6
| sk5
| ( sk43
@ ( sk10
@ ^ [A: a,B: a] : sk9 )
@ ( sk11
@ ^ [A: a,B: a] : sk9 ) ) ),
inference(pattern_uni,[status(thm)],[875:[bind(A,$thf( sk10 @ ^ [C: a] : ^ [D: a] : sk9 )),bind(B,$thf( sk11 @ ^ [C: a] : ^ [D: a] : sk9 ))]]) ).
thf(24717,plain,
( ~ sk5
| ~ ( sk2 @ ( sk38 @ sk2 ) @ ( sk39 @ sk2 ) )
| ( sk2 @ sk62 @ sk63 )
| ~ sk5 ),
inference(bool_ext,[status(thm)],[24585]) ).
thf(24796,plain,
( ~ sk5
| ( sk2 @ sk62 @ sk63 )
| ~ ( sk2 @ ( sk38 @ sk2 ) @ ( sk39 @ sk2 ) )
| ~ sk5 ),
inference(cnf,[status(esa)],[24717]) ).
thf(24797,plain,
( ~ sk5
| ( sk2 @ sk62 @ sk63 )
| ~ ( sk2 @ ( sk38 @ sk2 ) @ ( sk39 @ sk2 ) ) ),
inference(simp,[status(thm)],[24796]) ).
thf(16574,plain,
( ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5
| ( ( sk43 @ sk48 @ sk49 )
!= ( sk43 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[15606,11]) ).
thf(16663,plain,
( ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ~ sk5
| ( sk48 != sk3 )
| ( sk49 != sk4 ) ),
inference(simp,[status(thm)],[16574]) ).
thf(23495,plain,
( ( sk1 @ sk56 @ sk57 )
| ~ sk5
| ~ ( sk1 @ ( sk38 @ sk1 ) @ ( sk39 @ sk1 ) ) ),
inference(func_ext,[status(esa)],[23467]) ).
thf(40,plain,
! [A: a > a > $o] :
( ~ ( A @ ( sk10 @ A ) @ ( sk11 @ A ) )
| ~ ( A @ ( sk12 @ A ) @ ( sk14 @ A ) )
| ( A @ sk7 @ sk8 )
| sk9
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(139,plain,
( sk6
| ( sk30
@ ^ [A: a,B: a] : $false )
| $false
| $false
| sk5 ),
inference(prim_subst,[status(thm)],[45:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(171,plain,
( sk6
| ( sk30
@ ^ [A: a,B: a] : $false )
| sk5 ),
inference(simp,[status(thm)],[139]) ).
thf(4519,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ C @ D )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,712]) ).
thf(4520,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk43 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4519:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(4602,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk43 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[4520]) ).
thf(1257,plain,
( sk5
| sk9
| ~ sk6
| ( ( sk1
@ ( sk10
@ ^ [A: a,B: a] : sk5 )
@ ( sk11
@ ^ [A: a,B: a] : sk5 ) )
!= ( sk1 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[661,76]) ).
thf(1294,plain,
( sk5
| sk9
| ~ sk6
| ( ( sk10
@ ^ [A: a,B: a] : sk5 )
!= sk3 )
| ( ( sk11
@ ^ [A: a,B: a] : sk5 )
!= sk4 ) ),
inference(simp,[status(thm)],[1257]) ).
thf(9509,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,8788]) ).
thf(9510,plain,
! [A: a] :
( ~ ( sk2 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk2 @ A @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(pattern_uni,[status(thm)],[9509:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(9537,plain,
! [A: a] :
( ~ ( sk2 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk2 @ A @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(simp,[status(thm)],[9510]) ).
thf(861,plain,
! [A: a] :
( sk9
| ~ sk6
| sk5
| ~ ( sk43 @ sk3 @ A )
| ( ( sk1
@ ( sk10
@ ^ [B: a,C: a] : sk9 )
@ ( sk11
@ ^ [B: a,C: a] : sk9 ) )
!= ( sk1 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[648,489]) ).
thf(886,plain,
! [A: a] :
( sk9
| sk5
| ~ sk6
| ~ ( sk43 @ sk3 @ A )
| ( ( sk10
@ ^ [B: a,C: a] : sk9 )
!= A )
| ( ( sk11
@ ^ [B: a,C: a] : sk9 )
!= sk4 ) ),
inference(simp,[status(thm)],[861]) ).
thf(899,plain,
( sk9
| sk5
| ~ sk6
| ~ ( sk43 @ sk3
@ ( sk10
@ ^ [A: a,B: a] : sk9 ) )
| ( ( sk11
@ ^ [A: a,B: a] : sk9 )
!= sk4 ) ),
inference(simp,[status(thm)],[886]) ).
thf(5045,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ C @ D )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[72,746]) ).
thf(5046,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk43 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[5045:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(5128,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk43 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(simp,[status(thm)],[5046]) ).
thf(18646,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( ( sk43 @ sk54 @ sk55 )
!= ~ sk5 )
| ~ sk5
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) ) ) ),
inference(paramod_ordered,[status(thm)],[43,14764]) ).
thf(18647,plain,
( ~ ( sk2 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( ( sk43 @ sk54 @ sk55 )
!= ~ sk5 )
| ~ sk5 ),
inference(pattern_uni,[status(thm)],[18646:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( sk39 @ sk43 ))]]) ).
thf(5151,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ C @ D )
| ~ ( sk2 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[72,775]) ).
thf(5152,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk43 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[5151:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(5211,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk43 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(simp,[status(thm)],[5152]) ).
thf(5049,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ C @ D )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[43,746]) ).
thf(5050,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk43 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[5049:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(5129,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk43 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(simp,[status(thm)],[5050]) ).
thf(36,plain,
! [A: a > a > $o] :
( ( sk1 @ ( sk10 @ A ) @ ( sk11 @ A ) )
| ( A @ ( sk12 @ A ) @ ( sk13 @ A ) )
| ( A @ sk7 @ sk8 )
| sk9
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(8862,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,8784]) ).
thf(8863,plain,
! [A: a] :
( ~ ( sk2 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk1 @ A @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(pattern_uni,[status(thm)],[8862:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(8901,plain,
! [A: a] :
( ~ ( sk2 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk1 @ A @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(simp,[status(thm)],[8863]) ).
thf(23557,plain,
( ( ( sk1 @ sk58 @ sk59 )
!= ~ sk5 )
| ~ sk5
| ~ ( sk1 @ ( sk38 @ sk1 ) @ ( sk39 @ sk1 ) ) ),
inference(func_ext,[status(esa)],[23476]) ).
thf(1167,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( ( sk2 @ A @ sk4 )
!= ( sk2 @ sk3 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[734]) ).
thf(1172,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( ( sk2 @ A @ sk4 )
!= ( sk2 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[1167]) ).
thf(5653,plain,
( sk6
| ( sk24
@ ^ [A: a,B: a] : $false )
| $false
| $false
| sk5 ),
inference(prim_subst,[status(thm)],[52:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(5803,plain,
( sk6
| ( sk24
@ ^ [A: a,B: a] : $false )
| sk5 ),
inference(simp,[status(thm)],[5653]) ).
thf(1267,plain,
! [B: a,A: a] :
( sk5
| sk9
| ~ sk6
| ( sk43 @ A @ B )
| ( ( sk1
@ ( sk10
@ ^ [C: a,D: a] : sk5 )
@ ( sk11
@ ^ [C: a,D: a] : sk5 ) )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[661,72]) ).
thf(1268,plain,
( sk5
| sk9
| ~ sk6
| ( sk43
@ ( sk10
@ ^ [A: a,B: a] : sk5 )
@ ( sk11
@ ^ [A: a,B: a] : sk5 ) ) ),
inference(pattern_uni,[status(thm)],[1267:[bind(A,$thf( sk10 @ ^ [C: a] : ^ [D: a] : sk5 )),bind(B,$thf( sk11 @ ^ [C: a] : ^ [D: a] : sk5 ))]]) ).
thf(1955,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk43 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[43,519]) ).
thf(1956,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk43 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[1955:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1976,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk43 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[1956]) ).
thf(12,plain,
! [A: a > a > $o] :
( ~ sk9
| ~ ( A @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ( A @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( A @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(47,plain,
! [A: a > a > $o] :
( ~ sk9
| ~ ( A @ ( sk15 @ A ) @ ( sk16 @ A ) )
| ( A @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( A @ sk7 @ sk8 )
| ~ sk6
| sk5 ),
inference(simp,[status(thm)],[12]) ).
thf(32,plain,
! [A: a > a > $o] :
( sk6
| ( sk24 @ A )
| ~ ( A @ ( sk27 @ A ) @ ( sk29 @ A ) )
| ( A @ sk21 @ sk22 )
| sk5 ),
inference(cnf,[status(esa)],[3]) ).
thf(62,plain,
! [A: a > a > $o] :
( sk6
| ( sk24 @ A )
| ~ ( A @ ( sk27 @ A ) @ ( sk29 @ A ) )
| ( A @ sk21 @ sk22 )
| sk5 ),
inference(simp,[status(thm)],[32]) ).
thf(150,plain,
( sk6
| ( sk30
@ ^ [A: a,B: a] : sk6 )
| sk6
| sk6
| sk5 ),
inference(prim_subst,[status(thm)],[45:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk6 ))]]) ).
thf(178,plain,
( sk6
| ( sk30
@ ^ [A: a,B: a] : sk6 )
| sk5 ),
inference(simp,[status(thm)],[150]) ).
thf(6692,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk43 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[43,4269]) ).
thf(6693,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk43 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[6692:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(6778,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk43 @ sk3 @ B ) ),
inference(simp,[status(thm)],[6693]) ).
thf(9507,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,8788]) ).
thf(9508,plain,
! [A: a] :
( ~ ( sk1 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk2 @ A @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(pattern_uni,[status(thm)],[9507:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(9536,plain,
! [A: a] :
( ~ ( sk1 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk2 @ A @ ( sk38 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk39 @ sk43 )
!= ( sk38 @ sk43 ) ) ),
inference(simp,[status(thm)],[9508]) ).
thf(15127,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( ( sk43 @ sk44 @ sk45 )
!= ( sk43 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[13988,11]) ).
thf(15219,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk43 ) @ ( sk39 @ sk43 ) )
| ( sk44 != sk3 )
| ( sk45 != sk4 ) ),
inference(simp,[status(thm)],[15127]) ).
thf(13031,plain,
( ~ sk5
| ( sk37
@ ^ [A: a,B: a] : sk6 )
| sk6
| sk6 ),
inference(prim_subst,[status(thm)],[63:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk6 ))]]) ).
thf(13306,plain,
( ~ sk5
| ( sk37
@ ^ [A: a,B: a] : sk6 )
| sk6 ),
inference(simp,[status(thm)],[13031]) ).
thf(23681,plain,
( ~ sk5
| ~ ( sk1 @ ( sk38 @ sk1 ) @ ( sk39 @ sk1 ) )
| ( sk1 @ sk58 @ sk59 )
| ~ sk5 ),
inference(bool_ext,[status(thm)],[23557]) ).
thf(23754,plain,
( ~ sk5
| ( sk1 @ sk58 @ sk59 )
| ~ ( sk1 @ ( sk38 @ sk1 ) @ ( sk39 @ sk1 ) )
| ~ sk5 ),
inference(cnf,[status(esa)],[23681]) ).
thf(23755,plain,
( ~ sk5
| ( sk1 @ sk58 @ sk59 )
| ~ ( sk1 @ ( sk38 @ sk1 ) @ ( sk39 @ sk1 ) ) ),
inference(simp,[status(thm)],[23754]) ).
thf(6812,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk43 @ sk3 @ C )
| ( ( sk43 @ A @ B )
!= ( sk43 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[72,4275]) ).
thf(6813,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk43 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[6812:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(6886,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk43 @ sk3 @ B ) ),
inference(simp,[status(thm)],[6813]) ).
thf(3002,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk43 @ C @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 )
| ( ( sk43 @ A @ B )
!= ( sk43 @ ( sk38 @ sk43 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[72,476]) ).
thf(3003,plain,
! [A: a] :
( ~ ( sk1 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk43 @ A @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(pattern_uni,[status(thm)],[3002:[bind(A,$thf( sk38 @ sk43 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3035,plain,
! [A: a] :
( ~ ( sk1 @ ( sk38 @ sk43 ) @ A )
| ~ ( sk43 @ A @ ( sk39 @ sk43 ) )
| ~ sk5
| ~ ( sk37 @ sk43 ) ),
inference(simp,[status(thm)],[3003]) ).
thf(26107,plain,
$false,
inference(e,[status(thm)],[809,8784,892,69,24585,276,741,23406,6776,4603,56,3049,13623,21358,15541,1954,898,11645,37,25,52,14039,5150,4275,15264,4353,20,46,57,5792,179,15261,13295,514,13305,61,734,8823,3036,16028,74,1975,6,60,661,3995,24502,2307,102,15542,1636,18725,746,18722,5794,5044,70,15298,1223,894,92,3065,97,5021,493,15546,1634,8788,16371,65,6888,285,24519,15606,4048,53,499,519,13463,15545,5791,476,489,14882,2038,1207,22658,6908,3005,503,23476,13607,508,15535,18641,4995,23467,5048,45,64,4269,733,13988,14714,59,21703,44,8900,54,3051,2308,4672,49,18487,4526,71,15244,13638,15842,704,5212,3996,76,15455,477,8826,24425,15259,483,66,278,3,4626,3009,3031,680,14265,648,516,1958,13641,2037,15252,4355,48,712,63,18,705,4673,4630,50,4522,67,14319,177,502,5154,16839,72,13729,18295,11,4046,43,876,24797,16663,13752,23495,40,55,171,4602,58,18683,1294,9537,899,5128,18647,5211,5129,30,51,13753,15604,36,8901,24485,23557,13765,1172,283,5803,1268,14764,1976,47,68,62,178,6778,9536,15219,659,775,13306,23755,6886,3035]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEV155^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 21 18:45:10 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.99/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.32/1.02 % [INFO] Parsing done (130ms).
% 1.32/1.03 % [INFO] Running in sequential loop mode.
% 1.73/1.26 % [INFO] eprover registered as external prover.
% 1.73/1.27 % [INFO] Scanning for conjecture ...
% 2.01/1.35 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.01/1.39 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.01/1.39 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.40 % [INFO] Type checking passed.
% 2.24/1.40 % [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 ...
% 82.18/18.63 % External prover 'e' found a proof!
% 82.18/18.63 % [INFO] Killing All external provers ...
% 82.18/18.63 % Time passed: 18092ms (effective reasoning time: 17602ms)
% 82.18/18.63 % 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)>
% 82.18/18.63 % Axioms used in derivation (0):
% 82.18/18.63 % No. of inferences in proof: 479
% 82.18/18.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18092 ms resp. 17602 ms w/o parsing
% 82.92/18.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 82.92/18.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------