TSTP Solution File: SEV156^5 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV156^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n028.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 15:58:22 EDT 2024
% Result : Theorem 95.19s 21.90s
% Output : Refutation 95.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 474 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 2392 ( 220 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 6616 (1292 ~;1282 |; 57 &;3907 @)
% ( 0 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 272 ( 272 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 65 usr; 49 con; 0-2 aty)
% Number of variables : 1213 ( 418 ^ 795 !; 0 ?;1213 :)
% 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: a > a > $o ).
thf(sk6_type,type,
sk6: $o ).
thf(sk7_type,type,
sk7: ( a > a > $o ) > $o ).
thf(sk8_type,type,
sk8: ( a > a > $o ) > a ).
thf(sk9_type,type,
sk9: ( a > a > $o ) > a ).
thf(sk13_type,type,
sk13: $o ).
thf(sk14_type,type,
sk14: a ).
thf(sk15_type,type,
sk15: a ).
thf(sk16_type,type,
sk16: $o ).
thf(sk17_type,type,
sk17: ( a > a > $o ) > a ).
thf(sk18_type,type,
sk18: ( a > a > $o ) > a ).
thf(sk22_type,type,
sk22: ( a > a > $o ) > a ).
thf(sk23_type,type,
sk23: ( a > a > $o ) > a ).
thf(sk27_type,type,
sk27: a > a > $o ).
thf(sk28_type,type,
sk28: a ).
thf(sk30_type,type,
sk30: a ).
thf(sk31_type,type,
sk31: ( a > a > $o ) > $o ).
thf(sk32_type,type,
sk32: ( a > a > $o ) > a ).
thf(sk33_type,type,
sk33: ( a > a > $o ) > a ).
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(sk64_type,type,
sk64: a ).
thf(sk67_type,type,
sk67: a ).
thf(1,conjecture,
! [A: a > a > $o,B: a > a > $o,C: a,D: a] :
( ! [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 ) )
& ! [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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM250H_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > a > $o,B: a > a > $o,C: a,D: a] :
( ! [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 ) )
& ! [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 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > a > $o,B: a > a > $o,C: a,D: a] :
( ! [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 ) )
& ! [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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
! [A: a > a > $o] :
( sk6
| ~ sk16
| ~ ( A @ ( sk22 @ A ) @ ( sk23 @ A ) )
| ( A @ ( sk24 @ A ) @ ( sk25 @ A ) )
| ( A @ sk14 @ sk15 )
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(69,plain,
! [A: a > a > $o] :
( sk6
| ~ sk16
| ~ ( A @ ( sk22 @ A ) @ ( sk23 @ A ) )
| ( A @ ( sk24 @ A ) @ ( sk25 @ A ) )
| ( A @ sk14 @ sk15 )
| ~ sk13 ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk5 @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(23,plain,
! [C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ( sk5 @ A @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(73,plain,
! [C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ( sk5 @ A @ C ) ),
inference(simp,[status(thm)],[23]) ).
thf(27,plain,
~ ( sk5 @ sk3 @ sk4 ),
inference(cnf,[status(esa)],[3]) ).
thf(245,plain,
! [C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ( ( sk5 @ A @ C )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[73,27]) ).
thf(246,plain,
! [A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(266,plain,
! [A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ sk4 ) ),
inference(simp,[status(thm)],[246]) ).
thf(271,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ C @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,266]) ).
thf(272,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(288,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ sk4 ) ),
inference(simp,[status(thm)],[272]) ).
thf(424,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ~ ( sk1 @ sk3 @ D )
| ( ( sk5 @ A @ C )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[73,288]) ).
thf(425,plain,
! [B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk1 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[424:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( A ))]]) ).
thf(2126,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ D @ sk4 )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[18,425]) ).
thf(2127,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk1 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[2126:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(3966,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18,2127]) ).
thf(3967,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[3966:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(4005,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(simp,[status(thm)],[3967]) ).
thf(6,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk5 @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(283,plain,
! [A: a] :
( ~ ( sk5 @ sk3 @ A )
| ( ( sk5 @ A @ sk4 )
!= ( sk5 @ sk3 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[266]) ).
thf(286,plain,
! [A: a] :
( ~ ( sk5 @ sk3 @ A )
| ( A != sk3 )
| ( sk4 != A ) ),
inference(simp,[status(thm)],[283]) ).
thf(292,plain,
( ~ ( sk5 @ sk3 @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[286]) ).
thf(299,plain,
! [C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ C )
!= ( sk5 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[73,292]) ).
thf(300,plain,
! [A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[299:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(302,plain,
! [A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[300]) ).
thf(514,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[18,302]) ).
thf(515,plain,
! [A: a] :
( ~ ( sk1 @ A @ sk3 )
| ~ ( sk5 @ sk3 @ A )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[514:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(752,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,515]) ).
thf(753,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[752:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(762,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[753]) ).
thf(36,plain,
! [A: a > a > $o] :
( ~ ( A @ ( sk8 @ A ) @ ( sk9 @ A ) )
| ~ ( sk7 @ A )
| ( A @ sk3 @ sk4 )
| ~ sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(74,plain,
! [A: a > a > $o] :
( ~ ( A @ ( sk8 @ A ) @ ( sk9 @ A ) )
| ~ ( sk7 @ A )
| ( A @ sk3 @ sk4 )
| ~ sk6 ),
inference(simp,[status(thm)],[36]) ).
thf(101,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk1
@ ( A
@ ( sk8
@ ^ [C: a,D: a] : ( sk1 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk1 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk8
@ ^ [C: a,D: a] : ( sk1 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk1 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk7
@ ^ [C: a,D: a] : ( sk1 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk1 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[74:[bind(A,$thf( ^ [D: a] : ^ [E: a] : ( sk1 @ ( B @ D @ E ) @ ( C @ D @ E ) ) ))]]) ).
thf(115,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk1
@ ( A
@ ( sk8
@ ^ [C: a,D: a] : ( sk1 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk1 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk8
@ ^ [C: a,D: a] : ( sk1 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk1 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk7
@ ^ [C: a,D: a] : ( sk1 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk1 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[101]) ).
thf(2110,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ D @ sk4 )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6,425]) ).
thf(2111,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk1 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[2110:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(3830,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18,2111]) ).
thf(3831,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[3830:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(3858,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(simp,[status(thm)],[3831]) ).
thf(273,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18,266]) ).
thf(274,plain,
! [A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk5 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[273:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(391,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk5 @ A @ C )
!= ( sk5 @ sk3 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[73,274]) ).
thf(392,plain,
! [B: a,A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(399,plain,
! [B: a,A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[392]) ).
thf(2013,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6,399]) ).
thf(2014,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ sk3 @ A )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2013:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(41,plain,
! [A: a > a > $o] :
( ( sk7 @ A )
| ( A @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( A @ sk3 @ sk4 )
| ~ sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(62,plain,
! [A: a > a > $o] :
( ( sk7 @ A )
| ( A @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( A @ sk3 @ sk4 )
| ~ sk6 ),
inference(simp,[status(thm)],[41]) ).
thf(6217,plain,
( ( sk7
@ ^ [A: a,B: a] : $false )
| $false
| $false
| ~ sk6 ),
inference(prim_subst,[status(thm)],[62:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(6403,plain,
( ( sk7
@ ^ [A: a,B: a] : $false )
| ~ sk6 ),
inference(simp,[status(thm)],[6217]) ).
thf(104,plain,
( ~ ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ ( sk7 @ sk5 )
| ( sk5 @ sk3 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[74:[bind(A,$thf( sk5 ))]]) ).
thf(17776,plain,
( ~ ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ ( sk7 @ sk5 )
| $false
| ~ sk6 ),
inference(rewrite,[status(thm)],[104,27]) ).
thf(17777,plain,
( ~ ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ ( sk7 @ sk5 )
| ~ sk6 ),
inference(simp,[status(thm)],[17776]) ).
thf(17788,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk7 @ sk5 )
| ~ sk6
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,17777]) ).
thf(17789,plain,
( ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ ( sk7 @ sk5 )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[17788:[bind(A,$thf( sk8 @ sk5 )),bind(B,$thf( sk9 @ sk5 ))]]) ).
thf(17903,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( ( sk7 @ sk5 )
!= ( sk7
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[6403,17789]) ).
thf(17928,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk5
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[17903]) ).
thf(18113,plain,
( ( sk5 @ sk54 @ sk55 )
| ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[17928]) ).
thf(18944,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( ( sk5 @ sk54 @ sk55 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18113,27]) ).
thf(19037,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk54 != sk3 )
| ( sk55 != sk4 ) ),
inference(simp,[status(thm)],[18944]) ).
thf(281,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ~ ( sk5 @ sk3 @ D )
| ( ( sk5 @ A @ C )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[73,266]) ).
thf(282,plain,
! [B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk5 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[281:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( A ))]]) ).
thf(1590,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ D @ sk4 )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[18,282]) ).
thf(1591,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk5 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[1590:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(17812,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( ( sk7 @ sk5 )
!= ( sk7
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[6403,17777]) ).
thf(17851,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk5
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[17812]) ).
thf(18047,plain,
( ( sk5 @ sk52 @ sk53 )
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[17851]) ).
thf(18829,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk5 @ sk52 @ sk53 )
| ~ sk6
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,18047]) ).
thf(18830,plain,
( ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk5 @ sk52 @ sk53 )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[18829:[bind(A,$thf( sk8 @ sk5 )),bind(B,$thf( sk9 @ sk5 ))]]) ).
thf(20070,plain,
( ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ sk6
| ( ( sk5 @ sk52 @ sk53 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18830,27]) ).
thf(20145,plain,
( ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ sk6
| ( sk52 != sk3 )
| ( sk53 != sk4 ) ),
inference(simp,[status(thm)],[20070]) ).
thf(29,plain,
! [A: a > a > $o] :
( sk6
| ~ sk16
| ~ ( A @ ( sk22 @ A ) @ ( sk23 @ A ) )
| ~ ( A @ ( sk24 @ A ) @ ( sk26 @ A ) )
| ( A @ sk14 @ sk15 )
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(56,plain,
! [A: a > a > $o] :
( sk6
| ~ sk16
| ~ ( A @ ( sk22 @ A ) @ ( sk23 @ A ) )
| ~ ( A @ ( sk24 @ A ) @ ( sk26 @ A ) )
| ( A @ sk14 @ sk15 )
| ~ sk13 ),
inference(simp,[status(thm)],[29]) ).
thf(82,plain,
! [C: a > a > $o,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk7 @ C )
| ( C @ sk3 @ sk4 )
| ~ sk6
| ( ( sk5 @ A @ B )
!= ( C @ ( sk8 @ C ) @ ( sk9 @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,74]) ).
thf(108,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk1
@ ( A
@ ( sk8
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk8
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk7
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk5 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) )
| ~ sk6 ),
inference(pre_uni,[status(thm)],[82:[bind(A,$thf( D @ ( sk8 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) @ ( sk9 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) )),bind(B,$thf( E @ ( sk8 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) @ ( sk9 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) )),bind(C,$thf( ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ))]]) ).
thf(116,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk1
@ ( A
@ ( sk8
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk8
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk7
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk5 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[108]) ).
thf(24107,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk1
@ ( A
@ ( sk8
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk8
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk7
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ~ sk6
| ( ( sk5 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[116,27]) ).
thf(24218,plain,
( ~ ( sk1
@ ( sk8
@ ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
@ sk4 )
| ~ ( sk7
@ ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
| ~ sk6 ),
inference(pre_uni,[status(thm)],[24107:[bind(A,$thf( ^ [C: a] : ^ [D: a] : C )),bind(B,$thf( ^ [C: a] : ^ [D: a] : sk4 ))]]) ).
thf(24464,plain,
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
@ sk4 )
| ( ( sk7
@ ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
!= ( sk7
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[6403,24218]) ).
thf(24501,plain,
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
@ sk4 )
| ( ( ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[24464]) ).
thf(24619,plain,
( ( sk5 @ sk64 @ sk4 )
| ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
@ sk4 ) ),
inference(func_ext,[status(esa)],[24501]) ).
thf(285,plain,
! [A: a] :
( ~ ( sk5 @ sk3 @ A )
| ( ( sk5 @ A @ sk4 )
!= ( sk5 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[283]) ).
thf(25547,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [B: a,C: a] : ( sk5 @ B @ sk4 ) )
@ sk4 )
| ~ ( sk5 @ sk3 @ A )
| ( ( sk5 @ sk64 @ sk4 )
!= ( sk5 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[24619,285]) ).
thf(25548,plain,
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
@ sk4 )
| ~ ( sk5 @ sk3 @ sk64 ) ),
inference(pattern_uni,[status(thm)],[25547:[bind(A,$thf( sk64 ))]]) ).
thf(6206,plain,
! [A: a > a > $o] :
( ( sk7 @ A )
| ( A @ sk3 @ sk4 )
| ~ sk6
| ( ( A @ ( sk11 @ A ) @ ( sk12 @ A ) )
!= ~ sk6 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[62]) ).
thf(6356,plain,
( ( sk7
@ ^ [A: a,B: a] : ~ sk6 )
| ~ sk6
| ~ sk6 ),
inference(pre_uni,[status(thm)],[6206:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ~ ( sk6 ) ))]]) ).
thf(6531,plain,
( ~ sk6
| ~ sk6
| ( sk7
@ ^ [A: a,B: a] : ~ sk6 ) ),
inference(cnf,[status(esa)],[6356]) ).
thf(6532,plain,
( ~ sk6
| ( sk7
@ ^ [A: a,B: a] : ~ sk6 ) ),
inference(simp,[status(thm)],[6531]) ).
thf(90,plain,
( ~ ( sk1 @ ( sk8 @ sk1 ) @ ( sk9 @ sk1 ) )
| ~ ( sk7 @ sk1 )
| ( sk1 @ sk3 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[74:[bind(A,$thf( sk1 ))]]) ).
thf(79,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18,27]) ).
thf(80,plain,
~ ( sk1 @ sk3 @ sk4 ),
inference(pattern_uni,[status(thm)],[79:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(213,plain,
( ~ ( sk1 @ ( sk8 @ sk1 ) @ ( sk9 @ sk1 ) )
| ~ ( sk7 @ sk1 )
| $false
| ~ sk6 ),
inference(rewrite,[status(thm)],[90,80]) ).
thf(214,plain,
( ~ ( sk1 @ ( sk8 @ sk1 ) @ ( sk9 @ sk1 ) )
| ~ ( sk7 @ sk1 )
| ~ sk6 ),
inference(simp,[status(thm)],[213]) ).
thf(6637,plain,
( ~ sk6
| ~ ( sk1 @ ( sk8 @ sk1 ) @ ( sk9 @ sk1 ) )
| ( ( sk7 @ sk1 )
!= ( sk7
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[6532,214]) ).
thf(6655,plain,
( ~ sk6
| ~ ( sk1 @ ( sk8 @ sk1 ) @ ( sk9 @ sk1 ) )
| ( sk1
!= ( ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[6637]) ).
thf(81,plain,
! [C: a > a > $o,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk7 @ C )
| ( C @ sk3 @ sk4 )
| ~ sk6
| ( ( sk5 @ A @ B )
!= ( C @ ( sk8 @ C ) @ ( sk9 @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,74]) ).
thf(109,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk2
@ ( A
@ ( sk8
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk8
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk7
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk5 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) )
| ~ sk6 ),
inference(pre_uni,[status(thm)],[81:[bind(A,$thf( D @ ( sk8 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) @ ( sk9 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) )),bind(B,$thf( E @ ( sk8 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) @ ( sk9 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) )),bind(C,$thf( ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ))]]) ).
thf(117,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk2
@ ( A
@ ( sk8
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk8
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk7
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk5 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[109]) ).
thf(25156,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk2
@ ( A
@ ( sk8
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk8
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk7
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ~ sk6
| ( ( sk5 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[117,27]) ).
thf(25279,plain,
( ~ ( sk2
@ ( sk8
@ ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
@ sk4 )
| ~ ( sk7
@ ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
| ~ sk6 ),
inference(pre_uni,[status(thm)],[25156:[bind(A,$thf( ^ [C: a] : ^ [D: a] : C )),bind(B,$thf( ^ [C: a] : ^ [D: a] : sk4 ))]]) ).
thf(25579,plain,
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
@ sk4 )
| ( ( sk5 @ sk64 @ sk4 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[24619,27]) ).
thf(25668,plain,
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
@ sk4 )
| ( sk64 != sk3 )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[25579]) ).
thf(25727,plain,
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
@ sk4 )
| ( sk64 != sk3 ) ),
inference(simp,[status(thm)],[25668]) ).
thf(504,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[6,302]) ).
thf(505,plain,
! [A: a] :
( ~ ( sk2 @ A @ sk3 )
| ~ ( sk5 @ sk3 @ A )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[504:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(532,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,505]) ).
thf(533,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[532:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(538,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[533]) ).
thf(14,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk31 @ A )
| ( A @ ( sk35 @ A ) @ ( sk36 @ A ) )
| ( A @ sk28 @ sk29 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(45,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk31 @ A )
| ( A @ ( sk35 @ A ) @ ( sk36 @ A ) )
| ( A @ sk28 @ sk29 ) ),
inference(simp,[status(thm)],[14]) ).
thf(157,plain,
( sk6
| sk13
| ( sk31
@ ^ [A: a,B: a] : $false )
| $false
| $false ),
inference(prim_subst,[status(thm)],[45:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(185,plain,
( sk6
| sk13
| ( sk31
@ ^ [A: a,B: a] : $false ) ),
inference(simp,[status(thm)],[157]) ).
thf(17904,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( ( sk7 @ sk5 )
!= ( sk7
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[6532,17789]) ).
thf(17940,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk5
!= ( ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[17904]) ).
thf(18390,plain,
( ( ( sk5 @ sk60 @ sk61 )
!= ~ sk6 )
| ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[17940]) ).
thf(22619,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk5 @ sk60 @ sk61 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[18390]) ).
thf(22719,plain,
( ~ sk6
| ( sk5 @ sk60 @ sk61 )
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[22619]) ).
thf(22720,plain,
( ~ sk6
| ( sk5 @ sk60 @ sk61 )
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ),
inference(simp,[status(thm)],[22719]) ).
thf(22798,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( ( sk5 @ sk60 @ sk61 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[22720,27]) ).
thf(22925,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk60 != sk3 )
| ( sk61 != sk4 ) ),
inference(simp,[status(thm)],[22798]) ).
thf(17813,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( ( sk7 @ sk5 )
!= ( sk7
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[6532,17777]) ).
thf(17840,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk5
!= ( ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[17813]) ).
thf(18324,plain,
( ( ( sk5 @ sk58 @ sk59 )
!= ~ sk6 )
| ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[17840]) ).
thf(20487,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( ( sk5 @ sk58 @ sk59 )
!= ~ sk6 )
| ~ sk6
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,18324]) ).
thf(20488,plain,
( ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( ( sk5 @ sk58 @ sk59 )
!= ~ sk6 )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[20487:[bind(A,$thf( sk8 @ sk5 )),bind(B,$thf( sk9 @ sk5 ))]]) ).
thf(24,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( A @ ( sk20 @ A ) @ ( sk21 @ A ) )
| ( A @ sk14 @ sk15 )
| sk16
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(53,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( A @ ( sk20 @ A ) @ ( sk21 @ A ) )
| ( A @ sk14 @ sk15 )
| sk16
| ~ sk13 ),
inference(simp,[status(thm)],[24]) ).
thf(1766,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( A @ sk14 @ sk15 )
| sk16
| ~ sk13
| ( ( A @ ( sk20 @ A ) @ ( sk21 @ A ) )
!= sk16 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[53]) ).
thf(1874,plain,
( sk6
| ( sk1
@ ( sk17
@ ^ [A: a,B: a] : sk16 )
@ ( sk18
@ ^ [A: a,B: a] : sk16 ) )
| sk16
| sk16
| ~ sk13 ),
inference(pre_uni,[status(thm)],[1766:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk16 ))]]) ).
thf(1967,plain,
( sk6
| ( sk1
@ ( sk17
@ ^ [A: a,B: a] : sk16 )
@ ( sk18
@ ^ [A: a,B: a] : sk16 ) )
| sk16
| ~ sk13 ),
inference(simp,[status(thm)],[1874]) ).
thf(37,plain,
( sk6
| ~ ( sk27 @ sk14 @ sk15 )
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk37 @ A )
| ( A @ ( sk41 @ A ) @ ( sk42 @ A ) )
| ( A @ sk29 @ sk30 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(51,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk37 @ A )
| ( A @ ( sk41 @ A ) @ ( sk42 @ A ) )
| ( A @ sk29 @ sk30 ) ),
inference(simp,[status(thm)],[15]) ).
thf(1288,plain,
( sk6
| sk13
| ( sk37
@ ^ [A: a,B: a] : sk13 )
| sk13
| sk13 ),
inference(prim_subst,[status(thm)],[51:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk13 ))]]) ).
thf(1391,plain,
( sk6
| sk13
| ( sk37
@ ^ [A: a,B: a] : sk13 ) ),
inference(simp,[status(thm)],[1288]) ).
thf(1575,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ D @ sk4 )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6,282]) ).
thf(1576,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk5 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[1575:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1577,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ C @ D )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6,282]) ).
thf(1578,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[1577:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(1613,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(simp,[status(thm)],[1578]) ).
thf(42,plain,
! [C: a,B: a,A: a] :
( sk6
| ~ ( sk27 @ A @ B )
| ~ ( sk27 @ B @ C )
| ( sk27 @ A @ C )
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(52,plain,
! [C: a,B: a,A: a] :
( sk6
| ~ ( sk27 @ A @ B )
| ~ ( sk27 @ B @ C )
| ( sk27 @ A @ C )
| ~ sk13 ),
inference(simp,[status(thm)],[42]) ).
thf(156,plain,
( sk6
| sk13
| ( sk31
@ ^ [A: a,B: a] : sk6 )
| sk6
| sk6 ),
inference(prim_subst,[status(thm)],[45:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk6 ))]]) ).
thf(184,plain,
( sk6
| sk13
| ( sk31
@ ^ [A: a,B: a] : sk6 ) ),
inference(simp,[status(thm)],[156]) ).
thf(83,plain,
! [A: a > a > $o] :
( ~ ( sk7 @ A )
| ( A @ sk3 @ sk4 )
| ~ sk6
| ( ( A @ ( sk8 @ A ) @ ( sk9 @ A ) )
!= ( ~ ( A @ sk3 @ sk4 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[74]) ).
thf(110,plain,
! [A: a > a > $o] :
( ( A @ sk3 @ sk4 )
| ~ ( sk7 @ A )
| ~ sk6
| ( ( A @ ( sk8 @ A ) @ ( sk9 @ A ) )
!= ( ~ ( A @ sk3 @ sk4 ) ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(6587,plain,
( ~ sk6
| ~ ( sk1 @ ( sk8 @ sk1 ) @ ( sk9 @ sk1 ) )
| ( ( sk7 @ sk1 )
!= ( sk7
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[6403,214]) ).
thf(6593,plain,
( ~ sk6
| ~ ( sk1 @ ( sk8 @ sk1 ) @ ( sk9 @ sk1 ) )
| ( sk1
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[6587]) ).
thf(6749,plain,
( ( sk1 @ sk44 @ sk45 )
| ~ sk6
| ~ ( sk1 @ ( sk8 @ sk1 ) @ ( sk9 @ sk1 ) ) ),
inference(func_ext,[status(esa)],[6593]) ).
thf(525,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,505]) ).
thf(526,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[525:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(542,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[526]) ).
thf(2642,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6,1576]) ).
thf(2643,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2642:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2691,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2643]) ).
thf(161,plain,
( sk6
| sk13
| ( sk31
@ ^ [A: a,B: a] : sk13 )
| sk13
| sk13 ),
inference(prim_subst,[status(thm)],[45:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk13 ))]]) ).
thf(189,plain,
( sk6
| sk13
| ( sk31
@ ^ [A: a,B: a] : sk13 ) ),
inference(simp,[status(thm)],[161]) ).
thf(9,plain,
! [B: a,A: a] :
( sk6
| sk13
| ~ ( sk2 @ A @ B )
| ( sk43 @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(46,plain,
! [B: a,A: a] :
( sk6
| sk13
| ~ ( sk2 @ A @ B )
| ( sk43 @ A @ B ) ),
inference(simp,[status(thm)],[9]) ).
thf(93,plain,
( ~ ( sk27 @ ( sk8 @ sk27 ) @ ( sk9 @ sk27 ) )
| ~ ( sk7 @ sk27 )
| ( sk27 @ sk3 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[74:[bind(A,$thf( sk27 ))]]) ).
thf(277,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6,266]) ).
thf(278,plain,
! [A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk5 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[277:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(406,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ C )
!= ( sk5 @ sk3 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[73,278]) ).
thf(407,plain,
! [B: a,A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[406:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(416,plain,
! [B: a,A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[407]) ).
thf(275,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ C @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,266]) ).
thf(276,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(289,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ sk4 ) ),
inference(simp,[status(thm)],[276]) ).
thf(436,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ~ ( sk2 @ sk3 @ D )
| ( ( sk5 @ A @ C )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[73,289]) ).
thf(437,plain,
! [B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk2 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[436:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( A ))]]) ).
thf(2587,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ C @ D )
| ~ ( sk2 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6,437]) ).
thf(2588,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2587:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2635,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2588]) ).
thf(2029,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[18,399]) ).
thf(2030,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ sk3 @ A )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2029:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(3267,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,2030]) ).
thf(3268,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[3267:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3312,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[3268]) ).
thf(21,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk31 @ A )
| ~ ( A @ ( sk34 @ A ) @ ( sk36 @ A ) )
| ( A @ sk28 @ sk29 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(57,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk31 @ A )
| ~ ( A @ ( sk34 @ A ) @ ( sk36 @ A ) )
| ( A @ sk28 @ sk29 ) ),
inference(simp,[status(thm)],[21]) ).
thf(77,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6,27]) ).
thf(78,plain,
~ ( sk2 @ sk3 @ sk4 ),
inference(pattern_uni,[status(thm)],[77:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(2077,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ C @ D )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,416]) ).
thf(2078,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2077:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2105,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[2078]) ).
thf(2603,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ D @ sk4 )
| ~ ( sk2 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[18,437]) ).
thf(2604,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk2 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[2603:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4272,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk2 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18,2604]) ).
thf(4273,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[4272:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(4297,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(simp,[status(thm)],[4273]) ).
thf(6226,plain,
( ( sk7
@ ^ [A: a,B: a] : sk13 )
| sk13
| sk13
| ~ sk6 ),
inference(prim_subst,[status(thm)],[62:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk13 ))]]) ).
thf(6410,plain,
( ( sk7
@ ^ [A: a,B: a] : sk13 )
| sk13
| ~ sk6 ),
inference(simp,[status(thm)],[6226]) ).
thf(5,plain,
! [B: a,A: a] :
( sk6
| sk13
| ~ ( sk1 @ A @ B )
| ( sk43 @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(43,plain,
! [B: a,A: a] :
( sk6
| sk13
| ~ ( sk1 @ A @ B )
| ( sk43 @ A @ B ) ),
inference(simp,[status(thm)],[5]) ).
thf(12,plain,
( sk6
| sk13
| ~ ( sk43 @ sk28 @ sk30 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(232,plain,
! [B: a,A: a] :
( sk6
| sk13
| ~ ( sk1 @ A @ B )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk28 @ sk30 ) ) ),
inference(paramod_ordered,[status(thm)],[43,12]) ).
thf(233,plain,
( sk6
| sk13
| ~ ( sk1 @ sk28 @ sk30 ) ),
inference(pattern_uni,[status(thm)],[232:[bind(A,$thf( sk28 )),bind(B,$thf( sk30 ))]]) ).
thf(237,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk31 @ A )
| ( A @ sk28 @ sk29 )
| ( ( A @ ( sk35 @ A ) @ ( sk36 @ A ) )
!= ( sk1 @ sk28 @ sk30 ) ) ),
inference(paramod_ordered,[status(thm)],[45,233]) ).
thf(238,plain,
( sk6
| sk13
| ( sk31
@ ^ [A: a,B: a] : ( sk1 @ sk28 @ sk30 ) )
| ( sk1 @ sk28 @ sk30 ) ),
inference(pre_uni,[status(thm)],[237:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk1 @ sk28 @ sk30 ) ))]]) ).
thf(88,plain,
! [B: a > a > $o,A: a > a > $o] :
( ~ ( ( A
@ ( sk8
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) )
| ( B
@ ( sk8
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) ) )
| ~ ( sk7
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
| ( A @ sk3 @ sk4 )
| ( B @ sk3 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[74:[bind(A,$thf( ^ [D: a] : ^ [E: a] : ( ( B @ D @ E ) | ( C @ D @ E ) ) ))]]) ).
thf(119,plain,
! [B: a > a > $o,A: a > a > $o] :
( ~ sk6
| ( A @ sk3 @ sk4 )
| ( B @ sk3 @ sk4 )
| ~ ( sk7
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
| ~ ( A
@ ( sk8
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) ) ),
inference(cnf,[status(esa)],[88]) ).
thf(121,plain,
! [B: a > a > $o,A: a > a > $o] :
( ~ sk6
| ( A @ sk3 @ sk4 )
| ( B @ sk3 @ sk4 )
| ~ ( sk7
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
| ~ ( A
@ ( sk8
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(387,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,274]) ).
thf(388,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[387:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(397,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ sk4 ) ),
inference(simp,[status(thm)],[388]) ).
thf(20475,plain,
( ~ sk6
| ~ ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk5 @ sk58 @ sk59 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[18324]) ).
thf(20574,plain,
( ~ sk6
| ( sk5 @ sk58 @ sk59 )
| ~ ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[20475]) ).
thf(20575,plain,
( ~ sk6
| ( sk5 @ sk58 @ sk59 )
| ~ ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ),
inference(simp,[status(thm)],[20574]) ).
thf(20604,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ sk6
| ( sk5 @ sk58 @ sk59 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,20575]) ).
thf(20605,plain,
( ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ sk6
| ( sk5 @ sk58 @ sk59 ) ),
inference(pattern_uni,[status(thm)],[20604:[bind(A,$thf( sk8 @ sk5 )),bind(B,$thf( sk9 @ sk5 ))]]) ).
thf(21002,plain,
( ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ sk6
| ( ( sk5 @ sk58 @ sk59 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[20605,27]) ).
thf(21118,plain,
( ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ sk6
| ( sk58 != sk3 )
| ( sk59 != sk4 ) ),
inference(simp,[status(thm)],[21002]) ).
thf(13,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk37 @ A )
| ( A @ ( sk40 @ A ) @ ( sk41 @ A ) )
| ( A @ sk29 @ sk30 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(61,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk37 @ A )
| ( A @ ( sk40 @ A ) @ ( sk41 @ A ) )
| ( A @ sk29 @ sk30 ) ),
inference(simp,[status(thm)],[13]) ).
thf(91,plain,
( ~ ( sk2 @ ( sk8 @ sk2 ) @ ( sk9 @ sk2 ) )
| ~ ( sk7 @ sk2 )
| ( sk2 @ sk3 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[74:[bind(A,$thf( sk2 ))]]) ).
thf(220,plain,
( ~ ( sk2 @ ( sk8 @ sk2 ) @ ( sk9 @ sk2 ) )
| ~ ( sk7 @ sk2 )
| $false
| ~ sk6 ),
inference(rewrite,[status(thm)],[91,78]) ).
thf(221,plain,
( ~ ( sk2 @ ( sk8 @ sk2 ) @ ( sk9 @ sk2 ) )
| ~ ( sk7 @ sk2 )
| ~ sk6 ),
inference(simp,[status(thm)],[220]) ).
thf(18810,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk5 @ sk52 @ sk53 )
| ~ sk6
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,18047]) ).
thf(18811,plain,
( ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk5 @ sk52 @ sk53 )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[18810:[bind(A,$thf( sk8 @ sk5 )),bind(B,$thf( sk9 @ sk5 ))]]) ).
thf(19804,plain,
( ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ sk6
| ( ( sk5 @ sk52 @ sk53 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18811,27]) ).
thf(19872,plain,
( ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ sk6
| ( sk52 != sk3 )
| ( sk53 != sk4 ) ),
inference(simp,[status(thm)],[19804]) ).
thf(2585,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ D @ sk4 )
| ~ ( sk2 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6,437]) ).
thf(2586,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk2 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[2585:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(2062,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ C @ D )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,416]) ).
thf(2063,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2062:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2103,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[2063]) ).
thf(20584,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ sk6
| ( sk5 @ sk58 @ sk59 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,20575]) ).
thf(20585,plain,
( ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ sk6
| ( sk5 @ sk58 @ sk59 ) ),
inference(pattern_uni,[status(thm)],[20584:[bind(A,$thf( sk8 @ sk5 )),bind(B,$thf( sk9 @ sk5 ))]]) ).
thf(2079,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[18,416]) ).
thf(2080,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ sk3 @ A )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2079:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(3660,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,2080]) ).
thf(3661,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[3660:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3679,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[3661]) ).
thf(449,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( ( sk1 @ A @ sk4 )
!= ( sk1 @ sk3 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[397]) ).
thf(452,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( ( sk1 @ A @ sk4 )
!= ( sk1 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[449]) ).
thf(38,plain,
! [A: a > a > $o] :
( sk6
| ~ ( A @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( A @ ( sk20 @ A ) @ ( sk21 @ A ) )
| ( A @ sk14 @ sk15 )
| sk16
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(60,plain,
! [A: a > a > $o] :
( sk6
| ~ ( A @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( A @ ( sk20 @ A ) @ ( sk21 @ A ) )
| ( A @ sk14 @ sk15 )
| sk16
| ~ sk13 ),
inference(simp,[status(thm)],[38]) ).
thf(1280,plain,
( sk6
| sk13
| ( sk37
@ ^ [A: a,B: a] : sk16 )
| sk16
| sk16 ),
inference(prim_subst,[status(thm)],[51:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk16 ))]]) ).
thf(1387,plain,
( sk6
| sk13
| ( sk37
@ ^ [A: a,B: a] : sk16 )
| sk16 ),
inference(simp,[status(thm)],[1280]) ).
thf(31,plain,
! [A: a > a > $o] :
( sk6
| ~ sk16
| ~ ( A @ ( sk22 @ A ) @ ( sk23 @ A ) )
| ( A @ ( sk25 @ A ) @ ( sk26 @ A ) )
| ( A @ sk14 @ sk15 )
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(70,plain,
! [A: a > a > $o] :
( sk6
| ~ sk16
| ~ ( A @ ( sk22 @ A ) @ ( sk23 @ A ) )
| ( A @ ( sk25 @ A ) @ ( sk26 @ A ) )
| ( A @ sk14 @ sk15 )
| ~ sk13 ),
inference(simp,[status(thm)],[31]) ).
thf(20520,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( ( sk5 @ sk58 @ sk59 )
!= ~ sk6 )
| ~ sk6
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,18324]) ).
thf(20521,plain,
( ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( ( sk5 @ sk58 @ sk59 )
!= ~ sk6 )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[20520:[bind(A,$thf( sk8 @ sk5 )),bind(B,$thf( sk9 @ sk5 ))]]) ).
thf(18890,plain,
! [A: a] :
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ ( sk2 @ sk3 @ A )
| ( ( sk5 @ sk54 @ sk55 )
!= ( sk5 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18113,289]) ).
thf(19077,plain,
! [A: a] :
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ ( sk2 @ sk3 @ A )
| ( sk54 != A )
| ( sk55 != sk4 ) ),
inference(simp,[status(thm)],[18890]) ).
thf(19082,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ ( sk2 @ sk3 @ sk54 )
| ( sk55 != sk4 ) ),
inference(simp,[status(thm)],[19077]) ).
thf(2064,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[6,416]) ).
thf(2065,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ sk3 @ A )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2064:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(3598,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,2065]) ).
thf(3599,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[3598:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3618,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[3599]) ).
thf(24219,plain,
( ~ ( sk1 @ sk3
@ ( sk9
@ ^ [A: a] : ( sk5 @ sk3 ) ) )
| ~ ( sk7
@ ^ [A: a] : ( sk5 @ sk3 ) )
| ~ sk6 ),
inference(pre_uni,[status(thm)],[24107:[bind(A,$thf( ^ [C: a] : ^ [D: a] : sk3 )),bind(B,$thf( ^ [C: a] : ^ [D: a] : D ))]]) ).
thf(24557,plain,
( ~ sk6
| ~ ( sk1 @ sk3
@ ( sk9
@ ^ [A: a] : ( sk5 @ sk3 ) ) )
| ( ( sk7
@ ^ [A: a] : ( sk5 @ sk3 ) )
!= ( sk7
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[6403,24219]) ).
thf(24588,plain,
( ~ sk6
| ~ ( sk1 @ sk3
@ ( sk9
@ ^ [A: a] : ( sk5 @ sk3 ) ) )
| ( ( ^ [A: a] : ( sk5 @ sk3 ) )
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[24557]) ).
thf(24684,plain,
( ( sk5 @ sk3 @ sk67 )
| ~ sk6
| ~ ( sk1 @ sk3
@ ( sk9
@ ^ [A: a] : ( sk5 @ sk3 ) ) ) ),
inference(func_ext,[status(esa)],[24588]) ).
thf(641,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( ( sk5 @ C @ sk4 )
!= ( sk5 @ sk3 @ C ) )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,285]) ).
thf(642,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( ( sk5 @ A @ sk4 )
!= ( sk5 @ sk3 @ A ) ) ),
inference(pattern_uni,[status(thm)],[641:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(665,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( ( sk5 @ A @ sk4 )
!= ( sk5 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[642]) ).
thf(502,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,302]) ).
thf(503,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[502:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(522,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[503]) ).
thf(7,plain,
! [A: a > a > $o] :
( ( sk1 @ ( sk8 @ A ) @ ( sk9 @ A ) )
| ( sk2 @ ( sk8 @ A ) @ ( sk9 @ A ) )
| ~ ( sk7 @ A )
| ( A @ sk3 @ sk4 )
| ~ sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(67,plain,
! [A: a > a > $o] :
( ( sk1 @ ( sk8 @ A ) @ ( sk9 @ A ) )
| ( sk2 @ ( sk8 @ A ) @ ( sk9 @ A ) )
| ~ ( sk7 @ A )
| ( A @ sk3 @ sk4 )
| ~ sk6 ),
inference(simp,[status(thm)],[7]) ).
thf(9584,plain,
! [A: a > a > $o] :
( ~ sk6
| ( sk1 @ ( sk8 @ A ) @ ( sk9 @ A ) )
| ( sk2 @ ( sk8 @ A ) @ ( sk9 @ A ) )
| ( A @ sk3 @ sk4 )
| ( ( sk7
@ ^ [B: a,C: a] : ~ sk6 )
!= ( sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6532,67]) ).
thf(9585,plain,
( ~ sk6
| ( sk1
@ ( sk8
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk9
@ ^ [A: a,B: a] : ~ sk6 ) )
| ( sk2
@ ( sk8
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk9
@ ^ [A: a,B: a] : ~ sk6 ) )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[9584:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ~ ( sk6 ) ))]]) ).
thf(9774,plain,
( ~ sk6
| ( sk2
@ ( sk8
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk9
@ ^ [A: a,B: a] : ~ sk6 ) )
| ( sk1
@ ( sk8
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk9
@ ^ [A: a,B: a] : ~ sk6 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[9585]) ).
thf(9775,plain,
( ~ sk6
| ( sk2
@ ( sk8
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk9
@ ^ [A: a,B: a] : ~ sk6 ) )
| ( sk1
@ ( sk8
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk9
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[9774]) ).
thf(11205,plain,
! [B: a,A: a] :
( ~ sk6
| ( sk1
@ ( sk8
@ ^ [C: a,D: a] : ~ sk6 )
@ ( sk9
@ ^ [C: a,D: a] : ~ sk6 ) )
| ( sk5 @ A @ B )
| ( ( sk2
@ ( sk8
@ ^ [C: a,D: a] : ~ sk6 )
@ ( sk9
@ ^ [C: a,D: a] : ~ sk6 ) )
!= ( sk2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9775,6]) ).
thf(11206,plain,
( ~ sk6
| ( sk1
@ ( sk8
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk9
@ ^ [A: a,B: a] : ~ sk6 ) )
| ( sk5
@ ( sk8
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk9
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[11205:[bind(A,$thf( sk8 @ ^ [C: a] : ^ [D: a] : ~ ( sk6 ) )),bind(B,$thf( sk9 @ ^ [C: a] : ^ [D: a] : ~ ( sk6 ) ))]]) ).
thf(6618,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk2 ) @ ( sk9 @ sk2 ) )
| ( ( sk7 @ sk2 )
!= ( sk7
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[6532,221]) ).
thf(6653,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk2 ) @ ( sk9 @ sk2 ) )
| ( sk2
!= ( ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[6618]) ).
thf(7049,plain,
( ( ( sk2 @ sk48 @ sk49 )
!= ~ sk6 )
| ~ sk6
| ~ ( sk2 @ ( sk8 @ sk2 ) @ ( sk9 @ sk2 ) ) ),
inference(func_ext,[status(esa)],[6653]) ).
thf(8005,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk2 ) @ ( sk9 @ sk2 ) )
| ( sk2 @ sk48 @ sk49 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[7049]) ).
thf(8047,plain,
( ~ sk6
| ( sk2 @ sk48 @ sk49 )
| ~ ( sk2 @ ( sk8 @ sk2 ) @ ( sk9 @ sk2 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[8005]) ).
thf(8048,plain,
( ~ sk6
| ( sk2 @ sk48 @ sk49 )
| ~ ( sk2 @ ( sk8 @ sk2 ) @ ( sk9 @ sk2 ) ) ),
inference(simp,[status(thm)],[8047]) ).
thf(28,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk2 @ A @ B )
| ( sk27 @ A @ B )
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(59,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk2 @ A @ B )
| ( sk27 @ A @ B )
| ~ sk13 ),
inference(simp,[status(thm)],[28]) ).
thf(4191,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk2 @ A @ B )
| ~ sk13
| ( ( sk27 @ A @ B )
!= ( sk27 @ sk14 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[59,37]) ).
thf(4192,plain,
( sk6
| ~ ( sk2 @ sk14 @ sk15 )
| ~ sk13 ),
inference(pattern_uni,[status(thm)],[4191:[bind(A,$thf( sk14 )),bind(B,$thf( sk15 ))]]) ).
thf(34,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk31 @ A )
| ( A @ ( sk34 @ A ) @ ( sk35 @ A ) )
| ( A @ sk28 @ sk29 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(65,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk31 @ A )
| ( A @ ( sk34 @ A ) @ ( sk35 @ A ) )
| ( A @ sk28 @ sk29 ) ),
inference(simp,[status(thm)],[34]) ).
thf(6572,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk2 ) @ ( sk9 @ sk2 ) )
| ( ( sk7 @ sk2 )
!= ( sk7
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[6403,221]) ).
thf(6603,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk2 ) @ ( sk9 @ sk2 ) )
| ( sk2
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[6572]) ).
thf(9582,plain,
! [A: a > a > $o] :
( ~ sk6
| ( sk1 @ ( sk8 @ A ) @ ( sk9 @ A ) )
| ( sk2 @ ( sk8 @ A ) @ ( sk9 @ A ) )
| ( A @ sk3 @ sk4 )
| ( ( sk7
@ ^ [B: a,C: a] : $false )
!= ( sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6403,67]) ).
thf(9583,plain,
( ~ sk6
| ( sk1
@ ( sk8
@ ^ [A: a,B: a] : $false )
@ ( sk9
@ ^ [A: a,B: a] : $false ) )
| ( sk2
@ ( sk8
@ ^ [A: a,B: a] : $false )
@ ( sk9
@ ^ [A: a,B: a] : $false ) )
| $false ),
inference(pattern_uni,[status(thm)],[9582:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(9773,plain,
( ~ sk6
| ( sk1
@ ( sk8
@ ^ [A: a,B: a] : $false )
@ ( sk9
@ ^ [A: a,B: a] : $false ) )
| ( sk2
@ ( sk8
@ ^ [A: a,B: a] : $false )
@ ( sk9
@ ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[9583]) ).
thf(17817,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk7 @ sk5 )
| ~ sk6
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,17777]) ).
thf(17818,plain,
( ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ ( sk7 @ sk5 )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[17817:[bind(A,$thf( sk8 @ sk5 )),bind(B,$thf( sk9 @ sk5 ))]]) ).
thf(17994,plain,
( ~ sk6
| ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( ( sk7 @ sk5 )
!= ( sk7
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[6403,17818]) ).
thf(18017,plain,
( ~ sk6
| ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk5
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[17994]) ).
thf(17995,plain,
( ~ sk6
| ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( ( sk7 @ sk5 )
!= ( sk7
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[6532,17818]) ).
thf(18021,plain,
( ~ sk6
| ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk5
!= ( ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[17995]) ).
thf(18456,plain,
( ( ( sk5 @ sk62 @ sk63 )
!= ~ sk6 )
| ~ sk6
| ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[18021]) ).
thf(23004,plain,
( ~ sk6
| ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk5 @ sk62 @ sk63 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[18456]) ).
thf(23093,plain,
( ~ sk6
| ( sk5 @ sk62 @ sk63 )
| ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[23004]) ).
thf(23094,plain,
( ~ sk6
| ( sk5 @ sk62 @ sk63 )
| ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ),
inference(simp,[status(thm)],[23093]) ).
thf(6780,plain,
( ( sk2 @ sk46 @ sk47 )
| ~ sk6
| ~ ( sk2 @ ( sk8 @ sk2 ) @ ( sk9 @ sk2 ) ) ),
inference(func_ext,[status(esa)],[6603]) ).
thf(160,plain,
( sk6
| sk13
| ( sk31
@ ^ [A: a,B: a] : sk16 )
| sk16
| sk16 ),
inference(prim_subst,[status(thm)],[45:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk16 ))]]) ).
thf(188,plain,
( sk6
| sk13
| ( sk31
@ ^ [A: a,B: a] : sk16 )
| sk16 ),
inference(simp,[status(thm)],[160]) ).
thf(4130,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk2 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6,2586]) ).
thf(4131,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[4130:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(4167,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(simp,[status(thm)],[4131]) ).
thf(656,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( ( sk5 @ C @ sk4 )
!= ( sk5 @ sk3 @ C ) )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,285]) ).
thf(657,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( ( sk5 @ A @ sk4 )
!= ( sk5 @ sk3 @ A ) ) ),
inference(pattern_uni,[status(thm)],[656:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(669,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( ( sk5 @ A @ sk4 )
!= ( sk5 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[657]) ).
thf(493,plain,
! [B: a,A: a] :
( sk6
| sk13
| ~ ( sk2 @ A @ B )
| ( ( sk43 @ A @ B )
!= ( sk43 @ sk28 @ sk30 ) ) ),
inference(paramod_ordered,[status(thm)],[46,12]) ).
thf(494,plain,
( sk6
| sk13
| ~ ( sk2 @ sk28 @ sk30 ) ),
inference(pattern_uni,[status(thm)],[493:[bind(A,$thf( sk28 )),bind(B,$thf( sk30 ))]]) ).
thf(545,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk31 @ A )
| ( A @ sk28 @ sk29 )
| ( ( A @ ( sk35 @ A ) @ ( sk36 @ A ) )
!= ( sk2 @ sk28 @ sk30 ) ) ),
inference(paramod_ordered,[status(thm)],[45,494]) ).
thf(547,plain,
( sk6
| sk13
| ( sk31
@ ^ [A: a,B: a] : ( sk2 @ sk28 @ sk30 ) )
| ( sk2 @ sk28 @ sk30 ) ),
inference(pre_uni,[status(thm)],[545:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk2 @ sk28 @ sk30 ) ))]]) ).
thf(1291,plain,
( sk6
| sk13
| ( sk37
@ ^ [A: a,B: a] : sk6 )
| sk6
| sk6 ),
inference(prim_subst,[status(thm)],[51:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk6 ))]]) ).
thf(1393,plain,
( sk6
| sk13
| ( sk37
@ ^ [A: a,B: a] : sk6 ) ),
inference(simp,[status(thm)],[1291]) ).
thf(105,plain,
( ~ ( sk43 @ ( sk8 @ sk43 ) @ ( sk9 @ sk43 ) )
| ~ ( sk7 @ sk43 )
| ( sk43 @ sk3 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[74:[bind(A,$thf( sk43 ))]]) ).
thf(2011,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ C @ D )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,399]) ).
thf(2012,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2011:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2057,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[2012]) ).
thf(389,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,274]) ).
thf(390,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[389:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(398,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ sk4 ) ),
inference(simp,[status(thm)],[390]) ).
thf(6214,plain,
( ( sk7
@ ^ [A: a,B: a] : sk16 )
| sk16
| sk16
| ~ sk6 ),
inference(prim_subst,[status(thm)],[62:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk16 ))]]) ).
thf(6400,plain,
( ( sk7
@ ^ [A: a,B: a] : sk16 )
| sk16
| ~ sk6 ),
inference(simp,[status(thm)],[6214]) ).
thf(297,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[6,292]) ).
thf(298,plain,
( ~ ( sk2 @ sk3 @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(32,plain,
! [A: a > a > $o] :
( sk6
| ~ sk16
| ( sk2 @ ( sk22 @ A ) @ ( sk23 @ A ) )
| ( A @ ( sk24 @ A ) @ ( sk25 @ A ) )
| ( A @ sk14 @ sk15 )
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(64,plain,
! [A: a > a > $o] :
( sk6
| ~ sk16
| ( sk2 @ ( sk22 @ A ) @ ( sk23 @ A ) )
| ( A @ ( sk24 @ A ) @ ( sk25 @ A ) )
| ( A @ sk14 @ sk15 )
| ~ sk13 ),
inference(simp,[status(thm)],[32]) ).
thf(295,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[18,292]) ).
thf(296,plain,
( ~ ( sk1 @ sk3 @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[295:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(18179,plain,
( ( sk5 @ sk56 @ sk57 )
| ~ sk6
| ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[18017]) ).
thf(19208,plain,
( ~ sk6
| ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( ( sk5 @ sk56 @ sk57 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18179,27]) ).
thf(19303,plain,
( ~ sk6
| ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk56 != sk3 )
| ( sk57 != sk4 ) ),
inference(simp,[status(thm)],[19208]) ).
thf(3209,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,2014]) ).
thf(3210,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[3209:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3255,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[3210]) ).
thf(10,plain,
! [A: a > a > $o] :
( sk6
| ~ sk16
| ( sk2 @ ( sk22 @ A ) @ ( sk23 @ A ) )
| ~ ( A @ ( sk24 @ A ) @ ( sk26 @ A ) )
| ( A @ sk14 @ sk15 )
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(44,plain,
! [A: a > a > $o] :
( sk6
| ~ sk16
| ( sk2 @ ( sk22 @ A ) @ ( sk23 @ A ) )
| ~ ( A @ ( sk24 @ A ) @ ( sk26 @ A ) )
| ( A @ sk14 @ sk15 )
| ~ sk13 ),
inference(simp,[status(thm)],[10]) ).
thf(25505,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [B: a,C: a] : ( sk5 @ B @ sk4 ) )
@ sk4 )
| ~ ( sk1 @ sk3 @ A )
| ( ( sk5 @ sk64 @ sk4 )
!= ( sk5 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[24619,288]) ).
thf(25506,plain,
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
@ sk4 )
| ~ ( sk1 @ sk3 @ sk64 ) ),
inference(pattern_uni,[status(thm)],[25505:[bind(A,$thf( sk64 ))]]) ).
thf(1282,plain,
( sk6
| sk13
| ( sk37
@ ^ [A: a,B: a] : $false )
| $false
| $false ),
inference(prim_subst,[status(thm)],[51:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(1388,plain,
( sk6
| sk13
| ( sk37
@ ^ [A: a,B: a] : $false ) ),
inference(simp,[status(thm)],[1282]) ).
thf(203,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk31 @ A )
| ( A @ sk28 @ sk29 )
| ( ( A @ ( sk35 @ A ) @ ( sk36 @ A ) )
!= ( sk43 @ sk28 @ sk30 ) ) ),
inference(paramod_ordered,[status(thm)],[45,12]) ).
thf(204,plain,
( sk6
| sk13
| ( sk31
@ ^ [A: a,B: a] : ( sk43 @ sk28 @ sk30 ) )
| ( sk43 @ sk28 @ sk30 ) ),
inference(pre_uni,[status(thm)],[203:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk43 @ sk28 @ sk30 ) ))]]) ).
thf(86,plain,
! [A: a > a > a > a > $o] :
( ~ ( sk7
@ ( A
@ ( sk8
@ ^ [B: a,C: a] : ( sk7 @ ( A @ B @ C ) ) )
@ ( sk9
@ ^ [B: a,C: a] : ( sk7 @ ( A @ B @ C ) ) ) ) )
| ~ ( sk7
@ ^ [B: a,C: a] : ( sk7 @ ( A @ B @ C ) ) )
| ( sk7 @ ( A @ sk3 @ sk4 ) )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[74:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ( sk7 @ ( B @ C @ D ) ) ))]]) ).
thf(118,plain,
! [A: a > a > a > a > $o] :
( ~ ( sk7
@ ( A
@ ( sk8
@ ^ [B: a,C: a] : ( sk7 @ ( A @ B @ C ) ) )
@ ( sk9
@ ^ [B: a,C: a] : ( sk7 @ ( A @ B @ C ) ) ) ) )
| ~ ( sk7
@ ^ [B: a,C: a] : ( sk7 @ ( A @ B @ C ) ) )
| ( sk7 @ ( A @ sk3 @ sk4 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[86]) ).
thf(40,plain,
! [A: a > a > $o] :
( sk6
| ~ ( A @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ~ ( A @ ( sk19 @ A ) @ ( sk21 @ A ) )
| ( A @ sk14 @ sk15 )
| sk16
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(71,plain,
! [A: a > a > $o] :
( sk6
| ~ ( A @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ~ ( A @ ( sk19 @ A ) @ ( sk21 @ A ) )
| ( A @ sk14 @ sk15 )
| sk16
| ~ sk13 ),
inference(simp,[status(thm)],[40]) ).
thf(25,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( A @ ( sk19 @ A ) @ ( sk20 @ A ) )
| ( A @ sk14 @ sk15 )
| sk16
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(54,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( A @ ( sk19 @ A ) @ ( sk20 @ A ) )
| ( A @ sk14 @ sk15 )
| sk16
| ~ sk13 ),
inference(simp,[status(thm)],[25]) ).
thf(4146,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk2 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18,2586]) ).
thf(4147,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[4146:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(4171,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(simp,[status(thm)],[4147]) ).
thf(8,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ~ ( A @ ( sk19 @ A ) @ ( sk21 @ A ) )
| ( A @ sk14 @ sk15 )
| sk16
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(49,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ~ ( A @ ( sk19 @ A ) @ ( sk21 @ A ) )
| ( A @ sk14 @ sk15 )
| sk16
| ~ sk13 ),
inference(simp,[status(thm)],[8]) ).
thf(758,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,515]) ).
thf(759,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[758:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(764,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[759]) ).
thf(99,plain,
! [A: a > a > $o] :
( ~ ~ ( A
@ ( sk8
@ ^ [B: a,C: a] :
~ ( A @ B @ C ) )
@ ( sk9
@ ^ [B: a,C: a] :
~ ( A @ B @ C ) ) )
| ~ ( sk7
@ ^ [B: a,C: a] :
~ ( A @ B @ C ) )
| ~ ( A @ sk3 @ sk4 )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[74:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ~ ( B @ C @ D ) ))]]) ).
thf(112,plain,
! [A: a > a > $o] :
( ~ sk6
| ~ ( A @ sk3 @ sk4 )
| ~ ( sk7
@ ^ [B: a,C: a] :
~ ( A @ B @ C ) )
| ( A
@ ( sk8
@ ^ [B: a,C: a] :
~ ( A @ B @ C ) )
@ ( sk9
@ ^ [B: a,C: a] :
~ ( A @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[99]) ).
thf(113,plain,
! [A: a > a > $o] :
( ~ sk6
| ~ ( A @ sk3 @ sk4 )
| ~ ( sk7
@ ^ [B: a,C: a] :
~ ( A @ B @ C ) )
| ( A
@ ( sk8
@ ^ [B: a,C: a] :
~ ( A @ B @ C ) )
@ ( sk9
@ ^ [B: a,C: a] :
~ ( A @ B @ C ) ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(25517,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [B: a,C: a] : ( sk5 @ B @ sk4 ) )
@ sk4 )
| ~ ( sk2 @ sk3 @ A )
| ( ( sk5 @ sk64 @ sk4 )
!= ( sk5 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[24619,289]) ).
thf(25518,plain,
( ~ sk6
| ~ ( sk1
@ ( sk8
@ ^ [A: a,B: a] : ( sk5 @ A @ sk4 ) )
@ sk4 )
| ~ ( sk2 @ sk3 @ sk64 ) ),
inference(pattern_uni,[status(thm)],[25517:[bind(A,$thf( sk64 ))]]) ).
thf(19,plain,
! [A: a > a > $o] :
( sk6
| ~ ( A @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( A @ ( sk19 @ A ) @ ( sk20 @ A ) )
| ( A @ sk14 @ sk15 )
| sk16
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(76,plain,
! [A: a > a > $o] :
( sk6
| ~ ( A @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( A @ ( sk19 @ A ) @ ( sk20 @ A ) )
| ( A @ sk14 @ sk15 )
| sk16
| ~ sk13 ),
inference(simp,[status(thm)],[19]) ).
thf(25919,plain,
( ~ sk6
| ~ ( sk1 @ sk3
@ ( sk9
@ ^ [A: a] : ( sk5 @ sk3 ) ) )
| ( ( sk5 @ sk3 @ sk67 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[24684,27]) ).
thf(26028,plain,
( ~ sk6
| ~ ( sk1 @ sk3
@ ( sk9
@ ^ [A: a] : ( sk5 @ sk3 ) ) )
| ( sk3 != sk3 )
| ( sk67 != sk4 ) ),
inference(simp,[status(thm)],[25919]) ).
thf(26070,plain,
( ~ sk6
| ~ ( sk1 @ sk3
@ ( sk9
@ ^ [A: a] : ( sk5 @ sk3 ) ) )
| ( sk67 != sk4 ) ),
inference(simp,[status(thm)],[26028]) ).
thf(512,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,302]) ).
thf(513,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[512:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(520,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[513]) ).
thf(22,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk37 @ A )
| ~ ( A @ ( sk40 @ A ) @ ( sk42 @ A ) )
| ( A @ sk29 @ sk30 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(66,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk37 @ A )
| ~ ( A @ ( sk40 @ A ) @ ( sk42 @ A ) )
| ( A @ sk29 @ sk30 ) ),
inference(simp,[status(thm)],[22]) ).
thf(25280,plain,
( ~ ( sk2 @ sk3
@ ( sk9
@ ^ [A: a] : ( sk5 @ sk3 ) ) )
| ~ ( sk7
@ ^ [A: a] : ( sk5 @ sk3 ) )
| ~ sk6 ),
inference(pre_uni,[status(thm)],[25156:[bind(A,$thf( ^ [C: a] : ^ [D: a] : sk3 )),bind(B,$thf( ^ [C: a] : ^ [D: a] : D ))]]) ).
thf(1762,plain,
! [A: a > a > $o] :
( sk6
| ( sk1 @ ( sk17 @ A ) @ ( sk18 @ A ) )
| ( A @ sk14 @ sk15 )
| sk16
| ~ sk13
| ( ( A @ ( sk20 @ A ) @ ( sk21 @ A ) )
!= sk6 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[53]) ).
thf(1824,plain,
( sk6
| ( sk1
@ ( sk17
@ ^ [A: a,B: a] : sk6 )
@ ( sk18
@ ^ [A: a,B: a] : sk6 ) )
| sk6
| sk16
| ~ sk13 ),
inference(pre_uni,[status(thm)],[1762:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk6 ))]]) ).
thf(1926,plain,
( sk6
| ( sk1
@ ( sk17
@ ^ [A: a,B: a] : sk6 )
@ ( sk18
@ ^ [A: a,B: a] : sk6 ) )
| sk16
| ~ sk13 ),
inference(simp,[status(thm)],[1824]) ).
thf(23459,plain,
( ~ sk6
| ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( ( sk5 @ sk62 @ sk63 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[23094,27]) ).
thf(23585,plain,
( ~ sk6
| ~ ( sk1 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ( sk62 != sk3 )
| ( sk63 != sk4 ) ),
inference(simp,[status(thm)],[23459]) ).
thf(7080,plain,
( ( ( sk1 @ sk50 @ sk51 )
!= ~ sk6 )
| ~ sk6
| ~ ( sk1 @ ( sk8 @ sk1 ) @ ( sk9 @ sk1 ) ) ),
inference(func_ext,[status(esa)],[6655]) ).
thf(8057,plain,
( ~ sk6
| ~ ( sk1 @ ( sk8 @ sk1 ) @ ( sk9 @ sk1 ) )
| ( sk1 @ sk50 @ sk51 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[7080]) ).
thf(8098,plain,
( ~ sk6
| ( sk1 @ sk50 @ sk51 )
| ~ ( sk1 @ ( sk8 @ sk1 ) @ ( sk9 @ sk1 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[8057]) ).
thf(8099,plain,
( ~ sk6
| ( sk1 @ sk50 @ sk51 )
| ~ ( sk1 @ ( sk8 @ sk1 ) @ ( sk9 @ sk1 ) ) ),
inference(simp,[status(thm)],[8098]) ).
thf(1769,plain,
( sk6
| ( sk1
@ ( sk17
@ ^ [A: a,B: a] : $false )
@ ( sk18
@ ^ [A: a,B: a] : $false ) )
| $false
| $false
| sk16
| ~ sk13 ),
inference(prim_subst,[status(thm)],[53:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(1990,plain,
( sk6
| ( sk1
@ ( sk17
@ ^ [A: a,B: a] : $false )
@ ( sk18
@ ^ [A: a,B: a] : $false ) )
| sk16
| ~ sk13 ),
inference(simp,[status(thm)],[1769]) ).
thf(11,plain,
! [C: a,B: a,A: a] :
( sk6
| sk13
| ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ C )
| ( sk43 @ A @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(48,plain,
! [C: a,B: a,A: a] :
( sk6
| sk13
| ~ ( sk43 @ A @ B )
| ~ ( sk43 @ B @ C )
| ( sk43 @ A @ C ) ),
inference(simp,[status(thm)],[11]) ).
thf(17,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk1 @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ( sk2 @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ~ ( sk37 @ A )
| ( A @ sk29 @ sk30 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(63,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk1 @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ( sk2 @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ~ ( sk37 @ A )
| ( A @ sk29 @ sk30 ) ),
inference(simp,[status(thm)],[17]) ).
thf(2112,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ C @ D )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6,425]) ).
thf(2113,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2112:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2143,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2113]) ).
thf(3227,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,2014]) ).
thf(3228,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[3227:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3260,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[3228]) ).
thf(402,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,278]) ).
thf(403,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[402:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(414,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ sk4 ) ),
inference(simp,[status(thm)],[403]) ).
thf(4,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ~ ( A @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ~ ( sk37 @ A )
| ( A @ sk29 @ sk30 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(50,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ~ ( A @ ( sk38 @ A ) @ ( sk39 @ A ) )
| ~ ( sk37 @ A )
| ( A @ sk29 @ sk30 ) ),
inference(simp,[status(thm)],[4]) ).
thf(3640,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,2080]) ).
thf(3641,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[3640:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3691,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[3641]) ).
thf(1215,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk37 @ A )
| ( A @ sk29 @ sk30 )
| ( ( A @ ( sk41 @ A ) @ ( sk42 @ A ) )
!= ( sk1 @ sk28 @ sk30 ) ) ),
inference(paramod_ordered,[status(thm)],[51,233]) ).
thf(1317,plain,
( sk6
| sk13
| ( sk37
@ ^ [A: a,B: a] : ( sk1 @ sk28 @ sk30 ) )
| ( sk1 @ sk28 @ sk30 ) ),
inference(pre_uni,[status(thm)],[1215:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk1 @ sk28 @ sk30 ) ))]]) ).
thf(3812,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6,2111]) ).
thf(3813,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[3812:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(3853,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(simp,[status(thm)],[3813]) ).
thf(2128,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ C @ D )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18,425]) ).
thf(2129,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2128:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2145,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2129]) ).
thf(26,plain,
! [A: a > a > $o] :
( ( sk7 @ A )
| ( A @ ( sk10 @ A ) @ ( sk11 @ A ) )
| ( A @ sk3 @ sk4 )
| ~ sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(72,plain,
! [A: a > a > $o] :
( ( sk7 @ A )
| ( A @ ( sk10 @ A ) @ ( sk11 @ A ) )
| ( A @ sk3 @ sk4 )
| ~ sk6 ),
inference(simp,[status(thm)],[26]) ).
thf(1592,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ C @ D )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18,282]) ).
thf(1593,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[1592:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(1617,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(simp,[status(thm)],[1593]) ).
thf(2027,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ C @ D )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,399]) ).
thf(2028,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2027:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2045,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[2028]) ).
thf(33,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk1 @ A @ B )
| ( sk27 @ A @ B )
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(58,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk1 @ A @ B )
| ( sk27 @ A @ B )
| ~ sk13 ),
inference(simp,[status(thm)],[33]) ).
thf(3873,plain,
! [B: a,A: a] :
( sk6
| ~ ( sk1 @ A @ B )
| ~ sk13
| ( ( sk27 @ A @ B )
!= ( sk27 @ sk14 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[58,37]) ).
thf(3874,plain,
( sk6
| ~ ( sk1 @ sk14 @ sk15 )
| ~ sk13 ),
inference(pattern_uni,[status(thm)],[3873:[bind(A,$thf( sk14 )),bind(B,$thf( sk15 ))]]) ).
thf(2887,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18,1591]) ).
thf(2888,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2887:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2907,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2888]) ).
thf(20,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk1 @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ( sk2 @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( A @ sk28 @ sk29 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(55,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ( sk1 @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ( sk2 @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( A @ sk28 @ sk29 ) ),
inference(simp,[status(thm)],[20]) ).
thf(100,plain,
! [A: a > a > a > a > $o] :
( ~ ( sk37
@ ( A
@ ( sk8
@ ^ [B: a,C: a] : ( sk37 @ ( A @ B @ C ) ) )
@ ( sk9
@ ^ [B: a,C: a] : ( sk37 @ ( A @ B @ C ) ) ) ) )
| ~ ( sk7
@ ^ [B: a,C: a] : ( sk37 @ ( A @ B @ C ) ) )
| ( sk37 @ ( A @ sk3 @ sk4 ) )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[74:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ( sk37 @ ( B @ C @ D ) ) ))]]) ).
thf(114,plain,
! [A: a > a > a > a > $o] :
( ~ ( sk37
@ ( A
@ ( sk8
@ ^ [B: a,C: a] : ( sk37 @ ( A @ B @ C ) ) )
@ ( sk9
@ ^ [B: a,C: a] : ( sk37 @ ( A @ B @ C ) ) ) ) )
| ~ ( sk7
@ ^ [B: a,C: a] : ( sk37 @ ( A @ B @ C ) ) )
| ( sk37 @ ( A @ sk3 @ sk4 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[100]) ).
thf(30,plain,
! [A: a > a > $o] :
( ( sk7 @ A )
| ~ ( A @ ( sk10 @ A ) @ ( sk12 @ A ) )
| ( A @ sk3 @ sk4 )
| ~ sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(75,plain,
! [A: a > a > $o] :
( ( sk7 @ A )
| ~ ( A @ ( sk10 @ A ) @ ( sk12 @ A ) )
| ( A @ sk3 @ sk4 )
| ~ sk6 ),
inference(simp,[status(thm)],[30]) ).
thf(3289,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,2030]) ).
thf(3290,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[3289:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3324,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[3290]) ).
thf(2661,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18,1576]) ).
thf(2662,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2661:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2680,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2662]) ).
thf(3944,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6,2127]) ).
thf(3945,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[3944:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(3993,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(simp,[status(thm)],[3945]) ).
thf(2605,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ C @ D )
| ~ ( sk2 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18,437]) ).
thf(2606,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2605:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2623,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2606]) ).
thf(4252,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk2 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6,2604]) ).
thf(4253,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[4252:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(4306,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(simp,[status(thm)],[4253]) ).
thf(9822,plain,
! [B: a,A: a] :
( ~ sk6
| ( sk1
@ ( sk8
@ ^ [C: a,D: a] : $false )
@ ( sk9
@ ^ [C: a,D: a] : $false ) )
| ( sk5 @ A @ B )
| ( ( sk2
@ ( sk8
@ ^ [C: a,D: a] : $false )
@ ( sk9
@ ^ [C: a,D: a] : $false ) )
!= ( sk2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9773,6]) ).
thf(9823,plain,
( ~ sk6
| ( sk1
@ ( sk8
@ ^ [A: a,B: a] : $false )
@ ( sk9
@ ^ [A: a,B: a] : $false ) )
| ( sk5
@ ( sk8
@ ^ [A: a,B: a] : $false )
@ ( sk9
@ ^ [A: a,B: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[9822:[bind(A,$thf( sk8 @ ^ [C: a] : ^ [D: a] : $false )),bind(B,$thf( sk9 @ ^ [C: a] : ^ [D: a] : $false ))]]) ).
thf(20730,plain,
( ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ sk6
| ( ( sk5 @ sk58 @ sk59 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[20585,27]) ).
thf(20831,plain,
( ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ sk6
| ( sk58 != sk3 )
| ( sk59 != sk4 ) ),
inference(simp,[status(thm)],[20730]) ).
thf(85,plain,
! [A: a > a > $o] :
( ~ ( A @ ( sk8 @ A ) @ ( sk9 @ A ) )
| ( A @ sk3 @ sk4 )
| ~ sk6
| ( ( sk7 @ A )
!= ( A @ ( sk8 @ A ) @ ( sk9 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[74]) ).
thf(107,plain,
! [A: a > a > $o] :
( ( A @ sk3 @ sk4 )
| ~ ( A @ ( sk8 @ A ) @ ( sk9 @ A ) )
| ~ sk6
| ( ( sk7 @ A )
!= ( A @ ( sk8 @ A ) @ ( sk9 @ A ) ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(2864,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[6,1591]) ).
thf(2865,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2864:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2913,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2865]) ).
thf(3582,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,2065]) ).
thf(3583,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[3582:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3633,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[3583]) ).
thf(404,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,278]) ).
thf(405,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[404:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(415,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ sk4 ) ),
inference(simp,[status(thm)],[405]) ).
thf(35,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ~ ( A @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( A @ sk28 @ sk29 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(47,plain,
! [A: a > a > $o] :
( sk6
| sk13
| ~ ( A @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( A @ sk28 @ sk29 ) ),
inference(simp,[status(thm)],[35]) ).
thf(39,plain,
! [A: a > a > $o] :
( sk6
| ~ sk16
| ( sk2 @ ( sk22 @ A ) @ ( sk23 @ A ) )
| ( A @ ( sk25 @ A ) @ ( sk26 @ A ) )
| ( A @ sk14 @ sk15 )
| ~ sk13 ),
inference(cnf,[status(esa)],[3]) ).
thf(68,plain,
! [A: a > a > $o] :
( sk6
| ~ sk16
| ( sk2 @ ( sk22 @ A ) @ ( sk23 @ A ) )
| ( A @ ( sk25 @ A ) @ ( sk26 @ A ) )
| ( A @ sk14 @ sk15 )
| ~ sk13 ),
inference(simp,[status(thm)],[39]) ).
thf(18929,plain,
! [A: a] :
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ ( sk5 @ A @ sk4 )
| ( ( sk5 @ sk54 @ sk55 )
!= ( sk5 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18113,266]) ).
thf(19074,plain,
! [A: a] :
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ ( sk5 @ A @ sk4 )
| ( sk54 != sk3 )
| ( sk55 != A ) ),
inference(simp,[status(thm)],[18929]) ).
thf(19079,plain,
( ~ sk6
| ~ ( sk2 @ ( sk8 @ sk5 ) @ ( sk9 @ sk5 ) )
| ~ ( sk5 @ sk55 @ sk4 )
| ( sk54 != sk3 ) ),
inference(simp,[status(thm)],[19074]) ).
thf(98,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk27
@ ( A
@ ( sk8
@ ^ [C: a,D: a] : ( sk27 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk27 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk8
@ ^ [C: a,D: a] : ( sk27 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk27 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk7
@ ^ [C: a,D: a] : ( sk27 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk27 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) )
| ~ sk6 ),
inference(prim_subst,[status(thm)],[74:[bind(A,$thf( ^ [D: a] : ^ [E: a] : ( sk27 @ ( B @ D @ E ) @ ( C @ D @ E ) ) ))]]) ).
thf(111,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk27
@ ( A
@ ( sk8
@ ^ [C: a,D: a] : ( sk27 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk27 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk8
@ ^ [C: a,D: a] : ( sk27 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk9
@ ^ [C: a,D: a] : ( sk27 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk7
@ ^ [C: a,D: a] : ( sk27 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk27 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) )
| ~ sk6 ),
inference(simp,[status(thm)],[98]) ).
thf(481,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( ( sk2 @ A @ sk4 )
!= ( sk2 @ sk3 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[415]) ).
thf(486,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( ( sk2 @ A @ sk4 )
!= ( sk2 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[481]) ).
thf(44344,plain,
$false,
inference(e,[status(thm)],[69,4005,762,115,3858,2014,19037,1591,20145,56,24501,25548,6655,25279,25727,538,185,22925,20488,1967,37,1391,1576,288,1613,52,184,110,6749,542,2691,17928,189,46,93,416,2635,3312,289,57,78,2105,4297,6410,238,121,18324,397,21118,61,221,19872,20605,74,2586,18047,116,2103,292,20585,3679,6,233,452,60,117,1387,18113,302,70,20521,19082,3618,24684,665,522,11206,285,8048,4192,65,6603,9773,18017,53,23094,6780,188,24588,6593,4167,669,2080,547,515,1393,73,105,266,2057,398,6400,298,425,17851,45,64,296,19303,24619,3255,44,25506,1388,204,27,59,118,71,12,17818,54,6403,6532,4171,17789,49,24218,764,113,274,25518,76,26070,2065,494,2111,520,66,278,25280,17840,17940,3,505,80,7049,1926,399,23585,8099,1990,48,63,18,282,2143,3260,414,18390,50,67,17777,3691,1317,6653,3853,18456,9775,2145,20575,72,2030,43,1617,2045,18811,18179,3874,2907,55,114,75,3324,58,22720,2680,3993,7080,2623,4306,214,9823,20831,51,2604,107,18830,24219,437,2913,3633,415,2127,18021,47,68,19079,62,111,486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV156^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:27:25 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/0.98 % [INFO] Parsing done (114ms).
% 1.16/0.99 % [INFO] Running in sequential loop mode.
% 1.72/1.19 % [INFO] eprover registered as external prover.
% 1.72/1.19 % [INFO] Scanning for conjecture ...
% 1.92/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.92/1.31 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.92/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 1.92/1.31 % [INFO] Type checking passed.
% 1.92/1.32 % [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 ...
% 95.19/21.89 % External prover 'e' found a proof!
% 95.19/21.89 % [INFO] Killing All external provers ...
% 95.19/21.90 % Time passed: 21366ms (effective reasoning time: 20904ms)
% 95.19/21.90 % 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)>
% 95.19/21.90 % Axioms used in derivation (0):
% 95.19/21.90 % No. of inferences in proof: 474
% 95.19/21.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21366 ms resp. 20904 ms w/o parsing
% 95.57/22.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 95.57/22.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------