TSTP Solution File: SEV157^5 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV157^5 : 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 80.55s 18.28s
% Output : Refutation 81.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 484 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 2441 ( 231 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 6780 (1318 ~;1320 |; 54 &;4007 @)
% ( 0 <=>; 81 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 280 ( 280 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 63 usr; 47 con; 0-2 aty)
% Number of variables : 1220 ( 360 ^ 860 !; 0 ?;1220 :)
% 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: $o ).
thf(sk8_type,type,
sk8: a ).
thf(sk9_type,type,
sk9: a ).
thf(sk10_type,type,
sk10: $o ).
thf(sk11_type,type,
sk11: ( a > a > $o ) > a ).
thf(sk12_type,type,
sk12: ( a > a > $o ) > a ).
thf(sk16_type,type,
sk16: ( a > a > $o ) > a ).
thf(sk17_type,type,
sk17: ( a > a > $o ) > a ).
thf(sk21_type,type,
sk21: a > a > $o ).
thf(sk22_type,type,
sk22: a ).
thf(sk24_type,type,
sk24: a ).
thf(sk25_type,type,
sk25: ( a > a > $o ) > $o ).
thf(sk26_type,type,
sk26: ( a > a > $o ) > a ).
thf(sk27_type,type,
sk27: ( a > a > $o ) > 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 ).
thf(sk38_type,type,
sk38: ( a > a > $o ) > $o ).
thf(sk39_type,type,
sk39: ( a > a > $o ) > a ).
thf(sk40_type,type,
sk40: ( a > a > $o ) > a ).
thf(sk44_type,type,
sk44: a ).
thf(sk45_type,type,
sk45: a ).
thf(sk46_type,type,
sk46: a ).
thf(sk47_type,type,
sk47: a ).
thf(sk48_type,type,
sk48: a ).
thf(sk49_type,type,
sk49: a ).
thf(sk50_type,type,
sk50: a ).
thf(sk51_type,type,
sk51: a ).
thf(sk52_type,type,
sk52: a ).
thf(sk53_type,type,
sk53: a ).
thf(sk54_type,type,
sk54: a ).
thf(sk55_type,type,
sk55: a ).
thf(sk56_type,type,
sk56: a ).
thf(sk57_type,type,
sk57: a ).
thf(sk58_type,type,
sk58: a ).
thf(sk59_type,type,
sk59: a ).
thf(sk60_type,type,
sk60: a ).
thf(sk61_type,type,
sk61: a ).
thf(sk62_type,type,
sk62: a ).
thf(sk63_type,type,
sk63: a ).
thf(1,conjecture,
! [A: a > a > $o,B: a > a > $o,C: a,D: a] :
( ! [E: a > 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 ) ) ) )
=> ! [E: a > a > $o] :
( ( ! [F: a,G: a] :
( ( ( A @ F @ G )
| ( B @ F @ G ) )
=> ( E @ F @ G ) )
& ! [F: a,G: a,H: a] :
( ( ( E @ F @ G )
& ( E @ G @ H ) )
=> ( E @ F @ H ) ) )
=> ( E @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM250G_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,F: a] :
( ( ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( A @ H @ I )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) )
| ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( B @ H @ I )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) ) )
=> ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( ( A @ H @ I )
| ( B @ H @ I ) )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) ) )
& ! [E: a,F: a,G: a] :
( ( ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ E @ F ) )
& ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ F @ G ) ) )
=> ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ E @ G ) ) ) )
=> ! [E: a > a > $o] :
( ( ! [F: a,G: a] :
( ( ( A @ F @ G )
| ( B @ F @ G ) )
=> ( E @ F @ G ) )
& ! [F: a,G: a,H: a] :
( ( ( E @ F @ G )
& ( E @ G @ H ) )
=> ( E @ F @ H ) ) )
=> ( E @ C @ D ) ) ) ),
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,F: a] :
( ( ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( A @ H @ I )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) )
| ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( B @ H @ I )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) ) )
=> ! [G: a > a > $o] :
( ( ! [H: a,I: a] :
( ( ( A @ H @ I )
| ( B @ H @ I ) )
=> ( G @ H @ I ) )
& ! [H: a,I: a,J: a] :
( ( ( G @ H @ I )
& ( G @ I @ J ) )
=> ( G @ H @ J ) ) )
=> ( G @ E @ F ) ) )
& ! [E: a,F: a,G: a] :
( ( ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ E @ F ) )
& ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ F @ G ) ) )
=> ! [H: a > a > $o] :
( ( ! [I: a,J: a] :
( ( ( A @ I @ J )
| ( B @ I @ J ) )
=> ( H @ I @ J ) )
& ! [I: a,J: a,K: a] :
( ( ( H @ I @ J )
& ( H @ J @ K ) )
=> ( H @ I @ K ) ) )
=> ( H @ E @ G ) ) ) )
=> ! [E: a > a > $o] :
( ( ! [F: a,G: a] :
( ( ( A @ F @ G )
| ( B @ F @ G ) )
=> ( E @ F @ G ) )
& ! [F: a,G: a,H: a] :
( ( ( E @ F @ G )
& ( E @ G @ H ) )
=> ( E @ F @ H ) ) )
=> ( E @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,plain,
! [A: a > a > $o] :
( sk7
| ( sk25 @ A )
| ~ ( A @ ( sk28 @ A ) @ ( sk30 @ A ) )
| ( A @ sk22 @ sk23 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(69,plain,
! [A: a > a > $o] :
( sk7
| ( sk25 @ A )
| ~ ( A @ ( sk28 @ A ) @ ( sk30 @ A ) )
| ( A @ sk22 @ sk23 )
| sk6 ),
inference(simp,[status(thm)],[39]) ).
thf(21,plain,
! [A: a > a > $o] :
( ~ sk6
| ( sk38 @ A )
| ( A @ ( sk41 @ A ) @ ( sk42 @ A ) )
| ( A @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(58,plain,
! [A: a > a > $o] :
( ~ sk6
| ( sk38 @ A )
| ( A @ ( sk41 @ A ) @ ( sk42 @ A ) )
| ( A @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[21]) ).
thf(5284,plain,
! [A: a > a > $o] :
( ~ sk6
| ( sk38 @ A )
| ( A @ sk3 @ sk4 )
| ( ( A @ ( sk41 @ A ) @ ( sk42 @ A ) )
!= ~ sk6 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[58]) ).
thf(5329,plain,
( ~ sk6
| ( sk38
@ ^ [A: a,B: a] : ~ sk6 )
| ~ sk6 ),
inference(pre_uni,[status(thm)],[5284:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ~ ( sk6 ) ))]]) ).
thf(5550,plain,
( ~ sk6
| ( sk38
@ ^ [A: a,B: a] : ~ sk6 )
| ~ sk6 ),
inference(cnf,[status(esa)],[5329]) ).
thf(5551,plain,
( ~ sk6
| ( sk38
@ ^ [A: a,B: a] : ~ sk6 ) ),
inference(simp,[status(thm)],[5550]) ).
thf(28,plain,
! [A: a > a > $o] :
( ~ sk6
| ~ ( A @ ( sk39 @ A ) @ ( sk40 @ A ) )
| ~ ( sk38 @ A )
| ( A @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(60,plain,
! [A: a > a > $o] :
( ~ sk6
| ~ ( A @ ( sk39 @ A ) @ ( sk40 @ A ) )
| ~ ( sk38 @ A )
| ( A @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[28]) ).
thf(92,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk1 ) @ ( sk40 @ sk1 ) )
| ~ ( sk38 @ sk1 )
| ( sk1 @ sk3 @ sk4 ) ),
inference(prim_subst,[status(thm)],[60:[bind(A,$thf( sk1 ))]]) ).
thf(20,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk5 @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(32,plain,
~ ( sk5 @ sk3 @ sk4 ),
inference(cnf,[status(esa)],[3]) ).
thf(77,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[20,32]) ).
thf(78,plain,
~ ( sk1 @ sk3 @ sk4 ),
inference(pattern_uni,[status(thm)],[77:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(218,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk1 ) @ ( sk40 @ sk1 ) )
| ~ ( sk38 @ sk1 )
| $false ),
inference(rewrite,[status(thm)],[92,78]) ).
thf(219,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk1 ) @ ( sk40 @ sk1 ) )
| ~ ( sk38 @ sk1 ) ),
inference(simp,[status(thm)],[218]) ).
thf(5660,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk1 ) @ ( sk40 @ sk1 ) )
| ( ( sk38 @ sk1 )
!= ( sk38
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[5551,219]) ).
thf(5693,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk1 ) @ ( sk40 @ sk1 ) )
| ( sk1
!= ( ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[5660]) ).
thf(5818,plain,
( ( ( sk1 @ sk46 @ sk47 )
!= ~ sk6 )
| ~ sk6
| ~ ( sk1 @ ( sk39 @ sk1 ) @ ( sk40 @ sk1 ) ) ),
inference(func_ext,[status(esa)],[5693]) ).
thf(6129,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk1 ) @ ( sk40 @ sk1 ) )
| ( sk1 @ sk46 @ sk47 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[5818]) ).
thf(6166,plain,
( ~ sk6
| ( sk1 @ sk46 @ sk47 )
| ~ ( sk1 @ ( sk39 @ sk1 ) @ ( sk40 @ sk1 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[6129]) ).
thf(6167,plain,
( ~ sk6
| ( sk1 @ sk46 @ sk47 )
| ~ ( sk1 @ ( sk39 @ sk1 ) @ ( sk40 @ sk1 ) ) ),
inference(simp,[status(thm)],[6166]) ).
thf(27,plain,
! [C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ( sk5 @ A @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(67,plain,
! [C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ( sk5 @ A @ C ) ),
inference(simp,[status(thm)],[27]) ).
thf(314,plain,
! [C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ( ( sk5 @ A @ C )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[67,32]) ).
thf(315,plain,
! [A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[314:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(329,plain,
! [A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ sk4 ) ),
inference(simp,[status(thm)],[315]) ).
thf(346,plain,
! [A: a] :
( ~ ( sk5 @ sk3 @ A )
| ( ( sk5 @ A @ sk4 )
!= ( sk5 @ sk3 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[329]) ).
thf(349,plain,
! [A: a] :
( ~ ( sk5 @ sk3 @ A )
| ( A != sk3 )
| ( sk4 != A ) ),
inference(simp,[status(thm)],[346]) ).
thf(355,plain,
( ~ ( sk5 @ sk3 @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[349]) ).
thf(357,plain,
! [C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ C )
!= ( sk5 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[67,355]) ).
thf(358,plain,
! [A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(365,plain,
! [A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[358]) ).
thf(31,plain,
! [A: a > a > $o] :
( ~ sk6
| ( sk1 @ ( sk39 @ A ) @ ( sk40 @ A ) )
| ( sk2 @ ( sk39 @ A ) @ ( sk40 @ A ) )
| ~ ( sk38 @ A )
| ( A @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(71,plain,
! [A: a > a > $o] :
( ~ sk6
| ( sk1 @ ( sk39 @ A ) @ ( sk40 @ A ) )
| ( sk2 @ ( sk39 @ A ) @ ( sk40 @ A ) )
| ~ ( sk38 @ A )
| ( A @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[31]) ).
thf(12466,plain,
! [A: a > a > $o] :
( ~ sk6
| ( sk1 @ ( sk39 @ A ) @ ( sk40 @ A ) )
| ( sk2 @ ( sk39 @ A ) @ ( sk40 @ A ) )
| ( A @ sk3 @ sk4 )
| ( ( sk38
@ ^ [B: a,C: a] : ~ sk6 )
!= ( sk38 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5551,71]) ).
thf(12467,plain,
( ~ sk6
| ( sk1
@ ( sk39
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk40
@ ^ [A: a,B: a] : ~ sk6 ) )
| ( sk2
@ ( sk39
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk40
@ ^ [A: a,B: a] : ~ sk6 ) )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[12466:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ~ ( sk6 ) ))]]) ).
thf(12720,plain,
( ~ sk6
| ( sk2
@ ( sk39
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk40
@ ^ [A: a,B: a] : ~ sk6 ) )
| ( sk1
@ ( sk39
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk40
@ ^ [A: a,B: a] : ~ sk6 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[12467]) ).
thf(12721,plain,
( ~ sk6
| ( sk2
@ ( sk39
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk40
@ ^ [A: a,B: a] : ~ sk6 ) )
| ( sk1
@ ( sk39
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk40
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[12720]) ).
thf(5303,plain,
( ~ sk6
| ( sk38
@ ^ [A: a,B: a] : $false )
| $false
| $false ),
inference(prim_subst,[status(thm)],[58:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(5529,plain,
( ~ sk6
| ( sk38
@ ^ [A: a,B: a] : $false ) ),
inference(simp,[status(thm)],[5303]) ).
thf(101,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk2 ) @ ( sk40 @ sk2 ) )
| ~ ( sk38 @ sk2 )
| ( sk2 @ sk3 @ sk4 ) ),
inference(prim_subst,[status(thm)],[60:[bind(A,$thf( sk2 ))]]) ).
thf(23,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk5 @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(79,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[23,32]) ).
thf(80,plain,
~ ( sk2 @ sk3 @ sk4 ),
inference(pattern_uni,[status(thm)],[79:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(18012,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk2 ) @ ( sk40 @ sk2 ) )
| ~ ( sk38 @ sk2 )
| $false ),
inference(rewrite,[status(thm)],[101,80]) ).
thf(18013,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk2 ) @ ( sk40 @ sk2 ) )
| ~ ( sk38 @ sk2 ) ),
inference(simp,[status(thm)],[18012]) ).
thf(18015,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk2 ) @ ( sk40 @ sk2 ) )
| ( ( sk38 @ sk2 )
!= ( sk38
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[5529,18013]) ).
thf(18073,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk2 ) @ ( sk40 @ sk2 ) )
| ( sk2
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[18015]) ).
thf(18107,plain,
( ( sk2 @ sk60 @ sk61 )
| ~ sk6
| ~ ( sk2 @ ( sk39 @ sk2 ) @ ( sk40 @ sk2 ) ) ),
inference(func_ext,[status(esa)],[18073]) ).
thf(668,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[23,365]) ).
thf(669,plain,
! [A: a] :
( ~ ( sk2 @ A @ sk3 )
| ~ ( sk5 @ sk3 @ A )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[668:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(922,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)],[20,669]) ).
thf(923,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[922:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(941,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[923]) ).
thf(342,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ C @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,329]) ).
thf(343,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[342:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(352,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ sk4 ) ),
inference(simp,[status(thm)],[343]) ).
thf(100,plain,
! [B: a > a > $o,A: a > a > $o] :
( ~ sk6
| ~ ( ( A
@ ( sk39
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) )
| ( B
@ ( sk39
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) ) )
| ~ ( sk38
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
| ( A @ sk3 @ sk4 )
| ( B @ sk3 @ sk4 ) ),
inference(prim_subst,[status(thm)],[60:[bind(A,$thf( ^ [D: a] : ^ [E: a] : ( ( B @ D @ E ) | ( C @ D @ E ) ) ))]]) ).
thf(113,plain,
! [B: a > a > $o,A: a > a > $o] :
( ( A @ sk3 @ sk4 )
| ( B @ sk3 @ sk4 )
| ~ ( sk38
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
| ~ ( A
@ ( sk39
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[100]) ).
thf(115,plain,
! [B: a > a > $o,A: a > a > $o] :
( ( A @ sk3 @ sk4 )
| ( B @ sk3 @ sk4 )
| ~ ( sk38
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
| ~ ( A
@ ( sk39
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) )
| ~ sk6 ),
inference(simp,[status(thm)],[113]) ).
thf(307,plain,
! [E: a,D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ C @ D )
| ( sk5 @ C @ E )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[23,67]) ).
thf(308,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ C @ A )
| ( sk5 @ C @ B ) ),
inference(pattern_uni,[status(thm)],[307:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(82,plain,
! [C: a > a > $o,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ sk6
| ~ ( sk38 @ C )
| ( C @ sk3 @ sk4 )
| ( ( sk5 @ A @ B )
!= ( C @ ( sk39 @ C ) @ ( sk40 @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,60]) ).
thf(108,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk1
@ ( A
@ ( sk39
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk39
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ sk6
| ~ ( sk38
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk5 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) ) ),
inference(pre_uni,[status(thm)],[82:[bind(A,$thf( D @ ( sk39 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) @ ( sk40 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) )),bind(B,$thf( E @ ( sk39 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) @ ( sk40 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) )),bind(C,$thf( ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ))]]) ).
thf(120,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk1
@ ( A
@ ( sk39
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk39
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ sk6
| ~ ( sk38
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk5 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(27463,plain,
! [E: a,D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ D )
| ( sk5 @ E @ D )
| ( ( sk5 @ A @ B )
!= ( sk5 @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,308]) ).
thf(27464,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ C )
| ( sk5 @ A @ C ) ),
inference(pattern_uni,[status(thm)],[27463:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(27562,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ C )
| ( sk5 @ A @ C ) ),
inference(simp,[status(thm)],[27464]) ).
thf(29474,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk5 @ A @ C )
| ( ( sk2 @ B @ C )
!= ( sk2 @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[27562]) ).
thf(29514,plain,
! [A: a] :
( ~ ( sk2 @ A @ A )
| ( sk5 @ A @ A ) ),
inference(pattern_uni,[status(thm)],[29474:[bind(A,$thf( C )),bind(B,$thf( C ))]]) ).
thf(29584,plain,
! [A: a] :
( ~ ( sk2 @ A @ A )
| ( sk5 @ A @ A ) ),
inference(simp,[status(thm)],[29514]) ).
thf(93,plain,
( ~ sk6
| ~ ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk38 @ sk5 )
| ( sk5 @ sk3 @ sk4 ) ),
inference(prim_subst,[status(thm)],[60:[bind(A,$thf( sk5 ))]]) ).
thf(17274,plain,
( ~ sk6
| ~ ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk38 @ sk5 )
| $false ),
inference(rewrite,[status(thm)],[93,32]) ).
thf(17275,plain,
( ~ sk6
| ~ ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk38 @ sk5 ) ),
inference(simp,[status(thm)],[17274]) ).
thf(25,plain,
! [A: a > a > $o] :
( ~ sk10
| ( sk2 @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( A @ ( sk19 @ A ) @ ( sk20 @ A ) )
| ( A @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(56,plain,
! [A: a > a > $o] :
( ~ sk10
| ( sk2 @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( A @ ( sk19 @ A ) @ ( sk20 @ A ) )
| ( A @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[25]) ).
thf(340,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[23,329]) ).
thf(341,plain,
! [A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk5 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[340:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(370,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)],[67,341]) ).
thf(371,plain,
! [B: a,A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[370:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(380,plain,
! [B: a,A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[371]) ).
thf(2638,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)],[20,380]) ).
thf(2639,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2638:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2686,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[2639]) ).
thf(17323,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ sk6
| ~ ( sk38 @ sk5 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,17275]) ).
thf(17324,plain,
( ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6
| ~ ( sk38 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[17323:[bind(A,$thf( sk39 @ sk5 )),bind(B,$thf( sk40 @ sk5 ))]]) ).
thf(17467,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( ( sk38 @ sk5 )
!= ( sk38
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[5551,17324]) ).
thf(17513,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk5
!= ( ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[17467]) ).
thf(17946,plain,
( ( ( sk5 @ sk58 @ sk59 )
!= ~ sk6 )
| ~ sk6
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[17513]) ).
thf(21350,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk5 @ sk58 @ sk59 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[17946]) ).
thf(21434,plain,
( ~ sk6
| ( sk5 @ sk58 @ sk59 )
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[21350]) ).
thf(21435,plain,
( ~ sk6
| ( sk5 @ sk58 @ sk59 )
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ),
inference(simp,[status(thm)],[21434]) ).
thf(348,plain,
! [A: a] :
( ~ ( sk5 @ sk3 @ A )
| ( ( sk5 @ A @ sk4 )
!= ( sk5 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[346]) ).
thf(792,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( ( sk5 @ C @ sk4 )
!= ( sk5 @ sk3 @ C ) )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,348]) ).
thf(793,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( ( sk5 @ A @ sk4 )
!= ( sk5 @ sk3 @ A ) ) ),
inference(pattern_uni,[status(thm)],[792:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(814,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( ( sk5 @ A @ sk4 )
!= ( sk5 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[793]) ).
thf(11,plain,
! [A: a > a > $o] :
( sk7
| ( sk25 @ A )
| ( A @ ( sk29 @ A ) @ ( sk30 @ A ) )
| ( A @ sk22 @ sk23 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(49,plain,
! [A: a > a > $o] :
( sk7
| ( sk25 @ A )
| ( A @ ( sk29 @ A ) @ ( sk30 @ A ) )
| ( A @ sk22 @ sk23 )
| sk6 ),
inference(simp,[status(thm)],[11]) ).
thf(29,plain,
! [B: a,A: a] :
( sk7
| ~ ( sk2 @ A @ B )
| ( sk37 @ A @ B )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(57,plain,
! [B: a,A: a] :
( sk7
| ~ ( sk2 @ A @ B )
| ( sk37 @ A @ B )
| sk6 ),
inference(simp,[status(thm)],[29]) ).
thf(6,plain,
( sk7
| ~ ( sk37 @ sk22 @ sk24 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(4603,plain,
! [B: a,A: a] :
( sk7
| ~ ( sk2 @ A @ B )
| sk6
| ( ( sk37 @ A @ B )
!= ( sk37 @ sk22 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[57,6]) ).
thf(4604,plain,
( sk7
| ~ ( sk2 @ sk22 @ sk24 )
| sk6 ),
inference(pattern_uni,[status(thm)],[4603:[bind(A,$thf( sk22 )),bind(B,$thf( sk24 ))]]) ).
thf(4641,plain,
! [A: a > a > $o] :
( sk7
| ( sk25 @ A )
| ( A @ sk22 @ sk23 )
| sk6
| ( ( A @ ( sk29 @ A ) @ ( sk30 @ A ) )
!= ( sk2 @ sk22 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[49,4604]) ).
thf(4650,plain,
( sk7
| ( sk25
@ ^ [A: a,B: a] : ( sk2 @ sk22 @ sk24 ) )
| ( sk2 @ sk22 @ sk24 )
| sk6 ),
inference(pre_uni,[status(thm)],[4641:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk2 @ sk22 @ sk24 ) ))]]) ).
thf(17280,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ sk6
| ~ ( sk38 @ sk5 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,17275]) ).
thf(17281,plain,
( ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6
| ~ ( sk38 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[17280:[bind(A,$thf( sk39 @ sk5 )),bind(B,$thf( sk40 @ sk5 ))]]) ).
thf(17382,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( ( sk38 @ sk5 )
!= ( sk38
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[5551,17281]) ).
thf(17434,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk5
!= ( ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[17382]) ).
thf(17888,plain,
( ( ( sk5 @ sk56 @ sk57 )
!= ~ sk6 )
| ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[17434]) ).
thf(17291,plain,
( ~ sk6
| ~ ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( ( sk38 @ sk5 )
!= ( sk38
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[5551,17275]) ).
thf(17339,plain,
( ~ sk6
| ~ ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk5
!= ( ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[17291]) ).
thf(17822,plain,
( ( ( sk5 @ sk54 @ sk55 )
!= ~ sk6 )
| ~ sk6
| ~ ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[17339]) ).
thf(20103,plain,
( ~ sk6
| ~ ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk5 @ sk54 @ sk55 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[17822]) ).
thf(20191,plain,
( ~ sk6
| ( sk5 @ sk54 @ sk55 )
| ~ ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[20103]) ).
thf(20192,plain,
( ~ sk6
| ( sk5 @ sk54 @ sk55 )
| ~ ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ),
inference(simp,[status(thm)],[20191]) ).
thf(20208,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ sk6
| ( sk5 @ sk54 @ sk55 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,20192]) ).
thf(20209,plain,
( ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6
| ( sk5 @ sk54 @ sk55 ) ),
inference(pattern_uni,[status(thm)],[20208:[bind(A,$thf( sk39 @ sk5 )),bind(B,$thf( sk40 @ sk5 ))]]) ).
thf(15,plain,
! [A: a > a > $o] :
( ( sk1 @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ~ ( A @ ( sk13 @ A ) @ ( sk15 @ A ) )
| ( A @ sk8 @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(52,plain,
! [A: a > a > $o] :
( ( sk1 @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ~ ( A @ ( sk13 @ A ) @ ( sk15 @ A ) )
| ( A @ sk8 @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[15]) ).
thf(14,plain,
( ~ ( sk21 @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(17368,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( ( sk38 @ sk5 )
!= ( sk38
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[5529,17281]) ).
thf(17435,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk5
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[17368]) ).
thf(17611,plain,
( ( sk5 @ sk50 @ sk51 )
| ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[17435]) ).
thf(18242,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk1 @ sk3 @ A )
| ( ( sk5 @ sk50 @ sk51 )
!= ( sk5 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[17611,352]) ).
thf(18404,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk1 @ sk3 @ A )
| ( sk50 != A )
| ( sk51 != sk4 ) ),
inference(simp,[status(thm)],[18242]) ).
thf(18468,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk1 @ sk3 @ sk50 )
| ( sk51 != sk4 ) ),
inference(simp,[status(thm)],[18404]) ).
thf(344,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[20,329]) ).
thf(345,plain,
! [A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk5 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[344:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(522,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)],[67,345]) ).
thf(523,plain,
! [B: a,A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[522:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(541,plain,
! [B: a,A: a] :
( ~ ( sk5 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[523]) ).
thf(2731,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)],[23,541]) ).
thf(2732,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2731:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2755,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[2732]) ).
thf(334,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ~ ( sk5 @ sk3 @ D )
| ( ( sk5 @ A @ C )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[67,329]) ).
thf(335,plain,
! [B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk5 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[334:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( A ))]]) ).
thf(2443,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ D @ sk4 )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[20,335]) ).
thf(2444,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk5 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[2443:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(18296,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( ( sk5 @ sk50 @ sk51 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[17611,32]) ).
thf(18385,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk50 != sk3 )
| ( sk51 != sk4 ) ),
inference(simp,[status(thm)],[18296]) ).
thf(526,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,345]) ).
thf(527,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[526:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(542,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ sk4 ) ),
inference(simp,[status(thm)],[527]) ).
thf(17276,plain,
( ~ sk6
| ~ ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( ( sk38 @ sk5 )
!= ( sk38
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[5529,17275]) ).
thf(17349,plain,
( ~ sk6
| ~ ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk5
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[17276]) ).
thf(17545,plain,
( ( sk5 @ sk48 @ sk49 )
| ~ sk6
| ~ ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[17349]) ).
thf(12,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk21 @ A @ B )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(46,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk21 @ A @ B )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[12]) ).
thf(338,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ C @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,329]) ).
thf(339,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[338:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(351,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ sk4 ) ),
inference(simp,[status(thm)],[339]) ).
thf(543,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)],[67,351]) ).
thf(544,plain,
! [B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk2 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[543:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( A ))]]) ).
thf(2773,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)],[20,544]) ).
thf(2774,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk2 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[2773:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4897,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)],[20,2774]) ).
thf(4898,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[4897:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(4967,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(simp,[status(thm)],[4898]) ).
thf(13364,plain,
! [B: a,A: a] :
( ~ sk6
| ( sk1
@ ( sk39
@ ^ [C: a,D: a] : ~ sk6 )
@ ( sk40
@ ^ [C: a,D: a] : ~ sk6 ) )
| ( sk5 @ A @ B )
| ( ( sk2
@ ( sk39
@ ^ [C: a,D: a] : ~ sk6 )
@ ( sk40
@ ^ [C: a,D: a] : ~ sk6 ) )
!= ( sk2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12721,23]) ).
thf(13365,plain,
( ~ sk6
| ( sk1
@ ( sk39
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk40
@ ^ [A: a,B: a] : ~ sk6 ) )
| ( sk5
@ ( sk39
@ ^ [A: a,B: a] : ~ sk6 )
@ ( sk40
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[13364:[bind(A,$thf( sk39 @ ^ [C: a] : ^ [D: a] : ~ ( sk6 ) )),bind(B,$thf( sk40 @ ^ [C: a] : ^ [D: a] : ~ ( sk6 ) ))]]) ).
thf(5300,plain,
( ~ sk6
| ( sk38
@ ^ [A: a,B: a] : sk10 )
| sk10
| sk10 ),
inference(prim_subst,[status(thm)],[58:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk10 ))]]) ).
thf(5526,plain,
( ~ sk6
| ( sk38
@ ^ [A: a,B: a] : sk10 )
| sk10 ),
inference(simp,[status(thm)],[5300]) ).
thf(2733,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23,541]) ).
thf(2734,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ sk3 @ A )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2733:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4657,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,2734]) ).
thf(4658,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4657:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(4733,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[4658]) ).
thf(84,plain,
! [A: a > a > $o] :
( ~ sk6
| ~ ( sk38 @ A )
| ( A @ sk3 @ sk4 )
| ( ( A @ ( sk39 @ A ) @ ( sk40 @ A ) )
!= ( ~ ( A @ sk3 @ sk4 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[60]) ).
thf(106,plain,
! [A: a > a > $o] :
( ( A @ sk3 @ sk4 )
| ~ sk6
| ~ ( sk38 @ A )
| ( ( A @ ( sk39 @ A ) @ ( sk40 @ A ) )
!= ( ~ ( A @ sk3 @ sk4 ) ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(81,plain,
! [C: a > a > $o,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ sk6
| ~ ( sk38 @ C )
| ( C @ sk3 @ sk4 )
| ( ( sk5 @ A @ B )
!= ( C @ ( sk39 @ C ) @ ( sk40 @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,60]) ).
thf(109,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk2
@ ( A
@ ( sk39
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk39
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ sk6
| ~ ( sk38
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk5 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) ) ),
inference(pre_uni,[status(thm)],[81:[bind(A,$thf( D @ ( sk39 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) @ ( sk40 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) )),bind(B,$thf( E @ ( sk39 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) @ ( sk40 @ ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ) )),bind(C,$thf( ^ [F: a] : ^ [G: a] : ( sk5 @ ( D @ F @ G ) @ ( E @ F @ G ) ) ))]]) ).
thf(121,plain,
! [B: a > a > a,A: a > a > a] :
( ~ ( sk2
@ ( A
@ ( sk39
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk39
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ sk6
| ~ ( sk38
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk5 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(2470,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)],[23,335]) ).
thf(2471,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk5 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[2470:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(3020,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)],[20,2471]) ).
thf(3021,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[3020:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(3068,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(simp,[status(thm)],[3021]) ).
thf(38,plain,
! [A: a > a > $o] :
( ~ ( A @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ~ ( A @ ( sk13 @ A ) @ ( sk15 @ A ) )
| ( A @ sk8 @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(61,plain,
! [A: a > a > $o] :
( ~ ( A @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ~ ( A @ ( sk13 @ A ) @ ( sk15 @ A ) )
| ( A @ sk8 @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[38]) ).
thf(114,plain,
! [B: a > a > $o,A: a > a > $o] :
( ( A @ sk3 @ sk4 )
| ( B @ sk3 @ sk4 )
| ~ ( sk38
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
| ~ ( B
@ ( sk39
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[100]) ).
thf(116,plain,
! [B: a > a > $o,A: a > a > $o] :
( ( A @ sk3 @ sk4 )
| ( B @ sk3 @ sk4 )
| ~ ( sk38
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
| ~ ( B
@ ( sk39
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) )
| ~ sk6 ),
inference(simp,[status(thm)],[114]) ).
thf(311,plain,
! [E: a,D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ C @ D )
| ( sk5 @ C @ E )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[20,67]) ).
thf(312,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ C @ A )
| ( sk5 @ C @ B ) ),
inference(pattern_uni,[status(thm)],[311:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(36,plain,
! [A: a > a > $o] :
( ( sk1 @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( A @ ( sk13 @ A ) @ ( sk14 @ A ) )
| ( A @ sk8 @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(74,plain,
! [A: a > a > $o] :
( ( sk1 @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( A @ ( sk13 @ A ) @ ( sk14 @ A ) )
| ( A @ sk8 @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[36]) ).
thf(662,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[20,365]) ).
thf(663,plain,
! [A: a] :
( ~ ( sk1 @ A @ sk3 )
| ~ ( sk5 @ sk3 @ A )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[662:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(909,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)],[23,663]) ).
thf(910,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[909:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(920,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[910]) ).
thf(561,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ C )
| ~ ( sk1 @ sk3 @ D )
| ( ( sk5 @ A @ C )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[67,352]) ).
thf(562,plain,
! [B: a,A: a] :
( ~ ( sk5 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk1 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[561:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( A ))]]) ).
thf(2909,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ D @ sk4 )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23,562]) ).
thf(2910,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk1 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[2909:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(5304,plain,
( ~ sk6
| ( sk38
@ ^ [A: a,B: a] : sk7 )
| sk7
| sk7 ),
inference(prim_subst,[status(thm)],[58:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk7 ))]]) ).
thf(5530,plain,
( ~ sk6
| ( sk38
@ ^ [A: a,B: a] : sk7 )
| sk7 ),
inference(simp,[status(thm)],[5304]) ).
thf(374,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,341]) ).
thf(375,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[374:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(381,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ sk4 ) ),
inference(simp,[status(thm)],[375]) ).
thf(2640,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[20,380]) ).
thf(2641,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ sk3 @ A )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2640:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(103,plain,
! [A: a > a > a > a > $o] :
( ~ sk6
| ~ ( sk38
@ ( A
@ ( sk39
@ ^ [B: a,C: a] : ( sk38 @ ( A @ B @ C ) ) )
@ ( sk40
@ ^ [B: a,C: a] : ( sk38 @ ( A @ B @ C ) ) ) ) )
| ~ ( sk38
@ ^ [B: a,C: a] : ( sk38 @ ( A @ B @ C ) ) )
| ( sk38 @ ( A @ sk3 @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[60:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ( sk38 @ ( B @ C @ D ) ) ))]]) ).
thf(117,plain,
! [A: a > a > a > a > $o] :
( ~ sk6
| ~ ( sk38
@ ( A
@ ( sk39
@ ^ [B: a,C: a] : ( sk38 @ ( A @ B @ C ) ) )
@ ( sk40
@ ^ [B: a,C: a] : ( sk38 @ ( A @ B @ C ) ) ) ) )
| ~ ( sk38
@ ^ [B: a,C: a] : ( sk38 @ ( A @ B @ C ) ) )
| ( sk38 @ ( A @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(1512,plain,
( sk7
| ( sk25
@ ^ [A: a,B: a] : sk10 )
| sk10
| sk10
| sk6 ),
inference(prim_subst,[status(thm)],[49:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk10 ))]]) ).
thf(1666,plain,
( sk7
| ( sk25
@ ^ [A: a,B: a] : sk10 )
| sk10
| sk6 ),
inference(simp,[status(thm)],[1512]) ).
thf(16,plain,
! [A: a > a > $o] :
( ~ sk10
| ~ ( A @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( A @ ( sk19 @ A ) @ ( sk20 @ A ) )
| ( A @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(70,plain,
! [A: a > a > $o] :
( ~ sk10
| ~ ( A @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( A @ ( sk19 @ A ) @ ( sk20 @ A ) )
| ( A @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[16]) ).
thf(12430,plain,
! [A: a > a > $o] :
( ~ sk6
| ( sk1 @ ( sk39 @ A ) @ ( sk40 @ A ) )
| ( sk2 @ ( sk39 @ A ) @ ( sk40 @ A ) )
| ( A @ sk3 @ sk4 )
| ( ( sk38
@ ^ [B: a,C: a] : $false )
!= ( sk38 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5529,71]) ).
thf(12431,plain,
( ~ sk6
| ( sk1
@ ( sk39
@ ^ [A: a,B: a] : $false )
@ ( sk40
@ ^ [A: a,B: a] : $false ) )
| ( sk2
@ ( sk39
@ ^ [A: a,B: a] : $false )
@ ( sk40
@ ^ [A: a,B: a] : $false ) )
| $false ),
inference(pattern_uni,[status(thm)],[12430:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(12715,plain,
( ~ sk6
| ( sk1
@ ( sk39
@ ^ [A: a,B: a] : $false )
@ ( sk40
@ ^ [A: a,B: a] : $false ) )
| ( sk2
@ ( sk39
@ ^ [A: a,B: a] : $false )
@ ( sk40
@ ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[12431]) ).
thf(8,plain,
! [A: a > a > $o] :
( ~ sk10
| ( sk2 @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( A @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ( A @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(50,plain,
! [A: a > a > $o] :
( ~ sk10
| ( sk2 @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( A @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ( A @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[8]) ).
thf(1902,plain,
( ~ sk10
| ( sk2
@ ( sk16
@ ^ [A: a,B: a] : sk6 )
@ ( sk17
@ ^ [A: a,B: a] : sk6 ) )
| sk6
| sk6
| ~ sk7
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk6 ))]]) ).
thf(2032,plain,
( ~ sk10
| ( sk2
@ ( sk16
@ ^ [A: a,B: a] : sk6 )
@ ( sk17
@ ^ [A: a,B: a] : sk6 ) )
| sk6
| ~ sk7 ),
inference(simp,[status(thm)],[1902]) ).
thf(2775,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)],[20,544]) ).
thf(2776,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2775:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2826,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2776]) ).
thf(2797,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)],[23,544]) ).
thf(2798,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk2 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[2797:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4981,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)],[20,2798]) ).
thf(4982,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[4981:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(5066,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(simp,[status(thm)],[4982]) ).
thf(360,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[23,355]) ).
thf(361,plain,
( ~ ( sk2 @ sk3 @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[360:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(34,plain,
! [A: a > a > $o] :
( ( sk1 @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( A @ ( sk14 @ A ) @ ( sk15 @ A ) )
| ( A @ sk8 @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(65,plain,
! [A: a > a > $o] :
( ( sk1 @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( A @ ( sk14 @ A ) @ ( sk15 @ A ) )
| ( A @ sk8 @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[34]) ).
thf(18203,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( sk5 @ sk48 @ sk49 )
| ~ sk6
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,17545]) ).
thf(18204,plain,
( ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk5 @ sk48 @ sk49 )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[18203:[bind(A,$thf( sk39 @ sk5 )),bind(B,$thf( sk40 @ sk5 ))]]) ).
thf(2445,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ C @ D )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[20,335]) ).
thf(2446,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2445:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2498,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2446]) ).
thf(42,plain,
! [A: a > a > $o] :
( sk7
| ~ ( A @ ( sk26 @ A ) @ ( sk27 @ A ) )
| ~ ( sk25 @ A )
| ( A @ sk22 @ sk23 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(53,plain,
! [A: a > a > $o] :
( sk7
| ~ ( A @ ( sk26 @ A ) @ ( sk27 @ A ) )
| ~ ( sk25 @ A )
| ( A @ sk22 @ sk23 )
| sk6 ),
inference(simp,[status(thm)],[42]) ).
thf(17453,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( ( sk38 @ sk5 )
!= ( sk38
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[5529,17324]) ).
thf(17511,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk5
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[17453]) ).
thf(17669,plain,
( ( sk5 @ sk52 @ sk53 )
| ~ sk6
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[17511]) ).
thf(18515,plain,
! [A: a] :
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk5 @ sk3 @ A )
| ( ( sk5 @ sk52 @ sk53 )
!= ( sk5 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[17669,348]) ).
thf(18691,plain,
! [A: a] :
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk5 @ sk3 @ A )
| ( sk52 != A )
| ( sk53 != sk4 ) ),
inference(simp,[status(thm)],[18515]) ).
thf(18701,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk5 @ sk3 @ sk52 )
| ( sk53 != sk4 ) ),
inference(simp,[status(thm)],[18691]) ).
thf(309,plain,
! [E: a,D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ D @ E )
| ( sk5 @ C @ E )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[20,67]) ).
thf(310,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ B @ C )
| ( sk5 @ A @ C ) ),
inference(pattern_uni,[status(thm)],[309:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(328,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ B @ C )
| ( sk5 @ A @ C ) ),
inference(simp,[status(thm)],[310]) ).
thf(1503,plain,
( sk7
| ( sk25
@ ^ [A: a,B: a] : $false )
| $false
| $false
| sk6 ),
inference(prim_subst,[status(thm)],[49:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(1659,plain,
( sk7
| ( sk25
@ ^ [A: a,B: a] : $false )
| sk6 ),
inference(simp,[status(thm)],[1503]) ).
thf(7,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk21 @ A @ B )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(68,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk21 @ A @ B )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[7]) ).
thf(10719,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ sk7
| sk6
| ( ( sk21 @ A @ B )
!= ( sk21 @ sk8 @ sk9 ) ) ),
inference(paramod_ordered,[status(thm)],[68,14]) ).
thf(10720,plain,
( ~ ( sk1 @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(pattern_uni,[status(thm)],[10719:[bind(A,$thf( sk8 )),bind(B,$thf( sk9 ))]]) ).
thf(18175,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk5 @ sk48 @ sk49 )
| ~ sk6
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,17545]) ).
thf(18176,plain,
( ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk5 @ sk48 @ sk49 )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[18175:[bind(A,$thf( sk39 @ sk5 )),bind(B,$thf( sk40 @ sk5 ))]]) ).
thf(4202,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,2641]) ).
thf(4203,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4202:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(4237,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[4203]) ).
thf(2953,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)],[20,2444]) ).
thf(2954,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2953:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(3005,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2954]) ).
thf(1426,plain,
! [A: a > a > $o] :
( sk7
| ( sk25 @ A )
| ( A @ sk22 @ sk23 )
| sk6
| ( ( A @ ( sk29 @ A ) @ ( sk30 @ A ) )
!= ( sk37 @ sk22 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[49,6]) ).
thf(1525,plain,
( sk7
| ( sk25
@ ^ [A: a,B: a] : ( sk37 @ sk22 @ sk24 ) )
| ( sk37 @ sk22 @ sk24 )
| sk6 ),
inference(pre_uni,[status(thm)],[1426:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk37 @ sk22 @ sk24 ) ))]]) ).
thf(7343,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)],[23,2910]) ).
thf(7344,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[7343:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(7407,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(simp,[status(thm)],[7344]) ).
thf(20240,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ sk6
| ( sk5 @ sk54 @ sk55 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,20192]) ).
thf(20241,plain,
( ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6
| ( sk5 @ sk54 @ sk55 ) ),
inference(pattern_uni,[status(thm)],[20240:[bind(A,$thf( sk39 @ sk5 )),bind(B,$thf( sk40 @ sk5 ))]]) ).
thf(2710,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)],[20,541]) ).
thf(2711,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ sk3 @ A )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2710:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4546,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)],[23,2711]) ).
thf(4547,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4546:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(4572,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[4547]) ).
thf(26,plain,
! [A: a > a > $o] :
( ~ sk10
| ~ ( A @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ~ ( A @ ( sk18 @ A ) @ ( sk20 @ A ) )
| ( A @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(73,plain,
! [A: a > a > $o] :
( ~ sk10
| ~ ( A @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ~ ( A @ ( sk18 @ A ) @ ( sk20 @ A ) )
| ( A @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[26]) ).
thf(20596,plain,
( ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6
| ( ( sk5 @ sk54 @ sk55 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[20209,32]) ).
thf(20730,plain,
( ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6
| ( sk54 != sk3 )
| ( sk55 != sk4 ) ),
inference(simp,[status(thm)],[20596]) ).
thf(4681,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,2734]) ).
thf(4682,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4681:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(4708,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[4682]) ).
thf(5,plain,
! [A: a > a > $o] :
( sk7
| ( sk31 @ A )
| ( A @ ( sk34 @ A ) @ ( sk35 @ A ) )
| ( A @ sk23 @ sk24 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(43,plain,
! [A: a > a > $o] :
( sk7
| ( sk31 @ A )
| ( A @ ( sk34 @ A ) @ ( sk35 @ A ) )
| ( A @ sk23 @ sk24 )
| sk6 ),
inference(simp,[status(thm)],[5]) ).
thf(152,plain,
( sk7
| ( sk31
@ ^ [A: a,B: a] : $false )
| $false
| $false
| sk6 ),
inference(prim_subst,[status(thm)],[43:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(180,plain,
( sk7
| ( sk31
@ ^ [A: a,B: a] : $false )
| sk6 ),
inference(simp,[status(thm)],[152]) ).
thf(9,plain,
! [A: a > a > $o] :
( ~ ( A @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( A @ ( sk14 @ A ) @ ( sk15 @ A ) )
| ( A @ sk8 @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(45,plain,
! [A: a > a > $o] :
( ~ ( A @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( A @ ( sk14 @ A ) @ ( sk15 @ A ) )
| ( A @ sk8 @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[9]) ).
thf(29682,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ A )
| ( ( sk5 @ B @ sk4 )
!= ( sk5 @ sk3 @ B ) )
| ( ( sk5 @ A @ A )
!= ( sk5 @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29584,348]) ).
thf(29683,plain,
( ~ ( sk2 @ sk3 @ sk3 )
| ( ( sk5 @ sk3 @ sk4 )
!= ( sk5 @ sk3 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[29682:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(30470,plain,
( ~ ( sk2 @ sk3 @ sk3 )
| ( sk5 @ sk3 @ sk3 ) ),
inference(rewrite,[status(thm)],[29683,32]) ).
thf(17,plain,
! [A: a > a > $o] :
( ~ sk6
| ( sk38 @ A )
| ( A @ ( sk42 @ A ) @ ( sk43 @ A ) )
| ( A @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(64,plain,
! [A: a > a > $o] :
( ~ sk6
| ( sk38 @ A )
| ( A @ ( sk42 @ A ) @ ( sk43 @ A ) )
| ( A @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[17]) ).
thf(144,plain,
( sk7
| ( sk31
@ ^ [A: a,B: a] : sk7 )
| sk7
| sk7
| sk6 ),
inference(prim_subst,[status(thm)],[43:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk7 ))]]) ).
thf(176,plain,
( sk7
| ( sk31
@ ^ [A: a,B: a] : sk7 )
| sk6 ),
inference(simp,[status(thm)],[144]) ).
thf(10,plain,
! [A: a > a > $o] :
( sk7
| ( sk31 @ A )
| ~ ( A @ ( sk34 @ A ) @ ( sk36 @ A ) )
| ( A @ sk23 @ sk24 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(44,plain,
! [A: a > a > $o] :
( sk7
| ( sk31 @ A )
| ~ ( A @ ( sk34 @ A ) @ ( sk36 @ A ) )
| ( A @ sk23 @ sk24 )
| sk6 ),
inference(simp,[status(thm)],[10]) ).
thf(203,plain,
! [A: a > a > $o] :
( sk7
| ( sk31 @ A )
| ( A @ sk23 @ sk24 )
| sk6
| ( ( A @ ( sk34 @ A ) @ ( sk35 @ A ) )
!= ( sk37 @ sk22 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[43,6]) ).
thf(204,plain,
( sk7
| ( sk31
@ ^ [A: a,B: a] : ( sk37 @ sk22 @ sk24 ) )
| ( sk37 @ sk22 @ sk24 )
| sk6 ),
inference(pre_uni,[status(thm)],[203:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk37 @ sk22 @ sk24 ) ))]]) ).
thf(33,plain,
! [A: a > a > $o] :
( ~ sk10
| ( sk2 @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ~ ( A @ ( sk18 @ A ) @ ( sk20 @ A ) )
| ( A @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(59,plain,
! [A: a > a > $o] :
( ~ sk10
| ( sk2 @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ~ ( A @ ( sk18 @ A ) @ ( sk20 @ A ) )
| ( A @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[33]) ).
thf(104,plain,
! [B: a > a > a,A: a > a > a] :
( ~ sk6
| ~ ( sk5
@ ( A
@ ( sk39
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk39
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk38
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk5 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[60:[bind(A,$thf( ^ [D: a] : ^ [E: a] : ( sk5 @ ( B @ D @ E ) @ ( C @ D @ E ) ) ))]]) ).
thf(118,plain,
! [B: a > a > a,A: a > a > a] :
( ~ sk6
| ~ ( sk5
@ ( A
@ ( sk39
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk39
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk38
@ ^ [C: a,D: a] : ( sk5 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk5 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(5006,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)],[23,2798]) ).
thf(5007,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[5006:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(5039,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(simp,[status(thm)],[5007]) ).
thf(930,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)],[23,669]) ).
thf(931,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[930:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(936,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[931]) ).
thf(18355,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk2 @ sk3 @ A )
| ( ( sk5 @ sk50 @ sk51 )
!= ( sk5 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[17611,351]) ).
thf(18423,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk2 @ sk3 @ A )
| ( sk50 != A )
| ( sk51 != sk4 ) ),
inference(simp,[status(thm)],[18355]) ).
thf(18484,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk2 @ sk3 @ sk50 )
| ( sk51 != sk4 ) ),
inference(simp,[status(thm)],[18423]) ).
thf(21725,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( ( sk5 @ sk58 @ sk59 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[21435,32]) ).
thf(21859,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk58 != sk3 )
| ( sk59 != sk4 ) ),
inference(simp,[status(thm)],[21725]) ).
thf(18279,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk5 @ A @ sk4 )
| ( ( sk5 @ sk50 @ sk51 )
!= ( sk5 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17611,329]) ).
thf(18376,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk5 @ A @ sk4 )
| ( sk50 != sk3 )
| ( sk51 != A ) ),
inference(simp,[status(thm)],[18279]) ).
thf(18444,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk5 @ sk51 @ sk4 )
| ( sk50 != sk3 ) ),
inference(simp,[status(thm)],[18376]) ).
thf(20345,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk5 @ sk56 @ sk57 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[17888]) ).
thf(20425,plain,
( ~ sk6
| ( sk5 @ sk56 @ sk57 )
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[20345]) ).
thf(20426,plain,
( ~ sk6
| ( sk5 @ sk56 @ sk57 )
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ),
inference(simp,[status(thm)],[20425]) ).
thf(376,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,341]) ).
thf(377,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[376:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(382,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ sk4 ) ),
inference(simp,[status(thm)],[377]) ).
thf(24,plain,
! [C: a,B: a,A: a] :
( sk7
| ~ ( sk37 @ A @ B )
| ~ ( sk37 @ B @ C )
| ( sk37 @ A @ C )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(54,plain,
! [C: a,B: a,A: a] :
( sk7
| ~ ( sk37 @ A @ B )
| ~ ( sk37 @ B @ C )
| ( sk37 @ A @ C )
| sk6 ),
inference(simp,[status(thm)],[24]) ).
thf(157,plain,
( sk7
| ( sk31
@ ^ [A: a,B: a] : sk10 )
| sk10
| sk10
| sk6 ),
inference(prim_subst,[status(thm)],[43:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk10 ))]]) ).
thf(187,plain,
( sk7
| ( sk31
@ ^ [A: a,B: a] : sk10 )
| sk10
| sk6 ),
inference(simp,[status(thm)],[157]) ).
thf(666,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,365]) ).
thf(667,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[666:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(681,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[667]) ).
thf(18029,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk2 ) @ ( sk40 @ sk2 ) )
| ( ( sk38 @ sk2 )
!= ( sk38
@ ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[5551,18013]) ).
thf(18092,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk2 ) @ ( sk40 @ sk2 ) )
| ( sk2
!= ( ^ [A: a,B: a] : ~ sk6 ) ) ),
inference(simp,[status(thm)],[18029]) ).
thf(19,plain,
! [A: a > a > $o] :
( sk7
| ~ ( A @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( A @ sk23 @ sk24 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(76,plain,
! [A: a > a > $o] :
( sk7
| ~ ( A @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( A @ sk23 @ sk24 )
| sk6 ),
inference(simp,[status(thm)],[19]) ).
thf(98,plain,
( ~ sk6
| ~ ( sk37 @ ( sk39 @ sk37 ) @ ( sk40 @ sk37 ) )
| ~ ( sk38 @ sk37 )
| ( sk37 @ sk3 @ sk4 ) ),
inference(prim_subst,[status(thm)],[60:[bind(A,$thf( sk37 ))]]) ).
thf(19213,plain,
( ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6
| ( ( sk5 @ sk48 @ sk49 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18176,32]) ).
thf(19289,plain,
( ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6
| ( sk48 != sk3 )
| ( sk49 != sk4 ) ),
inference(simp,[status(thm)],[19213]) ).
thf(3045,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)],[23,2471]) ).
thf(3046,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[3045:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(3073,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(simp,[status(thm)],[3046]) ).
thf(22,plain,
! [A: a > a > $o] :
( sk7
| ( sk1 @ ( sk26 @ A ) @ ( sk27 @ A ) )
| ( sk2 @ ( sk26 @ A ) @ ( sk27 @ A ) )
| ~ ( sk25 @ A )
| ( A @ sk22 @ sk23 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(66,plain,
! [A: a > a > $o] :
( sk7
| ( sk1 @ ( sk26 @ A ) @ ( sk27 @ A ) )
| ( sk2 @ ( sk26 @ A ) @ ( sk27 @ A ) )
| ~ ( sk25 @ A )
| ( A @ sk22 @ sk23 )
| sk6 ),
inference(simp,[status(thm)],[22]) ).
thf(20864,plain,
( ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6
| ( ( sk5 @ sk54 @ sk55 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[20241,32]) ).
thf(20999,plain,
( ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6
| ( sk54 != sk3 )
| ( sk55 != sk4 ) ),
inference(simp,[status(thm)],[20864]) ).
thf(2886,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ D @ sk4 )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[20,562]) ).
thf(2887,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ B @ sk4 )
| ~ ( sk1 @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[2886:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(6612,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[23,2887]) ).
thf(6613,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[6612:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(6645,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(simp,[status(thm)],[6613]) ).
thf(2911,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ C @ D )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[23,562]) ).
thf(2912,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2911:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2931,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2912]) ).
thf(18280,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk5 @ sk3 @ A )
| ( ( sk5 @ sk50 @ sk51 )
!= ( sk5 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[17611,329]) ).
thf(18402,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk5 @ sk3 @ A )
| ( sk50 != A )
| ( sk51 != sk4 ) ),
inference(simp,[status(thm)],[18280]) ).
thf(18466,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk5 @ sk3 @ sk50 )
| ( sk51 != sk4 ) ),
inference(simp,[status(thm)],[18402]) ).
thf(6590,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[20,2887]) ).
thf(6591,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[6590:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(6672,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(simp,[status(thm)],[6591]) ).
thf(2664,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ sk3 @ C )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23,380]) ).
thf(2665,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ sk3 @ A )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2664:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(7317,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk1 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[20,2910]) ).
thf(7318,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[7317:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(7403,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk2 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(simp,[status(thm)],[7318]) ).
thf(660,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk5 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,365]) ).
thf(661,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[660:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(680,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[661]) ).
thf(4288,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)],[23,2665]) ).
thf(4289,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4288:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(4319,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[4289]) ).
thf(5608,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk1 ) @ ( sk40 @ sk1 ) )
| ( ( sk38 @ sk1 )
!= ( sk38
@ ^ [A: a,B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[5529,219]) ).
thf(5632,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk1 ) @ ( sk40 @ sk1 ) )
| ( sk1
!= ( ^ [A: a,B: a] : $false ) ) ),
inference(simp,[status(thm)],[5608]) ).
thf(5785,plain,
( ( sk1 @ sk44 @ sk45 )
| ~ sk6
| ~ ( sk1 @ ( sk39 @ sk1 ) @ ( sk40 @ sk1 ) ) ),
inference(func_ext,[status(esa)],[5632]) ).
thf(97,plain,
! [B: a > a > a,A: a > a > a] :
( ~ sk6
| ~ ( sk21
@ ( A
@ ( sk39
@ ^ [C: a,D: a] : ( sk21 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk21 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk39
@ ^ [C: a,D: a] : ( sk21 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk21 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk38
@ ^ [C: a,D: a] : ( sk21 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk21 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[60:[bind(A,$thf( ^ [D: a] : ^ [E: a] : ( sk21 @ ( B @ D @ E ) @ ( C @ D @ E ) ) ))]]) ).
thf(112,plain,
! [B: a > a > a,A: a > a > a] :
( ~ sk6
| ~ ( sk21
@ ( A
@ ( sk39
@ ^ [C: a,D: a] : ( sk21 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk21 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk39
@ ^ [C: a,D: a] : ( sk21 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk21 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk38
@ ^ [C: a,D: a] : ( sk21 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk21 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(783,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)],[20,348]) ).
thf(784,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( ( sk5 @ A @ sk4 )
!= ( sk5 @ sk3 @ A ) ) ),
inference(pattern_uni,[status(thm)],[783:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(812,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( ( sk5 @ A @ sk4 )
!= ( sk5 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[784]) ).
thf(18551,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( ( sk5 @ sk52 @ sk53 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[17669,32]) ).
thf(18676,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk52 != sk3 )
| ( sk53 != sk4 ) ),
inference(simp,[status(thm)],[18551]) ).
thf(18,plain,
! [A: a > a > $o] :
( ~ sk10
| ~ ( A @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( A @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ( A @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(48,plain,
! [A: a > a > $o] :
( ~ sk10
| ~ ( A @ ( sk16 @ A ) @ ( sk17 @ A ) )
| ( A @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ( A @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[18]) ).
thf(41,plain,
! [A: a > a > $o] :
( sk7
| ( sk31 @ A )
| ( A @ ( sk35 @ A ) @ ( sk36 @ A ) )
| ( A @ sk23 @ sk24 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(63,plain,
! [A: a > a > $o] :
( sk7
| ( sk31 @ A )
| ( A @ ( sk35 @ A ) @ ( sk36 @ A ) )
| ( A @ sk23 @ sk24 )
| sk6 ),
inference(simp,[status(thm)],[41]) ).
thf(305,plain,
! [E: a,D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ D @ E )
| ( sk5 @ C @ E )
| ( ( sk5 @ A @ B )
!= ( sk5 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23,67]) ).
thf(306,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ B @ C )
| ( sk5 @ A @ C ) ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(327,plain,
! [C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ B @ C )
| ( sk5 @ A @ C ) ),
inference(simp,[status(thm)],[306]) ).
thf(1490,plain,
! [A: a > a > $o] :
( sk7
| ( sk25 @ A )
| ( A @ sk22 @ sk23 )
| sk6
| ( ( A @ ( sk29 @ A ) @ ( sk30 @ A ) )
!= sk7 )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[49]) ).
thf(1595,plain,
( sk7
| ( sk25
@ ^ [A: a,B: a] : sk7 )
| sk7
| sk6 ),
inference(pre_uni,[status(thm)],[1490:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk7 ))]]) ).
thf(1647,plain,
( sk7
| ( sk25
@ ^ [A: a,B: a] : sk7 )
| sk6 ),
inference(simp,[status(thm)],[1595]) ).
thf(12840,plain,
! [B: a,A: a] :
( ~ sk6
| ( sk1
@ ( sk39
@ ^ [C: a,D: a] : $false )
@ ( sk40
@ ^ [C: a,D: a] : $false ) )
| ( sk5 @ A @ B )
| ( ( sk2
@ ( sk39
@ ^ [C: a,D: a] : $false )
@ ( sk40
@ ^ [C: a,D: a] : $false ) )
!= ( sk2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12715,23]) ).
thf(12841,plain,
( ~ sk6
| ( sk1
@ ( sk39
@ ^ [A: a,B: a] : $false )
@ ( sk40
@ ^ [A: a,B: a] : $false ) )
| ( sk5
@ ( sk39
@ ^ [A: a,B: a] : $false )
@ ( sk40
@ ^ [A: a,B: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[12840:[bind(A,$thf( sk39 @ ^ [C: a] : ^ [D: a] : $false )),bind(B,$thf( sk40 @ ^ [C: a] : ^ [D: a] : $false ))]]) ).
thf(18756,plain,
( ( ( sk2 @ sk62 @ sk63 )
!= ~ sk6 )
| ~ sk6
| ~ ( sk2 @ ( sk39 @ sk2 ) @ ( sk40 @ sk2 ) ) ),
inference(func_ext,[status(esa)],[18092]) ).
thf(2662,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk5 @ C @ D )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,380]) ).
thf(2663,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2662:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2688,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[2663]) ).
thf(583,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( ( sk2 @ A @ sk4 )
!= ( sk2 @ sk3 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[381]) ).
thf(585,plain,
! [A: a] :
( ~ ( sk2 @ sk3 @ A )
| ( ( sk2 @ A @ sk4 )
!= ( sk2 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[583]) ).
thf(30,plain,
! [B: a,A: a] :
( sk7
| ~ ( sk1 @ A @ B )
| ( sk37 @ A @ B )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(75,plain,
! [B: a,A: a] :
( sk7
| ~ ( sk1 @ A @ B )
| ( sk37 @ A @ B )
| sk6 ),
inference(simp,[status(thm)],[30]) ).
thf(16326,plain,
! [B: a,A: a] :
( sk7
| ~ ( sk1 @ A @ B )
| sk6
| ( ( sk37 @ A @ B )
!= ( sk37 @ sk22 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[75,6]) ).
thf(16327,plain,
( sk7
| ~ ( sk1 @ sk22 @ sk24 )
| sk6 ),
inference(pattern_uni,[status(thm)],[16326:[bind(A,$thf( sk22 )),bind(B,$thf( sk24 ))]]) ).
thf(19892,plain,
( ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6
| ( ( sk5 @ sk48 @ sk49 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18204,32]) ).
thf(19988,plain,
( ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ sk6
| ( sk48 != sk3 )
| ( sk49 != sk4 ) ),
inference(simp,[status(thm)],[19892]) ).
thf(21141,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( ( sk5 @ sk56 @ sk57 )
!= ( sk5 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[20426,32]) ).
thf(21266,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( sk56 != sk3 )
| ( sk57 != sk4 ) ),
inference(simp,[status(thm)],[21141]) ).
thf(4263,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,2665]) ).
thf(4264,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4263:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(4346,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[4264]) ).
thf(528,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,345]) ).
thf(529,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[528:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(536,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ sk4 ) ),
inference(simp,[status(thm)],[529]) ).
thf(611,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( ( sk1 @ A @ sk4 )
!= ( sk1 @ sk3 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[536]) ).
thf(613,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ( ( sk1 @ A @ sk4 )
!= ( sk1 @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[611]) ).
thf(40,plain,
! [C: a,B: a,A: a] :
( ~ ( sk21 @ A @ B )
| ~ ( sk21 @ B @ C )
| ( sk21 @ A @ C )
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(72,plain,
! [C: a,B: a,A: a] :
( ~ ( sk21 @ A @ B )
| ~ ( sk21 @ B @ C )
| ( sk21 @ A @ C )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[40]) ).
thf(4179,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk2 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,2641]) ).
thf(4180,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4179:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(4235,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk2 @ B @ sk4 ) ),
inference(simp,[status(thm)],[4180]) ).
thf(2888,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)],[20,562]) ).
thf(2889,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2888:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2939,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk1 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2889]) ).
thf(2708,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)],[20,541]) ).
thf(2709,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2708:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2760,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk5 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[2709]) ).
thf(362,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[20,355]) ).
thf(363,plain,
( ~ ( sk1 @ sk3 @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[362:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(87,plain,
( ~ sk6
| ~ ( sk21 @ ( sk39 @ sk21 ) @ ( sk40 @ sk21 ) )
| ~ ( sk38 @ sk21 )
| ( sk21 @ sk3 @ sk4 ) ),
inference(prim_subst,[status(thm)],[60:[bind(A,$thf( sk21 ))]]) ).
thf(2799,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)],[23,544]) ).
thf(2800,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2799:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2828,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2800]) ).
thf(1497,plain,
( sk7
| ( sk25
@ ^ [A: a,B: a] : sk6 )
| sk6
| sk6
| sk6 ),
inference(prim_subst,[status(thm)],[49:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk6 ))]]) ).
thf(1654,plain,
( sk7
| ( sk25
@ ^ [A: a,B: a] : sk6 )
| sk6 ),
inference(simp,[status(thm)],[1497]) ).
thf(2976,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk5 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[23,2444]) ).
thf(2977,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2976:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2997,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2977]) ).
thf(21942,plain,
( ~ sk6
| ~ ( sk2 @ ( sk39 @ sk2 ) @ ( sk40 @ sk2 ) )
| ( sk2 @ sk62 @ sk63 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[18756]) ).
thf(22024,plain,
( ~ sk6
| ( sk2 @ sk62 @ sk63 )
| ~ ( sk2 @ ( sk39 @ sk2 ) @ ( sk40 @ sk2 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[21942]) ).
thf(22025,plain,
( ~ sk6
| ( sk2 @ sk62 @ sk63 )
| ~ ( sk2 @ ( sk39 @ sk2 ) @ ( sk40 @ sk2 ) ) ),
inference(simp,[status(thm)],[22024]) ).
thf(4920,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk2 @ sk3 @ C )
| ( ( sk5 @ A @ B )
!= ( sk5 @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[23,2774]) ).
thf(4921,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[4920:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(4969,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk1 @ B @ A )
| ~ ( sk2 @ sk3 @ B ) ),
inference(simp,[status(thm)],[4921]) ).
thf(37,plain,
! [A: a > a > $o] :
( ~ ( A @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( A @ ( sk13 @ A ) @ ( sk14 @ A ) )
| ( A @ sk8 @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(55,plain,
! [A: a > a > $o] :
( ~ ( A @ ( sk11 @ A ) @ ( sk12 @ A ) )
| ( A @ ( sk13 @ A ) @ ( sk14 @ A ) )
| ( A @ sk8 @ sk9 )
| sk10
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[37]) ).
thf(1891,plain,
( ~ sk10
| ( sk2
@ ( sk16
@ ^ [A: a,B: a] : $false )
@ ( sk17
@ ^ [A: a,B: a] : $false ) )
| $false
| $false
| ~ sk7
| sk6 ),
inference(prim_subst,[status(thm)],[50:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $false ))]]) ).
thf(2026,plain,
( ~ sk10
| ( sk2
@ ( sk16
@ ^ [A: a,B: a] : $false )
@ ( sk17
@ ^ [A: a,B: a] : $false ) )
| ~ sk7
| sk6 ),
inference(simp,[status(thm)],[1891]) ).
thf(4645,plain,
! [A: a > a > $o] :
( sk7
| ( sk31 @ A )
| ( A @ sk23 @ sk24 )
| sk6
| ( ( A @ ( sk34 @ A ) @ ( sk35 @ A ) )
!= ( sk2 @ sk22 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[43,4604]) ).
thf(4649,plain,
( sk7
| ( sk31
@ ^ [A: a,B: a] : ( sk2 @ sk22 @ sk24 ) )
| ( sk2 @ sk22 @ sk24 )
| sk6 ),
inference(pre_uni,[status(thm)],[4645:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk2 @ sk22 @ sk24 ) ))]]) ).
thf(20162,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ( ( sk5 @ sk54 @ sk55 )
!= ~ sk6 )
| ~ sk6
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,17822]) ).
thf(20163,plain,
( ~ ( sk2 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( ( sk5 @ sk54 @ sk55 )
!= ~ sk6 )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[20162:[bind(A,$thf( sk39 @ sk5 )),bind(B,$thf( sk40 @ sk5 ))]]) ).
thf(105,plain,
! [A: a > a > a > a > $o] :
( ~ sk6
| ~ ( sk25
@ ( A
@ ( sk39
@ ^ [B: a,C: a] : ( sk25 @ ( A @ B @ C ) ) )
@ ( sk40
@ ^ [B: a,C: a] : ( sk25 @ ( A @ B @ C ) ) ) ) )
| ~ ( sk38
@ ^ [B: a,C: a] : ( sk25 @ ( A @ B @ C ) ) )
| ( sk25 @ ( A @ sk3 @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[60:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ( sk25 @ ( B @ C @ D ) ) ))]]) ).
thf(119,plain,
! [A: a > a > a > a > $o] :
( ~ sk6
| ~ ( sk25
@ ( A
@ ( sk39
@ ^ [B: a,C: a] : ( sk25 @ ( A @ B @ C ) ) )
@ ( sk40
@ ^ [B: a,C: a] : ( sk25 @ ( A @ B @ C ) ) ) ) )
| ~ ( sk38
@ ^ [B: a,C: a] : ( sk25 @ ( A @ B @ C ) ) )
| ( sk25 @ ( A @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(18317,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk1 @ A @ sk4 )
| ( ( sk5 @ sk50 @ sk51 )
!= ( sk5 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17611,345]) ).
thf(18430,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk1 @ A @ sk4 )
| ( sk50 != sk3 )
| ( sk51 != A ) ),
inference(simp,[status(thm)],[18317]) ).
thf(18491,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk1 @ sk51 @ sk4 )
| ( sk50 != sk3 ) ),
inference(simp,[status(thm)],[18430]) ).
thf(4524,plain,
! [D: a,C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( sk1 @ D @ sk4 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,2711]) ).
thf(4525,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(pattern_uni,[status(thm)],[4524:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(4596,plain,
! [B: a,A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ B )
| ~ ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[4525]) ).
thf(4,plain,
! [A: a > a > $o] :
( sk7
| ( sk1 @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ( sk2 @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( A @ sk23 @ sk24 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(51,plain,
! [A: a > a > $o] :
( sk7
| ( sk1 @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ( sk2 @ ( sk32 @ A ) @ ( sk33 @ A ) )
| ~ ( sk31 @ A )
| ( A @ sk23 @ sk24 )
| sk6 ),
inference(simp,[status(thm)],[4]) ).
thf(18361,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk2 @ A @ sk4 )
| ( ( sk5 @ sk50 @ sk51 )
!= ( sk5 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17611,341]) ).
thf(18382,plain,
! [A: a] :
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk2 @ A @ sk4 )
| ( sk50 != sk3 )
| ( sk51 != A ) ),
inference(simp,[status(thm)],[18361]) ).
thf(18450,plain,
( ~ sk6
| ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ~ ( sk2 @ sk51 @ sk4 )
| ( sk50 != sk3 ) ),
inference(simp,[status(thm)],[18382]) ).
thf(154,plain,
( sk7
| ( sk31
@ ^ [A: a,B: a] : sk6 )
| sk6
| sk6
| sk6 ),
inference(prim_subst,[status(thm)],[43:[bind(A,$thf( ^ [B: a] : ^ [C: a] : sk6 ))]]) ).
thf(183,plain,
( sk7
| ( sk31
@ ^ [A: a,B: a] : sk6 )
| sk6 ),
inference(simp,[status(thm)],[154]) ).
thf(85,plain,
! [A: a > a > $o] :
( ~ sk6
| ~ ( A @ ( sk39 @ A ) @ ( sk40 @ A ) )
| ( A @ sk3 @ sk4 )
| ( ( sk38 @ A )
!= ( A @ ( sk39 @ A ) @ ( sk40 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[60]) ).
thf(107,plain,
! [A: a > a > $o] :
( ( A @ sk3 @ sk4 )
| ~ sk6
| ~ ( A @ ( sk39 @ A ) @ ( sk40 @ A ) )
| ( ( sk38 @ A )
!= ( A @ ( sk39 @ A ) @ ( sk40 @ A ) ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(901,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ sk3 )
| ( sk4 != sk3 )
| ( ( sk5 @ A @ B )
!= ( sk5 @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,663]) ).
thf(902,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[901:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(918,plain,
! [A: a] :
( ~ ( sk1 @ sk3 @ A )
| ~ ( sk1 @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[902]) ).
thf(623,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ B )
| ~ sk7
| sk6
| ( ( sk21 @ A @ B )
!= ( sk21 @ sk8 @ sk9 ) ) ),
inference(paramod_ordered,[status(thm)],[46,14]) ).
thf(624,plain,
( ~ ( sk2 @ sk8 @ sk9 )
| ~ sk7
| sk6 ),
inference(pattern_uni,[status(thm)],[623:[bind(A,$thf( sk8 )),bind(B,$thf( sk9 ))]]) ).
thf(2472,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)],[23,335]) ).
thf(2473,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[2472:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2502,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A @ sk4 )
| ~ ( sk5 @ B @ A )
| ~ ( sk5 @ sk3 @ B ) ),
inference(simp,[status(thm)],[2473]) ).
thf(20109,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( ( sk5 @ sk54 @ sk55 )
!= ~ sk6 )
| ~ sk6
| ( ( sk5 @ A @ B )
!= ( sk5 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,17822]) ).
thf(20110,plain,
( ~ ( sk1 @ ( sk39 @ sk5 ) @ ( sk40 @ sk5 ) )
| ( ( sk5 @ sk54 @ sk55 )
!= ~ sk6 )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[20109:[bind(A,$thf( sk39 @ sk5 )),bind(B,$thf( sk40 @ sk5 ))]]) ).
thf(35,plain,
! [A: a > a > $o] :
( ~ sk6
| ( sk38 @ A )
| ~ ( A @ ( sk41 @ A ) @ ( sk43 @ A ) )
| ( A @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(47,plain,
! [A: a > a > $o] :
( ~ sk6
| ( sk38 @ A )
| ~ ( A @ ( sk41 @ A ) @ ( sk43 @ A ) )
| ( A @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[35]) ).
thf(13,plain,
! [A: a > a > $o] :
( sk7
| ( sk25 @ A )
| ( A @ ( sk28 @ A ) @ ( sk29 @ A ) )
| ( A @ sk22 @ sk23 )
| sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(62,plain,
! [A: a > a > $o] :
( sk7
| ( sk25 @ A )
| ( A @ ( sk28 @ A ) @ ( sk29 @ A ) )
| ( A @ sk22 @ sk23 )
| sk6 ),
inference(simp,[status(thm)],[13]) ).
thf(96,plain,
! [A: a > a > a > a > $o] :
( ~ sk6
| ~ ( sk31
@ ( A
@ ( sk39
@ ^ [B: a,C: a] : ( sk31 @ ( A @ B @ C ) ) )
@ ( sk40
@ ^ [B: a,C: a] : ( sk31 @ ( A @ B @ C ) ) ) ) )
| ~ ( sk38
@ ^ [B: a,C: a] : ( sk31 @ ( A @ B @ C ) ) )
| ( sk31 @ ( A @ sk3 @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[60:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ( sk31 @ ( B @ C @ D ) ) ))]]) ).
thf(111,plain,
! [A: a > a > a > a > $o] :
( ~ sk6
| ~ ( sk31
@ ( A
@ ( sk39
@ ^ [B: a,C: a] : ( sk31 @ ( A @ B @ C ) ) )
@ ( sk40
@ ^ [B: a,C: a] : ( sk31 @ ( A @ B @ C ) ) ) ) )
| ~ ( sk38
@ ^ [B: a,C: a] : ( sk31 @ ( A @ B @ C ) ) )
| ( sk31 @ ( A @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(86,plain,
! [B: a > a > a,A: a > a > a] :
( ~ sk6
| ~ ( sk2
@ ( A
@ ( sk39
@ ^ [C: a,D: a] : ( sk2 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk2 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk39
@ ^ [C: a,D: a] : ( sk2 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk2 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk38
@ ^ [C: a,D: a] : ( sk2 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk2 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) ) ),
inference(prim_subst,[status(thm)],[60:[bind(A,$thf( ^ [D: a] : ^ [E: a] : ( sk2 @ ( B @ D @ E ) @ ( C @ D @ E ) ) ))]]) ).
thf(122,plain,
! [B: a > a > a,A: a > a > a] :
( ~ sk6
| ~ ( sk2
@ ( A
@ ( sk39
@ ^ [C: a,D: a] : ( sk2 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk2 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) )
@ ( B
@ ( sk39
@ ^ [C: a,D: a] : ( sk2 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
@ ( sk40
@ ^ [C: a,D: a] : ( sk2 @ ( A @ C @ D ) @ ( B @ C @ D ) ) ) ) )
| ~ ( sk38
@ ^ [C: a,D: a] : ( sk2 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ( sk2 @ ( A @ sk3 @ sk4 ) @ ( B @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(36441,plain,
$false,
inference(e,[status(thm)],[69,6167,365,12721,18107,941,352,115,308,120,5529,29584,17275,56,2686,21435,17946,814,4650,17888,20209,52,14,18468,2755,2444,17339,18385,542,17545,20,46,78,4967,13365,57,5526,4733,106,121,348,17513,3068,61,17349,116,312,74,920,2910,5530,381,2641,6,4604,60,380,117,1666,70,12715,2032,2826,329,5551,5066,361,65,18204,2498,18073,53,18701,328,2798,669,5818,1659,10720,18176,4237,3005,1525,7407,20241,541,4572,73,20730,4708,32,2734,180,45,20192,30470,64,562,176,44,18013,204,59,118,17669,71,5039,936,18484,21859,49,18444,335,17611,20426,382,54,187,681,219,2774,18092,76,98,19289,345,3073,66,20999,6645,2931,3,18466,5693,80,6672,2665,7403,680,4319,17281,355,663,2471,5785,112,812,18676,48,63,17435,17324,327,1647,50,12841,18756,2688,17822,585,16327,19988,21266,544,67,4346,613,2711,72,4235,2939,43,2760,363,87,2828,1654,2997,351,22025,17434,4969,23,5632,17511,55,2026,75,4649,20163,27562,536,119,58,18491,4596,51,18450,183,107,918,341,624,2502,20110,47,68,62,111,122,2887]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEV157^5 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 21 19:07:10 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.97/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.97 % [INFO] Parsing done (114ms).
% 1.21/0.98 % [INFO] Running in sequential loop mode.
% 1.70/1.17 % [INFO] eprover registered as external prover.
% 1.70/1.18 % [INFO] Scanning for conjecture ...
% 1.93/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.93/1.29 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.93/1.29 % [INFO] Problem is higher-order (TPTP THF).
% 1.93/1.29 % [INFO] Type checking passed.
% 1.93/1.30 % [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 ...
% 80.55/18.28 % External prover 'e' found a proof!
% 80.55/18.28 % [INFO] Killing All external provers ...
% 80.55/18.28 % Time passed: 17760ms (effective reasoning time: 17303ms)
% 80.55/18.28 % 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)>
% 80.55/18.28 % Axioms used in derivation (0):
% 80.55/18.28 % No. of inferences in proof: 484
% 80.55/18.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 17760 ms resp. 17303 ms w/o parsing
% 81.24/18.40 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 81.24/18.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------