%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV245^6 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:37:04 AM UTC 2026
% Result : Theorem 200.13s 57.99s
% Output : Refutation 202.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 9
% Syntax : Number of formulae : 368 ( 39 unt; 0 typ; 8 def)
% Number of atoms : 1964 ( 262 equ; 9 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 5293 ( 595 ~; 682 |; 111 &;3785 @)
% ( 0 <=>; 120 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 593 ( 593 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 1306 ( 457 ^; 744 !; 97 ?;1306 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(cK_decl,type,
cK: ( a > $o ) > a > $o ).
thf(sk1_decl,type,
sk1: ( a > $o ) > ( a > $o ) > a ).
thf(sk2_decl,type,
sk2: a ).
thf(sk3_decl,type,
sk3: a > $o ).
thf(sk4_decl,type,
sk4: a ).
thf(sk5_decl,type,
sk5: ( a > $o ) > a ).
thf(sk6_decl,type,
sk6: a > $o ).
thf(sk9_decl,type,
sk9: ( a > $o ) > ( a > $o ) > a ).
thf(sk20_decl,type,
sk20: a ).
thf(sk28_decl,type,
sk28: a > $o ).
thf(sk29_decl,type,
sk29: a ).
thf(sk30_decl,type,
sk30: ( a > $o ) > a ).
thf(sk35_decl,type,
sk35: a ).
thf(sk37_decl,type,
sk37: a ).
thf(sk78_decl,type,
sk78: a > $o ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: a > $o,B: a > $o] :
@+[C: a] :
~ ( ( B @ C )
=> ( A @ C ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a] :
~ ( ? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
=> ( cK
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ A ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> ( cK @ A @ B ) )
& ( A @ sk2 ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: a > $o] :
@+[B: a] :
~ ( ( A @ B )
=> ( cK @ A @ B ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> ( cK @ A @ B ) )
& ( A @ sk4 ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: a > $o,B: a > $o] :
@+[C: a] :
~ ( ( A @ C )
=> ( cK @ A @ C ) ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( @+[A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> ( cK @ A @ B ) )
& ( A @ sk4 ) ) ) ) ).
thf(sk78_def,definition,
( sk78
= ( @+[A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> ( cK @ A @ B ) )
& ( A @ sk37 ) ) ) ) ).
thf(1,conjecture,
( ! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ! [C: a] :
( ( cK @ A @ C )
=> ( cK @ B @ C ) ) )
=> ! [A: a] :
( ? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
=> ( cK
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM116_2S) ).
thf(2,negated_conjecture,
~ ( ! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ! [C: a] :
( ( cK @ A @ C )
=> ( cK @ B @ C ) ) )
=> ! [A: a] :
( ? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
=> ( cK
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ! [C: a] :
( ( cK @ A @ C )
=> ( cK @ B @ C ) ) )
=> ! [A: a] :
( ? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
=> ( cK
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [D: a,C: a,B: a > $o,A: a > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( cK @ B @ C ) )
& ( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( cK @ B @ C ) )
& ( ~ ( sk3 @ D )
| ( cK @ sk3 @ D ) )
& ( sk3 @ sk2 )
& ~ ( cK
@ ^ [E: a] :
? [F: a > $o] :
( ! [G: a] :
( ( F @ G )
=> ( cK @ F @ G ) )
& ( F @ E ) )
@ sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
sk3 @ sk2,
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( cK @ sk3 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( cK @ sk3 @ A ) ),
inference(simp,[status(thm)],[5]) ).
thf(13,plain,
! [A: a] :
( ~ $true
| ( cK @ sk3 @ A )
| ( ( sk3 @ sk2 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,10]) ).
thf(14,plain,
! [A: a] :
( ( cK @ sk3 @ A )
| ( ( sk3 @ sk2 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(15,plain,
cK @ sk3 @ sk2,
inference(pattern_uni,[status(thm)],[14:[bind(A,$thf( sk2 ))]]) ).
thf(6,plain,
~ ( cK
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk2 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(18,plain,
( ~ $true
| ( ( cK @ sk3 @ sk2 )
!= ( cK
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[15,6]) ).
thf(19,plain,
( ( cK @ sk3 @ sk2 )
!= ( cK
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk2 ) ),
inference(simp,[status(thm)],[18]) ).
thf(20,plain,
( ( sk3
!= ( ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) ) ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[19]) ).
thf(21,plain,
( sk3
!= ( ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(22,plain,
( ( sk3 @ sk4 )
!= ( ? [A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> ( cK @ A @ B ) )
& ( A @ sk4 ) ) ) ),
inference(func_ext,[status(esa)],[21]) ).
thf(65,plain,
( ( sk3 @ sk4 )
| ? [A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> ( cK @ A @ B ) )
& ( A @ sk4 ) ) ),
inference(bool_ext,[status(thm)],[22]) ).
thf(74,plain,
! [A: a] :
( ( ( sk3 @ sk4 )
| ~ ( sk6 @ A )
| ( cK @ sk6 @ A ) )
& ( ( sk3 @ sk4 )
| ( sk6 @ sk4 ) ) ),
inference(cnf,[status(esa)],[65]) ).
thf(76,plain,
( ( sk3 @ sk4 )
| ( sk6 @ sk4 ) ),
inference(cnfConj,[status(thm)],[74]) ).
thf(64,plain,
( ~ ( sk3 @ sk4 )
| ~ ? [A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> ( cK @ A @ B ) )
& ( A @ sk4 ) ) ),
inference(bool_ext,[status(thm)],[22]) ).
thf(71,plain,
! [A: a > $o] :
( ( ~ ( sk3 @ sk4 )
| ( A @ ( sk5 @ A ) )
| ~ ( A @ sk4 ) )
& ( ~ ( sk3 @ sk4 )
| ~ ( cK @ A @ ( sk5 @ A ) )
| ~ ( A @ sk4 ) ) ),
inference(cnf,[status(esa)],[64]) ).
thf(72,plain,
! [A: a > $o] :
( ~ ( sk3 @ sk4 )
| ( A @ ( sk5 @ A ) )
| ~ ( A @ sk4 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(73,plain,
! [A: a > $o] :
( ~ ( sk3 @ sk4 )
| ~ ( cK @ A @ ( sk5 @ A ) )
| ~ ( A @ sk4 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(281,plain,
! [B: a > $o,A: a] :
( ~ ( sk3 @ A )
| ~ ( sk3 @ sk4 )
| ~ $true
| ~ ( B @ sk4 )
| ( ( cK @ sk3 @ A )
!= ( cK @ B @ ( sk5 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,73]) ).
thf(282,plain,
! [B: a > $o,A: a] :
( ~ ( sk3 @ A )
| ~ ( sk3 @ sk4 )
| ~ ( B @ sk4 )
| ( ( cK @ sk3 @ A )
!= ( cK @ B @ ( sk5 @ B ) ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(283,plain,
( ~ ( sk3 @ ( sk5 @ sk3 ) )
| ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( sk5 @ sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(348,plain,
( ~ ( sk3 @ ( sk5 @ sk3 ) )
| ~ ( sk3 @ sk4 ) ),
inference(simp,[status(thm)],[283]) ).
thf(6428,plain,
! [A: a > $o] :
( ~ ( sk3 @ sk4 )
| ~ ( A @ sk4 )
| ~ $true
| ~ ( sk3 @ sk4 )
| ( ( A @ ( sk5 @ A ) )
!= ( sk3 @ ( sk5 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[72,348]) ).
thf(6429,plain,
! [A: a > $o] :
( ~ ( sk3 @ sk4 )
| ~ ( A @ sk4 )
| ( ( A @ ( sk5 @ A ) )
!= ( sk3 @ ( sk5 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[6428]) ).
thf(6788,plain,
( ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 ) ),
inference(pre_uni,[status(thm)],[6429:[bind(A,$thf( sk3 ))]]) ).
thf(6937,plain,
~ ( sk3 @ sk4 ),
inference(simp,[status(thm)],[6788]) ).
thf(6993,plain,
( $false
| ( sk6 @ sk4 ) ),
inference(rewrite,[status(thm)],[76,6937]) ).
thf(6994,plain,
sk6 @ sk4,
inference(simp,[status(thm)],[6993]) ).
thf(75,plain,
! [A: a] :
( ( sk3 @ sk4 )
| ~ ( sk6 @ A )
| ( cK @ sk6 @ A ) ),
inference(cnfConj,[status(thm)],[74]) ).
thf(7067,plain,
! [A: a] :
( $false
| ~ ( sk6 @ A )
| ( cK @ sk6 @ A ) ),
inference(rewrite,[status(thm)],[75,6937]) ).
thf(7068,plain,
! [A: a] :
( ~ ( sk6 @ A )
| ( cK @ sk6 @ A ) ),
inference(simp,[status(thm)],[7067]) ).
thf(7100,plain,
! [A: a] :
( ~ $true
| ( cK @ sk6 @ A )
| ( ( sk6 @ sk4 )
!= ( sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6994,7068]) ).
thf(7101,plain,
! [A: a] :
( ( cK @ sk6 @ A )
| ( ( sk6 @ sk4 )
!= ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[7100]) ).
thf(7102,plain,
cK @ sk6 @ sk4,
inference(pattern_uni,[status(thm)],[7101:[bind(A,$thf( sk4 ))]]) ).
thf(7,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( cK @ B @ C ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7160,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ $true
| ( cK @ B @ C )
| ( ( cK @ sk6 @ sk4 )
!= ( cK @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[7102,7]) ).
thf(7161,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ( cK @ B @ C )
| ( ( cK @ sk6 @ sk4 )
!= ( cK @ A @ C ) ) ),
inference(simp,[status(thm)],[7160]) ).
thf(7162,plain,
! [A: a > $o] :
( ( sk6 @ ( sk1 @ A @ sk6 ) )
| ( cK @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[7161:[bind(A,$thf( sk6 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(7203,plain,
! [A: a > $o] :
( ( sk6 @ ( sk1 @ A @ sk6 ) )
| ( cK @ A @ sk4 ) ),
inference(simp,[status(thm)],[7162]) ).
thf(44,plain,
! [B: a,A: a > $o] :
( $false
| ~ ( cK
@ ^ [C: a] : $false
@ B )
| ( cK @ A @ B ) ),
inference(prim_subst,[status(thm)],[7:[bind(A,$thf( ^ [D: a] : $false ))]]) ).
thf(57,plain,
! [B: a,A: a > $o] :
( ~ ( cK
@ ^ [C: a] : $false
@ B )
| ( cK @ A @ B ) ),
inference(simp,[status(thm)],[44]) ).
thf(7253,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( sk6 @ ( sk1 @ A @ sk6 ) )
| ~ $true
| ( cK @ B @ C )
| ( ( cK @ A @ sk4 )
!= ( cK
@ ^ [D: a] : $false
@ C ) ) ),
inference(paramod_ordered,[status(thm)],[7203,57]) ).
thf(7254,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( sk6 @ ( sk1 @ A @ sk6 ) )
| ( cK @ B @ C )
| ( ( cK @ A @ sk4 )
!= ( cK
@ ^ [D: a] : $false
@ C ) ) ),
inference(simp,[status(thm)],[7253]) ).
thf(7255,plain,
! [A: a > $o] :
( ( sk6
@ ( sk1
@ ^ [B: a] : $false
@ sk6 ) )
| ( cK @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[7254:[bind(A,$thf( ^ [D: a] : $false )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(7321,plain,
! [A: a > $o] :
( ( sk6
@ ( sk1
@ ^ [B: a] : $false
@ sk6 ) )
| ( cK @ A @ sk4 ) ),
inference(simp,[status(thm)],[7255]) ).
thf(7395,plain,
! [B: a,A: a > $o] :
( ( cK @ A @ sk4 )
| ~ $true
| ( cK @ sk6 @ B )
| ( ( sk6
@ ( sk1
@ ^ [C: a] : $false
@ sk6 ) )
!= ( sk6 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7321,7068]) ).
thf(7396,plain,
! [B: a,A: a > $o] :
( ( cK @ A @ sk4 )
| ( cK @ sk6 @ B )
| ( ( sk6
@ ( sk1
@ ^ [C: a] : $false
@ sk6 ) )
!= ( sk6 @ B ) ) ),
inference(simp,[status(thm)],[7395]) ).
thf(7397,plain,
! [A: a > $o] :
( ( cK @ A @ sk4 )
| ( cK @ sk6
@ ( sk1
@ ^ [B: a] : $false
@ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[7396:[bind(A,$thf( A )),bind(B,$thf( sk1 @ ^ [C: a] : $false @ sk6 ))]]) ).
thf(8,plain,
! [C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( cK @ B @ C ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(87,plain,
! [D: a,C: a > $o,B: a > $o,A: a] :
( ~ ( sk3 @ A )
| ~ ( C @ ( sk1 @ C @ B ) )
| ~ $true
| ( cK @ C @ D )
| ( ( cK @ sk3 @ A )
!= ( cK @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10,8]) ).
thf(88,plain,
! [D: a,C: a > $o,B: a > $o,A: a] :
( ~ ( sk3 @ A )
| ~ ( C @ ( sk1 @ C @ B ) )
| ( cK @ C @ D )
| ( ( cK @ sk3 @ A )
!= ( cK @ B @ D ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(89,plain,
! [B: a > $o,A: a] :
( ~ ( sk3 @ A )
| ~ ( B @ ( sk1 @ B @ sk3 ) )
| ( cK @ B @ A ) ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(151,plain,
! [B: a > $o,A: a] :
( ~ ( sk3 @ A )
| ~ ( B @ ( sk1 @ B @ sk3 ) )
| ( cK @ B @ A ) ),
inference(simp,[status(thm)],[89]) ).
thf(7154,plain,
! [B: a,A: a > $o] :
( ~ $true
| ( cK @ A @ B )
| ( ( cK @ sk6 @ sk4 )
!= ( cK
@ ^ [C: a] : $false
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[7102,57]) ).
thf(7155,plain,
! [B: a,A: a > $o] :
( ( cK @ A @ B )
| ( ( cK @ sk6 @ sk4 )
!= ( cK
@ ^ [C: a] : $false
@ B ) ) ),
inference(simp,[status(thm)],[7154]) ).
thf(7187,plain,
! [B: a,A: a > $o] :
( ( cK @ A @ B )
| ( sk6
!= ( ^ [C: a] : $false ) )
| ( sk4 != B ) ),
inference(simp,[status(thm)],[7155]) ).
thf(7199,plain,
! [A: a > $o] :
( ( cK @ A @ sk4 )
| ( sk6
!= ( ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[7187]) ).
thf(85,plain,
! [D: a,C: a > $o,B: a > $o,A: a] :
( ~ ( sk3 @ A )
| ~ $true
| ~ ( cK @ B @ D )
| ( cK @ C @ D )
| ( ( cK @ sk3 @ A )
!= ( C @ ( sk1 @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,8]) ).
thf(86,plain,
! [D: a,C: a > $o,B: a > $o,A: a] :
( ~ ( sk3 @ A )
| ~ ( cK @ B @ D )
| ( cK @ C @ D )
| ( ( cK @ sk3 @ A )
!= ( C @ ( sk1 @ C @ B ) ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(128,plain,
! [C: a > a,B: a,A: a > $o] :
( ~ ( sk3
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ sk3 @ ( C @ D ) )
@ A ) ) )
| ~ ( cK @ A @ B )
| ( cK
@ ^ [D: a] : ( cK @ sk3 @ ( C @ D ) )
@ B ) ),
inference(pre_uni,[status(thm)],[86:[bind(A,$thf( F @ ( sk1 @ ^ [F: a] : ( cK @ sk3 @ ( F @ F ) ) @ B ) )),bind(B,$thf( B )),bind(C,$thf( ^ [F: a] : ( cK @ sk3 @ ( F @ F ) ) )),bind(D,$thf( D ))]]) ).
thf(138,plain,
! [C: a > a,B: a,A: a > $o] :
( ~ ( sk3
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ sk3 @ ( C @ D ) )
@ A ) ) )
| ~ ( cK @ A @ B )
| ( cK
@ ^ [D: a] : ( cK @ sk3 @ ( C @ D ) )
@ B ) ),
inference(simp,[status(thm)],[128]) ).
thf(39,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ $true
| ( cK @ B @ C )
| ( ( cK @ sk3 @ sk2 )
!= ( cK @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,7]) ).
thf(40,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ( cK @ B @ C )
| ( ( cK @ sk3 @ sk2 )
!= ( cK @ A @ C ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(41,plain,
! [A: a > $o] :
( ( sk3 @ ( sk1 @ A @ sk3 ) )
| ( cK @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(56,plain,
! [A: a > $o] :
( ( sk3 @ ( sk1 @ A @ sk3 ) )
| ( cK @ A @ sk2 ) ),
inference(simp,[status(thm)],[41]) ).
thf(175,plain,
! [B: a,A: a > $o] :
( ( cK @ A @ sk2 )
| ~ $true
| ( cK @ sk3 @ B )
| ( ( sk3 @ ( sk1 @ A @ sk3 ) )
!= ( sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56,10]) ).
thf(176,plain,
! [B: a,A: a > $o] :
( ( cK @ A @ sk2 )
| ( cK @ sk3 @ B )
| ( ( sk3 @ ( sk1 @ A @ sk3 ) )
!= ( sk3 @ B ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(177,plain,
! [A: a > $o] :
( ( cK @ A @ sk2 )
| ( cK @ sk3 @ ( sk1 @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( C )),bind(B,$thf( sk1 @ C @ sk3 ))]]) ).
thf(185,plain,
! [A: a > $o] :
( ( cK @ A @ sk2 )
| ( cK @ sk3 @ ( sk1 @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(102,plain,
! [C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ~ $true
| ( cK @ B @ C )
| ( ( cK @ sk3 @ sk2 )
!= ( cK @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,8]) ).
thf(103,plain,
! [C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ( cK @ B @ C )
| ( ( cK @ sk3 @ sk2 )
!= ( cK @ A @ C ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(104,plain,
! [A: a > $o] :
( ~ ( A @ ( sk1 @ A @ sk3 ) )
| ( cK @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(144,plain,
! [A: a > $o] :
( ~ ( A @ ( sk1 @ A @ sk3 ) )
| ( cK @ A @ sk2 ) ),
inference(simp,[status(thm)],[104]) ).
thf(13133,plain,
! [B: a > $o,A: a > $o] :
( ( cK @ A @ sk2 )
| ~ $true
| ( cK @ B @ sk2 )
| ( ( cK @ sk3 @ ( sk1 @ A @ sk3 ) )
!= ( B @ ( sk1 @ B @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[185,144]) ).
thf(13134,plain,
! [B: a > $o,A: a > $o] :
( ( cK @ A @ sk2 )
| ( cK @ B @ sk2 )
| ( ( cK @ sk3 @ ( sk1 @ A @ sk3 ) )
!= ( B @ ( sk1 @ B @ sk3 ) ) ) ),
inference(simp,[status(thm)],[13133]) ).
thf(13290,plain,
( ( cK @ ( cK @ sk3 ) @ sk2 )
| ( cK @ ( cK @ sk3 ) @ sk2 ) ),
inference(pre_uni,[status(thm)],[13134:[bind(A,$thf( cK @ sk3 )),bind(B,$thf( cK @ sk3 ))]]) ).
thf(13422,plain,
cK @ ( cK @ sk3 ) @ sk2,
inference(simp,[status(thm)],[13290]) ).
thf(13459,plain,
( ~ $true
| ( ( cK @ ( cK @ sk3 ) @ sk2 )
!= ( cK
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[13422,6]) ).
thf(13460,plain,
( ( cK @ ( cK @ sk3 ) @ sk2 )
!= ( cK
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk2 ) ),
inference(simp,[status(thm)],[13459]) ).
thf(13519,plain,
( ( ( cK @ sk3 )
!= ( ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) ) ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[13460]) ).
thf(13532,plain,
( ( cK @ sk3 )
!= ( ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) ) ) ),
inference(simp,[status(thm)],[13519]) ).
thf(17584,plain,
( ( cK @ sk3 @ sk37 )
!= ( ? [A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> ( cK @ A @ B ) )
& ( A @ sk37 ) ) ) ),
inference(func_ext,[status(esa)],[13532]) ).
thf(17586,plain,
( ( cK @ sk3 @ sk37 )
| ? [A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> ( cK @ A @ B ) )
& ( A @ sk37 ) ) ),
inference(bool_ext,[status(thm)],[17584]) ).
thf(17906,plain,
! [A: a] :
( ( ( cK @ sk3 @ sk37 )
| ~ ( sk78 @ A )
| ( cK @ sk78 @ A ) )
& ( ( cK @ sk3 @ sk37 )
| ( sk78 @ sk37 ) ) ),
inference(cnf,[status(esa)],[17586]) ).
thf(17908,plain,
( ( cK @ sk3 @ sk37 )
| ( sk78 @ sk37 ) ),
inference(cnfConj,[status(thm)],[17906]) ).
thf(18058,plain,
! [A: a > $o] :
( ( sk78 @ sk37 )
| ~ $true
| ( cK @ A @ sk2 )
| ( ( A @ ( sk1 @ A @ sk3 ) )
!= ( cK @ sk3 @ sk37 ) ) ),
inference(paramod_ordered,[status(thm)],[17908,144]) ).
thf(18059,plain,
! [A: a > $o] :
( ( sk78 @ sk37 )
| ( cK @ A @ sk2 )
| ( ( A @ ( sk1 @ A @ sk3 ) )
!= ( cK @ sk3 @ sk37 ) ) ),
inference(simp,[status(thm)],[18058]) ).
thf(18112,plain,
( ( sk78 @ sk37 )
| ( cK
@ ^ [A: a] : ( cK @ sk3 @ sk37 )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[18059:[bind(A,$thf( ^ [B: a] : ( cK @ sk3 @ sk37 ) ))]]) ).
thf(2796,plain,
! [B: a,A: a > $o] :
( ~ ( cK
@ ^ [C: a] : $false
@ B )
| ~ $true
| ( ( cK @ A @ B )
!= ( cK
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[57,6]) ).
thf(2797,plain,
! [B: a,A: a > $o] :
( ~ ( cK
@ ^ [C: a] : $false
@ B )
| ( ( cK @ A @ B )
!= ( cK
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ sk2 ) ) ),
inference(simp,[status(thm)],[2796]) ).
thf(2798,plain,
~ ( cK
@ ^ [A: a] : $false
@ sk2 ),
inference(pattern_uni,[status(thm)],[2797:[bind(A,$thf( ^ [C: a] : ? [D: a > $o] : ( ! [E: a] : ( ( D @ E ) => ( cK @ D @ E ) ) & ( D @ C ) ) )),bind(B,$thf( sk2 ))]]) ).
thf(20111,plain,
( ( sk78 @ sk37 )
| ~ $true
| ( ( cK
@ ^ [A: a] : ( cK @ sk3 @ sk37 )
@ sk2 )
!= ( cK
@ ^ [A: a] : $false
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[18112,2798]) ).
thf(20112,plain,
( ( sk78 @ sk37 )
| ( ( cK
@ ^ [A: a] : ( cK @ sk3 @ sk37 )
@ sk2 )
!= ( cK
@ ^ [A: a] : $false
@ sk2 ) ) ),
inference(simp,[status(thm)],[20111]) ).
thf(20268,plain,
( ( sk78 @ sk37 )
| ( ( ^ [A: a] : ( cK @ sk3 @ sk37 ) )
!= ( ^ [A: a] : $false ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[20112]) ).
thf(20332,plain,
( ( sk78 @ sk37 )
| ( ( ^ [A: a] : ( cK @ sk3 @ sk37 ) )
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[20268]) ).
thf(114,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ~ $true
| ~ ( cK @ D @ F )
| ( cK @ E @ F )
| ( ( cK @ B @ C )
!= ( E @ ( sk1 @ E @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,8]) ).
thf(115,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ~ ( cK @ D @ F )
| ( cK @ E @ F )
| ( ( cK @ B @ C )
!= ( E @ ( sk1 @ E @ D ) ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(134,plain,
! [E: a > a,D: a > a > $o,C: a,B: a > $o,A: a > $o] :
( ( A
@ ( sk1
@ ( D
@ ( sk1
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ B ) )
@ A ) )
| ~ ( cK @ A
@ ( E
@ ( sk1
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ B ) ) )
| ~ ( cK @ B @ C )
| ( cK
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ C ) ),
inference(pre_uni,[status(thm)],[115:[bind(A,$thf( A )),bind(B,$thf( G @ ( sk1 @ ^ [I: a] : ( cK @ ( G @ I ) @ ( H @ I ) ) @ D ) )),bind(C,$thf( H @ ( sk1 @ ^ [I: a] : ( cK @ ( G @ I ) @ ( H @ I ) ) @ D ) )),bind(D,$thf( D )),bind(E,$thf( ^ [I: a] : ( cK @ ( G @ I ) @ ( H @ I ) ) ))]]) ).
thf(142,plain,
! [E: a > a,D: a > a > $o,C: a,B: a > $o,A: a > $o] :
( ( A
@ ( sk1
@ ( D
@ ( sk1
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ B ) )
@ A ) )
| ~ ( cK @ A
@ ( E
@ ( sk1
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ B ) ) )
| ~ ( cK @ B @ C )
| ( cK
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ C ) ),
inference(simp,[status(thm)],[134]) ).
thf(2979,plain,
! [A: a > $o] :
( ( sk3 @ ( sk1 @ A @ sk3 ) )
| ~ $true
| ( ( cK @ A @ sk2 )
!= ( cK
@ ^ [B: a] : $false
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[56,2798]) ).
thf(2980,plain,
! [A: a > $o] :
( ( sk3 @ ( sk1 @ A @ sk3 ) )
| ( ( cK @ A @ sk2 )
!= ( cK
@ ^ [B: a] : $false
@ sk2 ) ) ),
inference(simp,[status(thm)],[2979]) ).
thf(2981,plain,
( sk3
@ ( sk1
@ ^ [A: a] : $false
@ sk3 ) ),
inference(pattern_uni,[status(thm)],[2980:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(6998,plain,
( ~ $true
| ( ( sk3
@ ( sk1
@ ^ [A: a] : $false
@ sk3 ) )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[2981,6937]) ).
thf(6999,plain,
( ( sk3
@ ( sk1
@ ^ [A: a] : $false
@ sk3 ) )
!= ( sk3 @ sk4 ) ),
inference(simp,[status(thm)],[6998]) ).
thf(7028,plain,
( ( sk1
@ ^ [A: a] : $false
@ sk3 )
!= sk4 ),
inference(simp,[status(thm)],[6999]) ).
thf(42,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( ( cK @ B @ C )
!= ( A @ ( sk1 @ B @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[7]) ).
thf(48,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( cK
@ ( B
@ ( sk1 @ A
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) ) ) ) )
| ~ ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1 @ A
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) ) ) ) )
| ( A
!= ( B
@ ( sk1 @ A
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[42:[bind(A,$thf( ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) )),bind(B,$thf( B )),bind(C,$thf( E @ ( sk1 @ B @ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) ) ))]]) ).
thf(49,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ~ ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1 @ A
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) ) ) ) )
| ( cK
@ ( B
@ ( sk1 @ A
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) ) ) ) )
| ( A
!= ( B
@ ( sk1 @ A
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[48:[]]) ).
thf(52,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ~ ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1 @ A
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) ) ) ) )
| ( cK
@ ( B
@ ( sk1 @ A
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) ) ) ) )
| ( A
!= ( B
@ ( sk1 @ A
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(7075,plain,
! [A: a] :
( ~ ( sk6 @ A )
| ~ $true
| ( ( cK @ sk6 @ A )
!= ( cK
@ ^ [B: a] : $false
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[7068,2798]) ).
thf(7076,plain,
! [A: a] :
( ~ ( sk6 @ A )
| ( ( cK @ sk6 @ A )
!= ( cK
@ ^ [B: a] : $false
@ sk2 ) ) ),
inference(simp,[status(thm)],[7075]) ).
thf(7122,plain,
! [A: a] :
( ~ ( sk6 @ A )
| ( sk6
!= ( ^ [B: a] : $false ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[7076]) ).
thf(7142,plain,
( ~ ( sk6 @ sk2 )
| ( sk6
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[7122]) ).
thf(7224,plain,
( ( sk6 @ sk29 )
| ~ ( sk6 @ sk2 ) ),
inference(func_ext,[status(esa)],[7142]) ).
thf(7335,plain,
! [A: a] :
( ~ ( sk6 @ sk2 )
| ~ $true
| ( cK @ sk6 @ A )
| ( ( sk6 @ sk29 )
!= ( sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7224,7068]) ).
thf(7336,plain,
! [A: a] :
( ~ ( sk6 @ sk2 )
| ( cK @ sk6 @ A )
| ( ( sk6 @ sk29 )
!= ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[7335]) ).
thf(7337,plain,
( ~ ( sk6 @ sk2 )
| ( cK @ sk6 @ sk29 ) ),
inference(pattern_uni,[status(thm)],[7336:[bind(A,$thf( sk29 ))]]) ).
thf(105,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( sk3 @ sk4 )
| ~ $true
| ~ ( cK @ A @ C )
| ( cK @ B @ C )
| ( ( B @ ( sk1 @ B @ A ) )
!= ( sk6 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[76,8]) ).
thf(106,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( sk3 @ sk4 )
| ~ ( cK @ A @ C )
| ( cK @ B @ C )
| ( ( B @ ( sk1 @ B @ A ) )
!= ( sk6 @ sk4 ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(135,plain,
! [B: a,A: a > $o] :
( ( sk3 @ sk4 )
| ~ ( cK @ A @ B )
| ( cK
@ ^ [C: a] : ( sk6 @ sk4 )
@ B ) ),
inference(pre_uni,[status(thm)],[106:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : ( sk6 @ sk4 ) )),bind(C,$thf( C ))]]) ).
thf(143,plain,
! [B: a,A: a > $o] :
( ( sk3 @ sk4 )
| ~ ( cK @ A @ B )
| ( cK
@ ^ [C: a] : ( sk6 @ sk4 )
@ B ) ),
inference(simp,[status(thm)],[135]) ).
thf(12479,plain,
! [B: a,A: a > $o] :
( $false
| ~ ( cK @ A @ B )
| ( cK
@ ^ [C: a] : $true
@ B ) ),
inference(rewrite,[status(thm)],[143,6994,6937]) ).
thf(12480,plain,
! [B: a,A: a > $o] :
( ~ ( cK @ A @ B )
| ( cK
@ ^ [C: a] : $true
@ B ) ),
inference(simp,[status(thm)],[12479]) ).
thf(12550,plain,
! [B: a,A: a > $o] :
( ~ ( sk6 @ sk2 )
| ~ $true
| ( cK
@ ^ [C: a] : $true
@ B )
| ( ( cK @ sk6 @ sk29 )
!= ( cK @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7337,12480]) ).
thf(12551,plain,
! [B: a,A: a > $o] :
( ~ ( sk6 @ sk2 )
| ( cK
@ ^ [C: a] : $true
@ B )
| ( ( cK @ sk6 @ sk29 )
!= ( cK @ A @ B ) ) ),
inference(simp,[status(thm)],[12550]) ).
thf(12552,plain,
( ~ ( sk6 @ sk2 )
| ( cK
@ ^ [A: a] : $true
@ sk29 ) ),
inference(pattern_uni,[status(thm)],[12551:[bind(A,$thf( sk6 )),bind(B,$thf( sk29 ))]]) ).
thf(119,plain,
! [C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ( cK @ B @ C )
| ( ( cK @ A @ C )
!= ( B @ ( sk1 @ B @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8]) ).
thf(130,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ~ ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ),
inference(pre_uni,[status(thm)],[119:[bind(A,$thf( A )),bind(B,$thf( ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) )),bind(C,$thf( E @ ( sk1 @ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) @ A ) ))]]) ).
thf(131,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ~ ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ),
inference(pre_uni,[status(thm)],[130:[]]) ).
thf(141,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ~ ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(12969,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ~ ( sk6 @ sk2 )
| ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ~ $true
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
!= ( cK
@ ^ [D: a] : $true
@ sk29 ) ) ),
inference(paramod_ordered,[status(thm)],[12552,141]) ).
thf(12970,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ~ ( sk6 @ sk2 )
| ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
!= ( cK
@ ^ [D: a] : $true
@ sk29 ) ) ),
inference(simp,[status(thm)],[12969]) ).
thf(13024,plain,
! [A: a > $o] :
( ~ ( sk6 @ sk2 )
| ( cK
@ ^ [B: a] :
( cK
@ ^ [C: a] : $true
@ sk29 )
@ sk29 )
| ( A
!= ( ^ [B: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[12970:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : ^ [E: a] : $true )),bind(C,$thf( ^ [D: a] : sk29 ))]]) ).
thf(13025,plain,
( ( cK
@ ^ [A: a] :
( cK
@ ^ [B: a] : $true
@ sk29 )
@ sk29 )
| ~ ( sk6 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[13024:[bind(A,$thf( ^ [B: a] : $true ))]]) ).
thf(13109,plain,
! [A: a > $o] :
( ~ ( sk6 @ sk2 )
| ~ $true
| ( cK @ A @ sk2 )
| ( ( A @ ( sk1 @ A @ sk3 ) )
!= ( sk6 @ sk29 ) ) ),
inference(paramod_ordered,[status(thm)],[7224,144]) ).
thf(13110,plain,
! [A: a > $o] :
( ~ ( sk6 @ sk2 )
| ( cK @ A @ sk2 )
| ( ( A @ ( sk1 @ A @ sk3 ) )
!= ( sk6 @ sk29 ) ) ),
inference(simp,[status(thm)],[13109]) ).
thf(13277,plain,
( ~ ( sk6 @ sk2 )
| ( cK
@ ^ [A: a] : ( sk6 @ sk29 )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[13110:[bind(A,$thf( ^ [B: a] : ( sk6 @ sk29 ) ))]]) ).
thf(14949,plain,
( ~ ( sk6 @ sk2 )
| ~ $true
| ( ( cK
@ ^ [A: a] : ( sk6 @ sk29 )
@ sk2 )
!= ( cK
@ ^ [A: a] : $false
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[13277,2798]) ).
thf(14950,plain,
( ~ ( sk6 @ sk2 )
| ( ( cK
@ ^ [A: a] : ( sk6 @ sk29 )
@ sk2 )
!= ( cK
@ ^ [A: a] : $false
@ sk2 ) ) ),
inference(simp,[status(thm)],[14949]) ).
thf(15033,plain,
( ~ ( sk6 @ sk2 )
| ( ( ^ [A: a] : ( sk6 @ sk29 ) )
!= ( ^ [A: a] : $false ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[14950]) ).
thf(15073,plain,
( ~ ( sk6 @ sk2 )
| ( ( ^ [A: a] : ( sk6 @ sk29 ) )
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[15033]) ).
thf(164,plain,
! [A: a > $o] :
( ( sk3 @ ( sk1 @ A @ sk3 ) )
| ~ $true
| ( ( cK
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ sk2 )
!= ( cK @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[56,6]) ).
thf(165,plain,
! [A: a > $o] :
( ( sk3 @ ( sk1 @ A @ sk3 ) )
| ( ( cK
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ sk2 )
!= ( cK @ A @ sk2 ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(166,plain,
( sk3
@ ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 ) ),
inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( ^ [B: a] : ? [C: a > $o] : ( ! [D: a] : ( ( C @ D ) => ( cK @ C @ D ) ) & ( C @ B ) ) ))]]) ).
thf(197,plain,
! [A: a] :
( ~ $true
| ( cK @ sk3 @ A )
| ( ( sk3
@ ( sk1
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ sk3 ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[166,10]) ).
thf(198,plain,
! [A: a] :
( ( cK @ sk3 @ A )
| ( ( sk3
@ ( sk1
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ sk3 ) )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[197]) ).
thf(199,plain,
( cK @ sk3
@ ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 ) ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( sk1 @ ^ [B: a] : ? [C: a > $o] : ( ! [D: a] : ( ( C @ D ) => ( cK @ C @ D ) ) & ( C @ B ) ) @ sk3 ))]]) ).
thf(211,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ $true
| ( cK @ B @ C )
| ( ( cK @ sk3
@ ( sk1
@ ^ [D: a] :
? [E: a > $o] :
( ! [F: a] :
( ( E @ F )
=> ( cK @ E @ F ) )
& ( E @ D ) )
@ sk3 ) )
!= ( cK @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[199,7]) ).
thf(212,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ( cK @ B @ C )
| ( ( cK @ sk3
@ ( sk1
@ ^ [D: a] :
? [E: a > $o] :
( ! [F: a] :
( ( E @ F )
=> ( cK @ E @ F ) )
& ( E @ D ) )
@ sk3 ) )
!= ( cK @ A @ C ) ) ),
inference(simp,[status(thm)],[211]) ).
thf(213,plain,
! [A: a > $o] :
( ( sk3 @ ( sk1 @ A @ sk3 ) )
| ( cK @ A
@ ( sk1
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[212:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk1 @ ^ [D: a] : ? [E: a > $o] : ( ! [F: a] : ( ( E @ F ) => ( cK @ E @ F ) ) & ( E @ D ) ) @ sk3 ))]]) ).
thf(216,plain,
! [A: a > $o] :
( ( sk3 @ ( sk1 @ A @ sk3 ) )
| ( cK @ A
@ ( sk1
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ sk3 ) ) ),
inference(simp,[status(thm)],[213]) ).
thf(13470,plain,
( ~ $true
| ( ( cK @ ( cK @ sk3 ) @ sk2 )
!= ( cK
@ ^ [A: a] : $false
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[13422,2798]) ).
thf(13471,plain,
( ( cK @ ( cK @ sk3 ) @ sk2 )
!= ( cK
@ ^ [A: a] : $false
@ sk2 ) ),
inference(simp,[status(thm)],[13470]) ).
thf(13507,plain,
( ( ( cK @ sk3 )
!= ( ^ [A: a] : $false ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[13471]) ).
thf(13523,plain,
( ( cK @ sk3 )
!= ( ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[13507]) ).
thf(13540,plain,
cK @ sk3 @ sk35,
inference(func_ext,[status(esa)],[13523]) ).
thf(13602,plain,
! [B: a,A: a > $o] :
( ~ $true
| ( cK
@ ^ [C: a] : $true
@ B )
| ( ( cK @ sk3 @ sk35 )
!= ( cK @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13540,12480]) ).
thf(13603,plain,
! [B: a,A: a > $o] :
( ( cK
@ ^ [C: a] : $true
@ B )
| ( ( cK @ sk3 @ sk35 )
!= ( cK @ A @ B ) ) ),
inference(simp,[status(thm)],[13602]) ).
thf(13604,plain,
( cK
@ ^ [A: a] : $true
@ sk35 ),
inference(pattern_uni,[status(thm)],[13603:[bind(A,$thf( sk3 )),bind(B,$thf( sk35 ))]]) ).
thf(107,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( D @ ( sk1 @ E @ D ) )
| ~ $true
| ( cK @ E @ F )
| ( ( cK @ B @ C )
!= ( cK @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[8,7]) ).
thf(108,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( D @ ( sk1 @ E @ D ) )
| ( cK @ E @ F )
| ( ( cK @ B @ C )
!= ( cK @ D @ F ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(109,plain,
! [D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( B @ ( sk1 @ D @ B ) )
| ( cK @ D @ C ) ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( E )),bind(F,$thf( C ))]]) ).
thf(147,plain,
! [D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( B @ ( sk1 @ D @ B ) )
| ( cK @ D @ C ) ),
inference(simp,[status(thm)],[109]) ).
thf(46,plain,
! [D: a > a,C: a > a > $o,B: a,A: a > $o] :
( ( cK
@ ( C
@ ( sk1 @ A
@ ^ [E: a] : ( cK @ ( C @ E ) @ ( D @ E ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [E: a] : ( cK @ ( C @ E ) @ ( D @ E ) ) ) ) )
| ~ ( cK
@ ^ [E: a] : ( cK @ ( C @ E ) @ ( D @ E ) )
@ B )
| ( cK @ A @ B ) ),
inference(prim_subst,[status(thm)],[7:[bind(A,$thf( ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) ))]]) ).
thf(61,plain,
! [D: a > a,C: a > a > $o,B: a,A: a > $o] :
( ( cK
@ ( C
@ ( sk1 @ A
@ ^ [E: a] : ( cK @ ( C @ E ) @ ( D @ E ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [E: a] : ( cK @ ( C @ E ) @ ( D @ E ) ) ) ) )
| ~ ( cK
@ ^ [E: a] : ( cK @ ( C @ E ) @ ( D @ E ) )
@ B )
| ( cK @ A @ B ) ),
inference(simp,[status(thm)],[46]) ).
thf(3217,plain,
! [A: a] :
( ~ $true
| ( cK @ sk3 @ A )
| ( ( sk3
@ ( sk1
@ ^ [B: a] : $false
@ sk3 ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2981,10]) ).
thf(3218,plain,
! [A: a] :
( ( cK @ sk3 @ A )
| ( ( sk3
@ ( sk1
@ ^ [B: a] : $false
@ sk3 ) )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[3217]) ).
thf(3219,plain,
( cK @ sk3
@ ( sk1
@ ^ [A: a] : $false
@ sk3 ) ),
inference(pattern_uni,[status(thm)],[3218:[bind(A,$thf( sk1 @ ^ [B: a] : $false @ sk3 ))]]) ).
thf(10834,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ~ $true
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK @ sk3
@ ( sk1
@ ^ [D: a] : $false
@ sk3 ) )
!= ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3219,141]) ).
thf(10835,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK @ sk3
@ ( sk1
@ ^ [D: a] : $false
@ sk3 ) )
!= ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ) ),
inference(simp,[status(thm)],[10834]) ).
thf(11012,plain,
! [A: a > $o] :
( ( cK
@ ^ [B: a] :
( cK @ sk3
@ ( sk1
@ ^ [C: a] : $false
@ sk3 ) )
@ ( sk1
@ ^ [B: a] : $false
@ sk3 ) )
| ( A != sk3 ) ),
inference(pre_uni,[status(thm)],[10835:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : sk3 )),bind(C,$thf( ^ [D: a] : ( sk1 @ ^ [E: a] : $false @ sk3 ) ))]]) ).
thf(11013,plain,
( cK
@ ^ [A: a] :
( cK @ sk3
@ ( sk1
@ ^ [B: a] : $false
@ sk3 ) )
@ ( sk1
@ ^ [A: a] : $false
@ sk3 ) ),
inference(pattern_uni,[status(thm)],[11012:[bind(A,$thf( sk3 ))]]) ).
thf(12249,plain,
( cK
@ ^ [A: a] : $true
@ ( sk1
@ ^ [A: a] : $false
@ sk3 ) ),
inference(rewrite,[status(thm)],[11013,3219]) ).
thf(110,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( cK @ A @ C )
| ( cK @ B @ C )
| ~ $true
| ~ ( cK @ D @ F )
| ( cK @ E @ F )
| ( ( A @ ( sk1 @ B @ A ) )
!= ( E @ ( sk1 @ E @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,8]) ).
thf(111,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( cK @ A @ C )
| ( cK @ B @ C )
| ~ ( cK @ D @ F )
| ( cK @ E @ F )
| ( ( A @ ( sk1 @ B @ A ) )
!= ( E @ ( sk1 @ E @ D ) ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(132,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( cK @ A @ C )
| ( cK @ B @ C )
| ~ ( cK @ D @ F )
| ( cK @ E @ F )
| ( ( A @ ( sk1 @ B @ A ) )
!= ( E @ ( sk1 @ E @ D ) ) ) ),
inference(pre_uni,[status(thm)],[111:[]]) ).
thf(133,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ( cK @ E @ F )
| ~ ( cK @ D @ F )
| ( cK @ B @ C )
| ~ ( cK @ A @ C )
| ( ( A @ ( sk1 @ B @ A ) )
!= ( E @ ( sk1 @ E @ D ) ) ) ),
inference(pre_uni,[status(thm)],[132:[]]) ).
thf(45,plain,
! [C: a > $o,B: a,A: a > $o] :
( ~ ( C
@ ( sk1 @ A
@ ^ [D: a] :
~ ( C @ D ) ) )
| ~ ( cK
@ ^ [D: a] :
~ ( C @ D )
@ B )
| ( cK @ A @ B ) ),
inference(prim_subst,[status(thm)],[7:[bind(A,$thf( ^ [E: a] : ~ ( D @ E ) ))]]) ).
thf(59,plain,
! [C: a > $o,B: a,A: a > $o] :
( ~ ( C
@ ( sk1 @ A
@ ^ [D: a] :
~ ( C @ D ) ) )
| ~ ( cK
@ ^ [D: a] :
~ ( C @ D )
@ B )
| ( cK @ A @ B ) ),
inference(cnf,[status(esa)],[45]) ).
thf(60,plain,
! [C: a > $o,B: a,A: a > $o] :
( ~ ( C
@ ( sk1 @ A
@ ^ [D: a] :
~ ( C @ D ) ) )
| ~ ( cK
@ ^ [D: a] :
~ ( C @ D )
@ B )
| ( cK @ A @ B ) ),
inference(simp,[status(thm)],[59]) ).
thf(7018,plain,
( ~ $true
| ( ( sk3
@ ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 ) )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[166,6937]) ).
thf(7019,plain,
( ( sk3
@ ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 ) )
!= ( sk3 @ sk4 ) ),
inference(simp,[status(thm)],[7018]) ).
thf(7037,plain,
( ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 )
!= sk4 ),
inference(simp,[status(thm)],[7019]) ).
thf(18093,plain,
! [B: a,A: a > $o] :
( ( sk78 @ sk37 )
| ~ $true
| ( cK
@ ^ [C: a] : $true
@ B )
| ( ( cK @ sk3 @ sk37 )
!= ( cK @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17908,12480]) ).
thf(18094,plain,
! [B: a,A: a > $o] :
( ( sk78 @ sk37 )
| ( cK
@ ^ [C: a] : $true
@ B )
| ( ( cK @ sk3 @ sk37 )
!= ( cK @ A @ B ) ) ),
inference(simp,[status(thm)],[18093]) ).
thf(18095,plain,
( ( sk78 @ sk37 )
| ( cK
@ ^ [A: a] : $true
@ sk37 ) ),
inference(pattern_uni,[status(thm)],[18094:[bind(A,$thf( sk3 )),bind(B,$thf( sk37 ))]]) ).
thf(18198,plain,
! [A: a > $o] :
( ( sk78 @ sk37 )
| ~ $true
| ( cK @ A @ sk2 )
| ( ( A @ ( sk1 @ A @ sk3 ) )
!= ( cK
@ ^ [B: a] : $true
@ sk37 ) ) ),
inference(paramod_ordered,[status(thm)],[18095,144]) ).
thf(18199,plain,
! [A: a > $o] :
( ( sk78 @ sk37 )
| ( cK @ A @ sk2 )
| ( ( A @ ( sk1 @ A @ sk3 ) )
!= ( cK
@ ^ [B: a] : $true
@ sk37 ) ) ),
inference(simp,[status(thm)],[18198]) ).
thf(18244,plain,
( ( sk78 @ sk37 )
| ( cK
@ ^ [A: a] :
( cK
@ ^ [B: a] : $true
@ sk37 )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[18199:[bind(A,$thf( ^ [B: a] : ( cK @ ^ [C: a] : $true @ sk37 ) ))]]) ).
thf(22378,plain,
( ( sk78 @ sk37 )
| ~ $true
| ( ( cK
@ ^ [A: a] :
( cK
@ ^ [B: a] : $true
@ sk37 )
@ sk2 )
!= ( cK
@ ^ [A: a] : $false
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[18244,2798]) ).
thf(22379,plain,
( ( sk78 @ sk37 )
| ( ( cK
@ ^ [A: a] :
( cK
@ ^ [B: a] : $true
@ sk37 )
@ sk2 )
!= ( cK
@ ^ [A: a] : $false
@ sk2 ) ) ),
inference(simp,[status(thm)],[22378]) ).
thf(22509,plain,
( ( sk78 @ sk37 )
| ( ( ^ [A: a] :
( cK
@ ^ [B: a] : $true
@ sk37 ) )
!= ( ^ [A: a] : $false ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[22379]) ).
thf(22682,plain,
( ( sk78 @ sk37 )
| ( ( ^ [A: a] :
( cK
@ ^ [B: a] : $true
@ sk37 ) )
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[22509]) ).
thf(10780,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ~ ( sk6 @ sk2 )
| ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ~ $true
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK @ sk6 @ sk29 )
!= ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7337,141]) ).
thf(10781,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ~ ( sk6 @ sk2 )
| ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK @ sk6 @ sk29 )
!= ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ) ),
inference(simp,[status(thm)],[10780]) ).
thf(11036,plain,
! [A: a > $o] :
( ~ ( sk6 @ sk2 )
| ( cK
@ ^ [B: a] : ( cK @ sk6 @ sk29 )
@ sk29 )
| ( A != sk6 ) ),
inference(pre_uni,[status(thm)],[10781:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : sk6 )),bind(C,$thf( ^ [D: a] : sk29 ))]]) ).
thf(11037,plain,
( ( cK
@ ^ [A: a] : ( cK @ sk6 @ sk29 )
@ sk29 )
| ~ ( sk6 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[11036:[bind(A,$thf( sk6 ))]]) ).
thf(90,plain,
! [C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ~ $true
| ( ( cK @ B @ C )
!= ( cK
@ ^ [D: a] :
? [E: a > $o] :
( ! [F: a] :
( ( E @ F )
=> ( cK @ E @ F ) )
& ( E @ D ) )
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[8,6]) ).
thf(91,plain,
! [C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( ( cK @ B @ C )
!= ( cK
@ ^ [D: a] :
? [E: a > $o] :
( ! [F: a] :
( ( E @ F )
=> ( cK @ E @ F ) )
& ( E @ D ) )
@ sk2 ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(92,plain,
! [A: a > $o] :
( ~ ? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ A ) ) )
| ~ ( cK @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : ? [E: a > $o] : ( ! [F: a] : ( ( E @ F ) => ( cK @ E @ F ) ) & ( E @ D ) ) )),bind(C,$thf( sk2 ))]]) ).
thf(158,plain,
! [B: a > $o,A: a > $o] :
( ( ( B @ ( sk9 @ B @ A ) )
| ~ ( B
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ A ) )
| ~ ( cK @ A @ sk2 ) )
& ( ~ ( cK @ B @ ( sk9 @ B @ A ) )
| ~ ( B
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ A ) )
| ~ ( cK @ A @ sk2 ) ) ),
inference(cnf,[status(esa)],[92]) ).
thf(160,plain,
! [B: a > $o,A: a > $o] :
( ~ ( cK @ B @ ( sk9 @ B @ A ) )
| ~ ( B
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ A ) )
| ~ ( cK @ A @ sk2 ) ),
inference(cnfConj,[status(thm)],[158]) ).
thf(3017,plain,
( ~ $true
| ( ( cK @ sk3 @ sk2 )
!= ( cK
@ ^ [A: a] : $false
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[15,2798]) ).
thf(3018,plain,
( ( cK @ sk3 @ sk2 )
!= ( cK
@ ^ [A: a] : $false
@ sk2 ) ),
inference(simp,[status(thm)],[3017]) ).
thf(3034,plain,
( ( sk3
!= ( ^ [A: a] : $false ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[3018]) ).
thf(3050,plain,
( sk3
!= ( ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[3034]) ).
thf(3056,plain,
sk3 @ sk20,
inference(func_ext,[status(esa)],[3050]) ).
thf(3072,plain,
! [A: a] :
( ~ $true
| ( cK @ sk3 @ A )
| ( ( sk3 @ sk20 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3056,10]) ).
thf(3073,plain,
! [A: a] :
( ( cK @ sk3 @ A )
| ( ( sk3 @ sk20 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[3072]) ).
thf(3074,plain,
cK @ sk3 @ sk20,
inference(pattern_uni,[status(thm)],[3073:[bind(A,$thf( sk20 ))]]) ).
thf(3162,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ $true
| ( cK @ B @ C )
| ( ( cK @ sk3 @ sk20 )
!= ( cK @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[3074,7]) ).
thf(3163,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ( cK @ B @ C )
| ( ( cK @ sk3 @ sk20 )
!= ( cK @ A @ C ) ) ),
inference(simp,[status(thm)],[3162]) ).
thf(3164,plain,
! [A: a > $o] :
( ( sk3 @ ( sk1 @ A @ sk3 ) )
| ( cK @ A @ sk20 ) ),
inference(pattern_uni,[status(thm)],[3163:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk20 ))]]) ).
thf(3198,plain,
! [A: a > $o] :
( ( sk3 @ ( sk1 @ A @ sk3 ) )
| ( cK @ A @ sk20 ) ),
inference(simp,[status(thm)],[3164]) ).
thf(12690,plain,
! [B: a,A: a > $o] :
( ~ $true
| ( cK
@ ^ [C: a] : $true
@ B )
| ( ( cK @ sk3
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ sk3 ) )
!= ( cK @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[199,12480]) ).
thf(12691,plain,
! [B: a,A: a > $o] :
( ( cK
@ ^ [C: a] : $true
@ B )
| ( ( cK @ sk3
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ sk3 ) )
!= ( cK @ A @ B ) ) ),
inference(simp,[status(thm)],[12690]) ).
thf(12692,plain,
( cK
@ ^ [A: a] : $true
@ ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 ) ),
inference(pattern_uni,[status(thm)],[12691:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 @ ^ [C: a] : ? [D: a > $o] : ( ! [E: a] : ( ( D @ E ) => ( cK @ D @ E ) ) & ( D @ C ) ) @ sk3 ))]]) ).
thf(10752,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ~ $true
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK @ sk3 @ sk2 )
!= ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,141]) ).
thf(10753,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK @ sk3 @ sk2 )
!= ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ) ),
inference(simp,[status(thm)],[10752]) ).
thf(10905,plain,
! [A: a > $o] :
( ( cK
@ ^ [B: a] : ( cK @ sk3 @ sk2 )
@ sk2 )
| ( A != sk3 ) ),
inference(pre_uni,[status(thm)],[10753:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : sk3 )),bind(C,$thf( ^ [D: a] : sk2 ))]]) ).
thf(10906,plain,
( cK
@ ^ [A: a] : ( cK @ sk3 @ sk2 )
@ sk2 ),
inference(pattern_uni,[status(thm)],[10905:[bind(A,$thf( sk3 ))]]) ).
thf(11123,plain,
( cK
@ ^ [A: a] : $true
@ sk2 ),
inference(rewrite,[status(thm)],[10906,15]) ).
thf(159,plain,
! [B: a > $o,A: a > $o] :
( ( B @ ( sk9 @ B @ A ) )
| ~ ( B
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ A ) )
| ~ ( cK @ A @ sk2 ) ),
inference(cnfConj,[status(thm)],[158]) ).
thf(26004,plain,
! [B: a > $o,A: a > $o] :
( ( B @ ( sk9 @ B @ A ) )
| ~ ( B
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ A ) )
| ~ $true
| ( ( cK
@ ^ [C: a] : $true
@ sk2 )
!= ( cK @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[11123,159]) ).
thf(26005,plain,
! [B: a > $o,A: a > $o] :
( ( B @ ( sk9 @ B @ A ) )
| ~ ( B
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ A ) )
| ( ( cK
@ ^ [C: a] : $true
@ sk2 )
!= ( cK @ A @ sk2 ) ) ),
inference(simp,[status(thm)],[26004]) ).
thf(26006,plain,
! [A: a > $o] :
( ( A
@ ( sk9 @ A
@ ^ [B: a] : $true ) )
| ~ ( A
@ ( sk1
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ ^ [B: a] : $true ) ) ),
inference(pattern_uni,[status(thm)],[26005:[bind(A,$thf( ^ [C: a] : $true ))]]) ).
thf(26142,plain,
( ( ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ^ [A: a] : $true )
= ( sk9
@ ( (=) @ a
@ ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ^ [A: a] : $true ) )
@ ^ [A: a] : $true ) )
| ( ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ^ [A: a] : $true )
!= ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ^ [A: a] : $true ) ) ),
inference(replace_leibeq,[status(thm)],[26006:[bind(A,$thf( (=) @ a @ ( sk1 @ ^ [B: a] : ? [C: a > $o] : ( ! [D: a] : ( ( C @ D ) => ( cK @ C @ D ) ) & ( C @ B ) ) @ ^ [B: a] : $true ) ))]]) ).
thf(26206,plain,
( ( ( sk9
@ ( (=) @ a
@ ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ^ [A: a] : $true ) )
@ ^ [A: a] : $true )
= ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ^ [A: a] : $true ) )
| ( ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ^ [A: a] : $true )
!= ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ^ [A: a] : $true ) ) ),
inference(lifteq,[status(thm)],[26142]) ).
thf(26410,plain,
( ( sk9
@ ( (=) @ a
@ ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ^ [A: a] : $true ) )
@ ^ [A: a] : $true )
= ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ^ [A: a] : $true ) ),
inference(pattern_uni,[status(thm)],[26206:[]]) ).
thf(25884,plain,
! [B: a > $o,A: a > $o] :
( ( B @ ( sk9 @ B @ A ) )
| ~ ( B
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ A ) )
| ~ $true
| ( ( cK @ ( cK @ sk3 ) @ sk2 )
!= ( cK @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[13422,159]) ).
thf(25885,plain,
! [B: a > $o,A: a > $o] :
( ( B @ ( sk9 @ B @ A ) )
| ~ ( B
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ A ) )
| ( ( cK @ ( cK @ sk3 ) @ sk2 )
!= ( cK @ A @ sk2 ) ) ),
inference(simp,[status(thm)],[25884]) ).
thf(25886,plain,
! [A: a > $o] :
( ( A @ ( sk9 @ A @ ( cK @ sk3 ) ) )
| ~ ( A
@ ( sk1
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ ( cK @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[25885:[bind(A,$thf( cK @ sk3 )),bind(B,$thf( B ))]]) ).
thf(26149,plain,
( ( ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ( cK @ sk3 ) )
= ( sk9
@ ( (=) @ a
@ ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ( cK @ sk3 ) ) )
@ ( cK @ sk3 ) ) )
| ( ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ( cK @ sk3 ) )
!= ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ( cK @ sk3 ) ) ) ),
inference(replace_leibeq,[status(thm)],[25886:[bind(A,$thf( (=) @ a @ ( sk1 @ ^ [B: a] : ? [C: a > $o] : ( ! [D: a] : ( ( C @ D ) => ( cK @ C @ D ) ) & ( C @ B ) ) @ ( cK @ sk3 ) ) ))]]) ).
thf(26196,plain,
( ( ( sk9
@ ( (=) @ a
@ ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ( cK @ sk3 ) ) )
@ ( cK @ sk3 ) )
= ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ( cK @ sk3 ) ) )
| ( ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ( cK @ sk3 ) )
!= ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ( cK @ sk3 ) ) ) ),
inference(lifteq,[status(thm)],[26149]) ).
thf(26521,plain,
( ( sk9
@ ( (=) @ a
@ ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ( cK @ sk3 ) ) )
@ ( cK @ sk3 ) )
= ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ ( cK @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[26196:[]]) ).
thf(121,plain,
! [D: a > $o,C: a > $o,B: a,A: a > $o] :
( ~ ( ( C
@ ( sk1
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ A ) )
| ( D
@ ( sk1
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ A ) ) )
| ~ ( cK @ A @ B )
| ( cK
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ B ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( A )),bind(B,$thf( ^ [F: a] : ( ( D @ F ) | ( E @ F ) ) ))]]) ).
thf(152,plain,
! [D: a > $o,C: a > $o,B: a,A: a > $o] :
( ( ~ ( C
@ ( sk1
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ A ) )
| ~ ( cK @ A @ B )
| ( cK
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ B ) )
& ( ~ ( D
@ ( sk1
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ A ) )
| ~ ( cK @ A @ B )
| ( cK
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ B ) ) ),
inference(cnf,[status(esa)],[121]) ).
thf(154,plain,
! [D: a > $o,C: a > $o,B: a,A: a > $o] :
( ~ ( D
@ ( sk1
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ A ) )
| ~ ( cK @ A @ B )
| ( cK
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ B ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(156,plain,
! [D: a > $o,C: a > $o,B: a,A: a > $o] :
( ~ ( D
@ ( sk1
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ A ) )
| ~ ( cK @ A @ B )
| ( cK
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ B ) ),
inference(simp,[status(thm)],[154]) ).
thf(34,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( cK @ A @ C )
| ( cK @ B @ C )
| ( D @ ( sk1 @ E @ D ) )
| ~ $true
| ( cK @ E @ F )
| ( ( A @ ( sk1 @ B @ A ) )
!= ( cK @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(35,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( cK @ A @ C )
| ( cK @ B @ C )
| ( D @ ( sk1 @ E @ D ) )
| ( cK @ E @ F )
| ( ( A @ ( sk1 @ B @ A ) )
!= ( cK @ D @ F ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(50,plain,
! [E: a > a,D: a > a > $o,C: a > $o,B: a,A: a > $o] :
( ~ ( cK
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ B )
| ( cK @ A @ B )
| ( D
@ ( sk1 @ A
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) )
@ ( sk1 @ C
@ ( D
@ ( sk1 @ A
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) ) ) ) )
| ( cK @ C
@ ( E
@ ( sk1 @ A
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[35:[bind(A,$thf( ^ [I: a] : ( cK @ ( G @ I ) @ ( H @ I ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G @ ( sk1 @ B @ ^ [I: a] : ( cK @ ( G @ I ) @ ( H @ I ) ) ) )),bind(E,$thf( E )),bind(F,$thf( H @ ( sk1 @ B @ ^ [I: a] : ( cK @ ( G @ I ) @ ( H @ I ) ) ) ))]]) ).
thf(53,plain,
! [E: a > a,D: a > a > $o,C: a > $o,B: a,A: a > $o] :
( ~ ( cK
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ B )
| ( cK @ A @ B )
| ( D
@ ( sk1 @ A
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) )
@ ( sk1 @ C
@ ( D
@ ( sk1 @ A
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) ) ) ) )
| ( cK @ C
@ ( E
@ ( sk1 @ A
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) ) ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(380,plain,
! [B: a,A: a > $o] :
( ( cK @ A
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ sk3 ) )
| ~ $true
| ( cK @ sk3 @ B )
| ( ( sk3 @ ( sk1 @ A @ sk3 ) )
!= ( sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[216,10]) ).
thf(381,plain,
! [B: a,A: a > $o] :
( ( cK @ A
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ sk3 ) )
| ( cK @ sk3 @ B )
| ( ( sk3 @ ( sk1 @ A @ sk3 ) )
!= ( sk3 @ B ) ) ),
inference(simp,[status(thm)],[380]) ).
thf(382,plain,
! [A: a > $o] :
( ( cK @ A
@ ( sk1
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ sk3 ) )
| ( cK @ sk3 @ ( sk1 @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[381:[bind(A,$thf( C )),bind(B,$thf( sk1 @ C @ sk3 ))]]) ).
thf(403,plain,
! [A: a > $o] :
( ( cK @ A
@ ( sk1
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ sk3 ) )
| ( cK @ sk3 @ ( sk1 @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[382]) ).
thf(10852,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ~ $true
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK @ sk6 @ sk4 )
!= ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7102,141]) ).
thf(10853,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK @ sk6 @ sk4 )
!= ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ) ),
inference(simp,[status(thm)],[10852]) ).
thf(11031,plain,
! [A: a > $o] :
( ( cK
@ ^ [B: a] : ( cK @ sk6 @ sk4 )
@ sk4 )
| ( A != sk6 ) ),
inference(pre_uni,[status(thm)],[10853:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : sk6 )),bind(C,$thf( ^ [D: a] : sk4 ))]]) ).
thf(11032,plain,
( cK
@ ^ [A: a] : ( cK @ sk6 @ sk4 )
@ sk4 ),
inference(pattern_uni,[status(thm)],[11031:[bind(A,$thf( sk6 ))]]) ).
thf(11229,plain,
( cK
@ ^ [A: a] : $true
@ sk4 ),
inference(rewrite,[status(thm)],[11032,7102]) ).
thf(7267,plain,
! [B: a,A: a > $o] :
( ( cK @ A @ sk4 )
| ~ $true
| ( cK @ sk6 @ B )
| ( ( sk6 @ ( sk1 @ A @ sk6 ) )
!= ( sk6 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7203,7068]) ).
thf(7268,plain,
! [B: a,A: a > $o] :
( ( cK @ A @ sk4 )
| ( cK @ sk6 @ B )
| ( ( sk6 @ ( sk1 @ A @ sk6 ) )
!= ( sk6 @ B ) ) ),
inference(simp,[status(thm)],[7267]) ).
thf(7269,plain,
! [A: a > $o] :
( ( cK @ A @ sk4 )
| ( cK @ sk6 @ ( sk1 @ A @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[7268:[bind(A,$thf( C )),bind(B,$thf( sk1 @ C @ sk6 ))]]) ).
thf(7313,plain,
! [A: a > $o] :
( ( cK @ A @ sk4 )
| ( cK @ sk6 @ ( sk1 @ A @ sk6 ) ) ),
inference(simp,[status(thm)],[7269]) ).
thf(18186,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( sk78 @ sk37 )
| ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ~ $true
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
!= ( cK
@ ^ [D: a] : $true
@ sk37 ) ) ),
inference(paramod_ordered,[status(thm)],[18095,141]) ).
thf(18187,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( sk78 @ sk37 )
| ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
!= ( cK
@ ^ [D: a] : $true
@ sk37 ) ) ),
inference(simp,[status(thm)],[18186]) ).
thf(18254,plain,
! [A: a > $o] :
( ( sk78 @ sk37 )
| ( cK
@ ^ [B: a] :
( cK
@ ^ [C: a] : $true
@ sk37 )
@ sk37 )
| ( A
!= ( ^ [B: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[18187:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : ^ [E: a] : $true )),bind(C,$thf( ^ [D: a] : sk37 ))]]) ).
thf(18255,plain,
( ( cK
@ ^ [A: a] :
( cK
@ ^ [B: a] : $true
@ sk37 )
@ sk37 )
| ( sk78 @ sk37 ) ),
inference(pattern_uni,[status(thm)],[18254:[bind(A,$thf( ^ [B: a] : $true ))]]) ).
thf(116,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ~ ( E @ ( sk1 @ E @ D ) )
| ~ $true
| ( cK @ E @ F )
| ( ( cK @ B @ C )
!= ( cK @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[7,8]) ).
thf(117,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ~ ( E @ ( sk1 @ E @ D ) )
| ( cK @ E @ F )
| ( ( cK @ B @ C )
!= ( cK @ D @ F ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(118,plain,
! [D: a > $o,C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ~ ( D @ ( sk1 @ D @ B ) )
| ( cK @ D @ C ) ),
inference(pattern_uni,[status(thm)],[117:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( E )),bind(F,$thf( C ))]]) ).
thf(148,plain,
! [D: a > $o,C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ~ ( D @ ( sk1 @ D @ B ) )
| ( cK @ D @ C ) ),
inference(simp,[status(thm)],[118]) ).
thf(13237,plain,
! [A: a > $o] :
( ~ ( sk6 @ sk2 )
| ~ $true
| ( cK @ A @ sk2 )
| ( ( A @ ( sk1 @ A @ sk3 ) )
!= ( cK
@ ^ [B: a] : $true
@ sk29 ) ) ),
inference(paramod_ordered,[status(thm)],[12552,144]) ).
thf(13238,plain,
! [A: a > $o] :
( ~ ( sk6 @ sk2 )
| ( cK @ A @ sk2 )
| ( ( A @ ( sk1 @ A @ sk3 ) )
!= ( cK
@ ^ [B: a] : $true
@ sk29 ) ) ),
inference(simp,[status(thm)],[13237]) ).
thf(13285,plain,
( ~ ( sk6 @ sk2 )
| ( cK
@ ^ [A: a] :
( cK
@ ^ [B: a] : $true
@ sk29 )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[13238:[bind(A,$thf( ^ [B: a] : ( cK @ ^ [C: a] : $true @ sk29 ) ))]]) ).
thf(23899,plain,
( ~ ( sk6 @ sk2 )
| ~ $true
| ( ( cK
@ ^ [A: a] :
( cK
@ ^ [B: a] : $true
@ sk29 )
@ sk2 )
!= ( cK
@ ^ [A: a] : $false
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[13285,2798]) ).
thf(23900,plain,
( ~ ( sk6 @ sk2 )
| ( ( cK
@ ^ [A: a] :
( cK
@ ^ [B: a] : $true
@ sk29 )
@ sk2 )
!= ( cK
@ ^ [A: a] : $false
@ sk2 ) ) ),
inference(simp,[status(thm)],[23899]) ).
thf(24090,plain,
( ~ ( sk6 @ sk2 )
| ( ( ^ [A: a] :
( cK
@ ^ [B: a] : $true
@ sk29 ) )
!= ( ^ [A: a] : $false ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[23900]) ).
thf(24185,plain,
( ~ ( sk6 @ sk2 )
| ( ( ^ [A: a] :
( cK
@ ^ [B: a] : $true
@ sk29 ) )
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[24090]) ).
thf(10744,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ~ $true
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK @ sk3 @ sk20 )
!= ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3074,141]) ).
thf(10745,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK @ sk3 @ sk20 )
!= ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ) ),
inference(simp,[status(thm)],[10744]) ).
thf(11052,plain,
! [A: a > $o] :
( ( cK
@ ^ [B: a] : ( cK @ sk3 @ sk20 )
@ sk20 )
| ( A != sk3 ) ),
inference(pre_uni,[status(thm)],[10745:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : sk3 )),bind(C,$thf( ^ [D: a] : sk20 ))]]) ).
thf(11053,plain,
( cK
@ ^ [A: a] : ( cK @ sk3 @ sk20 )
@ sk20 ),
inference(pattern_uni,[status(thm)],[11052:[bind(A,$thf( sk3 ))]]) ).
thf(11333,plain,
( cK
@ ^ [A: a] : $true
@ sk20 ),
inference(rewrite,[status(thm)],[11053,3074]) ).
thf(7004,plain,
( ~ $true
| ( ( sk3 @ sk20 )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[3056,6937]) ).
thf(7005,plain,
( ( sk3 @ sk20 )
!= ( sk3 @ sk4 ) ),
inference(simp,[status(thm)],[7004]) ).
thf(7038,plain,
sk20 != sk4,
inference(simp,[status(thm)],[7005]) ).
thf(25,plain,
! [D: a,C: a,B: a > $o,A: a > $o] :
( ~ ( cK @ A @ C )
| ( cK @ B @ C )
| ~ $true
| ( cK @ sk3 @ D )
| ( ( A @ ( sk1 @ B @ A ) )
!= ( sk3 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[7,10]) ).
thf(26,plain,
! [D: a,C: a,B: a > $o,A: a > $o] :
( ~ ( cK @ A @ C )
| ( cK @ B @ C )
| ( cK @ sk3 @ D )
| ( ( A @ ( sk1 @ B @ A ) )
!= ( sk3 @ D ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(51,plain,
! [C: a > a,B: a,A: a > $o] :
( ~ ( cK
@ ^ [D: a] : ( sk3 @ ( C @ D ) )
@ B )
| ( cK @ A @ B )
| ( cK @ sk3
@ ( C
@ ( sk1 @ A
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[26:[bind(A,$thf( ^ [F: a] : ( sk3 @ ( E @ F ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( E @ ( sk1 @ B @ ^ [F: a] : ( sk3 @ ( E @ F ) ) ) ))]]) ).
thf(54,plain,
! [C: a > a,B: a,A: a > $o] :
( ~ ( cK
@ ^ [D: a] : ( sk3 @ ( C @ D ) )
@ B )
| ( cK @ A @ B )
| ( cK @ sk3
@ ( C
@ ( sk1 @ A
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(235,plain,
! [D: a,C: a > $o,B: a > $o,A: a > $o] :
( ( cK @ A @ sk2 )
| ( B @ ( sk1 @ C @ B ) )
| ~ $true
| ( cK @ C @ D )
| ( ( cK @ sk3 @ ( sk1 @ A @ sk3 ) )
!= ( cK @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[185,7]) ).
thf(236,plain,
! [D: a,C: a > $o,B: a > $o,A: a > $o] :
( ( cK @ A @ sk2 )
| ( B @ ( sk1 @ C @ B ) )
| ( cK @ C @ D )
| ( ( cK @ sk3 @ ( sk1 @ A @ sk3 ) )
!= ( cK @ B @ D ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(237,plain,
! [B: a > $o,A: a > $o] :
( ( cK @ B @ sk2 )
| ( sk3 @ ( sk1 @ A @ sk3 ) )
| ( cK @ A @ ( sk1 @ B @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[236:[bind(A,$thf( F )),bind(B,$thf( sk3 )),bind(C,$thf( C )),bind(D,$thf( sk1 @ F @ sk3 ))]]) ).
thf(251,plain,
! [B: a > $o,A: a > $o] :
( ( cK @ B @ sk2 )
| ( sk3 @ ( sk1 @ A @ sk3 ) )
| ( cK @ A @ ( sk1 @ B @ sk3 ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(1231,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( cK @ B @ sk2 )
| ( cK @ A @ ( sk1 @ B @ sk3 ) )
| ~ $true
| ( cK @ sk3 @ C )
| ( ( sk3 @ ( sk1 @ A @ sk3 ) )
!= ( sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[251,10]) ).
thf(1232,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( cK @ B @ sk2 )
| ( cK @ A @ ( sk1 @ B @ sk3 ) )
| ( cK @ sk3 @ C )
| ( ( sk3 @ ( sk1 @ A @ sk3 ) )
!= ( sk3 @ C ) ) ),
inference(simp,[status(thm)],[1231]) ).
thf(1233,plain,
! [B: a > $o,A: a > $o] :
( ( cK @ A @ sk2 )
| ( cK @ B @ ( sk1 @ A @ sk3 ) )
| ( cK @ sk3 @ ( sk1 @ B @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[1232:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( sk1 @ D @ sk3 ))]]) ).
thf(1332,plain,
! [B: a > $o,A: a > $o] :
( ( cK @ A @ sk2 )
| ( cK @ B @ ( sk1 @ A @ sk3 ) )
| ( cK @ sk3 @ ( sk1 @ B @ sk3 ) ) ),
inference(simp,[status(thm)],[1233]) ).
thf(7801,plain,
! [A: a > $o] :
( ( sk6 @ ( sk30 @ A ) )
| ( cK @ A @ sk4 ) ),
inference(func_ext,[status(esa)],[7199]) ).
thf(7863,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( sk6 @ ( sk30 @ A ) )
| ~ $true
| ( cK @ B @ C )
| ( ( cK @ A @ sk4 )
!= ( cK
@ ^ [D: a] : $false
@ C ) ) ),
inference(paramod_ordered,[status(thm)],[7801,57]) ).
thf(7864,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( sk6 @ ( sk30 @ A ) )
| ( cK @ B @ C )
| ( ( cK @ A @ sk4 )
!= ( cK
@ ^ [D: a] : $false
@ C ) ) ),
inference(simp,[status(thm)],[7863]) ).
thf(7865,plain,
! [A: a > $o] :
( ( sk6
@ ( sk30
@ ^ [B: a] : $false ) )
| ( cK @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[7864:[bind(A,$thf( ^ [D: a] : $false )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(7933,plain,
! [A: a > $o] :
( ( sk6
@ ( sk30
@ ^ [B: a] : $false ) )
| ( cK @ A @ sk4 ) ),
inference(simp,[status(thm)],[7865]) ).
thf(97,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ~ ( E @ ( sk1 @ E @ D ) )
| ~ $true
| ( cK @ E @ F )
| ( ( cK @ B @ C )
!= ( cK @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[8,8]) ).
thf(98,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ~ ( E @ ( sk1 @ E @ D ) )
| ( cK @ E @ F )
| ( ( cK @ B @ C )
!= ( cK @ D @ F ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(99,plain,
! [D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ~ ( D @ ( sk1 @ D @ B ) )
| ( cK @ D @ C ) ),
inference(pattern_uni,[status(thm)],[98:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( E )),bind(F,$thf( C ))]]) ).
thf(140,plain,
! [D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ~ ( D @ ( sk1 @ D @ B ) )
| ( cK @ D @ C ) ),
inference(simp,[status(thm)],[99]) ).
thf(7016,plain,
( ~ $true
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[9,6937]) ).
thf(7017,plain,
( ( sk3 @ sk4 )
!= ( sk3 @ sk2 ) ),
inference(simp,[status(thm)],[7016]) ).
thf(7033,plain,
sk4 != sk2,
inference(simp,[status(thm)],[7017]) ).
thf(153,plain,
! [D: a > $o,C: a > $o,B: a,A: a > $o] :
( ~ ( C
@ ( sk1
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ A ) )
| ~ ( cK @ A @ B )
| ( cK
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ B ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(155,plain,
! [D: a > $o,C: a > $o,B: a,A: a > $o] :
( ~ ( C
@ ( sk1
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ A ) )
| ~ ( cK @ A @ B )
| ( cK
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ B ) ),
inference(simp,[status(thm)],[153]) ).
thf(13139,plain,
! [A: a > $o] :
( ~ ( sk6 @ sk2 )
| ~ $true
| ( cK @ A @ sk2 )
| ( ( A @ ( sk1 @ A @ sk3 ) )
!= ( cK @ sk6 @ sk29 ) ) ),
inference(paramod_ordered,[status(thm)],[7337,144]) ).
thf(13140,plain,
! [A: a > $o] :
( ~ ( sk6 @ sk2 )
| ( cK @ A @ sk2 )
| ( ( A @ ( sk1 @ A @ sk3 ) )
!= ( cK @ sk6 @ sk29 ) ) ),
inference(simp,[status(thm)],[13139]) ).
thf(13339,plain,
( ~ ( sk6 @ sk2 )
| ( cK
@ ^ [A: a] : ( cK @ sk6 @ sk29 )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[13140:[bind(A,$thf( ^ [B: a] : ( cK @ sk6 @ sk29 ) ))]]) ).
thf(3159,plain,
! [C: a > a,B: a,A: a > $o] :
( ~ $true
| ( cK @ A @ B )
| ( cK @ sk3
@ ( C
@ ( sk1 @ A
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) )
| ( ( cK
@ ^ [D: a] : ( sk3 @ ( C @ D ) )
@ B )
!= ( cK @ sk3 @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[3074,54]) ).
thf(3160,plain,
! [C: a > a,B: a,A: a > $o] :
( ( cK @ A @ B )
| ( cK @ sk3
@ ( C
@ ( sk1 @ A
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) )
| ( ( cK
@ ^ [D: a] : ( sk3 @ ( C @ D ) )
@ B )
!= ( cK @ sk3 @ sk20 ) ) ),
inference(simp,[status(thm)],[3159]) ).
thf(3161,plain,
! [A: a > $o] :
( ( cK @ A @ sk20 )
| ( cK @ sk3 @ ( sk1 @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[3160:[bind(A,$thf( A )),bind(B,$thf( sk20 )),bind(C,$thf( ^ [D: a] : D ))]]) ).
thf(24993,plain,
( ~ ( sk6 @ sk2 )
| ~ $true
| ( ( cK
@ ^ [A: a] : ( cK @ sk6 @ sk29 )
@ sk2 )
!= ( cK
@ ^ [A: a] : $false
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[13339,2798]) ).
thf(24994,plain,
( ~ ( sk6 @ sk2 )
| ( ( cK
@ ^ [A: a] : ( cK @ sk6 @ sk29 )
@ sk2 )
!= ( cK
@ ^ [A: a] : $false
@ sk2 ) ) ),
inference(simp,[status(thm)],[24993]) ).
thf(25224,plain,
( ~ ( sk6 @ sk2 )
| ( ( ^ [A: a] : ( cK @ sk6 @ sk29 ) )
!= ( ^ [A: a] : $false ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[24994]) ).
thf(25312,plain,
( ~ ( sk6 @ sk2 )
| ( ( ^ [A: a] : ( cK @ sk6 @ sk29 ) )
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[25224]) ).
thf(25531,plain,
! [B: a > $o,A: a > $o] :
( ( B @ ( sk9 @ B @ A ) )
| ~ ( B
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ A ) )
| ~ $true
| ( ( cK @ sk3 @ sk2 )
!= ( cK @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[15,159]) ).
thf(25532,plain,
! [B: a > $o,A: a > $o] :
( ( B @ ( sk9 @ B @ A ) )
| ~ ( B
@ ( sk1
@ ^ [C: a] :
? [D: a > $o] :
( ! [E: a] :
( ( D @ E )
=> ( cK @ D @ E ) )
& ( D @ C ) )
@ A ) )
| ( ( cK @ sk3 @ sk2 )
!= ( cK @ A @ sk2 ) ) ),
inference(simp,[status(thm)],[25531]) ).
thf(25533,plain,
! [A: a > $o] :
( ( A @ ( sk9 @ A @ sk3 ) )
| ~ ( A
@ ( sk1
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cK @ C @ D ) )
& ( C @ B ) )
@ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[25532:[bind(A,$thf( sk3 )),bind(B,$thf( B ))]]) ).
thf(26134,plain,
( ( ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 )
= ( sk9
@ ( (=) @ a
@ ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 ) )
@ sk3 ) )
| ( ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 )
!= ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 ) ) ),
inference(replace_leibeq,[status(thm)],[25533:[bind(A,$thf( (=) @ a @ ( sk1 @ ^ [B: a] : ? [C: a > $o] : ( ! [D: a] : ( ( C @ D ) => ( cK @ C @ D ) ) & ( C @ B ) ) @ sk3 ) ))]]) ).
thf(26235,plain,
( ( ( sk9
@ ( (=) @ a
@ ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 ) )
@ sk3 )
= ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 ) )
| ( ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 )
!= ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 ) ) ),
inference(lifteq,[status(thm)],[26134]) ).
thf(26459,plain,
( ( sk9
@ ( (=) @ a
@ ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 ) )
@ sk3 )
= ( sk1
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk3 ) ),
inference(pattern_uni,[status(thm)],[26235:[]]) ).
thf(95,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ~ $true
| ~ ( cK @ D @ F )
| ( cK @ E @ F )
| ( ( cK @ B @ C )
!= ( E @ ( sk1 @ E @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,8]) ).
thf(96,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ~ ( cK @ D @ F )
| ( cK @ E @ F )
| ( ( cK @ B @ C )
!= ( E @ ( sk1 @ E @ D ) ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(136,plain,
! [E: a > a,D: a > a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( D
@ ( sk1
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ B )
@ ( sk1
@ ( D
@ ( sk1
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ B ) )
@ A ) )
| ~ ( cK @ A
@ ( E
@ ( sk1
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ B ) ) )
| ~ ( cK @ B @ C )
| ( cK
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ C ) ),
inference(pre_uni,[status(thm)],[96:[bind(A,$thf( A )),bind(B,$thf( G @ ( sk1 @ ^ [I: a] : ( cK @ ( G @ I ) @ ( H @ I ) ) @ D ) )),bind(C,$thf( H @ ( sk1 @ ^ [I: a] : ( cK @ ( G @ I ) @ ( H @ I ) ) @ D ) )),bind(D,$thf( D )),bind(E,$thf( ^ [I: a] : ( cK @ ( G @ I ) @ ( H @ I ) ) ))]]) ).
thf(145,plain,
! [E: a > a,D: a > a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( D
@ ( sk1
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ B )
@ ( sk1
@ ( D
@ ( sk1
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ B ) )
@ A ) )
| ~ ( cK @ A
@ ( E
@ ( sk1
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ B ) ) )
| ~ ( cK @ B @ C )
| ( cK
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ C ) ),
inference(simp,[status(thm)],[136]) ).
thf(47,plain,
! [D: a > $o,C: a > $o,B: a,A: a > $o] :
( ( C
@ ( sk1 @ A
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) ) ) )
| ( D
@ ( sk1 @ A
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) ) ) )
| ~ ( cK
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ B )
| ( cK @ A @ B ) ),
inference(prim_subst,[status(thm)],[7:[bind(A,$thf( ^ [F: a] : ( ( D @ F ) | ( E @ F ) ) ))]]) ).
thf(62,plain,
! [D: a > $o,C: a > $o,B: a,A: a > $o] :
( ( C
@ ( sk1 @ A
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) ) ) )
| ( D
@ ( sk1 @ A
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) ) ) )
| ~ ( cK
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ B )
| ( cK @ A @ B ) ),
inference(cnf,[status(esa)],[47]) ).
thf(63,plain,
! [D: a > $o,C: a > $o,B: a,A: a > $o] :
( ( C
@ ( sk1 @ A
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) ) ) )
| ( D
@ ( sk1 @ A
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) ) ) )
| ~ ( cK
@ ^ [E: a] :
( ( C @ E )
| ( D @ E ) )
@ B )
| ( cK @ A @ B ) ),
inference(simp,[status(thm)],[62]) ).
thf(120,plain,
! [C: a > $o,B: a,A: a > $o] :
( ~ ~ ( C
@ ( sk1
@ ^ [D: a] :
~ ( C @ D )
@ A ) )
| ~ ( cK @ A @ B )
| ( cK
@ ^ [D: a] :
~ ( C @ D )
@ B ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( A )),bind(B,$thf( ^ [E: a] : ~ ( D @ E ) ))]]) ).
thf(149,plain,
! [C: a > $o,B: a,A: a > $o] :
( ( C
@ ( sk1
@ ^ [D: a] :
~ ( C @ D )
@ A ) )
| ~ ( cK @ A @ B )
| ( cK
@ ^ [D: a] :
~ ( C @ D )
@ B ) ),
inference(cnf,[status(esa)],[120]) ).
thf(150,plain,
! [C: a > $o,B: a,A: a > $o] :
( ( C
@ ( sk1
@ ^ [D: a] :
~ ( C @ D )
@ A ) )
| ~ ( cK @ A @ B )
| ( cK
@ ^ [D: a] :
~ ( C @ D )
@ B ) ),
inference(simp,[status(thm)],[149]) ).
thf(6992,plain,
? [A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> ( cK @ A @ B ) )
& ( A @ sk4 ) ),
inference(rewrite,[status(thm)],[22,6937]) ).
thf(7042,plain,
! [A: a] :
( ( ~ ( sk28 @ A )
| ( cK @ sk28 @ A ) )
& ( sk28 @ sk4 ) ),
inference(cnf,[status(esa)],[6992]) ).
thf(7044,plain,
sk28 @ sk4,
inference(cnfConj,[status(thm)],[7042]) ).
thf(36,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( D @ ( sk1 @ E @ D ) )
| ~ $true
| ( cK @ E @ F )
| ( ( cK @ B @ C )
!= ( cK @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(37,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( D @ ( sk1 @ E @ D ) )
| ( cK @ E @ F )
| ( ( cK @ B @ C )
!= ( cK @ D @ F ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
! [D: a > $o,C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( B @ ( sk1 @ D @ B ) )
| ( cK @ D @ C ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( E )),bind(F,$thf( C ))]]) ).
thf(55,plain,
! [D: a > $o,C: a,B: a > $o,A: a > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( B @ ( sk1 @ D @ B ) )
| ( cK @ D @ C ) ),
inference(simp,[status(thm)],[38]) ).
thf(112,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( cK @ A @ C )
| ( cK @ B @ C )
| ~ ( E @ ( sk1 @ E @ D ) )
| ~ $true
| ( cK @ E @ F )
| ( ( A @ ( sk1 @ B @ A ) )
!= ( cK @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[7,8]) ).
thf(113,plain,
! [F: a,E: a > $o,D: a > $o,C: a,B: a > $o,A: a > $o] :
( ~ ( cK @ A @ C )
| ( cK @ B @ C )
| ~ ( E @ ( sk1 @ E @ D ) )
| ( cK @ E @ F )
| ( ( A @ ( sk1 @ B @ A ) )
!= ( cK @ D @ F ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(129,plain,
! [E: a > a,D: a > a > $o,C: a > $o,B: a,A: a > $o] :
( ~ ( cK
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ B )
| ( cK @ A @ B )
| ~ ( C
@ ( sk1 @ C
@ ( D
@ ( sk1 @ A
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) ) ) ) )
| ( cK @ C
@ ( E
@ ( sk1 @ A
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[113:[bind(A,$thf( ^ [I: a] : ( cK @ ( G @ I ) @ ( H @ I ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G @ ( sk1 @ B @ ^ [I: a] : ( cK @ ( G @ I ) @ ( H @ I ) ) ) )),bind(E,$thf( E )),bind(F,$thf( H @ ( sk1 @ B @ ^ [I: a] : ( cK @ ( G @ I ) @ ( H @ I ) ) ) ))]]) ).
thf(139,plain,
! [E: a > a,D: a > a > $o,C: a > $o,B: a,A: a > $o] :
( ~ ( cK
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) )
@ B )
| ( cK @ A @ B )
| ~ ( C
@ ( sk1 @ C
@ ( D
@ ( sk1 @ A
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) ) ) ) )
| ( cK @ C
@ ( E
@ ( sk1 @ A
@ ^ [F: a] : ( cK @ ( D @ F ) @ ( E @ F ) ) ) ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(11139,plain,
( ~ $true
| ( ( cK
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk2 )
!= ( cK
@ ^ [A: a] : $true
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[11123,6]) ).
thf(11140,plain,
( ( cK
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) )
@ sk2 )
!= ( cK
@ ^ [A: a] : $true
@ sk2 ) ),
inference(simp,[status(thm)],[11139]) ).
thf(11203,plain,
( ( ( ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) ) )
!= ( ^ [A: a] : $true ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[11140]) ).
thf(11210,plain,
( ( ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cK @ B @ C ) )
& ( B @ A ) ) )
!= ( ^ [A: a] : $true ) ),
inference(simp,[status(thm)],[11203]) ).
thf(27,plain,
! [D: a,C: a > $o,B: a > $o,A: a] :
( ~ ( sk3 @ A )
| ( B @ ( sk1 @ C @ B ) )
| ~ $true
| ( cK @ C @ D )
| ( ( cK @ sk3 @ A )
!= ( cK @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10,7]) ).
thf(28,plain,
! [D: a,C: a > $o,B: a > $o,A: a] :
( ~ ( sk3 @ A )
| ( B @ ( sk1 @ C @ B ) )
| ( cK @ C @ D )
| ( ( cK @ sk3 @ A )
!= ( cK @ B @ D ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(29,plain,
! [B: a > $o,A: a] :
( ~ ( sk3 @ A )
| ( sk3 @ ( sk1 @ B @ sk3 ) )
| ( cK @ B @ A ) ),
inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(58,plain,
! [B: a > $o,A: a] :
( ~ ( sk3 @ A )
| ( sk3 @ ( sk1 @ B @ sk3 ) )
| ( cK @ B @ A ) ),
inference(simp,[status(thm)],[29]) ).
thf(18046,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( sk78 @ sk37 )
| ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ~ $true
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK @ sk3 @ sk37 )
!= ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17908,141]) ).
thf(18047,plain,
! [C: a > a,B: a > a > $o,A: a > $o] :
( ( sk78 @ sk37 )
| ( cK
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( A
!= ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) )
| ( ( cK @ sk3 @ sk37 )
!= ( cK
@ ( B
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( cK @ ( B @ D ) @ ( C @ D ) )
@ A ) ) ) ) ),
inference(simp,[status(thm)],[18046]) ).
thf(18105,plain,
! [A: a > $o] :
( ( sk78 @ sk37 )
| ( cK
@ ^ [B: a] : ( cK @ sk3 @ sk37 )
@ sk37 )
| ( A != sk3 ) ),
inference(pre_uni,[status(thm)],[18047:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : sk3 )),bind(C,$thf( ^ [D: a] : sk37 ))]]) ).
thf(18106,plain,
( ( cK
@ ^ [A: a] : ( cK @ sk3 @ sk37 )
@ sk37 )
| ( sk78 @ sk37 ) ),
inference(pattern_uni,[status(thm)],[18105:[bind(A,$thf( sk3 ))]]) ).
thf(28450,plain,
$false,
inference(e,[status(thm)],[7397,151,7199,15,138,20332,10,56,7203,142,7068,7028,185,52,13025,57,15073,216,13604,147,61,7337,12249,133,7321,6,60,13532,7037,18112,22682,11037,160,21,3198,17908,3050,12692,26410,7142,26521,156,53,141,403,9,2798,11229,7313,13277,3074,18255,166,148,24185,18095,18244,11333,2981,7038,54,6937,144,1332,159,7933,7,13422,3219,140,7033,251,155,13339,3,3161,13540,25312,26459,7102,145,63,7801,150,13523,13285,199,6994,17584,7224,11123,3056,7044,12552,55,139,8,11210,58,18106,12480]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV245^6 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n026.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 15:29:42 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.00/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/1.07 % [INFO] Parsing done (211ms).
% 1.45/1.09 % [INFO] Running in sequential loop mode.
% 2.21/1.66 % [INFO] eprover registered as external prover.
% 2.21/1.66 % [INFO] Scanning for conjecture ...
% 2.41/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.58/1.83 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.58/1.83 % [INFO] Problem is higher-order (TPTP THF).
% 2.58/1.84 % [INFO] Type checking passed.
% 2.58/1.84 % [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 ...
% 200.13/57.98 % External prover 'e' found a proof!
% 200.13/57.99 % [INFO] Killing All external provers ...
% 200.13/57.99 % Time passed: 57668ms (effective reasoning time: 56892ms)
% 200.13/57.99 % 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)>
% 200.13/57.99 % Axioms used in derivation (0):
% 200.13/57.99 % No. of inferences in proof: 360
% 200.13/57.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 57668 ms resp. 56892 ms w/o parsing
% 202.16/58.39 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 202.16/58.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------