%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV080^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n017.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 08:36:48 AM UTC 2026
% Result : Theorem 273.25s 116.75s
% Output : Refutation 276.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 4
% Syntax : Number of formulae : 344 ( 81 unt; 0 typ; 3 def)
% Number of atoms : 1626 ( 869 equ; 100 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 7084 ( 562 ~; 412 |; 178 &;5922 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 356 ( 356 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 24 usr; 8 con; 0-2 aty)
% Number of variables : 3532 (3104 ^; 416 !; 9 ?;3532 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > $o ).
thf(sk2_decl,type,
sk2: ( a > a ) > a ).
thf(sk3_decl,type,
sk3: ( a > a ) > a ).
thf(sk4_decl,type,
sk4: a > ( a > a ) > a ).
thf(sk5_decl,type,
sk5: ( a > a > a ) > a > a ).
thf(sk6_decl,type,
sk6: a > ( a > a ) > a ).
thf(sk7_decl,type,
sk7: a ).
thf(sk13_decl,type,
sk13: a > a ).
thf(sk14_decl,type,
sk14: a ).
thf(sk16_decl,type,
sk16: a > a ).
thf(sk17_decl,type,
sk17: a > a ).
thf(sk18_decl,type,
sk18: a > a ).
thf(sk20_decl,type,
sk20: a > a ).
thf(sk22_decl,type,
sk22: a > a ).
thf(sk23_decl,type,
sk23: a > a ).
thf(sk28_decl,type,
sk28: a > a ).
thf(sk29_decl,type,
sk29: a ).
thf(sk30_decl,type,
sk30: a ).
thf(sk31_decl,type,
sk31: a ).
thf(sk32_decl,type,
sk32: a > a ).
thf(sk33_decl,type,
sk33: a > a ).
thf(sk34_decl,type,
sk34: a > a ).
thf(sk37_decl,type,
sk37: a > a ).
thf(sk38_decl,type,
sk38: a > a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ? [B: a > a] :
( ! [C: a] :
( ( A @ C )
=> ( A @ ( B @ C ) ) )
& ! [C: a] :
( ( A @ C )
=> ? [D: a] :
( ( ^ [E: a] :
( ( A @ E )
& ( C
= ( B @ E ) ) ) )
= ( (=) @ a @ D ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: a > a] :
@+[B: a] :
~ ( ( sk1 @ B )
=> ( sk1 @ ( A @ B ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: a > a] :
@+[B: a] :
~ ( ( sk1 @ B )
=> ? [C: a] :
( ( ^ [D: a] :
( ( sk1 @ D )
& ( B
= ( A @ D ) ) ) )
= ( (=) @ a @ C ) ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o] :
? [B: a > a] :
( ! [C: a] :
( ( A @ C )
=> ( A @ ( B @ C ) ) )
& ! [C: a] :
( ( A @ C )
=> ? [D: a] :
( ( ^ [E: a] :
( ( A @ E )
& ( C
= ( B @ E ) ) ) )
= ( (=) @ a @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEQP_1A_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o] :
? [B: a > a] :
( ! [C: a] :
( ( A @ C )
=> ( A @ ( B @ C ) ) )
& ! [C: a] :
( ( A @ C )
=> ? [D: a] :
( ( ^ [E: a] :
( ( A @ E )
& ( C
= ( B @ E ) ) ) )
= ( (=) @ a @ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o] :
? [B: a > a] :
( ! [C: a] :
( ( A @ C )
=> ( A @ ( B @ C ) ) )
& ! [C: a] :
( ( A @ C )
=> ? [D: a] :
( ( ^ [E: a] :
( ( A @ E )
& ( C
= ( B @ E ) ) ) )
= ( (=) @ a @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: a,A: a > a] :
( ( ( sk1 @ ( sk2 @ A ) )
| ( sk1 @ ( sk3 @ A ) ) )
& ( ( sk1 @ ( sk2 @ A ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) ) )
& ( ~ ( sk1 @ ( A @ ( sk2 @ A ) ) )
| ( sk1 @ ( sk3 @ A ) ) )
& ( ~ ( sk1 @ ( A @ ( sk2 @ A ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: a > a] :
( ( sk1 @ ( sk2 @ A ) )
| ( sk1 @ ( sk3 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [A: a > a] :
( ~ ( sk1 @ ( A @ ( sk2 @ A ) ) )
| ( sk1 @ ( sk3 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(14,plain,
! [B: a > a,A: a > a] :
( ( sk1 @ ( sk2 @ A ) )
| ~ $true
| ( sk1 @ ( sk3 @ B ) )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,7]) ).
thf(15,plain,
! [B: a > a,A: a > a] :
( ( sk1 @ ( sk2 @ A ) )
| ( sk1 @ ( sk3 @ B ) )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(18,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[15:[bind(A,$thf( C @ ( sk2 @ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk3 @ ( C @ D ) ) ))]]) ).
thf(20,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(16,plain,
! [B: a > a,A: a > a] :
( ~ ( sk1 @ ( A @ ( sk2 @ A ) ) )
| ~ $true
| ( sk1 @ ( sk3 @ B ) )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(17,plain,
! [B: a > a,A: a > a] :
( ~ ( sk1 @ ( A @ ( sk2 @ A ) ) )
| ( sk1 @ ( sk3 @ B ) )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(19,plain,
! [A: a > a > a] :
( ~ ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) )
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[17:[bind(A,$thf( C @ ( sk2 @ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk3 @ ( C @ D ) ) ))]]) ).
thf(21,plain,
! [A: a > a > a] :
( ~ ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) )
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(199,plain,
! [B: a > a > a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) )
| ~ $true
| ( sk1
@ ( sk3
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) )
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,21]) ).
thf(200,plain,
! [B: a > a > a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) )
| ( sk1
@ ( sk3
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) )
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(244,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : B ) ) )
| ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : B ) ) ) ),
inference(pre_uni,[status(thm)],[200:[bind(A,$thf( ^ [C: a] : ^ [D: a] : D )),bind(B,$thf( ^ [C: a] : ^ [D: a] : D ))]]) ).
thf(254,plain,
( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : B ) ) ),
inference(simp,[status(thm)],[244]) ).
thf(8,plain,
! [B: a,A: a > a] :
( ~ ( sk1 @ ( A @ ( sk2 @ A ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ~ ( sk1 @ ( A @ ( sk2 @ A ) ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(33,plain,
! [C: a,B: a > a,A: a > a] :
( ~ ( sk1 @ ( A @ ( sk2 @ A ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3 @ B )
= ( B @ D ) ) ) )
!= ( (=) @ a @ C ) )
| ~ $true
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,10]) ).
thf(34,plain,
! [C: a,B: a > a,A: a > a] :
( ~ ( sk1 @ ( A @ ( sk2 @ A ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3 @ B )
= ( B @ D ) ) ) )
!= ( (=) @ a @ C ) )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(36,plain,
! [B: a > a > a,A: a] :
( ~ ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[34:[bind(A,$thf( D @ ( sk2 @ ^ [E: a] : ( sk3 @ ( D @ E ) ) ) )),bind(B,$thf( ^ [E: a] : ( sk3 @ ( D @ E ) ) ))]]) ).
thf(38,plain,
! [B: a > a > a,A: a] :
( ~ ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(263,plain,
! [B: a > a > a,A: a] :
( ~ $true
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[254,38]) ).
thf(264,plain,
! [B: a > a > a,A: a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[263]) ).
thf(268,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[264:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : F ) ) ))]]) ).
thf(573,plain,
! [A: a] :
( ( ( sk1 @ ( sk16 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) )
!= ( A
= ( sk16 @ A ) ) ),
inference(func_ext,[status(esa)],[268]) ).
thf(245,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : B ) ) ) )
| ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) ) ),
inference(pre_uni,[status(thm)],[200:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ( sk3 @ ^ [E: a] : D ) )),bind(B,$thf( ^ [C: a] : ^ [D: a] : C ))]]) ).
thf(771,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) )
| ( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : B ) ) ) )
!= ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[245]) ).
thf(785,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) )
| ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : B ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) ) ),
inference(simp,[status(thm)],[771]) ).
thf(2621,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : B ) ) )
!= ( ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) ) ),
inference(simp,[status(thm)],[785]) ).
thf(2970,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) )
| ( ( ^ [A: a,B: a] :
( sk3
@ ^ [C: a] : B ) )
!= ( ^ [A: a,B: a] : A ) ) ),
inference(simp,[status(thm)],[2621]) ).
thf(261,plain,
! [A: a > a] :
( ~ $true
| ( sk1 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[254,7]) ).
thf(262,plain,
! [A: a > a] :
( ( sk1 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(270,plain,
( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) ),
inference(pre_uni,[status(thm)],[262:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk3 @ ^ [D: a] : D ) ) ))]]) ).
thf(278,plain,
! [B: a > a > a,A: a] :
( ~ $true
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,38]) ).
thf(279,plain,
! [B: a > a > a,A: a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(282,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[279:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : G ) ) ) ))]]) ).
thf(59,plain,
! [B: a > a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) )
| ~ $true
| ( sk1 @ ( sk3 @ B ) )
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) ) ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,7]) ).
thf(60,plain,
! [B: a > a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) )
| ( sk1 @ ( sk3 @ B ) )
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) ) ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(64,plain,
! [B: a > a > a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) )
| ( sk1
@ ( sk3
@ ^ [C: a] : ( sk2 @ ( B @ C ) ) ) )
| ( ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) )
!= ( B
@ ( sk2
@ ^ [C: a] : ( sk2 @ ( B @ C ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[60:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : ( sk2 @ ( C @ D ) ) ))]]) ).
thf(66,plain,
! [B: a > a > a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [C: a] : ( sk2 @ ( B @ C ) ) ) )
| ( sk1
@ ( sk3
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) )
| ( ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) )
!= ( B
@ ( sk2
@ ^ [C: a] : ( sk2 @ ( B @ C ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[64:[]]) ).
thf(77,plain,
! [B: a > a > a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [C: a] : ( sk2 @ ( B @ C ) ) ) )
| ( sk1
@ ( sk3
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) )
| ( ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) )
!= ( B
@ ( sk2
@ ^ [C: a] : ( sk2 @ ( B @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(2088,plain,
! [C: a > a > a,B: a > a > a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
| ( ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
!= ( B
@ ( sk2
@ ^ [D: a] : ( sk2 @ ( B @ D ) ) ) ) )
| ~ $true
| ( sk1
@ ( sk3
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [D: a] : ( sk2 @ ( B @ D ) ) ) )
!= ( sk1
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) )
@ ( sk2
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,21]) ).
thf(2089,plain,
! [C: a > a > a,B: a > a > a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
| ( ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
!= ( B
@ ( sk2
@ ^ [D: a] : ( sk2 @ ( B @ D ) ) ) ) )
| ( sk1
@ ( sk3
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [D: a] : ( sk2 @ ( B @ D ) ) ) )
!= ( sk1
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) )
@ ( sk2
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2088]) ).
thf(2155,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
!= ( ^ [B: a] :
( sk3
@ ^ [C: a] : B ) ) )
| ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) ),
inference(pre_uni,[status(thm)],[2089:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : ^ [E: a] : ( sk3 @ ^ [F: a] : E ) )),bind(C,$thf( ^ [D: a] : ^ [E: a] : ( sk3 @ ^ [F: a] : E ) ))]]) ).
thf(2158,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : B ) ) ) )
| ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : B ) ) ) ) ),
inference(pre_uni,[status(thm)],[2155:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : C ) ))]]) ).
thf(2266,plain,
( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : B ) ) ) ),
inference(simp,[status(thm)],[2158]) ).
thf(2289,plain,
! [A: a > a > a] :
( ~ $true
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2266,21]) ).
thf(2290,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2289]) ).
thf(2330,plain,
( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2290:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : E ) ) ) ))]]) ).
thf(65,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : B ) ) )
| ( sk1
@ ( sk3
@ ^ [A: a] : A ) ) ),
inference(pre_uni,[status(thm)],[60:[bind(A,$thf( ^ [C: a] : ^ [D: a] : D )),bind(B,$thf( ^ [C: a] : C ))]]) ).
thf(94,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] : A ) )
| ( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : B ) ) )
!= ( sk1
@ ( sk3
@ ^ [A: a] : A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[65]) ).
thf(99,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] : A ) )
| ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : B ) )
!= ( sk3
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(101,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] : B ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(2291,plain,
! [A: a > a] :
( ~ $true
| ( sk1 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2266,7]) ).
thf(2292,plain,
! [A: a > a] :
( ( sk1 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[2291]) ).
thf(2322,plain,
( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) ),
inference(pre_uni,[status(thm)],[2292:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : D ) ) ) ))]]) ).
thf(2374,plain,
! [A: a > a > a] :
( ~ $true
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2322,21]) ).
thf(2375,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2374]) ).
thf(2408,plain,
( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2375:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : F ) ) ) ) ))]]) ).
thf(42,plain,
! [C: a > a > a,B: a,A: a > a] :
( ~ ( sk1 @ ( A @ ( sk2 @ A ) ) )
| ~ $true
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3
@ ^ [E: a] : ( sk3 @ ( C @ E ) ) )
= ( sk3 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) )
@ ( sk2
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,38]) ).
thf(43,plain,
! [C: a > a > a,B: a,A: a > a] :
( ~ ( sk1 @ ( A @ ( sk2 @ A ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3
@ ^ [E: a] : ( sk3 @ ( C @ E ) ) )
= ( sk3 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) )
@ ( sk2
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(45,plain,
! [B: a > a > a > a,A: a] :
( ~ ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
= ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[43:[bind(A,$thf( D @ ( sk2 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ( D @ E @ F ) ) ) ) @ ( sk2 @ ^ [E: a] : ( sk3 @ ( D @ ( sk2 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ( D @ F @ G ) ) ) ) @ E ) ) ) )),bind(B,$thf( B )),bind(C,$thf( ^ [E: a] : ^ [F: a] : ( sk3 @ ( D @ E @ F ) ) ))]]) ).
thf(47,plain,
! [B: a > a > a > a,A: a] :
( ~ ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
= ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(2568,plain,
! [B: a > a > a > a,A: a] :
( ~ $true
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
= ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2408,47]) ).
thf(2569,plain,
! [B: a > a > a > a,A: a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
= ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2568]) ).
thf(2595,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] :
( sk3
@ ^ [J: a] :
( sk3
@ ^ [K: a] : J ) ) ) ) ) ) ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] :
( sk3
@ ^ [J: a] : I ) ) ) ) ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[2569:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ^ [H: a] : ( sk3 @ ^ [I: a] : ( sk3 @ ^ [J: a] : ( sk3 @ ^ [K: a] : J ) ) ) ) ) ) ))]]) ).
thf(104,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a] :
( sk3
@ ^ [D: a] : D ) )
!= ( ^ [C: a] : C ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ~ $true
| ( ( sk1
@ ( sk3
@ ^ [C: a] : C ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[101,10]) ).
thf(105,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a] :
( sk3
@ ^ [D: a] : D ) )
!= ( ^ [C: a] : C ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] : C ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(112,plain,
! [A: a] :
( ( ( ^ [B: a] :
( sk3
@ ^ [C: a] : C ) )
!= ( ^ [B: a] : B ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) )
= ( sk3
@ ^ [C: a] : C ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[105:[bind(A,$thf( ^ [C: a] : ( sk3 @ ^ [D: a] : D ) )),bind(B,$thf( B ))]]) ).
thf(115,plain,
! [A: a] :
( ( ( ^ [B: a] :
( sk3
@ ^ [C: a] : C ) )
!= ( ^ [B: a] : B ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) )
= ( sk3
@ ^ [C: a] : C ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(280,plain,
! [A: a > a > a] :
( ~ $true
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,21]) ).
thf(281,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[280]) ).
thf(283,plain,
( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[281:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : F ) ) ) ))]]) ).
thf(265,plain,
! [A: a > a > a] :
( ~ $true
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[254,21]) ).
thf(266,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(267,plain,
( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ),
inference(pre_uni,[status(thm)],[266:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : E ) ) ))]]) ).
thf(293,plain,
! [B: a > a > a,A: a] :
( ~ $true
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[267,38]) ).
thf(294,plain,
! [B: a > a > a,A: a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[293]) ).
thf(300,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[294:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ^ [H: a] : H ) ) ) ) ))]]) ).
thf(752,plain,
! [A: a] :
( ( ( sk1 @ ( sk18 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) ) )
!= ( A
= ( sk18 @ A ) ) ),
inference(func_ext,[status(esa)],[300]) ).
thf(1952,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) ) )
!= ( A
= ( sk18 @ A ) ) )
| ( ( sk1 @ ( sk18 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[283,752]) ).
thf(1953,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) )
!= ( A
= ( sk18 @ A ) ) )
| ( ( sk1 @ ( sk18 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[1952]) ).
thf(1975,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) )
!= A )
| ( ( sk18 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) )
| ( ( sk18 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) ) ),
inference(simp,[status(thm)],[1953]) ).
thf(2035,plain,
( ( sk18
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) ),
inference(simp,[status(thm)],[1975]) ).
thf(63,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
!= ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[20]) ).
thf(73,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
| ( ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
!= ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(1680,plain,
! [B: a > a,A: a > a > a] :
( ( ( sk3
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) )
!= ( sk2
@ ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) ) ) )
| ~ $true
| ( sk1 @ ( sk3 @ B ) )
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) ) ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,7]) ).
thf(1681,plain,
! [B: a > a,A: a > a > a] :
( ( ( sk3
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) )
!= ( sk2
@ ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) ) ) )
| ( sk1 @ ( sk3 @ B ) )
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) ) ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[1680]) ).
thf(1735,plain,
( ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : B ) )
!= ( sk2
@ ^ [A: a] : A ) )
| ( sk1
@ ( sk3
@ ^ [A: a] : A ) ) ),
inference(pre_uni,[status(thm)],[1681:[bind(A,$thf( ^ [C: a] : ^ [D: a] : D )),bind(B,$thf( ^ [C: a] : C ))]]) ).
thf(2285,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ~ $true
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2266,10]) ).
thf(2286,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[2285]) ).
thf(2317,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[2286:[bind(A,$thf( ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : E ) ) ) )),bind(B,$thf( B ))]]) ).
thf(2348,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(simp,[status(thm)],[2317]) ).
thf(2482,plain,
! [B: a > a > a > a,A: a] :
( ~ $true
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
= ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2330,47]) ).
thf(2483,plain,
! [B: a > a > a > a,A: a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
= ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2482]) ).
thf(2491,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] :
( sk3
@ ^ [J: a] : I ) ) ) ) ) ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : H ) ) ) ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[2483:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ^ [H: a] : ( sk3 @ ^ [I: a] : ( sk3 @ ^ [J: a] : I ) ) ) ) ) ))]]) ).
thf(92,plain,
! [A: a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] : B ) )
| ~ $true
| ( sk1 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,7]) ).
thf(93,plain,
! [A: a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] : B ) )
| ( sk1 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(95,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] : A ) )
| ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) ) ),
inference(pre_uni,[status(thm)],[93:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk3 @ ^ [D: a] : D ) ) ))]]) ).
thf(163,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] : A ) )
| ( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) )
!= ( sk1
@ ( sk3
@ ^ [A: a] : A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[95]) ).
thf(168,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] : A ) )
| ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) )
!= ( sk3
@ ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(320,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] : A ) )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) )
!= ( ^ [A: a] : A ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(31,plain,
! [C: a,B: a > a,A: a > a] :
( ( sk1 @ ( sk2 @ A ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3 @ B )
= ( B @ D ) ) ) )
!= ( (=) @ a @ C ) )
| ~ $true
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,10]) ).
thf(32,plain,
! [C: a,B: a > a,A: a > a] :
( ( sk1 @ ( sk2 @ A ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3 @ B )
= ( B @ D ) ) ) )
!= ( (=) @ a @ C ) )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(35,plain,
! [B: a > a > a,A: a] :
( ( sk1
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[32:[bind(A,$thf( D @ ( sk2 @ ^ [E: a] : ( sk3 @ ( D @ E ) ) ) )),bind(B,$thf( ^ [E: a] : ( sk3 @ ( D @ E ) ) ))]]) ).
thf(37,plain,
! [B: a > a > a,A: a] :
( ( sk1
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(2312,plain,
! [B: a > a > a > a,A: a] :
( ~ $true
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
= ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2266,47]) ).
thf(2313,plain,
! [B: a > a > a > a,A: a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
= ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2312]) ).
thf(2318,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[2313:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ^ [H: a] : G ) ) ) ))]]) ).
thf(3195,plain,
! [A: a] :
( ( ( sk1 @ ( sk33 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) ) )
!= ( A
= ( sk33 @ A ) ) ),
inference(func_ext,[status(esa)],[2318]) ).
thf(4215,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) ) )
!= ( A
= ( sk33 @ A ) ) )
| ( ( sk1 @ ( sk33 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2330,3195]) ).
thf(4216,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) )
!= ( A
= ( sk33 @ A ) ) )
| ( ( sk1 @ ( sk33 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[4215]) ).
thf(4303,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) )
!= A )
| ( ( sk33 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) )
| ( ( sk33 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) ) ),
inference(simp,[status(thm)],[4216]) ).
thf(4439,plain,
( ( sk33
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) ),
inference(simp,[status(thm)],[4303]) ).
thf(751,plain,
! [A: a] :
( ( ( sk1 @ ( sk17 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) )
!= ( A
= ( sk17 @ A ) ) ),
inference(func_ext,[status(esa)],[282]) ).
thf(295,plain,
! [A: a > a > a] :
( ~ $true
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[267,21]) ).
thf(296,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[295]) ).
thf(299,plain,
( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[296:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : G ) ) ) ) ))]]) ).
thf(459,plain,
! [B: a > a > a,A: a] :
( ~ $true
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[299,38]) ).
thf(460,plain,
! [B: a > a > a,A: a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[459]) ).
thf(470,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] :
( sk3
@ ^ [J: a] : J ) ) ) ) ) ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : I ) ) ) ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[460:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ^ [H: a] : ( sk3 @ ^ [I: a] : ( sk3 @ ^ [J: a] : J ) ) ) ) ) ) ))]]) ).
thf(1059,plain,
! [A: a] :
( ( ( sk1 @ ( sk22 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : I ) ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) ) ) )
!= ( A
= ( sk22 @ A ) ) ),
inference(func_ext,[status(esa)],[470]) ).
thf(40,plain,
! [C: a > a > a,B: a,A: a > a] :
( ( sk1 @ ( sk2 @ A ) )
| ~ $true
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3
@ ^ [E: a] : ( sk3 @ ( C @ E ) ) )
= ( sk3 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) )
@ ( sk2
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,38]) ).
thf(41,plain,
! [C: a > a > a,B: a,A: a > a] :
( ( sk1 @ ( sk2 @ A ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3
@ ^ [E: a] : ( sk3 @ ( C @ E ) ) )
= ( sk3 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) )
@ ( sk2
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(44,plain,
! [B: a > a > a > a,A: a] :
( ( sk1
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
= ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[41:[bind(A,$thf( D @ ( sk2 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ( D @ E @ F ) ) ) ) @ ( sk2 @ ^ [E: a] : ( sk3 @ ( D @ ( sk2 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ( D @ F @ G ) ) ) ) @ E ) ) ) )),bind(B,$thf( B )),bind(C,$thf( ^ [E: a] : ^ [F: a] : ( sk3 @ ( D @ E @ F ) ) ))]]) ).
thf(46,plain,
! [B: a > a > a > a,A: a] :
( ( sk1
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
= ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(257,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ~ $true
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[254,10]) ).
thf(258,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(269,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[258:[bind(A,$thf( ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : E ) ) )),bind(B,$thf( B ))]]) ).
thf(271,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(simp,[status(thm)],[269]) ).
thf(303,plain,
! [A: a] :
( ( ( sk1 @ ( sk13 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) )
!= ( A
= ( sk13 @ A ) ) ),
inference(func_ext,[status(esa)],[271]) ).
thf(851,plain,
! [A: a] :
( ( ( sk1 @ ( sk13 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) )
| ( A
= ( sk13 @ A ) ) ),
inference(bool_ext,[status(thm)],[303]) ).
thf(886,plain,
! [A: a] :
( ( ( sk13 @ A )
= A )
| ( ( sk1 @ ( sk13 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) ) ),
inference(lifteq,[status(thm)],[851]) ).
thf(968,plain,
! [A: a] :
( ( ( ( sk13 @ A )
= A )
| ( sk1 @ ( sk13 @ A ) ) )
& ( ( ( sk13 @ A )
= A )
| ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) ) ),
inference(cnf,[status(esa)],[886]) ).
thf(969,plain,
! [A: a] :
( ( ( sk13 @ A )
= A )
| ( sk1 @ ( sk13 @ A ) ) ),
inference(cnfConj,[status(thm)],[968]) ).
thf(2154,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
!= ( ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : B ) ) ) )
| ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : B ) ) ) ) ),
inference(pre_uni,[status(thm)],[2089:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : E ) ) )),bind(C,$thf( ^ [D: a] : ^ [E: a] : ( sk3 @ ^ [F: a] : D ) ))]]) ).
thf(2157,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : A ) ) ) )
| ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : B ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2154:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : C ) ) ))]]) ).
thf(2894,plain,
! [A: a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : B ) ) ) )
| ~ $true
| ( sk1 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : C ) ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2157,7]) ).
thf(2895,plain,
! [A: a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : B ) ) ) )
| ( sk1 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : C ) ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[2894]) ).
thf(2929,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : A ) ) ) )
| ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : C ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2895:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : D ) ) ) ) ))]]) ).
thf(52,plain,
! [C: a > a > a,B: a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
| ~ $true
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3
@ ^ [E: a] : ( sk3 @ ( C @ E ) ) )
= ( sk3 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) ) ) )
!= ( sk1
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) )
@ ( sk2
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,38]) ).
thf(53,plain,
! [C: a > a > a,B: a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3
@ ^ [E: a] : ( sk3 @ ( C @ E ) ) )
= ( sk3 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) ) ) )
!= ( sk1
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) )
@ ( sk2
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(67,plain,
! [C: a > a > a > a,B: a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : ( sk2 @ ( C @ E @ F ) ) ) )
= ( sk3
@ ^ [E: a] : ( sk2 @ ( C @ D @ E ) ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
!= ( C
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk2 @ ( C @ D @ E ) ) ) )
@ ( sk2
@ ^ [D: a] :
( sk2
@ ( C
@ ( sk2
@ ^ [E: a] :
( sk3
@ ^ [F: a] : ( sk2 @ ( C @ E @ F ) ) ) )
@ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[53:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [E: a] : ^ [F: a] : ( sk2 @ ( D @ E @ F ) ) ))]]) ).
thf(78,plain,
! [C: a > a > a > a,B: a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : ( sk2 @ ( C @ E @ F ) ) ) )
= ( sk3
@ ^ [E: a] : ( sk2 @ ( C @ D @ E ) ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
!= ( C
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk2 @ ( C @ D @ E ) ) ) )
@ ( sk2
@ ^ [D: a] :
( sk2
@ ( C
@ ( sk2
@ ^ [E: a] :
( sk3
@ ^ [F: a] : ( sk2 @ ( C @ E @ F ) ) ) )
@ D ) ) ) ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(39,plain,
! [B: a > a > a,A: a] :
( ( ( ( sk1 @ ( sk5 @ B @ A ) )
& ( ( sk3
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
= ( sk3 @ ( B @ ( sk5 @ B @ A ) ) ) ) )
!= ( A
= ( sk5 @ B @ A ) ) )
| ~ ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ),
inference(func_ext,[status(esa)],[38]) ).
thf(2297,plain,
! [B: a > a > a,A: a] :
( ( ( ( sk1 @ ( sk5 @ B @ A ) )
& ( ( sk3
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
= ( sk3 @ ( B @ ( sk5 @ B @ A ) ) ) ) )
!= ( A
= ( sk5 @ B @ A ) ) )
| ~ $true
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2266,39]) ).
thf(2298,plain,
! [B: a > a > a,A: a] :
( ( ( ( sk1 @ ( sk5 @ B @ A ) )
& ( ( sk3
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
= ( sk3 @ ( B @ ( sk5 @ B @ A ) ) ) ) )
!= ( A
= ( sk5 @ B @ A ) ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2297]) ).
thf(2326,plain,
! [A: a] :
( ( ( sk1
@ ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) )
@ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) )
!= ( A
= ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) )
@ A ) ) ),
inference(pre_uni,[status(thm)],[2298:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : F ) ) ) ))]]) ).
thf(6760,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) )
!= ( A
= ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) )
@ A ) ) )
| ( ( sk1
@ ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) )
@ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2322,2326]) ).
thf(6761,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) )
!= ( A
= ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) )
@ A ) ) )
| ( ( sk1
@ ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) )
@ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) ) ),
inference(simp,[status(thm)],[6760]) ).
thf(6896,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
!= A )
| ( ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) )
@ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) )
| ( ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) )
@ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) ),
inference(simp,[status(thm)],[6761]) ).
thf(6983,plain,
( ( sk5
@ ^ [A: a,B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) )
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) ),
inference(simp,[status(thm)],[6896]) ).
thf(461,plain,
! [A: a > a > a] :
( ~ $true
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[299,21]) ).
thf(462,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[461]) ).
thf(475,plain,
( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[462:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ^ [H: a] : ( sk3 @ ^ [I: a] : I ) ) ) ) ) ) ))]]) ).
thf(2880,plain,
! [A: a] :
( ( ( sk1 @ ( sk28 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) )
!= ( A
= ( sk28 @ A ) ) ),
inference(func_ext,[status(esa)],[2348]) ).
thf(2892,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : B ) ) ) )
| ~ $true
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : C ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2157,21]) ).
thf(2893,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : B ) ) ) )
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : C ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2892]) ).
thf(2925,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : A ) ) ) )
| ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : D ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2893:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : E ) ) ) ) ))]]) ).
thf(30,plain,
! [B: a,A: a > a] :
( ( ( ( sk1 @ ( sk4 @ B @ A ) )
& ( ( sk3 @ A )
= ( A @ ( sk4 @ B @ A ) ) ) )
!= ( B
= ( sk4 @ B @ A ) ) )
| ~ ( sk1 @ ( A @ ( sk2 @ A ) ) ) ),
inference(func_ext,[status(esa)],[10]) ).
thf(2393,plain,
! [B: a,A: a > a] :
( ( ( ( sk1 @ ( sk4 @ B @ A ) )
& ( ( sk3 @ A )
= ( A @ ( sk4 @ B @ A ) ) ) )
!= ( B
= ( sk4 @ B @ A ) ) )
| ~ $true
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2322,30]) ).
thf(2394,plain,
! [B: a,A: a > a] :
( ( ( ( sk1 @ ( sk4 @ B @ A ) )
& ( ( sk3 @ A )
= ( A @ ( sk4 @ B @ A ) ) ) )
!= ( B
= ( sk4 @ B @ A ) ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[2393]) ).
thf(2412,plain,
! [A: a] :
( ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2394:[bind(A,$thf( ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : F ) ) ) ) )),bind(B,$thf( B ))]]) ).
thf(2437,plain,
! [A: a] :
( ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2412]) ).
thf(308,plain,
! [B: a > a > a,A: a] :
( ~ $true
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[283,38]) ).
thf(309,plain,
! [B: a > a > a,A: a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[308]) ).
thf(317,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : I ) ) ) ) ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[309:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ^ [H: a] : ( sk3 @ ^ [I: a] : I ) ) ) ) ) ))]]) ).
thf(849,plain,
! [A: a] :
( ( ( sk1 @ ( sk20 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) ) ) )
!= ( A
= ( sk20 @ A ) ) ),
inference(func_ext,[status(esa)],[317]) ).
thf(507,plain,
( ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : B ) )
!= sk14 )
| ( sk1
@ ( sk3
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[320]) ).
thf(61,plain,
! [B: a > a,A: a > a > a] :
( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) ) ) )
| ~ $true
| ( sk1 @ ( sk3 @ B ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,7]) ).
thf(62,plain,
! [B: a > a,A: a > a > a] :
( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) ) ) )
| ( sk1 @ ( sk3 @ B ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(76,plain,
! [A: a > a > a > a] :
( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] :
( sk3
@ ^ [C: a] : ( sk3 @ ( A @ B @ C ) ) ) )
@ ( sk2
@ ^ [B: a] :
( sk3
@ ( A
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( A @ C @ D ) ) ) )
@ B ) ) ) ) ) )
| ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : ( sk3 @ ( A @ B @ C ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[62:[bind(A,$thf( D @ ( sk2 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ( D @ D @ E ) ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ( D @ D @ E ) ) ) ))]]) ).
thf(85,plain,
! [A: a > a > a > a] :
( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] :
( sk3
@ ^ [C: a] : ( sk3 @ ( A @ B @ C ) ) ) )
@ ( sk2
@ ^ [B: a] :
( sk3
@ ( A
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( A @ C @ D ) ) ) )
@ B ) ) ) ) ) )
| ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : ( sk3 @ ( A @ B @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(6,plain,
! [B: a,A: a > a] :
( ( sk1 @ ( sk2 @ A ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ( sk1 @ ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(102,plain,
! [B: a,A: a > a] :
( ( ( ( sk1 @ ( sk6 @ B @ A ) )
& ( ( sk3 @ A )
= ( A @ ( sk6 @ B @ A ) ) ) )
!= ( B
= ( sk6 @ B @ A ) ) )
| ( sk1 @ ( sk2 @ A ) ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(3573,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) )
!= ( A
= ( sk28 @ A ) ) )
| ( ( sk1 @ ( sk28 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2266,2880]) ).
thf(3574,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) )
!= ( A
= ( sk28 @ A ) ) )
| ( ( sk1 @ ( sk28 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) ) ),
inference(simp,[status(thm)],[3573]) ).
thf(3621,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
!= A )
| ( ( sk28 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) )
| ( ( sk28 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) ),
inference(simp,[status(thm)],[3574]) ).
thf(3711,plain,
( ( sk28
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : B ) ) ) ),
inference(simp,[status(thm)],[3621]) ).
thf(337,plain,
! [B: a,A: a > a] :
( ( ( ( sk1 @ ( sk4 @ B @ A ) )
& ( ( sk3 @ A )
= ( A @ ( sk4 @ B @ A ) ) ) )
!= ( B
= ( sk4 @ B @ A ) ) )
| ~ $true
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,30]) ).
thf(338,plain,
! [B: a,A: a > a] :
( ( ( ( sk1 @ ( sk4 @ B @ A ) )
& ( ( sk3 @ A )
= ( A @ ( sk4 @ B @ A ) ) ) )
!= ( B
= ( sk4 @ B @ A ) ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[337]) ).
thf(398,plain,
! [A: a] :
( ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[338:[bind(A,$thf( ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : F ) ) ) )),bind(B,$thf( B ))]]) ).
thf(424,plain,
! [A: a] :
( ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) ),
inference(simp,[status(thm)],[398]) ).
thf(2287,plain,
! [B: a > a > a,A: a] :
( ~ $true
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2266,38]) ).
thf(2288,plain,
! [B: a > a > a,A: a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ D ) ) )
= ( sk3 @ ( B @ C ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2287]) ).
thf(2344,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[2288:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : F ) ) ) ))]]) ).
thf(3194,plain,
! [A: a] :
( ( ( sk1 @ ( sk32 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) )
!= ( A
= ( sk32 @ A ) ) ),
inference(func_ext,[status(esa)],[2344]) ).
thf(4007,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) )
!= ( A
= ( sk32 @ A ) ) )
| ( ( sk1 @ ( sk32 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2322,3194]) ).
thf(4008,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) )
!= ( A
= ( sk32 @ A ) ) )
| ( ( sk1 @ ( sk32 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) ) ),
inference(simp,[status(thm)],[4007]) ).
thf(4086,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
!= A )
| ( ( sk32 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) )
| ( ( sk32 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) ),
inference(simp,[status(thm)],[4008]) ).
thf(4204,plain,
( ( sk32
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) ),
inference(simp,[status(thm)],[4086]) ).
thf(3514,plain,
! [A: a] :
( ( ( sk1 @ ( sk37 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : H ) ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) ) ) )
!= ( A
= ( sk37 @ A ) ) ),
inference(func_ext,[status(esa)],[2491]) ).
thf(597,plain,
! [B: a > a > a,A: a] :
( ( ( ( sk1 @ ( sk5 @ B @ A ) )
& ( ( sk3
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
= ( sk3 @ ( B @ ( sk5 @ B @ A ) ) ) ) )
!= ( A
= ( sk5 @ B @ A ) ) )
| ~ $true
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,39]) ).
thf(598,plain,
! [B: a > a > a,A: a] :
( ( ( ( sk1 @ ( sk5 @ B @ A ) )
& ( ( sk3
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
= ( sk3 @ ( B @ ( sk5 @ B @ A ) ) ) ) )
!= ( A
= ( sk5 @ B @ A ) ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[597]) ).
thf(665,plain,
! [A: a] :
( ( ( sk1
@ ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) )
@ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) )
!= ( A
= ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) )
@ A ) ) ),
inference(pre_uni,[status(thm)],[598:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : G ) ) ) ))]]) ).
thf(761,plain,
! [A: a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : B ) ) )
| ~ $true
| ( sk1 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[245,7]) ).
thf(762,plain,
! [A: a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : B ) ) )
| ( sk1 @ ( sk3 @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[761]) ).
thf(773,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) )
| ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[762:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : D ) ) ) ))]]) ).
thf(1214,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) )
| ( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) )
!= ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[773]) ).
thf(1234,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) )
| ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) ) ),
inference(simp,[status(thm)],[1214]) ).
thf(310,plain,
! [A: a > a > a] :
( ~ $true
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[283,21]) ).
thf(311,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[310]) ).
thf(314,plain,
( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[311:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ^ [H: a] : H ) ) ) ) ) ))]]) ).
thf(6472,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : I ) ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) ) ) )
!= ( A
= ( sk22 @ A ) ) )
| ( ( sk1 @ ( sk22 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[314,1059]) ).
thf(6473,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : I ) ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) ) )
!= ( A
= ( sk22 @ A ) ) )
| ( ( sk1 @ ( sk22 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[6472]) ).
thf(6604,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : I ) ) ) ) ) ) ) )
!= A )
| ( ( sk22 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) ) )
| ( ( sk22 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[6473]) ).
thf(6691,plain,
( ( sk22
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[6604]) ).
thf(1678,plain,
! [B: a > a > a,A: a > a > a] :
( ( ( sk3
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) )
!= ( sk2
@ ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) ) ) )
| ~ $true
| ( sk1
@ ( sk3
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) )
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,21]) ).
thf(1679,plain,
! [B: a > a > a,A: a > a > a] :
( ( ( sk3
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) )
!= ( sk2
@ ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) ) ) )
| ( sk1
@ ( sk3
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) )
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( A @ C ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[1678]) ).
thf(1719,plain,
( ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : B ) ) )
!= ( sk2
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) )
| ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) ) ),
inference(pre_uni,[status(thm)],[1679:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ( sk3 @ ^ [E: a] : D ) )),bind(B,$thf( ^ [C: a] : ^ [D: a] : C ))]]) ).
thf(2308,plain,
! [B: a,A: a > a] :
( ( ( ( sk1 @ ( sk4 @ B @ A ) )
& ( ( sk3 @ A )
= ( A @ ( sk4 @ B @ A ) ) ) )
!= ( B
= ( sk4 @ B @ A ) ) )
| ~ $true
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2266,30]) ).
thf(2309,plain,
! [B: a,A: a > a] :
( ( ( ( sk1 @ ( sk4 @ B @ A ) )
& ( ( sk3 @ A )
= ( A @ ( sk4 @ B @ A ) ) ) )
!= ( B
= ( sk4 @ B @ A ) ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[2308]) ).
thf(2334,plain,
! [A: a] :
( ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2309:[bind(A,$thf( ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : E ) ) ) )),bind(B,$thf( B ))]]) ).
thf(2357,plain,
! [A: a] :
( ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) ),
inference(simp,[status(thm)],[2334]) ).
thf(5329,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) )
| ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2266,2357]) ).
thf(5330,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) )
| ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) ) ),
inference(simp,[status(thm)],[5329]) ).
thf(5413,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
!= A )
| ( ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) )
| ( ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) ),
inference(simp,[status(thm)],[5330]) ).
thf(5481,plain,
( ( sk4
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) )
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : B ) ) ) ),
inference(simp,[status(thm)],[5413]) ).
thf(2545,plain,
! [A: a > a > a] :
( ~ $true
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2408,21]) ).
thf(2546,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2545]) ).
thf(2581,plain,
( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2546:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ^ [H: a] : ( sk3 @ ^ [I: a] : H ) ) ) ) ) ) ))]]) ).
thf(1669,plain,
! [C: a,B: a > a,A: a > a > a] :
( ( ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) )
!= ( sk2
@ ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3 @ B )
= ( B @ D ) ) ) )
!= ( (=) @ a @ C ) )
| ~ $true
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) ) ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,10]) ).
thf(1670,plain,
! [C: a,B: a > a,A: a > a > a] :
( ( ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) )
!= ( sk2
@ ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3 @ B )
= ( B @ D ) ) ) )
!= ( (=) @ a @ C ) )
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) ) ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[1669]) ).
thf(1721,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) )
!= ( sk2
@ ^ [B: a] : B ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] : C )
= B ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[1670:[bind(A,$thf( ^ [D: a] : ^ [E: a] : E )),bind(B,$thf( ^ [D: a] : D ))]]) ).
thf(1759,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) )
!= ( sk2
@ ^ [B: a] : B ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] : C )
= B ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[1721]) ).
thf(11,plain,
! [A: a > a] :
( ( sk1 @ ( sk2 @ A ) )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1 @ ( sk2 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[5]) ).
thf(13,plain,
! [A: a > a] :
( ( sk1 @ ( sk2 @ A ) )
| ( ( sk3 @ A )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(8439,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) )
!= ( ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) ) ),
inference(simp,[status(thm)],[1234]) ).
thf(12,plain,
! [A: a > a] :
( ( sk1 @ ( sk2 @ A ) )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1 @ ( sk2 @ A ) ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(6178,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) )
!= ( A
= ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) )
@ A ) ) )
| ( ( sk1
@ ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) )
@ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[267,665]) ).
thf(6179,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) )
!= ( A
= ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) )
@ A ) ) )
| ( ( sk1
@ ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) )
@ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) ) ),
inference(simp,[status(thm)],[6178]) ).
thf(6289,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
!= A )
| ( ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) )
@ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) )
| ( ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) )
@ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) ),
inference(simp,[status(thm)],[6179]) ).
thf(6385,plain,
( ( sk5
@ ^ [A: a,B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) )
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ),
inference(simp,[status(thm)],[6289]) ).
thf(345,plain,
! [B: a,A: a > a] :
( ( ( ( sk1 @ ( sk4 @ B @ A ) )
& ( ( sk3 @ A )
= ( A @ ( sk4 @ B @ A ) ) ) )
!= ( B
= ( sk4 @ B @ A ) ) )
| ~ $true
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[267,30]) ).
thf(346,plain,
! [B: a,A: a > a] :
( ( ( ( sk1 @ ( sk4 @ B @ A ) )
& ( ( sk3 @ A )
= ( A @ ( sk4 @ B @ A ) ) ) )
!= ( B
= ( sk4 @ B @ A ) ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[345]) ).
thf(402,plain,
! [A: a] :
( ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[346:[bind(A,$thf( ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : G ) ) ) ) )),bind(B,$thf( B ))]]) ).
thf(427,plain,
! [A: a] :
( ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) ) ),
inference(simp,[status(thm)],[402]) ).
thf(7720,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) ) )
| ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[267,427]) ).
thf(7721,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) ) )
| ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) ) ),
inference(simp,[status(thm)],[7720]) ).
thf(7829,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
!= A )
| ( ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) )
| ( ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) ),
inference(simp,[status(thm)],[7721]) ).
thf(7933,plain,
( ( sk4
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) )
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ),
inference(simp,[status(thm)],[7829]) ).
thf(2459,plain,
! [A: a > a > a] :
( ~ $true
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2330,21]) ).
thf(2460,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2459]) ).
thf(2493,plain,
( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2460:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ^ [H: a] : G ) ) ) ) ) ))]]) ).
thf(2971,plain,
( ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) )
!= ( sk3
@ ^ [A: a] : sk29 ) )
| ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) ) ),
inference(func_ext,[status(esa)],[2621]) ).
thf(3287,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] : A ) )
!= ( ^ [A: a] : sk29 ) ) ),
inference(simp,[status(thm)],[2971]) ).
thf(48,plain,
! [C: a,B: a > a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3 @ B )
= ( B @ D ) ) ) )
!= ( (=) @ a @ C ) )
| ~ $true
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) ) ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,10]) ).
thf(49,plain,
! [C: a,B: a > a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3 @ B )
= ( B @ D ) ) ) )
!= ( (=) @ a @ C ) )
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) ) ) )
!= ( sk1 @ ( B @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(70,plain,
! [C: a > a > a,B: a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3
@ ^ [E: a] : ( sk2 @ ( C @ E ) ) )
= ( sk2 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
!= ( C
@ ( sk2
@ ^ [D: a] : ( sk2 @ ( C @ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[49:[bind(A,$thf( A )),bind(B,$thf( ^ [E: a] : ( sk2 @ ( D @ E ) ) ))]]) ).
thf(81,plain,
! [C: a > a > a,B: a,A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3
@ ^ [E: a] : ( sk2 @ ( C @ E ) ) )
= ( sk2 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
!= ( C
@ ( sk2
@ ^ [D: a] : ( sk2 @ ( C @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(353,plain,
! [B: a,A: a > a] :
( ( ( ( sk1 @ ( sk4 @ B @ A ) )
& ( ( sk3 @ A )
= ( A @ ( sk4 @ B @ A ) ) ) )
!= ( B
= ( sk4 @ B @ A ) ) )
| ~ $true
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[254,30]) ).
thf(354,plain,
! [B: a,A: a > a] :
( ( ( ( sk1 @ ( sk4 @ B @ A ) )
& ( ( sk3 @ A )
= ( A @ ( sk4 @ B @ A ) ) ) )
!= ( B
= ( sk4 @ B @ A ) ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[353]) ).
thf(410,plain,
! [A: a] :
( ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ),
inference(pre_uni,[status(thm)],[354:[bind(A,$thf( ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : E ) ) )),bind(B,$thf( B ))]]) ).
thf(434,plain,
! [A: a] :
( ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ),
inference(simp,[status(thm)],[410]) ).
thf(103,plain,
( ( ( sk3
@ ^ [A: a] : A )
!= sk7 )
| ( sk1
@ ( sk3
@ ^ [A: a] : A ) ) ),
inference(func_ext,[status(esa)],[101]) ).
thf(862,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) )
!= ( A
= ( sk13 @ A ) ) )
| ( ( sk1 @ ( sk13 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[254,303]) ).
thf(863,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) )
!= ( A
= ( sk13 @ A ) ) )
| ( ( sk1 @ ( sk13 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) ) ),
inference(simp,[status(thm)],[862]) ).
thf(902,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
!= A )
| ( ( sk13 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) )
| ( ( sk13 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) ),
inference(simp,[status(thm)],[863]) ).
thf(943,plain,
( ( sk13
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : B ) ) ),
inference(simp,[status(thm)],[902]) ).
thf(1066,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) )
!= ( A
= ( sk16 @ A ) ) )
| ( ( sk1 @ ( sk16 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,573]) ).
thf(1067,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) )
!= ( A
= ( sk16 @ A ) ) )
| ( ( sk1 @ ( sk16 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ) ),
inference(simp,[status(thm)],[1066]) ).
thf(1115,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
!= A )
| ( ( sk16 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) )
| ( ( sk16 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ),
inference(simp,[status(thm)],[1067]) ).
thf(1166,plain,
( ( sk16
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) ),
inference(simp,[status(thm)],[1115]) ).
thf(609,plain,
! [B: a > a > a,A: a] :
( ( ( ( sk1 @ ( sk5 @ B @ A ) )
& ( ( sk3
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
= ( sk3 @ ( B @ ( sk5 @ B @ A ) ) ) ) )
!= ( A
= ( sk5 @ B @ A ) ) )
| ~ $true
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[254,39]) ).
thf(610,plain,
! [B: a > a > a,A: a] :
( ( ( ( sk1 @ ( sk5 @ B @ A ) )
& ( ( sk3
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
= ( sk3 @ ( B @ ( sk5 @ B @ A ) ) ) ) )
!= ( A
= ( sk5 @ B @ A ) ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[609]) ).
thf(644,plain,
! [A: a] :
( ( ( sk1
@ ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) )
@ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) )
!= ( A
= ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) )
@ A ) ) ),
inference(pre_uni,[status(thm)],[610:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : F ) ) ))]]) ).
thf(1770,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) )
!= ( A
= ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) )
@ A ) ) )
| ( ( sk1
@ ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) )
@ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,644]) ).
thf(1771,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) )
!= ( A
= ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) )
@ A ) ) )
| ( ( sk1
@ ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) )
@ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ) ),
inference(simp,[status(thm)],[1770]) ).
thf(1855,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
!= A )
| ( ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) )
@ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) )
| ( ( sk5
@ ^ [B: a,C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) )
@ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ),
inference(simp,[status(thm)],[1771]) ).
thf(1905,plain,
( ( sk5
@ ^ [A: a,B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) )
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) ),
inference(simp,[status(thm)],[1855]) ).
thf(1011,plain,
! [B: a > a > a > a,A: a] :
( ~ $true
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
= ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[299,47]) ).
thf(1012,plain,
! [B: a > a > a > a,A: a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
= ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[1011]) ).
thf(1018,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] :
( sk3
@ ^ [J: a] :
( sk3
@ ^ [K: a] : K ) ) ) ) ) ) ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] :
( sk3
@ ^ [J: a] : J ) ) ) ) ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[1012:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ^ [H: a] : ( sk3 @ ^ [I: a] : ( sk3 @ ^ [J: a] : ( sk3 @ ^ [K: a] : K ) ) ) ) ) ) ))]]) ).
thf(116,plain,
! [B: a,A: a > a] :
( ( ( sk3
@ ^ [C: a] : C )
!= sk7 )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ~ $true
| ( ( sk1
@ ( sk3
@ ^ [C: a] : C ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[103,10]) ).
thf(117,plain,
! [B: a,A: a > a] :
( ( ( sk3
@ ^ [C: a] : C )
!= sk7 )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] : C ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(124,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] : B )
!= sk7 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) )
= ( sk3
@ ^ [C: a] : C ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[117:[bind(A,$thf( ^ [C: a] : ( sk3 @ ^ [D: a] : D ) )),bind(B,$thf( B ))]]) ).
thf(127,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] : B )
!= sk7 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) )
= ( sk3
@ ^ [C: a] : C ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(4924,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) ) ) )
!= ( A
= ( sk20 @ A ) ) )
| ( ( sk1 @ ( sk20 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[299,849]) ).
thf(4925,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) ) )
!= ( A
= ( sk20 @ A ) ) )
| ( ( sk1 @ ( sk20 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[4924]) ).
thf(5009,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) )
!= A )
| ( ( sk20 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) ) )
| ( ( sk20 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[4925]) ).
thf(5106,plain,
( ( sk20
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : G ) ) ) ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) ) ) ),
inference(simp,[status(thm)],[5009]) ).
thf(3107,plain,
( ( ( sk3
@ ^ [A: a] : sk31 )
!= sk30 )
| ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : A ) ) ) ),
inference(func_ext,[status(esa)],[2970]) ).
thf(3773,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : B ) ) ) )
| ~ $true
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : D ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2929,21]) ).
thf(3774,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : B ) ) ) )
| ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : D ) ) ) ) ) )
!= ( sk1
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[3773]) ).
thf(3829,plain,
( ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : A ) ) ) )
| ( sk1
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : E ) ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3774:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ^ [H: a] : F ) ) ) ) ) ))]]) ).
thf(72,plain,
! [A: a > a > a] :
( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
| ( ( sk1
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) )
!= ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(7034,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : H ) ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) ) ) )
!= ( A
= ( sk37 @ A ) ) )
| ( ( sk1 @ ( sk37 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2493,3514]) ).
thf(7035,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : H ) ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) ) )
!= ( A
= ( sk37 @ A ) ) )
| ( ( sk1 @ ( sk37 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[7034]) ).
thf(7174,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : H ) ) ) ) ) ) ) )
!= A )
| ( ( sk37 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) ) )
| ( ( sk37 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[7035]) ).
thf(7192,plain,
( ( sk37
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[7174]) ).
thf(2397,plain,
! [B: a > a > a > a,A: a] :
( ~ $true
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
= ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2322,47]) ).
thf(2398,plain,
! [B: a > a > a > a,A: a] :
( ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
= ( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) ) ) )
!= ( (=) @ a @ A ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
!= ( sk1
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) )
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk3 @ ( B @ C @ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ D @ E ) ) ) )
@ C ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2397]) ).
thf(2406,plain,
! [A: a] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : H ) ) ) ) ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ),
inference(pre_uni,[status(thm)],[2398:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ^ [D: a] : ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ^ [H: a] : ( sk3 @ ^ [I: a] : H ) ) ) ) ))]]) ).
thf(3284,plain,
! [A: a] :
( ( ( sk1 @ ( sk34 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) ) ) )
!= ( A
= ( sk34 @ A ) ) ),
inference(func_ext,[status(esa)],[2406]) ).
thf(3112,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a,D: a] :
( sk3
@ ^ [E: a] : D ) )
!= ( ^ [C: a,D: a] : C ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ~ $true
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2970,10]) ).
thf(3113,plain,
! [B: a,A: a > a] :
( ( ( ^ [C: a,D: a] :
( sk3
@ ^ [E: a] : D ) )
!= ( ^ [C: a,D: a] : C ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1
@ ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) )
!= ( sk1 @ ( A @ ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[3112]) ).
thf(3167,plain,
! [A: a] :
( ( ( ^ [B: a,C: a] :
( sk3
@ ^ [D: a] : C ) )
!= ( ^ [B: a,C: a] : B ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[3113:[bind(A,$thf( ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : D ) ) )),bind(B,$thf( B ))]]) ).
thf(3188,plain,
! [A: a] :
( ( ( ^ [B: a,C: a] :
( sk3
@ ^ [D: a] : C ) )
!= ( ^ [B: a,C: a] : B ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) )
= ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[3167]) ).
thf(1676,plain,
! [C: a > a > a,B: a,A: a > a > a] :
( ( ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) )
!= ( sk2
@ ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) ) ) )
| ~ $true
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3
@ ^ [E: a] : ( sk3 @ ( C @ E ) ) )
= ( sk3 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) ) ) )
!= ( sk1
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) )
@ ( sk2
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,38]) ).
thf(1677,plain,
! [C: a > a > a,B: a,A: a > a > a] :
( ( ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) )
!= ( sk2
@ ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3
@ ^ [E: a] : ( sk3 @ ( C @ E ) ) )
= ( sk3 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) ) ) )
!= ( sk1
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) )
@ ( sk2
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[1676]) ).
thf(1699,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) )
!= ( sk2
@ ^ [B: a] : B ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) )
= ( sk3
@ ^ [C: a] : C ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[1677:[bind(A,$thf( ^ [D: a] : ^ [E: a] : E )),bind(B,$thf( B )),bind(C,$thf( ^ [D: a] : ^ [E: a] : E ))]]) ).
thf(1742,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) )
!= ( sk2
@ ^ [B: a] : B ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( ( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) )
= ( sk3
@ ^ [C: a] : C ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[1699]) ).
thf(5581,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) ) ) )
!= ( A
= ( sk34 @ A ) ) )
| ( ( sk1 @ ( sk34 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2408,3284]) ).
thf(5582,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) ) )
!= ( A
= ( sk34 @ A ) ) )
| ( ( sk1 @ ( sk34 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[5581]) ).
thf(5617,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : G ) ) ) ) ) ) )
!= A )
| ( ( sk34 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) ) )
| ( ( sk34 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[5582]) ).
thf(5803,plain,
( ( sk34
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : F ) ) ) ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) ) ),
inference(simp,[status(thm)],[5617]) ).
thf(1487,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) )
!= ( A
= ( sk17 @ A ) ) )
| ( ( sk1 @ ( sk17 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[267,751]) ).
thf(1488,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) )
!= ( A
= ( sk17 @ A ) ) )
| ( ( sk1 @ ( sk17 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) ) ),
inference(simp,[status(thm)],[1487]) ).
thf(1520,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : F ) ) ) ) )
!= A )
| ( ( sk17 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) )
| ( ( sk17 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) ),
inference(simp,[status(thm)],[1488]) ).
thf(1582,plain,
( ( sk17
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ),
inference(simp,[status(thm)],[1520]) ).
thf(1320,plain,
! [A: a] :
( ( ( sk1 @ ( sk23 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] :
( sk3
@ ^ [J: a] : J ) ) ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : I ) ) ) ) ) ) ) ) ) )
!= ( A
= ( sk23 @ A ) ) ),
inference(func_ext,[status(esa)],[1018]) ).
thf(7984,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] :
( sk3
@ ^ [J: a] : J ) ) ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : I ) ) ) ) ) ) ) ) ) )
!= ( A
= ( sk23 @ A ) ) )
| ( ( sk1 @ ( sk23 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : I ) ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[475,1320]) ).
thf(7985,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] :
( sk3
@ ^ [J: a] : J ) ) ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : I ) ) ) ) ) ) ) ) )
!= ( A
= ( sk23 @ A ) ) )
| ( ( sk1 @ ( sk23 @ A ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : I ) ) ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[7984]) ).
thf(8061,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] :
( sk3
@ ^ [J: a] : J ) ) ) ) ) ) ) ) )
!= A )
| ( ( sk23 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : I ) ) ) ) ) ) ) ) )
| ( ( sk23 @ A )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : I ) ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[7985]) ).
thf(8189,plain,
( ( sk23
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : I ) ) ) ) ) ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : H ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[8061]) ).
thf(8821,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) ) )
| ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2322,2437]) ).
thf(8822,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) ) )
| ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) ) ),
inference(simp,[status(thm)],[8821]) ).
thf(8967,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
!= A )
| ( ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) )
| ( ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : E ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) ) ),
inference(simp,[status(thm)],[8822]) ).
thf(8978,plain,
( ( sk4
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) )
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : D ) ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : C ) ) ) ) ),
inference(simp,[status(thm)],[8967]) ).
thf(1061,plain,
! [A: a] :
( ( ( sk1 @ ( sk16 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) )
| ( A
= ( sk16 @ A ) ) ),
inference(bool_ext,[status(thm)],[573]) ).
thf(1097,plain,
! [A: a] :
( ( ( sk16 @ A )
= A )
| ( ( sk1 @ ( sk16 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ) ),
inference(lifteq,[status(thm)],[1061]) ).
thf(1151,plain,
! [A: a] :
( ( ( ( sk16 @ A )
= A )
| ( sk1 @ ( sk16 @ A ) ) )
& ( ( ( sk16 @ A )
= A )
| ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ) ),
inference(cnf,[status(esa)],[1097]) ).
thf(1152,plain,
! [A: a] :
( ( ( sk16 @ A )
= A )
| ( sk1 @ ( sk16 @ A ) ) ),
inference(cnfConj,[status(thm)],[1151]) ).
thf(3950,plain,
! [A: a] :
( ( ( sk1 @ ( sk38 @ A ) )
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] :
( sk3
@ ^ [J: a] : I ) ) ) ) ) ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] :
( sk3
@ ^ [I: a] : H ) ) ) ) ) ) ) ) ) )
!= ( A
= ( sk38 @ A ) ) ),
inference(func_ext,[status(esa)],[2595]) ).
thf(54,plain,
! [C: a > a > a,B: a,A: a > a > a] :
( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) ) ) )
| ~ $true
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3
@ ^ [E: a] : ( sk3 @ ( C @ E ) ) )
= ( sk3 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1
@ ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
!= ( sk1
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) )
@ ( sk2
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,38]) ).
thf(55,plain,
! [C: a > a > a,B: a,A: a > a > a] :
( ( sk1
@ ( sk2
@ ( A
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) ) ) )
| ( ( ^ [D: a] :
( ( sk1 @ D )
& ( ( sk3
@ ^ [E: a] : ( sk3 @ ( C @ E ) ) )
= ( sk3 @ ( C @ D ) ) ) ) )
!= ( (=) @ a @ B ) )
| ( ( sk1
@ ( sk3
@ ^ [D: a] : ( sk3 @ ( A @ D ) ) ) )
!= ( sk1
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) )
@ ( sk2
@ ( C
@ ( sk2
@ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(74,plain,
! [B: a > a > a > a > a,A: a] :
( ( sk1
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ C @ D @ E ) ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : ( sk3 @ ( B @ E @ F @ G ) ) ) ) )
@ C
@ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : ( sk3 @ ( B @ D @ E @ F ) ) ) ) )
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : ( sk3 @ ( B @ F @ G @ H ) ) ) ) )
@ D
@ E ) ) ) )
@ C ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : ( sk3 @ ( B @ D @ E @ F ) ) ) ) )
= ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ C @ D @ E ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(pre_uni,[status(thm)],[55:[bind(A,$thf( E @ ( sk2 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ( E @ E @ F @ G ) ) ) ) ) @ ( sk2 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ( E @ ( sk2 @ ^ [G: a] : ( sk3 @ ^ [H: a] : ( sk3 @ ^ [I: a] : ( sk3 @ ( E @ G @ H @ I ) ) ) ) ) @ E @ F ) ) ) ) )),bind(B,$thf( B )),bind(C,$thf( ^ [E: a] : ^ [F: a] : ( sk3 @ ^ [G: a] : ( sk3 @ ( E @ E @ F @ G ) ) ) ))]]) ).
thf(83,plain,
! [B: a > a > a > a > a,A: a] :
( ( sk1
@ ( sk2
@ ( B
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ C @ D @ E ) ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [E: a] :
( sk3
@ ^ [F: a] :
( sk3
@ ^ [G: a] : ( sk3 @ ( B @ E @ F @ G ) ) ) ) )
@ C
@ D ) ) ) )
@ ( sk2
@ ^ [C: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : ( sk3 @ ( B @ D @ E @ F ) ) ) ) )
@ ( sk2
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ( B
@ ( sk2
@ ^ [F: a] :
( sk3
@ ^ [G: a] :
( sk3
@ ^ [H: a] : ( sk3 @ ( B @ F @ G @ H ) ) ) ) )
@ D
@ E ) ) ) )
@ C ) ) ) ) ) )
| ( ( ^ [C: a] :
( ( sk1 @ C )
& ( ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : ( sk3 @ ( B @ D @ E @ F ) ) ) ) )
= ( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : ( sk3 @ ( B @ C @ D @ E ) ) ) ) ) ) )
!= ( (=) @ a @ A ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(4629,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) )
| ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,424]) ).
thf(4630,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) ) )
| ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ) ),
inference(simp,[status(thm)],[4629]) ).
thf(4779,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
!= A )
| ( ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) )
| ( ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : E ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) ),
inference(simp,[status(thm)],[4630]) ).
thf(4863,plain,
( ( sk4
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) )
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) ),
inference(simp,[status(thm)],[4779]) ).
thf(1331,plain,
! [A: a] :
( ( ( $true
& ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) )
| ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[254,434]) ).
thf(1332,plain,
! [A: a] :
( ( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) )
!= ( A
= ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) ) )
| ( ( sk1
@ ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) ) )
!= ( sk1
@ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) ) ),
inference(simp,[status(thm)],[1331]) ).
thf(1411,plain,
! [A: a] :
( ( ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
!= A )
| ( ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) )
| ( ( sk4 @ A
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : D ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) ) ),
inference(simp,[status(thm)],[1332]) ).
thf(1417,plain,
( ( sk4
@ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) )
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : C ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : B ) ) ),
inference(simp,[status(thm)],[1411]) ).
thf(9574,plain,
$false,
inference(e,[status(thm)],[573,2970,282,2330,101,2595,115,5,10,2035,1735,2348,2491,320,37,4439,3195,785,751,1059,20,46,969,2929,78,6983,475,2880,2925,2437,849,507,270,85,102,2621,3711,38,424,4204,21,3514,665,2344,1234,2157,317,6691,9,1719,77,3194,5481,2581,1759,13,8439,73,2408,12,6385,2326,7933,2493,7,303,271,3287,81,39,434,103,943,299,3,267,1166,2318,1905,1018,127,5106,470,2322,3107,3829,2357,72,2266,7192,314,3284,99,3188,2406,2971,300,752,168,30,268,283,1742,5803,1582,644,47,8189,8978,1152,427,254,3950,1320,83,4863,1417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV080^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.10 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.25/0.29 % Computer : n017.cluster.edu
% 0.25/0.29 % Model : x86_64 x86_64
% 0.25/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.29 % Memory : 8046.5625MB
% 0.25/0.29 % OS : Linux 6.8.0-71-generic
% 0.25/0.29 % CPULimit : 300
% 0.25/0.29 % WCLimit : 300
% 0.25/0.29 % DateTime : Tue Sep 29 15:02:22 UTC 2026
% 0.25/0.30 % CPUTime :
% 0.25/0.30 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.36/1.12 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.79/1.38 % [INFO] Parsing done (256ms).
% 1.79/1.40 % [INFO] Running in sequential loop mode.
% 2.71/1.99 % [INFO] eprover registered as external prover.
% 2.71/2.00 % [INFO] Scanning for conjecture ...
% 3.02/2.12 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.21/2.18 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.21/2.18 % [INFO] Problem is higher-order (TPTP THF).
% 3.21/2.18 % [INFO] Type checking passed.
% 3.21/2.19 % [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 ...
% 273.25/116.74 % External prover 'e' found a proof!
% 273.25/116.74 % [INFO] Killing All external provers ...
% 273.25/116.74 % Time passed: 116244ms (effective reasoning time: 115340ms)
% 273.25/116.74 % 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)>
% 273.25/116.75 % Axioms used in derivation (0):
% 273.25/116.75 % No. of inferences in proof: 341
% 273.25/116.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 116244 ms resp. 115340 ms w/o parsing
% 276.41/117.21 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 276.41/117.21 % [INFO] Killing All external provers ...
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