TSTP Solution File: SEV011^5 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEV011^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:09:48 EDT 2024
% Result : Theorem 231.50s 47.77s
% Output : Refutation 232.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of formulae : 349 ( 20 unt; 9 typ; 0 def)
% Number of atoms : 2224 ( 328 equ; 54 cnn)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 4373 ( 774 ~; 674 |; 18 &;2889 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 314 ( 314 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 1440 (1133 ^ 304 !; 3 ?;1440 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_type,type,
sk1: a > a > $o ).
thf(sk2_type,type,
sk2: a ).
thf(sk3_type,type,
sk3: ( a > $o ) > $o ).
thf(sk4_type,type,
sk4: ( a > $o ) > a ).
thf(sk5_type,type,
sk5: ( a > $o ) > a ).
thf(sk6_type,type,
sk6: ( a > $o ) > a > $o ).
thf(sk7_type,type,
sk7: ( a > $o ) > a ).
thf(sk8_type,type,
sk8: a ).
thf(1,conjecture,
! [A: a > a > $o] :
( ( ! [B: a] : ( A @ B @ B )
& ! [B: a,C: a] :
( ( A @ B @ C )
=> ( A @ C @ B ) )
& ! [B: a,C: a,D: a] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) )
=> ! [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ! [E: a] :
( ( C @ E )
= ( A @ D @ E ) ) )
& ( C @ B )
& ! [D: a > $o] :
( ( ! [E: a] :
( ( D @ E )
=> ! [F: a] :
( ( D @ F )
= ( A @ E @ F ) ) )
& ( D @ B ) )
=> ( D = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM260_B_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > a > $o] :
( ( ! [B: a] : ( A @ B @ B )
& ! [B: a,C: a] :
( ( A @ B @ C )
=> ( A @ C @ B ) )
& ! [B: a,C: a,D: a] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) )
=> ! [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ! [E: a] :
( ( C @ E )
= ( A @ D @ E ) ) )
& ( C @ B )
& ! [D: a > $o] :
( ( ! [E: a] :
( ( D @ E )
=> ! [F: a] :
( ( D @ F )
= ( A @ E @ F ) ) )
& ( D @ B ) )
=> ( D = C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > a > $o] :
( ( ! [B: a] : ( A @ B @ B )
& ! [B: a,C: a] :
( ( A @ B @ C )
=> ( A @ C @ B ) )
& ! [B: a,C: a,D: a] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) )
=> ! [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ! [E: a] :
( ( C @ E )
= ( A @ D @ E ) ) )
& ( C @ B )
& ! [D: a > $o] :
( ( ! [E: a] :
( ( D @ E )
=> ! [F: a] :
( ( D @ F )
= ( A @ E @ F ) ) )
& ( D @ B ) )
=> ( D = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
! [A: a > $o] :
( ( A @ ( sk4 @ A ) )
| ~ ( sk3 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(19,plain,
! [A: a > $o] :
( ( A @ ( sk4 @ A ) )
| ~ ( sk3 @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(23,plain,
! [A: a > $o] :
( ~ ( A
@ ( sk4
@ ^ [B: a] :
~ ( A @ B ) ) )
| ~ ( sk3
@ ^ [B: a] :
~ ( A @ B ) ) ),
inference(prim_subst,[status(thm)],[19:[bind(A,$thf( ^ [C: a] : ~ ( B @ C ) ))]]) ).
thf(31,plain,
! [A: a > $o] :
( ~ ( sk3
@ ^ [B: a] :
~ ( A @ B ) )
| ~ ( A
@ ( sk4
@ ^ [B: a] :
~ ( A @ B ) ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(32,plain,
! [A: a > $o] :
( ~ ( sk3
@ ^ [B: a] :
~ ( A @ B ) )
| ~ ( A
@ ( sk4
@ ^ [B: a] :
~ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(52,plain,
! [B: a > a,A: a > a > $o] :
( ~ ( sk3
@ ^ [C: a] :
~ ( sk6 @ ( A @ C ) @ ( B @ C ) ) )
| ~ ( sk6
@ ( A
@ ( sk4
@ ^ [C: a] :
~ ( sk6 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk4
@ ^ [C: a] :
~ ( sk6 @ ( A @ C ) @ ( B @ C ) ) ) ) ) ),
inference(prim_subst,[status(thm)],[32:[bind(A,$thf( ^ [D: a] : ( sk6 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(65,plain,
! [B: a > a,A: a > a > $o] :
( ~ ( sk3
@ ^ [C: a] :
~ ( sk6 @ ( A @ C ) @ ( B @ C ) ) )
| ~ ( sk6
@ ( A
@ ( sk4
@ ^ [C: a] :
~ ( sk6 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk4
@ ^ [C: a] :
~ ( sk6 @ ( A @ C ) @ ( B @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(5,plain,
! [A: a > $o] :
( ( sk3 @ A )
| ~ ( A @ sk2 )
| ( sk6 @ A @ sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(12,plain,
! [A: a > $o] :
( ( sk3 @ A )
| ~ ( A @ sk2 )
| ( sk6 @ A @ sk2 ) ),
inference(simp,[status(thm)],[5]) ).
thf(85,plain,
( ( sk3
@ ^ [A: a] : $true )
| ~ $true
| ( sk6
@ ^ [A: a] : $true
@ sk2 ) ),
inference(prim_subst,[status(thm)],[12:[bind(A,$thf( ^ [B: a] : $true ))]]) ).
thf(105,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( sk6
@ ^ [A: a] : $true
@ sk2 ) ),
inference(simp,[status(thm)],[85]) ).
thf(118,plain,
! [A: a > $o] :
( ( sk3
@ ^ [B: a] : $true )
| ( sk3 @ A )
| ( sk6 @ A @ sk2 )
| ( ( sk6
@ ^ [B: a] : $true
@ sk2 )
!= ( A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[105,12]) ).
thf(121,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( sk3
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk2 ) )
| ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk2 )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[118:[bind(A,$thf( ^ [B: a] : ( sk6 @ ^ [C: a] : $true @ sk2 ) ))]]) ).
thf(609,plain,
! [A: a > $o] :
( ( sk3
@ ^ [B: a] : $true )
| ( sk3
@ ^ [B: a] :
( sk6
@ ^ [C: a] : $true
@ sk2 ) )
| ( sk3 @ A )
| ( sk6 @ A @ sk2 )
| ( ( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : $true
@ sk2 )
@ sk2 )
!= ( A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[121,12]) ).
thf(650,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( sk3
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk2 ) )
| ( sk3
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk2 ) ) )
| ( sk6
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk2 ) )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[609:[bind(A,$thf( sk6 @ ^ [B: a] : ( sk6 @ ^ [C: a] : $true @ sk2 ) ))]]) ).
thf(87,plain,
! [B: a > $o,A: a > $o] :
( ( sk3
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ~ ( ( A @ sk2 )
| ( B @ sk2 ) )
| ( sk6
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) )
@ sk2 ) ),
inference(prim_subst,[status(thm)],[12:[bind(A,$thf( ^ [D: a] : ( ( B @ D ) | ( C @ D ) ) ))]]) ).
thf(107,plain,
! [B: a > $o,A: a > $o] :
( ( sk6
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) )
@ sk2 )
| ~ ( A @ sk2 )
| ( sk3
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(109,plain,
! [B: a > $o,A: a > $o] :
( ( sk6
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) )
@ sk2 )
| ~ ( A @ sk2 )
| ( sk3
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(54,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk3
@ ^ [C: a] :
~ ( ( A @ C )
| ( B @ C ) ) )
| ~ ( ( A
@ ( sk4
@ ^ [C: a] :
~ ( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk4
@ ^ [C: a] :
~ ( ( A @ C )
| ( B @ C ) ) ) ) ) ),
inference(prim_subst,[status(thm)],[32:[bind(A,$thf( ^ [D: a] : ( ( B @ D ) | ( C @ D ) ) ))]]) ).
thf(67,plain,
! [B: a > $o,A: a > $o] :
( ~ ( B
@ ( sk4
@ ^ [C: a] :
~ ( ( A @ C )
| ( B @ C ) ) ) )
| ~ ( sk3
@ ^ [C: a] :
~ ( ( A @ C )
| ( B @ C ) ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(69,plain,
! [B: a > $o,A: a > $o] :
( ~ ( B
@ ( sk4
@ ^ [C: a] :
~ ( ( A @ C )
| ( B @ C ) ) ) )
| ~ ( sk3
@ ^ [C: a] :
~ ( ( A @ C )
| ( B @ C ) ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(28,plain,
! [A: a > a > $o] :
( ( sk3
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) )
| ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ),
inference(prim_subst,[status(thm)],[19:[bind(A,$thf( ^ [C: a] : ( sk3 @ ( B @ C ) ) ))]]) ).
thf(37,plain,
! [A: a > a > $o] :
( ( sk3
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) )
| ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(47,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk3 @ A )
| ~ ( sk3
@ ^ [C: a] :
~ ( B @ C ) )
| ( ( A @ ( sk4 @ A ) )
!= ( B
@ ( sk4
@ ^ [C: a] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,32]) ).
thf(60,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk3 @ A )
| ~ ( sk3
@ ^ [C: a] :
~ ( B @ C ) )
| ( ( A @ ( sk4 @ A ) )
!= ( B
@ ( sk4
@ ^ [C: a] :
~ ( B @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[47:[]]) ).
thf(61,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk3
@ ^ [C: a] :
~ ( B @ C ) )
| ~ ( sk3 @ A )
| ( ( A @ ( sk4 @ A ) )
!= ( B
@ ( sk4
@ ^ [C: a] :
~ ( B @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[60:[]]) ).
thf(3036,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk3
@ ^ [C: a] :
~ ( B @ C ) )
| ~ ( sk3 @ A )
| ~ ( A @ ( sk4 @ A ) )
| ( ( B
@ ( sk4
@ ^ [C: a] :
~ ( B @ C ) ) )
!= ( sk3 @ A ) ) ),
inference(eqfactor_ordered,[status(thm)],[61]) ).
thf(3039,plain,
( ~ ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) )
| ~ ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[3036:[bind(A,$thf( ^ [C: a] : $true )),bind(B,$thf( ^ [C: a] : ( sk3 @ ^ [D: a] : $true ) ))]]) ).
thf(3241,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ~ ( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) )
| ( ( sk3
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) )
!= ( sk3
@ ^ [B: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[37,3039]) ).
thf(3283,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ~ ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[3241:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $true ))]]) ).
thf(3853,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ~ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) )
| ( ( sk3
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,3283]) ).
thf(3907,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) )
| ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[3853:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ~ ( sk3 @ ^ [D: a] : $true ) ))]]) ).
thf(9077,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) )
!= ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3907]) ).
thf(9106,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) )
!= ( ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) ) ) ),
inference(simp,[status(thm)],[9077]) ).
thf(23197,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ~ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) )
| ( ( ^ [B: a] :
( sk3
@ ^ [C: a] : $false ) )
!= ( ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[19,9106]) ).
thf(23300,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] : $false ) )
!= ( ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[23197:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : $true ) ))]]) ).
thf(23306,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] : $false ) )
!= ( ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) ) ) ),
inference(simp,[status(thm)],[23300]) ).
thf(25,plain,
( $false
| ~ ( sk3
@ ^ [A: a] : $false ) ),
inference(prim_subst,[status(thm)],[19:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(35,plain,
~ ( sk3
@ ^ [A: a] : $false ),
inference(simp,[status(thm)],[25]) ).
thf(23519,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
!= ( ^ [A: a] : $false ) ) ),
inference(rewrite,[status(thm)],[23306,35]) ).
thf(80,plain,
! [B: a > $o,A: a > $o] :
( ( sk3 @ A )
| ~ ( A @ sk2 )
| ( sk3 @ B )
| ( sk6 @ B @ sk2 )
| ( ( sk6 @ A @ sk2 )
!= ( B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[12,12]) ).
thf(96,plain,
! [A: a > a > $o] :
( ( sk3 @ ( A @ sk2 ) )
| ~ ( A @ sk2 @ sk2 )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ sk2 ) )
| ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ sk2 )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[80:[bind(A,$thf( C @ sk2 )),bind(B,$thf( ^ [D: a] : ( sk6 @ ( C @ D ) @ sk2 ) ))]]) ).
thf(101,plain,
! [A: a > a > $o] :
( ( sk3 @ ( A @ sk2 ) )
| ~ ( A @ sk2 @ sk2 )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ sk2 ) )
| ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ sk2 )
@ sk2 ) ),
inference(simp,[status(thm)],[96]) ).
thf(22,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk3 @ A )
| ( B @ ( sk4 @ B ) )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19,19]) ).
thf(30,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[22:[bind(A,$thf( ^ [D: a] : ( sk3 @ ( C @ D ) ) )),bind(B,$thf( C @ ( sk4 @ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) ))]]) ).
thf(39,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(3881,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ~ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,3283]) ).
thf(3905,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk3
@ ^ [D: a] : $true ) ) ) )
| ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[3881:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ~ ( sk3 @ ^ [E: a] : $true ) ) ))]]) ).
thf(97,plain,
! [A: a > a > $o] :
( ( sk3 @ ( A @ sk2 ) )
| ~ ( A @ sk2 @ sk2 )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ B ) )
| ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ B )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[80:[bind(A,$thf( C @ sk2 )),bind(B,$thf( ^ [D: a] : ( sk6 @ ( C @ D ) @ D ) ))]]) ).
thf(102,plain,
! [A: a > a > $o] :
( ( sk3 @ ( A @ sk2 ) )
| ~ ( A @ sk2 @ sk2 )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ B ) )
| ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ B )
@ sk2 ) ),
inference(simp,[status(thm)],[97]) ).
thf(7965,plain,
! [B: a > $o,A: a > a > $o] :
( ( sk3 @ ( A @ sk2 ) )
| ~ ( A @ sk2 @ sk2 )
| ( sk3
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ C ) )
| ( sk3 @ B )
| ( sk6 @ B @ sk2 )
| ( ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ C )
@ sk2 )
!= ( B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[102,12]) ).
thf(8113,plain,
! [A: a > $o] :
( ( sk3 @ ( (=) @ a @ sk2 ) )
| ( sk2 != sk2 )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B ) )
| ( sk3 @ A )
| ( sk6 @ A @ sk2 )
| ( ( sk6
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B )
@ sk2 )
!= ( A @ sk2 ) ) ),
inference(replace_andrewseq,[status(thm)],[7965:[bind(A,$thf( (=) @ a ))]]) ).
thf(8284,plain,
! [A: a > $o] :
( ( sk2 != sk2 )
| ( sk3 @ ( (=) @ a @ sk2 ) )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B ) )
| ( sk3 @ A )
| ( sk6 @ A @ sk2 )
| ( ( sk6
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B )
@ sk2 )
!= ( A @ sk2 ) ) ),
inference(lifteq,[status(thm)],[8113]) ).
thf(8447,plain,
( ( sk6
@ ( sk6
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ A ) )
@ sk2 )
| ( sk3
@ ( sk6
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ A ) ) )
| ( sk3
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ A ) )
| ( sk3 @ ( (=) @ a @ sk2 ) ) ),
inference(pre_uni,[status(thm)],[8284:[bind(A,$thf( sk6 @ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B ) ))]]) ).
thf(117,plain,
! [A: a > $o] :
( ( sk3
@ ^ [B: a] : $true )
| ~ ( sk3
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk6
@ ^ [B: a] : $true
@ sk2 )
!= ( A
@ ( sk4
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[105,32]) ).
thf(120,plain,
( ( sk3
@ ^ [A: a] : $true )
| ~ ( sk3
@ ^ [A: a] :
~ ( sk6
@ ^ [B: a] : $true
@ sk2 ) ) ),
inference(pre_uni,[status(thm)],[117:[bind(A,$thf( ^ [B: a] : ( sk6 @ ^ [C: a] : $true @ sk2 ) ))]]) ).
thf(50,plain,
! [A: a > $o] :
( ~ ( sk3
@ ^ [B: a] :
~ ~ ( A @ B ) )
| ~ ~ ( A
@ ( sk4
@ ^ [B: a] :
~ ~ ( A @ B ) ) ) ),
inference(prim_subst,[status(thm)],[32:[bind(A,$thf( ^ [C: a] : ~ ( B @ C ) ))]]) ).
thf(63,plain,
! [A: a > $o] :
( ( A
@ ( sk4
@ ^ [B: a] :
~ ~ ( A @ B ) ) )
| ~ ( sk3
@ ^ [B: a] :
~ ~ ( A @ B ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(64,plain,
! [A: a > $o] :
( ( A @ ( sk4 @ A ) )
| ~ ( sk3 @ A ) ),
inference(simp,[status(thm)],[63]) ).
thf(3277,plain,
( ~ ( sk3
@ ^ [A: a] : $true )
| ( ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) )
!= ( sk3
@ ^ [A: a] : $true ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3039]) ).
thf(3289,plain,
( ~ ( sk3
@ ^ [A: a] : $true )
| ( ( ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) )
!= ( ^ [A: a] : $true ) ) ),
inference(simp,[status(thm)],[3277]) ).
thf(3482,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( ( ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) )
!= ( ^ [B: a] : $true ) )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[64,3289]) ).
thf(3513,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ( ( ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) )
!= ( ^ [A: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[3482:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : $true ) ))]]) ).
thf(4585,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( ( ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) )
!= ( ^ [B: a] : $true ) )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,3513]) ).
thf(4614,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : $true ) ) ) )
| ( ( ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) )
!= ( ^ [A: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[4585:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : $true ) ) ))]]) ).
thf(6,plain,
! [A: a > $o] :
( ( sk3 @ A )
| ~ ( A @ sk2 )
| ( ( sk6 @ A )
!= A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
! [A: a > $o] :
( ( ( sk6 @ A )
!= A )
| ( sk3 @ A )
| ~ ( A @ sk2 ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(14,plain,
! [A: a > $o] :
( ( ( sk6 @ A )
!= A )
| ( sk3 @ A )
| ~ ( A @ sk2 ) ),
inference(simp,[status(thm)],[13]) ).
thf(173,plain,
! [B: a > $o,A: a > $o] :
( ( sk3 @ A )
| ~ ( A @ sk2 )
| ( ( sk6 @ B )
!= B )
| ( sk3 @ B )
| ( ( sk6 @ A @ sk2 )
!= ( B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[12,14]) ).
thf(193,plain,
! [A: a > a > $o] :
( ( sk3 @ ( A @ sk2 ) )
| ~ ( A @ sk2 @ sk2 )
| ( ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ sk2 ) )
!= ( ^ [B: a] : ( sk6 @ ( A @ B ) @ sk2 ) ) )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ sk2 ) ) ),
inference(pre_uni,[status(thm)],[173:[bind(A,$thf( C @ sk2 )),bind(B,$thf( ^ [D: a] : ( sk6 @ ( C @ D ) @ sk2 ) ))]]) ).
thf(202,plain,
! [A: a > a > $o] :
( ( sk3 @ ( A @ sk2 ) )
| ~ ( A @ sk2 @ sk2 )
| ( ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ sk2 ) )
!= ( ^ [B: a] : ( sk6 @ ( A @ B ) @ sk2 ) ) )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ sk2 ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(91,plain,
! [A: a > $o] :
( ( sk3
@ ^ [B: a] :
~ ( A @ B ) )
| ~ ~ ( A @ sk2 )
| ( sk6
@ ^ [B: a] :
~ ( A @ B )
@ sk2 ) ),
inference(prim_subst,[status(thm)],[12:[bind(A,$thf( ^ [C: a] : ~ ( B @ C ) ))]]) ).
thf(113,plain,
! [A: a > $o] :
( ( sk6
@ ^ [B: a] :
~ ( A @ B )
@ sk2 )
| ( A @ sk2 )
| ( sk3
@ ^ [B: a] :
~ ( A @ B ) ) ),
inference(cnf,[status(esa)],[91]) ).
thf(114,plain,
! [A: a > $o] :
( ( sk6
@ ^ [B: a] :
~ ( A @ B )
@ sk2 )
| ( A @ sk2 )
| ( sk3
@ ^ [B: a] :
~ ( A @ B ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(4557,plain,
( ~ ~ ( sk3
@ ^ [A: a] : $true )
| ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) ) ),
inference(func_ext,[status(esa)],[3513]) ).
thf(4642,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(cnf,[status(esa)],[4557]) ).
thf(12543,plain,
! [A: a > $o] :
( ( sk6
@ ^ [B: a] :
~ ( A @ B )
@ sk2 )
| ( sk3
@ ^ [B: a] :
~ ( A @ B ) )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A @ sk2 )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[114,4642]) ).
thf(12602,plain,
( ( sk6
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) )
@ sk2 )
| ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[12543:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk3 @ ^ [D: a] : $true ) ) ))]]) ).
thf(78,plain,
! [B: a > $o,A: a > $o] :
( ( sk3 @ A )
| ~ ( A @ sk2 )
| ~ ( sk3
@ ^ [C: a] :
~ ( B @ C ) )
| ( ( sk6 @ A @ sk2 )
!= ( B
@ ( sk4
@ ^ [C: a] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,32]) ).
thf(92,plain,
! [A: a > a > $o] :
( ( sk3
@ ( A
@ ( sk4
@ ^ [B: a] :
~ ( sk6 @ ( A @ B ) @ sk2 ) ) ) )
| ~ ( A
@ ( sk4
@ ^ [B: a] :
~ ( sk6 @ ( A @ B ) @ sk2 ) )
@ sk2 )
| ~ ( sk3
@ ^ [B: a] :
~ ( sk6 @ ( A @ B ) @ sk2 ) ) ),
inference(pre_uni,[status(thm)],[78:[bind(A,$thf( C @ ( sk4 @ ^ [D: a] : ~ ( sk6 @ ( C @ D ) @ sk2 ) ) )),bind(B,$thf( ^ [D: a] : ( sk6 @ ( C @ D ) @ sk2 ) ))]]) ).
thf(115,plain,
! [A: a > a > $o] :
( ( sk3
@ ( A
@ ( sk4
@ ^ [B: a] :
~ ( sk6 @ ( A @ B ) @ sk2 ) ) ) )
| ~ ( A
@ ( sk4
@ ^ [B: a] :
~ ( sk6 @ ( A @ B ) @ sk2 ) )
@ sk2 )
| ~ ( sk3
@ ^ [B: a] :
~ ( sk6 @ ( A @ B ) @ sk2 ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(10,plain,
! [A: a] : ( sk1 @ A @ A ),
inference(cnf,[status(esa)],[3]) ).
thf(186,plain,
( ( ( sk6
@ ^ [A: a] : $true )
!= ( ^ [A: a] : $true ) )
| ( sk3
@ ^ [A: a] : $true )
| ~ $true ),
inference(prim_subst,[status(thm)],[14:[bind(A,$thf( ^ [B: a] : $true ))]]) ).
thf(216,plain,
( ( ( sk6
@ ^ [A: a] : $true )
!= ( ^ [A: a] : $true ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(simp,[status(thm)],[186]) ).
thf(223,plain,
( ~ ( sk6
@ ^ [A: a] : $true
@ sk8 )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(func_ext,[status(esa)],[216]) ).
thf(228,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( ( sk6
@ ^ [A: a] : $true
@ sk8 )
!= ( sk6
@ ^ [A: a] : $true
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[105,223]) ).
thf(234,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( ( ^ [A: a] : $true )
!= ( ^ [A: a] : $true ) )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[228]) ).
thf(240,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[234]) ).
thf(313,plain,
! [A: a > $o] :
( ( sk8 != sk2 )
| ~ ( sk3
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( A
@ ( sk4
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( sk3
@ ^ [B: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[240,32]) ).
thf(330,plain,
( ( sk8 != sk2 )
| ~ ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[313:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : $true ) ))]]) ).
thf(545,plain,
( ( sk8 != sk2 )
| ( ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[240,330]) ).
thf(550,plain,
( ( sk8 != sk2 )
| ( ( ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) )
!= ( ^ [A: a] : $true ) ) ),
inference(simp,[status(thm)],[545]) ).
thf(538,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk8 != sk2 )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,330]) ).
thf(546,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) )
| ( sk8 != sk2 ) ),
inference(pre_uni,[status(thm)],[538:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ~ ( sk3 @ ^ [D: a] : $true ) ) ))]]) ).
thf(583,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk8 != sk2 )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk3
@ ^ [D: a] : $true ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,546]) ).
thf(599,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk3
@ ^ [D: a] : $true ) ) ) )
| ( sk8 != sk2 ) ),
inference(pre_uni,[status(thm)],[583:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk3 @ ^ [D: a] : ~ ( sk3 @ ^ [E: a] : $true ) ) ) ))]]) ).
thf(862,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk8 != sk2 )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
~ ( sk3
@ ^ [E: a] : $true ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,599]) ).
thf(880,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
~ ( sk3
@ ^ [E: a] : $true ) ) ) ) )
| ( sk8 != sk2 ) ),
inference(pre_uni,[status(thm)],[862:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ~ ( sk3 @ ^ [F: a] : $true ) ) ) ) ))]]) ).
thf(2202,plain,
( ( sk8 != sk2 )
| ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : $false ) ) ) )
| ( ( sk3
@ ^ [A: a] : $true )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[240,880]) ).
thf(2203,plain,
( ( sk8 != sk2 )
| ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : $false ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2202:[]]) ).
thf(2257,plain,
( ( sk8 != sk2 )
| ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $false ) ) ) ),
inference(rewrite,[status(thm)],[2203,35]) ).
thf(2682,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( sk8 != sk2 )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : $false ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,2257]) ).
thf(2778,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : $false ) ) ) ) )
| ( sk8 != sk2 ) ),
inference(pre_uni,[status(thm)],[2682:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : $false ) ) ) ))]]) ).
thf(2723,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[39,35]) ).
thf(2759,plain,
~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $false ) ) ),
inference(pre_uni,[status(thm)],[2723:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : $false ) ))]]) ).
thf(2928,plain,
~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $false ) ),
inference(rewrite,[status(thm)],[2759,35]) ).
thf(5178,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $false ) ) )
| ( sk8 != sk2 ) ),
inference(rewrite,[status(thm)],[2778,2928]) ).
thf(651,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( sk3
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk2 ) )
| ( sk3
@ ^ [A: a] :
( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : $true
@ A )
@ A ) )
| ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : $true
@ A )
@ A )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[609:[bind(A,$thf( ^ [B: a] : ( sk6 @ ^ [C: a] : ( sk6 @ ^ [D: a] : $true @ B ) @ B ) ))]]) ).
thf(4672,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,4642]) ).
thf(4679,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[4672:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk3 @ ^ [D: a] : $true ) ) ))]]) ).
thf(9,plain,
! [C: a,B: a,A: a > $o] :
( ( sk3 @ A )
| ~ ( A @ sk2 )
| ~ ( sk6 @ A @ B )
| ( ( sk6 @ A @ C )
= ( sk1 @ B @ C ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
! [C: a,B: a,A: a > $o] :
( ( ( sk6 @ A @ C )
= ( sk1 @ B @ C ) )
| ( sk3 @ A )
| ~ ( A @ sk2 )
| ~ ( sk6 @ A @ B ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(16,plain,
! [C: a,B: a,A: a > $o] :
( ( ( sk6 @ A @ C )
= ( sk1 @ B @ C ) )
| ( sk3 @ A )
| ~ ( A @ sk2 )
| ~ ( sk6 @ A @ B ) ),
inference(simp,[status(thm)],[15]) ).
thf(399,plain,
! [C: a,B: a,A: a > $o] :
( ( sk3
@ ^ [D: a] : $true )
| ( ( sk6 @ A @ C )
= ( sk1 @ B @ C ) )
| ( sk3 @ A )
| ~ ( A @ sk2 )
| ( ( sk6
@ ^ [D: a] : $true
@ sk2 )
!= ( sk6 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[105,16]) ).
thf(400,plain,
! [A: a] :
( ( sk3
@ ^ [B: a] : $true )
| ( ( sk6
@ ^ [B: a] : $true
@ A )
= ( sk1 @ sk2 @ A ) )
| ( sk3
@ ^ [B: a] : $true )
| ~ $true ),
inference(pattern_uni,[status(thm)],[399:[bind(A,$thf( ^ [D: a] : $true )),bind(B,$thf( sk2 ))]]) ).
thf(478,plain,
! [A: a] :
( ( sk3
@ ^ [B: a] : $true )
| ( ( sk6
@ ^ [B: a] : $true
@ A )
= ( sk1 @ sk2 @ A ) ) ),
inference(simp,[status(thm)],[400]) ).
thf(672,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] :
~ ( sk6
@ ^ [C: a] : $true
@ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,120]) ).
thf(685,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk6
@ ^ [C: a] : $true
@ sk2 ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[672:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ~ ( sk6 @ ^ [D: a] : $true @ sk2 ) ) ))]]) ).
thf(1038,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk6
@ ^ [D: a] : $true
@ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[64,685]) ).
thf(1052,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk6
@ ^ [D: a] : $true
@ sk2 ) ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[1038:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk3 @ ^ [D: a] : ~ ( sk6 @ ^ [E: a] : $true @ sk2 ) ) ) ))]]) ).
thf(2535,plain,
! [A: a] :
( ( sk3
@ ^ [B: a] : $true )
| ~ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
~ ( sk1 @ sk2 @ A ) ) ) )
| ( ( sk6
@ ^ [B: a] : $true
@ A )
!= ( sk6
@ ^ [B: a] : $true
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[478,1052]) ).
thf(2536,plain,
( ( sk3
@ ^ [A: a] : $true )
| ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk1 @ sk2 @ sk2 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2535:[bind(A,$thf( sk2 ))]]) ).
thf(15921,plain,
( ( sk3
@ ^ [A: a] : $true )
| ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : ~ $true ) ) ) ),
inference(rewrite,[status(thm)],[2536,10]) ).
thf(15922,plain,
( ( sk3
@ ^ [A: a] : $true )
| ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $false ) ) ) ),
inference(simp,[status(thm)],[15921]) ).
thf(88,plain,
! [A: a > a > $o] :
( ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ~ ( sk3 @ ( A @ sk2 ) )
| ( sk6
@ ^ [B: a] : ( sk3 @ ( A @ B ) )
@ sk2 ) ),
inference(prim_subst,[status(thm)],[12:[bind(A,$thf( ^ [C: a] : ( sk3 @ ( B @ C ) ) ))]]) ).
thf(110,plain,
! [A: a > a > $o] :
( ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ~ ( sk3 @ ( A @ sk2 ) )
| ( sk6
@ ^ [B: a] : ( sk3 @ ( A @ B ) )
@ sk2 ) ),
inference(simp,[status(thm)],[88]) ).
thf(4,plain,
! [A: a > $o] :
( ( ( A @ ( sk5 @ A ) )
!= ( sk1 @ ( sk4 @ A ) @ ( sk5 @ A ) ) )
| ~ ( sk3 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(20,plain,
! [A: a > $o] :
( ( ( A @ ( sk5 @ A ) )
!= ( sk1 @ ( sk4 @ A ) @ ( sk5 @ A ) ) )
| ~ ( sk3 @ A ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(21,plain,
! [A: a > $o] :
( ( ( A @ ( sk5 @ A ) )
!= ( sk1 @ ( sk4 @ A ) @ ( sk5 @ A ) ) )
| ~ ( sk3 @ A ) ),
inference(simp,[status(thm)],[20]) ).
thf(952,plain,
! [A: a > $o] :
( ( sk8 != sk2 )
| ( ( A @ ( sk5 @ A ) )
!= ( sk1 @ ( sk4 @ A ) @ ( sk5 @ A ) ) )
| ( ( sk3
@ ^ [B: a] : $true )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[240,21]) ).
thf(953,plain,
( ( sk8 != sk2 )
| ~ ( sk1
@ ( sk4
@ ^ [A: a] : $true )
@ ( sk5
@ ^ [A: a] : $true ) ) ),
inference(pattern_uni,[status(thm)],[952:[bind(A,$thf( ^ [B: a] : $true ))]]) ).
thf(1000,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk8 != sk2 )
| ( ( A @ ( sk4 @ A ) )
!= ( sk1
@ ( sk4
@ ^ [B: a] : $true )
@ ( sk5
@ ^ [B: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,953]) ).
thf(1009,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk1
@ ( sk4
@ ^ [B: a] : $true )
@ ( sk5
@ ^ [B: a] : $true ) ) )
| ( sk8 != sk2 ) ),
inference(pre_uni,[status(thm)],[1000:[bind(A,$thf( ^ [B: a] : ( sk1 @ ( sk4 @ ^ [C: a] : $true ) @ ( sk5 @ ^ [C: a] : $true ) ) ))]]) ).
thf(1872,plain,
( ( sk8 != sk2 )
| ( ( sk3
@ ^ [A: a] :
( sk1
@ ( sk4
@ ^ [B: a] : $true )
@ ( sk5
@ ^ [B: a] : $true ) ) )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[240,1009]) ).
thf(1890,plain,
( ( sk8 != sk2 )
| ( ( ^ [A: a] :
( sk1
@ ( sk4
@ ^ [B: a] : $true )
@ ( sk5
@ ^ [B: a] : $true ) ) )
!= ( ^ [A: a] : $true ) ) ),
inference(simp,[status(thm)],[1872]) ).
thf(3260,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ~ ( sk3
@ ^ [B: a] : $true )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( ~ ( sk3
@ ^ [B: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,3039]) ).
thf(3284,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) )
| ~ ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[3260:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ~ ( sk3 @ ^ [D: a] : $true ) ))]]) ).
thf(4433,plain,
( ~ ( sk3
@ ^ [A: a] : $true )
| ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) )
!= ( sk3
@ ^ [A: a] : $true ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3284]) ).
thf(4442,plain,
( ~ ( sk3
@ ^ [A: a] : $true )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) )
!= ( ^ [A: a] : $true ) ) ),
inference(simp,[status(thm)],[4433]) ).
thf(4892,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( ( ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk3
@ ^ [D: a] : $true ) ) )
!= ( ^ [B: a] : $true ) )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[64,4442]) ).
thf(4952,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) )
!= ( ^ [A: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[4892:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : $true ) ))]]) ).
thf(4406,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ~ ( sk3
@ ^ [B: a] : $true )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk3
@ ^ [D: a] : $true ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,3284]) ).
thf(4460,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
~ ( sk3
@ ^ [E: a] : $true ) ) ) ) )
| ~ ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[4406:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ~ ( sk3 @ ^ [F: a] : $true ) ) ) ))]]) ).
thf(79,plain,
! [B: a > $o,A: a > $o] :
( ~ ( A @ sk2 )
| ( sk6 @ A @ sk2 )
| ( sk3 @ B )
| ( sk6 @ B @ sk2 )
| ( ( sk3 @ A )
!= ( B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[12,12]) ).
thf(100,plain,
! [A: a > a > $o] :
( ~ ( A @ sk2 @ sk2 )
| ( sk6 @ ( A @ sk2 ) @ sk2 )
| ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( sk6
@ ^ [B: a] : ( sk3 @ ( A @ B ) )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[79:[bind(A,$thf( C @ sk2 )),bind(B,$thf( ^ [D: a] : ( sk3 @ ( C @ D ) ) ))]]) ).
thf(104,plain,
! [A: a > a > $o] :
( ~ ( A @ sk2 @ sk2 )
| ( sk6 @ ( A @ sk2 ) @ sk2 )
| ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( sk6
@ ^ [B: a] : ( sk3 @ ( A @ B ) )
@ sk2 ) ),
inference(simp,[status(thm)],[100]) ).
thf(9529,plain,
! [A: a > a > $o] :
( ( sk3
@ ^ [B: a] : $true )
| ( sk6 @ ( A @ sk2 ) @ sk2 )
| ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( sk6
@ ^ [B: a] : ( sk3 @ ( A @ B ) )
@ sk2 )
| ( ( sk6
@ ^ [B: a] : $true
@ sk2 )
!= ( A @ sk2 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[105,104]) ).
thf(9768,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( sk6
@ ( sk6
@ ^ [A: a] : $true )
@ sk2 )
| ( sk3
@ ^ [A: a] :
( sk3
@ ( sk6
@ ^ [B: a] : $true ) ) )
| ( sk6
@ ^ [A: a] :
( sk3
@ ( sk6
@ ^ [B: a] : $true ) )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[9529:[bind(A,$thf( ^ [B: a] : ( sk6 @ ^ [C: a] : $true ) ))]]) ).
thf(230,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A @ ( sk4 @ A ) )
!= ( sk6
@ ^ [B: a] : $true
@ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[19,223]) ).
thf(237,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk8 ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[230:[bind(A,$thf( ^ [B: a] : ( sk6 @ ^ [C: a] : $true @ sk8 ) ))]]) ).
thf(344,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] :
( sk6
@ ^ [C: a] : $true
@ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[64,237]) ).
thf(345,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk6
@ ^ [C: a] : $true
@ sk8 ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[344:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk6 @ ^ [D: a] : $true @ sk8 ) ) ))]]) ).
thf(746,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk6
@ ^ [D: a] : $true
@ sk8 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[64,345]) ).
thf(752,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk6
@ ^ [D: a] : $true
@ sk8 ) ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[746:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk6 @ ^ [E: a] : $true @ sk8 ) ) ) ))]]) ).
thf(2539,plain,
! [A: a] :
( ( sk3
@ ^ [B: a] : $true )
| ~ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk1 @ sk2 @ A ) ) ) )
| ( ( sk6
@ ^ [B: a] : $true
@ A )
!= ( sk6
@ ^ [B: a] : $true
@ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[478,752]) ).
thf(2540,plain,
( ( sk3
@ ^ [A: a] : $true )
| ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : ( sk1 @ sk2 @ sk8 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2539:[bind(A,$thf( sk8 ))]]) ).
thf(3263,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ~ ( sk3
@ ^ [B: a] : $true )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,3039]) ).
thf(3293,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk3
@ ^ [D: a] : $true ) ) ) )
| ~ ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[3263:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ~ ( sk3 @ ^ [E: a] : $true ) ) ))]]) ).
thf(7626,plain,
( ~ ( sk3
@ ^ [A: a] : $true )
| ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk3
@ ^ [D: a] : $true ) ) ) )
!= ( sk3
@ ^ [A: a] : $true ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3293]) ).
thf(7677,plain,
( ~ ( sk3
@ ^ [A: a] : $true )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk3
@ ^ [D: a] : $true ) ) ) )
!= ( ^ [A: a] : $true ) ) ),
inference(simp,[status(thm)],[7626]) ).
thf(2529,plain,
! [A: a] :
( ( sk3
@ ^ [B: a] : $true )
| ~ ( sk1 @ sk2 @ A )
| ( ( sk6
@ ^ [B: a] : $true
@ A )
!= ( sk6
@ ^ [B: a] : $true
@ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[478,223]) ).
thf(2530,plain,
( ( sk3
@ ^ [A: a] : $true )
| ~ ( sk1 @ sk2 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[2529:[bind(A,$thf( sk8 ))]]) ).
thf(77,plain,
! [B: a > $o,A: a > $o] :
( ~ ( A @ sk2 )
| ( sk6 @ A @ sk2 )
| ~ ( sk3
@ ^ [C: a] :
~ ( B @ C ) )
| ( ( sk3 @ A )
!= ( B
@ ( sk4
@ ^ [C: a] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,32]) ).
thf(95,plain,
! [A: a > a > $o] :
( ~ ( A
@ ( sk4
@ ^ [B: a] :
~ ( sk3 @ ( A @ B ) ) )
@ sk2 )
| ( sk6
@ ( A
@ ( sk4
@ ^ [B: a] :
~ ( sk3 @ ( A @ B ) ) ) )
@ sk2 )
| ~ ( sk3
@ ^ [B: a] :
~ ( sk3 @ ( A @ B ) ) ) ),
inference(pre_uni,[status(thm)],[77:[bind(A,$thf( C @ ( sk4 @ ^ [D: a] : ~ ( sk3 @ ( C @ D ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk3 @ ( C @ D ) ) ))]]) ).
thf(116,plain,
! [A: a > a > $o] :
( ~ ( A
@ ( sk4
@ ^ [B: a] :
~ ( sk3 @ ( A @ B ) ) )
@ sk2 )
| ( sk6
@ ( A
@ ( sk4
@ ^ [B: a] :
~ ( sk3 @ ( A @ B ) ) ) )
@ sk2 )
| ~ ( sk3
@ ^ [B: a] :
~ ( sk3 @ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(48,plain,
! [B: a > $o,A: a] :
( ~ ( sk3
@ ^ [C: a] :
~ ( B @ C ) )
| ( ( sk1 @ A @ A )
!= ( B
@ ( sk4
@ ^ [C: a] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,32]) ).
thf(58,plain,
! [B: a > a,A: a > a] :
( ~ ( sk3
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( ( A
@ ( sk4
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
!= ( B
@ ( sk4
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[48:[bind(A,$thf( C @ ( sk4 @ ^ [E: a] : ~ ( sk1 @ ( C @ E ) @ ( D @ E ) ) ) )),bind(B,$thf( ^ [E: a] : ( sk1 @ ( C @ E ) @ ( D @ E ) ) ))]]) ).
thf(59,plain,
! [B: a > a,A: a > a] :
( ~ ( sk3
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( ( A
@ ( sk4
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
!= ( B
@ ( sk4
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[58:[]]) ).
thf(74,plain,
! [B: a > a,A: a > a] :
( ~ ( sk3
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( ( A
@ ( sk4
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
!= ( B
@ ( sk4
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(167,plain,
! [A: a > $o] :
( ( ( sk6 @ A @ ( sk7 @ A ) )
!= ( A @ ( sk7 @ A ) ) )
| ( sk3 @ A )
| ~ ( A @ sk2 ) ),
inference(func_ext,[status(esa)],[14]) ).
thf(19750,plain,
! [B: a > $o,A: a] :
( ( sk3
@ ^ [C: a] : $true )
| ( ( sk1 @ sk2 @ A )
!= ( B @ ( sk7 @ B ) ) )
| ( sk3 @ B )
| ~ ( B @ sk2 )
| ( ( sk6
@ ^ [C: a] : $true
@ A )
!= ( sk6 @ B @ ( sk7 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[478,167]) ).
thf(19751,plain,
( ( sk3
@ ^ [A: a] : $true )
| ~ ( sk1 @ sk2
@ ( sk7
@ ^ [A: a] : $true ) )
| ( sk3
@ ^ [A: a] : $true )
| ~ $true ),
inference(pattern_uni,[status(thm)],[19750:[bind(A,$thf( sk7 @ ^ [C: a] : $true )),bind(B,$thf( ^ [C: a] : $true ))]]) ).
thf(19977,plain,
( ( sk3
@ ^ [A: a] : $true )
| ~ ( sk1 @ sk2
@ ( sk7
@ ^ [A: a] : $true ) ) ),
inference(simp,[status(thm)],[19751]) ).
thf(20122,plain,
! [A: a] :
( ( sk3
@ ^ [B: a] : $true )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk2
@ ( sk7
@ ^ [B: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,19977]) ).
thf(20147,plain,
! [A: a] :
( ( sk3
@ ^ [B: a] : $true )
| ( A != sk2 )
| ( A
!= ( sk7
@ ^ [B: a] : $true ) ) ),
inference(simp,[status(thm)],[20122]) ).
thf(20157,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( ( sk7
@ ^ [A: a] : $true )
!= sk2 ) ),
inference(simp,[status(thm)],[20147]) ).
thf(9597,plain,
( ~ $true
| ( sk6
@ ^ [A: a] : $true
@ sk2 )
| ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ( sk6
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true )
@ sk2 ) ),
inference(prim_subst,[status(thm)],[104:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $true ))]]) ).
thf(10139,plain,
( ( sk6
@ ^ [A: a] : $true
@ sk2 )
| ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ( sk6
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true )
@ sk2 ) ),
inference(simp,[status(thm)],[9597]) ).
thf(4662,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,4642]) ).
thf(4678,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : $true ) ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[4662:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : $true ) ) ))]]) ).
thf(5013,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : $true ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,4678]) ).
thf(5049,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] :
( sk3
@ ^ [F: a] : $true ) ) ) ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[5013:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : ( sk3 @ ^ [G: a] : $true ) ) ) ) ))]]) ).
thf(19779,plain,
( ~ ( sk6
@ ^ [A: a] : $true
@ ( sk7
@ ^ [A: a] : $true ) )
| ( sk3
@ ^ [A: a] : $true )
| ~ $true ),
inference(prim_subst,[status(thm)],[167:[bind(A,$thf( ^ [B: a] : $true ))]]) ).
thf(19987,plain,
( ~ ( sk6
@ ^ [A: a] : $true
@ ( sk7
@ ^ [A: a] : $true ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(simp,[status(thm)],[19779]) ).
thf(29,plain,
! [B: a > a,A: a > a > $o] :
( ( sk6
@ ( A
@ ( sk4
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk4
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ~ ( sk3
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(prim_subst,[status(thm)],[19:[bind(A,$thf( ^ [D: a] : ( sk6 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(38,plain,
! [B: a > a,A: a > a > $o] :
( ( sk6
@ ( A
@ ( sk4
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk4
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ~ ( sk3
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(68,plain,
! [B: a > $o,A: a > $o] :
( ~ ( A
@ ( sk4
@ ^ [C: a] :
~ ( ( A @ C )
| ( B @ C ) ) ) )
| ~ ( sk3
@ ^ [C: a] :
~ ( ( A @ C )
| ( B @ C ) ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(70,plain,
! [B: a > $o,A: a > $o] :
( ~ ( A
@ ( sk4
@ ^ [C: a] :
~ ( ( A @ C )
| ( B @ C ) ) ) )
| ~ ( sk3
@ ^ [C: a] :
~ ( ( A @ C )
| ( B @ C ) ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(170,plain,
! [A: a > $o] :
( ( sk3
@ ^ [B: a] : $true )
| ( ( sk6 @ A )
!= A )
| ( sk3 @ A )
| ( ( sk6
@ ^ [B: a] : $true
@ sk2 )
!= ( A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[105,14]) ).
thf(192,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( ( sk6
@ ( sk6
@ ^ [A: a] : $true ) )
!= ( sk6
@ ^ [A: a] : $true ) )
| ( sk3
@ ( sk6
@ ^ [A: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[170:[bind(A,$thf( sk6 @ ^ [B: a] : $true ))]]) ).
thf(3288,plain,
( ~ ( sk3
@ ^ [A: a] : $true )
| ( ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(simp,[status(thm)],[3277]) ).
thf(6331,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( ( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) )
!= ( sk3
@ ^ [B: a] : $true ) )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[19,3288]) ).
thf(6349,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ( ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[6331:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : $true ) ))]]) ).
thf(82,plain,
! [B: a > $o,A: a > $o] :
( ~ ( A @ sk2 )
| ( sk6 @ A @ sk2 )
| ( B @ ( sk4 @ B ) )
| ( ( sk3 @ A )
!= ( sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,19]) ).
thf(83,plain,
! [A: a > $o] :
( ~ ( A @ sk2 )
| ( sk6 @ A @ sk2 )
| ( A @ ( sk4 @ A ) ) ),
inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(8068,plain,
! [B: a > $o,A: a > a > $o] :
( ~ ( A @ sk2 @ sk2 )
| ( sk3
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ C ) )
| ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ C )
@ sk2 )
| ( sk6 @ B @ sk2 )
| ( B @ ( sk4 @ B ) )
| ( ( sk3 @ ( A @ sk2 ) )
!= ( B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[102,83]) ).
thf(8143,plain,
! [A: a > $o] :
( ( sk2 != sk2 )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B ) )
| ( sk6
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B )
@ sk2 )
| ( sk6 @ A @ sk2 )
| ( A @ ( sk4 @ A ) )
| ( ( sk3 @ ( (=) @ a @ sk2 ) )
!= ( A @ sk2 ) ) ),
inference(replace_andrewseq,[status(thm)],[8068:[bind(A,$thf( (=) @ a ))]]) ).
thf(8355,plain,
! [A: a > $o] :
( ( sk2 != sk2 )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B ) )
| ( sk6
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B )
@ sk2 )
| ( sk6 @ A @ sk2 )
| ( A @ ( sk4 @ A ) )
| ( ( sk3 @ ( (=) @ a @ sk2 ) )
!= ( A @ sk2 ) ) ),
inference(lifteq,[status(thm)],[8143]) ).
thf(8599,plain,
( ( sk3 @ ( (=) @ a @ sk2 ) )
| ( sk6
@ ^ [A: a] : ( sk3 @ ( (=) @ a @ sk2 ) )
@ sk2 )
| ( sk6
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ A )
@ sk2 )
| ( sk3
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ A ) ) ),
inference(pre_uni,[status(thm)],[8355:[bind(A,$thf( ^ [B: a] : ( sk3 @ ( (=) @ a @ sk2 ) ) ))]]) ).
thf(23107,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ( ( ^ [A: a,B: a] :
~ ( sk3
@ ^ [C: a] : $true ) )
!= ( ^ [A: a,B: a] : $true ) ) ),
inference(simp,[status(thm)],[9106]) ).
thf(10181,plain,
! [A: a > a > $o] :
( ~ ( A @ sk2 @ sk2 )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ B ) )
| ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ B )
@ sk2 )
| ( sk6
@ ^ [B: a] : $true
@ sk2 )
| ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) )
| ( ( sk3 @ ( A @ sk2 ) )
!= ( sk3
@ ^ [B: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[102,10139]) ).
thf(10237,plain,
( ~ $true
| ( sk3
@ ( sk6
@ ^ [A: a] : $true ) )
| ( sk6
@ ( sk6
@ ^ [A: a] : $true )
@ sk2 )
| ( sk6
@ ^ [A: a] : $true
@ sk2 )
| ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[10181:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $true ))]]) ).
thf(10302,plain,
( ( sk3
@ ( sk6
@ ^ [A: a] : $true ) )
| ( sk6
@ ( sk6
@ ^ [A: a] : $true )
@ sk2 )
| ( sk6
@ ^ [A: a] : $true
@ sk2 )
| ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) ) ),
inference(simp,[status(thm)],[10237]) ).
thf(874,plain,
( ( sk8 != sk2 )
| ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk3
@ ^ [D: a] : $true ) ) ) )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[240,599]) ).
thf(890,plain,
( ( sk8 != sk2 )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk3
@ ^ [D: a] : $true ) ) ) )
!= ( ^ [A: a] : $true ) ) ),
inference(simp,[status(thm)],[874]) ).
thf(1679,plain,
( ( sk8 != sk2 )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $false ) ) )
!= ( ^ [A: a] : $true ) )
| ( ( sk3
@ ^ [A: a] : $true )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[240,890]) ).
thf(1680,plain,
( ( sk8 != sk2 )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $false ) ) )
!= ( ^ [A: a] : $true ) ) ),
inference(pattern_uni,[status(thm)],[1679:[]]) ).
thf(1715,plain,
( ( sk8 != sk2 )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] : $false ) )
!= ( ^ [A: a] : $true ) ) ),
inference(rewrite,[status(thm)],[1680,35]) ).
thf(46,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk3 @ A )
| ~ ( B
@ ( sk4
@ ^ [C: a] :
~ ( B @ C ) ) )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [C: a] :
~ ( B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,32]) ).
thf(57,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( A @ B @ C ) ) )
| ~ ( A
@ ( sk4
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( A @ B @ C ) ) )
@ ( sk4
@ ^ [B: a] :
~ ( A
@ ( sk4
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
~ ( A @ C @ D ) ) )
@ B ) ) ) ),
inference(pre_uni,[status(thm)],[46:[bind(A,$thf( ^ [D: a] : ( sk3 @ ^ [E: a] : ~ ( D @ D @ E ) ) )),bind(B,$thf( D @ ( sk4 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ~ ( D @ D @ E ) ) ) ))]]) ).
thf(73,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( A @ B @ C ) ) )
| ~ ( A
@ ( sk4
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( A @ B @ C ) ) )
@ ( sk4
@ ^ [B: a] :
~ ( A
@ ( sk4
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
~ ( A @ C @ D ) ) )
@ B ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(4913,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( ( ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk3
@ ^ [D: a] : $true ) ) )
!= ( ^ [B: a] : $true ) )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[39,4442]) ).
thf(4966,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) )
!= ( ^ [A: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[4913:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : $true ) ))]]) ).
thf(4410,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ~ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
~ ( sk3
@ ^ [D: a] : $true ) ) )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[39,3284]) ).
thf(4476,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) )
| ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[4410:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : $true ) ))]]) ).
thf(23565,plain,
( ( sk8 != sk2 )
| ~ ( sk3
@ ^ [A: a] : $true )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
!= ( ^ [A: a] : $false ) )
| ( ( sk3
@ ^ [A: a] : $true )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[240,23519]) ).
thf(23566,plain,
( ( sk8 != sk2 )
| ~ ( sk3
@ ^ [A: a] : $true )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
!= ( ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[23565:[]]) ).
thf(27712,plain,
( ( sk8 != sk2 )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
!= ( ^ [A: a] : $false ) )
| ( ( sk3
@ ^ [A: a] : $true )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[240,23566]) ).
thf(27713,plain,
( ( sk8 != sk2 )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
!= ( ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[27712:[]]) ).
thf(20124,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A @ ( sk4 @ A ) )
!= ( sk1 @ sk2
@ ( sk7
@ ^ [B: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[64,19977]) ).
thf(20140,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk1 @ sk2
@ ( sk7
@ ^ [B: a] : $true ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[20124:[bind(A,$thf( ^ [B: a] : ( sk1 @ sk2 @ ( sk7 @ ^ [C: a] : $true ) ) ))]]) ).
thf(7,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk1 @ B @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(17,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk1 @ B @ A ) ),
inference(simp,[status(thm)],[7]) ).
thf(12428,plain,
! [A: a > $o] :
( ( sk6
@ ^ [B: a] :
~ ( A @ B )
@ sk2 )
| ( sk3
@ ^ [B: a] :
~ ( A @ B ) )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A @ sk2 )
!= ( sk6
@ ^ [B: a] : $true
@ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[114,223]) ).
thf(12752,plain,
( ( sk6
@ ^ [A: a] :
~ ( sk6
@ ^ [B: a] : $true
@ sk8 )
@ sk2 )
| ( sk3
@ ^ [A: a] :
~ ( sk6
@ ^ [B: a] : $true
@ sk8 ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[12428:[bind(A,$thf( ^ [B: a] : ( sk6 @ ^ [C: a] : $true @ sk8 ) ))]]) ).
thf(16342,plain,
! [A: a] :
( ( sk3
@ ^ [B: a] : $true )
| ( sk6
@ ^ [B: a] :
~ ( sk1 @ sk2 @ A )
@ sk2 )
| ( sk3
@ ^ [B: a] :
~ ( sk6
@ ^ [C: a] : $true
@ sk8 ) )
| ( ( sk6
@ ^ [B: a] : $true
@ A )
!= ( sk6
@ ^ [B: a] : $true
@ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[478,12752]) ).
thf(16343,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( sk6
@ ^ [A: a] :
~ ( sk1 @ sk2 @ sk8 )
@ sk2 )
| ( sk3
@ ^ [A: a] :
~ ( sk6
@ ^ [B: a] : $true
@ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[16342:[bind(A,$thf( sk8 ))]]) ).
thf(24,plain,
! [B: a > $o,A: a > $o] :
( ( A
@ ( sk4
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk4
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ~ ( sk3
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ),
inference(prim_subst,[status(thm)],[19:[bind(A,$thf( ^ [D: a] : ( ( B @ D ) | ( C @ D ) ) ))]]) ).
thf(33,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk3
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ( A
@ ( sk4
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk4
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(34,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk3
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ( A
@ ( sk4
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk4
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(175,plain,
! [B: a > $o,A: a > $o] :
( ( ( sk6 @ A )
!= A )
| ~ ( A @ sk2 )
| ( B @ ( sk4 @ B ) )
| ( ( sk3 @ A )
!= ( sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,19]) ).
thf(176,plain,
! [A: a > $o] :
( ( ( sk6 @ A )
!= A )
| ~ ( A @ sk2 )
| ( A @ ( sk4 @ A ) ) ),
inference(pattern_uni,[status(thm)],[175:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(191,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk2 ) )
!= ( ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk2 ) ) )
| ( sk3
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk2 ) ) ),
inference(pre_uni,[status(thm)],[170:[bind(A,$thf( ^ [B: a] : ( sk6 @ ^ [C: a] : $true @ sk2 ) ))]]) ).
thf(5364,plain,
! [A: a > $o] :
( ( sk3
@ ^ [B: a] : $true )
| ( sk6 @ A @ sk2 )
| ( A @ ( sk4 @ A ) )
| ( ( sk6
@ ^ [B: a] : $true
@ sk2 )
!= ( A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[105,83]) ).
thf(5752,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( sk6
@ ( sk6
@ ^ [A: a] : $true )
@ sk2 )
| ( sk6
@ ^ [A: a] : $true
@ ( sk4
@ ( sk6
@ ^ [A: a] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[5364:[bind(A,$thf( sk6 @ ^ [B: a] : $true ))]]) ).
thf(55,plain,
! [B: a > a,A: a > a] :
( ~ ( sk3
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ~ ( sk1
@ ( A
@ ( sk4
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk4
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) ) ),
inference(prim_subst,[status(thm)],[32:[bind(A,$thf( ^ [D: a] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(71,plain,
! [B: a > a,A: a > a] :
( ~ ( sk3
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ~ ( sk1
@ ( A
@ ( sk4
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk4
@ ^ [C: a] :
~ ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(2525,plain,
! [A: a] :
( ( sk3
@ ^ [B: a] : $true )
| ~ ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : ( sk1 @ sk2 @ A ) ) )
| ( ( sk6
@ ^ [B: a] : $true
@ A )
!= ( sk6
@ ^ [B: a] : $true
@ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[478,345]) ).
thf(2526,plain,
( ( sk3
@ ^ [A: a] : $true )
| ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : ( sk1 @ sk2 @ sk8 ) ) ) ),
inference(pattern_uni,[status(thm)],[2525:[bind(A,$thf( sk8 ))]]) ).
thf(3568,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : ( sk1 @ sk2 @ sk8 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,2526]) ).
thf(3579,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : ( sk1 @ sk2 @ sk8 ) ) ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[3568:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk1 @ sk2 @ sk8 ) ) ) ))]]) ).
thf(2509,plain,
! [A: a] :
( ( sk3
@ ^ [B: a] : $true )
| ~ ( sk3
@ ^ [B: a] : ( sk1 @ sk2 @ A ) )
| ( ( sk6
@ ^ [B: a] : $true
@ A )
!= ( sk6
@ ^ [B: a] : $true
@ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[478,237]) ).
thf(2510,plain,
( ( sk3
@ ^ [A: a] : $true )
| ~ ( sk3
@ ^ [A: a] : ( sk1 @ sk2 @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[2509:[bind(A,$thf( sk8 ))]]) ).
thf(3264,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ~ ( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[39,3039]) ).
thf(3287,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) )
| ~ ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[3264:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : $true ) ))]]) ).
thf(6320,plain,
( ( sk8 != sk2 )
| ( ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) )
!= ( sk3
@ ^ [A: a] : $true ) )
| ( ( sk3
@ ^ [A: a] : $true )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[240,3288]) ).
thf(6321,plain,
( ( sk8 != sk2 )
| ( ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(pattern_uni,[status(thm)],[6320:[]]) ).
thf(649,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( sk3
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk2 ) )
| ( sk3
@ ^ [A: a] :
( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : $true
@ A )
@ sk2 ) )
| ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] :
( sk6
@ ^ [C: a] : $true
@ A )
@ sk2 )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[609:[bind(A,$thf( ^ [B: a] : ( sk6 @ ^ [C: a] : ( sk6 @ ^ [D: a] : $true @ B ) @ sk2 ) ))]]) ).
thf(12323,plain,
! [A: a > $o] :
( ( sk6
@ ^ [B: a] :
~ ( A @ B )
@ sk2 )
| ( sk3
@ ^ [B: a] :
~ ( A @ B ) )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A @ sk2 )
!= ( sk1 @ sk2 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[114,2530]) ).
thf(12850,plain,
( ( sk6
@ ^ [A: a] :
~ ( sk1 @ sk2 @ sk8 )
@ sk2 )
| ( sk3
@ ^ [A: a] :
~ ( sk1 @ sk2 @ sk8 ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[12323:[bind(A,$thf( ^ [B: a] : ( sk1 @ sk2 @ sk8 ) ))]]) ).
thf(75,plain,
! [B: a > $o,A: a] :
( ( sk3 @ B )
| ( sk6 @ B @ sk2 )
| ( ( sk1 @ A @ A )
!= ( B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[10,12]) ).
thf(98,plain,
! [B: a > a,A: a > a] :
( ( sk3
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk6
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) )
@ sk2 )
| ( ( A @ sk2 )
!= ( B @ sk2 ) ) ),
inference(pre_uni,[status(thm)],[75:[bind(A,$thf( C @ sk2 )),bind(B,$thf( ^ [E: a] : ( sk1 @ ( C @ E ) @ ( D @ E ) ) ))]]) ).
thf(99,plain,
! [B: a > a,A: a > a] :
( ( sk6
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) )
@ sk2 )
| ( sk3
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( ( A @ sk2 )
!= ( B @ sk2 ) ) ),
inference(pre_uni,[status(thm)],[98:[]]) ).
thf(103,plain,
! [B: a > a,A: a > a] :
( ( sk6
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) )
@ sk2 )
| ( sk3
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ( ( A @ sk2 )
!= ( B @ sk2 ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(1617,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk6
@ ^ [E: a] : $true
@ sk8 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,752]) ).
thf(1630,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk6
@ ^ [E: a] : $true
@ sk8 ) ) ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[1617:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk6 @ ^ [F: a] : $true @ sk8 ) ) ) ) ))]]) ).
thf(177,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk3 @ A )
| ( ( sk6 @ B )
!= B )
| ( sk3 @ B )
| ( ( A @ ( sk4 @ A ) )
!= ( B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[19,14]) ).
thf(198,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk3 @ A )
| ( ( sk6 @ B )
!= B )
| ( sk3 @ B )
| ( ( A @ ( sk4 @ A ) )
!= ( B @ sk2 ) ) ),
inference(pre_uni,[status(thm)],[177:[]]) ).
thf(106,plain,
! [B: a > $o,A: a > $o] :
( ( sk6
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) )
@ sk2 )
| ~ ( B @ sk2 )
| ( sk3
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(108,plain,
! [B: a > $o,A: a > $o] :
( ( sk6
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) )
@ sk2 )
| ~ ( B @ sk2 )
| ( sk3
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(122,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( sk3
@ ( sk6
@ ^ [A: a] : $true ) )
| ( sk6
@ ( sk6
@ ^ [A: a] : $true )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[118:[bind(A,$thf( sk6 @ ^ [B: a] : $true ))]]) ).
thf(293,plain,
! [A: a > $o] :
( ( sk3
@ ^ [B: a] : $true )
| ( sk3
@ ( sk6
@ ^ [B: a] : $true ) )
| ( sk3 @ A )
| ( sk6 @ A @ sk2 )
| ( ( sk6
@ ( sk6
@ ^ [B: a] : $true )
@ sk2 )
!= ( A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[122,12]) ).
thf(299,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( sk3
@ ( sk6
@ ^ [A: a] : $true ) )
| ( sk3
@ ^ [A: a] :
( sk6
@ ( sk6
@ ^ [B: a] : $true )
@ sk2 ) )
| ( sk6
@ ^ [A: a] :
( sk6
@ ( sk6
@ ^ [B: a] : $true )
@ sk2 )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[293:[bind(A,$thf( ^ [B: a] : ( sk6 @ ( sk6 @ ^ [C: a] : $true ) @ sk2 ) ))]]) ).
thf(2201,plain,
( ( sk8 != sk2 )
| ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
~ ( sk3
@ ^ [E: a] : $true ) ) ) ) )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[240,880]) ).
thf(2244,plain,
( ( sk8 != sk2 )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
~ ( sk3
@ ^ [E: a] : $true ) ) ) ) )
!= ( ^ [A: a] : $true ) ) ),
inference(simp,[status(thm)],[2201]) ).
thf(4441,plain,
( ~ ( sk3
@ ^ [A: a] : $true )
| ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(simp,[status(thm)],[4433]) ).
thf(3875,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ~ ( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,3283]) ).
thf(3936,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : $true ) ) ) )
| ~ ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[3875:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : $true ) ) ))]]) ).
thf(14498,plain,
( ~ $true
| ( sk6
@ ^ [A: a] : $true
@ sk2 )
| ~ ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) ) ),
inference(prim_subst,[status(thm)],[116:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $true ))]]) ).
thf(14827,plain,
( ( sk6
@ ^ [A: a] : $true
@ sk2 )
| ~ ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) ) ),
inference(simp,[status(thm)],[14498]) ).
thf(20134,plain,
! [A: a > $o] :
( ( sk6
@ ^ [B: a] :
~ ( A @ B )
@ sk2 )
| ( sk3
@ ^ [B: a] :
~ ( A @ B ) )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A @ sk2 )
!= ( sk1 @ sk2
@ ( sk7
@ ^ [B: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[114,19977]) ).
thf(20144,plain,
( ( sk6
@ ^ [A: a] :
~ ( sk1 @ A
@ ( sk7
@ ^ [B: a] : $true ) )
@ sk2 )
| ( sk3
@ ^ [A: a] :
~ ( sk1 @ A
@ ( sk7
@ ^ [B: a] : $true ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[20134:[bind(A,$thf( ^ [B: a] : ( sk1 @ B @ ( sk7 @ ^ [C: a] : $true ) ) ))]]) ).
thf(90,plain,
! [B: a > a,A: a > a > $o] :
( ( sk3
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ ( B @ C ) ) )
| ~ ( sk6 @ ( A @ sk2 ) @ ( B @ sk2 ) )
| ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ ( B @ C ) )
@ sk2 ) ),
inference(prim_subst,[status(thm)],[12:[bind(A,$thf( ^ [D: a] : ( sk6 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(112,plain,
! [B: a > a,A: a > a > $o] :
( ( sk3
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ ( B @ C ) ) )
| ~ ( sk6 @ ( A @ sk2 ) @ ( B @ sk2 ) )
| ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ ( B @ C ) )
@ sk2 ) ),
inference(simp,[status(thm)],[90]) ).
thf(23536,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( ( ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) )
!= ( ^ [B: a] : $false ) )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[64,23519]) ).
thf(23630,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
!= ( ^ [A: a] : $false ) ) ),
inference(pre_uni,[status(thm)],[23536:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk3 @ ^ [D: a] : $true ) ) ))]]) ).
thf(11,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ B @ C )
| ( sk1 @ A @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(18,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ B @ C )
| ( sk1 @ A @ C ) ),
inference(simp,[status(thm)],[11]) ).
thf(7964,plain,
! [B: a > $o,A: a > a > $o] :
( ~ ( A @ sk2 @ sk2 )
| ( sk3
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ C ) )
| ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ C )
@ sk2 )
| ( sk3 @ B )
| ( sk6 @ B @ sk2 )
| ( ( sk3 @ ( A @ sk2 ) )
!= ( B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[102,12]) ).
thf(8218,plain,
! [A: a > $o] :
( ( sk2 != sk2 )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B ) )
| ( sk6
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B )
@ sk2 )
| ( sk3 @ A )
| ( sk6 @ A @ sk2 )
| ( ( sk3 @ ( (=) @ a @ sk2 ) )
!= ( A @ sk2 ) ) ),
inference(replace_andrewseq,[status(thm)],[7964:[bind(A,$thf( (=) @ a ))]]) ).
thf(8356,plain,
! [A: a > $o] :
( ( sk2 != sk2 )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B ) )
| ( sk6
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B )
@ sk2 )
| ( sk3 @ A )
| ( sk6 @ A @ sk2 )
| ( ( sk3 @ ( (=) @ a @ sk2 ) )
!= ( A @ sk2 ) ) ),
inference(lifteq,[status(thm)],[8218]) ).
thf(8669,plain,
( ( sk6
@ ^ [A: a] : ( sk3 @ ( (=) @ a @ A ) )
@ sk2 )
| ( sk3
@ ^ [A: a] : ( sk3 @ ( (=) @ a @ A ) ) )
| ( sk6
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ A )
@ sk2 )
| ( sk3
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ A ) ) ),
inference(pre_uni,[status(thm)],[8356:[bind(A,$thf( ^ [B: a] : ( sk3 @ ( (=) @ a @ B ) ) ))]]) ).
thf(3622,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( sk3
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk2 ) )
| ( sk3
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk2 ) ) )
| ( sk6
@ ( sk6
@ ^ [A: a] : $true )
@ sk2 )
| ( ( sk6
@ ^ [A: a] : $true
@ sk2 )
!= ( sk6
@ ^ [A: a] : $true
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[105,650]) ).
thf(3623,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( sk3
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk2 ) )
| ( sk3
@ ( sk6
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ sk2 ) ) )
| ( sk6
@ ( sk6
@ ^ [A: a] : $true )
@ sk2 ) ),
inference(pattern_uni,[status(thm)],[3622:[]]) ).
thf(20207,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk6
@ ^ [B: a] : $true
@ ( sk7
@ ^ [B: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,19987]) ).
thf(20287,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk6
@ ^ [C: a] : $true
@ ( sk7
@ ^ [C: a] : $true ) ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[20207:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk6 @ ^ [D: a] : $true @ ( sk7 @ ^ [D: a] : $true ) ) ))]]) ).
thf(8053,plain,
! [B: a > $o,A: a > a > $o] :
( ~ ( A @ sk2 @ sk2 )
| ( sk3
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ C ) )
| ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ C )
@ sk2 )
| ( B @ ( sk4 @ B ) )
| ( ( sk3 @ ( A @ sk2 ) )
!= ( sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[102,19]) ).
thf(8152,plain,
! [A: a > $o] :
( ( sk2 != sk2 )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B ) )
| ( sk6
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B )
@ sk2 )
| ( A @ ( sk4 @ A ) )
| ( ( sk3 @ ( (=) @ a @ sk2 ) )
!= ( sk3 @ A ) ) ),
inference(replace_andrewseq,[status(thm)],[8053:[bind(A,$thf( (=) @ a ))]]) ).
thf(8333,plain,
! [A: a > $o] :
( ( sk2 != sk2 )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B ) )
| ( sk6
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ B )
@ sk2 )
| ( A @ ( sk4 @ A ) )
| ( ( sk3 @ ( (=) @ a @ sk2 ) )
!= ( sk3 @ A ) ) ),
inference(lifteq,[status(thm)],[8152]) ).
thf(8561,plain,
( ( sk2
= ( sk4 @ ( (=) @ a @ sk2 ) ) )
| ( sk6
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ A )
@ sk2 )
| ( sk3
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[8333:[bind(A,$thf( (=) @ a @ sk2 ))]]) ).
thf(8893,plain,
( ( ( sk4 @ ( (=) @ a @ sk2 ) )
= sk2 )
| ( sk6
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ A )
@ sk2 )
| ( sk3
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ A ) ) ),
inference(lifteq,[status(thm)],[8561]) ).
thf(12377,plain,
! [A: a > $o] :
( ( sk6
@ ^ [B: a] :
~ ( A @ B )
@ sk2 )
| ( sk3
@ ^ [B: a] :
~ ( A @ B ) )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A @ sk2 )
!= ( sk3
@ ^ [B: a] : ( sk1 @ sk2 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[114,2510]) ).
thf(12790,plain,
( ( sk6
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : ( sk1 @ A @ sk8 ) )
@ sk2 )
| ( sk3
@ ^ [A: a] :
~ ( sk3
@ ^ [B: a] : ( sk1 @ A @ sk8 ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[12377:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk1 @ B @ sk8 ) ) ))]]) ).
thf(135,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( ( A @ ( sk4 @ A ) )
!= ( ~ ( sk3 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[64]) ).
thf(154,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( ( A @ ( sk4 @ A ) )
!= ( ~ ( sk3 @ A ) ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(56,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] :
~ ( sk3 @ ( A @ B ) ) )
| ~ ( sk3
@ ( A
@ ( sk4
@ ^ [B: a] :
~ ( sk3 @ ( A @ B ) ) ) ) ) ),
inference(prim_subst,[status(thm)],[32:[bind(A,$thf( ^ [C: a] : ( sk3 @ ( B @ C ) ) ))]]) ).
thf(72,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] :
~ ( sk3 @ ( A @ B ) ) )
| ~ ( sk3
@ ( A
@ ( sk4
@ ^ [B: a] :
~ ( sk3 @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(14900,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk6
@ ^ [B: a] : $true
@ sk2 )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[64,14827]) ).
thf(14992,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) )
| ( sk6
@ ^ [A: a] : $true
@ sk2 ) ),
inference(pre_uni,[status(thm)],[14900:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ~ ( sk3 @ ^ [D: a] : $true ) ) ))]]) ).
thf(3497,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( ( ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) )
!= ( ^ [B: a] : $true ) )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[39,3289]) ).
thf(3520,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) )
| ( ( ^ [A: a] :
~ ( sk3
@ ^ [B: a] : $true ) )
!= ( ^ [A: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[3497:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : $true ) ))]]) ).
thf(194,plain,
! [A: a > a > $o] :
( ( sk3 @ ( A @ sk2 ) )
| ~ ( A @ sk2 @ sk2 )
| ( ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ B ) )
!= ( ^ [B: a] : ( sk6 @ ( A @ B ) @ B ) ) )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ B ) ) ),
inference(pre_uni,[status(thm)],[173:[bind(A,$thf( C @ sk2 )),bind(B,$thf( ^ [D: a] : ( sk6 @ ( C @ D ) @ D ) ))]]) ).
thf(203,plain,
! [A: a > a > $o] :
( ( sk3 @ ( A @ sk2 ) )
| ~ ( A @ sk2 @ sk2 )
| ( ( sk6
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ B ) )
!= ( ^ [B: a] : ( sk6 @ ( A @ B ) @ B ) ) )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( A @ B ) @ B ) ) ),
inference(simp,[status(thm)],[194]) ).
thf(10198,plain,
( ( sk8 != sk2 )
| ( sk6
@ ^ [A: a] : $true
@ sk2 )
| ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) )
| ( ( sk3
@ ^ [A: a] : $true )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[240,10139]) ).
thf(10199,plain,
( ( sk8 != sk2 )
| ( sk6
@ ^ [A: a] : $true
@ sk2 )
| ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] : $true ) ) ),
inference(pattern_uni,[status(thm)],[10198:[]]) ).
thf(12851,plain,
( ( sk6
@ ^ [A: a] :
~ ( sk1 @ A @ sk8 )
@ sk2 )
| ( sk3
@ ^ [A: a] :
~ ( sk1 @ A @ sk8 ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[12323:[bind(A,$thf( ^ [B: a] : ( sk1 @ B @ sk8 ) ))]]) ).
thf(300,plain,
( ( sk3
@ ^ [A: a] : $true )
| ( sk3
@ ( sk6
@ ^ [A: a] : $true ) )
| ( sk3
@ ( sk6
@ ( sk6
@ ^ [A: a] : $true ) ) )
| ( sk6
@ ( sk6
@ ( sk6
@ ^ [A: a] : $true ) )
@ sk2 ) ),
inference(pre_uni,[status(thm)],[293:[bind(A,$thf( sk6 @ ( sk6 @ ^ [B: a] : $true ) ))]]) ).
thf(26,plain,
! [B: a > a,A: a > a] :
( ( sk1
@ ( A
@ ( sk4
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk4
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ~ ( sk3
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(prim_subst,[status(thm)],[19:[bind(A,$thf( ^ [D: a] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(36,plain,
! [B: a > a,A: a > a] :
( ( sk1
@ ( A
@ ( sk4
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk4
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ) )
| ~ ( sk3
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(20236,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A @ ( sk4 @ A ) )
!= ( sk6
@ ^ [B: a] : $true
@ ( sk7
@ ^ [B: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,19987]) ).
thf(20286,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk6
@ ^ [B: a] : $true
@ ( sk7
@ ^ [B: a] : $true ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[20236:[bind(A,$thf( ^ [B: a] : ( sk6 @ ^ [C: a] : $true @ ( sk7 @ ^ [C: a] : $true ) ) ))]]) ).
thf(84,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk3 @ A )
| ( sk3 @ B )
| ( sk6 @ B @ sk2 )
| ( ( A @ ( sk4 @ A ) )
!= ( B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[19,12]) ).
thf(93,plain,
! [B: a > $o,A: a > $o] :
( ~ ( sk3 @ A )
| ( sk3 @ B )
| ( sk6 @ B @ sk2 )
| ( ( A @ ( sk4 @ A ) )
!= ( B @ sk2 ) ) ),
inference(pre_uni,[status(thm)],[84:[]]) ).
thf(94,plain,
! [B: a > $o,A: a > $o] :
( ( sk6 @ B @ sk2 )
| ( sk3 @ B )
| ~ ( sk3 @ A )
| ( ( A @ ( sk4 @ A ) )
!= ( B @ sk2 ) ) ),
inference(pre_uni,[status(thm)],[93:[]]) ).
thf(23355,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( ( ^ [B: a,C: a] :
~ ( sk3
@ ^ [D: a] : $true ) )
!= ( ^ [B: a,C: a] : $true ) )
| ( ( sk3
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,23107]) ).
thf(23446,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] : $true ) ) )
| ( ( ^ [A: a,B: a] :
~ ( sk3
@ ^ [C: a] : $true ) )
!= ( ^ [A: a,B: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[23355:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : $true ) ))]]) ).
thf(592,plain,
( ( sk8 != sk2 )
| ( ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) )
!= ( sk3
@ ^ [A: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[240,546]) ).
thf(607,plain,
( ( sk8 != sk2 )
| ( ( ^ [A: a] :
( sk3
@ ^ [B: a] :
~ ( sk3
@ ^ [C: a] : $true ) ) )
!= ( ^ [A: a] : $true ) ) ),
inference(simp,[status(thm)],[592]) ).
thf(49,plain,
! [A: a > $o] :
( ~ ( sk3
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( A
@ ( sk4
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( sk3
@ ^ [B: a] :
~ ( A @ B ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[32]) ).
thf(62,plain,
! [A: a > $o] :
( ~ ( sk3
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( A
@ ( sk4
@ ^ [B: a] :
~ ( A @ B ) ) )
!= ( sk3
@ ^ [B: a] :
~ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(1874,plain,
! [A: a > $o] :
( ~ ( sk3 @ A )
| ( sk8 != sk2 )
| ( ( A @ ( sk4 @ A ) )
!= ( sk3
@ ^ [B: a] :
( sk1
@ ( sk4
@ ^ [C: a] : $true )
@ ( sk5
@ ^ [C: a] : $true ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,1009]) ).
thf(1880,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk1
@ ( sk4
@ ^ [C: a] : $true )
@ ( sk5
@ ^ [C: a] : $true ) ) ) )
| ( sk8 != sk2 ) ),
inference(pre_uni,[status(thm)],[1874:[bind(A,$thf( ^ [B: a] : ( sk3 @ ^ [C: a] : ( sk1 @ ( sk4 @ ^ [D: a] : $true ) @ ( sk5 @ ^ [D: a] : $true ) ) ) ))]]) ).
thf(89,plain,
! [B: a > a,A: a > a] :
( ( sk3
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ~ ( sk1 @ ( A @ sk2 ) @ ( B @ sk2 ) )
| ( sk6
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) )
@ sk2 ) ),
inference(prim_subst,[status(thm)],[12:[bind(A,$thf( ^ [D: a] : ( sk1 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(111,plain,
! [B: a > a,A: a > a] :
( ( sk3
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) ) )
| ~ ( sk1 @ ( A @ sk2 ) @ ( B @ sk2 ) )
| ( sk6
@ ^ [C: a] : ( sk1 @ ( A @ C ) @ ( B @ C ) )
@ sk2 ) ),
inference(simp,[status(thm)],[89]) ).
thf(20131,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk1 @ sk2
@ ( sk7
@ ^ [B: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,19977]) ).
thf(20155,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk1 @ sk2
@ ( sk7
@ ^ [C: a] : $true ) ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[20131:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk1 @ sk2 @ ( sk7 @ ^ [D: a] : $true ) ) ))]]) ).
thf(6656,plain,
! [B: a > $o,A: a > a > $o] :
( ~ ( A @ sk2 @ sk2 )
| ( sk3
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ sk2 ) )
| ( sk6
@ ^ [C: a] : ( sk6 @ ( A @ C ) @ sk2 )
@ sk2 )
| ( B @ ( sk4 @ B ) )
| ( ( sk3 @ ( A @ sk2 ) )
!= ( sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[101,19]) ).
thf(6744,plain,
! [A: a > $o] :
( ( sk2 != sk2 )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ sk2 ) )
| ( sk6
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ sk2 )
@ sk2 )
| ( A @ ( sk4 @ A ) )
| ( ( sk3 @ ( (=) @ a @ sk2 ) )
!= ( sk3 @ A ) ) ),
inference(replace_andrewseq,[status(thm)],[6656:[bind(A,$thf( (=) @ a ))]]) ).
thf(6838,plain,
! [A: a > $o] :
( ( sk2 != sk2 )
| ( sk3
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ sk2 ) )
| ( sk6
@ ^ [B: a] : ( sk6 @ ( (=) @ a @ B ) @ sk2 )
@ sk2 )
| ( A @ ( sk4 @ A ) )
| ( ( sk3 @ ( (=) @ a @ sk2 ) )
!= ( sk3 @ A ) ) ),
inference(lifteq,[status(thm)],[6744]) ).
thf(7183,plain,
( ( sk2
= ( sk4 @ ( (=) @ a @ sk2 ) ) )
| ( sk6
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ sk2 )
@ sk2 )
| ( sk3
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[6838:[bind(A,$thf( (=) @ a @ sk2 ))]]) ).
thf(7284,plain,
( ( ( sk4 @ ( (=) @ a @ sk2 ) )
= sk2 )
| ( sk6
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ sk2 )
@ sk2 )
| ( sk3
@ ^ [A: a] : ( sk6 @ ( (=) @ a @ A ) @ sk2 ) ) ),
inference(lifteq,[status(thm)],[7183]) ).
thf(4713,plain,
! [A: a > a > $o] :
( ~ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( sk3
@ ^ [B: a] : $true )
| ( ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
@ ( sk4
@ ( A
@ ( sk4
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) )
!= ( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] : $true ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,4679]) ).
thf(4742,plain,
( ~ ( sk3
@ ^ [A: a] :
( sk3
@ ^ [B: a] :
( sk3
@ ^ [C: a] :
( sk3
@ ^ [D: a] :
( sk3
@ ^ [E: a] : $true ) ) ) ) )
| ( sk3
@ ^ [A: a] : $true ) ),
inference(pre_uni,[status(thm)],[4713:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( sk3 @ ^ [D: a] : ( sk3 @ ^ [E: a] : ( sk3 @ ^ [F: a] : $true ) ) ) ))]]) ).
thf(1001,plain,
! [A: a] :
( ( sk8 != sk2 )
| ( ( sk1 @ A @ A )
!= ( sk1
@ ( sk4
@ ^ [B: a] : $true )
@ ( sk5
@ ^ [B: a] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,953]) ).
thf(1006,plain,
! [A: a] :
( ( sk8 != sk2 )
| ( A
!= ( sk4
@ ^ [B: a] : $true ) )
| ( A
!= ( sk5
@ ^ [B: a] : $true ) ) ),
inference(simp,[status(thm)],[1001]) ).
thf(1014,plain,
( ( sk8 != sk2 )
| ( ( sk5
@ ^ [A: a] : $true )
!= ( sk4
@ ^ [A: a] : $true ) ) ),
inference(simp,[status(thm)],[1006]) ).
thf(33743,plain,
$false,
inference(e,[status(thm)],[65,650,109,69,23519,101,3905,8447,120,4614,202,12602,115,10,550,5178,37,651,3513,4679,14,15922,110,1890,4952,4460,9768,216,2540,7677,121,61,2530,116,74,20157,546,10139,102,5049,19987,38,70,192,21,6349,8599,23107,10302,1715,73,237,105,4966,953,19977,4476,27713,20140,3289,64,17,16343,32,34,176,191,3283,5752,71,12,3579,2510,3287,6321,599,880,39,649,890,12850,345,103,1630,240,2928,198,108,330,685,223,299,3,167,35,9106,2244,4441,3936,3293,14827,20144,112,23630,18,8669,12752,3623,20287,16,8893,12790,154,1052,72,14992,3520,3288,3284,203,10199,104,4678,3039,114,2526,478,12851,300,752,3907,36,19,20286,4442,94,23446,607,62,1880,111,20155,122,4642,83,1009,7284,4742,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : SEV011^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 19:11:24 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.99/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.37/1.13 % [INFO] Parsing done (168ms).
% 1.37/1.14 % [INFO] Running in sequential loop mode.
% 1.82/1.52 % [INFO] eprover registered as external prover.
% 1.82/1.52 % [INFO] cvc4 registered as external prover.
% 1.82/1.53 % [INFO] Scanning for conjecture ...
% 2.06/1.62 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.66 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.66 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.67 % [INFO] Type checking passed.
% 2.21/1.67 % [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 ...
% 231.50/47.76 % External prover 'e' found a proof!
% 231.50/47.76 % [INFO] Killing All external provers ...
% 231.50/47.76 % Time passed: 47300ms (effective reasoning time: 46615ms)
% 231.50/47.76 % 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)>
% 231.50/47.77 % Axioms used in derivation (0):
% 231.50/47.77 % No. of inferences in proof: 340
% 231.50/47.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 47300 ms resp. 46615 ms w/o parsing
% 232.30/47.96 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 232.30/47.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------