%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV190^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 08:36:58 AM UTC 2026
% Result : Theorem 265.31s 93.26s
% Output : Refutation 253.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 7
% Syntax : Number of formulae : 342 ( 83 unt; 0 typ; 6 def)
% Number of atoms : 1553 ( 621 equ; 119 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 6402 ( 655 ~; 558 |; 47 &;5121 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 160 ( 160 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 1066 ( 579 ^; 478 !; 4 ?;1066 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(iS_type,type,
iS: $tType ).
thf(c0_decl,type,
c0: iS ).
thf(cJOIN_decl,type,
cJOIN: iS > iS > iS > $o ).
thf(cP_decl,type,
cP: iS > iS > iS ).
thf(cS_JOIN_CLOS_decl,type,
cS_JOIN_CLOS: iS > ( iS > iS > iS ) > ( iS > iS > iS > $o ) > $o ).
thf(sk1_decl,type,
sk1: ( iS > $o ) > iS ).
thf(sk2_decl,type,
sk2: ( iS > $o ) > iS ).
thf(sk3_decl,type,
sk3: iS ).
thf(sk4_decl,type,
sk4: iS > iS > iS ).
thf(sk5_decl,type,
sk5: iS > iS > iS ).
thf(sk7_decl,type,
sk7: iS ).
thf(cS_JOIN_CLOS_def,definition,
( cS_JOIN_CLOS
= ( ^ [A: iS,B: iS > iS > iS,C: iS > iS > iS > $o] :
( ! [D: iS] : ( C @ D @ A @ D )
& ! [D: iS] : ( C @ A @ D @ D )
& ! [D: iS,E: iS,F: iS,G: iS,H: iS,I: iS] :
( ( ( C @ D @ E @ F )
& ( C @ G @ H @ I ) )
=> ( C @ ( B @ D @ G ) @ ( B @ E @ H ) @ ( B @ F @ I ) ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: iS > $o] :
@+[B: iS] :
~ ! [C: iS] :
( ( ( A @ B )
& ( A @ C ) )
=> ( A @ ( cP @ B @ C ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: iS > $o] :
@+[B: iS] :
~ ( ( ( A @ ( sk1 @ A ) )
& ( A @ B ) )
=> ( A @ ( cP @ ( sk1 @ A ) @ B ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: iS] :
~ ( cJOIN @ A @ A @ A ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: iS > iS > iS] :
! [B: iS,C: iS] :
( ( A @ B @ ( cP @ B @ C ) )
= C ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: iS > iS > iS] :
! [B: iS,C: iS] :
( ( A @ C @ ( cP @ B @ C ) )
= B ) ) ) ).
thf(1,conjecture,
( ( ! [A: iS,B: iS] :
( ( cP @ A @ B )
!= c0 )
& ! [A: iS,B: iS,C: iS,D: iS] :
( ( ( cP @ A @ C )
= ( cP @ B @ D ) )
=> ( ( A = B )
& ( C = D ) ) )
& ! [A: iS > $o] :
( ( ( A @ c0 )
& ! [B: iS,C: iS] :
( ( ( A @ B )
& ( A @ C ) )
=> ( A @ ( cP @ B @ C ) ) ) )
=> ! [B: iS] : ( A @ B ) )
& ( cS_JOIN_CLOS @ c0 @ cP @ cJOIN ) )
=> ! [A: iS] : ( cJOIN @ A @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM580_pme) ).
thf(2,negated_conjecture,
~ ( ( ! [A: iS,B: iS] :
( ( cP @ A @ B )
!= c0 )
& ! [A: iS,B: iS,C: iS,D: iS] :
( ( ( cP @ A @ C )
= ( cP @ B @ D ) )
=> ( ( A = B )
& ( C = D ) ) )
& ! [A: iS > $o] :
( ( ( A @ c0 )
& ! [B: iS,C: iS] :
( ( ( A @ B )
& ( A @ C ) )
=> ( A @ ( cP @ B @ C ) ) ) )
=> ! [B: iS] : ( A @ B ) )
& ( cS_JOIN_CLOS @ c0 @ cP @ cJOIN ) )
=> ! [A: iS] : ( cJOIN @ A @ A @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: iS,B: iS] :
( ( cP @ A @ B )
!= c0 )
& ! [A: iS,B: iS,C: iS,D: iS] :
( ( ( cP @ A @ C )
= ( cP @ B @ D ) )
=> ( ( A = B )
& ( C = D ) ) )
& ! [A: iS > $o] :
( ( ( A @ c0 )
& ! [B: iS,C: iS] :
( ( ( A @ B )
& ( A @ C ) )
=> ( A @ ( cP @ B @ C ) ) ) )
=> ! [B: iS] : ( A @ B ) )
& ! [A: iS] : ( cJOIN @ A @ c0 @ A )
& ! [A: iS] : ( cJOIN @ c0 @ A @ A )
& ! [A: iS,B: iS,C: iS,D: iS,E: iS,F: iS] :
( ( ( cJOIN @ A @ B @ C )
& ( cJOIN @ D @ E @ F ) )
=> ( cJOIN @ ( cP @ A @ D ) @ ( cP @ B @ E ) @ ( cP @ C @ F ) ) ) )
=> ! [A: iS] : ( cJOIN @ A @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ~ ? [A: iS,B: iS] :
( ( cP @ A @ B )
= c0 )
& ! [A: iS,B: iS,C: iS,D: iS] :
( ( ( cP @ A @ C )
= ( cP @ B @ D ) )
=> ( ( A = B )
& ( C = D ) ) )
& ! [A: iS > $o] :
( ( ( A @ c0 )
& ! [B: iS,C: iS] :
( ( ( A @ B )
& ( A @ C ) )
=> ( A @ ( cP @ B @ C ) ) ) )
=> ! [B: iS] : ( A @ B ) )
& ! [A: iS] : ( cJOIN @ A @ c0 @ A )
& ! [A: iS] : ( cJOIN @ c0 @ A @ A )
& ! [A: iS,B: iS,C: iS,D: iS,E: iS,F: iS] :
( ( ( cJOIN @ A @ B @ C )
& ( cJOIN @ D @ E @ F ) )
=> ( cJOIN @ ( cP @ A @ D ) @ ( cP @ B @ E ) @ ( cP @ C @ F ) ) ) )
=> ! [A: iS] : ( cJOIN @ A @ A @ A ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [P: iS,O: iS,N: iS,M: iS,L: iS,K: iS,J: iS,I: iS,H: iS,G: iS > $o,F: iS,E: iS,D: iS,C: iS,B: iS,A: iS] :
( ( ( cP @ A @ B )
!= c0 )
& ( ( ( cP @ C @ E )
!= ( cP @ D @ F ) )
| ( C = D ) )
& ( ( ( cP @ C @ E )
!= ( cP @ D @ F ) )
| ( E = F ) )
& ( ~ ( G @ c0 )
| ( G @ ( sk1 @ G ) )
| ( G @ H ) )
& ( ~ ( G @ c0 )
| ( G @ ( sk2 @ G ) )
| ( G @ H ) )
& ( ~ ( G @ c0 )
| ~ ( G @ ( cP @ ( sk1 @ G ) @ ( sk2 @ G ) ) )
| ( G @ H ) )
& ( cJOIN @ I @ c0 @ I )
& ( cJOIN @ c0 @ J @ J )
& ( ~ ( cJOIN @ K @ L @ M )
| ~ ( cJOIN @ N @ O @ P )
| ( cJOIN @ ( cP @ K @ N ) @ ( cP @ L @ O ) @ ( cP @ M @ P ) ) )
& ~ ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(10,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ A ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(19,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ A ) )
| ( A @ B ) ),
inference(simp,[status(thm)],[10]) ).
thf(222,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ A ) )
| ( ( A @ B )
!= ( A @ ( sk2 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(240,plain,
! [A: iS] :
( ( c0 != c0 )
| ( c0
= ( sk2 @ ( (=) @ iS @ c0 ) ) )
| ( ( c0 = A )
!= ( c0
= ( sk2 @ ( (=) @ iS @ c0 ) ) ) )
| ~ $true ),
inference(replace_leibeq,[status(thm)],[222:[bind(A,$thf( (=) @ iS @ c0 ))]]) ).
thf(249,plain,
! [A: iS] :
( ( c0 != c0 )
| ( ( sk2 @ ( (=) @ iS @ c0 ) )
= c0 )
| ( ( c0 = A )
!= ( c0
= ( sk2 @ ( (=) @ iS @ c0 ) ) ) )
| ~ $true ),
inference(lifteq,[status(thm)],[240]) ).
thf(253,plain,
( ~ $true
| ( ( sk2 @ ( (=) @ iS @ c0 ) )
= c0 ) ),
inference(pattern_uni,[status(thm)],[249:[bind(A,$thf( sk2 @ ( (=) @ iS @ c0 ) ))]]) ).
thf(324,plain,
( ( sk2 @ ( (=) @ iS @ c0 ) )
= c0 ),
inference(simp,[status(thm)],[253]) ).
thf(9,plain,
! [A: iS] : ( cJOIN @ c0 @ A @ A ),
inference(cnfConj,[status(thm)],[5]) ).
thf(22,plain,
! [A: iS] : ( cJOIN @ c0 @ A @ A ),
inference(simp,[status(thm)],[9]) ).
thf(6,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(21,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( A @ B ) ),
inference(simp,[status(thm)],[6]) ).
thf(52,plain,
! [C: iS,B: iS > $o,A: iS] :
( ~ $true
| ~ ( B @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) )
| ( B @ C )
| ( ( cJOIN @ c0 @ A @ A )
!= ( B @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[22,21]) ).
thf(53,plain,
! [C: iS,B: iS > $o,A: iS] :
( ~ ( B @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) )
| ( B @ C )
| ( ( cJOIN @ c0 @ A @ A )
!= ( B @ c0 ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(95,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ~ ( cJOIN
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) ) )
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) ) ) )
| ( cJOIN @ A @ ( B @ A ) @ ( C @ A ) )
| ( ( B @ c0 )
!= ( C @ c0 ) ) ),
inference(pre_uni,[status(thm)],[53:[bind(A,$thf( E @ c0 )),bind(B,$thf( ^ [F: iS] : ( cJOIN @ F @ ( E @ F ) @ ( F @ F ) ) )),bind(C,$thf( C ))]]) ).
thf(97,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ( cJOIN @ A @ ( B @ A ) @ ( C @ A ) )
| ~ ( cJOIN
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) ) )
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) ) ) )
| ( ( B @ c0 )
!= ( C @ c0 ) ) ),
inference(pre_uni,[status(thm)],[95:[]]) ).
thf(132,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ( cJOIN @ A @ ( B @ A ) @ ( C @ A ) )
| ~ ( cJOIN
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) ) )
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) ) ) )
| ( ( B @ c0 )
!= ( C @ c0 ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(12,plain,
~ ( cJOIN @ sk3 @ sk3 @ sk3 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(19246,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ~ ( cJOIN
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) ) )
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) ) ) )
| ( ( B @ c0 )
!= ( C @ c0 ) )
| ~ $true
| ( ( cJOIN @ A @ ( B @ A ) @ ( C @ A ) )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[132,12]) ).
thf(19247,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ~ ( cJOIN
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) ) )
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ D @ ( B @ D ) @ ( C @ D ) ) ) ) ) )
| ( ( B @ c0 )
!= ( C @ c0 ) )
| ( ( cJOIN @ A @ ( B @ A ) @ ( C @ A ) )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(simp,[status(thm)],[19246]) ).
thf(19971,plain,
( ~ ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) )
| ( c0 != c0 ) ),
inference(pre_uni,[status(thm)],[19247:[bind(A,$thf( sk3 )),bind(B,$thf( ^ [D: iS] : D )),bind(C,$thf( ^ [D: iS] : D ))]]) ).
thf(19973,plain,
~ ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[19971:[]]) ).
thf(20380,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ A ) )
| ~ $true
| ( ( A @ B )
!= ( cJOIN
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,19973]) ).
thf(20381,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ A ) )
| ( ( A @ B )
!= ( cJOIN
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[20380]) ).
thf(20409,plain,
( ~ ( cJOIN @ c0 @ c0 @ c0 )
| ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
inference(pre_uni,[status(thm)],[20381:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ C @ C ) )),bind(B,$thf( cP @ ( sk1 @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) @ ( sk2 @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) ))]]) ).
thf(13,plain,
! [A: iS] : ( cJOIN @ A @ c0 @ A ),
inference(cnfConj,[status(thm)],[5]) ).
thf(23,plain,
! [A: iS] : ( cJOIN @ A @ c0 @ A ),
inference(simp,[status(thm)],[13]) ).
thf(60,plain,
! [C: iS,B: iS > $o,A: iS] :
( ~ ( B @ c0 )
| ~ $true
| ( B @ C )
| ( ( cJOIN @ A @ c0 @ A )
!= ( B @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,21]) ).
thf(61,plain,
! [C: iS,B: iS > $o,A: iS] :
( ~ ( B @ c0 )
| ( B @ C )
| ( ( cJOIN @ A @ c0 @ A )
!= ( B @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(91,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ~ ( cJOIN @ ( B @ c0 ) @ c0 @ ( C @ c0 ) )
| ( cJOIN @ ( B @ A ) @ c0 @ ( C @ A ) )
| ( ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
!= ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[61:[bind(A,$thf( D @ ( cP @ ( sk1 @ ^ [F: iS] : ( cJOIN @ ( D @ F ) @ c0 @ ( F @ F ) ) ) @ ( sk2 @ ^ [F: iS] : ( cJOIN @ ( D @ F ) @ c0 @ ( F @ F ) ) ) ) )),bind(B,$thf( ^ [F: iS] : ( cJOIN @ ( D @ F ) @ c0 @ ( F @ F ) ) )),bind(C,$thf( C ))]]) ).
thf(92,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ( cJOIN @ ( B @ A ) @ c0 @ ( C @ A ) )
| ~ ( cJOIN @ ( B @ c0 ) @ c0 @ ( C @ c0 ) )
| ( ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
!= ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[91:[]]) ).
thf(130,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ( cJOIN @ ( B @ A ) @ c0 @ ( C @ A ) )
| ~ ( cJOIN @ ( B @ c0 ) @ c0 @ ( C @ c0 ) )
| ( ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
!= ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(17016,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ( cJOIN @ ( B @ A ) @ c0 @ c0 )
| ~ ( cJOIN @ ( B @ c0 ) @ c0 @ ( C @ c0 ) )
| ( ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
!= ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) )
| ( ( sk2 @ ( (=) @ iS @ c0 ) )
!= ( C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[324,130]) ).
thf(17413,plain,
! [A: iS > iS] :
( ( cJOIN @ ( A @ ( sk2 @ ( (=) @ iS @ c0 ) ) ) @ c0 @ c0 )
| ~ ( cJOIN @ ( A @ c0 ) @ c0 @ c0 )
| ( ( A
@ ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ ( A @ B ) @ c0 @ B ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ ( A @ B ) @ c0 @ B ) ) ) )
!= ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ ( A @ B ) @ c0 @ B ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ ( A @ B ) @ c0 @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[17016:[bind(A,$thf( sk2 @ ( (=) @ iS @ c0 ) )),bind(B,$thf( B )),bind(C,$thf( ^ [D: iS] : D ))]]) ).
thf(17416,plain,
( ~ ( cJOIN @ c0 @ c0 @ c0 )
| ( cJOIN @ ( sk2 @ ( (=) @ iS @ c0 ) ) @ c0 @ c0 ) ),
inference(pre_uni,[status(thm)],[17413:[bind(A,$thf( ^ [B: iS] : B ))]]) ).
thf(18776,plain,
( ~ $true
| ( cJOIN @ c0 @ c0 @ c0 ) ),
inference(rewrite,[status(thm)],[17416,324,22]) ).
thf(18777,plain,
cJOIN @ c0 @ c0 @ c0,
inference(simp,[status(thm)],[18776]) ).
thf(23621,plain,
( ~ $true
| ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
inference(rewrite,[status(thm)],[20409,18777]) ).
thf(23622,plain,
( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ),
inference(simp,[status(thm)],[23621]) ).
thf(23710,plain,
( ~ $true
| ( ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) )
!= ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[23622,19973]) ).
thf(23711,plain,
( ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) )
!= ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
inference(simp,[status(thm)],[23710]) ).
thf(23828,plain,
( ( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
inference(simp,[status(thm)],[23711]) ).
thf(23859,plain,
( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ),
inference(simp,[status(thm)],[23828]) ).
thf(23897,plain,
( ( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( sk2 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[324,23859]) ).
thf(23929,plain,
( ( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[23897]) ).
thf(68,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ~ ( ( B @ c0 )
| ( C @ c0 ) )
| ~ ( ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(prim_subst,[status(thm)],[21:[bind(A,$thf( ^ [E: iS] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(114,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ( ~ ( B @ c0 )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) )
& ( ~ ( B @ c0 )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) )
& ( ~ ( C @ c0 )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) )
& ( ~ ( C @ c0 )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ) ),
inference(cnf,[status(esa)],[68]) ).
thf(117,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ~ ( C @ c0 )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(121,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ~ ( C @ c0 )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(simp,[status(thm)],[117]) ).
thf(11,plain,
! [D: iS,C: iS,B: iS,A: iS] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( C = D ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(31,plain,
! [D: iS,C: iS,B: iS,A: iS] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( C = D ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(32,plain,
! [D: iS,C: iS,B: iS,A: iS] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( C = D ) ),
inference(simp,[status(thm)],[31]) ).
thf(212,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ A ) )
| ~ $true
| ( ( A @ B )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[19,12]) ).
thf(213,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ A ) )
| ( ( A @ B )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(simp,[status(thm)],[212]) ).
thf(275,plain,
( ~ ( cJOIN @ sk3 @ c0 @ sk3 )
| ( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[213:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(466,plain,
( ~ $true
| ( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ) ),
inference(rewrite,[status(thm)],[275,23]) ).
thf(467,plain,
( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ),
inference(simp,[status(thm)],[466]) ).
thf(56,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ $true
| ( ( A @ B )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[21,12]) ).
thf(57,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(88,plain,
( ~ ( cJOIN @ sk3 @ c0 @ sk3 )
| ~ ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[57:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(336,plain,
( ~ $true
| ~ ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
@ sk3 ) ),
inference(rewrite,[status(thm)],[88,23]) ).
thf(337,plain,
~ ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
@ sk3 ),
inference(simp,[status(thm)],[336]) ).
thf(480,plain,
( ~ $true
| ( ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
@ sk3 )
!= ( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[467,337]) ).
thf(481,plain,
( ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
@ sk3 )
!= ( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ) ),
inference(simp,[status(thm)],[480]) ).
thf(491,plain,
( ( sk3 != sk3 )
| ( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[481]) ).
thf(495,plain,
( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[491]) ).
thf(8,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(18,plain,
! [A: iS] :
( ( c0 != c0 )
| ( c0
= ( sk1 @ ( (=) @ iS @ c0 ) ) )
| ( c0 = A ) ),
inference(replace_leibeq,[status(thm)],[8:[bind(A,$thf( (=) @ iS @ c0 ))]]) ).
thf(27,plain,
! [A: iS] :
( ( c0 != c0 )
| ( ( sk1 @ ( (=) @ iS @ c0 ) )
= c0 )
| ( c0 = A ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(28,plain,
! [A: iS] :
( ( ( sk1 @ ( (=) @ iS @ c0 ) )
= c0 )
| ( c0 = A ) ),
inference(simp,[status(thm)],[27]) ).
thf(7,plain,
! [B: iS,A: iS] :
( ( cP @ A @ B )
!= c0 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(26,plain,
! [B: iS,A: iS] :
( ( cP @ A @ B )
!= c0 ),
inference(lifteq,[status(thm)],[7]) ).
thf(166,plain,
! [C: iS,B: iS,A: iS] :
( ( ( sk1 @ ( (=) @ iS @ c0 ) )
= c0 )
| ( c0 != c0 )
| ( A
!= ( cP @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,26]) ).
thf(167,plain,
! [C: iS,B: iS,A: iS] :
( ( ( sk1 @ ( (=) @ iS @ c0 ) )
= c0 )
| ( A
!= ( cP @ B @ C ) ) ),
inference(simp,[status(thm)],[166]) ).
thf(168,plain,
( ( sk1 @ ( (=) @ iS @ c0 ) )
= c0 ),
inference(pattern_uni,[status(thm)],[167:[bind(A,$thf( cP @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(340,plain,
( ~ ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ c0 )
@ sk3 )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( sk2 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[324,337]) ).
thf(354,plain,
( ~ ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ c0 )
@ sk3 )
| ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[340]) ).
thf(806,plain,
( ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
| ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( sk1 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,354]) ).
thf(823,plain,
( ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
| ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) )
| ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[806]) ).
thf(839,plain,
( ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
| ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[823]) ).
thf(892,plain,
( ( ( cJOIN @ sk3 @ sk7 @ sk3 )
!= ( c0 = sk7 ) )
| ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ),
inference(func_ext,[status(esa)],[839]) ).
thf(15,plain,
! [D: iS,C: iS,B: iS,A: iS] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(36,plain,
! [D: iS,C: iS,B: iS,A: iS] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(37,plain,
! [D: iS,C: iS,B: iS,A: iS] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( A = B ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
? [A: iS > iS > iS] :
! [B: iS,C: iS] :
( ( A @ C @ ( cP @ B @ C ) )
= B ),
inference(detectInverse,[status(thm)],[37]) ).
thf(39,plain,
! [B: iS,A: iS] :
( ( sk5 @ B @ ( cP @ A @ B ) )
= A ),
inference(cnf,[status(esa)],[38]) ).
thf(333,plain,
! [B: iS,A: iS] :
( ( sk5 @ B @ ( cP @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[39]) ).
thf(8188,plain,
( ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
| ~ ( cJOIN @ sk3 @ sk7 @ sk3 )
| ( c0 != sk7 ) ),
inference(bool_ext,[status(thm)],[892]) ).
thf(8296,plain,
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
| ~ ( cJOIN @ sk3 @ sk7 @ sk3 ) ),
inference(lifteq,[status(thm)],[8188]) ).
thf(9438,plain,
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ sk7 @ sk3 )
| ( ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
!= ( cJOIN @ sk3 @ sk7 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8296]) ).
thf(9531,plain,
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ sk7 @ sk3 )
| ( sk3 != sk3 )
| ( ( cP @ c0 @ c0 )
!= sk7 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[9438]) ).
thf(9556,plain,
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ sk7 @ sk3 )
| ( ( cP @ c0 @ c0 )
!= sk7 ) ),
inference(simp,[status(thm)],[9531]) ).
thf(10558,plain,
! [A: iS] :
( ( sk7 != c0 )
| ~ $true
| ( ( cP @ c0 @ c0 )
!= sk7 )
| ( ( cJOIN @ A @ c0 @ A )
!= ( cJOIN @ sk3 @ sk7 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[23,9556]) ).
thf(10559,plain,
! [A: iS] :
( ( sk7 != c0 )
| ( ( cP @ c0 @ c0 )
!= sk7 )
| ( ( cJOIN @ A @ c0 @ A )
!= ( cJOIN @ sk3 @ sk7 @ sk3 ) ) ),
inference(simp,[status(thm)],[10558]) ).
thf(10621,plain,
! [A: iS] :
( ( sk7 != c0 )
| ( ( cP @ c0 @ c0 )
!= sk7 )
| ( A != sk3 )
| ( sk7 != c0 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[10559]) ).
thf(10658,plain,
( ( sk7 != c0 )
| ( ( cP @ c0 @ c0 )
!= sk7 ) ),
inference(simp,[status(thm)],[10621]) ).
thf(23685,plain,
( ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( sk2 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[324,23622]) ).
thf(23825,plain,
( ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[23685]) ).
thf(116,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ~ ( B @ c0 )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(120,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ~ ( B @ c0 )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(simp,[status(thm)],[116]) ).
thf(18903,plain,
! [B: iS,A: iS > $o] :
( ~ $true
| ( A @ ( sk2 @ A ) )
| ( A @ B )
| ( ( cJOIN @ c0 @ c0 @ c0 )
!= ( A @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[18777,19]) ).
thf(18904,plain,
! [B: iS,A: iS > $o] :
( ( A @ ( sk2 @ A ) )
| ( A @ B )
| ( ( cJOIN @ c0 @ c0 @ c0 )
!= ( A @ c0 ) ) ),
inference(simp,[status(thm)],[18903]) ).
thf(18974,plain,
! [A: iS] :
( ( cJOIN @ c0
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
@ c0 )
| ( cJOIN @ c0 @ A @ c0 ) ),
inference(pre_uni,[status(thm)],[18904:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ c0 @ C @ c0 ) )),bind(B,$thf( B ))]]) ).
thf(19123,plain,
! [A: iS] :
( ( cJOIN @ c0
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
@ c0 )
| ( cJOIN @ c0 @ A @ c0 ) ),
inference(simp,[status(thm)],[18974]) ).
thf(28344,plain,
! [A: iS] :
( ( cJOIN @ c0
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
@ c0 )
| ( ( cJOIN @ c0 @ A @ c0 )
!= ( cJOIN @ c0
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
@ c0 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[19123]) ).
thf(28550,plain,
( cJOIN @ c0
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ c0 @ A @ c0 ) )
@ c0 ),
inference(pattern_uni,[status(thm)],[28344:[bind(A,$thf( sk2 @ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) ))]]) ).
thf(35,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( A @ B ) ),
inference(simp,[status(thm)],[8]) ).
thf(568,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ~ $true
| ( ( A @ B )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[35,12]) ).
thf(569,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( ( A @ B )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(simp,[status(thm)],[568]) ).
thf(689,plain,
( ~ ( cJOIN @ sk3 @ c0 @ sk3 )
| ( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[569:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(850,plain,
( ~ $true
| ( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ) ),
inference(rewrite,[status(thm)],[689,23]) ).
thf(851,plain,
( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ),
inference(simp,[status(thm)],[850]) ).
thf(862,plain,
( ~ $true
| ( ( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[851,12]) ).
thf(863,plain,
( ( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
inference(simp,[status(thm)],[862]) ).
thf(879,plain,
( ( sk3 != sk3 )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= sk3 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[863]) ).
thf(885,plain,
( ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= sk3 ),
inference(simp,[status(thm)],[879]) ).
thf(9420,plain,
! [A: iS] :
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
| ~ $true
| ( ( cJOIN @ A @ c0 @ A )
!= ( cJOIN @ sk3 @ sk7 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[23,8296]) ).
thf(9421,plain,
! [A: iS] :
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
| ( ( cJOIN @ A @ c0 @ A )
!= ( cJOIN @ sk3 @ sk7 @ sk3 ) ) ),
inference(simp,[status(thm)],[9420]) ).
thf(9537,plain,
! [A: iS] :
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
| ( A != sk3 )
| ( sk7 != c0 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[9421]) ).
thf(9559,plain,
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ),
inference(simp,[status(thm)],[9537]) ).
thf(9602,plain,
( ( sk7 != c0 )
| ~ $true
| ( ( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[851,9559]) ).
thf(9603,plain,
( ( sk7 != c0 )
| ( ( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ) ),
inference(simp,[status(thm)],[9602]) ).
thf(9645,plain,
( ( sk7 != c0 )
| ( sk3 != sk3 )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( cP @ c0 @ c0 ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[9603]) ).
thf(9693,plain,
( ( sk7 != c0 )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( cP @ c0 @ c0 ) ) ),
inference(simp,[status(thm)],[9645]) ).
thf(48,plain,
! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ $true
| ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[21,21]) ).
thf(49,plain,
! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ c0 ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(109,plain,
! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ c0 ) ) ),
inference(pre_uni,[status(thm)],[49:[]]) ).
thf(110,plain,
! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
( ( C @ D )
| ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( A @ c0 )
| ( ( A @ B )
!= ( C @ c0 ) ) ),
inference(pre_uni,[status(thm)],[109:[]]) ).
thf(20350,plain,
! [A: iS] :
( ~ $true
| ( ( cJOIN @ A @ c0 @ A )
!= ( cJOIN
@ ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) )
@ ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) )
@ ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,19973]) ).
thf(20351,plain,
! [A: iS] :
( ( cJOIN @ A @ c0 @ A )
!= ( cJOIN
@ ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) )
@ ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) )
@ ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) ) ) ),
inference(simp,[status(thm)],[20350]) ).
thf(20437,plain,
! [A: iS] :
( ( A
!= ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) ) )
| ( ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) )
!= c0 )
| ( A
!= ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) ) ) ),
inference(simp,[status(thm)],[20351]) ).
thf(20472,plain,
( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= c0 ),
inference(simp,[status(thm)],[20437]) ).
thf(903,plain,
( ~ $true
| ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) )
| ( ( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[851,839]) ).
thf(904,plain,
( ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) )
| ( ( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ) ),
inference(simp,[status(thm)],[903]) ).
thf(926,plain,
( ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) )
| ( sk3 != sk3 )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( cP @ c0 @ c0 ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[904]) ).
thf(949,plain,
( ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( cP @ c0 @ c0 ) ) ),
inference(simp,[status(thm)],[926]) ).
thf(14,plain,
! [F: iS,E: iS,D: iS,C: iS,B: iS,A: iS] :
( ~ ( cJOIN @ A @ B @ C )
| ~ ( cJOIN @ D @ E @ F )
| ( cJOIN @ ( cP @ A @ D ) @ ( cP @ B @ E ) @ ( cP @ C @ F ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(20,plain,
! [F: iS,E: iS,D: iS,C: iS,B: iS,A: iS] :
( ~ ( cJOIN @ A @ B @ C )
| ~ ( cJOIN @ D @ E @ F )
| ( cJOIN @ ( cP @ A @ D ) @ ( cP @ B @ E ) @ ( cP @ C @ F ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(65,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21]) ).
thf(93,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(20348,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ~ $true
| ( ( A @ B )
!= ( cJOIN
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,19973]) ).
thf(20349,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( ( A @ B )
!= ( cJOIN
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[20348]) ).
thf(20416,plain,
( ~ ( cJOIN @ c0 @ c0 @ c0 )
| ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
inference(pre_uni,[status(thm)],[20349:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ C @ C ) )),bind(B,$thf( cP @ ( sk1 @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) @ ( sk2 @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) ))]]) ).
thf(26815,plain,
( ~ $true
| ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
inference(rewrite,[status(thm)],[20416,18777]) ).
thf(26816,plain,
( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ),
inference(simp,[status(thm)],[26815]) ).
thf(26892,plain,
( ~ $true
| ( ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) )
!= ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[26816,19973]) ).
thf(26893,plain,
( ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) )
!= ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
inference(simp,[status(thm)],[26892]) ).
thf(27038,plain,
( ( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
inference(simp,[status(thm)],[26893]) ).
thf(27054,plain,
( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ),
inference(simp,[status(thm)],[27038]) ).
thf(27116,plain,
( ( ( cP @ c0
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( sk1 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,27054]) ).
thf(27119,plain,
( ( ( cP @ c0
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[27116]) ).
thf(23927,plain,
( ( ( cP @ c0
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( sk1 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,23859]) ).
thf(23928,plain,
( ( ( cP @ c0
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[23927]) ).
thf(58,plain,
! [C: iS,B: iS > $o,A: iS] :
( ~ $true
| ~ ( B @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) )
| ( B @ C )
| ( ( cJOIN @ A @ c0 @ A )
!= ( B @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[23,21]) ).
thf(59,plain,
! [C: iS,B: iS > $o,A: iS] :
( ~ ( B @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) )
| ( B @ C )
| ( ( cJOIN @ A @ c0 @ A )
!= ( B @ c0 ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(99,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ~ ( cJOIN
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
@ c0
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) )
| ( cJOIN @ ( B @ A ) @ c0 @ ( C @ A ) )
| ( ( B @ c0 )
!= ( C @ c0 ) ) ),
inference(pre_uni,[status(thm)],[59:[bind(A,$thf( D @ c0 )),bind(B,$thf( ^ [F: iS] : ( cJOIN @ ( D @ F ) @ c0 @ ( F @ F ) ) )),bind(C,$thf( C ))]]) ).
thf(101,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ( cJOIN @ ( B @ A ) @ c0 @ ( C @ A ) )
| ~ ( cJOIN
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
@ c0
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) )
| ( ( B @ c0 )
!= ( C @ c0 ) ) ),
inference(pre_uni,[status(thm)],[99:[]]) ).
thf(133,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ( cJOIN @ ( B @ A ) @ c0 @ ( C @ A ) )
| ~ ( cJOIN
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
@ c0
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) )
| ( ( B @ c0 )
!= ( C @ c0 ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(74,plain,
! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) )
!= ( cP @ ( sk1 @ ( (=) @ iS @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) @ ( sk2 @ ( (=) @ iS @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ) )
| ( ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) )
= D )
| ( ( A @ B )
!= ( ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) )
= c0 ) ) ),
inference(replace_leibeq,[status(thm)],[49:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( (=) @ iS @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ))]]) ).
thf(85,plain,
! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
( ( ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) )
!= ( cP @ ( sk1 @ ( (=) @ iS @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) @ ( sk2 @ ( (=) @ iS @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ) )
| ( ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) )
= D )
| ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) )
= c0 ) ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(26939,plain,
( ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( sk1 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,26816]) ).
thf(27039,plain,
( ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[26939]) ).
thf(27249,plain,
( ( cJOIN @ c0
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( sk1 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,27039]) ).
thf(27335,plain,
( ( cJOIN @ c0
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[27249]) ).
thf(27364,plain,
( ( cJOIN @ c0
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[27335]) ).
thf(691,plain,
( ~ ( cJOIN @ c0 @ c0 @ sk3 )
| ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[569:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ C @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(4850,plain,
( ~ ( cJOIN @ c0 @ c0 @ sk3 )
| ~ $true
| ( ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[691,12]) ).
thf(4851,plain,
( ~ ( cJOIN @ c0 @ c0 @ sk3 )
| ( ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(simp,[status(thm)],[4850]) ).
thf(4941,plain,
( ~ ( cJOIN @ c0 @ c0 @ sk3 )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
!= sk3 )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
!= sk3 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[4851]) ).
thf(4979,plain,
( ~ ( cJOIN @ c0 @ c0 @ sk3 )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[4941]) ).
thf(71,plain,
! [B: iS,A: iS] :
( ( c0 != c0 )
| ( c0 = B )
| ( ( cJOIN @ A @ c0 @ A )
!= ( c0
= ( cP @ ( sk1 @ ( (=) @ iS @ c0 ) ) @ ( sk2 @ ( (=) @ iS @ c0 ) ) ) ) ) ),
inference(replace_leibeq,[status(thm)],[61:[bind(A,$thf( A )),bind(B,$thf( (=) @ iS @ c0 ))]]) ).
thf(86,plain,
! [B: iS,A: iS] :
( ( c0 != c0 )
| ( c0 = B )
| ( ( cJOIN @ A @ c0 @ A )
!= ( c0
= ( cP @ ( sk1 @ ( (=) @ iS @ c0 ) ) @ ( sk2 @ ( (=) @ iS @ c0 ) ) ) ) ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(128,plain,
! [B: iS,A: iS] :
( ( c0 = B )
| ( ( cJOIN @ A @ c0 @ A )
!= ( c0
= ( cP @ ( sk1 @ ( (=) @ iS @ c0 ) ) @ ( sk2 @ ( (=) @ iS @ c0 ) ) ) ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(15513,plain,
! [B: iS,A: iS] :
( ( c0 = B )
| ( ( cJOIN @ A @ c0 @ A )
!= ( c0
= ( cP @ c0 @ c0 ) ) ) ),
inference(rewrite,[status(thm)],[128,324,168]) ).
thf(54,plain,
! [C: iS,B: iS > $o,A: iS] :
( ~ ( B @ c0 )
| ~ $true
| ( B @ C )
| ( ( cJOIN @ c0 @ A @ A )
!= ( B @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,21]) ).
thf(55,plain,
! [C: iS,B: iS > $o,A: iS] :
( ~ ( B @ c0 )
| ( B @ C )
| ( ( cJOIN @ c0 @ A @ A )
!= ( B @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(76,plain,
! [B: iS,A: iS] :
( ( c0 != c0 )
| ( c0 = B )
| ( ( cJOIN @ c0 @ A @ A )
!= ( c0
= ( cP @ ( sk1 @ ( (=) @ iS @ c0 ) ) @ ( sk2 @ ( (=) @ iS @ c0 ) ) ) ) ) ),
inference(replace_leibeq,[status(thm)],[55:[bind(A,$thf( A )),bind(B,$thf( (=) @ iS @ c0 ))]]) ).
thf(81,plain,
! [B: iS,A: iS] :
( ( c0 != c0 )
| ( c0 = B )
| ( ( cJOIN @ c0 @ A @ A )
!= ( c0
= ( cP @ ( sk1 @ ( (=) @ iS @ c0 ) ) @ ( sk2 @ ( (=) @ iS @ c0 ) ) ) ) ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(125,plain,
! [B: iS,A: iS] :
( ( c0 = B )
| ( ( cJOIN @ c0 @ A @ A )
!= ( c0
= ( cP @ ( sk1 @ ( (=) @ iS @ c0 ) ) @ ( sk2 @ ( (=) @ iS @ c0 ) ) ) ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(14125,plain,
! [B: iS,A: iS] :
( ( c0 = B )
| ( ( cJOIN @ c0 @ A @ A )
!= ( c0
= ( cP @ c0 @ c0 ) ) ) ),
inference(rewrite,[status(thm)],[125,324,168]) ).
thf(40,plain,
! [A: iS] :
( ~ $true
| ( ( cJOIN @ c0 @ A @ A )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[22,12]) ).
thf(41,plain,
! [A: iS] :
( ( cJOIN @ c0 @ A @ A )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
inference(simp,[status(thm)],[40]) ).
thf(42,plain,
! [A: iS] :
( ( sk3 != c0 )
| ( A != sk3 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[41]) ).
thf(43,plain,
sk3 != c0,
inference(simp,[status(thm)],[42]) ).
thf(14242,plain,
! [B: iS,A: iS] :
( ( ( cJOIN @ c0 @ A @ A )
!= ( c0
= ( cP @ c0 @ c0 ) ) )
| ( c0 != c0 )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[14125,43]) ).
thf(14243,plain,
! [B: iS,A: iS] :
( ( ( cJOIN @ c0 @ A @ A )
!= ( c0
= ( cP @ c0 @ c0 ) ) )
| ( B != sk3 ) ),
inference(simp,[status(thm)],[14242]) ).
thf(14244,plain,
! [A: iS] :
( ( cJOIN @ c0 @ A @ A )
!= ( c0
= ( cP @ c0 @ c0 ) ) ),
inference(pattern_uni,[status(thm)],[14243:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(23995,plain,
( ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( sk2 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[324,23825]) ).
thf(24137,plain,
( ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[23995]) ).
thf(24170,plain,
( ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[24137]) ).
thf(869,plain,
( ~ $true
| ( ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
@ sk3 )
!= ( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[851,337]) ).
thf(870,plain,
( ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
@ sk3 )
!= ( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ) ),
inference(simp,[status(thm)],[869]) ).
thf(877,plain,
( ( sk3 != sk3 )
| ( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[870]) ).
thf(884,plain,
( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[877]) ).
thf(69,plain,
! [B: iS > $o,A: iS] :
( ~ ~ ( B @ c0 )
| ~ ~ ( B
@ ( cP
@ ( sk1
@ ^ [C: iS] :
~ ( B @ C ) )
@ ( sk2
@ ^ [C: iS] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[21:[bind(A,$thf( ^ [D: iS] : ~ ( C @ D ) ))]]) ).
thf(123,plain,
! [B: iS > $o,A: iS] :
( ( B @ c0 )
| ( B
@ ( cP
@ ( sk1
@ ^ [C: iS] :
~ ( B @ C ) )
@ ( sk2
@ ^ [C: iS] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(cnf,[status(esa)],[69]) ).
thf(124,plain,
! [B: iS > $o,A: iS] :
( ( B @ c0 )
| ( B
@ ( cP
@ ( sk1
@ ^ [C: iS] :
~ ( B @ C ) )
@ ( sk2
@ ^ [C: iS] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[123]) ).
thf(216,plain,
! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ B )
| ~ $true
| ( C @ ( sk2 @ C ) )
| ( C @ D )
| ( ( A @ ( sk2 @ A ) )
!= ( C @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[19,19]) ).
thf(217,plain,
! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ B )
| ( C @ ( sk2 @ C ) )
| ( C @ D )
| ( ( A @ ( sk2 @ A ) )
!= ( C @ c0 ) ) ),
inference(simp,[status(thm)],[216]) ).
thf(229,plain,
! [C: iS,B: iS > $o,A: iS] :
( ( c0 != c0 )
| ( c0 = A )
| ( B @ ( sk2 @ B ) )
| ( B @ C )
| ( ( c0
= ( sk2 @ ( (=) @ iS @ c0 ) ) )
!= ( B @ c0 ) ) ),
inference(replace_leibeq,[status(thm)],[217:[bind(A,$thf( (=) @ iS @ c0 ))]]) ).
thf(246,plain,
! [C: iS,B: iS > $o,A: iS] :
( ( c0 != c0 )
| ( c0 = A )
| ( B @ ( sk2 @ B ) )
| ( B @ C )
| ( ( c0
= ( sk2 @ ( (=) @ iS @ c0 ) ) )
!= ( B @ c0 ) ) ),
inference(lifteq,[status(thm)],[229]) ).
thf(281,plain,
! [B: iS,A: iS] :
( ( c0
= ( sk2 @ ( (=) @ iS @ B ) ) )
| ( c0
= ( sk2
@ ( (=) @ iS
@ ( sk2
@ ^ [C: iS] :
( c0
= ( sk2 @ ( (=) @ iS @ C ) ) ) ) ) ) )
| ( c0 = A ) ),
inference(pre_uni,[status(thm)],[246:[bind(A,$thf( A )),bind(B,$thf( ^ [D: iS] : ( c0 = ( sk2 @ ( (=) @ iS @ D ) ) ) )),bind(C,$thf( C ))]]) ).
thf(301,plain,
! [B: iS,A: iS] :
( ( ( sk2 @ ( (=) @ iS @ B ) )
= c0 )
| ( ( sk2
@ ( (=) @ iS
@ ( sk2
@ ^ [C: iS] :
( c0
= ( sk2 @ ( (=) @ iS @ C ) ) ) ) ) )
= c0 )
| ( c0 = A ) ),
inference(lifteq,[status(thm)],[281]) ).
thf(302,plain,
! [B: iS,A: iS] :
( ( ( sk2 @ ( (=) @ iS @ B ) )
= c0 )
| ( ( sk2
@ ( (=) @ iS
@ ( sk2
@ ^ [C: iS] :
( c0
= ( sk2 @ ( (=) @ iS @ C ) ) ) ) ) )
= c0 )
| ( c0 = A ) ),
inference(simp,[status(thm)],[301]) ).
thf(1741,plain,
! [B: iS,A: iS] :
( ( ( sk2 @ ( (=) @ iS @ B ) )
= c0 )
| ( c0 = A )
| ( ( sk2
@ ( (=) @ iS
@ ( sk2
@ ^ [C: iS] :
( c0
= ( sk2 @ ( (=) @ iS @ C ) ) ) ) ) )
!= ( sk2 @ ( (=) @ iS @ B ) ) )
| ( c0 != c0 ) ),
inference(eqfactor_ordered,[status(thm)],[302]) ).
thf(1768,plain,
! [A: iS] :
( ( ( sk2
@ ( (=) @ iS
@ ( sk2
@ ^ [B: iS] :
( c0
= ( sk2 @ ( (=) @ iS @ B ) ) ) ) ) )
= c0 )
| ( c0 = A ) ),
inference(pattern_uni,[status(thm)],[1741:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ^ [C: iS] : ( c0 = ( sk2 @ ( (=) @ iS @ C ) ) ) ))]]) ).
thf(343,plain,
! [A: iS] :
( ~ $true
| ( ( cJOIN @ A @ c0 @ A )
!= ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) )
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[23,337]) ).
thf(344,plain,
! [A: iS] :
( ( cJOIN @ A @ c0 @ A )
!= ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) )
@ sk3 ) ),
inference(simp,[status(thm)],[343]) ).
thf(355,plain,
! [A: iS] :
( ( A != sk3 )
| ( ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) )
!= c0 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[344]) ).
thf(362,plain,
( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
!= c0 ),
inference(simp,[status(thm)],[355]) ).
thf(2998,plain,
! [A: iS] :
( ( ( sk2
@ ( (=) @ iS
@ ( sk2
@ ^ [B: iS] :
( c0
= ( sk2 @ ( (=) @ iS @ B ) ) ) ) ) )
= c0 )
| ( c0 != c0 )
| ( A
!= ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1768,362]) ).
thf(2999,plain,
! [A: iS] :
( ( ( sk2
@ ( (=) @ iS
@ ( sk2
@ ^ [B: iS] :
( c0
= ( sk2 @ ( (=) @ iS @ B ) ) ) ) ) )
= c0 )
| ( A
!= ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) ) ) ),
inference(simp,[status(thm)],[2998]) ).
thf(3000,plain,
( ( sk2
@ ( (=) @ iS
@ ( sk2
@ ^ [A: iS] :
( c0
= ( sk2 @ ( (=) @ iS @ A ) ) ) ) ) )
= c0 ),
inference(pattern_uni,[status(thm)],[2999:[bind(A,$thf( cP @ ( sk1 @ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) @ ( sk2 @ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) ))]]) ).
thf(690,plain,
( ~ ( cJOIN @ c0 @ sk3 @ sk3 )
| ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ) ),
inference(pre_uni,[status(thm)],[569:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(1388,plain,
( ~ $true
| ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ) ),
inference(rewrite,[status(thm)],[690,22]) ).
thf(1389,plain,
( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ),
inference(simp,[status(thm)],[1388]) ).
thf(89,plain,
( ~ ( cJOIN @ c0 @ sk3 @ sk3 )
| ~ ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
@ sk3
@ sk3 ) ),
inference(pre_uni,[status(thm)],[57:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(4345,plain,
( ~ $true
| ~ ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
@ sk3
@ sk3 ) ),
inference(rewrite,[status(thm)],[89,22]) ).
thf(4346,plain,
~ ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
@ sk3
@ sk3 ),
inference(simp,[status(thm)],[4345]) ).
thf(4385,plain,
( ~ $true
| ( ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
@ sk3
@ sk3 )
!= ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1389,4346]) ).
thf(4386,plain,
( ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
@ sk3
@ sk3 )
!= ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ) ),
inference(simp,[status(thm)],[4385]) ).
thf(4426,plain,
( ( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
| ( sk3 != sk3 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[4386]) ).
thf(4444,plain,
( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) ),
inference(simp,[status(thm)],[4426]) ).
thf(23994,plain,
( ( cJOIN @ c0
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( sk2 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[324,23825]) ).
thf(24154,plain,
( ( cJOIN @ c0
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[23994]) ).
thf(24176,plain,
( ( cJOIN @ c0
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[24154]) ).
thf(26890,plain,
( ~ $true
| ( ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[26816,12]) ).
thf(26891,plain,
( ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
inference(simp,[status(thm)],[26890]) ).
thf(27020,plain,
( ( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= sk3 )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= sk3 )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= sk3 ) ),
inference(simp,[status(thm)],[26891]) ).
thf(27044,plain,
( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= sk3 ),
inference(simp,[status(thm)],[27020]) ).
thf(276,plain,
( ~ ( cJOIN @ c0 @ sk3 @ sk3 )
| ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ) ),
inference(pre_uni,[status(thm)],[213:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(508,plain,
( ~ $true
| ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ) ),
inference(rewrite,[status(thm)],[276,22]) ).
thf(509,plain,
( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ),
inference(simp,[status(thm)],[508]) ).
thf(520,plain,
( ~ $true
| ( ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[509,12]) ).
thf(521,plain,
( ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
inference(simp,[status(thm)],[520]) ).
thf(532,plain,
( ( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
!= sk3 )
| ( sk3 != sk3 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[521]) ).
thf(537,plain,
( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
!= sk3 ),
inference(simp,[status(thm)],[532]) ).
thf(18888,plain,
! [B: iS,A: iS > $o] :
( ~ $true
| ( A @ ( sk1 @ A ) )
| ( A @ B )
| ( ( cJOIN @ c0 @ c0 @ c0 )
!= ( A @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[18777,35]) ).
thf(18889,plain,
! [B: iS,A: iS > $o] :
( ( A @ ( sk1 @ A ) )
| ( A @ B )
| ( ( cJOIN @ c0 @ c0 @ c0 )
!= ( A @ c0 ) ) ),
inference(simp,[status(thm)],[18888]) ).
thf(18970,plain,
! [A: iS] :
( ( cJOIN @ c0
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
@ c0 )
| ( cJOIN @ c0 @ A @ c0 ) ),
inference(pre_uni,[status(thm)],[18889:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ c0 @ C @ c0 ) )),bind(B,$thf( B ))]]) ).
thf(19119,plain,
! [A: iS] :
( ( cJOIN @ c0
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
@ c0 )
| ( cJOIN @ c0 @ A @ c0 ) ),
inference(simp,[status(thm)],[18970]) ).
thf(20826,plain,
! [A: iS] :
( ( cJOIN @ c0
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
@ c0 )
| ( ( cJOIN @ c0 @ A @ c0 )
!= ( cJOIN @ c0
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
@ c0 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[19119]) ).
thf(20940,plain,
( cJOIN @ c0
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ c0 @ A @ c0 ) )
@ c0 ),
inference(pattern_uni,[status(thm)],[20826:[bind(A,$thf( sk1 @ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) ))]]) ).
thf(100,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ~ ( cJOIN
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) )
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) )
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) ) )
| ( cJOIN @ ( B @ A ) @ A @ ( C @ A ) )
| ( ( B @ c0 )
!= ( C @ c0 ) ) ),
inference(pre_uni,[status(thm)],[59:[bind(A,$thf( D @ c0 )),bind(B,$thf( ^ [F: iS] : ( cJOIN @ ( D @ F ) @ F @ ( F @ F ) ) )),bind(C,$thf( C ))]]) ).
thf(102,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ( cJOIN @ ( B @ A ) @ A @ ( C @ A ) )
| ~ ( cJOIN
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) )
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) )
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) ) )
| ( ( B @ c0 )
!= ( C @ c0 ) ) ),
inference(pre_uni,[status(thm)],[100:[]]) ).
thf(134,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ( cJOIN @ ( B @ A ) @ A @ ( C @ A ) )
| ~ ( cJOIN
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) )
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) )
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) ) )
| ( ( B @ c0 )
!= ( C @ c0 ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(1400,plain,
( ~ $true
| ( ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1389,12]) ).
thf(1401,plain,
( ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
inference(simp,[status(thm)],[1400]) ).
thf(1428,plain,
( ( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
!= sk3 )
| ( sk3 != sk3 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[1401]) ).
thf(1434,plain,
( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
!= sk3 ),
inference(simp,[status(thm)],[1428]) ).
thf(4387,plain,
( ~ $true
| ( ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
@ sk3
@ sk3 )
!= ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[509,4346]) ).
thf(4388,plain,
( ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
@ sk3
@ sk3 )
!= ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ) ),
inference(simp,[status(thm)],[4387]) ).
thf(4432,plain,
( ( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
| ( sk3 != sk3 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[4388]) ).
thf(4448,plain,
( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) ),
inference(simp,[status(thm)],[4432]) ).
thf(27086,plain,
( ( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( sk2 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[324,27054]) ).
thf(27118,plain,
( ( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[27086]) ).
thf(66,plain,
! [D: iS > iS,C: iS > iS,B: iS > iS,A: iS] :
( ~ ( cJOIN @ ( B @ c0 ) @ ( C @ c0 ) @ ( D @ c0 ) )
| ~ ( cJOIN
@ ( B
@ ( cP
@ ( sk1
@ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
@ ( sk2
@ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) ) ) )
@ ( C
@ ( cP
@ ( sk1
@ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
@ ( sk2
@ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) ) ) )
@ ( D
@ ( cP
@ ( sk1
@ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
@ ( sk2
@ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) ) ) ) )
| ( cJOIN @ ( B @ A ) @ ( C @ A ) @ ( D @ A ) ) ),
inference(prim_subst,[status(thm)],[21:[bind(A,$thf( ^ [F: iS] : ( cJOIN @ ( C @ F ) @ ( D @ F ) @ ( E @ F ) ) ))]]) ).
thf(113,plain,
! [D: iS > iS,C: iS > iS,B: iS > iS,A: iS] :
( ~ ( cJOIN @ ( B @ c0 ) @ ( C @ c0 ) @ ( D @ c0 ) )
| ~ ( cJOIN
@ ( B
@ ( cP
@ ( sk1
@ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
@ ( sk2
@ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) ) ) )
@ ( C
@ ( cP
@ ( sk1
@ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
@ ( sk2
@ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) ) ) )
@ ( D
@ ( cP
@ ( sk1
@ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
@ ( sk2
@ ^ [E: iS] : ( cJOIN @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) ) ) ) )
| ( cJOIN @ ( B @ A ) @ ( C @ A ) @ ( D @ A ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(64,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ c0 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21]) ).
thf(98,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ c0 ) ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(478,plain,
( ~ $true
| ( ( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[467,12]) ).
thf(479,plain,
( ( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
inference(simp,[status(thm)],[478]) ).
thf(490,plain,
( ( sk3 != sk3 )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= sk3 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[479]) ).
thf(494,plain,
( ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= sk3 ),
inference(simp,[status(thm)],[490]) ).
thf(18971,plain,
! [A: iS] :
( ( cJOIN
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ c0 @ c0 ) )
@ c0
@ c0 )
| ( cJOIN @ A @ c0 @ c0 ) ),
inference(pre_uni,[status(thm)],[18889:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ c0 @ c0 ) )),bind(B,$thf( B ))]]) ).
thf(19120,plain,
! [A: iS] :
( ( cJOIN
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ c0 @ c0 ) )
@ c0
@ c0 )
| ( cJOIN @ A @ c0 @ c0 ) ),
inference(simp,[status(thm)],[18971]) ).
thf(25937,plain,
! [A: iS] :
( ( cJOIN
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ c0 @ c0 ) )
@ c0
@ c0 )
| ( ( cJOIN @ A @ c0 @ c0 )
!= ( cJOIN
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ c0 @ c0 ) )
@ c0
@ c0 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[19120]) ).
thf(26174,plain,
( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ c0 @ c0 ) )
@ c0
@ c0 ),
inference(pattern_uni,[status(thm)],[25937:[bind(A,$thf( sk1 @ ^ [B: iS] : ( cJOIN @ B @ c0 @ c0 ) ))]]) ).
thf(15624,plain,
! [B: iS,A: iS] :
( ( ( cJOIN @ A @ c0 @ A )
!= ( c0
= ( cP @ c0 @ c0 ) ) )
| ( c0 != c0 )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[15513,43]) ).
thf(15625,plain,
! [B: iS,A: iS] :
( ( ( cJOIN @ A @ c0 @ A )
!= ( c0
= ( cP @ c0 @ c0 ) ) )
| ( B != sk3 ) ),
inference(simp,[status(thm)],[15624]) ).
thf(15626,plain,
! [A: iS] :
( ( cJOIN @ A @ c0 @ A )
!= ( c0
= ( cP @ c0 @ c0 ) ) ),
inference(pattern_uni,[status(thm)],[15625:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(4383,plain,
! [A: iS] :
( ~ $true
| ( ( cJOIN @ c0 @ A @ A )
!= ( cJOIN
@ ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) ) )
@ sk3
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[22,4346]) ).
thf(4384,plain,
! [A: iS] :
( ( cJOIN @ c0 @ A @ A )
!= ( cJOIN
@ ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) ) )
@ sk3
@ sk3 ) ),
inference(simp,[status(thm)],[4383]) ).
thf(4429,plain,
! [A: iS] :
( ( ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) ) )
!= c0 )
| ( A != sk3 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[4384]) ).
thf(4445,plain,
( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
!= c0 ),
inference(simp,[status(thm)],[4429]) ).
thf(277,plain,
( ~ ( cJOIN @ c0 @ c0 @ sk3 )
| ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[213:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ C @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(2579,plain,
( ~ ( cJOIN @ c0 @ c0 @ sk3 )
| ~ $true
| ( ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[277,12]) ).
thf(2580,plain,
( ~ ( cJOIN @ c0 @ c0 @ sk3 )
| ( ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(simp,[status(thm)],[2579]) ).
thf(2684,plain,
( ~ ( cJOIN @ c0 @ c0 @ sk3 )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
!= sk3 )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
!= sk3 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[2580]) ).
thf(2725,plain,
( ~ ( cJOIN @ c0 @ c0 @ sk3 )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[2684]) ).
thf(9592,plain,
( ( sk7 != c0 )
| ~ $true
| ( ( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[467,9559]) ).
thf(9593,plain,
( ( sk7 != c0 )
| ( ( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ) ),
inference(simp,[status(thm)],[9592]) ).
thf(9658,plain,
( ( sk7 != c0 )
| ( sk3 != sk3 )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( cP @ c0 @ c0 ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[9593]) ).
thf(9698,plain,
( ( sk7 != c0 )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( cP @ c0 @ c0 ) ) ),
inference(simp,[status(thm)],[9658]) ).
thf(73,plain,
! [C: iS,B: iS > $o,A: iS] :
( ( ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) )
!= ( cP @ ( sk1 @ ( (=) @ iS @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) @ ( sk2 @ ( (=) @ iS @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ) )
| ( ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) )
= C )
| ( ( cJOIN @ A @ c0 @ A )
!= ( ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) )
= c0 ) ) ),
inference(replace_leibeq,[status(thm)],[59:[bind(A,$thf( A )),bind(B,$thf( (=) @ iS @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ))]]) ).
thf(80,plain,
! [C: iS,B: iS > $o,A: iS] :
( ( ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) )
!= ( cP @ ( sk1 @ ( (=) @ iS @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) @ ( sk2 @ ( (=) @ iS @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ) )
| ( ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) )
= C )
| ( ( cJOIN @ A @ c0 @ A )
!= ( ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) )
= c0 ) ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(221,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ A ) )
| ( ( A @ B )
!= ( ~ ( A @ c0 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(255,plain,
! [B: iS,A: iS > $o] :
( ( A @ ( sk2 @ A ) )
| ~ ( A @ c0 )
| ( ( A @ B )
!= ( ~ ( A @ c0 ) ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(62,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ B )
| ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( A @ c0 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21]) ).
thf(111,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ B )
| ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( A @ c0 ) ) ),
inference(pre_uni,[status(thm)],[62:[]]) ).
thf(112,plain,
! [B: iS,A: iS > $o] :
( ( A @ B )
| ~ ( A @ c0 )
| ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( A @ c0 ) ) ),
inference(pre_uni,[status(thm)],[111:[]]) ).
thf(15419,plain,
! [B: iS,A: iS] :
( ( c0
!= ( cP @ c0 @ c0 ) )
| ( ( cJOIN @ A @ c0 @ A )
!= ( cJOIN @ c0 @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[23,14244]) ).
thf(15420,plain,
( c0
!= ( cP @ c0 @ c0 ) ),
inference(pattern_uni,[status(thm)],[15419:[bind(A,$thf( c0 )),bind(B,$thf( c0 ))]]) ).
thf(15443,plain,
( ( cP @ c0 @ c0 )
!= c0 ),
inference(lifteq,[status(thm)],[15420]) ).
thf(115,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ~ ( B @ c0 )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(119,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ~ ( B @ c0 )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(simp,[status(thm)],[115]) ).
thf(26637,plain,
( ( ( cP @ c0 @ c0 )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( sk2 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[324,23928]) ).
thf(26671,plain,
( ( ( cP @ c0 @ c0 )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[26637]) ).
thf(26681,plain,
( ( ( cP @ c0 @ c0 )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[26671]) ).
thf(23708,plain,
( ~ $true
| ( ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[23622,12]) ).
thf(23709,plain,
( ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
inference(simp,[status(thm)],[23708]) ).
thf(23841,plain,
( ( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= sk3 )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= sk3 )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= sk3 ) ),
inference(simp,[status(thm)],[23709]) ).
thf(23866,plain,
( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= sk3 ),
inference(simp,[status(thm)],[23841]) ).
thf(72,plain,
! [C: iS,B: iS > $o,A: iS] :
( ( ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) )
!= ( cP @ ( sk1 @ ( (=) @ iS @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) @ ( sk2 @ ( (=) @ iS @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ) )
| ( ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) )
= C )
| ( ( cJOIN @ c0 @ A @ A )
!= ( ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) )
= c0 ) ) ),
inference(replace_leibeq,[status(thm)],[53:[bind(A,$thf( A )),bind(B,$thf( (=) @ iS @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ))]]) ).
thf(82,plain,
! [C: iS,B: iS > $o,A: iS] :
( ( ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) )
!= ( cP @ ( sk1 @ ( (=) @ iS @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) @ ( sk2 @ ( (=) @ iS @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ) )
| ( ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) )
= C )
| ( ( cJOIN @ c0 @ A @ A )
!= ( ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) )
= c0 ) ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(27905,plain,
( ( ( cP @ c0 @ c0 )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( sk1 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,27118]) ).
thf(27906,plain,
( ( ( cP @ c0 @ c0 )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[27905]) ).
thf(27919,plain,
( ( ( cP @ c0 @ c0 )
!= ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[27906]) ).
thf(899,plain,
( ~ $true
| ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) )
| ( ( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[467,839]) ).
thf(900,plain,
( ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) )
| ( ( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ) ),
inference(simp,[status(thm)],[899]) ).
thf(927,plain,
( ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) )
| ( sk3 != sk3 )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( cP @ c0 @ c0 ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[900]) ).
thf(950,plain,
( ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( cP @ c0 @ c0 ) ) ),
inference(simp,[status(thm)],[927]) ).
thf(50,plain,
! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ c0 )
| ~ $true
| ( C @ D )
| ( ( A @ B )
!= ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,21]) ).
thf(51,plain,
! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ c0 )
| ( C @ D )
| ( ( A @ B )
!= ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(106,plain,
! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ c0 )
| ( C @ D )
| ( ( A @ B )
!= ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[51:[]]) ).
thf(107,plain,
! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
( ( C @ D )
| ~ ( C @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( A @ c0 )
| ( ( A @ B )
!= ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[106:[]]) ).
thf(104,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ~ ( cJOIN @ c0 @ ( B @ c0 ) @ ( C @ c0 ) )
| ( cJOIN @ c0 @ ( B @ A ) @ ( C @ A ) )
| ( ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) ) ) )
!= ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[55:[bind(A,$thf( E @ ( cP @ ( sk1 @ ^ [F: iS] : ( cJOIN @ c0 @ ( E @ F ) @ ( F @ F ) ) ) @ ( sk2 @ ^ [F: iS] : ( cJOIN @ c0 @ ( E @ F ) @ ( F @ F ) ) ) ) )),bind(B,$thf( ^ [F: iS] : ( cJOIN @ c0 @ ( E @ F ) @ ( F @ F ) ) )),bind(C,$thf( C ))]]) ).
thf(105,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ( cJOIN @ c0 @ ( B @ A ) @ ( C @ A ) )
| ~ ( cJOIN @ c0 @ ( B @ c0 ) @ ( C @ c0 ) )
| ( ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) ) ) )
!= ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[104:[]]) ).
thf(136,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ( cJOIN @ c0 @ ( B @ A ) @ ( C @ A ) )
| ~ ( cJOIN @ c0 @ ( B @ c0 ) @ ( C @ c0 ) )
| ( ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) ) ) )
!= ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) ) ) ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(33,plain,
? [A: iS > iS > iS] :
! [B: iS,C: iS] :
( ( A @ B @ ( cP @ B @ C ) )
= C ),
inference(detectInverse,[status(thm)],[32]) ).
thf(34,plain,
! [B: iS,A: iS] :
( ( sk4 @ A @ ( cP @ A @ B ) )
= B ),
inference(cnf,[status(esa)],[33]) ).
thf(332,plain,
! [B: iS,A: iS] :
( ( sk4 @ A @ ( cP @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[34]) ).
thf(94,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ~ ( cJOIN @ c0
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) ) ) )
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) ) ) ) )
| ( cJOIN @ c0 @ ( B @ A ) @ ( C @ A ) )
| ( ( B @ c0 )
!= ( C @ c0 ) ) ),
inference(pre_uni,[status(thm)],[53:[bind(A,$thf( E @ c0 )),bind(B,$thf( ^ [F: iS] : ( cJOIN @ c0 @ ( E @ F ) @ ( F @ F ) ) )),bind(C,$thf( C ))]]) ).
thf(96,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ( cJOIN @ c0 @ ( B @ A ) @ ( C @ A ) )
| ~ ( cJOIN @ c0
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) ) ) )
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) ) ) ) )
| ( ( B @ c0 )
!= ( C @ c0 ) ) ),
inference(pre_uni,[status(thm)],[94:[]]) ).
thf(131,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ( cJOIN @ c0 @ ( B @ A ) @ ( C @ A ) )
| ~ ( cJOIN @ c0
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) ) ) )
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ c0 @ ( B @ D ) @ ( C @ D ) ) ) ) ) )
| ( ( B @ c0 )
!= ( C @ c0 ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(90,plain,
( ~ ( cJOIN @ c0 @ c0 @ sk3 )
| ~ ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) ) )
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ sk3 ) ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[57:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ C @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(27250,plain,
( ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( sk1 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,27039]) ).
thf(27330,plain,
( ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[27250]) ).
thf(27363,plain,
( ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[27330]) ).
thf(118,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ~ ( C @ c0 )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(122,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ~ ( C @ c0 )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(simp,[status(thm)],[118]) ).
thf(32282,plain,
$false,
inference(e,[status(thm)],[23929,121,32,495,892,333,10658,23825,120,28550,885,37,9693,110,20472,949,20,93,27119,23928,132,133,18777,85,27364,27054,21,467,4979,324,15513,14244,24170,884,124,3000,4444,24176,27044,537,20940,14125,134,1434,4448,27118,22,1389,12,19973,26816,113,362,509,98,494,26174,15626,4445,130,2725,9698,3,851,80,35,255,112,4346,15443,27039,43,26,23622,23,119,26681,9559,23866,82,27919,19,950,168,107,136,839,332,23859,131,277,691,90,354,27363,337,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV190^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n015.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 15:23:03 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.00 % [INFO] Parsing done (203ms).
% 1.23/1.02 % [INFO] Running in sequential loop mode.
% 2.10/1.43 % [INFO] eprover registered as external prover.
% 2.10/1.44 % [INFO] Scanning for conjecture ...
% 2.30/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.49/1.60 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.49/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.49/1.61 % [INFO] Type checking passed.
% 2.49/1.61 % [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 ...
% 265.31/93.25 % External prover 'e' found a proof!
% 265.31/93.25 % [INFO] Killing All external provers ...
% 265.31/93.25 % Time passed: 92895ms (effective reasoning time: 92227ms)
% 265.31/93.25 % 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)>
% 265.31/93.25 % Axioms used in derivation (0):
% 265.31/93.25 % No. of inferences in proof: 336
% 265.31/93.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 92895 ms resp. 92227 ms w/o parsing
% 253.00/93.49 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 253.00/93.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------