TSTP Solution File: SEV190^5 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEV190^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 04:10:07 EDT 2024
% Result : Theorem 111.61s 22.25s
% Output : Refutation 112.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 15
% Syntax : Number of formulae : 271 ( 71 unt; 11 typ; 1 def)
% Number of atoms : 1023 ( 433 equ; 76 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 4299 ( 486 ~; 393 |; 33 &;3368 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 133 ( 133 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 775 ( 417 ^ 356 !; 2 ?; 775 :)
% Comments :
%------------------------------------------------------------------------------
thf(iS_type,type,
iS: $tType ).
thf(c0_type,type,
c0: iS ).
thf(cJOIN_type,type,
cJOIN: iS > iS > iS > $o ).
thf(cP_type,type,
cP: iS > iS > iS ).
thf(cS_JOIN_CLOS_type,type,
cS_JOIN_CLOS: iS > ( iS > iS > iS ) > ( iS > iS > iS > $o ) > $o ).
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_type,type,
sk1: ( iS > $o ) > iS ).
thf(sk2_type,type,
sk2: ( iS > $o ) > iS ).
thf(sk3_type,type,
sk3: iS ).
thf(sk4_type,type,
sk4: iS > iS > iS ).
thf(sk5_type,type,
sk5: iS > iS > iS ).
thf(sk7_type,type,
sk7: iS ).
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/sandbox2/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(8,plain,
! [A: iS] : ( cJOIN @ c0 @ A @ A ),
inference(cnf,[status(esa)],[4]) ).
thf(34,plain,
! [A: iS] : ( cJOIN @ c0 @ A @ A ),
inference(simp,[status(thm)],[8]) ).
thf(5,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(18,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( A @ B ) ),
inference(simp,[status(thm)],[5]) ).
thf(11,plain,
~ ( cJOIN @ sk3 @ sk3 @ sk3 ),
inference(cnf,[status(esa)],[4]) ).
thf(42,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[18,11]) ).
thf(64,plain,
( ~ ( cJOIN @ c0 @ sk3 @ sk3 )
| ~ ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
@ sk3
@ sk3 ) ),
inference(pre_uni,[status(thm)],[42:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(759,plain,
( ~ $true
| ~ ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
@ sk3
@ sk3 ) ),
inference(rewrite,[status(thm)],[64,34]) ).
thf(760,plain,
~ ( cJOIN
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
@ sk3
@ sk3 ),
inference(simp,[status(thm)],[759]) ).
thf(762,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(paramod_ordered,[status(thm)],[34,760]) ).
thf(775,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)],[762]) ).
thf(785,plain,
( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) ) )
!= c0 ),
inference(simp,[status(thm)],[775]) ).
thf(7,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(31,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( A @ B ) ),
inference(simp,[status(thm)],[7]) ).
thf(12,plain,
! [A: iS] : ( cJOIN @ A @ c0 @ A ),
inference(cnf,[status(esa)],[4]) ).
thf(30,plain,
! [A: iS] : ( cJOIN @ A @ c0 @ A ),
inference(simp,[status(thm)],[12]) ).
thf(47,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ c0 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[18]) ).
thf(79,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ c0 ) ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(41,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(paramod_ordered,[status(thm)],[18,18]) ).
thf(68,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)],[41:[]]) ).
thf(69,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)],[68:[]]) ).
thf(9,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(26,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ A ) )
| ( A @ B ) ),
inference(simp,[status(thm)],[9]) ).
thf(347,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(paramod_ordered,[status(thm)],[26,26]) ).
thf(360,plain,
! [C: iS,B: iS > $o,A: iS] :
( ( c0 != c0 )
| ( c0 = A )
| ( B @ ( sk2 @ B ) )
| ( B @ C )
| ( ( c0
= ( sk2 @ ( (=) @ iS @ c0 ) ) )
!= ( B @ c0 ) ) ),
inference(replace_leibeq,[status(thm)],[347:[bind(A,$thf( (=) @ iS @ c0 ))]]) ).
thf(371,plain,
! [C: iS,B: iS > $o,A: iS] :
( ( c0 != c0 )
| ( c0 = A )
| ( B @ ( sk2 @ B ) )
| ( B @ C )
| ( ( c0
= ( sk2 @ ( (=) @ iS @ c0 ) ) )
!= ( B @ c0 ) ) ),
inference(lifteq,[status(thm)],[360]) ).
thf(382,plain,
! [B: iS,A: iS] :
( ( c0
= ( sk2 @ ( (=) @ iS @ B ) ) )
| ( c0
= ( sk2
@ ( (=) @ iS
@ ( sk2
@ ^ [C: iS] :
( c0
= ( sk2 @ ( (=) @ iS @ C ) ) ) ) ) ) )
| ( c0 = A ) ),
inference(pre_uni,[status(thm)],[371:[bind(A,$thf( A )),bind(B,$thf( ^ [D: iS] : ( c0 = ( sk2 @ ( (=) @ iS @ D ) ) ) )),bind(C,$thf( C ))]]) ).
thf(448,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)],[382]) ).
thf(449,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)],[448]) ).
thf(5706,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)],[449]) ).
thf(5794,plain,
! [A: iS] :
( ( ( sk2
@ ( (=) @ iS
@ ( sk2
@ ^ [B: iS] :
( c0
= ( sk2 @ ( (=) @ iS @ B ) ) ) ) ) )
= c0 )
| ( c0 = A ) ),
inference(pattern_uni,[status(thm)],[5706:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ^ [C: iS] : ( c0 = ( sk2 @ ( (=) @ iS @ C ) ) ) ))]]) ).
thf(6818,plain,
! [A: iS] :
( ( ( sk2
@ ( (=) @ iS
@ ( sk2
@ ^ [B: iS] :
( c0
= ( sk2 @ ( (=) @ iS @ B ) ) ) ) ) )
= c0 )
| ( A
!= ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5794,785]) ).
thf(6819,plain,
( ( sk2
@ ( (=) @ iS
@ ( sk2
@ ^ [A: iS] :
( c0
= ( sk2 @ ( (=) @ iS @ A ) ) ) ) ) )
= c0 ),
inference(pattern_uni,[status(thm)],[6818:[bind(A,$thf( cP @ ( sk1 @ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) ) @ ( sk2 @ ^ [B: iS] : ( cJOIN @ B @ sk3 @ sk3 ) ) ))]]) ).
thf(43,plain,
! [C: iS,B: iS > $o,A: iS] :
( ~ ( B @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) )
| ( B @ C )
| ( ( cJOIN @ A @ c0 @ A )
!= ( B @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[30,18]) ).
thf(74,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ~ ( cJOIN
@ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) )
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) )
@ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ D @ ( C @ D ) ) ) ) ) )
| ( cJOIN @ ( B @ A ) @ A @ ( C @ A ) )
| ( ( B @ c0 )
!= ( C @ c0 ) ) ),
inference(pre_uni,[status(thm)],[43:[bind(A,$thf( D @ c0 )),bind(B,$thf( ^ [F: iS] : ( cJOIN @ ( D @ F ) @ F @ ( F @ F ) ) )),bind(C,$thf( C ))]]) ).
thf(76,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)],[74:[]]) ).
thf(86,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)],[76]) ).
thf(6226,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 ) ) ) ) ) )
| ( ( B @ c0 )
!= ( C @ c0 ) )
| ( ( cJOIN @ ( B @ A ) @ A @ ( C @ A ) )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[86,11]) ).
thf(6525,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)],[6226:[bind(A,$thf( sk3 )),bind(B,$thf( ^ [D: iS] : D )),bind(C,$thf( ^ [D: iS] : D ))]]) ).
thf(6527,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)],[6525:[]]) ).
thf(49,plain,
! [B: iS > $o,A: iS] :
( ~ ~ ( B @ c0 )
| ~ ~ ( B
@ ( cP
@ ( sk1
@ ^ [C: iS] :
~ ( B @ C ) )
@ ( sk2
@ ^ [C: iS] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[18:[bind(A,$thf( ^ [D: iS] : ~ ( C @ D ) ))]]) ).
thf(87,plain,
! [B: iS > $o,A: iS] :
( ~ ( B @ A )
| ( B
@ ( cP
@ ( sk1
@ ^ [C: iS] :
~ ( B @ C ) )
@ ( sk2
@ ^ [C: iS] :
~ ( B @ C ) ) ) )
| ( B @ c0 ) ),
inference(cnf,[status(esa)],[49]) ).
thf(88,plain,
! [B: iS > $o,A: iS] :
( ~ ( B @ A )
| ( B
@ ( cP
@ ( sk1
@ ^ [C: iS] :
~ ( B @ C ) )
@ ( sk2
@ ^ [C: iS] :
~ ( B @ C ) ) ) )
| ( B @ c0 ) ),
inference(simp,[status(thm)],[87]) ).
thf(353,plain,
! [B: iS > $o,A: iS] :
( ~ ~ ( B @ c0 )
| ~ ( B
@ ( sk2
@ ^ [C: iS] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[26:[bind(A,$thf( ^ [D: iS] : ~ ( C @ D ) ))]]) ).
thf(434,plain,
! [B: iS > $o,A: iS] :
( ~ ( B @ A )
| ~ ( B
@ ( sk2
@ ^ [C: iS] :
~ ( B @ C ) ) )
| ( B @ c0 ) ),
inference(cnf,[status(esa)],[353]) ).
thf(435,plain,
! [B: iS > $o,A: iS] :
( ~ ( B @ A )
| ~ ( B
@ ( sk2
@ ^ [C: iS] :
~ ( B @ C ) ) )
| ( B @ c0 ) ),
inference(simp,[status(thm)],[434]) ).
thf(850,plain,
! [B: iS > $o,A: iS] :
( ~ ( B @ A )
| ( B @ c0 )
| ~ ( B
@ ( sk2
@ ^ [C: iS] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(eqfactor_ordered,[status(thm)],[435]) ).
thf(871,plain,
! [A: iS] :
( ( A != A )
| ( A = c0 )
| ( A
!= ( sk2
@ ^ [B: iS] : ( A != B ) ) )
| ( A != A ) ),
inference(replace_leibeq,[status(thm)],[850:[bind(A,$thf( A )),bind(B,$thf( (=) @ iS @ A ))]]) ).
thf(886,plain,
! [A: iS] :
( ( A != A )
| ( A = c0 )
| ( A
!= ( sk2
@ ^ [B: iS] : ( A != B ) ) )
| ( A != A ) ),
inference(lifteq,[status(thm)],[871]) ).
thf(994,plain,
! [A: iS] :
( ( A = c0 )
| ( A
!= ( sk2
@ ^ [B: iS] : ( A != B ) ) ) ),
inference(simp,[status(thm)],[886]) ).
thf(6720,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ A ) )
| ( ( A @ B )
!= ( cJOIN
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,6527]) ).
thf(6737,plain,
( ~ ( cJOIN @ c0 @ c0 @ c0 )
| ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
inference(pre_uni,[status(thm)],[6720:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ C @ C ) )),bind(B,$thf( cP @ ( sk1 @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) @ ( sk2 @ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) ))]]) ).
thf(17,plain,
! [A: iS] :
( ( c0 != c0 )
| ( c0
= ( sk1 @ ( (=) @ iS @ c0 ) ) )
| ( c0 = A ) ),
inference(replace_leibeq,[status(thm)],[7:[bind(A,$thf( (=) @ iS @ c0 ))]]) ).
thf(28,plain,
! [A: iS] :
( ( c0 != c0 )
| ( ( sk1 @ ( (=) @ iS @ c0 ) )
= c0 )
| ( c0 = A ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(29,plain,
! [A: iS] :
( ( ( sk1 @ ( (=) @ iS @ c0 ) )
= c0 )
| ( c0 = A ) ),
inference(simp,[status(thm)],[28]) ).
thf(6,plain,
! [B: iS,A: iS] :
( ( cP @ A @ B )
!= c0 ),
inference(cnf,[status(esa)],[4]) ).
thf(25,plain,
! [B: iS,A: iS] :
( ( cP @ A @ B )
!= c0 ),
inference(lifteq,[status(thm)],[6]) ).
thf(110,plain,
! [C: iS,B: iS,A: iS] :
( ( ( sk1 @ ( (=) @ iS @ c0 ) )
= c0 )
| ( A
!= ( cP @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,25]) ).
thf(111,plain,
( ( sk1 @ ( (=) @ iS @ c0 ) )
= c0 ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( cP @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(44,plain,
! [C: iS,B: iS > $o,A: iS] :
( ~ ( B @ c0 )
| ( B @ C )
| ( ( cJOIN @ A @ c0 @ A )
!= ( B @ ( cP @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,18]) ).
thf(80,plain,
! [C: iS > iS,B: iS > iS,A: iS] :
( ~ ( cJOIN @ ( B @ c0 ) @ c0 @ ( C @ c0 ) )
| ( cJOIN @ ( B @ A ) @ c0 @ ( C @ A ) )
| ( ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) )
!= ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] : ( cJOIN @ ( B @ D ) @ c0 @ ( C @ D ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[44:[bind(A,$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(81,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)],[80:[]]) ).
thf(89,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)],[81]) ).
thf(8238,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 ) ) ) ) ) )
| ( ( sk1 @ ( (=) @ iS @ c0 ) )
!= ( C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[111,89]) ).
thf(8339,plain,
! [A: iS > iS] :
( ( cJOIN @ ( A @ ( sk1 @ ( (=) @ 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)],[8238:[bind(A,$thf( sk1 @ ( (=) @ iS @ c0 ) )),bind(B,$thf( B )),bind(C,$thf( ^ [D: iS] : D ))]]) ).
thf(8342,plain,
( ~ ( cJOIN @ c0 @ c0 @ c0 )
| ( cJOIN @ ( sk1 @ ( (=) @ iS @ c0 ) ) @ c0 @ c0 ) ),
inference(pre_uni,[status(thm)],[8339:[bind(A,$thf( ^ [B: iS] : B ))]]) ).
thf(9255,plain,
( ~ $true
| ( cJOIN @ c0 @ c0 @ c0 ) ),
inference(rewrite,[status(thm)],[8342,34,111]) ).
thf(9256,plain,
cJOIN @ c0 @ c0 @ c0,
inference(simp,[status(thm)],[9255]) ).
thf(13211,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)],[6737,9256]) ).
thf(13212,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)],[13211]) ).
thf(14,plain,
! [D: iS,C: iS,B: iS,A: iS] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(22,plain,
! [D: iS,C: iS,B: iS,A: iS] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(23,plain,
! [D: iS,C: iS,B: iS,A: iS] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( A = B ) ),
inference(simp,[status(thm)],[22]) ).
thf(24,plain,
! [B: iS,A: iS] :
( ( sk5 @ A @ ( cP @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(cP),[sk5])]) ).
thf(343,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk2 @ A ) )
| ( ( A @ B )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[26,11]) ).
thf(387,plain,
( ~ ( cJOIN @ c0 @ sk3 @ sk3 )
| ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ) ),
inference(pre_uni,[status(thm)],[343:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(1086,plain,
( ~ $true
| ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ) ),
inference(rewrite,[status(thm)],[387,34]) ).
thf(1087,plain,
( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ),
inference(simp,[status(thm)],[1086]) ).
thf(10,plain,
! [D: iS,C: iS,B: iS,A: iS] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( C = D ) ),
inference(cnf,[status(esa)],[4]) ).
thf(19,plain,
! [D: iS,C: iS,B: iS,A: iS] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( C = D ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(20,plain,
! [D: iS,C: iS,B: iS,A: iS] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( C = D ) ),
inference(simp,[status(thm)],[19]) ).
thf(562,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( ( A @ B )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[31,11]) ).
thf(657,plain,
( ~ ( cJOIN @ c0 @ sk3 @ sk3 )
| ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ) ),
inference(pre_uni,[status(thm)],[562:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(4387,plain,
( ~ $true
| ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ) ),
inference(rewrite,[status(thm)],[657,34]) ).
thf(4388,plain,
( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 ),
inference(simp,[status(thm)],[4387]) ).
thf(4399,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(paramod_ordered,[status(thm)],[4388,760]) ).
thf(4447,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)],[4399]) ).
thf(4471,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)],[4447]) ).
thf(40,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(paramod_ordered,[status(thm)],[18,18]) ).
thf(77,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)],[40:[]]) ).
thf(78,plain,
! [D: iS,C: iS > $o,B: iS,A: iS > $o] :
( ( C @ D )
| ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( A @ c0 )
| ( ( A @ B )
!= ( C @ c0 ) ) ),
inference(pre_uni,[status(thm)],[77:[]]) ).
thf(16,plain,
! [A: iS] :
( ( c0 != c0 )
| ( c0
= ( sk2 @ ( (=) @ iS @ c0 ) ) )
| ( c0 = A ) ),
inference(replace_leibeq,[status(thm)],[9:[bind(A,$thf( (=) @ iS @ c0 ))]]) ).
thf(32,plain,
! [A: iS] :
( ( c0 != c0 )
| ( ( sk2 @ ( (=) @ iS @ c0 ) )
= c0 )
| ( c0 = A ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(33,plain,
! [A: iS] :
( ( ( sk2 @ ( (=) @ iS @ c0 ) )
= c0 )
| ( c0 = A ) ),
inference(simp,[status(thm)],[32]) ).
thf(63,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)],[42:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(103,plain,
( ~ $true
| ~ ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
@ sk3 ) ),
inference(rewrite,[status(thm)],[63,30]) ).
thf(104,plain,
~ ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
@ sk3 ),
inference(simp,[status(thm)],[103]) ).
thf(106,plain,
! [A: iS] :
( ( cJOIN @ A @ c0 @ A )
!= ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) )
@ sk3 ) ),
inference(paramod_ordered,[status(thm)],[30,104]) ).
thf(108,plain,
! [A: iS] :
( ( A != sk3 )
| ( ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) )
!= c0 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[106]) ).
thf(109,plain,
( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
!= c0 ),
inference(simp,[status(thm)],[108]) ).
thf(210,plain,
! [A: iS] :
( ( ( sk2 @ ( (=) @ iS @ c0 ) )
= c0 )
| ( A
!= ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,109]) ).
thf(211,plain,
( ( sk2 @ ( (=) @ iS @ c0 ) )
= c0 ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( cP @ ( sk1 @ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) @ ( sk2 @ ^ [B: iS] : ( cJOIN @ sk3 @ B @ sk3 ) ) ))]]) ).
thf(564,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( ( A @ B )
!= ( cJOIN @ sk3
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) ) )
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[31,104]) ).
thf(637,plain,
( ~ ( cJOIN @ sk3 @ c0 @ sk3 )
| ( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[564:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) )),bind(B,$thf( cP @ ( sk1 @ ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) ) @ ( sk2 @ ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) ) ))]]) ).
thf(1841,plain,
( ~ $true
| ( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ) ),
inference(rewrite,[status(thm)],[637,30]) ).
thf(1842,plain,
( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ),
inference(simp,[status(thm)],[1841]) ).
thf(171,plain,
( ~ ( cJOIN @ sk3
@ ( cP @ c0
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
@ sk3 )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( sk1 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,104]) ).
thf(173,plain,
( ~ ( cJOIN @ sk3
@ ( cP @ c0
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) ) )
@ sk3 )
| ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[171]) ).
thf(317,plain,
( ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
| ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( sk2 @ ( (=) @ iS @ c0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[211,173]) ).
thf(322,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)],[317]) ).
thf(327,plain,
( ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
| ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[322]) ).
thf(524,plain,
( ( ( cJOIN @ sk3 @ sk7 @ sk3 )
!= ( c0 = sk7 ) )
| ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ),
inference(func_ext,[status(esa)],[327]) ).
thf(4248,plain,
( ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
| ~ ( cJOIN @ sk3 @ sk7 @ sk3 )
| ( c0 != sk7 ) ),
inference(bool_ext,[status(thm)],[524]) ).
thf(4308,plain,
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
| ~ ( cJOIN @ sk3 @ sk7 @ sk3 ) ),
inference(lifteq,[status(thm)],[4248]) ).
thf(4489,plain,
! [A: iS] :
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
| ( ( cJOIN @ A @ c0 @ A )
!= ( cJOIN @ sk3 @ sk7 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[30,4308]) ).
thf(4586,plain,
! [A: iS] :
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
| ( A != sk3 )
| ( sk7 != c0 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[4489]) ).
thf(4639,plain,
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ),
inference(simp,[status(thm)],[4586]) ).
thf(4657,plain,
( ( sk7 != c0 )
| ( ( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1842,4639]) ).
thf(4687,plain,
( ( sk7 != c0 )
| ( sk3 != sk3 )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( cP @ c0 @ c0 ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[4657]) ).
thf(4724,plain,
( ( sk7 != c0 )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( cP @ c0 @ c0 ) ) ),
inference(simp,[status(thm)],[4687]) ).
thf(386,plain,
( ~ ( cJOIN @ sk3 @ c0 @ sk3 )
| ( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ) ),
inference(pre_uni,[status(thm)],[343:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ sk3 @ C @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(793,plain,
( ~ $true
| ( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ) ),
inference(rewrite,[status(thm)],[386,30]) ).
thf(794,plain,
( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 ),
inference(simp,[status(thm)],[793]) ).
thf(803,plain,
( ( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[794,11]) ).
thf(814,plain,
( ( sk3 != sk3 )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= sk3 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[803]) ).
thf(821,plain,
( ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= sk3 ),
inference(simp,[status(thm)],[814]) ).
thf(1864,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(paramod_ordered,[status(thm)],[1842,104]) ).
thf(1883,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)],[1864]) ).
thf(1896,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)],[1883]) ).
thf(13227,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(paramod_ordered,[status(thm)],[13212,6527]) ).
thf(13304,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)],[13227]) ).
thf(13340,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)],[13304]) ).
thf(13349,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)],[211,13340]) ).
thf(13352,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)],[13349]) ).
thf(73,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)],[43:[bind(A,$thf( D @ c0 )),bind(B,$thf( ^ [F: iS] : ( cJOIN @ ( D @ F ) @ c0 @ ( F @ F ) ) )),bind(C,$thf( C ))]]) ).
thf(75,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)],[73:[]]) ).
thf(85,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)],[75]) ).
thf(6675,plain,
! [A: iS] :
( ( cJOIN @ c0 @ A @ 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)],[34,6527]) ).
thf(6747,plain,
! [A: iS] :
( ( ( 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 ) ) ) )
| ( A
!= ( cP
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) )
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ B @ B ) ) ) ) ),
inference(simp,[status(thm)],[6675]) ).
thf(6773,plain,
( ( cP
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
!= c0 ),
inference(simp,[status(thm)],[6747]) ).
thf(21,plain,
! [B: iS,A: iS] :
( ( sk4 @ A @ ( cP @ A @ B ) )
= B ),
introduced(tautology,[new_symbols(inverse(cP),[sk4])]) ).
thf(65,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)],[42:[bind(A,$thf( ^ [C: iS] : ( cJOIN @ C @ C @ sk3 ) )),bind(B,$thf( sk3 ))]]) ).
thf(53,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ~ ( ( B @ c0 )
| ( C @ c0 ) )
| ~ ( ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(prim_subst,[status(thm)],[18:[bind(A,$thf( ^ [E: iS] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(93,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ( B @ A )
| ( C @ A )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ c0 ) ),
inference(cnf,[status(esa)],[53]) ).
thf(97,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ( B @ A )
| ( C @ A )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ c0 ) ),
inference(simp,[status(thm)],[93]) ).
thf(15663,plain,
( ( ( cP @ c0 @ c0 )
!= ( sk2
@ ^ [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)],[111,13352]) ).
thf(15664,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)],[15663]) ).
thf(15665,plain,
( ( ( cP @ c0 @ c0 )
!= ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[15664]) ).
thf(6677,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( ( A @ B )
!= ( cJOIN
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) )
@ ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ C @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,6527]) ).
thf(6753,plain,
( ~ ( cJOIN @ c0 @ c0 @ c0 )
| ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) ) ) ),
inference(pre_uni,[status(thm)],[6677:[bind(A,$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(16523,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)],[6753,9256]) ).
thf(16524,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)],[16523]) ).
thf(16534,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(paramod_ordered,[status(thm)],[16524,6527]) ).
thf(16624,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)],[16534]) ).
thf(16652,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)],[16624]) ).
thf(587,plain,
! [B: iS > $o,A: iS] :
( ~ ~ ( B @ c0 )
| ~ ( B
@ ( sk1
@ ^ [C: iS] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[31:[bind(A,$thf( ^ [D: iS] : ~ ( C @ D ) ))]]) ).
thf(717,plain,
! [B: iS > $o,A: iS] :
( ~ ( B @ A )
| ~ ( B
@ ( sk1
@ ^ [C: iS] :
~ ( B @ C ) ) )
| ( B @ c0 ) ),
inference(cnf,[status(esa)],[587]) ).
thf(718,plain,
! [B: iS > $o,A: iS] :
( ~ ( B @ A )
| ~ ( B
@ ( sk1
@ ^ [C: iS] :
~ ( B @ C ) ) )
| ( B @ c0 ) ),
inference(simp,[status(thm)],[717]) ).
thf(1163,plain,
! [B: iS > $o,A: iS] :
( ~ ~ ( B @ A )
| ~ ~ ( B
@ ( sk1
@ ^ [C: iS] :
~ ~ ( B @ C ) ) )
| ~ ( B @ c0 ) ),
inference(prim_subst,[status(thm)],[718:[bind(A,$thf( A )),bind(B,$thf( ^ [D: iS] : ~ ( C @ D ) ))]]) ).
thf(1258,plain,
! [B: iS > $o,A: iS] :
( ~ ( B @ c0 )
| ( B
@ ( sk1
@ ^ [C: iS] :
~ ~ ( B @ C ) ) )
| ( B @ A ) ),
inference(cnf,[status(esa)],[1163]) ).
thf(1259,plain,
! [B: iS > $o,A: iS] :
( ~ ( B @ c0 )
| ( B @ ( sk1 @ B ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[1258]) ).
thf(854,plain,
! [B: iS > $o,A: iS] :
( ~ ~ ( B @ A )
| ~ ~ ( B
@ ( sk2
@ ^ [C: iS] :
~ ~ ( B @ C ) ) )
| ~ ( B @ c0 ) ),
inference(prim_subst,[status(thm)],[435:[bind(A,$thf( A )),bind(B,$thf( ^ [D: iS] : ~ ( C @ D ) ))]]) ).
thf(983,plain,
! [B: iS > $o,A: iS] :
( ~ ( B @ c0 )
| ( B
@ ( sk2
@ ^ [C: iS] :
~ ~ ( B @ C ) ) )
| ( B @ A ) ),
inference(cnf,[status(esa)],[854]) ).
thf(984,plain,
! [B: iS > $o,A: iS] :
( ~ ( B @ c0 )
| ( B @ ( sk2 @ B ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[983]) ).
thf(9278,plain,
! [B: iS > $o,A: iS] :
( ( B @ ( sk2 @ B ) )
| ( B @ A )
| ( ( cJOIN @ c0 @ c0 @ c0 )
!= ( B @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[9256,984]) ).
thf(9373,plain,
! [A: iS] :
( ( cJOIN
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ c0 @ c0 ) )
@ c0
@ c0 )
| ( cJOIN @ A @ c0 @ c0 ) ),
inference(pre_uni,[status(thm)],[9278:[bind(A,$thf( A )),bind(B,$thf( ^ [C: iS] : ( cJOIN @ C @ c0 @ c0 ) ))]]) ).
thf(15126,plain,
! [A: iS] :
( ( cJOIN
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ c0 @ c0 ) )
@ c0
@ c0 )
| ( ( cJOIN @ A @ c0 @ c0 )
!= ( cJOIN
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ B @ c0 @ c0 ) )
@ c0
@ c0 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9373]) ).
thf(15248,plain,
( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ c0 @ c0 ) )
@ c0
@ c0 ),
inference(pattern_uni,[status(thm)],[15126:[bind(A,$thf( sk2 @ ^ [B: iS] : ( cJOIN @ B @ c0 @ c0 ) ))]]) ).
thf(4516,plain,
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ sk7 @ sk3 )
| ( ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 )
!= ( cJOIN @ sk3 @ sk7 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4308]) ).
thf(4607,plain,
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ sk7 @ sk3 )
| ( sk3 != sk3 )
| ( ( cP @ c0 @ c0 )
!= sk7 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[4516]) ).
thf(4645,plain,
( ( sk7 != c0 )
| ~ ( cJOIN @ sk3 @ sk7 @ sk3 )
| ( ( cP @ c0 @ c0 )
!= sk7 ) ),
inference(simp,[status(thm)],[4607]) ).
thf(6030,plain,
! [A: iS] :
( ( sk7 != c0 )
| ( ( cP @ c0 @ c0 )
!= sk7 )
| ( ( cJOIN @ A @ c0 @ A )
!= ( cJOIN @ sk3 @ sk7 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[30,4645]) ).
thf(6077,plain,
! [A: iS] :
( ( sk7 != c0 )
| ( ( cP @ c0 @ c0 )
!= sk7 )
| ( A != sk3 )
| ( sk7 != c0 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[6030]) ).
thf(6116,plain,
( ( sk7 != c0 )
| ( ( cP @ c0 @ c0 )
!= sk7 ) ),
inference(simp,[status(thm)],[6077]) ).
thf(92,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ c0 ) ),
inference(cnf,[status(esa)],[53]) ).
thf(96,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ c0 ) ),
inference(simp,[status(thm)],[92]) ).
thf(57,plain,
! [B: iS,A: iS] :
( ( c0 != c0 )
| ( c0 = B )
| ( ( cJOIN @ A @ c0 @ A )
!= ( c0
= ( cP @ ( sk1 @ ( (=) @ iS @ c0 ) ) @ ( sk2 @ ( (=) @ iS @ c0 ) ) ) ) ) ),
inference(replace_leibeq,[status(thm)],[44:[bind(A,$thf( A )),bind(B,$thf( (=) @ iS @ c0 ))]]) ).
thf(59,plain,
! [B: iS,A: iS] :
( ( c0 != c0 )
| ( c0 = B )
| ( ( cJOIN @ A @ c0 @ A )
!= ( c0
= ( cP @ ( sk1 @ ( (=) @ iS @ c0 ) ) @ ( sk2 @ ( (=) @ iS @ c0 ) ) ) ) ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(100,plain,
! [B: iS,A: iS] :
( ( c0 = B )
| ( ( cJOIN @ A @ c0 @ A )
!= ( c0
= ( cP @ ( sk1 @ ( (=) @ iS @ c0 ) ) @ ( sk2 @ ( (=) @ iS @ c0 ) ) ) ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(13603,plain,
! [B: iS,A: iS] :
( ( c0 = B )
| ( ( cJOIN @ A @ c0 @ A )
!= ( c0
= ( cP @ c0 @ c0 ) ) ) ),
inference(rewrite,[status(thm)],[100,211,111]) ).
thf(13606,plain,
! [B: iS,A: iS] :
( ( ( cJOIN @ A @ c0 @ A )
!= ( c0
= ( cP @ c0 @ c0 ) ) )
| ( B
!= ( cP
@ ( sk1
@ ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) )
@ ( sk2
@ ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13603,785]) ).
thf(13607,plain,
! [A: iS] :
( ( cJOIN @ A @ c0 @ A )
!= ( c0
= ( cP @ c0 @ c0 ) ) ),
inference(pattern_uni,[status(thm)],[13606:[bind(A,$thf( A )),bind(B,$thf( cP @ ( sk1 @ ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) ) @ ( sk2 @ ^ [C: iS] : ( cJOIN @ C @ sk3 @ sk3 ) ) ))]]) ).
thf(9258,plain,
! [B: iS > $o,A: iS] :
( ( B @ ( sk1 @ B ) )
| ( B @ A )
| ( ( cJOIN @ c0 @ c0 @ c0 )
!= ( B @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[9256,1259]) ).
thf(9408,plain,
! [A: iS] :
( ( cJOIN @ c0
@ ( sk1
@ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
@ c0 )
| ( cJOIN @ c0 @ A @ c0 ) ),
inference(pre_uni,[status(thm)],[9258:[bind(A,$thf( A )),bind(B,$thf( ^ [C: iS] : ( cJOIN @ c0 @ C @ c0 ) ))]]) ).
thf(15991,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 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9408]) ).
thf(16115,plain,
( cJOIN @ c0
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ c0 @ A @ c0 ) )
@ c0 ),
inference(pattern_uni,[status(thm)],[15991:[bind(A,$thf( sk1 @ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) ))]]) ).
thf(1845,plain,
( ( cJOIN @ sk3
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[1842,11]) ).
thf(1882,plain,
( ( sk3 != sk3 )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= sk3 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[1845]) ).
thf(1895,plain,
( ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= sk3 ),
inference(simp,[status(thm)],[1882]) ).
thf(13261,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(paramod_ordered,[status(thm)],[13212,11]) ).
thf(13319,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)],[13261]) ).
thf(13326,plain,
( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= sk3 ),
inference(simp,[status(thm)],[13319]) ).
thf(804,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(paramod_ordered,[status(thm)],[794,104]) ).
thf(812,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)],[804]) ).
thf(819,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)],[812]) ).
thf(1091,plain,
( ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[1087,11]) ).
thf(1112,plain,
( ( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
!= sk3 )
| ( sk3 != sk3 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[1091]) ).
thf(1124,plain,
( ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
!= sk3 ),
inference(simp,[status(thm)],[1112]) ).
thf(13,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(cnf,[status(esa)],[4]) ).
thf(27,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)],[13]) ).
thf(45,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ B )
| ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( A @ c0 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[18]) ).
thf(70,plain,
! [B: iS,A: iS > $o] :
( ~ ( A @ c0 )
| ( A @ B )
| ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( A @ c0 ) ) ),
inference(pre_uni,[status(thm)],[45:[]]) ).
thf(71,plain,
! [B: iS,A: iS > $o] :
( ( A @ B )
| ~ ( A @ c0 )
| ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( A @ c0 ) ) ),
inference(pre_uni,[status(thm)],[70:[]]) ).
thf(1161,plain,
! [B: iS > $o,A: iS] :
( ~ ( B @ A )
| ( B @ c0 )
| ~ ( B
@ ( sk1
@ ^ [C: iS] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(eqfactor_ordered,[status(thm)],[718]) ).
thf(1173,plain,
! [A: iS] :
( ( A != A )
| ( A = c0 )
| ( A
!= ( sk1
@ ^ [B: iS] : ( A != B ) ) )
| ( A != A ) ),
inference(replace_leibeq,[status(thm)],[1161:[bind(A,$thf( A )),bind(B,$thf( (=) @ iS @ A ))]]) ).
thf(1188,plain,
! [A: iS] :
( ( A != A )
| ( A = c0 )
| ( A
!= ( sk1
@ ^ [B: iS] : ( A != B ) ) )
| ( A != A ) ),
inference(lifteq,[status(thm)],[1173]) ).
thf(1271,plain,
! [A: iS] :
( ( A = c0 )
| ( A
!= ( sk1
@ ^ [B: iS] : ( A != B ) ) ) ),
inference(simp,[status(thm)],[1188]) ).
thf(16589,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)],[111,16524]) ).
thf(16632,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)],[16589]) ).
thf(1863,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(paramod_ordered,[status(thm)],[1842,327]) ).
thf(1879,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)],[1863]) ).
thf(1894,plain,
( ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) )
| ( ( sk1
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( cP @ c0 @ c0 ) ) ),
inference(simp,[status(thm)],[1879]) ).
thf(13234,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)],[211,13212]) ).
thf(13303,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)],[13234]) ).
thf(13375,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)],[211,13303]) ).
thf(13455,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)],[13375]) ).
thf(13467,plain,
( ( cJOIN @ c0
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[13455]) ).
thf(13376,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)],[211,13303]) ).
thf(13450,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)],[13376]) ).
thf(13464,plain,
( ( cJOIN
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
@ c0
@ c0 )
| ( ( ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= ( (=) @ iS @ c0 ) ) ),
inference(simp,[status(thm)],[13450]) ).
thf(37,plain,
! [A: iS] :
( ( cJOIN @ A @ c0 @ A )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[30,11]) ).
thf(38,plain,
! [A: iS] :
( ( A != sk3 )
| ( sk3 != c0 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[37]) ).
thf(39,plain,
sk3 != c0,
inference(simp,[status(thm)],[38]) ).
thf(94,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ( B @ A )
| ( C @ A )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ c0 ) ),
inference(cnf,[status(esa)],[53]) ).
thf(98,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ( B @ A )
| ( C @ A )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ c0 ) ),
inference(simp,[status(thm)],[94]) ).
thf(9372,plain,
! [A: iS] :
( ( cJOIN @ c0
@ ( sk2
@ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) )
@ c0 )
| ( cJOIN @ c0 @ A @ c0 ) ),
inference(pre_uni,[status(thm)],[9278:[bind(A,$thf( A )),bind(B,$thf( ^ [C: iS] : ( cJOIN @ c0 @ C @ c0 ) ))]]) ).
thf(11978,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 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9372]) ).
thf(12135,plain,
( cJOIN @ c0
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ c0 @ A @ c0 ) )
@ c0 ),
inference(pattern_uni,[status(thm)],[11978:[bind(A,$thf( sk2 @ ^ [B: iS] : ( cJOIN @ c0 @ B @ c0 ) ))]]) ).
thf(807,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(paramod_ordered,[status(thm)],[794,327]) ).
thf(815,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)],[807]) ).
thf(823,plain,
( ( ( ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( (=) @ iS @ c0 ) )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( cP @ c0 @ c0 ) ) ),
inference(simp,[status(thm)],[815]) ).
thf(14905,plain,
! [B: iS,A: iS] :
( ( c0
!= ( cP @ c0 @ c0 ) )
| ( ( cJOIN @ c0 @ A @ A )
!= ( cJOIN @ B @ c0 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[34,13607]) ).
thf(14906,plain,
( c0
!= ( cP @ c0 @ c0 ) ),
inference(pattern_uni,[status(thm)],[14905:[bind(A,$thf( c0 )),bind(B,$thf( c0 ))]]) ).
thf(14934,plain,
( ( cP @ c0 @ c0 )
!= c0 ),
inference(lifteq,[status(thm)],[14906]) ).
thf(91,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ c0 ) ),
inference(cnf,[status(esa)],[53]) ).
thf(95,plain,
! [C: iS > $o,B: iS > $o,A: iS] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: iS] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ c0 ) ),
inference(simp,[status(thm)],[91]) ).
thf(4419,plain,
( ( cJOIN
@ ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
@ sk3
@ sk3 )
!= ( cJOIN @ sk3 @ sk3 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[4388,11]) ).
thf(4445,plain,
( ( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
!= sk3 )
| ( sk3 != sk3 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[4419]) ).
thf(4469,plain,
( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ sk3 @ sk3 ) )
!= sk3 ),
inference(simp,[status(thm)],[4445]) ).
thf(48,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)],[18]) ).
thf(72,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)],[48]) ).
thf(1088,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(paramod_ordered,[status(thm)],[1087,760]) ).
thf(1115,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)],[1088]) ).
thf(1126,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)],[1115]) ).
thf(4660,plain,
( ( sk7 != c0 )
| ( ( cJOIN @ sk3
@ ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
@ sk3 )
!= ( cJOIN @ sk3 @ ( cP @ c0 @ c0 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[794,4639]) ).
thf(4685,plain,
( ( sk7 != c0 )
| ( sk3 != sk3 )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( cP @ c0 @ c0 ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[4660]) ).
thf(4723,plain,
( ( sk7 != c0 )
| ( ( sk2
@ ^ [A: iS] : ( cJOIN @ sk3 @ A @ sk3 ) )
!= ( cP @ c0 @ c0 ) ) ),
inference(simp,[status(thm)],[4685]) ).
thf(50,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)],[18:[bind(A,$thf( ^ [F: iS] : ( cJOIN @ ( C @ F ) @ ( D @ F ) @ ( E @ F ) ) ))]]) ).
thf(90,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)],[50]) ).
thf(16575,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(paramod_ordered,[status(thm)],[16524,11]) ).
thf(16634,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)],[16575]) ).
thf(16659,plain,
( ( sk1
@ ^ [A: iS] : ( cJOIN @ A @ A @ A ) )
!= sk3 ),
inference(simp,[status(thm)],[16634]) ).
thf(13350,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)],[111,13340]) ).
thf(13353,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)],[13350]) ).
thf(21443,plain,
$false,
inference(cvc4,[status(thm)],[785,31,30,79,69,760,6819,6527,88,994,13212,24,25,1087,20,4471,78,211,4724,821,1896,89,13352,85,6773,21,65,435,97,15665,16652,1259,15248,109,6116,96,1842,16524,13607,13340,984,173,16115,1895,794,9256,13326,718,13603,34,819,1124,27,71,1271,86,16632,1894,13467,13464,39,98,4388,12135,3,823,14934,18,95,327,4469,11,72,4639,524,1126,104,13303,26,23,4723,90,111,16659,13353]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV190^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 18:49:54 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.94/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.13/0.97 % [INFO] Parsing done (106ms).
% 1.13/0.98 % [INFO] Running in sequential loop mode.
% 1.62/1.19 % [INFO] eprover registered as external prover.
% 1.62/1.19 % [INFO] cvc4 registered as external prover.
% 1.62/1.20 % [INFO] Scanning for conjecture ...
% 1.96/1.27 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.96/1.29 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.96/1.29 % [INFO] Problem is higher-order (TPTP THF).
% 1.96/1.30 % [INFO] Type checking passed.
% 1.96/1.30 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 111.61/22.24 % External prover 'cvc4' found a proof!
% 111.61/22.24 % [INFO] Killing All external provers ...
% 111.61/22.24 % Time passed: 21720ms (effective reasoning time: 21257ms)
% 111.61/22.24 % 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)>
% 111.61/22.25 % Axioms used in derivation (0):
% 111.61/22.25 % No. of inferences in proof: 259
% 111.61/22.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21720 ms resp. 21257 ms w/o parsing
% 112.05/22.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 112.05/22.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------