%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU678^2 : TPTP v9.3.1. Released v3.7.0.
% 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 08:29:00 AM UTC 2026
% Result : Theorem 28.15s 9.68s
% Output : Refutation 29.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 15
% Syntax : Number of formulae : 143 ( 19 unt; 0 typ; 14 def)
% Number of atoms : 839 ( 406 equ; 142 cnn)
% Maximal formula atoms : 34 ( 5 avg)
% Number of connectives : 3345 ( 325 ~; 302 |; 24 &;2640 @)
% ( 0 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 11 con; 0-3 aty)
% Number of variables : 400 ( 184 ^; 203 !; 7 ?; 400 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(dsetconstr_decl,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(kpair_decl,type,
kpair: $i > $i > $i ).
thf(cartprod_decl,type,
cartprod: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $o ).
thf(ex1_decl,type,
ex1: $i > ( $i > $o ) > $o ).
thf(ex1I_decl,type,
ex1I: $o ).
thf(breln_decl,type,
breln: $i > $i > $i > $o ).
thf(dpsetconstr_decl,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(dpsetconstrI_decl,type,
dpsetconstrI: $o ).
thf(setOfPairsIsBReln_decl,type,
setOfPairsIsBReln: $o ).
thf(dpsetconstrERa_decl,type,
dpsetconstrERa: $o ).
thf(func_decl,type,
func: $i > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i > ( $i > $o ) > $i > $i ).
thf(sk2_decl,type,
sk2: $i > ( $i > $o ) > $i > $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(singleton_def,definition,
( singleton
= ( ^ [A: $i] :
? [B: $i] :
( ( in @ B @ A )
& ( A
= ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(ex1_def,definition,
( ex1
= ( ^ [A: $i,B: $i > $o] : ( singleton @ ( dsetconstr @ A @ B ) ) ) ) ).
thf(ex1I_def,definition,
( ex1I
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( ! [D: $i] :
( ( in @ D @ A )
=> ( ( B @ D )
=> ( D = C ) ) )
=> ( ex1 @ A @ B ) ) ) ) ) ) ).
thf(breln_def,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf(dpsetconstrI_def,definition,
( dpsetconstrI
= ( ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( C @ D @ E )
=> ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) ) ) ) ) ) ) ).
thf(setOfPairsIsBReln_def,definition,
( setOfPairsIsBReln
= ( ! [A: $i,B: $i,C: $i > $i > $o] : ( breln @ A @ B @ ( dpsetconstr @ A @ B @ C ) ) ) ) ).
thf(dpsetconstrERa_def,definition,
( dpsetconstrERa
= ( ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) )
=> ( C @ D @ E ) ) ) ) ) ) ).
thf(func_def,definition,
( func
= ( ^ [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
& ! [D: $i] :
( ( in @ D @ A )
=> ( ex1 @ B
@ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i,B: $i > $o,C: $i] :
@+[D: $i] :
~ ( ( in @ D @ C )
=> ( ( B @ D )
=> ( D = A ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i > $o,C: $i] :
@+[D: $i] :
( ( in @ D @ ( dsetconstr @ C @ B ) )
& ( ( dsetconstr @ C @ B )
= ( setadjoin @ D @ emptyset ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i,C: $i > $i] :
( ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( C @ D ) @ B ) )
=> ( ( subset
@ ( dpsetconstr @ A @ B
@ ^ [D: $i] : ( (=) @ $i @ ( C @ D ) ) )
@ ( cartprod @ A @ B ) )
& ! [D: $i] :
( ( in @ D @ A )
=> ? [E: $i] :
( ( in @ E
@ ( dsetconstr @ B
@ ^ [F: $i] :
( in @ ( kpair @ D @ F )
@ ( dpsetconstr @ A @ B
@ ^ [G: $i] : ( (=) @ $i @ ( C @ G ) ) ) ) ) )
& ( ( dsetconstr @ B
@ ^ [F: $i] :
( in @ ( kpair @ D @ F )
@ ( dpsetconstr @ A @ B
@ ^ [G: $i] : ( (=) @ $i @ ( C @ G ) ) ) ) )
= ( setadjoin @ E @ emptyset ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ! [B: $i > $i] :
( ! [C: $i] :
( ( in @ C @ sk3 )
=> ( in @ ( B @ C ) @ A ) )
=> ( ( subset
@ ( dpsetconstr @ sk3 @ A
@ ^ [C: $i] : ( (=) @ $i @ ( B @ C ) ) )
@ ( cartprod @ sk3 @ A ) )
& ! [C: $i] :
( ( in @ C @ sk3 )
=> ? [D: $i] :
( ( in @ D
@ ( dsetconstr @ A
@ ^ [E: $i] :
( in @ ( kpair @ C @ E )
@ ( dpsetconstr @ sk3 @ A
@ ^ [F: $i] : ( (=) @ $i @ ( B @ F ) ) ) ) ) )
& ( ( dsetconstr @ A
@ ^ [E: $i] :
( in @ ( kpair @ C @ E )
@ ( dpsetconstr @ sk3 @ A
@ ^ [F: $i] : ( (=) @ $i @ ( B @ F ) ) ) ) )
= ( setadjoin @ D @ emptyset ) ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i > $i] :
~ ( ! [B: $i] :
( ( in @ B @ sk3 )
=> ( in @ ( A @ B ) @ sk4 ) )
=> ( ( subset
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( A @ B ) ) )
@ ( cartprod @ sk3 @ sk4 ) )
& ! [B: $i] :
( ( in @ B @ sk3 )
=> ? [C: $i] :
( ( in @ C
@ ( dsetconstr @ sk4
@ ^ [D: $i] :
( in @ ( kpair @ B @ D )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [E: $i] : ( (=) @ $i @ ( A @ E ) ) ) ) ) )
& ( ( dsetconstr @ sk4
@ ^ [D: $i] :
( in @ ( kpair @ B @ D )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [E: $i] : ( (=) @ $i @ ( A @ E ) ) ) ) )
= ( setadjoin @ C @ emptyset ) ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( in @ A @ sk3 )
=> ? [B: $i] :
( ( in @ B
@ ( dsetconstr @ sk4
@ ^ [C: $i] :
( in @ ( kpair @ A @ C )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [D: $i] : ( (=) @ $i @ ( sk5 @ D ) ) ) ) ) )
& ( ( dsetconstr @ sk4
@ ^ [C: $i] :
( in @ ( kpair @ A @ C )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [D: $i] : ( (=) @ $i @ ( sk5 @ D ) ) ) ) )
= ( setadjoin @ B @ emptyset ) ) ) ) ) ) ).
thf(1,conjecture,
( ex1I
=> ( dpsetconstrI
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ! [A: $i,B: $i,C: $i > $i] :
( ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( C @ D ) @ B ) )
=> ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [D: $i] : ( (=) @ $i @ ( C @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(2,negated_conjecture,
~ ( ex1I
=> ( dpsetconstrI
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ! [A: $i,B: $i,C: $i > $i] :
( ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( C @ D ) @ B ) )
=> ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [D: $i] : ( (=) @ $i @ ( C @ D ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( ! [D: $i] :
( ( in @ D @ A )
=> ( ( B @ D )
=> ( D = C ) ) )
=> ? [D: $i] :
( ( in @ D @ ( dsetconstr @ A @ B ) )
& ( ( dsetconstr @ A @ B )
= ( setadjoin @ D @ emptyset ) ) ) ) ) )
=> ( ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( C @ D @ E )
=> ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) ) ) ) )
=> ( ! [A: $i,B: $i,C: $i > $i > $o] : ( subset @ ( dpsetconstr @ A @ B @ C ) @ ( cartprod @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) )
=> ( C @ D @ E ) ) ) )
=> ! [A: $i,B: $i,C: $i > $i] :
( ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( C @ D ) @ B ) )
=> ( ( subset
@ ( dpsetconstr @ A @ B
@ ^ [D: $i] : ( (=) @ $i @ ( C @ D ) ) )
@ ( cartprod @ A @ B ) )
& ! [D: $i] :
( ( in @ D @ A )
=> ? [E: $i] :
( ( in @ E
@ ( dsetconstr @ B
@ ^ [F: $i] :
( in @ ( kpair @ D @ F )
@ ( dpsetconstr @ A @ B
@ ^ [G: $i] : ( (=) @ $i @ ( C @ G ) ) ) ) ) )
& ( ( dsetconstr @ B
@ ^ [F: $i] :
( in @ ( kpair @ D @ F )
@ ( dpsetconstr @ A @ B
@ ^ [G: $i] : ( (=) @ $i @ ( C @ G ) ) ) ) )
= ( setadjoin @ E @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [R: $i,Q: $i,P: $i,O: $i,N: $i > $i > $o,M: $i,L: $i,K: $i > $i > $o,J: $i,I: $i,H: $i,G: $i,F: $i > $i > $o,E: $i,D: $i,C: $i,B: $i > $o,A: $i] :
( ( ~ ( in @ C @ A )
| ~ ( B @ C )
| ( in @ ( sk1 @ C @ B @ A ) @ A )
| ( in @ ( sk2 @ C @ B @ A ) @ ( dsetconstr @ A @ B ) ) )
& ( ~ ( in @ C @ A )
| ~ ( B @ C )
| ( in @ ( sk1 @ C @ B @ A ) @ A )
| ( ( dsetconstr @ A @ B )
= ( setadjoin @ ( sk2 @ C @ B @ A ) @ emptyset ) ) )
& ( ~ ( in @ C @ A )
| ~ ( B @ C )
| ( B @ ( sk1 @ C @ B @ A ) )
| ( in @ ( sk2 @ C @ B @ A ) @ ( dsetconstr @ A @ B ) ) )
& ( ~ ( in @ C @ A )
| ~ ( B @ C )
| ( B @ ( sk1 @ C @ B @ A ) )
| ( ( dsetconstr @ A @ B )
= ( setadjoin @ ( sk2 @ C @ B @ A ) @ emptyset ) ) )
& ( ~ ( in @ C @ A )
| ~ ( B @ C )
| ( ( sk1 @ C @ B @ A )
!= C )
| ( in @ ( sk2 @ C @ B @ A ) @ ( dsetconstr @ A @ B ) ) )
& ( ~ ( in @ C @ A )
| ~ ( B @ C )
| ( ( sk1 @ C @ B @ A )
!= C )
| ( ( dsetconstr @ A @ B )
= ( setadjoin @ ( sk2 @ C @ B @ A ) @ emptyset ) ) )
& ( ~ ( in @ G @ D )
| ~ ( in @ H @ E )
| ~ ( F @ G @ H )
| ( in @ ( kpair @ G @ H ) @ ( dpsetconstr @ D @ E @ F ) ) )
& ( subset @ ( dpsetconstr @ I @ J @ K ) @ ( cartprod @ I @ J ) )
& ( ~ ( in @ O @ L )
| ~ ( in @ P @ M )
| ~ ( in @ ( kpair @ O @ P ) @ ( dpsetconstr @ L @ M @ N ) )
| ( N @ O @ P ) )
& ( ~ ( in @ Q @ sk3 )
| ( in @ ( sk5 @ Q ) @ sk4 ) )
& ( ~ ( subset
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [S: $i] : ( (=) @ $i @ ( sk5 @ S ) ) )
@ ( cartprod @ sk3 @ sk4 ) )
| ( in @ sk6 @ sk3 ) )
& ( ~ ( subset
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [S: $i] : ( (=) @ $i @ ( sk5 @ S ) ) )
@ ( cartprod @ sk3 @ sk4 ) )
| ~ ( in @ R
@ ( dsetconstr @ sk4
@ ^ [S: $i] :
( in @ ( kpair @ sk6 @ S )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [T: $i] : ( (=) @ $i @ ( sk5 @ T ) ) ) ) ) )
| ( ( dsetconstr @ sk4
@ ^ [S: $i] :
( in @ ( kpair @ sk6 @ S )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [T: $i] : ( (=) @ $i @ ( sk5 @ T ) ) ) ) )
!= ( setadjoin @ R @ emptyset ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
( ~ ( subset
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [A: $i] : ( (=) @ $i @ ( sk5 @ A ) ) )
@ ( cartprod @ sk3 @ sk4 ) )
| ( in @ sk6 @ sk3 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
! [C: $i > $i > $o,B: $i,A: $i] : ( subset @ ( dpsetconstr @ A @ B @ C ) @ ( cartprod @ A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(21,plain,
! [C: $i > $i > $o,B: $i,A: $i] : ( subset @ ( dpsetconstr @ A @ B @ C ) @ ( cartprod @ A @ B ) ),
inference(simp,[status(thm)],[6]) ).
thf(37,plain,
( ~ $true
| ( in @ sk6 @ sk3 ) ),
inference(rewrite,[status(thm)],[14,21]) ).
thf(38,plain,
in @ sk6 @ sk3,
inference(simp,[status(thm)],[37]) ).
thf(16,plain,
! [A: $i] :
( ~ ( in @ A @ sk3 )
| ( in @ ( sk5 @ A ) @ sk4 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(29,plain,
! [A: $i] :
( ~ ( in @ A @ sk3 )
| ( in @ ( sk5 @ A ) @ sk4 ) ),
inference(simp,[status(thm)],[16]) ).
thf(39,plain,
! [A: $i] :
( ~ $true
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ sk6 @ sk3 )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[38,29]) ).
thf(40,plain,
! [A: $i] :
( ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ sk6 @ sk3 )
!= ( in @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(41,plain,
in @ ( sk5 @ sk6 ) @ sk4,
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( sk6 ))]]) ).
thf(42,plain,
! [A: $i] :
( ~ $true
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk5 @ sk6 ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[41,29]) ).
thf(43,plain,
! [A: $i] :
( ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk5 @ sk6 ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(44,plain,
! [A: $i] :
( ( in @ ( sk5 @ A ) @ sk4 )
| ( ( sk5 @ sk6 )
!= A )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[43]) ).
thf(45,plain,
( ( in @ ( sk5 @ ( sk5 @ sk6 ) ) @ sk4 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[44]) ).
thf(85,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ~ $true
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ sk6 ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[45,29]) ).
thf(86,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ sk6 ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(89,plain,
! [A: $i] :
( ( in @ ( sk5 @ A ) @ sk4 )
| ( sk4 != sk3 )
| ( ( sk5 @ ( sk5 @ sk6 ) )
!= A )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[86]) ).
thf(91,plain,
( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) @ sk4 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[89]) ).
thf(96,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ~ $true
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[91,29]) ).
thf(97,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(100,plain,
! [A: $i] :
( ( in @ ( sk5 @ A ) @ sk4 )
| ( sk4 != sk3 )
| ( ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) )
!= A )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[97]) ).
thf(102,plain,
( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) @ sk4 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[100]) ).
thf(305,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ~ $true
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[102,29]) ).
thf(306,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[305]) ).
thf(321,plain,
! [A: $i] :
( ( in @ ( sk5 @ A ) @ sk4 )
| ( sk4 != sk3 )
| ( ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) )
!= A )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[306]) ).
thf(323,plain,
( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) @ sk4 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[321]) ).
thf(329,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ~ $true
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[323,29]) ).
thf(330,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[329]) ).
thf(344,plain,
! [A: $i] :
( ( in @ ( sk5 @ A ) @ sk4 )
| ( sk4 != sk3 )
| ( ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) )
!= A )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[330]) ).
thf(347,plain,
( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) @ sk4 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[344]) ).
thf(353,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ~ $true
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[347,29]) ).
thf(354,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[353]) ).
thf(369,plain,
! [A: $i] :
( ( in @ ( sk5 @ A ) @ sk4 )
| ( sk4 != sk3 )
| ( ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) )
!= A )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[354]) ).
thf(370,plain,
( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) @ sk4 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[369]) ).
thf(377,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ~ $true
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[370,29]) ).
thf(378,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[377]) ).
thf(389,plain,
! [A: $i] :
( ( in @ ( sk5 @ A ) @ sk4 )
| ( sk4 != sk3 )
| ( ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) )
!= A )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[378]) ).
thf(396,plain,
( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) ) @ sk4 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[389]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ~ $true
| ( in @ ( sk5 @ B ) @ sk4 )
| ( ( in @ ( sk5 @ A ) @ sk4 )
!= ( in @ B @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[29,29]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ( in @ ( sk5 @ B ) @ sk4 )
| ( ( in @ ( sk5 @ A ) @ sk4 )
!= ( in @ B @ sk3 ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( in @ ( sk5 @ B ) @ sk4 )
| ~ ( in @ A @ sk3 )
| ( ( sk5 @ A )
!= B )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[34]) ).
thf(36,plain,
! [A: $i] :
( ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
| ~ ( in @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[35]) ).
thf(521,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
| ~ $true
| ( sk4 != sk3 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[396,36]) ).
thf(522,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[521]) ).
thf(527,plain,
! [A: $i] :
( ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
| ( sk4 != sk3 )
| ( ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) )
!= A )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[522]) ).
thf(538,plain,
( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) ) ) ) @ sk4 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[527]) ).
thf(11,plain,
! [A: $i] :
( ~ ( subset
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) )
@ ( cartprod @ sk3 @ sk4 ) )
| ~ ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(30,plain,
! [A: $i] :
( ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ ( subset
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) )
@ ( cartprod @ sk3 @ sk4 ) )
| ~ ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(31,plain,
! [A: $i] :
( ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ ( subset
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) )
@ ( cartprod @ sk3 @ sk4 ) )
| ~ ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(46,plain,
! [A: $i] :
( ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ $true
| ~ ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[31,21]) ).
thf(47,plain,
! [A: $i] :
( ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(52,plain,
! [A: $i] :
( ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ $true
| ( ( in @ sk6 @ sk3 )
!= ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[38,47]) ).
thf(53,plain,
! [A: $i] :
( ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( in @ sk6 @ sk3 )
!= ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(56,plain,
! [A: $i] :
( ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ( sk6 != A )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= sk3 ) ),
inference(simp,[status(thm)],[53]) ).
thf(59,plain,
( ( ( dsetconstr @ sk4
@ ^ [A: $i] :
( in @ ( kpair @ sk6 @ A )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) ) ) )
!= ( setadjoin @ sk6 @ emptyset ) )
| ( ( dsetconstr @ sk4
@ ^ [A: $i] :
( in @ ( kpair @ sk6 @ A )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) ) ) )
!= sk3 ) ),
inference(simp,[status(thm)],[56]) ).
thf(12,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ A )
| ~ ( B @ C )
| ( B @ ( sk1 @ C @ B @ A ) )
| ( in @ ( sk2 @ C @ B @ A ) @ ( dsetconstr @ A @ B ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(50,plain,
! [A: $i] :
( ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ $true
| ( ( in @ ( sk5 @ sk6 ) @ sk4 )
!= ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,47]) ).
thf(51,plain,
! [A: $i] :
( ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( in @ ( sk5 @ sk6 ) @ sk4 )
!= ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(55,plain,
! [A: $i] :
( ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( sk5 @ sk6 )
!= A )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= sk4 ) ),
inference(simp,[status(thm)],[51]) ).
thf(58,plain,
( ( ( dsetconstr @ sk4
@ ^ [A: $i] :
( in @ ( kpair @ sk6 @ A )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) ) ) )
!= ( setadjoin @ ( sk5 @ sk6 ) @ emptyset ) )
| ( ( dsetconstr @ sk4
@ ^ [A: $i] :
( in @ ( kpair @ sk6 @ A )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) ) ) )
!= sk4 ) ),
inference(simp,[status(thm)],[55]) ).
thf(312,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ $true
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) @ sk4 )
!= ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[102,47]) ).
thf(313,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) @ sk4 )
!= ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(320,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) )
!= A )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= sk4 ) ),
inference(simp,[status(thm)],[313]) ).
thf(322,plain,
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [A: $i] :
( in @ ( kpair @ sk6 @ A )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) ) ) )
!= ( setadjoin @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) @ emptyset ) )
| ( ( dsetconstr @ sk4
@ ^ [A: $i] :
( in @ ( kpair @ sk6 @ A )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) ) ) )
!= sk4 ) ),
inference(simp,[status(thm)],[320]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( B != B )
| ( B
= ( sk1 @ B @ ( (=) @ $i @ B ) @ A ) )
| ( in @ ( sk2 @ B @ ( (=) @ $i @ B ) @ A ) @ ( dsetconstr @ A @ ( (=) @ $i @ B ) ) ) ),
inference(replace_leibeq,[status(thm)],[12:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ C ))]]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B != B )
| ( ( sk1 @ B @ ( (=) @ $i @ B ) @ A )
= B )
| ~ ( in @ B @ A )
| ( in @ ( sk2 @ B @ ( (=) @ $i @ B ) @ A ) @ ( dsetconstr @ A @ ( (=) @ $i @ B ) ) ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ B @ ( (=) @ $i @ B ) @ A )
= B )
| ~ ( in @ B @ A )
| ( in @ ( sk2 @ B @ ( (=) @ $i @ B ) @ A ) @ ( dsetconstr @ A @ ( (=) @ $i @ B ) ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ B @ ( (=) @ $i @ B ) @ A )
= B )
| ~ $true
| ( in @ ( sk2 @ B @ ( (=) @ $i @ B ) @ A ) @ ( dsetconstr @ A @ ( (=) @ $i @ B ) ) )
| ( ( in @ sk6 @ sk3 )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[38,25]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ B @ ( (=) @ $i @ B ) @ A )
= B )
| ( in @ ( sk2 @ B @ ( (=) @ $i @ B ) @ A ) @ ( dsetconstr @ A @ ( (=) @ $i @ B ) ) )
| ( ( in @ sk6 @ sk3 )
!= ( in @ B @ A ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(75,plain,
( ( ( sk1 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 )
= sk6 )
| ( in @ ( sk2 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 ) @ ( dsetconstr @ sk3 @ ( (=) @ $i @ sk6 ) ) ) ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( sk3 )),bind(B,$thf( sk6 ))]]) ).
thf(10,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ A )
| ~ ( B @ C )
| ( ( sk1 @ C @ B @ A )
!= C )
| ( in @ ( sk2 @ C @ B @ A ) @ ( dsetconstr @ A @ B ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(20,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( ( sk1 @ C @ B @ A )
!= C )
| ~ ( in @ C @ A )
| ~ ( B @ C )
| ( in @ ( sk2 @ C @ B @ A ) @ ( dsetconstr @ A @ B ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(1663,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( in @ ( sk2 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 ) @ ( dsetconstr @ sk3 @ ( (=) @ $i @ sk6 ) ) )
| ( sk6 != C )
| ~ ( in @ C @ A )
| ~ ( B @ C )
| ( in @ ( sk2 @ C @ B @ A ) @ ( dsetconstr @ A @ B ) )
| ( ( sk1 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 )
!= ( sk1 @ C @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[75,20]) ).
thf(1664,plain,
( ( in @ ( sk2 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 ) @ ( dsetconstr @ sk3 @ ( (=) @ $i @ sk6 ) ) )
| ( sk6 != sk6 )
| ~ ( in @ sk6 @ sk3 )
| ( sk6 != sk6 )
| ( in @ ( sk2 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 ) @ ( dsetconstr @ sk3 @ ( (=) @ $i @ sk6 ) ) ) ),
inference(pattern_uni,[status(thm)],[1663:[bind(A,$thf( sk3 )),bind(B,$thf( (=) @ $i @ sk6 )),bind(C,$thf( sk6 ))]]) ).
thf(1721,plain,
( ( sk6 != sk6 )
| ( in @ ( sk2 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 ) @ ( dsetconstr @ sk3 @ ( (=) @ $i @ sk6 ) ) )
| ( sk6 != sk6 )
| ~ ( in @ sk6 @ sk3 )
| ( in @ ( sk2 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 ) @ ( dsetconstr @ sk3 @ ( (=) @ $i @ sk6 ) ) ) ),
inference(lifteq,[status(thm)],[1664]) ).
thf(1864,plain,
( ( in @ ( sk2 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 ) @ ( dsetconstr @ sk3 @ ( (=) @ $i @ sk6 ) ) )
| ~ ( in @ sk6 @ sk3 ) ),
inference(simp,[status(thm)],[1721]) ).
thf(1903,plain,
( ( in @ ( sk2 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 ) @ ( dsetconstr @ sk3 @ ( (=) @ $i @ sk6 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1864,38]) ).
thf(1904,plain,
in @ ( sk2 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 ) @ ( dsetconstr @ sk3 @ ( (=) @ $i @ sk6 ) ),
inference(simp,[status(thm)],[1903]) ).
thf(435,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ( in @ ( sk5 @ ( sk5 @ B ) ) @ sk4 )
| ~ $true
| ( sk4 != sk3 )
| ( ( in @ ( sk5 @ A ) @ sk4 )
!= ( in @ B @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[29,36]) ).
thf(436,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ( in @ ( sk5 @ ( sk5 @ B ) ) @ sk4 )
| ( sk4 != sk3 )
| ( ( in @ ( sk5 @ A ) @ sk4 )
!= ( in @ B @ sk3 ) ) ),
inference(simp,[status(thm)],[435]) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( in @ ( sk5 @ ( sk5 @ B ) ) @ sk4 )
| ~ ( in @ A @ sk3 )
| ( sk4 != sk3 )
| ( ( sk5 @ A )
!= B )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[436]) ).
thf(492,plain,
! [A: $i] :
( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ A ) ) ) @ sk4 )
| ~ ( in @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[471]) ).
thf(336,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ $true
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) @ sk4 )
!= ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[323,47]) ).
thf(337,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) @ sk4 )
!= ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[336]) ).
thf(345,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) )
!= A )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= sk4 ) ),
inference(simp,[status(thm)],[337]) ).
thf(348,plain,
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [A: $i] :
( in @ ( kpair @ sk6 @ A )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) ) ) )
!= ( setadjoin @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) @ emptyset ) )
| ( ( dsetconstr @ sk4
@ ^ [A: $i] :
( in @ ( kpair @ sk6 @ A )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) ) ) )
!= sk4 ) ),
inference(simp,[status(thm)],[345]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ B @ ( (=) @ $i @ B ) @ A )
= B )
| ~ $true
| ( in @ ( sk2 @ B @ ( (=) @ $i @ B ) @ A ) @ ( dsetconstr @ A @ ( (=) @ $i @ B ) ) )
| ( ( in @ ( sk5 @ sk6 ) @ sk4 )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,25]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ B @ ( (=) @ $i @ B ) @ A )
= B )
| ( in @ ( sk2 @ B @ ( (=) @ $i @ B ) @ A ) @ ( dsetconstr @ A @ ( (=) @ $i @ B ) ) )
| ( ( in @ ( sk5 @ sk6 ) @ sk4 )
!= ( in @ B @ A ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(70,plain,
( ( ( sk1 @ ( sk5 @ sk6 ) @ ( (=) @ $i @ ( sk5 @ sk6 ) ) @ sk4 )
= ( sk5 @ sk6 ) )
| ( in @ ( sk2 @ ( sk5 @ sk6 ) @ ( (=) @ $i @ ( sk5 @ sk6 ) ) @ sk4 ) @ ( dsetconstr @ sk4 @ ( (=) @ $i @ ( sk5 @ sk6 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(87,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ $true
| ( ( in @ ( sk5 @ ( sk5 @ sk6 ) ) @ sk4 )
!= ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[45,47]) ).
thf(88,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( in @ ( sk5 @ ( sk5 @ sk6 ) ) @ sk4 )
!= ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(90,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( sk5 @ ( sk5 @ sk6 ) )
!= A )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= sk4 ) ),
inference(simp,[status(thm)],[88]) ).
thf(92,plain,
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [A: $i] :
( in @ ( kpair @ sk6 @ A )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) ) ) )
!= ( setadjoin @ ( sk5 @ ( sk5 @ sk6 ) ) @ emptyset ) )
| ( ( dsetconstr @ sk4
@ ^ [A: $i] :
( in @ ( kpair @ sk6 @ A )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) ) ) )
!= sk4 ) ),
inference(simp,[status(thm)],[90]) ).
thf(452,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
| ~ $true
| ( sk4 != sk3 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[370,36]) ).
thf(453,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[452]) ).
thf(472,plain,
! [A: $i] :
( ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
| ( sk4 != sk3 )
| ( ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) )
!= A )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[453]) ).
thf(493,plain,
( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) ) ) @ sk4 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[472]) ).
thf(98,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ $true
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) @ sk4 )
!= ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[91,47]) ).
thf(99,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) @ sk4 )
!= ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(101,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) )
!= A )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= sk4 ) ),
inference(simp,[status(thm)],[99]) ).
thf(103,plain,
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [A: $i] :
( in @ ( kpair @ sk6 @ A )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) ) ) )
!= ( setadjoin @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) @ emptyset ) )
| ( ( dsetconstr @ sk4
@ ^ [A: $i] :
( in @ ( kpair @ sk6 @ A )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) ) ) )
!= sk4 ) ),
inference(simp,[status(thm)],[101]) ).
thf(846,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
| ~ $true
| ( sk4 != sk3 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[538,36]) ).
thf(847,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[846]) ).
thf(867,plain,
! [A: $i] :
( ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
| ( sk4 != sk3 )
| ( ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) ) ) )
!= A )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[847]) ).
thf(868,plain,
( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) ) ) ) ) ) @ sk4 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[867]) ).
thf(1918,plain,
! [A: $i] :
( ~ $true
| ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk2 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 ) @ ( dsetconstr @ sk3 @ ( (=) @ $i @ sk6 ) ) )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1904,29]) ).
thf(1919,plain,
! [A: $i] :
( ( in @ ( sk5 @ A ) @ sk4 )
| ( ( in @ ( sk2 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 ) @ ( dsetconstr @ sk3 @ ( (=) @ $i @ sk6 ) ) )
!= ( in @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[1918]) ).
thf(1943,plain,
! [A: $i] :
( ( in @ ( sk5 @ A ) @ sk4 )
| ( ( sk2 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 )
!= A )
| ( ( dsetconstr @ sk3 @ ( (=) @ $i @ sk6 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[1919]) ).
thf(1957,plain,
( ( in @ ( sk5 @ ( sk2 @ sk6 @ ( (=) @ $i @ sk6 ) @ sk3 ) ) @ sk4 )
| ( ( dsetconstr @ sk3 @ ( (=) @ $i @ sk6 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[1943]) ).
thf(5,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ A )
| ~ ( B @ C )
| ( ( sk1 @ C @ B @ A )
!= C )
| ( ( dsetconstr @ A @ B )
= ( setadjoin @ ( sk2 @ C @ B @ A ) @ emptyset ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(19,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( ( sk1 @ C @ B @ A )
!= C )
| ( ( dsetconstr @ A @ B )
= ( setadjoin @ ( sk2 @ C @ B @ A ) @ emptyset ) )
| ~ ( in @ C @ A )
| ~ ( B @ C ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(360,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ~ $true
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) @ sk4 )
!= ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[347,47]) ).
thf(361,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) @ sk4 )
!= ( in @ A
@ ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[360]) ).
thf(364,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= ( setadjoin @ A @ emptyset ) )
| ( ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) )
!= A )
| ( ( dsetconstr @ sk4
@ ^ [B: $i] :
( in @ ( kpair @ sk6 @ B )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [C: $i] : ( (=) @ $i @ ( sk5 @ C ) ) ) ) )
!= sk4 ) ),
inference(simp,[status(thm)],[361]) ).
thf(373,plain,
( ( sk4 != sk3 )
| ( ( dsetconstr @ sk4
@ ^ [A: $i] :
( in @ ( kpair @ sk6 @ A )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) ) ) )
!= ( setadjoin @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) @ emptyset ) )
| ( ( dsetconstr @ sk4
@ ^ [A: $i] :
( in @ ( kpair @ sk6 @ A )
@ ( dpsetconstr @ sk3 @ sk4
@ ^ [B: $i] : ( (=) @ $i @ ( sk5 @ B ) ) ) ) )
!= sk4 ) ),
inference(simp,[status(thm)],[364]) ).
thf(808,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
| ~ $true
| ( sk4 != sk3 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[493,36]) ).
thf(809,plain,
! [A: $i] :
( ( sk4 != sk3 )
| ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) ) ) @ sk4 )
!= ( in @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[808]) ).
thf(819,plain,
! [A: $i] :
( ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
| ( sk4 != sk3 )
| ( ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) ) )
!= A )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[809]) ).
thf(833,plain,
( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ sk6 ) ) ) ) ) ) ) ) ) ) ) @ sk4 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[819]) ).
thf(15,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ A )
| ~ ( B @ C )
| ( in @ ( sk1 @ C @ B @ A ) @ A )
| ( in @ ( sk2 @ C @ B @ A ) @ ( dsetconstr @ A @ B ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(454,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ( sk4 != sk3 )
| ( in @ ( sk5 @ ( sk5 @ B ) ) @ sk4 )
| ~ $true
| ( sk4 != sk3 )
| ( ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
!= ( in @ B @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[36,36]) ).
thf(455,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ( sk4 != sk3 )
| ( in @ ( sk5 @ ( sk5 @ B ) ) @ sk4 )
| ( ( in @ ( sk5 @ ( sk5 @ A ) ) @ sk4 )
!= ( in @ B @ sk3 ) ) ),
inference(simp,[status(thm)],[454]) ).
thf(480,plain,
! [B: $i,A: $i] :
( ( in @ ( sk5 @ ( sk5 @ B ) ) @ sk4 )
| ~ ( in @ A @ sk3 )
| ( sk4 != sk3 )
| ( ( sk5 @ ( sk5 @ A ) )
!= B )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[455]) ).
thf(501,plain,
! [A: $i] :
( ( in @ ( sk5 @ ( sk5 @ ( sk5 @ ( sk5 @ A ) ) ) ) @ sk4 )
| ~ ( in @ A @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[480]) ).
thf(3073,plain,
$false,
inference(e,[status(thm)],[347,538,396,102,41,45,59,12,370,58,322,1904,25,20,29,492,348,38,70,21,92,493,103,323,91,868,3,1957,19,373,833,36,47,15,501]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU678^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22 % Computer : n015.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 14:11:03 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.00/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/1.01 % [INFO] Parsing done (209ms).
% 1.17/1.03 % [INFO] Running in sequential loop mode.
% 2.02/1.42 % [INFO] eprover registered as external prover.
% 2.02/1.43 % [INFO] Scanning for conjecture ...
% 2.19/1.58 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.38/1.61 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.38/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 2.38/1.62 % [INFO] Type checking passed.
% 2.38/1.62 % [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 ...
% 28.15/9.67 % External prover 'e' found a proof!
% 28.15/9.67 % [INFO] Killing All external provers ...
% 28.15/9.68 % Time passed: 9314ms (effective reasoning time: 8645ms)
% 28.15/9.68 % 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)>
% 28.15/9.68 % Axioms used in derivation (0):
% 28.15/9.68 % No. of inferences in proof: 129
% 28.15/9.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9314 ms resp. 8645 ms w/o parsing
% 29.06/9.85 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.06/9.85 % [INFO] Killing All external provers ...
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