TSTP Solution File: SEU703^2 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU703^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 03:39:10 EDT 2024
% Result : Theorem 163.41s 30.68s
% Output : Refutation 163.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 23
% Syntax : Number of formulae : 307 ( 58 unt; 16 typ; 6 def)
% Number of atoms : 1099 ( 528 equ; 0 cnn)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 3692 ( 573 ~; 416 |; 90 &;2562 @)
% ( 0 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 815 ( 278 ^ 537 !; 0 ?; 815 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(dsetconstrER_def,definition,
( dsetconstrER
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) ) ) ) ).
thf(setext_type,type,
setext: $o ).
thf(setext_def,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( A = B ) ) ) ) ) ).
thf(uniqinunit_type,type,
uniqinunit: $o ).
thf(uniqinunit_def,definition,
( uniqinunit
= ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ) ).
thf(eqinunit_type,type,
eqinunit: $o ).
thf(eqinunit_def,definition,
( eqinunit
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(in__Cong_type,type,
in__Cong: $o ).
thf(in__Cong_def,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) ) ) ) ).
thf(iftrueProp1_type,type,
iftrueProp1: $o ).
thf(iftrueProp1_def,definition,
( iftrueProp1
= ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( B
=> ( in @ C
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) ) ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i > $i > $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $o ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(1,conjecture,
( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( in__Cong
=> ( iftrueProp1
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( B
=> ( ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) )
= ( setadjoin @ C @ emptyset ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp2) ).
thf(2,negated_conjecture,
~ ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( in__Cong
=> ( iftrueProp1
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( B
=> ( ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) )
= ( setadjoin @ C @ emptyset ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( A = B ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( in @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) )
=> ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( B
=> ( in @ C
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) ) ) ) )
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( B
=> ( ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) )
= ( setadjoin @ C @ emptyset ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
in @ sk6 @ sk3,
inference(cnf,[status(esa)],[3]) ).
thf(4,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( in @ sk6 @ sk3 )
!= ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,30]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( sk6 != A )
| ( ( setadjoin @ B @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[174]) ).
thf(243,plain,
! [A: $i] :
( ( sk6 = A )
| ( ( setadjoin @ A @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[224]) ).
thf(6,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( in @ ( sk2 @ B @ A ) @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( in @ ( sk1 @ B @ A ) @ A )
| ( in @ ( sk2 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( in @ ( sk1 @ B @ A ) @ A )
| ( in @ ( sk2 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[22]) ).
thf(12,plain,
in @ sk5 @ sk3,
inference(cnf,[status(esa)],[3]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( in @ sk5 @ A )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[30,12]) ).
thf(164,plain,
! [A: $i] :
( ~ ( in @ A @ ( setadjoin @ sk3 @ emptyset ) )
| ( in @ sk5 @ A ) ),
inference(pattern_uni,[status(thm)],[163:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(10891,plain,
! [A: $i] :
( ( in @ sk5 @ A )
| ( ( in @ sk6 @ sk3 )
!= ( in @ A @ ( setadjoin @ sk3 @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,164]) ).
thf(10924,plain,
! [A: $i] :
( ( in @ sk5 @ A )
| ( sk6 != A )
| ( ( setadjoin @ sk3 @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[10891]) ).
thf(11017,plain,
( ( in @ sk5 @ sk6 )
| ( ( setadjoin @ sk3 @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[10924]) ).
thf(13389,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( in @ ( sk2 @ B @ A ) @ B )
| ( in @ sk5 @ sk6 )
| ( A != sk3 )
| ( B
!= ( setadjoin @ sk3 @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[23,11017]) ).
thf(13390,plain,
! [A: $i] :
( ( in @ ( sk1 @ ( setadjoin @ sk3 @ emptyset ) @ A ) @ A )
| ( in @ ( sk2 @ ( setadjoin @ sk3 @ emptyset ) @ A ) @ ( setadjoin @ sk3 @ emptyset ) )
| ( in @ sk5 @ sk6 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[13389:[bind(A,$thf( A )),bind(B,$thf( setadjoin @ sk3 @ emptyset ))]]) ).
thf(13412,plain,
( ( in @ ( sk1 @ ( setadjoin @ sk3 @ emptyset ) @ sk3 ) @ sk3 )
| ( in @ ( sk2 @ ( setadjoin @ sk3 @ emptyset ) @ sk3 ) @ ( setadjoin @ sk3 @ emptyset ) )
| ( in @ sk5 @ sk6 ) ),
inference(simp,[status(thm)],[13390]) ).
thf(19263,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ ( setadjoin @ sk3 @ emptyset ) @ sk3 ) @ sk3 )
| ( in @ sk5 @ sk6 )
| ( A = B )
| ( ( in @ ( sk2 @ ( setadjoin @ sk3 @ emptyset ) @ sk3 ) @ ( setadjoin @ sk3 @ emptyset ) )
!= ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[13412,30]) ).
thf(19264,plain,
( ( in @ ( sk1 @ ( setadjoin @ sk3 @ emptyset ) @ sk3 ) @ sk3 )
| ( in @ sk5 @ sk6 )
| ( ( sk2 @ ( setadjoin @ sk3 @ emptyset ) @ sk3 )
= sk3 ) ),
inference(pattern_uni,[status(thm)],[19263:[bind(A,$thf( sk2 @ ( setadjoin @ sk3 @ emptyset ) @ sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ~ ( in @ ( sk2 @ B @ A ) @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( in @ ( sk1 @ B @ A ) @ A )
| ~ ( in @ ( sk2 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( in @ ( sk1 @ B @ A ) @ A )
| ~ ( in @ ( sk2 @ B @ A ) @ A ) ),
inference(simp,[status(thm)],[17]) ).
thf(16,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( B @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [C: $i] : $false ) )
| $false ),
inference(prim_subst,[status(thm)],[16:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : $false ))]]) ).
thf(334,plain,
! [B: $i,A: $i] :
~ ( in @ B
@ ( dsetconstr @ A
@ ^ [C: $i] : $false ) ),
inference(simp,[status(thm)],[303]) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( in @ sk5 @ sk3 )
!= ( in @ B
@ ( dsetconstr @ A
@ ^ [C: $i] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[12,334]) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( sk5 != B )
| ( ( dsetconstr @ A
@ ^ [C: $i] : $false )
!= sk3 ) ),
inference(simp,[status(thm)],[353]) ).
thf(382,plain,
! [A: $i] :
( ( dsetconstr @ A
@ ^ [B: $i] : $false )
!= sk3 ),
inference(simp,[status(thm)],[369]) ).
thf(391,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B != sk3 )
| ( A
!= ( dsetconstr @ C
@ ^ [D: $i] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[30,382]) ).
thf(392,plain,
! [B: $i,A: $i] :
( ~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ ( setadjoin @ A @ emptyset ) )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( dsetconstr @ D @ ^ [E: $i] : $false )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(400,plain,
! [A: $i] :
~ ( in
@ ( dsetconstr @ A
@ ^ [B: $i] : $false )
@ ( setadjoin @ sk3 @ emptyset ) ),
inference(simp,[status(thm)],[392]) ).
thf(14,plain,
( ( dsetconstr @ sk3
@ ^ [A: $i] :
( ( sk4
& ( A = sk5 ) )
| ( ~ sk4
& ( A = sk6 ) ) ) )
!= ( setadjoin @ sk5 @ emptyset ) ),
inference(cnf,[status(esa)],[3]) ).
thf(21,plain,
( ( dsetconstr @ sk3
@ ^ [A: $i] :
( ( sk4
& ( A = sk5 ) )
| ( ~ sk4
& ( A = sk6 ) ) ) )
!= ( setadjoin @ sk5 @ emptyset ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(11,plain,
sk4,
inference(cnf,[status(esa)],[3]) ).
thf(33,plain,
( ( dsetconstr @ sk3
@ ^ [A: $i] :
( ( $true
& ( A = sk5 ) )
| ( ~ $true
& ( A = sk6 ) ) ) )
!= ( setadjoin @ sk5 @ emptyset ) ),
inference(rewrite,[status(thm)],[21,11]) ).
thf(34,plain,
( ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
!= ( setadjoin @ sk5 @ emptyset ) ),
inference(simp,[status(thm)],[33]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A
!= ( setadjoin @ sk5 @ emptyset ) )
| ( B
!= ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,34]) ).
thf(200,plain,
! [A: $i] :
( ~ ( in @ A
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ emptyset ) )
| ( A
!= ( setadjoin @ sk5 @ emptyset ) ) ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( A )),bind(B,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ))]]) ).
thf(231,plain,
~ ( in @ ( setadjoin @ sk5 @ emptyset )
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset ) ),
inference(simp,[status(thm)],[200]) ).
thf(579,plain,
( ( in @ ( setadjoin @ sk5 @ emptyset )
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset ) )
!= ( in @ sk6 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[8,231]) ).
thf(648,plain,
( ( ( setadjoin @ sk5 @ emptyset )
!= sk6 )
| ( ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[579]) ).
thf(3036,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B != sk6 )
| ( ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) )
@ emptyset )
!= sk3 )
| ( A
!= ( setadjoin @ sk5 @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[30,648]) ).
thf(3037,plain,
! [A: $i] :
( ~ ( in @ ( setadjoin @ sk5 @ emptyset ) @ ( setadjoin @ A @ emptyset ) )
| ( A != sk6 )
| ( ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ emptyset )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[3036:[bind(A,$thf( setadjoin @ sk5 @ emptyset )),bind(B,$thf( B ))]]) ).
thf(3096,plain,
( ~ ( in @ ( setadjoin @ sk5 @ emptyset ) @ ( setadjoin @ sk6 @ emptyset ) )
| ( ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[3037]) ).
thf(13,plain,
! [D: $i,C: $i,B: $o,A: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ D @ A )
| ~ B
| ( in @ C
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(26,plain,
! [D: $i,C: $i,B: $o,A: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ D @ A )
| ~ B
| ( in @ C
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(40,plain,
! [H: $i,G: $i,F: $o,E: $i,D: $i,C: $i,B: $o,A: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ D @ A )
| ~ B
| ~ ( in @ H @ E )
| ~ F
| ( in @ G
@ ( dsetconstr @ E
@ ^ [I: $i] :
( ( F
& ( I = G ) )
| ( ~ F
& ( I = H ) ) ) ) )
| ( ( in @ C
@ ( dsetconstr @ A
@ ^ [I: $i] :
( ( B
& ( I = C ) )
| ( ~ B
& ( I = D ) ) ) ) )
!= ( in @ G @ E ) ) ),
inference(paramod_ordered,[status(thm)],[26,26]) ).
thf(41,plain,
! [F: $i,E: $i,D: $o,C: $i,B: $i,A: $o] :
( ~ ( in @ B @ F )
| ~ ( in @ C @ F )
| ~ A
| ~ ( in @ E
@ ( dsetconstr @ F
@ ^ [G: $i] :
( ( A
& ( G = B ) )
| ( ~ A
& ( G = C ) ) ) ) )
| ~ D
| ( in @ B
@ ( dsetconstr
@ ( dsetconstr @ F
@ ^ [G: $i] :
( ( A
& ( G = B ) )
| ( ~ A
& ( G = C ) ) ) )
@ ^ [G: $i] :
( ( D
& ( G = B ) )
| ( ~ D
& ( G = E ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( dsetconstr @ I @ ^ [J: $i] : ( ( B & ( J = C ) ) | ( ~ ( B ) & ( J = D ) ) ) )),bind(F,$thf( F )),bind(G,$thf( C )),bind(H,$thf( H ))]]) ).
thf(69,plain,
! [F: $i,E: $i,D: $o,C: $i,B: $i,A: $o] :
( ~ ( in @ B @ F )
| ~ ( in @ C @ F )
| ~ A
| ~ ( in @ E
@ ( dsetconstr @ F
@ ^ [G: $i] :
( ( A
& ( G = B ) )
| ( ~ A
& ( G = C ) ) ) ) )
| ~ D
| ( in @ B
@ ( dsetconstr
@ ( dsetconstr @ F
@ ^ [G: $i] :
( ( A
& ( G = B ) )
| ( ~ A
& ( G = C ) ) ) )
@ ^ [G: $i] :
( ( D
& ( G = B ) )
| ( ~ D
& ( G = E ) ) ) ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(32,plain,
! [A: $i] : ( in @ A @ ( setadjoin @ A @ emptyset ) ),
inference(simp,[status(thm)],[31]) ).
thf(424,plain,
! [B: $i,A: $i] :
( ( in @ A @ ( setadjoin @ A @ emptyset ) )
!= ( in
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ ( setadjoin @ sk3 @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[32,400]) ).
thf(447,plain,
! [B: $i,A: $i] :
( ( A
!= ( dsetconstr @ B
@ ^ [C: $i] : $false ) )
| ( ( setadjoin @ A @ emptyset )
!= ( setadjoin @ sk3 @ emptyset ) ) ),
inference(simp,[status(thm)],[424]) ).
thf(479,plain,
! [A: $i] :
( ( setadjoin
@ ( dsetconstr @ A
@ ^ [B: $i] : $false )
@ emptyset )
!= ( setadjoin @ sk3 @ emptyset ) ),
inference(simp,[status(thm)],[447]) ).
thf(283,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( ( in @ sk6 @ sk3 )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,16]) ).
thf(319,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( sk6 != C )
| ( ( dsetconstr @ A @ B )
!= sk3 ) ),
inference(simp,[status(thm)],[283]) ).
thf(352,plain,
! [B: $i > $o,A: $i] :
( ( B @ sk6 )
| ( ( dsetconstr @ A @ B )
!= sk3 ) ),
inference(simp,[status(thm)],[319]) ).
thf(301,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( ~ ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[16]) ).
thf(311,plain,
! [A: $i] :
~ ( in
@ ( dsetconstr @ A
@ ^ [B: $i] :
~ ( in @ B @ B ) )
@ ( dsetconstr @ A
@ ^ [B: $i] :
~ ( in @ B @ B ) ) ),
inference(pre_uni,[status(thm)],[301:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( in @ D @ D ) )),bind(C,$thf( dsetconstr @ A @ ^ [D: $i] : ~ ( in @ D @ D ) ))]]) ).
thf(4248,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( in
@ ( dsetconstr @ D
@ ^ [E: $i] :
~ ( in @ E @ E ) )
@ ( dsetconstr @ D
@ ^ [E: $i] :
~ ( in @ E @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,311]) ).
thf(4286,plain,
! [B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ C ) )
@ ( dsetconstr @ A
@ ^ [C: $i] : ( in @ C @ C ) ) ),
inference(pre_uni,[status(thm)],[4248:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( in @ E @ E ) )),bind(C,$thf( dsetconstr @ D @ ^ [E: $i] : ~ ( in @ E @ E ) )),bind(D,$thf( D ))]]) ).
thf(4319,plain,
! [B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ C ) )
@ ( dsetconstr @ A
@ ^ [C: $i] : ( in @ C @ C ) ) ),
inference(simp,[status(thm)],[4286]) ).
thf(4347,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ A @ ( setadjoin @ A @ emptyset ) )
!= ( in
@ ( dsetconstr @ C
@ ^ [D: $i] :
~ ( in @ D @ D ) )
@ ( dsetconstr @ B
@ ^ [D: $i] : ( in @ D @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,4319]) ).
thf(4375,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( dsetconstr @ C
@ ^ [D: $i] :
~ ( in @ D @ D ) ) )
| ( ( setadjoin @ A @ emptyset )
!= ( dsetconstr @ B
@ ^ [D: $i] : ( in @ D @ D ) ) ) ),
inference(simp,[status(thm)],[4347]) ).
thf(4391,plain,
! [B: $i,A: $i] :
( ( setadjoin
@ ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ C ) )
@ emptyset )
!= ( dsetconstr @ A
@ ^ [C: $i] : ( in @ C @ C ) ) ),
inference(simp,[status(thm)],[4375]) ).
thf(425,plain,
! [A: $i] :
( ( in
@ ( dsetconstr @ A
@ ^ [B: $i] : $false )
@ ( setadjoin @ sk3 @ emptyset ) )
!= ( in @ sk5 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[12,400]) ).
thf(449,plain,
! [A: $i] :
( ( ( dsetconstr @ A
@ ^ [B: $i] : $false )
!= sk5 )
| ( ( setadjoin @ sk3 @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[425]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B
!= ( setadjoin @ sk5 @ emptyset ) )
| ( A
!= ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,34]) ).
thf(194,plain,
! [A: $i] :
( ~ ( in
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ ( setadjoin @ A @ emptyset ) )
| ( A
!= ( setadjoin @ sk5 @ emptyset ) ) ),
inference(pattern_uni,[status(thm)],[193:[bind(A,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) )),bind(B,$thf( B ))]]) ).
thf(228,plain,
~ ( in
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ),
inference(simp,[status(thm)],[194]) ).
thf(481,plain,
( ( in
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) )
!= ( in @ sk6 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[8,228]) ).
thf(550,plain,
( ( ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
!= sk6 )
| ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[481]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( in @ ( sk2 @ B @ A ) @ B )
| ( A
!= ( setadjoin @ sk5 @ emptyset ) )
| ( B
!= ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,34]) ).
thf(118,plain,
! [A: $i] :
( ( in
@ ( sk1
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ A )
@ A )
| ( in
@ ( sk2
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ A )
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) ) )
| ( A
!= ( setadjoin @ sk5 @ emptyset ) ) ),
inference(pattern_uni,[status(thm)],[117:[bind(A,$thf( A )),bind(B,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ))]]) ).
thf(154,plain,
( ( in
@ ( sk1
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
@ ( setadjoin @ sk5 @ emptyset ) )
| ( in
@ ( sk2
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(5138,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( in
@ ( sk1
@ ( dsetconstr @ sk3
@ ^ [D: $i] : ( D = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
@ ( setadjoin @ sk5 @ emptyset ) )
| ( B @ C )
| ( ( in
@ ( sk2
@ ( dsetconstr @ sk3
@ ^ [D: $i] : ( D = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
@ ( dsetconstr @ sk3
@ ^ [D: $i] : ( D = sk5 ) ) )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[154,16]) ).
thf(5139,plain,
( ( in
@ ( sk1
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
@ ( setadjoin @ sk5 @ emptyset ) )
| ( ( sk2
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
= sk5 ) ),
inference(pattern_uni,[status(thm)],[5138:[bind(A,$thf( sk3 )),bind(B,$thf( ^ [D: $i] : ( D = sk5 ) )),bind(C,$thf( sk2 @ ( dsetconstr @ sk3 @ ^ [D: $i] : ( D = sk5 ) ) @ ( setadjoin @ sk5 @ emptyset ) ))]]) ).
thf(5277,plain,
( ( ( sk2
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
= sk5 )
| ( in
@ ( sk1
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
@ ( setadjoin @ sk5 @ emptyset ) ) ),
inference(lifteq,[status(thm)],[5139]) ).
thf(6850,plain,
( ( in
@ ( sk1
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
@ ( setadjoin @ sk5 @ emptyset ) )
| ( in @ sk5
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) ) )
| ( ( sk2
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
!= ( sk2
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[5277,154]) ).
thf(6851,plain,
( ( in
@ ( sk1
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
@ ( setadjoin @ sk5 @ emptyset ) )
| ( in @ sk5
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) ) ) ),
inference(pattern_uni,[status(thm)],[6850:[]]) ).
thf(4259,plain,
! [B: $i,A: $i] :
( ( in @ A @ ( setadjoin @ A @ emptyset ) )
!= ( in
@ ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ C ) )
@ ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,311]) ).
thf(4289,plain,
! [B: $i,A: $i] :
( ( A
!= ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ C ) ) )
| ( ( setadjoin @ A @ emptyset )
!= ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ C ) ) ) ),
inference(simp,[status(thm)],[4259]) ).
thf(4294,plain,
! [A: $i] :
( ( setadjoin
@ ( dsetconstr @ A
@ ^ [B: $i] :
~ ( in @ B @ B ) )
@ emptyset )
!= ( dsetconstr @ A
@ ^ [B: $i] :
~ ( in @ B @ B ) ) ),
inference(simp,[status(thm)],[4289]) ).
thf(1433,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A != sk6 )
| ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 )
| ( B
!= ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,550]) ).
thf(1434,plain,
! [A: $i] :
( ~ ( in @ A
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ emptyset ) )
| ( A != sk6 )
| ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[1433:[bind(A,$thf( A )),bind(B,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ))]]) ).
thf(1458,plain,
( ~ ( in @ sk6
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset ) )
| ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[1434]) ).
thf(393,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A != sk3 )
| ( B
!= ( dsetconstr @ C
@ ^ [D: $i] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[30,382]) ).
thf(394,plain,
! [B: $i,A: $i] :
( ~ ( in @ A
@ ( setadjoin
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ emptyset ) )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[393:[bind(A,$thf( A )),bind(B,$thf( dsetconstr @ D @ ^ [E: $i] : $false )),bind(C,$thf( D ))]]) ).
thf(401,plain,
! [A: $i] :
~ ( in @ sk3
@ ( setadjoin
@ ( dsetconstr @ A
@ ^ [B: $i] : $false )
@ emptyset ) ),
inference(simp,[status(thm)],[394]) ).
thf(1156,plain,
! [A: $i] :
( ( in @ sk5 @ sk3 )
!= ( in @ sk3
@ ( setadjoin
@ ( dsetconstr @ A
@ ^ [B: $i] : $false )
@ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[12,401]) ).
thf(1196,plain,
! [A: $i] :
( ( sk5 != sk3 )
| ( ( setadjoin
@ ( dsetconstr @ A
@ ^ [B: $i] : $false )
@ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[1156]) ).
thf(613,plain,
( ( in @ ( setadjoin @ sk5 @ emptyset )
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset ) )
!= ( in @ sk5 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[12,231]) ).
thf(654,plain,
( ( ( setadjoin @ sk5 @ emptyset )
!= sk5 )
| ( ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[613]) ).
thf(3204,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B != sk5 )
| ( ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) )
@ emptyset )
!= sk3 )
| ( A
!= ( setadjoin @ sk5 @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[30,654]) ).
thf(3205,plain,
! [A: $i] :
( ~ ( in @ ( setadjoin @ sk5 @ emptyset ) @ ( setadjoin @ A @ emptyset ) )
| ( A != sk5 )
| ( ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ emptyset )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[3204:[bind(A,$thf( setadjoin @ sk5 @ emptyset )),bind(B,$thf( B ))]]) ).
thf(3236,plain,
( ~ ( in @ ( setadjoin @ sk5 @ emptyset ) @ ( setadjoin @ sk5 @ emptyset ) )
| ( ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[3205]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ~ ( in @ ( sk2 @ B @ A ) @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( in @ ( sk1 @ B @ A ) @ B )
| ~ ( in @ ( sk2 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( in @ ( sk1 @ B @ A ) @ B )
| ~ ( in @ ( sk2 @ B @ A ) @ A ) ),
inference(simp,[status(thm)],[24]) ).
thf(1269,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A
!= ( setadjoin @ sk3 @ emptyset ) )
| ( B
!= ( setadjoin
@ ( dsetconstr @ C
@ ^ [D: $i] : $false )
@ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[30,479]) ).
thf(1270,plain,
! [B: $i,A: $i] :
( ~ ( in @ A
@ ( setadjoin
@ ( setadjoin
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ emptyset )
@ emptyset ) )
| ( A
!= ( setadjoin @ sk3 @ emptyset ) ) ),
inference(pattern_uni,[status(thm)],[1269:[bind(A,$thf( A )),bind(B,$thf( setadjoin @ ( dsetconstr @ F @ ^ [E: $i] : $false ) @ emptyset )),bind(C,$thf( F ))]]) ).
thf(1287,plain,
! [A: $i] :
~ ( in @ ( setadjoin @ sk3 @ emptyset )
@ ( setadjoin
@ ( setadjoin
@ ( dsetconstr @ A
@ ^ [B: $i] : $false )
@ emptyset )
@ emptyset ) ),
inference(simp,[status(thm)],[1270]) ).
thf(281,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( ( in @ sk5 @ sk3 )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,16]) ).
thf(318,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( sk5 != C )
| ( ( dsetconstr @ A @ B )
!= sk3 ) ),
inference(simp,[status(thm)],[281]) ).
thf(351,plain,
! [B: $i > $o,A: $i] :
( ( B @ sk5 )
| ( ( dsetconstr @ A @ B )
!= sk3 ) ),
inference(simp,[status(thm)],[318]) ).
thf(1760,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ sk5 )
| ( ( dsetconstr @ A
@ ^ [C: $i] :
~ ( B @ C ) )
!= sk3 ) ),
inference(prim_subst,[status(thm)],[351:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(1791,plain,
! [B: $i > $o,A: $i] :
( ( ( dsetconstr @ A
@ ^ [C: $i] :
~ ( B @ C ) )
!= sk3 )
| ~ ( B @ sk5 ) ),
inference(cnf,[status(esa)],[1760]) ).
thf(1792,plain,
! [B: $i > $o,A: $i] :
( ( ( dsetconstr @ A
@ ^ [C: $i] :
~ ( B @ C ) )
!= sk3 )
| ~ ( B @ sk5 ) ),
inference(simp,[status(thm)],[1791]) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ A @ ( setadjoin @ A @ emptyset ) )
!= ( in @ C
@ ( dsetconstr @ B
@ ^ [D: $i] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[32,334]) ).
thf(370,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( setadjoin @ A @ emptyset )
!= ( dsetconstr @ B
@ ^ [D: $i] : $false ) ) ),
inference(simp,[status(thm)],[361]) ).
thf(383,plain,
! [B: $i,A: $i] :
( ( setadjoin @ B @ emptyset )
!= ( dsetconstr @ A
@ ^ [C: $i] : $false ) ),
inference(simp,[status(thm)],[370]) ).
thf(1321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B
!= ( dsetconstr @ C
@ ^ [E: $i] : $false ) )
| ( A
!= ( setadjoin @ D @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[30,383]) ).
thf(1322,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ A @ emptyset ) )
| ( A
!= ( dsetconstr @ B
@ ^ [D: $i] : $false ) ) ),
inference(pattern_uni,[status(thm)],[1321:[bind(A,$thf( setadjoin @ E @ emptyset )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).
thf(1339,plain,
! [B: $i,A: $i] :
~ ( in @ ( setadjoin @ B @ emptyset )
@ ( setadjoin
@ ( dsetconstr @ A
@ ^ [C: $i] : $false )
@ emptyset ) ),
inference(simp,[status(thm)],[1322]) ).
thf(4448,plain,
! [E: $i,D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( in @ ( setadjoin @ E @ emptyset )
@ ( setadjoin
@ ( dsetconstr @ D
@ ^ [F: $i] : $false )
@ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,1339]) ).
thf(4528,plain,
! [B: $i,A: $i] :
~ ( in
@ ( setadjoin
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ emptyset )
@ ( dsetconstr @ A
@ ^ [C: $i] : ( in @ C @ C ) ) ),
inference(pre_uni,[status(thm)],[4448:[bind(A,$thf( A )),bind(B,$thf( ^ [F: $i] : ( in @ F @ F ) )),bind(C,$thf( setadjoin @ ( dsetconstr @ D @ ^ [F: $i] : $false ) @ emptyset )),bind(D,$thf( D )),bind(E,$thf( dsetconstr @ D @ ^ [F: $i] : $false ))]]) ).
thf(4563,plain,
! [B: $i,A: $i] :
~ ( in
@ ( setadjoin
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ emptyset )
@ ( dsetconstr @ A
@ ^ [C: $i] : ( in @ C @ C ) ) ),
inference(simp,[status(thm)],[4528]) ).
thf(6978,plain,
! [B: $i > $o,A: $i] :
( ( ( dsetconstr @ A
@ ^ [C: $i] :
~ ( B @ C ) )
!= sk3 )
| ( ( in @ sk5 @ sk3 )
!= ( B @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[12,1792]) ).
thf(7015,plain,
! [A: $i] :
( ( dsetconstr @ A
@ ^ [B: $i] :
~ ( in @ B @ sk3 ) )
!= sk3 ),
inference(pre_uni,[status(thm)],[6978:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : ( in @ C @ sk3 ) ))]]) ).
thf(7278,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B != sk3 )
| ( A
!= ( dsetconstr @ C
@ ^ [D: $i] :
~ ( in @ D @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,7015]) ).
thf(7279,plain,
! [B: $i,A: $i] :
( ~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ sk3 ) )
@ ( setadjoin @ A @ emptyset ) )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[7278:[bind(A,$thf( dsetconstr @ D @ ^ [E: $i] : ~ ( in @ E @ sk3 ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(7294,plain,
! [A: $i] :
~ ( in
@ ( dsetconstr @ A
@ ^ [B: $i] :
~ ( in @ B @ sk3 ) )
@ ( setadjoin @ sk3 @ emptyset ) ),
inference(simp,[status(thm)],[7279]) ).
thf(407,plain,
! [A: $i] :
( ( in
@ ( dsetconstr @ A
@ ^ [B: $i] : $false )
@ ( setadjoin @ sk3 @ emptyset ) )
!= ( in @ sk6 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[8,400]) ).
thf(448,plain,
! [A: $i] :
( ( ( dsetconstr @ A
@ ^ [B: $i] : $false )
!= sk6 )
| ( ( setadjoin @ sk3 @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[407]) ).
thf(1417,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B != sk6 )
| ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 )
| ( A
!= ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,550]) ).
thf(1418,plain,
! [A: $i] :
( ~ ( in
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ ( setadjoin @ A @ emptyset ) )
| ( A != sk6 )
| ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[1417:[bind(A,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) )),bind(B,$thf( B ))]]) ).
thf(1450,plain,
( ~ ( in
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ sk6 @ emptyset ) )
| ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[1418]) ).
thf(4472,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ A @ ( setadjoin @ A @ emptyset ) )
!= ( in @ ( setadjoin @ C @ emptyset )
@ ( setadjoin
@ ( dsetconstr @ B
@ ^ [D: $i] : $false )
@ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[32,1339]) ).
thf(4520,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( setadjoin @ C @ emptyset ) )
| ( ( setadjoin @ A @ emptyset )
!= ( setadjoin
@ ( dsetconstr @ B
@ ^ [D: $i] : $false )
@ emptyset ) ) ),
inference(simp,[status(thm)],[4472]) ).
thf(4556,plain,
! [B: $i,A: $i] :
( ( setadjoin @ ( setadjoin @ B @ emptyset ) @ emptyset )
!= ( setadjoin
@ ( dsetconstr @ A
@ ^ [C: $i] : $false )
@ emptyset ) ),
inference(simp,[status(thm)],[4520]) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B
!= ( setadjoin @ sk3 @ emptyset ) )
| ( A
!= ( setadjoin
@ ( dsetconstr @ C
@ ^ [D: $i] : $false )
@ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[30,479]) ).
thf(1264,plain,
! [B: $i,A: $i] :
( ~ ( in
@ ( setadjoin
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ emptyset )
@ ( setadjoin @ A @ emptyset ) )
| ( A
!= ( setadjoin @ sk3 @ emptyset ) ) ),
inference(pattern_uni,[status(thm)],[1263:[bind(A,$thf( setadjoin @ ( dsetconstr @ F @ ^ [E: $i] : $false ) @ emptyset )),bind(B,$thf( B )),bind(C,$thf( F ))]]) ).
thf(1283,plain,
! [A: $i] :
~ ( in
@ ( setadjoin
@ ( dsetconstr @ A
@ ^ [B: $i] : $false )
@ emptyset )
@ ( setadjoin @ ( setadjoin @ sk3 @ emptyset ) @ emptyset ) ),
inference(simp,[status(thm)],[1264]) ).
thf(1153,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( in @ sk3
@ ( setadjoin
@ ( dsetconstr @ D
@ ^ [E: $i] : $false )
@ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,401]) ).
thf(1198,plain,
! [B: $i,A: $i] :
~ ( in
@ ( setadjoin
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ emptyset )
@ ( dsetconstr @ A @ ( in @ sk3 ) ) ),
inference(pre_uni,[status(thm)],[1153:[bind(A,$thf( A )),bind(B,$thf( in @ sk3 )),bind(C,$thf( setadjoin @ ( dsetconstr @ D @ ^ [E: $i] : $false ) @ emptyset )),bind(D,$thf( D ))]]) ).
thf(1223,plain,
! [B: $i,A: $i] :
~ ( in
@ ( setadjoin
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ emptyset )
@ ( dsetconstr @ A @ ( in @ sk3 ) ) ),
inference(simp,[status(thm)],[1198]) ).
thf(42,plain,
! [H: $i,G: $i,F: $o,E: $i,D: $i,C: $i,B: $o,A: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ D @ A )
| ~ B
| ~ ( in @ G @ E )
| ~ F
| ( in @ G
@ ( dsetconstr @ E
@ ^ [I: $i] :
( ( F
& ( I = G ) )
| ( ~ F
& ( I = H ) ) ) ) )
| ( ( in @ C
@ ( dsetconstr @ A
@ ^ [I: $i] :
( ( B
& ( I = C ) )
| ( ~ B
& ( I = D ) ) ) ) )
!= ( in @ H @ E ) ) ),
inference(paramod_ordered,[status(thm)],[26,26]) ).
thf(43,plain,
! [F: $i,E: $i,D: $o,C: $i,B: $i,A: $o] :
( ~ ( in @ B @ F )
| ~ ( in @ C @ F )
| ~ A
| ~ ( in @ E
@ ( dsetconstr @ F
@ ^ [G: $i] :
( ( A
& ( G = B ) )
| ( ~ A
& ( G = C ) ) ) ) )
| ~ D
| ( in @ E
@ ( dsetconstr
@ ( dsetconstr @ F
@ ^ [G: $i] :
( ( A
& ( G = B ) )
| ( ~ A
& ( G = C ) ) ) )
@ ^ [G: $i] :
( ( D
& ( G = E ) )
| ( ~ D
& ( G = B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( dsetconstr @ I @ ^ [J: $i] : ( ( B & ( J = C ) ) | ( ~ ( B ) & ( J = D ) ) ) )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( C ))]]) ).
thf(70,plain,
! [F: $i,E: $i,D: $o,C: $i,B: $i,A: $o] :
( ~ ( in @ B @ F )
| ~ ( in @ C @ F )
| ~ A
| ~ ( in @ E
@ ( dsetconstr @ F
@ ^ [G: $i] :
( ( A
& ( G = B ) )
| ( ~ A
& ( G = C ) ) ) ) )
| ~ D
| ( in @ E
@ ( dsetconstr
@ ( dsetconstr @ F
@ ^ [G: $i] :
( ( A
& ( G = B ) )
| ( ~ A
& ( G = C ) ) ) )
@ ^ [G: $i] :
( ( D
& ( G = E ) )
| ( ~ D
& ( G = B ) ) ) ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( in @ ( sk2 @ B @ A ) @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( in @ ( sk2 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( in @ ( sk2 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[27]) ).
thf(7880,plain,
! [B: $i,A: $i] :
( ( in @ sk5
@ ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) ) )
| ( A = B )
| ( ( in
@ ( sk1
@ ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
@ ( setadjoin @ sk5 @ emptyset ) )
!= ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[6851,30]) ).
thf(7881,plain,
( ( in @ sk5
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) ) )
| ( ( sk1
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
= sk5 ) ),
inference(pattern_uni,[status(thm)],[7880:[bind(A,$thf( sk1 @ ( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ) @ ( setadjoin @ sk5 @ emptyset ) )),bind(B,$thf( sk5 ))]]) ).
thf(54,plain,
! [D: $i,C: $i,B: $o,A: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ D @ A )
| ( in @ C
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) )
| ( B
!= ( in @ D @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[26]) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( in @ A
@ ( dsetconstr @ C
@ ^ [D: $i] :
( ( ( in @ B @ C )
& ( D = A ) )
| ( ~ ( in @ B @ C )
& ( D = B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[54:[bind(A,$thf( F )),bind(B,$thf( in @ E @ F )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( in @ A
@ ( dsetconstr @ C
@ ^ [D: $i] :
( ( ( in @ B @ C )
& ( D = A ) )
| ( ~ ( in @ B @ C )
& ( D = B ) ) ) ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(405,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( in
@ ( dsetconstr @ D
@ ^ [E: $i] : $false )
@ ( setadjoin @ sk3 @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,400]) ).
thf(451,plain,
! [B: $i > $i,A: $i] :
~ ( in @ ( setadjoin @ sk3 @ emptyset )
@ ( dsetconstr @ A
@ ^ [C: $i] :
( in
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : $false )
@ C ) ) ),
inference(pre_uni,[status(thm)],[405:[bind(A,$thf( A )),bind(B,$thf( ^ [F: $i] : ( in @ ( dsetconstr @ ( K @ F ) @ ^ [G: $i] : $false ) @ F ) )),bind(C,$thf( setadjoin @ sk3 @ emptyset )),bind(D,$thf( K @ ( setadjoin @ sk3 @ emptyset ) ))]]) ).
thf(456,plain,
! [B: $i > $i,A: $i] :
~ ( in @ ( setadjoin @ sk3 @ emptyset )
@ ( dsetconstr @ A
@ ^ [C: $i] :
( in
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : $false )
@ C ) ) ),
inference(simp,[status(thm)],[451]) ).
thf(3060,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( ( setadjoin @ sk5 @ emptyset )
!= sk6 )
| ( A != sk3 )
| ( B
!= ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) )
@ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[30,648]) ).
thf(3061,plain,
! [A: $i] :
( ~ ( in @ A
@ ( setadjoin
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ emptyset )
@ emptyset ) )
| ( ( setadjoin @ sk5 @ emptyset )
!= sk6 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[3060:[bind(A,$thf( A )),bind(B,$thf( setadjoin @ ( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ) @ emptyset ))]]) ).
thf(3105,plain,
( ~ ( in @ sk3
@ ( setadjoin
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset )
@ emptyset ) )
| ( ( setadjoin @ sk5 @ emptyset )
!= sk6 ) ),
inference(simp,[status(thm)],[3061]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( in @ sk6 @ A )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[30,8]) ).
thf(173,plain,
! [A: $i] :
( ~ ( in @ A @ ( setadjoin @ sk3 @ emptyset ) )
| ( in @ sk6 @ A ) ),
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(17299,plain,
! [A: $i] :
( ( in @ sk6 @ A )
| ( ( in @ sk6 @ sk3 )
!= ( in @ A @ ( setadjoin @ sk3 @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,173]) ).
thf(17348,plain,
! [A: $i] :
( ( in @ sk6 @ A )
| ( sk6 != A )
| ( ( setadjoin @ sk3 @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[17299]) ).
thf(17462,plain,
( ( in @ sk6 @ sk6 )
| ( ( setadjoin @ sk3 @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[17348]) ).
thf(1201,plain,
! [B: $i > $i,A: $i] :
~ ( in @ emptyset
@ ( dsetconstr @ A
@ ^ [C: $i] :
( in @ sk3
@ ( setadjoin
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : $false )
@ C ) ) ) ),
inference(pre_uni,[status(thm)],[1153:[bind(A,$thf( A )),bind(B,$thf( ^ [F: $i] : ( in @ sk3 @ ( setadjoin @ ( dsetconstr @ ( I @ F ) @ ^ [G: $i] : $false ) @ F ) ) )),bind(C,$thf( emptyset )),bind(D,$thf( I @ emptyset ))]]) ).
thf(1227,plain,
! [B: $i > $i,A: $i] :
~ ( in @ emptyset
@ ( dsetconstr @ A
@ ^ [C: $i] :
( in @ sk3
@ ( setadjoin
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : $false )
@ C ) ) ) ),
inference(simp,[status(thm)],[1201]) ).
thf(354,plain,
! [E: $i,D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( in @ E
@ ( dsetconstr @ D
@ ^ [F: $i] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,334]) ).
thf(375,plain,
! [C: $i > $i,B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [D: $i] : $false )
@ ( dsetconstr @ A
@ ^ [D: $i] : ( in @ ( C @ D ) @ D ) ) ),
inference(pre_uni,[status(thm)],[354:[bind(A,$thf( A )),bind(B,$thf( ^ [G: $i] : ( in @ ( F @ G ) @ G ) )),bind(C,$thf( dsetconstr @ D @ ^ [F: $i] : $false )),bind(D,$thf( D )),bind(E,$thf( F @ ( dsetconstr @ D @ ^ [G: $i] : $false ) ))]]) ).
thf(388,plain,
! [C: $i > $i,B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [D: $i] : $false )
@ ( dsetconstr @ A
@ ^ [D: $i] : ( in @ ( C @ D ) @ D ) ) ),
inference(simp,[status(thm)],[375]) ).
thf(6030,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ A @ ( setadjoin @ A @ emptyset ) )
!= ( in
@ ( setadjoin
@ ( dsetconstr @ C
@ ^ [D: $i] : $false )
@ emptyset )
@ ( dsetconstr @ B
@ ^ [D: $i] : ( in @ D @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,4563]) ).
thf(6073,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( setadjoin
@ ( dsetconstr @ C
@ ^ [D: $i] : $false )
@ emptyset ) )
| ( ( setadjoin @ A @ emptyset )
!= ( dsetconstr @ B
@ ^ [D: $i] : ( in @ D @ D ) ) ) ),
inference(simp,[status(thm)],[6030]) ).
thf(6111,plain,
! [B: $i,A: $i] :
( ( setadjoin
@ ( setadjoin
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ emptyset )
@ emptyset )
!= ( dsetconstr @ A
@ ^ [C: $i] : ( in @ C @ C ) ) ),
inference(simp,[status(thm)],[6073]) ).
thf(515,plain,
( ( in
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) )
!= ( in @ sk5 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[12,228]) ).
thf(554,plain,
( ( ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
!= sk5 )
| ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[515]) ).
thf(1565,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) )
!= sk5 )
| ( A != sk3 )
| ( B
!= ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[30,554]) ).
thf(1566,plain,
! [A: $i] :
( ~ ( in @ A @ ( setadjoin @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ emptyset ) )
| ( ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
!= sk5 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[1565:[bind(A,$thf( A )),bind(B,$thf( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ))]]) ).
thf(1584,plain,
( ~ ( in @ sk3 @ ( setadjoin @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ emptyset ) )
| ( ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
!= sk5 ) ),
inference(simp,[status(thm)],[1566]) ).
thf(452,plain,
! [B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ ( dsetconstr @ A
@ ^ [C: $i] : ( in @ C @ ( setadjoin @ sk3 @ emptyset ) ) ) ),
inference(pre_uni,[status(thm)],[405:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( in @ E @ ( setadjoin @ sk3 @ emptyset ) ) )),bind(C,$thf( dsetconstr @ D @ ^ [E: $i] : $false )),bind(D,$thf( D ))]]) ).
thf(457,plain,
! [B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ ( dsetconstr @ A
@ ^ [C: $i] : ( in @ C @ ( setadjoin @ sk3 @ emptyset ) ) ) ),
inference(simp,[status(thm)],[452]) ).
thf(514,plain,
! [A: $i] :
( ( in @ A @ ( setadjoin @ A @ emptyset ) )
!= ( in
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[32,228]) ).
thf(551,plain,
! [A: $i] :
( ( A
!= ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) ) )
| ( ( setadjoin @ A @ emptyset )
!= ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
inference(simp,[status(thm)],[514]) ).
thf(569,plain,
( ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset )
!= ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ),
inference(simp,[status(thm)],[551]) ).
thf(48,plain,
! [E: $i,D: $i,C: $o,B: $i,A: $i] :
( ~ ( in @ E @ B )
| ~ C
| ( in @ D
@ ( dsetconstr @ B
@ ^ [F: $i] :
( ( C
& ( F = D ) )
| ( ~ C
& ( F = E ) ) ) ) )
| ( ( in @ A @ ( setadjoin @ A @ emptyset ) )
!= ( in @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[32,26]) ).
thf(49,plain,
! [C: $i,B: $i,A: $o] :
( ~ ( in @ B @ ( setadjoin @ C @ emptyset ) )
| ~ A
| ( in @ C
@ ( dsetconstr @ ( setadjoin @ C @ emptyset )
@ ^ [D: $i] :
( ( A
& ( D = C ) )
| ( ~ A
& ( D = B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( F )),bind(B,$thf( setadjoin @ F @ emptyset )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( E ))]]) ).
thf(73,plain,
! [C: $i,B: $i,A: $o] :
( ~ ( in @ B @ ( setadjoin @ C @ emptyset ) )
| ~ A
| ( in @ C
@ ( dsetconstr @ ( setadjoin @ C @ emptyset )
@ ^ [D: $i] :
( ( A
& ( D = C ) )
| ( ~ A
& ( D = B ) ) ) ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( in @ sk5 @ sk3 )
!= ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,30]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( sk5 != A )
| ( ( setadjoin @ B @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[165]) ).
thf(244,plain,
! [A: $i] :
( ( sk5 = A )
| ( ( setadjoin @ A @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[225]) ).
thf(44,plain,
! [D: $i,C: $i,B: $o,A: $i] :
( ~ ( in @ D @ A )
| ~ B
| ( in @ C
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) )
| ( ( in @ sk6 @ sk3 )
!= ( in @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8,26]) ).
thf(45,plain,
! [B: $i,A: $o] :
( ~ ( in @ B @ sk3 )
| ~ A
| ( in @ sk6
@ ( dsetconstr @ sk3
@ ^ [C: $i] :
( ( A
& ( C = sk6 ) )
| ( ~ A
& ( C = B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk6 ))]]) ).
thf(71,plain,
! [B: $i,A: $o] :
( ~ ( in @ B @ sk3 )
| ~ A
| ( in @ sk6
@ ( dsetconstr @ sk3
@ ^ [C: $i] :
( ( A
& ( C = sk6 ) )
| ( ~ A
& ( C = B ) ) ) ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(1199,plain,
! [B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ ( dsetconstr @ A
@ ^ [C: $i] : ( in @ sk3 @ ( setadjoin @ C @ emptyset ) ) ) ),
inference(pre_uni,[status(thm)],[1153:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( in @ sk3 @ ( setadjoin @ E @ emptyset ) ) )),bind(C,$thf( dsetconstr @ D @ ^ [E: $i] : $false )),bind(D,$thf( D ))]]) ).
thf(1224,plain,
! [B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ ( dsetconstr @ A
@ ^ [C: $i] : ( in @ sk3 @ ( setadjoin @ C @ emptyset ) ) ) ),
inference(simp,[status(thm)],[1199]) ).
thf(1154,plain,
! [A: $i] :
( ( in @ sk6 @ sk3 )
!= ( in @ sk3
@ ( setadjoin
@ ( dsetconstr @ A
@ ^ [B: $i] : $false )
@ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[8,401]) ).
thf(1194,plain,
! [A: $i] :
( ( sk6 != sk3 )
| ( ( setadjoin
@ ( dsetconstr @ A
@ ^ [B: $i] : $false )
@ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[1154]) ).
thf(1325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B
!= ( setadjoin @ D @ emptyset ) )
| ( A
!= ( dsetconstr @ C
@ ^ [E: $i] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[30,383]) ).
thf(1326,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in
@ ( dsetconstr @ C
@ ^ [D: $i] : $false )
@ ( setadjoin @ A @ emptyset ) )
| ( A
!= ( setadjoin @ B @ emptyset ) ) ),
inference(pattern_uni,[status(thm)],[1325:[bind(A,$thf( dsetconstr @ E @ ^ [F: $i] : $false )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( D ))]]) ).
thf(1341,plain,
! [B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ emptyset ) ),
inference(simp,[status(thm)],[1326]) ).
thf(4666,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ A @ ( setadjoin @ A @ emptyset ) )
!= ( in
@ ( dsetconstr @ C
@ ^ [D: $i] : $false )
@ ( setadjoin @ ( setadjoin @ B @ emptyset ) @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[32,1341]) ).
thf(4729,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( dsetconstr @ C
@ ^ [D: $i] : $false ) )
| ( ( setadjoin @ A @ emptyset )
!= ( setadjoin @ ( setadjoin @ B @ emptyset ) @ emptyset ) ) ),
inference(simp,[status(thm)],[4666]) ).
thf(4790,plain,
! [B: $i,A: $i] :
( ( setadjoin
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ emptyset )
!= ( setadjoin @ ( setadjoin @ A @ emptyset ) @ emptyset ) ),
inference(simp,[status(thm)],[4729]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( in @ A @ sk3 )
| ( B != sk5 ) ),
inference(paramod_ordered,[status(thm)],[30,12]) ).
thf(162,plain,
! [A: $i] :
( ~ ( in @ A @ ( setadjoin @ sk5 @ emptyset ) )
| ( in @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( A )),bind(B,$thf( sk5 ))]]) ).
thf(9145,plain,
! [A: $i] :
( ( in @ sk5
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) ) )
| ( in @ A @ sk3 )
| ( ( in
@ ( sk1
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
@ ( setadjoin @ sk5 @ emptyset ) )
!= ( in @ A @ ( setadjoin @ sk5 @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[6851,162]) ).
thf(9146,plain,
( ( in @ sk5
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) ) )
| ( in
@ ( sk1
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
@ sk3 ) ),
inference(pattern_uni,[status(thm)],[9145:[bind(A,$thf( sk1 @ ( dsetconstr @ sk3 @ ^ [B: $i] : ( B = sk5 ) ) @ ( setadjoin @ sk5 @ emptyset ) ))]]) ).
thf(8818,plain,
( ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 )
| ( ( in @ sk6
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset ) )
!= ( in @ sk6 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[8,1458]) ).
thf(8879,plain,
( ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 )
| ( sk6 != sk6 )
| ( ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[8818]) ).
thf(8926,plain,
( ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 )
| ( ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[8879]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( in @ ( sk2 @ B @ A ) @ B )
| ( B
!= ( setadjoin @ sk5 @ emptyset ) )
| ( A
!= ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,34]) ).
thf(112,plain,
! [A: $i] :
( ( in
@ ( sk1 @ A
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) ) )
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) ) )
| ( in
@ ( sk2 @ A
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) ) )
@ A )
| ( A
!= ( setadjoin @ sk5 @ emptyset ) ) ),
inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) )),bind(B,$thf( B ))]]) ).
thf(151,plain,
( ( in
@ ( sk1 @ ( setadjoin @ sk5 @ emptyset )
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) ) )
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) ) )
| ( in
@ ( sk2 @ ( setadjoin @ sk5 @ emptyset )
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) ) )
@ ( setadjoin @ sk5 @ emptyset ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(725,plain,
! [B: $i,A: $i] :
( ( in
@ ( sk1 @ ( setadjoin @ sk5 @ emptyset )
@ ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) ) )
@ ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) ) )
| ( A = B )
| ( ( in
@ ( sk2 @ ( setadjoin @ sk5 @ emptyset )
@ ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) ) )
@ ( setadjoin @ sk5 @ emptyset ) )
!= ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[151,30]) ).
thf(726,plain,
( ( in
@ ( sk1 @ ( setadjoin @ sk5 @ emptyset )
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) ) )
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) ) )
| ( ( sk2 @ ( setadjoin @ sk5 @ emptyset )
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) ) )
= sk5 ) ),
inference(pattern_uni,[status(thm)],[725:[bind(A,$thf( sk2 @ ( setadjoin @ sk5 @ emptyset ) @ ( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ) )),bind(B,$thf( sk5 ))]]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B
@ ( dsetconstr @ A
@ ^ [D: $i] :
( ( $true
& ( D = B ) )
| ( ~ $true
& ( D = C ) ) ) ) )
| ~ ( in @ B @ A )
| ~ ( in @ C @ A ) ),
inference(simp,[status(thm)],[26]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B
@ ( dsetconstr @ A
@ ^ [D: $i] : ( D = B ) ) )
| ~ ( in @ B @ A )
| ~ ( in @ C @ A ) ),
inference(simp,[status(thm)],[35]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( in @ B @ sk3 )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[30,12]) ).
thf(158,plain,
! [A: $i] :
( ~ ( in @ sk5 @ ( setadjoin @ A @ emptyset ) )
| ( in @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( sk5 ))]]) ).
thf(240,plain,
! [A: $i] :
( ~ ( in @ sk5 @ ( setadjoin @ A @ emptyset ) )
| ( in @ A @ sk3 ) ),
inference(simp,[status(thm)],[158]) ).
thf(2455,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B
!= ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) )
| ( A
!= ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) )
@ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[30,569]) ).
thf(2456,plain,
! [A: $i] :
( ~ ( in
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ emptyset )
@ ( setadjoin @ A @ emptyset ) )
| ( A
!= ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
inference(pattern_uni,[status(thm)],[2455:[bind(A,$thf( setadjoin @ ( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ) @ emptyset )),bind(B,$thf( B ))]]) ).
thf(2481,plain,
~ ( in
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset )
@ ( setadjoin @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ emptyset ) ),
inference(simp,[status(thm)],[2456]) ).
thf(2564,plain,
! [B: $i,A: $i] :
( ( in @ A @ ( setadjoin @ A @ emptyset ) )
!= ( in
@ ( setadjoin
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ emptyset )
@ ( setadjoin @ ( setadjoin @ sk3 @ emptyset ) @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[32,1283]) ).
thf(2643,plain,
! [B: $i,A: $i] :
( ( A
!= ( setadjoin
@ ( dsetconstr @ B
@ ^ [C: $i] : $false )
@ emptyset ) )
| ( ( setadjoin @ A @ emptyset )
!= ( setadjoin @ ( setadjoin @ sk3 @ emptyset ) @ emptyset ) ) ),
inference(simp,[status(thm)],[2564]) ).
thf(2693,plain,
! [A: $i] :
( ( setadjoin
@ ( setadjoin
@ ( dsetconstr @ A
@ ^ [B: $i] : $false )
@ emptyset )
@ emptyset )
!= ( setadjoin @ ( setadjoin @ sk3 @ emptyset ) @ emptyset ) ),
inference(simp,[status(thm)],[2643]) ).
thf(1559,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A != sk5 )
| ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 )
| ( B
!= ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,554]) ).
thf(1560,plain,
! [A: $i] :
( ~ ( in @ A
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ emptyset ) )
| ( A != sk5 )
| ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[1559:[bind(A,$thf( A )),bind(B,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ))]]) ).
thf(1583,plain,
( ~ ( in @ sk5
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset ) )
| ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[1560]) ).
thf(7282,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A != sk3 )
| ( B
!= ( dsetconstr @ C
@ ^ [D: $i] :
~ ( in @ D @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,7015]) ).
thf(7283,plain,
! [B: $i,A: $i] :
( ~ ( in @ A
@ ( setadjoin
@ ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ sk3 ) )
@ emptyset ) )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[7282:[bind(A,$thf( A )),bind(B,$thf( dsetconstr @ D @ ^ [E: $i] : ~ ( in @ E @ sk3 ) )),bind(C,$thf( D ))]]) ).
thf(7298,plain,
! [A: $i] :
~ ( in @ sk3
@ ( setadjoin
@ ( dsetconstr @ A
@ ^ [B: $i] :
~ ( in @ B @ sk3 ) )
@ emptyset ) ),
inference(simp,[status(thm)],[7283]) ).
thf(36,plain,
! [D: $i,C: $i,B: $o,A: $i] :
( ~ ( in @ D @ A )
| ~ B
| ( in @ C
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) )
| ( ( in @ sk5 @ sk3 )
!= ( in @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12,26]) ).
thf(37,plain,
! [B: $i,A: $o] :
( ~ ( in @ B @ sk3 )
| ~ A
| ( in @ sk5
@ ( dsetconstr @ sk3
@ ^ [C: $i] :
( ( A
& ( C = sk5 ) )
| ( ~ A
& ( C = B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(67,plain,
! [B: $i,A: $o] :
( ~ ( in @ B @ sk3 )
| ~ A
| ( in @ sk5
@ ( dsetconstr @ sk3
@ ^ [C: $i] :
( ( A
& ( C = sk5 ) )
| ( ~ A
& ( C = B ) ) ) ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(10845,plain,
! [A: $i] :
( ( in @ sk5 @ A )
| ( ( in @ sk5 @ sk3 )
!= ( in @ A @ ( setadjoin @ sk3 @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,164]) ).
thf(10956,plain,
! [A: $i] :
( ( in @ sk5 @ A )
| ( sk5 != A )
| ( ( setadjoin @ sk3 @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[10845]) ).
thf(11049,plain,
( ( in @ sk5 @ sk5 )
| ( ( setadjoin @ sk3 @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[10956]) ).
thf(46,plain,
! [D: $i,C: $i,B: $o,A: $i] :
( ~ ( in @ C @ A )
| ~ B
| ( in @ C
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) )
| ( ( in @ sk6 @ sk3 )
!= ( in @ D @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8,26]) ).
thf(47,plain,
! [B: $i,A: $o] :
( ~ ( in @ B @ sk3 )
| ~ A
| ( in @ B
@ ( dsetconstr @ sk3
@ ^ [C: $i] :
( ( A
& ( C = B ) )
| ( ~ A
& ( C = sk6 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( sk6 ))]]) ).
thf(72,plain,
! [B: $i,A: $o] :
( ~ ( in @ B @ sk3 )
| ~ A
| ( in @ B
@ ( dsetconstr @ sk3
@ ^ [C: $i] :
( ( A
& ( C = B ) )
| ( ~ A
& ( C = sk6 ) ) ) ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(1439,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) )
!= sk6 )
| ( A != sk3 )
| ( B
!= ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[30,550]) ).
thf(1440,plain,
! [A: $i] :
( ~ ( in @ A @ ( setadjoin @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ emptyset ) )
| ( ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
!= sk6 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[1439:[bind(A,$thf( A )),bind(B,$thf( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ))]]) ).
thf(1459,plain,
( ~ ( in @ sk3 @ ( setadjoin @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ emptyset ) )
| ( ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
!= sk6 ) ),
inference(simp,[status(thm)],[1440]) ).
thf(2465,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A
!= ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) )
| ( B
!= ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) )
@ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[30,569]) ).
thf(2466,plain,
! [A: $i] :
( ~ ( in @ A
@ ( setadjoin
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ emptyset )
@ emptyset ) )
| ( A
!= ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
inference(pattern_uni,[status(thm)],[2465:[bind(A,$thf( A )),bind(B,$thf( setadjoin @ ( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ) @ emptyset ))]]) ).
thf(2490,plain,
~ ( in @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
@ ( setadjoin
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset )
@ emptyset ) ),
inference(simp,[status(thm)],[2466]) ).
thf(1423,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) )
!= sk6 )
| ( B != sk3 )
| ( A
!= ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[30,550]) ).
thf(1424,plain,
! [A: $i] :
( ~ ( in @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ ( setadjoin @ A @ emptyset ) )
| ( ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
!= sk6 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[1423:[bind(A,$thf( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )),bind(B,$thf( B ))]]) ).
thf(1453,plain,
( ~ ( in @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ ( setadjoin @ sk3 @ emptyset ) )
| ( ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
!= sk6 ) ),
inference(simp,[status(thm)],[1424]) ).
thf(13383,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( in @ ( sk2 @ B @ A ) @ B )
| ( in @ sk5 @ sk6 )
| ( B != sk3 )
| ( A
!= ( setadjoin @ sk3 @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[23,11017]) ).
thf(13384,plain,
! [A: $i] :
( ( in @ ( sk1 @ A @ ( setadjoin @ sk3 @ emptyset ) ) @ ( setadjoin @ sk3 @ emptyset ) )
| ( in @ ( sk2 @ A @ ( setadjoin @ sk3 @ emptyset ) ) @ A )
| ( in @ sk5 @ sk6 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[13383:[bind(A,$thf( setadjoin @ sk3 @ emptyset )),bind(B,$thf( B ))]]) ).
thf(13409,plain,
( ( in @ ( sk1 @ sk3 @ ( setadjoin @ sk3 @ emptyset ) ) @ ( setadjoin @ sk3 @ emptyset ) )
| ( in @ ( sk2 @ sk3 @ ( setadjoin @ sk3 @ emptyset ) ) @ sk3 )
| ( in @ sk5 @ sk6 ) ),
inference(simp,[status(thm)],[13384]) ).
thf(1543,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B != sk5 )
| ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 )
| ( A
!= ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,554]) ).
thf(1544,plain,
! [A: $i] :
( ~ ( in
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ ( setadjoin @ A @ emptyset ) )
| ( A != sk5 )
| ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[1543:[bind(A,$thf( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) )),bind(B,$thf( B ))]]) ).
thf(1575,plain,
( ~ ( in
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ ( setadjoin @ sk5 @ emptyset ) )
| ( ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[1544]) ).
thf(3052,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A != sk6 )
| ( ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) )
@ emptyset )
!= sk3 )
| ( B
!= ( setadjoin @ sk5 @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[30,648]) ).
thf(3053,plain,
! [A: $i] :
( ~ ( in @ A @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) )
| ( A != sk6 )
| ( ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ emptyset )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[3052:[bind(A,$thf( A )),bind(B,$thf( setadjoin @ sk5 @ emptyset ))]]) ).
thf(3104,plain,
( ~ ( in @ sk6 @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) )
| ( ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[3053]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( in @ A @ sk3 )
| ( B != sk6 ) ),
inference(paramod_ordered,[status(thm)],[30,8]) ).
thf(171,plain,
! [A: $i] :
( ~ ( in @ A @ ( setadjoin @ sk6 @ emptyset ) )
| ( in @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( A )),bind(B,$thf( sk6 ))]]) ).
thf(21519,plain,
! [A: $i] :
( ( in @ A @ sk3 )
| ( ( in @ sk5 @ ( setadjoin @ A @ emptyset ) )
!= ( in @ sk5 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[12,240]) ).
thf(21641,plain,
! [A: $i] :
( ( in @ A @ sk3 )
| ( sk5 != sk5 )
| ( ( setadjoin @ A @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[21519]) ).
thf(21745,plain,
! [A: $i] :
( ( in @ A @ sk3 )
| ( ( setadjoin @ A @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[21641]) ).
thf(7373,plain,
! [B: $i,A: $i] :
( ( in @ A @ ( setadjoin @ A @ emptyset ) )
!= ( in
@ ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ sk3 ) )
@ ( setadjoin @ sk3 @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[32,7294]) ).
thf(7426,plain,
! [B: $i,A: $i] :
( ( A
!= ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ sk3 ) ) )
| ( ( setadjoin @ A @ emptyset )
!= ( setadjoin @ sk3 @ emptyset ) ) ),
inference(simp,[status(thm)],[7373]) ).
thf(7437,plain,
! [A: $i] :
( ( setadjoin
@ ( dsetconstr @ A
@ ^ [B: $i] :
~ ( in @ B @ sk3 ) )
@ emptyset )
!= ( setadjoin @ sk3 @ emptyset ) ),
inference(simp,[status(thm)],[7426]) ).
thf(1549,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) )
!= sk5 )
| ( B != sk3 )
| ( A
!= ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[30,554]) ).
thf(1550,plain,
! [A: $i] :
( ~ ( in @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ ( setadjoin @ A @ emptyset ) )
| ( ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
!= sk5 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[1549:[bind(A,$thf( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset )),bind(B,$thf( B ))]]) ).
thf(1578,plain,
( ~ ( in @ ( setadjoin @ ( setadjoin @ sk5 @ emptyset ) @ emptyset ) @ ( setadjoin @ sk3 @ emptyset ) )
| ( ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
!= sk5 ) ),
inference(simp,[status(thm)],[1550]) ).
thf(18023,plain,
! [B: $i,A: $i] :
( ( ( dsetconstr @ B
@ ^ [C: $i] : $false )
!= ( setadjoin @ A @ emptyset ) )
| ( emptyset != emptyset ) ),
inference(simp,[status(thm)],[4790]) ).
thf(18220,plain,
! [B: $i,A: $i] :
( ( dsetconstr @ B
@ ^ [C: $i] : $false )
!= ( setadjoin @ A @ emptyset ) ),
inference(simp,[status(thm)],[18023]) ).
thf(3044,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( ( setadjoin @ sk5 @ emptyset )
!= sk6 )
| ( B != sk3 )
| ( A
!= ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [C: $i] : ( C = sk5 ) )
@ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[30,648]) ).
thf(3045,plain,
! [A: $i] :
( ~ ( in
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [B: $i] : ( B = sk5 ) )
@ emptyset )
@ ( setadjoin @ A @ emptyset ) )
| ( ( setadjoin @ sk5 @ emptyset )
!= sk6 )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[3044:[bind(A,$thf( setadjoin @ ( dsetconstr @ sk3 @ ^ [C: $i] : ( C = sk5 ) ) @ emptyset )),bind(B,$thf( B ))]]) ).
thf(3100,plain,
( ~ ( in
@ ( setadjoin
@ ( dsetconstr @ sk3
@ ^ [A: $i] : ( A = sk5 ) )
@ emptyset )
@ ( setadjoin @ sk3 @ emptyset ) )
| ( ( setadjoin @ sk5 @ emptyset )
!= sk6 ) ),
inference(simp,[status(thm)],[3045]) ).
thf(3336,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ sk6 )
| ( ( dsetconstr @ A
@ ^ [C: $i] :
~ ( B @ C ) )
!= sk3 ) ),
inference(prim_subst,[status(thm)],[352:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(3361,plain,
! [B: $i > $o,A: $i] :
( ( ( dsetconstr @ A
@ ^ [C: $i] :
~ ( B @ C ) )
!= sk3 )
| ~ ( B @ sk6 ) ),
inference(cnf,[status(esa)],[3336]) ).
thf(3362,plain,
! [B: $i > $o,A: $i] :
( ( ( dsetconstr @ A
@ ^ [C: $i] :
~ ( B @ C ) )
!= sk3 )
| ~ ( B @ sk6 ) ),
inference(simp,[status(thm)],[3361]) ).
thf(17246,plain,
! [A: $i] :
( ( in @ sk6 @ A )
| ( ( in @ sk5 @ sk3 )
!= ( in @ A @ ( setadjoin @ sk3 @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,173]) ).
thf(17327,plain,
! [A: $i] :
( ( in @ sk6 @ A )
| ( sk5 != A )
| ( ( setadjoin @ sk3 @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[17246]) ).
thf(17441,plain,
( ( in @ sk6 @ sk5 )
| ( ( setadjoin @ sk3 @ emptyset )
!= sk3 ) ),
inference(simp,[status(thm)],[17327]) ).
thf(454,plain,
! [B: $i > $i,A: $i] :
~ ( in @ emptyset
@ ( dsetconstr @ A
@ ^ [C: $i] :
( in
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : $false )
@ ( setadjoin @ sk3 @ C ) ) ) ),
inference(pre_uni,[status(thm)],[405:[bind(A,$thf( A )),bind(B,$thf( ^ [F: $i] : ( in @ ( dsetconstr @ ( I @ F ) @ ^ [G: $i] : $false ) @ ( setadjoin @ sk3 @ F ) ) )),bind(C,$thf( emptyset )),bind(D,$thf( I @ emptyset ))]]) ).
thf(459,plain,
! [B: $i > $i,A: $i] :
~ ( in @ emptyset
@ ( dsetconstr @ A
@ ^ [C: $i] :
( in
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : $false )
@ ( setadjoin @ sk3 @ C ) ) ) ),
inference(simp,[status(thm)],[454]) ).
thf(38,plain,
! [D: $i,C: $i,B: $o,A: $i] :
( ~ ( in @ C @ A )
| ~ B
| ( in @ C
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) )
| ( ( in @ sk5 @ sk3 )
!= ( in @ D @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12,26]) ).
thf(39,plain,
! [B: $i,A: $o] :
( ~ ( in @ B @ sk3 )
| ~ A
| ( in @ B
@ ( dsetconstr @ sk3
@ ^ [C: $i] :
( ( A
& ( C = B ) )
| ( ~ A
& ( C = sk5 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( sk5 ))]]) ).
thf(68,plain,
! [B: $i,A: $o] :
( ~ ( in @ B @ sk3 )
| ~ A
| ( in @ B
@ ( dsetconstr @ sk3
@ ^ [C: $i] :
( ( A
& ( C = B ) )
| ( ~ A
& ( C = sk5 ) ) ) ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(53836,plain,
$false,
inference(e,[status(thm)],[243,19264,18,400,3096,69,479,352,4391,449,550,6851,4294,1458,1196,3236,25,1287,1792,4563,7294,228,448,164,1450,7015,4556,1283,334,1223,70,28,7881,65,456,3105,17462,1227,388,6111,554,1584,654,457,173,569,73,244,311,32,34,71,12,382,1224,1194,4790,9146,8926,1339,13412,726,66,240,2481,3,2693,1583,162,7298,4319,648,67,16,11049,5277,154,11,72,11017,231,1459,2490,1453,13409,1575,1341,26,351,3104,401,171,23,21745,383,7437,8,151,1578,18220,30,3100,3362,17441,459,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU703^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n018.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 17:36:24 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.32/0.99 % [INFO] Parsing done (119ms).
% 1.32/1.00 % [INFO] Running in sequential loop mode.
% 1.71/1.22 % [INFO] eprover registered as external prover.
% 1.71/1.22 % [INFO] cvc4 registered as external prover.
% 1.71/1.22 % [INFO] Scanning for conjecture ...
% 2.14/1.37 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.14/1.39 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.14/1.39 % [INFO] Problem is higher-order (TPTP THF).
% 2.14/1.40 % [INFO] Type checking passed.
% 2.14/1.40 % [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 ...
% 163.41/30.68 % External prover 'e' found a proof!
% 163.41/30.68 % [INFO] Killing All external provers ...
% 163.41/30.68 % Time passed: 30150ms (effective reasoning time: 29679ms)
% 163.41/30.68 % 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)>
% 163.41/30.68 % Axioms used in derivation (0):
% 163.41/30.68 % No. of inferences in proof: 285
% 163.41/30.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 30150 ms resp. 29679 ms w/o parsing
% 163.96/30.83 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 163.96/30.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------