TSTP Solution File: NUM637^1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : NUM637^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 01:31:09 EDT 2024
% Result : Theorem 249.12s 47.01s
% Output : Refutation 249.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 26
% Syntax : Number of formulae : 465 ( 146 unt; 20 typ; 0 def)
% Number of atoms : 1371 ( 308 equ; 55 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 4601 ( 868 ~; 444 |; 0 &;3278 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 386 ( 386 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 18 con; 0-2 aty)
% Number of variables : 1316 ( 687 ^ 628 !; 1 ?;1316 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_type,type,
x: nat ).
thf(n_1_type,type,
n_1: nat ).
thf(suc_type,type,
suc: nat > nat ).
thf(set_type,type,
set: $tType ).
thf(esti_type,type,
esti: nat > set > $o ).
thf(setof_type,type,
setof: ( nat > $o ) > set ).
thf(sk1_type,type,
sk1: set > nat ).
thf(sk6_type,type,
sk6: ( nat > $o ) > nat ).
thf(sk7_type,type,
sk7: ( nat > $o ) > nat ).
thf(sk9_type,type,
sk9: ( nat > $o ) > nat ).
thf(sk12_type,type,
sk12: nat ).
thf(sk13_type,type,
sk13: nat ).
thf(sk14_type,type,
sk14: nat ).
thf(sk15_type,type,
sk15: nat ).
thf(sk16_type,type,
sk16: nat ).
thf(sk17_type,type,
sk17: nat ).
thf(sk18_type,type,
sk18: nat ).
thf(sk19_type,type,
sk19: nat ).
thf(sk20_type,type,
sk20: nat ).
thf(6,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( esti @ B @ ( setof @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',estii) ).
thf(21,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( esti @ B @ ( setof @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,plain,
! [B: nat,A: nat > $o] :
( ~ ( A @ B )
| ( esti @ B @ ( setof @ A ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(82,plain,
! [D: nat,C: nat > $o,B: nat,A: nat > $o] :
( ~ ( A @ B )
| ( esti @ D @ ( setof @ C ) )
| ( ( esti @ B @ ( setof @ A ) )
!= ( C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[22,22]) ).
thf(97,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( C @ A @ ( B @ A ) )
| ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[82:[bind(A,$thf( G @ D )),bind(B,$thf( E @ D )),bind(C,$thf( ^ [G: nat] : ( esti @ ( E @ G ) @ ( setof @ ( G @ G ) ) ) )),bind(D,$thf( D ))]]) ).
thf(99,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( C @ A @ ( B @ A ) )
| ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(4,axiom,
! [A: nat > $o,B: nat] :
( ( esti @ B @ ( setof @ A ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',estie) ).
thf(16,plain,
! [A: nat > $o,B: nat] :
( ( esti @ B @ ( setof @ A ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
! [B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[16]) ).
thf(5,axiom,
! [A: set] :
( ( esti @ n_1 @ A )
=> ( ! [B: nat] :
( ( esti @ B @ A )
=> ( esti @ ( suc @ B ) @ A ) )
=> ! [B: nat] : ( esti @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(18,plain,
! [A: set] :
( ( esti @ n_1 @ A )
=> ( ! [B: nat] :
( ( esti @ B @ A )
=> ( esti @ ( suc @ B ) @ A ) )
=> ! [B: nat] : ( esti @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,plain,
! [B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ( esti @ ( sk1 @ A ) @ A )
| ( esti @ B @ A ) ),
inference(cnf,[status(esa)],[18]) ).
thf(59,plain,
! [B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ( esti @ ( sk1 @ A ) @ A )
| ( ( esti @ B @ A )
!= ( esti @ ( sk1 @ A ) @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[20]) ).
thf(60,plain,
! [A: set] :
( ~ ( esti @ n_1 @ A )
| ( esti @ ( sk1 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( C )),bind(B,$thf( sk1 @ C ))]]) ).
thf(67,plain,
! [A: set] :
( ~ ( esti @ n_1 @ A )
| ( esti @ ( sk1 @ A ) @ A ) ),
inference(simp,[status(thm)],[60]) ).
thf(262,plain,
! [C: set,B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ( esti @ ( sk1 @ C ) @ C )
| ( ( A @ B )
!= ( esti @ n_1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17,67]) ).
thf(275,plain,
! [A: nat > set] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [B: nat] : ( esti @ B @ ( A @ B ) ) ) )
| ( esti @ ( sk1 @ ( A @ n_1 ) ) @ ( A @ n_1 ) ) ),
inference(pre_uni,[status(thm)],[262:[bind(A,$thf( ^ [E: nat] : ( esti @ E @ ( E @ E ) ) )),bind(B,$thf( n_1 )),bind(C,$thf( E @ n_1 ))]]) ).
thf(286,plain,
! [A: nat > set] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [B: nat] : ( esti @ B @ ( A @ B ) ) ) )
| ( esti @ ( sk1 @ ( A @ n_1 ) ) @ ( A @ n_1 ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(44208,plain,
! [D: nat > set,C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( C @ A @ ( B @ A ) )
| ( esti @ ( sk1 @ ( D @ n_1 ) ) @ ( D @ n_1 ) )
| ( ( esti @ A
@ ( setof
@ ^ [E: nat] : ( esti @ ( B @ E ) @ ( setof @ ( C @ E ) ) ) ) )
!= ( esti @ n_1
@ ( setof
@ ^ [E: nat] : ( esti @ E @ ( D @ E ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[99,286]) ).
thf(44209,plain,
! [A: nat > nat > $o] :
( ~ ( A @ n_1 @ n_1 )
| ( esti @ ( sk1 @ ( setof @ ( A @ n_1 ) ) ) @ ( setof @ ( A @ n_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[44208:[bind(A,$thf( n_1 )),bind(B,$thf( ^ [E: nat] : E )),bind(C,$thf( E )),bind(D,$thf( ^ [F: nat] : ( setof @ ( E @ F ) ) ))]]) ).
thf(44231,plain,
( ( n_1 != n_1 )
| ( esti @ ( sk1 @ ( setof @ ( (=) @ nat @ n_1 ) ) ) @ ( setof @ ( (=) @ nat @ n_1 ) ) ) ),
inference(replace_andrewseq,[status(thm)],[44209:[bind(A,$thf( (=) @ nat ))]]) ).
thf(44232,plain,
( ( n_1 != n_1 )
| ( esti @ ( sk1 @ ( setof @ ( (=) @ nat @ n_1 ) ) ) @ ( setof @ ( (=) @ nat @ n_1 ) ) ) ),
inference(lifteq,[status(thm)],[44231]) ).
thf(44456,plain,
esti @ ( sk1 @ ( setof @ ( (=) @ nat @ n_1 ) ) ) @ ( setof @ ( (=) @ nat @ n_1 ) ),
inference(pattern_uni,[status(thm)],[44232:[]]) ).
thf(26,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[17:[bind(A,$thf( ^ [D: nat] : ~ ( C @ D ) ))]]) ).
thf(33,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(34,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(205,plain,
! [B: nat > $o,A: nat] :
( ~ ~ ( B @ A )
| ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ~ ( B @ C ) ) ) ),
inference(prim_subst,[status(thm)],[34:[bind(A,$thf( A )),bind(B,$thf( ^ [D: nat] : ~ ( C @ D ) ))]]) ).
thf(228,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ~ ( B @ C ) ) )
| ( B @ A ) ),
inference(cnf,[status(esa)],[205]) ).
thf(229,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ A @ ( setof @ B ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[228]) ).
thf(44721,plain,
! [B: nat > $o,A: nat] :
( ( B @ A )
| ( ( esti @ ( sk1 @ ( setof @ ( (=) @ nat @ n_1 ) ) ) @ ( setof @ ( (=) @ nat @ n_1 ) ) )
!= ( esti @ A @ ( setof @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[44456,229]) ).
thf(44722,plain,
( n_1
= ( sk1 @ ( setof @ ( (=) @ nat @ n_1 ) ) ) ),
inference(pattern_uni,[status(thm)],[44721:[bind(A,$thf( sk1 @ ( setof @ ( (=) @ nat @ n_1 ) ) )),bind(B,$thf( (=) @ nat @ n_1 ))]]) ).
thf(44823,plain,
( ( sk1 @ ( setof @ ( (=) @ nat @ n_1 ) ) )
= n_1 ),
inference(lifteq,[status(thm)],[44722]) ).
thf(44954,plain,
esti @ n_1 @ ( setof @ ( (=) @ nat @ n_1 ) ),
inference(rewrite,[status(thm)],[44456,44823]) ).
thf(84,plain,
! [B: nat > $o,A: nat] :
( ~ ~ ( B @ A )
| ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) ),
inference(prim_subst,[status(thm)],[22:[bind(A,$thf( ^ [D: nat] : ~ ( C @ D ) ))]]) ).
thf(101,plain,
! [B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( B @ A ) ),
inference(cnf,[status(esa)],[84]) ).
thf(102,plain,
! [B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[101]) ).
thf(374,plain,
! [C: set,B: nat > $o,A: nat] :
( ( B @ A )
| ( esti @ ( sk1 @ C ) @ C )
| ( ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( B @ D ) ) )
!= ( esti @ n_1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[102,67]) ).
thf(375,plain,
! [A: nat > $o] :
( ( A @ n_1 )
| ( esti
@ ( sk1
@ ( setof
@ ^ [B: nat] :
~ ( A @ B ) ) )
@ ( setof
@ ^ [B: nat] :
~ ( A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[374:[bind(A,$thf( n_1 )),bind(B,$thf( E )),bind(C,$thf( setof @ ^ [E: nat] : ~ ( E @ E ) ))]]) ).
thf(470,plain,
! [A: nat > $o] :
( ( A @ n_1 )
| ( esti
@ ( sk1
@ ( setof
@ ^ [B: nat] :
~ ( A @ B ) ) )
@ ( setof
@ ^ [B: nat] :
~ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[375]) ).
thf(29,plain,
! [A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) )
| $false ),
inference(prim_subst,[status(thm)],[17:[bind(A,$thf( ^ [C: nat] : $false ))]]) ).
thf(38,plain,
! [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ),
inference(simp,[status(thm)],[29]) ).
thf(667,plain,
! [B: nat,A: nat > $o] :
( ( A @ n_1 )
| ( ( esti
@ ( sk1
@ ( setof
@ ^ [C: nat] :
~ ( A @ C ) ) )
@ ( setof
@ ^ [C: nat] :
~ ( A @ C ) ) )
!= ( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[470,38]) ).
thf(721,plain,
! [B: nat,A: nat > $o] :
( ( A @ n_1 )
| ( ( sk1
@ ( setof
@ ^ [C: nat] :
~ ( A @ C ) ) )
!= B )
| ( ( setof
@ ^ [C: nat] :
~ ( A @ C ) )
!= ( setof
@ ^ [C: nat] : $false ) ) ),
inference(simp,[status(thm)],[667]) ).
thf(765,plain,
! [A: nat > $o] :
( ( A @ n_1 )
| ( ( setof
@ ^ [B: nat] :
~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $false ) ) ),
inference(simp,[status(thm)],[721]) ).
thf(1777,plain,
! [A: nat > $o] :
( ~ ( A @ n_1 )
| ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $false ) ) ),
inference(prim_subst,[status(thm)],[765:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(1832,plain,
! [A: nat > $o] :
( ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $false ) )
| ~ ( A @ n_1 ) ),
inference(cnf,[status(esa)],[1777]) ).
thf(1833,plain,
! [A: nat > $o] :
( ( ( setof @ A )
!= ( setof
@ ^ [B: nat] : $false ) )
| ~ ( A @ n_1 ) ),
inference(simp,[status(thm)],[1832]) ).
thf(45231,plain,
! [A: nat > $o] :
( ( ( setof @ A )
!= ( setof
@ ^ [B: nat] : $false ) )
| ( ( esti @ n_1 @ ( setof @ ( (=) @ nat @ n_1 ) ) )
!= ( A @ n_1 ) ) ),
inference(paramod_ordered,[status(thm)],[44954,1833]) ).
thf(45410,plain,
( ( setof
@ ^ [A: nat] : ( esti @ A @ ( setof @ ( (=) @ nat @ A ) ) ) )
!= ( setof
@ ^ [A: nat] : $false ) ),
inference(pre_uni,[status(thm)],[45231:[bind(A,$thf( ^ [B: nat] : ( esti @ B @ ( setof @ ( (=) @ nat @ B ) ) ) ))]]) ).
thf(46636,plain,
( ( ^ [A: nat] : ( esti @ A @ ( setof @ ( (=) @ nat @ A ) ) ) )
!= ( ^ [A: nat] : $false ) ),
inference(simp,[status(thm)],[45410]) ).
thf(46984,plain,
esti @ sk16 @ ( setof @ ( (=) @ nat @ sk16 ) ),
inference(func_ext,[status(esa)],[46636]) ).
thf(48283,plain,
! [A: nat] :
( ( esti @ sk16 @ ( setof @ ( (=) @ nat @ sk16 ) ) )
!= ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[46984,38]) ).
thf(48505,plain,
! [A: nat] :
( ( sk16 != A )
| ( ( setof @ ( (=) @ nat @ sk16 ) )
!= ( setof
@ ^ [B: nat] : $false ) ) ),
inference(simp,[status(thm)],[48283]) ).
thf(48604,plain,
( ( setof @ ( (=) @ nat @ sk16 ) )
!= ( setof
@ ^ [A: nat] : $false ) ),
inference(simp,[status(thm)],[48505]) ).
thf(24,plain,
! [D: nat,C: nat > $o,B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ( C @ D )
| ( ( A @ B )
!= ( esti @ D @ ( setof @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,17]) ).
thf(31,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) )
| ( C @ A @ ( B @ A ) ) ),
inference(pre_uni,[status(thm)],[24:[bind(A,$thf( ^ [G: nat] : ( esti @ ( E @ G ) @ ( setof @ ( G @ G ) ) ) )),bind(B,$thf( B )),bind(C,$thf( G @ B )),bind(D,$thf( E @ B ))]]) ).
thf(39,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) )
| ( C @ A @ ( B @ A ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(83,plain,
! [A: nat] :
( ~ $true
| ( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ),
inference(prim_subst,[status(thm)],[22:[bind(A,$thf( ^ [C: nat] : $true ))]]) ).
thf(100,plain,
! [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ),
inference(simp,[status(thm)],[83]) ).
thf(258,plain,
! [C: nat > $o,B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ~ ( C @ B )
| ( ( esti @ ( sk1 @ A ) @ A )
!= ( esti @ B
@ ( setof
@ ^ [D: nat] :
~ ( C @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[67,34]) ).
thf(259,plain,
! [A: nat > $o] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] :
~ ( A @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( setof @ ^ [E: nat] : ~ ( F @ E ) )),bind(B,$thf( sk1 @ ( setof @ ^ [E: nat] : ~ ( F @ E ) ) )),bind(C,$thf( F ))]]) ).
thf(276,plain,
! [A: nat > $o] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] :
~ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[259]) ).
thf(605,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( esti @ A
@ ( setof
@ ^ [C: nat] : $true ) )
!= ( B
@ ( sk1
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[100,276]) ).
thf(619,plain,
! [A: nat > nat] :
~ ( esti @ n_1
@ ( setof
@ ^ [B: nat] :
~ ( esti @ ( A @ B )
@ ( setof
@ ^ [C: nat] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[605:[bind(A,$thf( C @ ( sk1 @ ( setof @ ^ [D: nat] : ~ ( esti @ ( C @ D ) @ ( setof @ ^ [E: nat] : $true ) ) ) ) )),bind(B,$thf( ^ [D: nat] : ( esti @ ( C @ D ) @ ( setof @ ^ [E: nat] : $true ) ) ))]]) ).
thf(648,plain,
! [A: nat > nat] :
~ ( esti @ n_1
@ ( setof
@ ^ [B: nat] :
~ ( esti @ ( A @ B )
@ ( setof
@ ^ [C: nat] : $true ) ) ) ),
inference(simp,[status(thm)],[619]) ).
thf(983,plain,
~ ( esti @ n_1
@ ( setof
@ ^ [A: nat] : ~ $true ) ),
inference(rewrite,[status(thm)],[648,100]) ).
thf(984,plain,
~ ( esti @ n_1
@ ( setof
@ ^ [A: nat] : $false ) ),
inference(simp,[status(thm)],[983]) ).
thf(1123,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) )
| ( ( C @ A @ ( B @ A ) )
!= ( esti @ n_1
@ ( setof
@ ^ [D: nat] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,984]) ).
thf(1152,plain,
~ ( esti @ n_1
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1123:[bind(A,$thf( n_1 )),bind(B,$thf( ^ [D: nat] : D )),bind(C,$thf( ^ [D: nat] : ^ [E: nat] : ( esti @ E @ ( setof @ ^ [F: nat] : $false ) ) ))]]) ).
thf(1454,plain,
~ ( esti @ n_1
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(rewrite,[status(thm)],[1152,38]) ).
thf(199,plain,
! [C: nat > $o,B: nat,A: nat] :
( ~ ( C @ B )
| ( ( esti @ A
@ ( setof
@ ^ [D: nat] : $true ) )
!= ( esti @ B
@ ( setof
@ ^ [D: nat] :
~ ( C @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[100,34]) ).
thf(213,plain,
! [C: nat > $o,B: nat,A: nat] :
( ~ ( C @ B )
| ( A != B )
| ( ( setof
@ ^ [D: nat] :
~ ( C @ D ) )
!= ( setof
@ ^ [D: nat] : $true ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(236,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( setof
@ ^ [C: nat] :
~ ( B @ C ) )
!= ( setof
@ ^ [C: nat] : $true ) ) ),
inference(simp,[status(thm)],[213]) ).
thf(336,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( ^ [C: nat] :
~ ( B @ C ) )
!= ( ^ [C: nat] : $true ) ) ),
inference(simp,[status(thm)],[236]) ).
thf(45287,plain,
! [B: nat > $o,A: nat] :
( ( ( ^ [C: nat] :
~ ( B @ C ) )
!= ( ^ [C: nat] : $true ) )
| ( ( esti @ n_1 @ ( setof @ ( (=) @ nat @ n_1 ) ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44954,336]) ).
thf(45350,plain,
( ( ^ [A: nat] :
~ ( esti @ A @ ( setof @ ( (=) @ nat @ A ) ) ) )
!= ( ^ [A: nat] : $true ) ),
inference(pre_uni,[status(thm)],[45287:[bind(A,$thf( n_1 )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ( (=) @ nat @ C ) ) ) ))]]) ).
thf(46632,plain,
~ ~ ( esti @ sk14 @ ( setof @ ( (=) @ nat @ sk14 ) ) ),
inference(func_ext,[status(esa)],[45350]) ).
thf(46633,plain,
esti @ sk14 @ ( setof @ ( (=) @ nat @ sk14 ) ),
inference(cnf,[status(esa)],[46632]) ).
thf(46698,plain,
! [B: nat,A: nat > $o] :
( ( esti @ B @ ( setof @ A ) )
| ( ( esti @ sk14 @ ( setof @ ( (=) @ nat @ sk14 ) ) )
!= ( A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[46633,22]) ).
thf(46773,plain,
( esti @ sk14
@ ( setof
@ ^ [A: nat] : ( esti @ A @ ( setof @ ( (=) @ nat @ A ) ) ) ) ),
inference(pre_uni,[status(thm)],[46698:[bind(A,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ( (=) @ nat @ C ) ) ) )),bind(B,$thf( sk14 ))]]) ).
thf(998,plain,
! [A: nat > $o] :
( ( esti
@ ( sk1
@ ( setof
@ ^ [B: nat] :
~ ( A @ B ) ) )
@ ( setof
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ( ( A @ n_1 )
!= ( esti @ n_1
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[470,984]) ).
thf(1008,plain,
( esti
@ ( sk1
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) )
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(pre_uni,[status(thm)],[998:[bind(A,$thf( ^ [B: nat] : ( esti @ B @ ( setof @ ^ [C: nat] : $false ) ) ))]]) ).
thf(1881,plain,
( esti
@ ( sk1
@ ( setof
@ ^ [A: nat] : ~ $false ) )
@ ( setof
@ ^ [A: nat] : ~ $false ) ),
inference(rewrite,[status(thm)],[1008,38]) ).
thf(1882,plain,
( esti
@ ( sk1
@ ( setof
@ ^ [A: nat] : $true ) )
@ ( setof
@ ^ [A: nat] : $true ) ),
inference(simp,[status(thm)],[1881]) ).
thf(4036,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) )
| ( ( esti
@ ( sk1
@ ( setof
@ ^ [D: nat] : $true ) )
@ ( setof
@ ^ [D: nat] : $true ) )
!= ( C @ A @ ( B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1882,99]) ).
thf(4143,plain,
( esti
@ ( sk1
@ ( setof
@ ^ [A: nat] : $true ) )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4036:[bind(A,$thf( sk1 @ ( setof @ ^ [D: nat] : $true ) )),bind(B,$thf( ^ [D: nat] : D )),bind(C,$thf( ^ [D: nat] : ^ [E: nat] : ( esti @ E @ ( setof @ ^ [F: nat] : $true ) ) ))]]) ).
thf(4787,plain,
( esti
@ ( sk1
@ ( setof
@ ^ [A: nat] : $true ) )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(rewrite,[status(thm)],[4143,100]) ).
thf(1920,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( esti
@ ( sk1
@ ( setof
@ ^ [C: nat] : $true ) )
@ ( setof
@ ^ [C: nat] : $true ) )
!= ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1882,34]) ).
thf(1959,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( sk1
@ ( setof
@ ^ [C: nat] : $true ) )
!= A )
| ( ( setof
@ ^ [C: nat] :
~ ( B @ C ) )
!= ( setof
@ ^ [C: nat] : $true ) ) ),
inference(simp,[status(thm)],[1920]) ).
thf(1980,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) )
| ( ( setof
@ ^ [B: nat] :
~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[1959]) ).
thf(8495,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) )
| ( ( ^ [B: nat] :
~ ( A @ B ) )
!= ( ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[1980]) ).
thf(8672,plain,
! [A: nat > $o] :
( ~ ~ ( A @ ( sk7 @ A ) )
| ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(func_ext,[status(esa)],[8495]) ).
thf(8845,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) )
| ( A @ ( sk7 @ A ) ) ),
inference(cnf,[status(esa)],[8672]) ).
thf(9694,plain,
! [A: nat > $o] :
( ( A @ ( sk7 @ A ) )
| ( ( esti
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) )
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) )
!= ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4787,8845]) ).
thf(9793,plain,
( esti
@ ( sk7
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) ) )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[9694:[bind(A,$thf( ^ [B: nat] : ( esti @ B @ ( setof @ ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $true ) ) ) ) ))]]) ).
thf(19898,plain,
( esti
@ ( sk7
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) )
@ ( setof
@ ^ [A: nat] : $true ) ),
inference(rewrite,[status(thm)],[9793,100]) ).
thf(86,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ ( B @ A ) @ ( C @ A ) )
| ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(prim_subst,[status(thm)],[22:[bind(A,$thf( ^ [E: nat] : ( esti @ ( C @ E ) @ ( D @ E ) ) ))]]) ).
thf(107,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ ( B @ A ) @ ( C @ A ) )
| ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(20017,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( C @ D ) ) ) )
| ( ( esti
@ ( sk7
@ ^ [D: nat] :
( esti @ D
@ ( setof
@ ^ [E: nat] : $true ) ) )
@ ( setof
@ ^ [D: nat] : $true ) )
!= ( esti @ ( B @ A ) @ ( C @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[19898,107]) ).
thf(20042,plain,
( esti
@ ( sk7
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[20017:[bind(A,$thf( sk7 @ ^ [D: nat] : ( esti @ D @ ( setof @ ^ [E: nat] : $true ) ) )),bind(B,$thf( ^ [D: nat] : D )),bind(C,$thf( ^ [D: nat] : ( setof @ ^ [E: nat] : $true ) ))]]) ).
thf(21299,plain,
( esti
@ ( sk7
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] : $true ) ),
inference(rewrite,[status(thm)],[20042,100]) ).
thf(21362,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( esti
@ ( sk7
@ ^ [C: nat] : $true )
@ ( setof
@ ^ [C: nat] : $true ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21299,34]) ).
thf(21528,plain,
~ ( esti
@ ( sk7
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[21362:[bind(A,$thf( sk7 @ ^ [C: nat] : $true )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $true ) ) ))]]) ).
thf(24176,plain,
~ ( esti
@ ( sk7
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] : ~ $true ) ),
inference(rewrite,[status(thm)],[21528,100]) ).
thf(24177,plain,
~ ( esti
@ ( sk7
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] : $false ) ),
inference(simp,[status(thm)],[24176]) ).
thf(24250,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) )
| ( ( C @ A @ ( B @ A ) )
!= ( esti
@ ( sk7
@ ^ [D: nat] : $true )
@ ( setof
@ ^ [D: nat] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,24177]) ).
thf(24387,plain,
~ ( esti
@ ( sk7
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[24250:[bind(A,$thf( sk7 @ ^ [D: nat] : $true )),bind(B,$thf( ^ [D: nat] : D )),bind(C,$thf( ^ [D: nat] : ^ [E: nat] : ( esti @ E @ ( setof @ ^ [F: nat] : $false ) ) ))]]) ).
thf(27257,plain,
~ ( esti
@ ( sk7
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(rewrite,[status(thm)],[24387,38]) ).
thf(27287,plain,
! [B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( B @ A )
!= ( esti
@ ( sk7
@ ^ [C: nat] : $true )
@ ( setof
@ ^ [C: nat] :
( esti @ C
@ ( setof
@ ^ [D: nat] : $false ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[102,27257]) ).
thf(27422,plain,
( esti
@ ( sk7
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[27287:[bind(A,$thf( sk7 @ ^ [C: nat] : $true )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : ( esti @ D @ ( setof @ ^ [E: nat] : $false ) ) ) ) ))]]) ).
thf(27529,plain,
( esti
@ ( sk7
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(rewrite,[status(thm)],[27422,38]) ).
thf(192,plain,
! [D: nat > $o,C: nat,B: nat,A: nat > $o] :
( ~ ( A @ B )
| ~ ( esti @ C
@ ( setof
@ ^ [E: nat] :
~ ( D @ E ) ) )
| ( ( esti @ B @ ( setof @ A ) )
!= ( D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[22,34]) ).
thf(211,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( C @ A @ ( B @ A ) )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[192:[bind(A,$thf( G @ C )),bind(B,$thf( E @ C )),bind(C,$thf( C )),bind(D,$thf( ^ [G: nat] : ( esti @ ( E @ G ) @ ( setof @ ( G @ G ) ) ) ))]]) ).
thf(234,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( C @ A @ ( B @ A ) )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[211]) ).
thf(988,plain,
! [B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( B @ A )
!= ( esti @ n_1
@ ( setof
@ ^ [C: nat] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[102,984]) ).
thf(1010,plain,
( esti @ n_1
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(pre_uni,[status(thm)],[988:[bind(A,$thf( n_1 )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $false ) ) ))]]) ).
thf(1032,plain,
( esti @ n_1
@ ( setof
@ ^ [A: nat] : ~ $false ) ),
inference(rewrite,[status(thm)],[1010,38]) ).
thf(1033,plain,
( esti @ n_1
@ ( setof
@ ^ [A: nat] : $true ) ),
inference(simp,[status(thm)],[1032]) ).
thf(1057,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( esti @ n_1
@ ( setof
@ ^ [C: nat] : $true ) )
!= ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1033,34]) ).
thf(1081,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( n_1 != A )
| ( ( setof
@ ^ [C: nat] :
~ ( B @ C ) )
!= ( setof
@ ^ [C: nat] : $true ) ) ),
inference(simp,[status(thm)],[1057]) ).
thf(1095,plain,
! [A: nat > $o] :
( ~ ( A @ n_1 )
| ( ( setof
@ ^ [B: nat] :
~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[1081]) ).
thf(4453,plain,
! [A: nat > $o] :
( ~ ~ ( A @ n_1 )
| ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(prim_subst,[status(thm)],[1095:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(4497,plain,
! [A: nat > $o] :
( ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) )
| ( A @ n_1 ) ),
inference(cnf,[status(esa)],[4453]) ).
thf(4498,plain,
! [A: nat > $o] :
( ( ( setof @ A )
!= ( setof
@ ^ [B: nat] : $true ) )
| ( A @ n_1 ) ),
inference(simp,[status(thm)],[4497]) ).
thf(6841,plain,
! [A: nat > $o] :
( ( ( setof @ A )
!= ( setof
@ ^ [B: nat] : $true ) )
| ( ( A @ n_1 )
!= ( esti @ n_1
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4498,1454]) ).
thf(6946,plain,
( ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) )
!= ( setof
@ ^ [A: nat] : $true ) ),
inference(pre_uni,[status(thm)],[6841:[bind(A,$thf( ^ [B: nat] : ( esti @ B @ ( setof @ ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $false ) ) ) ) ))]]) ).
thf(7601,plain,
( ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) )
!= ( setof
@ ^ [A: nat] : $true ) ),
inference(rewrite,[status(thm)],[6946,38]) ).
thf(4028,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) )
| ( ( esti @ n_1
@ ( setof
@ ^ [D: nat] : $true ) )
!= ( C @ A @ ( B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1033,99]) ).
thf(4160,plain,
( esti @ n_1
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4028:[bind(A,$thf( n_1 )),bind(B,$thf( ^ [D: nat] : D )),bind(C,$thf( ^ [D: nat] : ^ [E: nat] : ( esti @ E @ ( setof @ ^ [F: nat] : $true ) ) ))]]) ).
thf(4264,plain,
( esti @ n_1
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(rewrite,[status(thm)],[4160,100]) ).
thf(4417,plain,
! [A: nat > $o] :
( ~ ( A @ n_1 )
| ( ( ^ [B: nat] :
~ ( A @ B ) )
!= ( ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[1095]) ).
thf(4922,plain,
! [A: nat > $o] :
( ~ ~ ( A @ ( sk6 @ A ) )
| ~ ( A @ n_1 ) ),
inference(func_ext,[status(esa)],[4417]) ).
thf(5015,plain,
! [A: nat > $o] :
( ~ ( A @ n_1 )
| ( A @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[4922]) ).
thf(5357,plain,
! [A: nat > $o] :
( ( A @ ( sk6 @ A ) )
| ( ( esti @ n_1
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) )
!= ( A @ n_1 ) ) ),
inference(paramod_ordered,[status(thm)],[4264,5015]) ).
thf(5495,plain,
( esti
@ ( sk6
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) ) )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[5357:[bind(A,$thf( ^ [B: nat] : ( esti @ B @ ( setof @ ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $true ) ) ) ) ))]]) ).
thf(7641,plain,
( esti
@ ( sk6
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) )
@ ( setof
@ ^ [A: nat] : $true ) ),
inference(rewrite,[status(thm)],[5495,100]) ).
thf(7688,plain,
! [B: nat,A: nat > $o] :
( ( esti @ B @ ( setof @ A ) )
| ( ( esti
@ ( sk6
@ ^ [C: nat] :
( esti @ C
@ ( setof
@ ^ [D: nat] : $true ) ) )
@ ( setof
@ ^ [C: nat] : $true ) )
!= ( A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7641,22]) ).
thf(7738,plain,
( esti
@ ( sk6
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[7688:[bind(A,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $true ) ) )),bind(B,$thf( sk6 @ ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $true ) ) ))]]) ).
thf(8289,plain,
( esti
@ ( sk6
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] : $true ) ),
inference(rewrite,[status(thm)],[7738,100]) ).
thf(8335,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( esti
@ ( sk6
@ ^ [C: nat] : $true )
@ ( setof
@ ^ [C: nat] : $true ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8289,34]) ).
thf(8384,plain,
~ ( esti
@ ( sk6
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[8335:[bind(A,$thf( sk6 @ ^ [C: nat] : $true )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $true ) ) ))]]) ).
thf(9372,plain,
~ ( esti
@ ( sk6
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] : ~ $true ) ),
inference(rewrite,[status(thm)],[8384,100]) ).
thf(9373,plain,
~ ( esti
@ ( sk6
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] : $false ) ),
inference(simp,[status(thm)],[9372]) ).
thf(7686,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( esti
@ ( sk6
@ ^ [C: nat] :
( esti @ C
@ ( setof
@ ^ [D: nat] : $true ) ) )
@ ( setof
@ ^ [C: nat] : $true ) )
!= ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7641,34]) ).
thf(7747,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( sk6
@ ^ [C: nat] :
( esti @ C
@ ( setof
@ ^ [D: nat] : $true ) ) )
!= A )
| ( ( setof
@ ^ [C: nat] :
~ ( B @ C ) )
!= ( setof
@ ^ [C: nat] : $true ) ) ),
inference(simp,[status(thm)],[7686]) ).
thf(7792,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk6
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) )
| ( ( setof
@ ^ [B: nat] :
~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[7747]) ).
thf(20176,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) )
| ( ( setof
@ ^ [B: nat] :
~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(rewrite,[status(thm)],[7792,100]) ).
thf(20177,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) )
| ( ( ^ [B: nat] :
~ ( A @ B ) )
!= ( ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[20176]) ).
thf(20419,plain,
! [A: nat > $o] :
( ~ ~ ( A @ ( sk9 @ A ) )
| ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) ) ),
inference(func_ext,[status(esa)],[20177]) ).
thf(20623,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) )
| ( A @ ( sk9 @ A ) ) ),
inference(cnf,[status(esa)],[20419]) ).
thf(1919,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( esti
@ ( sk1
@ ( setof
@ ^ [C: nat] : $true ) )
@ ( setof
@ ^ [C: nat] : $true ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1882,34]) ).
thf(1927,plain,
~ ( esti
@ ( sk1
@ ( setof
@ ^ [A: nat] : $true ) )
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[1919:[bind(A,$thf( sk1 @ ( setof @ ^ [C: nat] : $true ) )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $true ) ) ))]]) ).
thf(2712,plain,
~ ( esti
@ ( sk1
@ ( setof
@ ^ [A: nat] : $true ) )
@ ( setof
@ ^ [A: nat] : ~ $true ) ),
inference(rewrite,[status(thm)],[1927,100]) ).
thf(2713,plain,
~ ( esti
@ ( sk1
@ ( setof
@ ^ [A: nat] : $true ) )
@ ( setof
@ ^ [A: nat] : $false ) ),
inference(simp,[status(thm)],[2712]) ).
thf(2750,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) )
| ( ( C @ A @ ( B @ A ) )
!= ( esti
@ ( sk1
@ ( setof
@ ^ [D: nat] : $true ) )
@ ( setof
@ ^ [D: nat] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,2713]) ).
thf(2776,plain,
~ ( esti
@ ( sk1
@ ( setof
@ ^ [A: nat] : $true ) )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2750:[bind(A,$thf( sk1 @ ( setof @ ^ [D: nat] : $true ) )),bind(B,$thf( ^ [D: nat] : D )),bind(C,$thf( ^ [D: nat] : ^ [E: nat] : ( esti @ E @ ( setof @ ^ [F: nat] : $false ) ) ))]]) ).
thf(3667,plain,
~ ( esti
@ ( sk1
@ ( setof
@ ^ [A: nat] : $true ) )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(rewrite,[status(thm)],[2776,38]) ).
thf(3672,plain,
! [B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( B @ A )
!= ( esti
@ ( sk1
@ ( setof
@ ^ [C: nat] : $true ) )
@ ( setof
@ ^ [C: nat] :
( esti @ C
@ ( setof
@ ^ [D: nat] : $false ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[102,3667]) ).
thf(3725,plain,
( esti
@ ( sk1
@ ( setof
@ ^ [A: nat] : $true ) )
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[3672:[bind(A,$thf( sk1 @ ( setof @ ^ [C: nat] : $true ) )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : ( esti @ D @ ( setof @ ^ [E: nat] : $false ) ) ) ) ))]]) ).
thf(3781,plain,
( esti
@ ( sk1
@ ( setof
@ ^ [A: nat] : $true ) )
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(rewrite,[status(thm)],[3725,38]) ).
thf(2717,plain,
! [B: nat > $o,A: nat] :
( ( B @ A )
| ( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
!= ( esti
@ ( sk1
@ ( setof
@ ^ [C: nat] : $true ) )
@ ( setof
@ ^ [C: nat] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[102,2713]) ).
thf(2788,plain,
! [B: nat > $o,A: nat] :
( ( B @ A )
| ( A
!= ( sk1
@ ( setof
@ ^ [C: nat] : $true ) ) )
| ( ( setof
@ ^ [C: nat] :
~ ( B @ C ) )
!= ( setof
@ ^ [C: nat] : $false ) ) ),
inference(simp,[status(thm)],[2717]) ).
thf(2816,plain,
! [A: nat > $o] :
( ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) )
| ( ( setof
@ ^ [B: nat] :
~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $false ) ) ),
inference(simp,[status(thm)],[2788]) ).
thf(15191,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) )
| ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $false ) ) ),
inference(prim_subst,[status(thm)],[2816:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(15330,plain,
! [A: nat > $o] :
( ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $false ) )
| ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(cnf,[status(esa)],[15191]) ).
thf(15331,plain,
! [A: nat > $o] :
( ( ( setof @ A )
!= ( setof
@ ^ [B: nat] : $false ) )
| ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(simp,[status(thm)],[15330]) ).
thf(44807,plain,
! [B: nat > $o,A: nat] :
( ( ( ^ [C: nat] :
~ ( B @ C ) )
!= ( ^ [C: nat] : $true ) )
| ( ( esti @ ( sk1 @ ( setof @ ( (=) @ nat @ n_1 ) ) ) @ ( setof @ ( (=) @ nat @ n_1 ) ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44456,336]) ).
thf(44848,plain,
( ( ^ [A: nat] :
~ ( esti @ A @ ( setof @ ( (=) @ nat @ n_1 ) ) ) )
!= ( ^ [A: nat] : $true ) ),
inference(pre_uni,[status(thm)],[44807:[bind(A,$thf( sk1 @ ( setof @ ( (=) @ nat @ n_1 ) ) )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ( (=) @ nat @ n_1 ) ) ) ))]]) ).
thf(9379,plain,
! [B: nat > $o,A: nat] :
( ( B @ A )
| ( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
!= ( esti
@ ( sk6
@ ^ [C: nat] : $true )
@ ( setof
@ ^ [C: nat] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[102,9373]) ).
thf(9469,plain,
! [B: nat > $o,A: nat] :
( ( B @ A )
| ( A
!= ( sk6
@ ^ [C: nat] : $true ) )
| ( ( setof
@ ^ [C: nat] :
~ ( B @ C ) )
!= ( setof
@ ^ [C: nat] : $false ) ) ),
inference(simp,[status(thm)],[9379]) ).
thf(9557,plain,
! [A: nat > $o] :
( ( A
@ ( sk6
@ ^ [B: nat] : $true ) )
| ( ( setof
@ ^ [B: nat] :
~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $false ) ) ),
inference(simp,[status(thm)],[9469]) ).
thf(32396,plain,
! [A: nat > $o] :
( ( A
@ ( sk6
@ ^ [B: nat] : $true ) )
| ( ( ^ [B: nat] :
~ ( A @ B ) )
!= ( ^ [B: nat] : $false ) ) ),
inference(simp,[status(thm)],[9557]) ).
thf(32955,plain,
! [A: nat > $o] :
( ~ ( A @ ( sk10 @ A ) )
| ( A
@ ( sk6
@ ^ [B: nat] : $true ) ) ),
inference(func_ext,[status(esa)],[32396]) ).
thf(33421,plain,
! [A: nat > $o] :
( ( A
@ ( sk6
@ ^ [B: nat] : $true ) )
| ~ ( A @ ( sk10 @ A ) ) ),
inference(cnf,[status(esa)],[32955]) ).
thf(46659,plain,
! [A: nat] :
( ( esti @ sk14 @ ( setof @ ( (=) @ nat @ sk14 ) ) )
!= ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[46633,38]) ).
thf(46803,plain,
! [A: nat] :
( ( sk14 != A )
| ( ( setof @ ( (=) @ nat @ sk14 ) )
!= ( setof
@ ^ [B: nat] : $false ) ) ),
inference(simp,[status(thm)],[46659]) ).
thf(46967,plain,
( ( setof @ ( (=) @ nat @ sk14 ) )
!= ( setof
@ ^ [A: nat] : $false ) ),
inference(simp,[status(thm)],[46803]) ).
thf(48221,plain,
( ( (=) @ nat @ sk14 )
!= ( ^ [A: nat] : $false ) ),
inference(simp,[status(thm)],[46967]) ).
thf(48222,plain,
sk14 = sk17,
inference(func_ext,[status(esa)],[48221]) ).
thf(48223,plain,
sk17 = sk14,
inference(lifteq,[status(thm)],[48222]) ).
thf(28,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
( ( B @ D )
| ( C @ D ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(prim_subst,[status(thm)],[17:[bind(A,$thf( ^ [E: nat] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(36,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ( B @ A )
| ( C @ A )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
( ( B @ D )
| ( C @ D ) ) ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(37,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ( B @ A )
| ( C @ A )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
( ( B @ D )
| ( C @ D ) ) ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(44718,plain,
! [A: nat] :
( ( esti @ ( sk1 @ ( setof @ ( (=) @ nat @ n_1 ) ) ) @ ( setof @ ( (=) @ nat @ n_1 ) ) )
!= ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[44456,38]) ).
thf(44853,plain,
! [A: nat] :
( ( ( sk1 @ ( setof @ ( (=) @ nat @ n_1 ) ) )
!= A )
| ( ( setof @ ( (=) @ nat @ n_1 ) )
!= ( setof
@ ^ [B: nat] : $false ) ) ),
inference(simp,[status(thm)],[44718]) ).
thf(44928,plain,
( ( setof @ ( (=) @ nat @ n_1 ) )
!= ( setof
@ ^ [A: nat] : $false ) ),
inference(simp,[status(thm)],[44853]) ).
thf(45351,plain,
( ( ^ [A: nat] :
~ ( esti @ n_1 @ ( setof @ ( (=) @ nat @ A ) ) ) )
!= ( ^ [A: nat] : $true ) ),
inference(pre_uni,[status(thm)],[45287:[bind(A,$thf( n_1 )),bind(B,$thf( ^ [C: nat] : ( esti @ n_1 @ ( setof @ ( (=) @ nat @ C ) ) ) ))]]) ).
thf(19,plain,
! [B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ~ ( esti @ ( suc @ ( sk1 @ A ) ) @ A )
| ( esti @ B @ A ) ),
inference(cnf,[status(esa)],[18]) ).
thf(123,plain,
! [D: nat,C: nat > $o,B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ~ ( esti @ ( suc @ ( sk1 @ A ) ) @ A )
| ( esti @ D @ ( setof @ C ) )
| ( ( esti @ B @ A )
!= ( C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[19,22]) ).
thf(143,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ n_1 @ ( C @ A ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( C @ A ) ) ) @ ( C @ A ) )
| ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(pre_uni,[status(thm)],[123:[bind(A,$thf( F @ D )),bind(B,$thf( E @ D )),bind(C,$thf( ^ [G: nat] : ( esti @ ( E @ G ) @ ( F @ G ) ) ))]]) ).
thf(152,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ n_1 @ ( C @ A ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( C @ A ) ) ) @ ( C @ A ) )
| ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(simp,[status(thm)],[143]) ).
thf(4273,plain,
! [B: nat > $o,A: nat] :
( ( ( ^ [C: nat] :
~ ( B @ C ) )
!= ( ^ [C: nat] : $true ) )
| ( ( esti @ n_1
@ ( setof
@ ^ [C: nat] :
( esti @ C
@ ( setof
@ ^ [D: nat] : $true ) ) ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4264,336]) ).
thf(4325,plain,
( ( ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) ) )
!= ( ^ [A: nat] : $true ) ),
inference(pre_uni,[status(thm)],[4273:[bind(A,$thf( n_1 )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : ( esti @ D @ ( setof @ ^ [E: nat] : $true ) ) ) ) ))]]) ).
thf(4383,plain,
( ( ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) )
!= ( ^ [A: nat] : $true ) ),
inference(rewrite,[status(thm)],[4325,100]) ).
thf(85,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ~ ( ( B @ A )
| ( C @ A ) )
| ( esti @ A
@ ( setof
@ ^ [D: nat] :
( ( B @ D )
| ( C @ D ) ) ) ) ),
inference(prim_subst,[status(thm)],[22:[bind(A,$thf( ^ [E: nat] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(104,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [D: nat] :
( ( B @ D )
| ( C @ D ) ) ) )
| ~ ( B @ A ) ),
inference(cnf,[status(esa)],[85]) ).
thf(106,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [D: nat] :
( ( B @ D )
| ( C @ D ) ) ) )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[104]) ).
thf(130,plain,
! [B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ( esti @ B @ A )
| ( ( esti @ ( suc @ ( sk1 @ A ) ) @ A )
!= ( esti @ n_1 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(135,plain,
! [B: nat,A: set] :
( ( esti @ B @ A )
| ~ ( esti @ n_1 @ A )
| ( ( suc @ ( sk1 @ A ) )
!= n_1 )
| ( A != A ) ),
inference(simp,[status(thm)],[130]) ).
thf(147,plain,
! [B: nat,A: set] :
( ( esti @ B @ A )
| ~ ( esti @ n_1 @ A )
| ( ( suc @ ( sk1 @ A ) )
!= n_1 ) ),
inference(simp,[status(thm)],[135]) ).
thf(8359,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) )
| ( ( esti
@ ( sk6
@ ^ [D: nat] : $true )
@ ( setof
@ ^ [D: nat] : $true ) )
!= ( C @ A @ ( B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8289,99]) ).
thf(8416,plain,
( esti
@ ( sk6
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[8359:[bind(A,$thf( sk6 @ ^ [D: nat] : $true )),bind(B,$thf( ^ [D: nat] : D )),bind(C,$thf( ^ [D: nat] : ^ [E: nat] : ( esti @ E @ ( setof @ ^ [F: nat] : $true ) ) ))]]) ).
thf(11474,plain,
( esti
@ ( sk6
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(rewrite,[status(thm)],[8416,100]) ).
thf(21702,plain,
! [A: nat > $o] :
( ( A @ ( sk9 @ A ) )
| ( ( esti
@ ( sk6
@ ^ [B: nat] : $true )
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) )
!= ( A
@ ( sk6
@ ^ [B: nat] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[11474,20623]) ).
thf(22122,plain,
( esti
@ ( sk9
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) ) )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[21702:[bind(A,$thf( ^ [B: nat] : ( esti @ B @ ( setof @ ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $true ) ) ) ) ))]]) ).
thf(33528,plain,
( esti
@ ( sk9
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) )
@ ( setof
@ ^ [A: nat] : $true ) ),
inference(rewrite,[status(thm)],[22122,100]) ).
thf(33617,plain,
! [B: nat,A: nat > $o] :
( ( esti @ B @ ( setof @ A ) )
| ( ( esti
@ ( sk9
@ ^ [C: nat] :
( esti @ C
@ ( setof
@ ^ [D: nat] : $true ) ) )
@ ( setof
@ ^ [C: nat] : $true ) )
!= ( A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[33528,22]) ).
thf(33793,plain,
( esti
@ ( sk9
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[33617:[bind(A,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $true ) ) )),bind(B,$thf( sk9 @ ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $true ) ) ))]]) ).
thf(34168,plain,
( esti
@ ( sk9
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] : $true ) ),
inference(rewrite,[status(thm)],[33793,100]) ).
thf(201,plain,
! [D: nat > $o,C: nat,B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ~ ( D @ C )
| ( ( A @ B )
!= ( esti @ C
@ ( setof
@ ^ [E: nat] :
~ ( D @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,34]) ).
thf(210,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
( esti @ ( B @ D )
@ ( setof
@ ^ [E: nat] :
~ ( C @ D @ E ) ) ) ) )
| ~ ( C @ A @ ( B @ A ) ) ),
inference(pre_uni,[status(thm)],[201:[bind(A,$thf( ^ [G: nat] : ( esti @ ( E @ G ) @ ( setof @ ^ [H: nat] : ~ ( H @ G @ H ) ) ) )),bind(B,$thf( B )),bind(C,$thf( E @ B )),bind(D,$thf( H @ B ))]]) ).
thf(233,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
( esti @ ( B @ D )
@ ( setof
@ ^ [E: nat] :
~ ( C @ D @ E ) ) ) ) )
| ~ ( C @ A @ ( B @ A ) ) ),
inference(simp,[status(thm)],[210]) ).
thf(46750,plain,
! [B: nat > $o,A: nat] :
( ( ( ^ [C: nat] :
~ ( B @ C ) )
!= ( ^ [C: nat] : $true ) )
| ( ( esti @ sk14 @ ( setof @ ( (=) @ nat @ sk14 ) ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[46633,336]) ).
thf(46858,plain,
( ( ^ [A: nat] :
~ ( esti @ sk14 @ ( setof @ ( (=) @ nat @ A ) ) ) )
!= ( ^ [A: nat] : $true ) ),
inference(pre_uni,[status(thm)],[46750:[bind(A,$thf( sk14 )),bind(B,$thf( ^ [C: nat] : ( esti @ sk14 @ ( setof @ ( (=) @ nat @ C ) ) ) ))]]) ).
thf(200,plain,
! [D: nat > $o,C: nat,B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ~ ( esti @ C
@ ( setof
@ ^ [E: nat] :
~ ( D @ E ) ) )
| ( ( A @ B )
!= ( D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17,34]) ).
thf(219,plain,
! [D: nat > $o,C: nat,B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ~ ( esti @ C
@ ( setof
@ ^ [E: nat] :
~ ( D @ E ) ) )
| ( ( A @ B )
!= ( D @ C ) ) ),
inference(pre_uni,[status(thm)],[200:[]]) ).
thf(220,plain,
! [D: nat > $o,C: nat,B: nat,A: nat > $o] :
( ~ ( esti @ C
@ ( setof
@ ^ [E: nat] :
~ ( D @ E ) ) )
| ~ ( esti @ B @ ( setof @ A ) )
| ( ( A @ B )
!= ( D @ C ) ) ),
inference(pre_uni,[status(thm)],[219:[]]) ).
thf(15062,plain,
! [A: nat > $o] :
( ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) )
| ( ( ^ [B: nat] :
~ ( A @ B ) )
!= ( ^ [B: nat] : $false ) ) ),
inference(simp,[status(thm)],[2816]) ).
thf(15433,plain,
! [A: nat > $o] :
( ~ ( A @ ( sk8 @ A ) )
| ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(func_ext,[status(esa)],[15062]) ).
thf(15756,plain,
! [A: nat > $o] :
( ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) )
| ~ ( A @ ( sk8 @ A ) ) ),
inference(cnf,[status(esa)],[15433]) ).
thf(16541,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) )
| ~ ~ ( A
@ ( sk8
@ ^ [B: nat] :
~ ( A @ B ) ) ) ),
inference(prim_subst,[status(thm)],[15756:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(16632,plain,
! [A: nat > $o] :
( ( A
@ ( sk8
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(cnf,[status(esa)],[16541]) ).
thf(16633,plain,
! [A: nat > $o] :
( ( A
@ ( sk8
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(simp,[status(thm)],[16632]) ).
thf(17724,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk8
@ ^ [B: nat] :
~ ~ ( A @ B ) ) )
| ~ ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(prim_subst,[status(thm)],[16633:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(18035,plain,
! [A: nat > $o] :
( ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) )
| ~ ( A
@ ( sk8
@ ^ [B: nat] :
~ ~ ( A @ B ) ) ) ),
inference(cnf,[status(esa)],[17724]) ).
thf(18036,plain,
! [A: nat > $o] :
( ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) )
| ~ ( A @ ( sk8 @ A ) ) ),
inference(simp,[status(thm)],[18035]) ).
thf(25,plain,
! [B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ( ( A @ B )
!= ( ~ ( esti @ B @ ( setof @ A ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[17]) ).
thf(32,plain,
! [B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ( ( A @ B )
!= ( ~ ( esti @ B @ ( setof @ A ) ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(295,plain,
! [C: nat,B: nat > $o,A: set] :
( ~ ( esti @ n_1 @ A )
| ( ( B @ C )
!= ( ~ ( esti @ C @ ( setof @ B ) ) ) )
| ( ( esti @ ( sk1 @ A ) @ A )
!= ( esti @ C @ ( setof @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[67,32]) ).
thf(296,plain,
! [A: nat > $o] :
( ~ ( esti @ n_1 @ ( setof @ A ) )
| ( ( A @ ( sk1 @ ( setof @ A ) ) )
!= ( ~ ( esti @ ( sk1 @ ( setof @ A ) ) @ ( setof @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[295:[bind(A,$thf( setof @ E )),bind(B,$thf( E )),bind(C,$thf( sk1 @ ( setof @ E ) ))]]) ).
thf(324,plain,
! [A: nat > $o] :
( ~ ( esti @ n_1 @ ( setof @ A ) )
| ( ( A @ ( sk1 @ ( setof @ A ) ) )
!= ( ~ ( esti @ ( sk1 @ ( setof @ A ) ) @ ( setof @ A ) ) ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(274,plain,
! [B: nat > set,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [C: nat] : ( esti @ n_1 @ ( B @ C ) ) ) )
| ( esti @ ( sk1 @ ( B @ A ) ) @ ( B @ A ) ) ),
inference(pre_uni,[status(thm)],[262:[bind(A,$thf( ^ [E: nat] : ( esti @ n_1 @ ( E @ E ) ) )),bind(B,$thf( B )),bind(C,$thf( E @ B ))]]) ).
thf(285,plain,
! [B: nat > set,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [C: nat] : ( esti @ n_1 @ ( B @ C ) ) ) )
| ( esti @ ( sk1 @ ( B @ A ) ) @ ( B @ A ) ) ),
inference(simp,[status(thm)],[274]) ).
thf(590,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ( B @ A )
| ~ ( C
@ ( sk1
@ ( setof
@ ^ [D: nat] :
~ ( C @ D ) ) ) )
| ( ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( B @ D ) ) )
!= ( esti @ n_1
@ ( setof
@ ^ [D: nat] :
~ ( C @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[102,276]) ).
thf(591,plain,
! [A: nat > $o] :
( ( A @ n_1 )
| ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] :
~ ( A @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[590:[bind(A,$thf( n_1 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(650,plain,
! [A: nat > $o] :
( ( A @ n_1 )
| ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] :
~ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[591]) ).
thf(126,plain,
! [D: nat,C: set,B: nat,A: nat > $o] :
( ~ ( A @ B )
| ~ ( esti @ n_1 @ C )
| ( esti @ D @ C )
| ( ( esti @ B @ ( setof @ A ) )
!= ( esti @ ( suc @ ( sk1 @ C ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[22,19]) ).
thf(127,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ ( suc @ ( sk1 @ ( setof @ B ) ) ) )
| ~ ( esti @ n_1 @ ( setof @ B ) )
| ( esti @ A @ ( setof @ B ) ) ),
inference(pattern_uni,[status(thm)],[126:[bind(A,$thf( G )),bind(B,$thf( suc @ ( sk1 @ ( setof @ G ) ) )),bind(C,$thf( setof @ G )),bind(D,$thf( D ))]]) ).
thf(156,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ ( suc @ ( sk1 @ ( setof @ B ) ) ) )
| ~ ( esti @ n_1 @ ( setof @ B ) )
| ( esti @ A @ ( setof @ B ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(20264,plain,
! [A: nat > $o] :
( ~ ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) )
| ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(prim_subst,[status(thm)],[20176:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(20359,plain,
! [A: nat > $o] :
( ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) )
| ( A
@ ( sk6
@ ^ [B: nat] : $true ) ) ),
inference(cnf,[status(esa)],[20264]) ).
thf(20360,plain,
! [A: nat > $o] :
( ( ( setof @ A )
!= ( setof
@ ^ [B: nat] : $true ) )
| ( A
@ ( sk6
@ ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[20359]) ).
thf(34001,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) )
| ~ ~ ( A
@ ( sk10
@ ^ [B: nat] :
~ ( A @ B ) ) ) ),
inference(prim_subst,[status(thm)],[33421:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(34134,plain,
! [A: nat > $o] :
( ( A
@ ( sk10
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) ) ),
inference(cnf,[status(esa)],[34001]) ).
thf(34135,plain,
! [A: nat > $o] :
( ( A
@ ( sk10
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[34134]) ).
thf(46856,plain,
( ( ^ [A: nat] :
~ ( esti @ A @ ( setof @ ( (=) @ nat @ sk14 ) ) ) )
!= ( ^ [A: nat] : $true ) ),
inference(pre_uni,[status(thm)],[46750:[bind(A,$thf( sk14 )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ( (=) @ nat @ sk14 ) ) ) ))]]) ).
thf(50008,plain,
~ ~ ( esti @ sk19 @ ( setof @ ( (=) @ nat @ sk14 ) ) ),
inference(func_ext,[status(esa)],[46856]) ).
thf(50009,plain,
esti @ sk19 @ ( setof @ ( (=) @ nat @ sk14 ) ),
inference(cnf,[status(esa)],[50008]) ).
thf(50035,plain,
! [B: nat > $o,A: nat] :
( ( B @ A )
| ( ( esti @ sk19 @ ( setof @ ( (=) @ nat @ sk14 ) ) )
!= ( esti @ A @ ( setof @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[50009,229]) ).
thf(50036,plain,
sk14 = sk19,
inference(pattern_uni,[status(thm)],[50035:[bind(A,$thf( sk19 )),bind(B,$thf( (=) @ nat @ sk14 ))]]) ).
thf(50144,plain,
sk19 = sk14,
inference(lifteq,[status(thm)],[50036]) ).
thf(1744,plain,
! [A: nat > $o] :
( ( A @ n_1 )
| ( ( ^ [B: nat] :
~ ( A @ B ) )
!= ( ^ [B: nat] : $false ) ) ),
inference(simp,[status(thm)],[765]) ).
thf(19961,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( esti
@ ( sk7
@ ^ [C: nat] :
( esti @ C
@ ( setof
@ ^ [D: nat] : $true ) ) )
@ ( setof
@ ^ [C: nat] : $true ) )
!= ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19898,34]) ).
thf(20112,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( sk7
@ ^ [C: nat] :
( esti @ C
@ ( setof
@ ^ [D: nat] : $true ) ) )
!= A )
| ( ( setof
@ ^ [C: nat] :
~ ( B @ C ) )
!= ( setof
@ ^ [C: nat] : $true ) ) ),
inference(simp,[status(thm)],[19961]) ).
thf(20168,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk7
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) )
| ( ( setof
@ ^ [B: nat] :
~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[20112]) ).
thf(38381,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk7
@ ^ [B: nat] : $true ) )
| ( ( setof
@ ^ [B: nat] :
~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(rewrite,[status(thm)],[20168,100]) ).
thf(38382,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk7
@ ^ [B: nat] : $true ) )
| ( ( ^ [B: nat] :
~ ( A @ B ) )
!= ( ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[38381]) ).
thf(38666,plain,
! [A: nat > $o] :
( ~ ~ ( A @ ( sk11 @ A ) )
| ~ ( A
@ ( sk7
@ ^ [B: nat] : $true ) ) ),
inference(func_ext,[status(esa)],[38382]) ).
thf(38872,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk7
@ ^ [B: nat] : $true ) )
| ( A @ ( sk11 @ A ) ) ),
inference(cnf,[status(esa)],[38666]) ).
thf(1745,plain,
! [A: nat > $o] :
( ( ( setof
@ ^ [B: nat] :
~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $false ) )
| ( ( A @ n_1 )
!= ( esti @ n_1
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[765,1454]) ).
thf(1797,plain,
( ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) )
!= ( setof
@ ^ [A: nat] : $false ) ),
inference(pre_uni,[status(thm)],[1745:[bind(A,$thf( ^ [B: nat] : ( esti @ B @ ( setof @ ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $false ) ) ) ) ))]]) ).
thf(1852,plain,
( ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) )
!= ( setof
@ ^ [A: nat] : $false ) ),
inference(rewrite,[status(thm)],[1797,38]) ).
thf(45128,plain,
( ( (=) @ nat @ n_1 )
!= ( ^ [A: nat] : $false ) ),
inference(simp,[status(thm)],[44928]) ).
thf(45129,plain,
n_1 = sk12,
inference(func_ext,[status(esa)],[45128]) ).
thf(45130,plain,
sk12 = n_1,
inference(lifteq,[status(thm)],[45129]) ).
thf(159,plain,
! [B: nat,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] : $true ) )
!= ( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[100,38]) ).
thf(168,plain,
! [B: nat,A: nat] :
( ( A != B )
| ( ( setof
@ ^ [C: nat] : $false )
!= ( setof
@ ^ [C: nat] : $true ) ) ),
inference(simp,[status(thm)],[159]) ).
thf(173,plain,
( ( setof
@ ^ [A: nat] : $false )
!= ( setof
@ ^ [A: nat] : $true ) ),
inference(simp,[status(thm)],[168]) ).
thf(3,axiom,
x != n_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(13,plain,
x != n_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(134,plain,
! [B: nat,A: set] :
( ( esti @ B @ A )
| ~ ( esti @ n_1 @ A )
| ( ( esti @ ( suc @ ( sk1 @ A ) ) @ A )
!= ( esti @ n_1 @ A ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(103,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [D: nat] :
( ( B @ D )
| ( C @ D ) ) ) )
| ~ ( C @ A ) ),
inference(cnf,[status(esa)],[85]) ).
thf(105,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [D: nat] :
( ( B @ D )
| ( C @ D ) ) ) )
| ~ ( C @ A ) ),
inference(simp,[status(thm)],[103]) ).
thf(1988,plain,
! [A: nat > $o] :
( ~ ( A @ ( sk3 @ A ) )
| ( A @ n_1 ) ),
inference(func_ext,[status(esa)],[1744]) ).
thf(2069,plain,
! [A: nat > $o] :
( ( A @ n_1 )
| ~ ( A @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[1988]) ).
thf(2398,plain,
! [A: nat > $o] :
( ~ ( A @ n_1 )
| ~ ~ ( A
@ ( sk3
@ ^ [B: nat] :
~ ( A @ B ) ) ) ),
inference(prim_subst,[status(thm)],[2069:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(2439,plain,
! [A: nat > $o] :
( ( A
@ ( sk3
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ~ ( A @ n_1 ) ),
inference(cnf,[status(esa)],[2398]) ).
thf(2440,plain,
! [A: nat > $o] :
( ( A
@ ( sk3
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ~ ( A @ n_1 ) ),
inference(simp,[status(thm)],[2439]) ).
thf(206,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ ( B @ A ) @ ( C @ A ) )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(prim_subst,[status(thm)],[34:[bind(A,$thf( A )),bind(B,$thf( ^ [E: nat] : ( esti @ ( C @ E ) @ ( D @ E ) ) ))]]) ).
thf(230,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ ( B @ A ) @ ( C @ A ) )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(34271,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( B @ D ) @ ( C @ D ) ) ) )
| ( ( esti
@ ( sk9
@ ^ [D: nat] : $true )
@ ( setof
@ ^ [D: nat] : $true ) )
!= ( esti @ ( B @ A ) @ ( C @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[34168,230]) ).
thf(34351,plain,
~ ( esti
@ ( sk9
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[34271:[bind(A,$thf( sk9 @ ^ [D: nat] : $true )),bind(B,$thf( ^ [D: nat] : D )),bind(C,$thf( ^ [D: nat] : ( setof @ ^ [E: nat] : $true ) ))]]) ).
thf(37124,plain,
~ ( esti
@ ( sk9
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] : ~ $true ) ),
inference(rewrite,[status(thm)],[34351,100]) ).
thf(37125,plain,
~ ( esti
@ ( sk9
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] : $false ) ),
inference(simp,[status(thm)],[37124]) ).
thf(122,plain,
! [D: nat,C: set,B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ~ ( esti @ n_1 @ C )
| ( esti @ D @ C )
| ( ( A @ B )
!= ( esti @ ( suc @ ( sk1 @ C ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17,19]) ).
thf(136,plain,
! [D: nat > set,C: nat > set,B: nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [E: nat] : ( esti @ ( suc @ ( sk1 @ ( D @ E ) ) ) @ ( C @ E ) ) ) )
| ~ ( esti @ n_1 @ ( C @ A ) )
| ( esti @ B @ ( C @ A ) )
| ( ( D @ A )
!= ( C @ A ) ) ),
inference(pre_uni,[status(thm)],[122:[bind(A,$thf( ^ [G: nat] : ( esti @ ( suc @ ( sk1 @ ( H @ G ) ) ) @ ( F @ G ) ) )),bind(B,$thf( B )),bind(C,$thf( F @ B )),bind(D,$thf( D ))]]) ).
thf(139,plain,
! [D: nat > set,C: nat > set,B: nat,A: nat] :
( ( esti @ B @ ( C @ A ) )
| ~ ( esti @ n_1 @ ( C @ A ) )
| ~ ( esti @ A
@ ( setof
@ ^ [E: nat] : ( esti @ ( suc @ ( sk1 @ ( D @ E ) ) ) @ ( C @ E ) ) ) )
| ( ( D @ A )
!= ( C @ A ) ) ),
inference(pre_uni,[status(thm)],[136:[]]) ).
thf(148,plain,
! [D: nat > set,C: nat > set,B: nat,A: nat] :
( ( esti @ B @ ( C @ A ) )
| ~ ( esti @ n_1 @ ( C @ A ) )
| ~ ( esti @ A
@ ( setof
@ ^ [E: nat] : ( esti @ ( suc @ ( sk1 @ ( D @ E ) ) ) @ ( C @ E ) ) ) )
| ( ( D @ A )
!= ( C @ A ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(257,plain,
! [C: nat > $o,B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ~ ( esti @ B
@ ( setof
@ ^ [D: nat] :
~ ( C @ D ) ) )
| ( ( esti @ ( sk1 @ A ) @ A )
!= ( C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[67,34]) ).
thf(264,plain,
! [B: set,A: nat > set] :
( ~ ( esti @ n_1 @ ( A @ ( sk1 @ B ) ) )
| ~ ( esti @ ( sk1 @ B )
@ ( setof
@ ^ [C: nat] :
~ ( esti @ C @ ( A @ C ) ) ) )
| ( ( A @ ( sk1 @ B ) )
!= B ) ),
inference(pre_uni,[status(thm)],[257:[bind(A,$thf( E @ ( sk1 @ G ) )),bind(B,$thf( sk1 @ G )),bind(C,$thf( ^ [E: nat] : ( esti @ E @ ( E @ E ) ) ))]]) ).
thf(266,plain,
! [B: set,A: nat > set] :
( ~ ( esti @ ( sk1 @ B )
@ ( setof
@ ^ [C: nat] :
~ ( esti @ C @ ( A @ C ) ) ) )
| ~ ( esti @ n_1 @ ( A @ ( sk1 @ B ) ) )
| ( ( A @ ( sk1 @ B ) )
!= B ) ),
inference(pre_uni,[status(thm)],[264:[]]) ).
thf(279,plain,
! [B: set,A: nat > set] :
( ~ ( esti @ ( sk1 @ B )
@ ( setof
@ ^ [C: nat] :
~ ( esti @ C @ ( A @ C ) ) ) )
| ~ ( esti @ n_1 @ ( A @ ( sk1 @ B ) ) )
| ( ( A @ ( sk1 @ B ) )
!= B ) ),
inference(simp,[status(thm)],[266]) ).
thf(137,plain,
! [C: set,B: nat > set,A: nat] :
( ~ ( esti @ ( sk1 @ C )
@ ( setof
@ ^ [D: nat] : ( esti @ ( suc @ D ) @ ( B @ D ) ) ) )
| ~ ( esti @ n_1 @ ( B @ ( sk1 @ C ) ) )
| ( esti @ A @ ( B @ ( sk1 @ C ) ) )
| ( C
!= ( B @ ( sk1 @ C ) ) ) ),
inference(pre_uni,[status(thm)],[122:[bind(A,$thf( ^ [F: nat] : ( esti @ ( suc @ F ) @ ( F @ F ) ) )),bind(B,$thf( sk1 @ J )),bind(C,$thf( F @ ( sk1 @ J ) )),bind(D,$thf( D ))]]) ).
thf(140,plain,
! [C: set,B: nat > set,A: nat] :
( ( esti @ A @ ( B @ ( sk1 @ C ) ) )
| ~ ( esti @ n_1 @ ( B @ ( sk1 @ C ) ) )
| ~ ( esti @ ( sk1 @ C )
@ ( setof
@ ^ [D: nat] : ( esti @ ( suc @ D ) @ ( B @ D ) ) ) )
| ( C
!= ( B @ ( sk1 @ C ) ) ) ),
inference(pre_uni,[status(thm)],[137:[]]) ).
thf(149,plain,
! [C: set,B: nat > set,A: nat] :
( ( esti @ A @ ( B @ ( sk1 @ C ) ) )
| ~ ( esti @ n_1 @ ( B @ ( sk1 @ C ) ) )
| ~ ( esti @ ( sk1 @ C )
@ ( setof
@ ^ [D: nat] : ( esti @ ( suc @ D ) @ ( B @ D ) ) ) )
| ( C
!= ( B @ ( sk1 @ C ) ) ) ),
inference(simp,[status(thm)],[140]) ).
thf(290,plain,
! [D: nat,C: nat > $o,B: nat,A: nat > $o] :
( ~ ( A @ B )
| ( ( C @ D )
!= ( ~ ( esti @ D @ ( setof @ C ) ) ) )
| ( ( esti @ B @ ( setof @ A ) )
!= ( esti @ D @ ( setof @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,32]) ).
thf(291,plain,
! [B: nat,A: nat > $o] :
( ~ ( A @ B )
| ( ( A @ B )
!= ( ~ ( esti @ B @ ( setof @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[290:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(248,plain,
! [C: nat,B: nat > $o,A: set] :
( ~ ( esti @ n_1 @ A )
| ( esti @ C @ ( setof @ B ) )
| ( ( esti @ ( sk1 @ A ) @ A )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[67,22]) ).
thf(268,plain,
! [C: nat > set,B: nat > set,A: nat] :
( ~ ( esti @ n_1 @ ( B @ A ) )
| ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( sk1 @ ( C @ D ) ) @ ( B @ D ) ) ) )
| ( ( B @ A )
!= ( C @ A ) ) ),
inference(pre_uni,[status(thm)],[248:[bind(A,$thf( E @ C )),bind(B,$thf( ^ [F: nat] : ( esti @ ( sk1 @ ( F @ F ) ) @ ( E @ F ) ) )),bind(C,$thf( C ))]]) ).
thf(270,plain,
! [C: nat > set,B: nat > set,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( sk1 @ ( C @ D ) ) @ ( B @ D ) ) ) )
| ~ ( esti @ n_1 @ ( B @ A ) )
| ( ( B @ A )
!= ( C @ A ) ) ),
inference(pre_uni,[status(thm)],[268:[]]) ).
thf(281,plain,
! [C: nat > set,B: nat > set,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( sk1 @ ( C @ D ) ) @ ( B @ D ) ) ) )
| ~ ( esti @ n_1 @ ( B @ A ) )
| ( ( B @ A )
!= ( C @ A ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(1,conjecture,
~ ! [A: nat] :
( x
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz3) ).
thf(2,negated_conjecture,
~ ~ ! [A: nat] :
( x
!= ( suc @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ~ ! [A: nat] :
( x
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
! [A: nat] :
( x
!= ( suc @ A ) ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
~ ? [A: nat] :
( x
= ( suc @ A ) ),
inference(miniscope,[status(thm)],[9]) ).
thf(11,plain,
! [A: nat] :
( x
!= ( suc @ A ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [A: nat] :
( ( suc @ A )
!= x ),
inference(lifteq,[status(thm)],[11]) ).
thf(8556,plain,
! [A: nat > $o] :
( ~ ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) )
| ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(prim_subst,[status(thm)],[1980:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(8655,plain,
! [A: nat > $o] :
( ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) )
| ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(cnf,[status(esa)],[8556]) ).
thf(8656,plain,
! [A: nat > $o] :
( ( ( setof @ A )
!= ( setof
@ ^ [B: nat] : $true ) )
| ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(simp,[status(thm)],[8655]) ).
thf(21746,plain,
! [B: nat > $o,A: nat > $o] :
( ( ( setof @ A )
!= ( setof
@ ^ [C: nat] : $true ) )
| ~ ( B
@ ( sk6
@ ^ [C: nat] : $true ) )
| ( B @ ( sk9 @ B ) )
| ~ ( A
@ ( sk1
@ ( setof
@ ^ [C: nat] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[8656,20623]) ).
thf(22030,plain,
! [A: nat > $o] :
( ( ( setof
@ ^ [B: nat] : $true )
!= ( setof
@ ^ [B: nat] : $true ) )
| ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) )
| ( A @ ( sk9 @ A ) ) ),
inference(pre_uni,[status(thm)],[21746:[bind(A,$thf( ^ [C: nat] : $true ))]]) ).
thf(22031,plain,
! [A: nat > $o] :
( ( A @ ( sk9 @ A ) )
| ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) ) ),
inference(pattern_uni,[status(thm)],[22030:[]]) ).
thf(22155,plain,
! [A: nat > $o] :
( ( A @ ( sk9 @ A ) )
| ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[22031]) ).
thf(121,plain,
! [D: nat,C: set,B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ~ ( esti @ ( suc @ ( sk1 @ C ) ) @ C )
| ( esti @ D @ C )
| ( ( A @ B )
!= ( esti @ n_1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17,19]) ).
thf(131,plain,
! [C: nat > set,B: nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ n_1 @ ( C @ D ) ) ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( C @ A ) ) ) @ ( C @ A ) )
| ( esti @ B @ ( C @ A ) ) ),
inference(pre_uni,[status(thm)],[121:[bind(A,$thf( ^ [F: nat] : ( esti @ n_1 @ ( F @ F ) ) )),bind(B,$thf( B )),bind(C,$thf( F @ B )),bind(D,$thf( D ))]]) ).
thf(144,plain,
! [C: nat > set,B: nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ n_1 @ ( C @ D ) ) ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( C @ A ) ) ) @ ( C @ A ) )
| ( esti @ B @ ( C @ A ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(50355,plain,
~ ~ ( esti @ sk14 @ ( setof @ ( (=) @ nat @ sk20 ) ) ),
inference(func_ext,[status(esa)],[46858]) ).
thf(50356,plain,
esti @ sk14 @ ( setof @ ( (=) @ nat @ sk20 ) ),
inference(cnf,[status(esa)],[50355]) ).
thf(1989,plain,
! [A: nat > $o] :
( ( ( ^ [B: nat] :
~ ( A @ B ) )
!= ( ^ [B: nat] : $false ) )
| ( ( A @ n_1 )
!= ( esti @ n_1
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1744,1454]) ).
thf(2065,plain,
( ( ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) )
!= ( ^ [A: nat] : $false ) ),
inference(pre_uni,[status(thm)],[1989:[bind(A,$thf( ^ [B: nat] : ( esti @ B @ ( setof @ ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $false ) ) ) ) ))]]) ).
thf(2346,plain,
( ( ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) )
!= ( ^ [A: nat] : $false ) ),
inference(rewrite,[status(thm)],[2065,38]) ).
thf(4300,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( esti @ n_1
@ ( setof
@ ^ [C: nat] :
( esti @ C
@ ( setof
@ ^ [D: nat] : $true ) ) ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4264,34]) ).
thf(4327,plain,
~ ( esti @ n_1
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[4300:[bind(A,$thf( n_1 )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : ( esti @ D @ ( setof @ ^ [E: nat] : $true ) ) ) ) ))]]) ).
thf(5827,plain,
~ ( esti @ n_1
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(rewrite,[status(thm)],[4327,100]) ).
thf(34896,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk10
@ ^ [B: nat] :
~ ~ ( A @ B ) ) )
| ~ ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) ) ),
inference(prim_subst,[status(thm)],[34135:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(35290,plain,
! [A: nat > $o] :
( ( A
@ ( sk6
@ ^ [B: nat] : $true ) )
| ~ ( A
@ ( sk10
@ ^ [B: nat] :
~ ~ ( A @ B ) ) ) ),
inference(cnf,[status(esa)],[34896]) ).
thf(35291,plain,
! [A: nat > $o] :
( ( A
@ ( sk6
@ ^ [B: nat] : $true ) )
| ~ ( A @ ( sk10 @ A ) ) ),
inference(simp,[status(thm)],[35290]) ).
thf(202,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
!= ( B @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[34]) ).
thf(208,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
!= ( B @ A ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(253,plain,
! [C: nat,B: set,A: set] :
( ~ ( esti @ n_1 @ A )
| ~ ( esti @ n_1 @ B )
| ( esti @ C @ B )
| ( ( esti @ ( sk1 @ A ) @ A )
!= ( esti @ ( suc @ ( sk1 @ B ) ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[67,19]) ).
thf(267,plain,
! [C: nat,B: set,A: set] :
( ( esti @ C @ B )
| ~ ( esti @ n_1 @ A )
| ~ ( esti @ n_1 @ B )
| ( ( sk1 @ A )
!= ( suc @ ( sk1 @ B ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[253]) ).
thf(280,plain,
! [B: nat,A: set] :
( ( esti @ B @ A )
| ~ ( esti @ n_1 @ A )
| ~ ( esti @ n_1 @ A )
| ( ( suc @ ( sk1 @ A ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(38941,plain,
! [B: nat,A: set] :
( ( esti @ B @ A )
| ~ ( esti @ n_1 @ A )
| ( ( suc @ ( sk1 @ A ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[280]) ).
thf(81,plain,
! [D: nat,C: nat > $o,B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ( esti @ D @ ( setof @ C ) )
| ( ( A @ B )
!= ( C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[17,22]) ).
thf(90,plain,
! [D: nat,C: nat > $o,B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ( esti @ D @ ( setof @ C ) )
| ( ( A @ B )
!= ( C @ D ) ) ),
inference(pre_uni,[status(thm)],[81:[]]) ).
thf(91,plain,
! [D: nat,C: nat > $o,B: nat,A: nat > $o] :
( ( esti @ D @ ( setof @ C ) )
| ~ ( esti @ B @ ( setof @ A ) )
| ( ( A @ B )
!= ( C @ D ) ) ),
inference(pre_uni,[status(thm)],[90:[]]) ).
thf(124,plain,
! [D: nat,C: set,B: nat,A: nat > $o] :
( ~ ( A @ B )
| ~ ( esti @ ( suc @ ( sk1 @ C ) ) @ C )
| ( esti @ D @ C )
| ( ( esti @ B @ ( setof @ A ) )
!= ( esti @ n_1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[22,19]) ).
thf(125,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ n_1 )
| ~ ( esti @ ( suc @ ( sk1 @ ( setof @ B ) ) ) @ ( setof @ B ) )
| ( esti @ A @ ( setof @ B ) ) ),
inference(pattern_uni,[status(thm)],[124:[bind(A,$thf( E )),bind(B,$thf( n_1 )),bind(C,$thf( setof @ E ))]]) ).
thf(155,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ n_1 )
| ~ ( esti @ ( suc @ ( sk1 @ ( setof @ B ) ) ) @ ( setof @ B ) )
| ( esti @ A @ ( setof @ B ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(21848,plain,
! [A: nat > $o] :
( ~ ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) )
| ~ ( A
@ ( sk9
@ ^ [B: nat] :
~ ( A @ B ) ) ) ),
inference(prim_subst,[status(thm)],[20623:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(22211,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk9
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ( A
@ ( sk6
@ ^ [B: nat] : $true ) ) ),
inference(cnf,[status(esa)],[21848]) ).
thf(22212,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk9
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ( A
@ ( sk6
@ ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[22211]) ).
thf(45232,plain,
! [B: nat,A: nat > $o] :
( ( esti @ B @ ( setof @ A ) )
| ( ( esti @ n_1 @ ( setof @ ( (=) @ nat @ n_1 ) ) )
!= ( A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44954,22]) ).
thf(45364,plain,
( esti @ n_1
@ ( setof
@ ^ [A: nat] : ( esti @ A @ ( setof @ ( (=) @ nat @ A ) ) ) ) ),
inference(pre_uni,[status(thm)],[45232:[bind(A,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ( (=) @ nat @ C ) ) ) )),bind(B,$thf( n_1 ))]]) ).
thf(73,plain,
! [D: nat,C: set,B: nat,A: nat > $o] :
( ~ ( A @ B )
| ( esti @ ( sk1 @ C ) @ C )
| ( esti @ D @ C )
| ( ( esti @ B @ ( setof @ A ) )
!= ( esti @ n_1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[22,20]) ).
thf(74,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ n_1 )
| ( esti @ ( sk1 @ ( setof @ B ) ) @ ( setof @ B ) )
| ( esti @ A @ ( setof @ B ) ) ),
inference(pattern_uni,[status(thm)],[73:[bind(A,$thf( E )),bind(B,$thf( n_1 )),bind(C,$thf( setof @ E ))]]) ).
thf(108,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ n_1 )
| ( esti @ ( sk1 @ ( setof @ B ) ) @ ( setof @ B ) )
| ( esti @ A @ ( setof @ B ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(39615,plain,
! [B: nat > $o,A: nat > $o] :
( ( ( ^ [C: nat] :
~ ( A @ C ) )
!= ( ^ [C: nat] : $false ) )
| ~ ( B
@ ( sk7
@ ^ [C: nat] : $true ) )
| ( B @ ( sk11 @ B ) )
| ~ ( A @ n_1 ) ),
inference(paramod_ordered,[status(thm)],[1744,38872]) ).
thf(39954,plain,
! [A: nat > $o] :
( ( ( ^ [B: nat] : ~ $true )
!= ( ^ [B: nat] : $false ) )
| ~ ( A
@ ( sk7
@ ^ [B: nat] : $true ) )
| ( A @ ( sk11 @ A ) ) ),
inference(pre_uni,[status(thm)],[39615:[bind(A,$thf( ^ [C: nat] : $true ))]]) ).
thf(40221,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk7
@ ^ [B: nat] : $true ) )
| ( A @ ( sk11 @ A ) ) ),
inference(simp,[status(thm)],[39954]) ).
thf(263,plain,
! [C: nat > set,B: nat > set,A: nat] :
( ~ ( esti @ n_1 @ ( B @ A ) )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( sk1 @ ( C @ D ) ) @ ( B @ D ) ) ) )
| ( ( B @ A )
!= ( C @ A ) ) ),
inference(pre_uni,[status(thm)],[257:[bind(A,$thf( E @ B )),bind(B,$thf( B )),bind(C,$thf( ^ [F: nat] : ( esti @ ( sk1 @ ( F @ F ) ) @ ( E @ F ) ) ))]]) ).
thf(265,plain,
! [C: nat > set,B: nat > set,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( sk1 @ ( C @ D ) ) @ ( B @ D ) ) ) )
| ~ ( esti @ n_1 @ ( B @ A ) )
| ( ( B @ A )
!= ( C @ A ) ) ),
inference(pre_uni,[status(thm)],[263:[]]) ).
thf(278,plain,
! [C: nat > set,B: nat > set,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( sk1 @ ( C @ D ) ) @ ( B @ D ) ) ) )
| ~ ( esti @ n_1 @ ( B @ A ) )
| ( ( B @ A )
!= ( C @ A ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(196,plain,
! [D: nat > $o,C: nat,B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ~ ( esti @ ( suc @ ( sk1 @ A ) ) @ A )
| ~ ( D @ C )
| ( ( esti @ B @ A )
!= ( esti @ C
@ ( setof
@ ^ [E: nat] :
~ ( D @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,34]) ).
thf(197,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ~ ( esti
@ ( suc
@ ( sk1
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) )
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(pattern_uni,[status(thm)],[196:[bind(A,$thf( setof @ ^ [F: nat] : ~ ( F @ F ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( F ))]]) ).
thf(223,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ~ ( esti
@ ( suc
@ ( sk1
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) )
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[197]) ).
thf(204,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ~ ( ( B @ A )
| ( C @ A ) )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( ( B @ D )
| ( C @ D ) ) ) ) ),
inference(prim_subst,[status(thm)],[34:[bind(A,$thf( A )),bind(B,$thf( ^ [E: nat] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(224,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( ( B @ D )
| ( C @ D ) ) ) )
| ~ ( C @ A ) ),
inference(cnf,[status(esa)],[204]) ).
thf(226,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( ( B @ D )
| ( C @ D ) ) ) )
| ~ ( C @ A ) ),
inference(simp,[status(thm)],[224]) ).
thf(27,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( C @ D ) ) ) )
| ( esti @ ( B @ A ) @ ( C @ A ) ) ),
inference(prim_subst,[status(thm)],[17:[bind(A,$thf( ^ [E: nat] : ( esti @ ( C @ E ) @ ( D @ E ) ) ))]]) ).
thf(35,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( C @ D ) ) ) )
| ( esti @ ( B @ A ) @ ( C @ A ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(2900,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk3
@ ^ [B: nat] :
~ ~ ( A @ B ) ) )
| ~ ~ ( A @ n_1 ) ),
inference(prim_subst,[status(thm)],[2440:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(3015,plain,
! [A: nat > $o] :
( ( A @ n_1 )
| ~ ( A
@ ( sk3
@ ^ [B: nat] :
~ ~ ( A @ B ) ) ) ),
inference(cnf,[status(esa)],[2900]) ).
thf(3016,plain,
! [A: nat > $o] :
( ( A @ n_1 )
| ~ ( A @ ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[3015]) ).
thf(9423,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) )
| ( ( C @ A @ ( B @ A ) )
!= ( esti
@ ( sk6
@ ^ [D: nat] : $true )
@ ( setof
@ ^ [D: nat] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,9373]) ).
thf(9487,plain,
~ ( esti
@ ( sk6
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[9423:[bind(A,$thf( sk6 @ ^ [D: nat] : $true )),bind(B,$thf( ^ [D: nat] : D )),bind(C,$thf( ^ [D: nat] : ^ [E: nat] : ( esti @ E @ ( setof @ ^ [F: nat] : $false ) ) ))]]) ).
thf(12723,plain,
~ ( esti
@ ( sk6
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(rewrite,[status(thm)],[9487,38]) ).
thf(48624,plain,
( ( (=) @ nat @ sk16 )
!= ( ^ [A: nat] : $false ) ),
inference(simp,[status(thm)],[48604]) ).
thf(32599,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) )
| ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $false ) ) ),
inference(prim_subst,[status(thm)],[9557:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(32825,plain,
! [A: nat > $o] :
( ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $false ) )
| ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) ) ),
inference(cnf,[status(esa)],[32599]) ).
thf(32826,plain,
! [A: nat > $o] :
( ( ( setof @ A )
!= ( setof
@ ^ [B: nat] : $false ) )
| ~ ( A
@ ( sk6
@ ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[32825]) ).
thf(812,plain,
! [A: nat > $o] :
( ~ ( A @ n_1 )
| ~ ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) ) ) ) ),
inference(prim_subst,[status(thm)],[650:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(835,plain,
! [A: nat > $o] :
( ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) ) ) )
| ~ ( A @ n_1 ) ),
inference(cnf,[status(esa)],[812]) ).
thf(836,plain,
! [A: nat > $o] :
( ( A @ ( sk1 @ ( setof @ A ) ) )
| ~ ( A @ n_1 ) ),
inference(simp,[status(thm)],[835]) ).
thf(132,plain,
! [B: nat > set,A: nat] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [C: nat] : ( esti @ C @ ( B @ C ) ) ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( B @ n_1 ) ) ) @ ( B @ n_1 ) )
| ( esti @ A @ ( B @ n_1 ) ) ),
inference(pre_uni,[status(thm)],[121:[bind(A,$thf( ^ [F: nat] : ( esti @ F @ ( F @ F ) ) )),bind(B,$thf( n_1 )),bind(C,$thf( F @ n_1 )),bind(D,$thf( D ))]]) ).
thf(145,plain,
! [B: nat > set,A: nat] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [C: nat] : ( esti @ C @ ( B @ C ) ) ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( B @ n_1 ) ) ) @ ( B @ n_1 ) )
| ( esti @ A @ ( B @ n_1 ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(9680,plain,
! [B: nat > $o,A: nat > $o] :
( ~ ( A @ n_1 )
| ~ ( B
@ ( sk1
@ ( setof
@ ^ [C: nat] : $true ) ) )
| ( B @ ( sk7 @ B ) )
| ~ ( A @ ( sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5015,8845]) ).
thf(9749,plain,
! [A: nat > $o] :
( ~ $true
| ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) )
| ( A @ ( sk7 @ A ) ) ),
inference(pre_uni,[status(thm)],[9680:[bind(A,$thf( ^ [C: nat] : $true ))]]) ).
thf(9926,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) )
| ( A @ ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[9749]) ).
thf(9711,plain,
! [A: nat > $o] :
( ~ ~ ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) )
| ~ ( A
@ ( sk7
@ ^ [B: nat] :
~ ( A @ B ) ) ) ),
inference(prim_subst,[status(thm)],[8845:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(10000,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk7
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(cnf,[status(esa)],[9711]) ).
thf(10001,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk7
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ( A
@ ( sk1
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(simp,[status(thm)],[10000]) ).
thf(269,plain,
! [B: set,A: nat > set] :
( ~ ( esti @ n_1 @ ( A @ ( sk1 @ B ) ) )
| ( esti @ ( sk1 @ B )
@ ( setof
@ ^ [C: nat] : ( esti @ C @ ( A @ C ) ) ) )
| ( ( A @ ( sk1 @ B ) )
!= B ) ),
inference(pre_uni,[status(thm)],[248:[bind(A,$thf( E @ ( sk1 @ G ) )),bind(B,$thf( ^ [E: nat] : ( esti @ E @ ( E @ E ) ) )),bind(C,$thf( sk1 @ G ))]]) ).
thf(271,plain,
! [B: set,A: nat > set] :
( ( esti @ ( sk1 @ B )
@ ( setof
@ ^ [C: nat] : ( esti @ C @ ( A @ C ) ) ) )
| ~ ( esti @ n_1 @ ( A @ ( sk1 @ B ) ) )
| ( ( A @ ( sk1 @ B ) )
!= B ) ),
inference(pre_uni,[status(thm)],[269:[]]) ).
thf(282,plain,
! [B: set,A: nat > set] :
( ( esti @ ( sk1 @ B )
@ ( setof
@ ^ [C: nat] : ( esti @ C @ ( A @ C ) ) ) )
| ~ ( esti @ n_1 @ ( A @ ( sk1 @ B ) ) )
| ( ( A @ ( sk1 @ B ) )
!= B ) ),
inference(simp,[status(thm)],[271]) ).
thf(138,plain,
! [C: set,B: nat > set,A: nat] :
( ~ ( esti @ ( suc @ ( sk1 @ C ) )
@ ( setof
@ ^ [D: nat] : ( esti @ D @ ( B @ D ) ) ) )
| ~ ( esti @ n_1 @ ( B @ ( suc @ ( sk1 @ C ) ) ) )
| ( esti @ A @ ( B @ ( suc @ ( sk1 @ C ) ) ) )
| ( C
!= ( B @ ( suc @ ( sk1 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[122:[bind(A,$thf( ^ [F: nat] : ( esti @ F @ ( F @ F ) ) )),bind(B,$thf( suc @ ( sk1 @ K ) )),bind(C,$thf( F @ ( suc @ ( sk1 @ K ) ) )),bind(D,$thf( D ))]]) ).
thf(141,plain,
! [C: set,B: nat > set,A: nat] :
( ( esti @ A @ ( B @ ( suc @ ( sk1 @ C ) ) ) )
| ~ ( esti @ n_1 @ ( B @ ( suc @ ( sk1 @ C ) ) ) )
| ~ ( esti @ ( suc @ ( sk1 @ C ) )
@ ( setof
@ ^ [D: nat] : ( esti @ D @ ( B @ D ) ) ) )
| ( C
!= ( B @ ( suc @ ( sk1 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[138:[]]) ).
thf(150,plain,
! [C: set,B: nat > set,A: nat] :
( ( esti @ A @ ( B @ ( suc @ ( sk1 @ C ) ) ) )
| ~ ( esti @ n_1 @ ( B @ ( suc @ ( sk1 @ C ) ) ) )
| ~ ( esti @ ( suc @ ( sk1 @ C ) )
@ ( setof
@ ^ [D: nat] : ( esti @ D @ ( B @ D ) ) ) )
| ( C
!= ( B @ ( suc @ ( sk1 @ C ) ) ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(45131,plain,
~ ~ ( esti @ sk13 @ ( setof @ ( (=) @ nat @ n_1 ) ) ),
inference(func_ext,[status(esa)],[44848]) ).
thf(45132,plain,
esti @ sk13 @ ( setof @ ( (=) @ nat @ n_1 ) ),
inference(cnf,[status(esa)],[45131]) ).
thf(45619,plain,
! [B: nat,A: nat > $o] :
( ( A @ B )
| ( ( esti @ sk13 @ ( setof @ ( (=) @ nat @ n_1 ) ) )
!= ( esti @ B @ ( setof @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[45132,17]) ).
thf(45620,plain,
n_1 = sk13,
inference(pattern_uni,[status(thm)],[45619:[bind(A,$thf( (=) @ nat @ n_1 )),bind(B,$thf( sk13 ))]]) ).
thf(45698,plain,
sk13 = n_1,
inference(lifteq,[status(thm)],[45620]) ).
thf(119,plain,
! [D: nat,C: nat > $o,B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ~ ( esti @ ( suc @ ( sk1 @ A ) ) @ A )
| ( C @ D )
| ( ( esti @ B @ A )
!= ( esti @ D @ ( setof @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,17]) ).
thf(120,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ n_1 @ ( setof @ B ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( setof @ B ) ) ) @ ( setof @ B ) )
| ( B @ A ) ),
inference(pattern_uni,[status(thm)],[119:[bind(A,$thf( setof @ E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( B ))]]) ).
thf(154,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ n_1 @ ( setof @ B ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( setof @ B ) ) ) @ ( setof @ B ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[120]) ).
thf(34326,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) )
| ( ( esti
@ ( sk9
@ ^ [D: nat] : $true )
@ ( setof
@ ^ [D: nat] : $true ) )
!= ( C @ A @ ( B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[34168,99]) ).
thf(34401,plain,
( esti
@ ( sk9
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[34326:[bind(A,$thf( sk9 @ ^ [D: nat] : $true )),bind(B,$thf( ^ [D: nat] : D )),bind(C,$thf( ^ [D: nat] : ^ [E: nat] : ( esti @ E @ ( setof @ ^ [F: nat] : $true ) ) ))]]) ).
thf(42862,plain,
( esti
@ ( sk9
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(rewrite,[status(thm)],[34401,100]) ).
thf(1458,plain,
! [B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( B @ A )
!= ( esti @ n_1
@ ( setof
@ ^ [C: nat] :
( esti @ C
@ ( setof
@ ^ [D: nat] : $false ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[102,1454]) ).
thf(1479,plain,
( esti @ n_1
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1458:[bind(A,$thf( n_1 )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : ( esti @ D @ ( setof @ ^ [E: nat] : $false ) ) ) ) ))]]) ).
thf(1517,plain,
( esti @ n_1
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(rewrite,[status(thm)],[1479,38]) ).
thf(48625,plain,
sk16 = sk18,
inference(func_ext,[status(esa)],[48624]) ).
thf(48626,plain,
sk18 = sk16,
inference(lifteq,[status(thm)],[48625]) ).
thf(21419,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) )
| ( ( esti
@ ( sk7
@ ^ [D: nat] : $true )
@ ( setof
@ ^ [D: nat] : $true ) )
!= ( C @ A @ ( B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[21299,99]) ).
thf(21540,plain,
( esti
@ ( sk7
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[21419:[bind(A,$thf( sk7 @ ^ [D: nat] : $true )),bind(B,$thf( ^ [D: nat] : D )),bind(C,$thf( ^ [D: nat] : ^ [E: nat] : ( esti @ E @ ( setof @ ^ [F: nat] : $true ) ) ))]]) ).
thf(25443,plain,
( esti
@ ( sk7
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(rewrite,[status(thm)],[21540,100]) ).
thf(7,axiom,
! [A: $o] :
( ~ ~ A
=> A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',et) ).
thf(23,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4304,plain,
! [B: nat > $o,A: nat] :
( ( ( setof
@ ^ [C: nat] :
~ ( B @ C ) )
!= ( setof
@ ^ [C: nat] : $true ) )
| ( ( esti @ n_1
@ ( setof
@ ^ [C: nat] :
( esti @ C
@ ( setof
@ ^ [D: nat] : $true ) ) ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4264,236]) ).
thf(4329,plain,
( ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) ) )
!= ( setof
@ ^ [A: nat] : $true ) ),
inference(pre_uni,[status(thm)],[4304:[bind(A,$thf( n_1 )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : ( esti @ D @ ( setof @ ^ [E: nat] : $true ) ) ) ) ))]]) ).
thf(6462,plain,
( ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) )
!= ( setof
@ ^ [A: nat] : $true ) ),
inference(rewrite,[status(thm)],[4329,100]) ).
thf(249,plain,
! [C: set,B: nat,A: nat > $o] :
( ~ ( A @ B )
| ( esti @ ( sk1 @ C ) @ C )
| ( ( esti @ B @ ( setof @ A ) )
!= ( esti @ n_1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[22,67]) ).
thf(250,plain,
! [A: nat > $o] :
( ~ ( A @ n_1 )
| ( esti @ ( sk1 @ ( setof @ A ) ) @ ( setof @ A ) ) ),
inference(pattern_uni,[status(thm)],[249:[bind(A,$thf( D )),bind(B,$thf( n_1 )),bind(C,$thf( setof @ D ))]]) ).
thf(287,plain,
! [A: nat > $o] :
( ~ ( A @ n_1 )
| ( esti @ ( sk1 @ ( setof @ A ) ) @ ( setof @ A ) ) ),
inference(simp,[status(thm)],[250]) ).
thf(12727,plain,
! [B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( B @ A )
!= ( esti
@ ( sk6
@ ^ [C: nat] : $true )
@ ( setof
@ ^ [C: nat] :
( esti @ C
@ ( setof
@ ^ [D: nat] : $false ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[102,12723]) ).
thf(12866,plain,
( esti
@ ( sk6
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[12727:[bind(A,$thf( sk6 @ ^ [C: nat] : $true )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : ( esti @ D @ ( setof @ ^ [E: nat] : $false ) ) ) ) ))]]) ).
thf(13577,plain,
( esti
@ ( sk6
@ ^ [A: nat] : $true )
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(rewrite,[status(thm)],[12866,38]) ).
thf(5387,plain,
! [A: nat > $o] :
( ~ ~ ( A @ n_1 )
| ~ ( A
@ ( sk6
@ ^ [B: nat] :
~ ( A @ B ) ) ) ),
inference(prim_subst,[status(thm)],[5015:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(5521,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk6
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ( A @ n_1 ) ),
inference(cnf,[status(esa)],[5387]) ).
thf(5522,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk6
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ( A @ n_1 ) ),
inference(simp,[status(thm)],[5521]) ).
thf(195,plain,
! [D: nat > $o,C: nat,B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ~ ( esti @ ( suc @ ( sk1 @ A ) ) @ A )
| ~ ( esti @ C
@ ( setof
@ ^ [E: nat] :
~ ( D @ E ) ) )
| ( ( esti @ B @ A )
!= ( D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[19,34]) ).
thf(218,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ n_1 @ ( C @ A ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( C @ A ) ) ) @ ( C @ A ) )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(pre_uni,[status(thm)],[195:[bind(A,$thf( F @ C )),bind(B,$thf( E @ C )),bind(C,$thf( C )),bind(D,$thf( ^ [G: nat] : ( esti @ ( E @ G ) @ ( F @ G ) ) ))]]) ).
thf(239,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ n_1 @ ( C @ A ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( C @ A ) ) ) @ ( C @ A ) )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(simp,[status(thm)],[218]) ).
thf(14,plain,
x != n_1,
inference(polarity_switch,[status(thm)],[13]) ).
thf(15,plain,
n_1 != x,
inference(lifteq,[status(thm)],[14]) ).
thf(260,plain,
! [C: nat,B: nat > $o,A: set] :
( ~ ( esti @ n_1 @ A )
| ( B @ C )
| ( ( esti @ ( sk1 @ A ) @ A )
!= ( esti @ C @ ( setof @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[67,17]) ).
thf(261,plain,
! [A: nat > $o] :
( ~ ( esti @ n_1 @ ( setof @ A ) )
| ( A @ ( sk1 @ ( setof @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( setof @ E )),bind(B,$thf( E )),bind(C,$thf( sk1 @ ( setof @ E ) ))]]) ).
thf(277,plain,
! [A: nat > $o] :
( ~ ( esti @ n_1 @ ( setof @ A ) )
| ( A @ ( sk1 @ ( setof @ A ) ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(46634,plain,
~ ~ ( esti @ n_1 @ ( setof @ ( (=) @ nat @ sk15 ) ) ),
inference(func_ext,[status(esa)],[45351]) ).
thf(46635,plain,
esti @ n_1 @ ( setof @ ( (=) @ nat @ sk15 ) ),
inference(cnf,[status(esa)],[46634]) ).
thf(47036,plain,
! [B: nat,A: nat > $o] :
( ( A @ B )
| ( ( esti @ n_1 @ ( setof @ ( (=) @ nat @ sk15 ) ) )
!= ( esti @ B @ ( setof @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[46635,17]) ).
thf(47037,plain,
sk15 = n_1,
inference(pattern_uni,[status(thm)],[47036:[bind(A,$thf( (=) @ nat @ sk15 )),bind(B,$thf( n_1 ))]]) ).
thf(47121,plain,
sk15 = n_1,
inference(lifteq,[status(thm)],[47037]) ).
thf(225,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( ( B @ D )
| ( C @ D ) ) ) )
| ~ ( B @ A ) ),
inference(cnf,[status(esa)],[204]) ).
thf(227,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( ( B @ D )
| ( C @ D ) ) ) )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[225]) ).
thf(4302,plain,
! [A: nat > $o] :
( ( ( setof @ A )
!= ( setof
@ ^ [B: nat] : $false ) )
| ( ( esti @ n_1
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) )
!= ( A @ n_1 ) ) ),
inference(paramod_ordered,[status(thm)],[4264,1833]) ).
thf(4340,plain,
( ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $true ) ) ) ) )
!= ( setof
@ ^ [A: nat] : $false ) ),
inference(pre_uni,[status(thm)],[4302:[bind(A,$thf( ^ [B: nat] : ( esti @ B @ ( setof @ ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $true ) ) ) ) ))]]) ).
thf(4752,plain,
( ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) )
!= ( setof
@ ^ [A: nat] : $false ) ),
inference(rewrite,[status(thm)],[4340,100]) ).
thf(5974,plain,
! [A: nat > $o] :
( ~ ~ ( A
@ ( sk6
@ ^ [B: nat] :
~ ~ ( A @ B ) ) )
| ~ ( A @ n_1 ) ),
inference(prim_subst,[status(thm)],[5522:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(6034,plain,
! [A: nat > $o] :
( ~ ( A @ n_1 )
| ( A
@ ( sk6
@ ^ [B: nat] :
~ ~ ( A @ B ) ) ) ),
inference(cnf,[status(esa)],[5974]) ).
thf(6035,plain,
! [A: nat > $o] :
( ~ ( A @ n_1 )
| ( A @ ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[6034]) ).
thf(61894,plain,
$false,
inference(e,[status(thm)],[48604,1454,46773,27529,234,21299,7601,46636,9373,1882,276,20623,7641,3781,15331,44848,1095,33421,48223,37,20177,44928,45351,2713,152,4383,9557,106,147,8289,34168,233,46858,46633,220,102,38,21,16633,18036,229,15756,4417,3667,324,285,650,156,20360,24177,34135,50144,1744,38872,11474,1852,45130,984,173,13,38381,134,105,765,2440,15062,37125,148,279,17,149,8495,32,34,1833,22,286,291,281,12,22155,144,27257,236,8656,44823,46856,50356,2346,4498,5827,230,35291,39,208,38941,19898,91,155,33528,22212,4264,45364,108,40221,38382,278,223,226,45410,35,2069,20176,3016,2816,12723,48624,32826,836,145,32396,9926,10001,18,282,150,45128,67,45698,8845,1980,470,5015,16,154,46967,44954,336,45350,42862,99,1517,48626,25443,23,8,6462,287,13577,48221,4787,5522,19,107,239,1033,15,277,47121,227,4752,6035,100,46984]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : NUM637^1 : TPTP v8.2.0. Released v3.7.0.
% 0.02/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n022.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 20 07:00:24 EDT 2024
% 0.11/0.32 % CPUTime :
% 1.01/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.12 % [INFO] Parsing done (164ms).
% 1.30/1.14 % [INFO] Running in sequential loop mode.
% 1.90/1.50 % [INFO] eprover registered as external prover.
% 1.90/1.51 % [INFO] cvc4 registered as external prover.
% 1.90/1.51 % [INFO] Scanning for conjecture ...
% 1.99/1.59 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.15/1.62 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.15/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.15/1.64 % [INFO] Type checking passed.
% 2.15/1.65 % [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 ...
% 249.12/47.00 % External prover 'e' found a proof!
% 249.12/47.00 % [INFO] Killing All external provers ...
% 249.12/47.00 % Time passed: 46524ms (effective reasoning time: 45857ms)
% 249.12/47.00 % 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)>
% 249.12/47.01 % Axioms used in derivation (5): n, estii, et, estie, ax5
% 249.12/47.01 % No. of inferences in proof: 445
% 249.12/47.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 46524 ms resp. 45857 ms w/o parsing
% 249.81/47.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 249.81/47.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------