TSTP Solution File: NUM636^1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : NUM636^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 7 08:00:16 EDT 2024
% Result : Theorem 152.62s 29.10s
% Output : Refutation 152.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 22
% Syntax : Number of formulae : 294 ( 122 unt; 15 typ; 0 def)
% Number of atoms : 832 ( 243 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2934 ( 639 ~; 342 |; 0 &;1941 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 250 ( 250 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 786 ( 338 ^ 447 !; 1 ?; 786 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_type,type,
x: 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(n_1_type,type,
n_1: nat ).
thf(sk1_type,type,
sk1: set > nat ).
thf(sk2_type,type,
sk2: nat > nat ).
thf(sk9_type,type,
sk9: nat ).
thf(sk10_type,type,
sk10: nat ).
thf(sk11_type,type,
sk11: nat ).
thf(sk12_type,type,
sk12: nat ).
thf(sk13_type,type,
sk13: nat ).
thf(sk14_type,type,
sk14: nat ).
thf(5,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( esti @ B @ ( setof @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',estii) ).
thf(16,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( esti @ B @ ( setof @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,plain,
! [B: nat,A: nat > $o] :
( ~ ( A @ B )
| ( esti @ B @ ( setof @ A ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(302,plain,
! [A: nat] :
( ~ $true
| ( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ),
inference(prim_subst,[status(thm)],[17:[bind(A,$thf( ^ [C: nat] : $true ))]]) ).
thf(328,plain,
! [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ),
inference(simp,[status(thm)],[302]) ).
thf(301,plain,
! [B: nat > $o,A: nat] :
( ~ ~ ( B @ A )
| ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) ),
inference(prim_subst,[status(thm)],[17:[bind(A,$thf( ^ [D: nat] : ~ ( C @ D ) ))]]) ).
thf(326,plain,
! [B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( B @ A ) ),
inference(cnf,[status(esa)],[301]) ).
thf(327,plain,
! [B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[326]) ).
thf(1,conjecture,
( ( suc @ x )
!= x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz2) ).
thf(2,negated_conjecture,
( ( suc @ x )
!= x ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
( ( suc @ x )
!= x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
( ( suc @ x )
= x ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( suc @ x )
= x ),
inference(lifteq,[status(thm)],[9]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( suc @ A )
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz1) ).
thf(22,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( suc @ A )
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(23,plain,
! [B: nat,A: nat] :
( ( A = B )
| ( ( suc @ A )
!= ( suc @ B ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [B: nat,A: nat] :
( ( A = B )
| ( ( suc @ A )
!= ( suc @ B ) ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(25,plain,
! [A: nat] :
( ( sk2 @ ( suc @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(suc),[sk2])]) ).
thf(28,plain,
! [A: nat] :
( ( ( sk2 @ x )
= A )
| ( ( suc @ x )
!= ( suc @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,25]) ).
thf(29,plain,
( ( sk2 @ x )
= x ),
inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( x ))]]) ).
thf(3,axiom,
! [A: nat > $o,B: nat] :
( ( esti @ B @ ( setof @ A ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',estie) ).
thf(11,plain,
! [A: nat > $o,B: nat] :
( ( esti @ B @ ( setof @ A ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[11]) ).
thf(67,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( C @ D ) ) ) )
| ( esti @ ( B @ A ) @ ( C @ A ) ) ),
inference(prim_subst,[status(thm)],[12:[bind(A,$thf( ^ [E: nat] : ( esti @ ( C @ E ) @ ( D @ E ) ) ))]]) ).
thf(86,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)],[67]) ).
thf(2031,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( C @ D ) ) ) )
| ( esti @ x @ ( C @ A ) )
| ( ( sk2 @ x )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,86]) ).
thf(2067,plain,
! [A: nat > set] :
( ~ ( esti @ ( sk2 @ x )
@ ( setof
@ ^ [B: nat] : ( esti @ B @ ( A @ B ) ) ) )
| ( esti @ x @ ( A @ ( sk2 @ x ) ) ) ),
inference(pre_uni,[status(thm)],[2031:[bind(A,$thf( sk2 @ x )),bind(B,$thf( ^ [D: nat] : D ))]]) ).
thf(2142,plain,
! [A: nat > set] :
( ~ ( esti @ ( sk2 @ x )
@ ( setof
@ ^ [B: nat] : ( esti @ B @ ( A @ B ) ) ) )
| ( esti @ x @ ( A @ ( sk2 @ x ) ) ) ),
inference(simp,[status(thm)],[2067]) ).
thf(2278,plain,
! [A: nat > set] :
( ~ ( esti @ x
@ ( setof
@ ^ [B: nat] : ( esti @ B @ ( A @ B ) ) ) )
| ( esti @ x @ ( A @ x ) ) ),
inference(rewrite,[status(thm)],[2142,29]) ).
thf(69,plain,
! [A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) )
| $false ),
inference(prim_subst,[status(thm)],[12:[bind(A,$thf( ^ [C: nat] : $false ))]]) ).
thf(89,plain,
! [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ),
inference(simp,[status(thm)],[69]) ).
thf(2282,plain,
! [B: nat,A: nat > set] :
( ~ ( esti @ x
@ ( setof
@ ^ [C: nat] : ( esti @ C @ ( A @ C ) ) ) )
| ( ( esti @ x @ ( A @ x ) )
!= ( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[2278,89]) ).
thf(2341,plain,
~ ( esti @ x
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(pre_uni,[status(thm)],[2282:[bind(A,$thf( ^ [C: nat] : ( setof @ ^ [D: nat] : $false ) )),bind(B,$thf( x ))]]) ).
thf(2433,plain,
~ ( esti @ x
@ ( setof
@ ^ [A: nat] : $false ) ),
inference(rewrite,[status(thm)],[2341,89]) ).
thf(2441,plain,
! [B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( B @ A )
!= ( esti @ x
@ ( setof
@ ^ [C: nat] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[327,2433]) ).
thf(2466,plain,
( esti @ x
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(pre_uni,[status(thm)],[2441:[bind(A,$thf( x )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $false ) ) ))]]) ).
thf(2752,plain,
( esti @ x
@ ( setof
@ ^ [A: nat] : ~ $false ) ),
inference(rewrite,[status(thm)],[2466,89]) ).
thf(2753,plain,
( esti @ x
@ ( setof
@ ^ [A: nat] : $true ) ),
inference(simp,[status(thm)],[2752]) ).
thf(68,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[12:[bind(A,$thf( ^ [D: nat] : ~ ( C @ D ) ))]]) ).
thf(87,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) ),
inference(cnf,[status(esa)],[68]) ).
thf(88,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(2763,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( esti @ x
@ ( setof
@ ^ [C: nat] : $true ) )
!= ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2753,88]) ).
thf(2796,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( x != A )
| ( ( setof
@ ^ [C: nat] :
~ ( B @ C ) )
!= ( setof
@ ^ [C: nat] : $true ) ) ),
inference(simp,[status(thm)],[2763]) ).
thf(2849,plain,
! [A: nat > $o] :
( ~ ( A @ x )
| ( ( setof
@ ^ [B: nat] :
~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[2796]) ).
thf(7672,plain,
! [A: nat > $o] :
( ~ ( A @ x )
| ( ( ^ [B: nat] :
~ ( A @ B ) )
!= ( ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[2849]) ).
thf(7786,plain,
! [A: nat > $o] :
( ~ ~ ( A @ ( sk8 @ A ) )
| ~ ( A @ x ) ),
inference(func_ext,[status(esa)],[7672]) ).
thf(7886,plain,
! [A: nat > $o] :
( ~ ( A @ x )
| ( A @ ( sk8 @ A ) ) ),
inference(cnf,[status(esa)],[7786]) ).
thf(8547,plain,
! [A: nat > $o] :
( ~ ~ ( A @ x )
| ~ ( A
@ ( sk8
@ ^ [B: nat] :
~ ( A @ B ) ) ) ),
inference(prim_subst,[status(thm)],[7886:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(8701,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk8
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ( A @ x ) ),
inference(cnf,[status(esa)],[8547]) ).
thf(8702,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk8
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ( A @ x ) ),
inference(simp,[status(thm)],[8701]) ).
thf(9408,plain,
! [A: nat > $o] :
( ~ ~ ( A
@ ( sk8
@ ^ [B: nat] :
~ ~ ( A @ B ) ) )
| ~ ( A @ x ) ),
inference(prim_subst,[status(thm)],[8702:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(9468,plain,
! [A: nat > $o] :
( ~ ( A @ x )
| ( A
@ ( sk8
@ ^ [B: nat] :
~ ~ ( A @ B ) ) ) ),
inference(cnf,[status(esa)],[9408]) ).
thf(9469,plain,
! [A: nat > $o] :
( ~ ( A @ x )
| ( A @ ( sk8 @ A ) ) ),
inference(simp,[status(thm)],[9468]) ).
thf(2315,plain,
! [C: nat,B: nat > $o,A: nat > set] :
( ~ ( esti @ x
@ ( setof
@ ^ [D: nat] : ( esti @ D @ ( A @ D ) ) ) )
| ( B @ C )
| ( ( esti @ x @ ( A @ x ) )
!= ( esti @ C @ ( setof @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[2278,12]) ).
thf(2384,plain,
! [A: nat > nat > $o] :
( ~ ( esti @ x
@ ( setof
@ ^ [B: nat] : ( esti @ B @ ( setof @ ( A @ B ) ) ) ) )
| ( A @ x @ x ) ),
inference(pre_uni,[status(thm)],[2315:[bind(A,$thf( ^ [E: nat] : ( setof @ ( D @ E ) ) )),bind(B,$thf( D @ x )),bind(C,$thf( x ))]]) ).
thf(2430,plain,
! [A: nat > nat > $o] :
( ~ ( esti @ x
@ ( setof
@ ^ [B: nat] : ( esti @ B @ ( setof @ ( A @ B ) ) ) ) )
| ( A @ x @ x ) ),
inference(simp,[status(thm)],[2384]) ).
thf(11543,plain,
! [C: nat > nat > $o,B: nat,A: nat > $o] :
( ~ ( A @ B )
| ( C @ x @ x )
| ( ( esti @ B @ ( setof @ A ) )
!= ( esti @ x
@ ( setof
@ ^ [D: nat] : ( esti @ D @ ( setof @ ( C @ D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,2430]) ).
thf(11544,plain,
! [A: nat > nat > $o] :
( ~ ( esti @ x @ ( setof @ ( A @ x ) ) )
| ( A @ x @ x ) ),
inference(pattern_uni,[status(thm)],[11543:[bind(A,$thf( ^ [E: nat] : ( esti @ E @ ( setof @ ( F @ E ) ) ) )),bind(B,$thf( x )),bind(C,$thf( F ))]]) ).
thf(11824,plain,
! [A: nat > nat > $o] :
( ~ ( esti @ x @ ( setof @ ( A @ x ) ) )
| ( A @ x @ x ) ),
inference(simp,[status(thm)],[11544]) ).
thf(12066,plain,
! [A: nat > nat > $o] :
( ~ ( esti @ x
@ ( setof
@ ^ [B: nat] :
~ ( A @ x @ B ) ) )
| ~ ( A @ x @ x ) ),
inference(prim_subst,[status(thm)],[11824:[bind(A,$thf( ^ [C: nat] : ^ [D: nat] : ~ ( B @ C @ D ) ))]]) ).
thf(12320,plain,
! [A: nat > nat > $o] :
( ~ ( A @ x @ x )
| ~ ( esti @ x
@ ( setof
@ ^ [B: nat] :
~ ( A @ x @ B ) ) ) ),
inference(cnf,[status(esa)],[12066]) ).
thf(12321,plain,
! [A: nat > nat > $o] :
( ~ ( A @ x @ x )
| ~ ( esti @ x
@ ( setof
@ ^ [B: nat] :
~ ( A @ x @ B ) ) ) ),
inference(simp,[status(thm)],[12320]) ).
thf(13850,plain,
! [B: nat > nat > $o,A: nat > $o] :
( ~ ( A @ x )
| ~ ( B @ x @ x )
| ( ( A @ ( sk8 @ A ) )
!= ( esti @ x
@ ( setof
@ ^ [C: nat] :
~ ( B @ x @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[9469,12321]) ).
thf(13949,plain,
! [A: nat > $o] :
( ~ ( A @ x )
| ( x != x )
| ( ( A @ ( sk8 @ A ) )
!= ( esti @ x
@ ( setof
@ ^ [B: nat] : ( x != B ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[13850:[bind(A,$thf( A )),bind(B,$thf( (=) @ nat ))]]) ).
thf(13997,plain,
! [A: nat > $o] :
( ( x != x )
| ~ ( A @ x )
| ( ( A @ ( sk8 @ A ) )
!= ( esti @ x
@ ( setof
@ ^ [B: nat] : ( x != B ) ) ) ) ),
inference(lifteq,[status(thm)],[13949]) ).
thf(14058,plain,
~ ( esti @ x
@ ( setof
@ ^ [A: nat] : ( x != A ) ) ),
inference(pre_uni,[status(thm)],[13997:[bind(A,$thf( ^ [B: nat] : ( esti @ x @ ( setof @ ^ [C: nat] : ( x != C ) ) ) ))]]) ).
thf(14421,plain,
! [A: nat] :
( ( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) )
!= ( esti @ x
@ ( setof
@ ^ [B: nat] : ( x != B ) ) ) ),
inference(paramod_ordered,[status(thm)],[328,14058]) ).
thf(14476,plain,
! [A: nat] :
( ( A != x )
| ( ( setof
@ ^ [B: nat] : ( x != B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[14421]) ).
thf(14540,plain,
( ( setof
@ ^ [A: nat] : ( x != A ) )
!= ( setof
@ ^ [A: nat] : $true ) ),
inference(simp,[status(thm)],[14476]) ).
thf(15105,plain,
( ( ^ [A: nat] : ( x != A ) )
!= ( ^ [A: nat] : $true ) ),
inference(simp,[status(thm)],[14540]) ).
thf(4,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(13,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)],[4]) ).
thf(14,plain,
! [B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ~ ( esti @ ( suc @ ( sk1 @ A ) ) @ A )
| ( esti @ B @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(30,plain,
! [B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ~ ( esti @ x @ A )
| ( esti @ B @ A )
| ( ( suc @ ( sk1 @ A ) )
!= ( suc @ x ) ) ),
inference(paramod_ordered,[status(thm)],[10,14]) ).
thf(34,plain,
! [B: nat,A: set] :
( ( esti @ B @ A )
| ~ ( esti @ n_1 @ A )
| ~ ( esti @ x @ A )
| ( ( sk1 @ A )
!= x ) ),
inference(simp,[status(thm)],[30]) ).
thf(57,plain,
! [D: nat,C: set,B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ( esti @ D @ C )
| ~ ( esti @ n_1 @ C )
| ( ( sk1 @ C )
!= x )
| ( ( A @ B )
!= ( esti @ x @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,34]) ).
thf(73,plain,
! [C: nat > set,B: nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ x @ ( C @ D ) ) ) )
| ( esti @ B @ ( C @ A ) )
| ~ ( esti @ n_1 @ ( C @ A ) )
| ( ( sk1 @ ( C @ A ) )
!= x ) ),
inference(pre_uni,[status(thm)],[57:[bind(A,$thf( ^ [F: nat] : ( esti @ x @ ( F @ F ) ) )),bind(B,$thf( B )),bind(C,$thf( F @ B )),bind(D,$thf( D ))]]) ).
thf(94,plain,
! [C: nat > set,B: nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ x @ ( C @ D ) ) ) )
| ( esti @ B @ ( C @ A ) )
| ~ ( esti @ n_1 @ ( C @ A ) )
| ( ( sk1 @ ( C @ A ) )
!= x ) ),
inference(simp,[status(thm)],[73]) ).
thf(2440,plain,
! [B: nat > $o,A: nat] :
( ( B @ A )
| ( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
!= ( esti @ x
@ ( setof
@ ^ [C: nat] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[327,2433]) ).
thf(2470,plain,
! [B: nat > $o,A: nat] :
( ( B @ A )
| ( A != x )
| ( ( setof
@ ^ [C: nat] :
~ ( B @ C ) )
!= ( setof
@ ^ [C: nat] : $false ) ) ),
inference(simp,[status(thm)],[2440]) ).
thf(2485,plain,
! [A: nat > $o] :
( ( A @ x )
| ( ( setof
@ ^ [B: nat] :
~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $false ) ) ),
inference(simp,[status(thm)],[2470]) ).
thf(3520,plain,
! [A: nat > $o] :
( ( A @ x )
| ( ( ^ [B: nat] :
~ ( A @ B ) )
!= ( ^ [B: nat] : $false ) ) ),
inference(simp,[status(thm)],[2485]) ).
thf(14440,plain,
! [A: nat > $o] :
( ( ( ^ [B: nat] :
~ ( A @ B ) )
!= ( ^ [B: nat] : $false ) )
| ( ( A @ x )
!= ( esti @ x
@ ( setof
@ ^ [B: nat] : ( x != B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3520,14058]) ).
thf(14462,plain,
( ( ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : ( A != B ) ) ) )
!= ( ^ [A: nat] : $false ) ),
inference(pre_uni,[status(thm)],[14440:[bind(A,$thf( ^ [B: nat] : ( esti @ B @ ( setof @ ^ [C: nat] : ( B != C ) ) ) ))]]) ).
thf(15103,plain,
~ ( esti @ sk9
@ ( setof
@ ^ [A: nat] : ( sk9 != A ) ) ),
inference(func_ext,[status(esa)],[14462]) ).
thf(15104,plain,
~ ( esti @ sk9
@ ( setof
@ ^ [A: nat] : ( sk9 != A ) ) ),
inference(cnf,[status(esa)],[15103]) ).
thf(15145,plain,
! [A: nat] :
( ( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) )
!= ( esti @ sk9
@ ( setof
@ ^ [B: nat] : ( sk9 != B ) ) ) ),
inference(paramod_ordered,[status(thm)],[328,15104]) ).
thf(15192,plain,
! [A: nat] :
( ( A != sk9 )
| ( ( setof
@ ^ [B: nat] : ( sk9 != B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[15145]) ).
thf(15252,plain,
( ( setof
@ ^ [A: nat] : ( sk9 != A ) )
!= ( setof
@ ^ [A: nat] : $true ) ),
inference(simp,[status(thm)],[15192]) ).
thf(15625,plain,
( ( ^ [A: nat] : ( sk9 != A ) )
!= ( ^ [A: nat] : $true ) ),
inference(simp,[status(thm)],[15252]) ).
thf(15626,plain,
sk9 != sk11,
inference(func_ext,[status(esa)],[15625]) ).
thf(15627,plain,
sk9 = sk11,
inference(cnf,[status(esa)],[15626]) ).
thf(15628,plain,
sk11 = sk9,
inference(lifteq,[status(thm)],[15627]) ).
thf(122,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)],[12,88]) ).
thf(137,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)],[122:[]]) ).
thf(138,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)],[137:[]]) ).
thf(62,plain,
! [D: nat,C: set,B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ~ ( esti @ n_1 @ C )
| ( esti @ D @ C )
| ( ( A @ B )
!= ( esti @ ( suc @ ( sk1 @ C ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,14]) ).
thf(81,plain,
! [C: set,B: nat > set,A: nat] :
( ~ ( esti @ ( suc @ ( sk1 @ C ) )
@ ( setof
@ ^ [D: nat] : ( esti @ D @ ( B @ D ) ) ) )
| ~ ( esti @ n_1 @ ( B @ ( suc @ ( sk1 @ C ) ) ) )
| ( esti @ A @ ( B @ ( suc @ ( sk1 @ C ) ) ) )
| ( C
!= ( B @ ( suc @ ( sk1 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[62:[bind(A,$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(84,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)],[81:[]]) ).
thf(101,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)],[84]) ).
thf(3569,plain,
! [A: nat > $o] :
( ~ ( A @ x )
| ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $false ) ) ),
inference(prim_subst,[status(thm)],[2485:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(3660,plain,
! [A: nat > $o] :
( ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $false ) )
| ~ ( A @ x ) ),
inference(cnf,[status(esa)],[3569]) ).
thf(3661,plain,
! [A: nat > $o] :
( ( ( setof @ A )
!= ( setof
@ ^ [B: nat] : $false ) )
| ~ ( A @ x ) ),
inference(simp,[status(thm)],[3660]) ).
thf(15,plain,
! [B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ( esti @ ( sk1 @ A ) @ A )
| ( esti @ B @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(510,plain,
! [D: nat,C: set,B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [E: nat] :
~ ( B @ E ) ) )
| ( esti @ ( sk1 @ C ) @ C )
| ( esti @ D @ C )
| ( ( B @ A )
!= ( esti @ n_1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[327,15]) ).
thf(572,plain,
! [B: nat > set,A: nat] :
( ( esti @ n_1
@ ( setof
@ ^ [C: nat] :
~ ( esti @ C @ ( B @ C ) ) ) )
| ( esti @ ( sk1 @ ( B @ n_1 ) ) @ ( B @ n_1 ) )
| ( esti @ A @ ( B @ n_1 ) ) ),
inference(pre_uni,[status(thm)],[510:[bind(A,$thf( n_1 )),bind(B,$thf( ^ [F: nat] : ( esti @ F @ ( F @ F ) ) )),bind(C,$thf( F @ n_1 )),bind(D,$thf( D ))]]) ).
thf(614,plain,
! [B: nat > set,A: nat] :
( ( esti @ n_1
@ ( setof
@ ^ [C: nat] :
~ ( esti @ C @ ( B @ C ) ) ) )
| ( esti @ ( sk1 @ ( B @ n_1 ) ) @ ( B @ n_1 ) )
| ( esti @ A @ ( B @ n_1 ) ) ),
inference(simp,[status(thm)],[572]) ).
thf(887,plain,
! [C: nat,B: nat > set,A: nat] :
( ( esti @ n_1
@ ( setof
@ ^ [D: nat] :
~ ( esti @ D @ ( B @ D ) ) ) )
| ( esti @ ( sk1 @ ( B @ n_1 ) ) @ ( B @ n_1 ) )
| ( ( esti @ A @ ( B @ n_1 ) )
!= ( esti @ C
@ ( setof
@ ^ [D: nat] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[614,89]) ).
thf(948,plain,
( ( esti @ n_1
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) )
| ( esti
@ ( sk1
@ ( setof
@ ^ [A: nat] : $false ) )
@ ( setof
@ ^ [A: nat] : $false ) ) ),
inference(pre_uni,[status(thm)],[887:[bind(A,$thf( C )),bind(B,$thf( ^ [D: nat] : ( setof @ ^ [E: nat] : $false ) )),bind(C,$thf( C ))]]) ).
thf(1249,plain,
( ( esti @ n_1
@ ( setof
@ ^ [A: nat] : ~ $false ) )
| $false ),
inference(rewrite,[status(thm)],[948,89]) ).
thf(1250,plain,
( esti @ n_1
@ ( setof
@ ^ [A: nat] : $true ) ),
inference(simp,[status(thm)],[1249]) ).
thf(1263,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)],[1250,88]) ).
thf(1296,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( n_1 != A )
| ( ( setof
@ ^ [C: nat] :
~ ( B @ C ) )
!= ( setof
@ ^ [C: nat] : $true ) ) ),
inference(simp,[status(thm)],[1263]) ).
thf(1307,plain,
! [A: nat > $o] :
( ~ ( A @ n_1 )
| ( ( setof
@ ^ [B: nat] :
~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[1296]) ).
thf(2227,plain,
! [A: nat > $o] :
( ~ ~ ( A @ n_1 )
| ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(prim_subst,[status(thm)],[1307:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(2262,plain,
! [A: nat > $o] :
( ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) )
| ( A @ n_1 ) ),
inference(cnf,[status(esa)],[2227]) ).
thf(2263,plain,
! [A: nat > $o] :
( ( ( setof @ A )
!= ( setof
@ ^ [B: nat] : $true ) )
| ( A @ n_1 ) ),
inference(simp,[status(thm)],[2262]) ).
thf(347,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)],[328,88]) ).
thf(365,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)],[347]) ).
thf(377,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( setof
@ ^ [C: nat] :
~ ( B @ C ) )
!= ( setof
@ ^ [C: nat] : $true ) ) ),
inference(simp,[status(thm)],[365]) ).
thf(392,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( ^ [C: nat] :
~ ( B @ C ) )
!= ( ^ [C: nat] : $true ) ) ),
inference(simp,[status(thm)],[377]) ).
thf(465,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ~ ( ( B @ A )
| ( C @ A ) )
| ( ( ^ [D: nat] :
~ ( ( B @ D )
| ( C @ D ) ) )
!= ( ^ [D: nat] : $true ) ) ),
inference(prim_subst,[status(thm)],[392:[bind(A,$thf( A )),bind(B,$thf( ^ [E: nat] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(479,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ( ( ^ [D: nat] :
~ ( ( B @ D )
| ( C @ D ) ) )
!= ( ^ [D: nat] : $true ) )
| ~ ( C @ A ) ),
inference(cnf,[status(esa)],[465]) ).
thf(481,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ( ( ^ [D: nat] :
~ ( ( B @ D )
| ( C @ D ) ) )
!= ( ^ [D: nat] : $true ) )
| ~ ( C @ A ) ),
inference(simp,[status(thm)],[479]) ).
thf(3967,plain,
! [A: nat > $o] :
( ~ ( A @ ( sk6 @ A ) )
| ( A @ x ) ),
inference(func_ext,[status(esa)],[3520]) ).
thf(4125,plain,
! [A: nat > $o] :
( ( A @ x )
| ~ ( A @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[3967]) ).
thf(4531,plain,
! [A: nat > $o] :
( ~ ( A @ x )
| ~ ~ ( A
@ ( sk6
@ ^ [B: nat] :
~ ( A @ B ) ) ) ),
inference(prim_subst,[status(thm)],[4125:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(4591,plain,
! [A: nat > $o] :
( ( A
@ ( sk6
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ~ ( A @ x ) ),
inference(cnf,[status(esa)],[4531]) ).
thf(4592,plain,
! [A: nat > $o] :
( ( A
@ ( sk6
@ ^ [B: nat] :
~ ( A @ B ) ) )
| ~ ( A @ x ) ),
inference(simp,[status(thm)],[4591]) ).
thf(129,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ~ ( ( B @ A )
| ( C @ A ) )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( ( B @ D )
| ( C @ D ) ) ) ) ),
inference(prim_subst,[status(thm)],[88:[bind(A,$thf( A )),bind(B,$thf( ^ [E: nat] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(140,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( ( B @ D )
| ( C @ D ) ) ) )
| ~ ( B @ A ) ),
inference(cnf,[status(esa)],[129]) ).
thf(142,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( ( B @ D )
| ( C @ D ) ) ) )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[140]) ).
thf(14461,plain,
( ( ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : ( x != B ) ) ) )
!= ( ^ [A: nat] : $false ) ),
inference(pre_uni,[status(thm)],[14440:[bind(A,$thf( ^ [B: nat] : ( esti @ B @ ( setof @ ^ [C: nat] : ( x != C ) ) ) ))]]) ).
thf(16604,plain,
~ ( esti @ sk13
@ ( setof
@ ^ [A: nat] : ( x != A ) ) ),
inference(func_ext,[status(esa)],[14461]) ).
thf(16605,plain,
~ ( esti @ sk13
@ ( setof
@ ^ [A: nat] : ( x != A ) ) ),
inference(cnf,[status(esa)],[16604]) ).
thf(16645,plain,
! [B: nat > $o,A: nat] :
( ( B @ A )
| ( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
!= ( esti @ sk13
@ ( setof
@ ^ [C: nat] : ( x != C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[327,16605]) ).
thf(16646,plain,
x = sk13,
inference(pattern_uni,[status(thm)],[16645:[bind(A,$thf( sk13 )),bind(B,$thf( (=) @ nat @ x ))]]) ).
thf(16658,plain,
sk13 = x,
inference(lifteq,[status(thm)],[16646]) ).
thf(404,plain,
! [B: nat > $o,A: nat] :
( ~ ~ ( B @ A )
| ( ( setof
@ ^ [C: nat] :
~ ~ ( B @ C ) )
!= ( setof
@ ^ [C: nat] : $true ) ) ),
inference(prim_subst,[status(thm)],[377:[bind(A,$thf( A )),bind(B,$thf( ^ [D: nat] : ~ ( C @ D ) ))]]) ).
thf(417,plain,
! [B: nat > $o,A: nat] :
( ( ( setof
@ ^ [C: nat] :
~ ~ ( B @ C ) )
!= ( setof
@ ^ [C: nat] : $true ) )
| ( B @ A ) ),
inference(cnf,[status(esa)],[404]) ).
thf(418,plain,
! [B: nat > $o,A: nat] :
( ( ( setof @ B )
!= ( setof
@ ^ [C: nat] : $true ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[417]) ).
thf(14443,plain,
! [B: nat > $o,A: nat] :
( ( ( setof @ B )
!= ( setof
@ ^ [C: nat] : $true ) )
| ( ( B @ A )
!= ( esti @ x
@ ( setof
@ ^ [C: nat] : ( x != C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[418,14058]) ).
thf(14535,plain,
( ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : ( A != B ) ) ) )
!= ( setof
@ ^ [A: nat] : $true ) ),
inference(pre_uni,[status(thm)],[14443:[bind(A,$thf( x )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : ( C != D ) ) ) ))]]) ).
thf(17446,plain,
( ( ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : ( A != B ) ) ) )
!= ( ^ [A: nat] : $true ) ),
inference(simp,[status(thm)],[14535]) ).
thf(50,plain,
! [A: nat] :
( ( x = A )
| ( ( sk2 @ ( suc @ A ) )
!= ( sk2 @ x ) ) ),
inference(paramod_ordered,[status(thm)],[29,25]) ).
thf(52,plain,
! [A: nat] :
( ( x = A )
| ( ( suc @ A )
!= x ) ),
inference(simp,[status(thm)],[50]) ).
thf(11579,plain,
! [C: nat > nat > $o,B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( B @ D ) ) )
| ( C @ x @ x )
| ( ( B @ A )
!= ( esti @ x
@ ( setof
@ ^ [D: nat] : ( esti @ D @ ( setof @ ( C @ D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[327,2430]) ).
thf(11745,plain,
! [A: nat > nat > nat > $o] :
( ( esti @ x
@ ( setof
@ ^ [B: nat] :
~ ( esti @ B
@ ( setof
@ ^ [C: nat] : ( esti @ C @ ( setof @ ( A @ B @ C ) ) ) ) ) ) )
| ( A @ x @ x @ x ) ),
inference(pre_uni,[status(thm)],[11579:[bind(A,$thf( x )),bind(B,$thf( ^ [E: nat] : ( esti @ E @ ( setof @ ^ [F: nat] : ( esti @ F @ ( setof @ ( L @ E @ F ) ) ) ) ) )),bind(C,$thf( L @ x ))]]) ).
thf(11913,plain,
! [A: nat > nat > nat > $o] :
( ( esti @ x
@ ( setof
@ ^ [B: nat] :
~ ( esti @ B
@ ( setof
@ ^ [C: nat] : ( esti @ C @ ( setof @ ( A @ B @ C ) ) ) ) ) ) )
| ( A @ x @ x @ x ) ),
inference(simp,[status(thm)],[11745]) ).
thf(13912,plain,
! [C: nat > nat > $o,B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( B @ D ) ) )
| ~ ( C @ x @ x )
| ( ( B @ A )
!= ( esti @ x
@ ( setof
@ ^ [D: nat] :
~ ( C @ x @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[327,12321]) ).
thf(13974,plain,
! [B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( x != x )
| ( ( B @ A )
!= ( esti @ x
@ ( setof
@ ^ [C: nat] : ( x != C ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[13912:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( (=) @ nat ))]]) ).
thf(14026,plain,
! [B: nat > $o,A: nat] :
( ( x != x )
| ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( B @ A )
!= ( esti @ x
@ ( setof
@ ^ [C: nat] : ( x != C ) ) ) ) ),
inference(lifteq,[status(thm)],[13974]) ).
thf(14228,plain,
( esti @ x
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : ( A != B ) ) ) ) ),
inference(pre_uni,[status(thm)],[14026:[bind(A,$thf( x )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : ( C != D ) ) ) ))]]) ).
thf(17447,plain,
~ ( esti @ sk14
@ ( setof
@ ^ [A: nat] : ( sk14 != A ) ) ),
inference(func_ext,[status(esa)],[17446]) ).
thf(17990,plain,
! [A: nat] :
( ( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) )
!= ( esti @ sk14
@ ( setof
@ ^ [B: nat] : ( sk14 != B ) ) ) ),
inference(paramod_ordered,[status(thm)],[328,17447]) ).
thf(18066,plain,
! [A: nat] :
( ( A != sk14 )
| ( ( setof
@ ^ [B: nat] : ( sk14 != B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[17990]) ).
thf(18096,plain,
( ( setof
@ ^ [A: nat] : ( sk14 != A ) )
!= ( setof
@ ^ [A: nat] : $true ) ),
inference(simp,[status(thm)],[18066]) ).
thf(18104,plain,
( ( ^ [A: nat] : ( sk14 != A ) )
!= ( ^ [A: nat] : $true ) ),
inference(simp,[status(thm)],[18096]) ).
thf(45,plain,
! [B: nat,A: set] :
( ( esti @ B @ A )
| ~ ( esti @ x @ A )
| ( ( sk1 @ A )
!= x )
| ( ( esti @ n_1 @ A )
!= ( esti @ x @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[34]) ).
thf(46,plain,
! [B: nat,A: set] :
( ( esti @ B @ A )
| ~ ( esti @ x @ A )
| ( ( sk1 @ A )
!= x )
| ( ( esti @ n_1 @ A )
!= ( esti @ x @ A ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(56,plain,
! [D: nat,C: set,B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ( esti @ D @ C )
| ~ ( esti @ x @ C )
| ( ( sk1 @ C )
!= x )
| ( ( A @ B )
!= ( esti @ n_1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,34]) ).
thf(72,plain,
! [B: nat > set,A: nat] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [C: nat] : ( esti @ C @ ( B @ C ) ) ) )
| ( esti @ A @ ( B @ n_1 ) )
| ~ ( esti @ x @ ( B @ n_1 ) )
| ( ( sk1 @ ( B @ n_1 ) )
!= x ) ),
inference(pre_uni,[status(thm)],[56:[bind(A,$thf( ^ [F: nat] : ( esti @ F @ ( F @ F ) ) )),bind(B,$thf( n_1 )),bind(C,$thf( F @ n_1 )),bind(D,$thf( D ))]]) ).
thf(93,plain,
! [B: nat > set,A: nat] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [C: nat] : ( esti @ C @ ( B @ C ) ) ) )
| ( esti @ A @ ( B @ n_1 ) )
| ~ ( esti @ x @ ( B @ n_1 ) )
| ( ( sk1 @ ( B @ n_1 ) )
!= x ) ),
inference(simp,[status(thm)],[72]) ).
thf(65,plain,
! [B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ( ( A @ B )
!= ( ~ ( esti @ B @ ( setof @ A ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[12]) ).
thf(78,plain,
! [B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ( ( A @ B )
!= ( ~ ( esti @ B @ ( setof @ A ) ) ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(124,plain,
! [D: nat > $o,C: nat,B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ~ ( esti @ ( suc @ ( sk1 @ A ) ) @ A )
| ~ ( esti @ C
@ ( setof
@ ^ [E: nat] :
~ ( D @ E ) ) )
| ( ( esti @ B @ A )
!= ( D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[14,88]) ).
thf(133,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ n_1 @ ( C @ A ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( C @ A ) ) ) @ ( C @ A ) )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(pre_uni,[status(thm)],[124:[bind(A,$thf( F @ C )),bind(B,$thf( E @ C )),bind(C,$thf( C )),bind(D,$thf( ^ [G: nat] : ( esti @ ( E @ G ) @ ( F @ G ) ) ))]]) ).
thf(147,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)],[133]) ).
thf(2204,plain,
! [A: nat > $o] :
( ~ ( A @ n_1 )
| ( ( ^ [B: nat] :
~ ( A @ B ) )
!= ( ^ [B: nat] : $true ) ) ),
inference(simp,[status(thm)],[1307]) ).
thf(63,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)],[14,12]) ).
thf(64,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ n_1 @ ( setof @ B ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( setof @ B ) ) ) @ ( setof @ B ) )
| ( B @ A ) ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( setof @ E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( B ))]]) ).
thf(85,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ n_1 @ ( setof @ B ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( setof @ B ) ) ) @ ( setof @ B ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[64]) ).
thf(58,plain,
! [D: nat,C: nat > $o,B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ~ ( esti @ x @ A )
| ( ( sk1 @ A )
!= x )
| ( C @ D )
| ( ( esti @ B @ A )
!= ( esti @ D @ ( setof @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,12]) ).
thf(59,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ n_1 @ ( setof @ B ) )
| ~ ( esti @ x @ ( setof @ B ) )
| ( ( sk1 @ ( setof @ B ) )
!= x )
| ( B @ A ) ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( setof @ E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( B ))]]) ).
thf(102,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ n_1 @ ( setof @ B ) )
| ~ ( esti @ x @ ( setof @ B ) )
| ( ( sk1 @ ( setof @ B ) )
!= x )
| ( B @ A ) ),
inference(simp,[status(thm)],[59]) ).
thf(6,axiom,
! [A: nat] :
( ( suc @ A )
!= n_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(18,plain,
! [A: nat] :
( ( suc @ A )
!= n_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,plain,
~ ? [A: nat] :
( ( suc @ A )
= n_1 ),
inference(miniscope,[status(thm)],[18]) ).
thf(20,plain,
! [A: nat] :
( ( suc @ A )
!= n_1 ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [A: nat] :
( ( suc @ A )
!= n_1 ),
inference(lifteq,[status(thm)],[20]) ).
thf(71,plain,
! [C: nat > set,B: nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ n_1 @ ( C @ D ) ) ) )
| ( esti @ B @ ( C @ A ) )
| ~ ( esti @ x @ ( C @ A ) )
| ( ( sk1 @ ( C @ A ) )
!= x ) ),
inference(pre_uni,[status(thm)],[56:[bind(A,$thf( ^ [F: nat] : ( esti @ n_1 @ ( F @ F ) ) )),bind(B,$thf( B )),bind(C,$thf( F @ B )),bind(D,$thf( D ))]]) ).
thf(92,plain,
! [C: nat > set,B: nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ n_1 @ ( C @ D ) ) ) )
| ( esti @ B @ ( C @ A ) )
| ~ ( esti @ x @ ( C @ A ) )
| ( ( sk1 @ ( C @ A ) )
!= x ) ),
inference(simp,[status(thm)],[71]) ).
thf(61,plain,
! [D: nat,C: set,B: nat,A: nat > $o] :
( ~ ( esti @ B @ ( setof @ A ) )
| ~ ( esti @ ( suc @ ( sk1 @ C ) ) @ C )
| ( esti @ D @ C )
| ( ( A @ B )
!= ( esti @ n_1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,14]) ).
thf(76,plain,
! [B: nat > set,A: nat] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [C: nat] : ( esti @ C @ ( B @ C ) ) ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( B @ n_1 ) ) ) @ ( B @ n_1 ) )
| ( esti @ A @ ( B @ n_1 ) ) ),
inference(pre_uni,[status(thm)],[61:[bind(A,$thf( ^ [F: nat] : ( esti @ F @ ( F @ F ) ) )),bind(B,$thf( n_1 )),bind(C,$thf( F @ n_1 )),bind(D,$thf( D ))]]) ).
thf(97,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)],[76]) ).
thf(60,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)],[12,12]) ).
thf(77,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( setof @ ( C @ D ) ) ) ) )
| ( C @ A @ ( B @ A ) ) ),
inference(pre_uni,[status(thm)],[60:[bind(A,$thf( ^ [G: nat] : ( esti @ ( E @ G ) @ ( setof @ ( G @ G ) ) ) )),bind(B,$thf( B )),bind(C,$thf( G @ B )),bind(D,$thf( E @ B ))]]) ).
thf(98,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)],[77]) ).
thf(1262,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( esti @ n_1
@ ( setof
@ ^ [C: nat] : $true ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1250,88]) ).
thf(1287,plain,
~ ( esti @ n_1
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $true ) ) ) ),
inference(pre_uni,[status(thm)],[1262:[bind(A,$thf( n_1 )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $true ) ) ))]]) ).
thf(1490,plain,
~ ( esti @ n_1
@ ( setof
@ ^ [A: nat] : ~ $true ) ),
inference(rewrite,[status(thm)],[1287,328]) ).
thf(1491,plain,
~ ( esti @ n_1
@ ( setof
@ ^ [A: nat] : $false ) ),
inference(simp,[status(thm)],[1490]) ).
thf(5509,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)],[98,1491]) ).
thf(5530,plain,
~ ( esti @ n_1
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[5509:[bind(A,$thf( n_1 )),bind(B,$thf( ^ [D: nat] : D )),bind(C,$thf( ^ [D: nat] : ^ [E: nat] : ( esti @ E @ ( setof @ ^ [F: nat] : $false ) ) ))]]) ).
thf(5885,plain,
~ ( esti @ n_1
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(rewrite,[status(thm)],[5530,89]) ).
thf(5924,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)],[327,5885]) ).
thf(5958,plain,
( esti @ n_1
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[5924:[bind(A,$thf( n_1 )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : ( esti @ D @ ( setof @ ^ [E: nat] : $false ) ) ) ) ))]]) ).
thf(5993,plain,
( esti @ n_1
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(rewrite,[status(thm)],[5958,89]) ).
thf(15164,plain,
! [B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( B @ A )
!= ( esti @ sk9
@ ( setof
@ ^ [C: nat] : ( sk9 != C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[327,15104]) ).
thf(15238,plain,
( esti @ sk9
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : ( A != B ) ) ) ) ),
inference(pre_uni,[status(thm)],[15164:[bind(A,$thf( sk9 )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : ( C != D ) ) ) ))]]) ).
thf(139,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( ( B @ D )
| ( C @ D ) ) ) )
| ~ ( C @ A ) ),
inference(cnf,[status(esa)],[129]) ).
thf(141,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( ( B @ D )
| ( C @ D ) ) ) )
| ~ ( C @ A ) ),
inference(simp,[status(thm)],[139]) ).
thf(75,plain,
! [C: nat > set,B: nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ n_1 @ ( C @ D ) ) ) )
| ~ ( esti @ ( suc @ ( sk1 @ ( C @ A ) ) ) @ ( C @ A ) )
| ( esti @ B @ ( C @ A ) ) ),
inference(pre_uni,[status(thm)],[61:[bind(A,$thf( ^ [F: nat] : ( esti @ n_1 @ ( F @ F ) ) )),bind(B,$thf( B )),bind(C,$thf( F @ B )),bind(D,$thf( D ))]]) ).
thf(96,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)],[75]) ).
thf(14460,plain,
( ( ^ [A: nat] :
~ ( esti @ x
@ ( setof
@ ^ [B: nat] : ( A != B ) ) ) )
!= ( ^ [A: nat] : $false ) ),
inference(pre_uni,[status(thm)],[14440:[bind(A,$thf( ^ [B: nat] : ( esti @ x @ ( setof @ ^ [C: nat] : ( B != C ) ) ) ))]]) ).
thf(123,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)],[12,88]) ).
thf(134,plain,
! [C: nat > nat > $o,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
( esti @ ( B @ D )
@ ( setof
@ ^ [E: nat] :
~ ( C @ D @ E ) ) ) ) )
| ~ ( C @ A @ ( B @ A ) ) ),
inference(pre_uni,[status(thm)],[123:[bind(A,$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(148,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)],[134]) ).
thf(119,plain,
! [D: nat > $o,C: nat,B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ~ ( esti @ x @ A )
| ( ( sk1 @ A )
!= x )
| ~ ( esti @ C
@ ( setof
@ ^ [E: nat] :
~ ( D @ E ) ) )
| ( ( esti @ B @ A )
!= ( D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[34,88]) ).
thf(136,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ n_1 @ ( C @ A ) )
| ~ ( esti @ x @ ( C @ A ) )
| ( ( sk1 @ ( C @ A ) )
!= x )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(pre_uni,[status(thm)],[119:[bind(A,$thf( F @ C )),bind(B,$thf( E @ C )),bind(C,$thf( C )),bind(D,$thf( ^ [G: nat] : ( esti @ ( E @ G ) @ ( F @ G ) ) ))]]) ).
thf(149,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ n_1 @ ( C @ A ) )
| ~ ( esti @ x @ ( C @ A ) )
| ( ( sk1 @ ( C @ A ) )
!= x )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(7712,plain,
! [A: nat > $o] :
( ~ ~ ( A @ x )
| ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) ) ),
inference(prim_subst,[status(thm)],[2849:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(7762,plain,
! [A: nat > $o] :
( ( ( setof
@ ^ [B: nat] :
~ ~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $true ) )
| ( A @ x ) ),
inference(cnf,[status(esa)],[7712]) ).
thf(7763,plain,
! [A: nat > $o] :
( ( ( setof @ A )
!= ( setof
@ ^ [B: nat] : $true ) )
| ( A @ x ) ),
inference(simp,[status(thm)],[7762]) ).
thf(26,plain,
! [A: nat] :
( ( n_1 != x )
| ( ( suc @ x )
!= ( suc @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,21]) ).
thf(27,plain,
n_1 != x,
inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( x ))]]) ).
thf(291,plain,
! [D: nat > set,C: nat,B: nat,A: nat > $o] :
( ~ ( A @ B )
| ( esti @ C @ ( D @ n_1 ) )
| ~ ( esti @ x @ ( D @ n_1 ) )
| ( ( sk1 @ ( D @ n_1 ) )
!= x )
| ( ( esti @ B @ ( setof @ A ) )
!= ( esti @ n_1
@ ( setof
@ ^ [E: nat] : ( esti @ E @ ( D @ E ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,93]) ).
thf(292,plain,
! [B: nat > set,A: nat] :
( ~ ( esti @ n_1 @ ( B @ n_1 ) )
| ( esti @ A @ ( B @ n_1 ) )
| ~ ( esti @ x @ ( B @ n_1 ) )
| ( ( sk1 @ ( B @ n_1 ) )
!= x ) ),
inference(pattern_uni,[status(thm)],[291:[bind(A,$thf( ^ [F: nat] : ( esti @ F @ ( F @ F ) ) )),bind(B,$thf( n_1 )),bind(C,$thf( C )),bind(D,$thf( F ))]]) ).
thf(323,plain,
! [B: nat > set,A: nat] :
( ~ ( esti @ n_1 @ ( B @ n_1 ) )
| ( esti @ A @ ( B @ n_1 ) )
| ~ ( esti @ x @ ( B @ n_1 ) )
| ( ( sk1 @ ( B @ n_1 ) )
!= x ) ),
inference(simp,[status(thm)],[292]) ).
thf(70,plain,
! [C: nat > $o,B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
( ( B @ D )
| ( C @ D ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(prim_subst,[status(thm)],[12:[bind(A,$thf( ^ [E: nat] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(90,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)],[70]) ).
thf(91,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)],[90]) ).
thf(5891,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)],[2263,5885]) ).
thf(5948,plain,
( ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) )
!= ( setof
@ ^ [A: nat] : $true ) ),
inference(pre_uni,[status(thm)],[5891:[bind(A,$thf( ^ [B: nat] : ( esti @ B @ ( setof @ ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $false ) ) ) ) ))]]) ).
thf(9327,plain,
( ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) )
!= ( setof
@ ^ [A: nat] : $true ) ),
inference(rewrite,[status(thm)],[5948,89]) ).
thf(127,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
!= ( B @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[88]) ).
thf(135,plain,
! [B: nat > $o,A: nat] :
( ~ ( B @ A )
| ( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
!= ( B @ A ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(33,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)],[14]) ).
thf(35,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)],[33]) ).
thf(120,plain,
! [D: nat > $o,C: nat,B: nat,A: set] :
( ~ ( esti @ n_1 @ A )
| ~ ( esti @ x @ A )
| ( ( sk1 @ A )
!= x )
| ~ ( D @ C )
| ( ( esti @ B @ A )
!= ( esti @ C
@ ( setof
@ ^ [E: nat] :
~ ( D @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,88]) ).
thf(121,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ~ ( esti @ x
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( sk1
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
!= x )
| ~ ( B @ A ) ),
inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( setof @ ^ [F: nat] : ~ ( F @ F ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( F ))]]) ).
thf(150,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ~ ( esti @ x
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( sk1
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
!= x )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[121]) ).
thf(74,plain,
! [B: nat > set,A: nat] :
( ~ ( esti @ x
@ ( setof
@ ^ [C: nat] : ( esti @ C @ ( B @ C ) ) ) )
| ( esti @ A @ ( B @ x ) )
| ~ ( esti @ n_1 @ ( B @ x ) )
| ( ( sk1 @ ( B @ x ) )
!= x ) ),
inference(pre_uni,[status(thm)],[57:[bind(A,$thf( ^ [F: nat] : ( esti @ F @ ( F @ F ) ) )),bind(B,$thf( x )),bind(C,$thf( F @ x )),bind(D,$thf( D ))]]) ).
thf(95,plain,
! [B: nat > set,A: nat] :
( ~ ( esti @ x
@ ( setof
@ ^ [C: nat] : ( esti @ C @ ( B @ C ) ) ) )
| ( esti @ A @ ( B @ x ) )
| ~ ( esti @ n_1 @ ( B @ x ) )
| ( ( sk1 @ ( B @ x ) )
!= x ) ),
inference(simp,[status(thm)],[74]) ).
thf(5464,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 @ x
@ ( setof
@ ^ [D: nat] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[98,2433]) ).
thf(5583,plain,
~ ( esti @ x
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[5464:[bind(A,$thf( x )),bind(B,$thf( ^ [D: nat] : D )),bind(C,$thf( ^ [D: nat] : ^ [E: nat] : ( esti @ E @ ( setof @ ^ [F: nat] : $false ) ) ))]]) ).
thf(6771,plain,
~ ( esti @ x
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(rewrite,[status(thm)],[5583,89]) ).
thf(6814,plain,
! [A: nat > $o] :
( ( ( setof
@ ^ [B: nat] :
~ ( A @ B ) )
!= ( setof
@ ^ [B: nat] : $false ) )
| ( ( A @ x )
!= ( esti @ x
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2485,6771]) ).
thf(6830,plain,
( ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) )
!= ( setof
@ ^ [A: nat] : $false ) ),
inference(pre_uni,[status(thm)],[6814:[bind(A,$thf( ^ [B: nat] : ( esti @ B @ ( setof @ ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $false ) ) ) ) ))]]) ).
thf(11126,plain,
( ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) )
!= ( setof
@ ^ [A: nat] : $false ) ),
inference(rewrite,[status(thm)],[6830,89]) ).
thf(13894,plain,
! [D: nat > nat > $o,C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [E: nat] : ( esti @ ( B @ E ) @ ( C @ E ) ) ) )
| ~ ( D @ x @ x )
| ( ( esti @ ( B @ A ) @ ( C @ A ) )
!= ( esti @ x
@ ( setof
@ ^ [E: nat] :
~ ( D @ x @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[86,12321]) ).
thf(13984,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( C @ D ) ) ) )
| ( x != x )
| ( ( esti @ ( B @ A ) @ ( C @ A ) )
!= ( esti @ x
@ ( setof
@ ^ [D: nat] : ( x != D ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[13894:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( (=) @ nat ))]]) ).
thf(14011,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ( x != x )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] : ( esti @ ( B @ D ) @ ( C @ D ) ) ) )
| ( ( esti @ ( B @ A ) @ ( C @ A ) )
!= ( esti @ x
@ ( setof
@ ^ [D: nat] : ( x != D ) ) ) ) ),
inference(lifteq,[status(thm)],[13984]) ).
thf(14101,plain,
~ ( esti @ x
@ ( setof
@ ^ [A: nat] :
( esti @ A
@ ( setof
@ ^ [B: nat] : ( A != B ) ) ) ) ),
inference(pre_uni,[status(thm)],[14011:[bind(A,$thf( x )),bind(B,$thf( ^ [D: nat] : D )),bind(C,$thf( ^ [D: nat] : ( setof @ ^ [E: nat] : ( D != E ) ) ))]]) ).
thf(5241,plain,
! [A: nat > $o] :
( ~ ( A
@ ( sk6
@ ^ [B: nat] :
~ ~ ( A @ B ) ) )
| ~ ~ ( A @ x ) ),
inference(prim_subst,[status(thm)],[4592:[bind(A,$thf( ^ [C: nat] : ~ ( B @ C ) ))]]) ).
thf(5417,plain,
! [A: nat > $o] :
( ( A @ x )
| ~ ( A
@ ( sk6
@ ^ [B: nat] :
~ ~ ( A @ B ) ) ) ),
inference(cnf,[status(esa)],[5241]) ).
thf(5418,plain,
! [A: nat > $o] :
( ( A @ x )
| ~ ( A @ ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[5417]) ).
thf(130,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ ( B @ A ) @ ( C @ A ) )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(prim_subst,[status(thm)],[88:[bind(A,$thf( A )),bind(B,$thf( ^ [E: nat] : ( esti @ ( C @ E ) @ ( D @ E ) ) ))]]) ).
thf(143,plain,
! [C: nat > set,B: nat > nat,A: nat] :
( ~ ( esti @ ( B @ A ) @ ( C @ A ) )
| ~ ( esti @ A
@ ( setof
@ ^ [D: nat] :
~ ( esti @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(79,plain,
! [D: nat > set,C: nat > set,B: nat,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [E: nat] : ( esti @ ( suc @ ( sk1 @ ( D @ E ) ) ) @ ( C @ E ) ) ) )
| ~ ( esti @ n_1 @ ( C @ A ) )
| ( esti @ B @ ( C @ A ) )
| ( ( D @ A )
!= ( C @ A ) ) ),
inference(pre_uni,[status(thm)],[62:[bind(A,$thf( ^ [G: nat] : ( esti @ ( suc @ ( sk1 @ ( H @ G ) ) ) @ ( F @ G ) ) )),bind(B,$thf( B )),bind(C,$thf( F @ B )),bind(D,$thf( D ))]]) ).
thf(82,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)],[79:[]]) ).
thf(99,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)],[82]) ).
thf(6772,plain,
! [A: nat > $o] :
( ( ( ^ [B: nat] :
~ ( A @ B ) )
!= ( ^ [B: nat] : $false ) )
| ( ( A @ x )
!= ( esti @ x
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3520,6771]) ).
thf(6840,plain,
( ( ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) )
!= ( ^ [A: nat] : $false ) ),
inference(pre_uni,[status(thm)],[6772:[bind(A,$thf( ^ [B: nat] : ( esti @ B @ ( setof @ ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : $false ) ) ) ) ))]]) ).
thf(6882,plain,
( ( ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) )
!= ( ^ [A: nat] : $false ) ),
inference(rewrite,[status(thm)],[6840,89]) ).
thf(6812,plain,
! [B: nat > $o,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ( ( B @ A )
!= ( esti @ x
@ ( setof
@ ^ [C: nat] :
( esti @ C
@ ( setof
@ ^ [D: nat] : $false ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[327,6771]) ).
thf(6823,plain,
( esti @ x
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] :
( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[6812:[bind(A,$thf( x )),bind(B,$thf( ^ [C: nat] : ( esti @ C @ ( setof @ ^ [D: nat] : ( esti @ D @ ( setof @ ^ [E: nat] : $false ) ) ) ) ))]]) ).
thf(6910,plain,
( esti @ x
@ ( setof
@ ^ [A: nat] :
~ ( esti @ A
@ ( setof
@ ^ [B: nat] : $false ) ) ) ),
inference(rewrite,[status(thm)],[6823,89]) ).
thf(348,plain,
! [B: nat,A: nat] :
( ( esti @ A
@ ( setof
@ ^ [C: nat] : $true ) )
!= ( esti @ B
@ ( setof
@ ^ [C: nat] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[328,89]) ).
thf(371,plain,
! [B: nat,A: nat] :
( ( A != B )
| ( ( setof
@ ^ [C: nat] : $false )
!= ( setof
@ ^ [C: nat] : $true ) ) ),
inference(simp,[status(thm)],[348]) ).
thf(383,plain,
( ( setof
@ ^ [A: nat] : $false )
!= ( setof
@ ^ [A: nat] : $true ) ),
inference(simp,[status(thm)],[371]) ).
thf(132,plain,
! [B: nat > $o,A: nat] :
( ~ ~ ( B @ A )
| ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ~ ( B @ C ) ) ) ),
inference(prim_subst,[status(thm)],[88:[bind(A,$thf( A )),bind(B,$thf( ^ [D: nat] : ~ ( C @ D ) ))]]) ).
thf(145,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ~ ( B @ C ) ) )
| ( B @ A ) ),
inference(cnf,[status(esa)],[132]) ).
thf(146,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ A @ ( setof @ B ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[145]) ).
thf(15106,plain,
x != sk10,
inference(func_ext,[status(esa)],[15105]) ).
thf(15107,plain,
x = sk10,
inference(cnf,[status(esa)],[15106]) ).
thf(15108,plain,
sk10 = x,
inference(lifteq,[status(thm)],[15107]) ).
thf(16442,plain,
~ ( esti @ x
@ ( setof
@ ^ [A: nat] : ( sk12 != A ) ) ),
inference(func_ext,[status(esa)],[14460]) ).
thf(16443,plain,
~ ( esti @ x
@ ( setof
@ ^ [A: nat] : ( sk12 != A ) ) ),
inference(cnf,[status(esa)],[16442]) ).
thf(16481,plain,
! [B: nat > $o,A: nat] :
( ( B @ A )
| ( ( esti @ A
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
!= ( esti @ x
@ ( setof
@ ^ [C: nat] : ( sk12 != C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[327,16443]) ).
thf(16482,plain,
sk12 = x,
inference(pattern_uni,[status(thm)],[16481:[bind(A,$thf( x )),bind(B,$thf( (=) @ nat @ sk12 ))]]) ).
thf(16494,plain,
sk12 = x,
inference(lifteq,[status(thm)],[16482]) ).
thf(125,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)],[14,88]) ).
thf(126,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ~ ( esti
@ ( suc
@ ( sk1
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) )
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( setof @ ^ [F: nat] : ~ ( F @ F ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( F ))]]) ).
thf(151,plain,
! [B: nat > $o,A: nat] :
( ~ ( esti @ n_1
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ~ ( esti
@ ( suc
@ ( sk1
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) ) )
@ ( setof
@ ^ [C: nat] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[126]) ).
thf(80,plain,
! [C: set,B: nat > set,A: nat] :
( ~ ( esti @ ( sk1 @ C )
@ ( setof
@ ^ [D: nat] : ( esti @ ( suc @ D ) @ ( B @ D ) ) ) )
| ~ ( esti @ n_1 @ ( B @ ( sk1 @ C ) ) )
| ( esti @ A @ ( B @ ( sk1 @ C ) ) )
| ( C
!= ( B @ ( sk1 @ C ) ) ) ),
inference(pre_uni,[status(thm)],[62:[bind(A,$thf( ^ [F: nat] : ( esti @ ( suc @ F ) @ ( F @ F ) ) )),bind(B,$thf( sk1 @ J )),bind(C,$thf( F @ ( sk1 @ J ) )),bind(D,$thf( D ))]]) ).
thf(83,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)],[80:[]]) ).
thf(100,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)],[83]) ).
thf(56556,plain,
$false,
inference(e,[status(thm)],[15105,13,94,15628,138,101,3661,2263,88,481,7886,9469,614,4592,10,142,16658,17446,24,25,15104,52,14,11913,14228,18104,46,93,78,29,147,89,14462,2204,85,102,392,21,92,2433,12321,97,5993,15238,141,328,96,14460,11824,34,148,17,149,18096,22,2849,7763,27,12,2753,14461,86,377,14540,98,1307,323,91,5885,2278,9327,135,1250,35,14535,15252,150,95,327,11126,14101,18,7672,5418,16,11,3520,143,14058,99,15625,6882,6910,418,8,1491,383,17447,146,15108,16494,4125,151,6771,2430,2485,15,8702,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM636^1 : TPTP v8.1.2. Released v3.7.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n004.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 12:31:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.95/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/0.97 % [INFO] Parsing done (115ms).
% 1.26/0.98 % [INFO] Running in sequential loop mode.
% 1.62/1.18 % [INFO] eprover registered as external prover.
% 1.62/1.19 % [INFO] cvc4 registered as external prover.
% 1.62/1.19 % [INFO] Scanning for conjecture ...
% 1.74/1.23 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.84/1.25 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.84/1.27 % [INFO] Problem is higher-order (TPTP THF).
% 1.84/1.27 % [INFO] Type checking passed.
% 1.84/1.27 % [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 ...
% 152.62/29.09 % External prover 'e' found a proof!
% 152.62/29.09 % [INFO] Killing All external provers ...
% 152.62/29.10 % Time passed: 28569ms (effective reasoning time: 28113ms)
% 152.62/29.10 % 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)>
% 152.62/29.10 % Axioms used in derivation (5): estii, satz1, estie, ax3, ax5
% 152.62/29.10 % No. of inferences in proof: 279
% 152.62/29.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 28569 ms resp. 28113 ms w/o parsing
% 152.89/29.22 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 152.89/29.22 % [INFO] Killing All external provers ...
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