TSTP Solution File: NUM581+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM581+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:41:14 EDT 2023
% Result : Theorem 12.29s 3.62s
% Output : Refutation 12.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 123
% Syntax : Number of formulae : 268 ( 53 unt; 35 typ; 0 def)
% Number of atoms : 1184 ( 222 equ; 0 cnn)
% Maximal formula atoms : 44 ( 5 avg)
% Number of connectives : 3817 ( 113 ~; 68 |; 451 &;2767 @)
% ( 29 <=>; 389 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 14 con; 0-2 aty)
% Number of variables : 413 ( 0 ^; 383 !; 30 ?; 413 :)
% Comments :
%------------------------------------------------------------------------------
thf(slcrc0_type,type,
slcrc0: $i ).
thf(aSet0_type,type,
aSet0: $i > $o ).
thf(aElementOf0_type,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_type,type,
aSubsetOf0: $i > $i > $o ).
thf(aElement0_type,type,
aElement0: $i > $o ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(sdtmndt0_type,type,
sdtmndt0: $i > $i > $i ).
thf(szNzAzT0_type,type,
szNzAzT0: $i ).
thf(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
thf(sdtlseqdt0_type,type,
sdtlseqdt0: $i > $i > $o ).
thf(isFinite0_type,type,
isFinite0: $i > $o ).
thf(szmzazxdt0_type,type,
szmzazxdt0: $i > $i ).
thf(slbdtrb0_type,type,
slbdtrb0: $i > $i ).
thf(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
thf(slbdtsldtrb0_type,type,
slbdtsldtrb0: $i > $i > $i ).
thf(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
thf(aFunction0_type,type,
aFunction0: $i > $o ).
thf(sdtlbdtrb0_type,type,
sdtlbdtrb0: $i > $i > $i ).
thf(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
thf(sdtlpdtrp0_type,type,
sdtlpdtrp0: $i > $i > $i ).
thf(sdtlcdtrc0_type,type,
sdtlcdtrc0: $i > $i > $i ).
thf(sdtexdt0_type,type,
sdtexdt0: $i > $i > $i ).
thf(xN_type,type,
xN: $i ).
thf(xi_type,type,
xi: $i ).
thf(xQ_type,type,
xQ: $i ).
thf(xS_type,type,
xS: $i ).
thf(sz00_type,type,
sz00: $i ).
thf(xK_type,type,
xK: $i ).
thf(isCountable0_type,type,
isCountable0: $i > $o ).
thf(xk_type,type,
xk: $i ).
thf(xc_type,type,
xc: $i ).
thf(xT_type,type,
xT: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(42,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElement0 @ ( sdtlpdtrp0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgElm) ).
thf(385,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElement0 @ ( sdtlpdtrp0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(39,axiom,
( ( aSet0 @ xT )
& ( isFinite0 @ xT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
thf(363,plain,
( ( aSet0 @ xT )
& ( isFinite0 @ xT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(365,plain,
aSet0 @ xT,
inference(cnf,[status(esa)],[363]) ).
thf(1,conjecture,
( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ ( sdtlpdtrp0 @ xN @ xi ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ A ) ) )
=> ( ( ( aSet0 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
<=> ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ xQ )
| ( A
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) ) ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
=> ( aElementOf0 @ A @ xS ) )
| ( aSubsetOf0 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) @ xS ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ ( sdtlpdtrp0 @ xN @ xi ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ A ) ) )
=> ( ( ( aSet0 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
<=> ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ xQ )
| ( A
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) ) ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
=> ( aElementOf0 @ A @ xS ) )
| ( aSubsetOf0 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) @ xS ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(90,plain,
~ ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ ( sdtlpdtrp0 @ xN @ xi ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ A ) ) )
=> ( ( ( aSet0 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
=> ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ xQ )
| ( A
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) ) )
& ( ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ xQ )
| ( A
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) )
=> ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) ) ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
=> ( aElementOf0 @ A @ xS ) )
| ( aSubsetOf0 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) @ xS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(91,plain,
~ ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ ( sdtlpdtrp0 @ xN @ xi ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ A ) ) )
=> ( ( ( aSet0 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
=> ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ xQ )
| ( A
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) ) )
& ! [A: $i] :
( ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ xQ )
| ( A
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) )
=> ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
=> ( aElementOf0 @ A @ xS ) )
| ( aSubsetOf0 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) @ xS ) ) ) ),
inference(miniscope,[status(thm)],[90]) ).
thf(101,plain,
~ ( aElementOf0 @ sk1 @ xS ),
inference(cnf,[status(esa)],[91]) ).
thf(65,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardS) ).
thf(518,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(54,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).
thf(481,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(72,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isCountable0 @ A )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCntRel) ).
thf(582,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(34,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).
thf(308,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( aElementOf0 @ A @ ( slbdtrb0 @ ( szszuzczcdt0 @ B ) ) )
<=> ( ( aElementOf0 @ A @ ( slbdtrb0 @ B ) )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegSucc) ).
thf(511,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( aElementOf0 @ A @ ( slbdtrb0 @ ( szszuzczcdt0 @ B ) ) )
=> ( ( aElementOf0 @ A @ ( slbdtrb0 @ B ) )
| ( A = B ) ) )
& ( ( ( aElementOf0 @ A @ ( slbdtrb0 @ B ) )
| ( A = B ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ ( szszuzczcdt0 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(25,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelFSet) ).
thf(288,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(69,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( A
!= ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatNSucc) ).
thf(565,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( A
!= ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(49,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
thf(428,plain,
! [A: $i] :
( ( ( A = slcrc0 )
=> ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) )
& ( ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) )
=> ( A = slcrc0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(429,plain,
( ! [A: $i] :
( ( A = slcrc0 )
=> ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) )
& ! [A: $i] :
( ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) )
=> ( A = slcrc0 ) ) ),
inference(miniscope,[status(thm)],[428]) ).
thf(431,plain,
! [A: $i] :
( ( A != slcrc0 )
| ( aSet0 @ A ) ),
inference(cnf,[status(esa)],[429]) ).
thf(435,plain,
! [A: $i] :
( ( A != slcrc0 )
| ( aSet0 @ A ) ),
inference(lifteq,[status(thm)],[431]) ).
thf(436,plain,
aSet0 @ slcrc0,
inference(simp,[status(thm)],[435]) ).
thf(61,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSeg) ).
thf(504,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(4,axiom,
xK != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3520) ).
thf(110,plain,
xK != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
<=> ( aSubsetOf0 @ ( slbdtrb0 @ A ) @ ( slbdtrb0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegLess) ).
thf(587,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
=> ( aSubsetOf0 @ ( slbdtrb0 @ A ) @ ( slbdtrb0 @ B ) ) )
& ( ( aSubsetOf0 @ ( slbdtrb0 @ A ) @ ( slbdtrb0 @ B ) )
=> ( sdtlseqdt0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(9,axiom,
( ( aSet0 @ xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ xS )
=> ( aElementOf0 @ A @ szNzAzT0 ) )
& ( aSubsetOf0 @ xS @ szNzAzT0 )
& ( isCountable0 @ xS ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
thf(121,plain,
( ( aSet0 @ xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ xS )
=> ( aElementOf0 @ A @ szNzAzT0 ) )
& ( aSubsetOf0 @ xS @ szNzAzT0 )
& ( isCountable0 @ xS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(125,plain,
aSet0 @ xS,
inference(cnf,[status(esa)],[121]) ).
thf(12,axiom,
( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ ( sdtlpdtrp0 @ xN @ xi ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ A ) )
& ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
<=> ( ( aElement0 @ A )
& ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
& ( A
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) )
& ( aSet0 @ xQ )
& ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) )
& ( aSubsetOf0 @ xQ @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
& ( ( sbrdtbr0 @ xQ )
= xk )
& ( aElementOf0 @ xQ @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) @ xk ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989_02) ).
thf(157,plain,
( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ ( sdtlpdtrp0 @ xN @ xi ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ A ) )
& ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
=> ( ( aElement0 @ A )
& ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
& ( A
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) )
& ( ( ( aElement0 @ A )
& ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
& ( A
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
=> ( aElementOf0 @ A @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) ) )
& ( aSet0 @ xQ )
& ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) )
& ( aSubsetOf0 @ xQ @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
& ( ( sbrdtbr0 @ xQ )
= xk )
& ( aElementOf0 @ xQ @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) @ xk ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ B @ A )
=> ( ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ B ) ) )
& ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( sdtlpdtrp0 @ xN @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3754) ).
thf(189,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ B @ A )
=> ( ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ B ) ) )
& ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( sdtlpdtrp0 @ xN @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(93,plain,
! [A: $i] :
( ~ ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
| ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ A ) ),
inference(cnf,[status(esa)],[91]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIHSort) ).
thf(228,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( szszuzczcdt0 @ A )
= ( szszuzczcdt0 @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEquSucc) ).
thf(492,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( szszuzczcdt0 @ A )
= ( szszuzczcdt0 @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(13,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
thf(179,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(86,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( aElementOf0 @ ( sbrdtbr0 @ A ) @ szNzAzT0 )
<=> ( isFinite0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
thf(692,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( aElementOf0 @ ( sbrdtbr0 @ A ) @ szNzAzT0 )
=> ( isFinite0 @ A ) )
& ( ( isFinite0 @ A )
=> ( aElementOf0 @ ( sbrdtbr0 @ A ) @ szNzAzT0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtlbdtrb0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPtt) ).
thf(396,plain,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtlbdtrb0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) ) )
& ( ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) ) )
& ( ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtlbdtrb0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(62,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(507,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(33,axiom,
aElementOf0 @ sz00 @ szNzAzT0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
thf(307,plain,
aElementOf0 @ sz00 @ szNzAzT0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(53,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ! [C: $i] :
( ( C
= ( sdtlcdtrc0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSImg) ).
thf(452,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ! [C: $i] :
( ( ( C
= ( sdtlcdtrc0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) ) )
& ( ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) ) )
& ( ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtlcdtrc0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(7,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFunSort) ).
thf(117,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(50,axiom,
! [A: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( isFinite0 @ A ) )
=> ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( aSubsetOf0 @ A @ ( slbdtrb0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFinSubSeg) ).
thf(439,plain,
! [A: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( isFinite0 @ A ) )
=> ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( aSubsetOf0 @ A @ ( slbdtrb0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(40,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ! [C: $i] :
( ( C
= ( sdtexdt0 @ A @ B ) )
<=> ( ( aFunction0 @ C )
& ( ( szDzozmdt0 @ C )
= B )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( ( sdtlpdtrp0 @ C @ D )
= ( sdtlpdtrp0 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefRst) ).
thf(366,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ! [C: $i] :
( ( ( C
= ( sdtexdt0 @ A @ B ) )
=> ( ( aFunction0 @ C )
& ( ( szDzozmdt0 @ C )
= B )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( ( sdtlpdtrp0 @ C @ D )
= ( sdtlpdtrp0 @ A @ D ) ) ) ) )
& ( ( ( aFunction0 @ C )
& ( ( szDzozmdt0 @ C )
= B )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( ( sdtlpdtrp0 @ C @ D )
= ( sdtlpdtrp0 @ A @ D ) ) ) )
=> ( C
= ( sdtexdt0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(98,plain,
! [A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aElementOf0 @ A @ xQ )
| ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) ),
inference(cnf,[status(esa)],[91]) ).
thf(102,plain,
! [A: $i] :
( ~ ( aElement0 @ A )
| ~ ( aElementOf0 @ A @ xQ )
| ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(31,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( ( isFinite0 @ A )
& ( aElementOf0 @ B @ A ) )
=> ( ( szszuzczcdt0 @ ( sbrdtbr0 @ ( sdtmndt0 @ A @ B ) ) )
= ( sbrdtbr0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
thf(302,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( ( isFinite0 @ A )
& ( aElementOf0 @ B @ A ) )
=> ( ( szszuzczcdt0 @ ( sbrdtbr0 @ ( sdtmndt0 @ A @ B ) ) )
= ( sbrdtbr0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( aSubsetOf0 @ B @ szNzAzT0 )
& ( A != slcrc0 )
& ( B != slcrc0 ) )
=> ( ( ( aElementOf0 @ ( szmzizndt0 @ A ) @ B )
& ( aElementOf0 @ ( szmzizndt0 @ B ) @ A ) )
=> ( ( szmzizndt0 @ A )
= ( szmzizndt0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMinMin) ).
thf(392,plain,
! [A: $i,B: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( aSubsetOf0 @ B @ szNzAzT0 )
& ( A != slcrc0 )
& ( B != slcrc0 ) )
=> ( ( ( aElementOf0 @ ( szmzizndt0 @ A ) @ B )
& ( aElementOf0 @ ( szmzizndt0 @ B ) @ A ) )
=> ( ( szmzizndt0 @ A )
= ( szmzizndt0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(29,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ A @ B ) @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgRng) ).
thf(297,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ A @ B ) @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(17,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ! [B: $i] :
( ( ( aElementOf0 @ B @ szNzAzT0 )
& ( B != sz00 ) )
=> ( isCountable0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelCSet) ).
thf(192,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ! [B: $i] :
( ( ( aElementOf0 @ B @ szNzAzT0 )
& ( B != sz00 ) )
=> ( isCountable0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(77,axiom,
( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ ( sdtlpdtrp0 @ xN @ xi ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ A ) )
& ( aSet0 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
<=> ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ xQ )
| ( A
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) ) )
& ( ( sbrdtbr0 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
= xK ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4007) ).
thf(630,plain,
( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ ( sdtlpdtrp0 @ xN @ xi ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ A ) )
& ( aSet0 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
=> ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ xQ )
| ( A
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) ) )
& ( ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ xQ )
| ( A
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) )
=> ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) ) )
& ( ( sbrdtbr0 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
= xK ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(73,axiom,
( ( aElementOf0 @ xk @ szNzAzT0 )
& ( ( szszuzczcdt0 @ xk )
= xK ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
thf(583,plain,
( ( aElementOf0 @ xk @ szNzAzT0 )
& ( ( szszuzczcdt0 @ xk )
= xK ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(81,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElement0 @ B )
=> ( ~ ( aElementOf0 @ B @ A )
=> ( ( sbrdtbr0 @ ( sdtpldt0 @ A @ B ) )
= ( szszuzczcdt0 @ ( sbrdtbr0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardCons) ).
thf(682,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElement0 @ B )
=> ( ~ ( aElementOf0 @ B @ A )
=> ( ( sbrdtbr0 @ ( sdtpldt0 @ A @ B ) )
= ( szszuzczcdt0 @ ( sbrdtbr0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(68,axiom,
! [A: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( isFinite0 @ A )
& ( A != slcrc0 ) )
=> ! [B: $i] :
( ( B
= ( szmzazxdt0 @ A ) )
<=> ( ( aElementOf0 @ B @ A )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMax) ).
thf(551,plain,
! [A: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( isFinite0 @ A )
& ( A != slcrc0 ) )
=> ! [B: $i] :
( ( ( B
= ( szmzazxdt0 @ A ) )
=> ( ( aElementOf0 @ B @ A )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ C @ B ) ) ) )
& ( ( ( aElementOf0 @ B @ A )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ C @ B ) ) )
=> ( B
= ( szmzazxdt0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(24,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ( ( ( isCountable0 @ ( szDzozmdt0 @ A ) )
& ( isFinite0 @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) )
=> ( ( aElement0 @ ( szDzizrdt0 @ A ) )
& ( isCountable0 @ ( sdtlbdtrb0 @ A @ ( szDzizrdt0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDirichlet) ).
thf(285,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ( ( ( isCountable0 @ ( szDzozmdt0 @ A ) )
& ( isFinite0 @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) )
=> ( ( aElement0 @ ( szDzizrdt0 @ A ) )
& ( isCountable0 @ ( sdtlbdtrb0 @ A @ ( szDzizrdt0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(21,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ szNzAzT0 ) ) )
| ( aSubsetOf0 @ B @ szNzAzT0 ) )
& ( isCountable0 @ B ) )
=> ! [C: $i] :
( ( ( aFunction0 @ C )
& ( ! [D: $i] :
( ( ( aElementOf0 @ D @ ( szDzozmdt0 @ C ) )
=> ( ( ( ( aSet0 @ D )
& ! [E: $i] :
( ( aElementOf0 @ E @ D )
=> ( aElementOf0 @ E @ B ) ) )
| ( aSubsetOf0 @ D @ B ) )
& ( ( sbrdtbr0 @ D )
= A ) ) )
& ( ( ( aSet0 @ D )
& ! [E: $i] :
( ( aElementOf0 @ E @ D )
=> ( aElementOf0 @ E @ B ) )
& ( aSubsetOf0 @ D @ B )
& ( ( sbrdtbr0 @ D )
= A ) )
=> ( aElementOf0 @ D @ ( szDzozmdt0 @ C ) ) ) )
| ( ( szDzozmdt0 @ C )
= ( slbdtsldtrb0 @ B @ A ) ) )
& ( ( ( aSet0 @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) )
& ! [D: $i] :
( ( aElementOf0 @ D @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) )
<=> ? [E: $i] :
( ( aElementOf0 @ E @ ( szDzozmdt0 @ C ) )
& ( ( sdtlpdtrp0 @ C @ E )
= D ) ) ) )
=> ( ! [D: $i] :
( ( aElementOf0 @ D @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) )
=> ( aElementOf0 @ D @ xT ) )
| ( aSubsetOf0 @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) @ xT ) ) ) )
=> ( ( iLess0 @ A @ xK )
=> ? [D: $i] :
( ( aElementOf0 @ D @ xT )
& ? [E: $i] :
( ( aSet0 @ E )
& ! [F: $i] :
( ( aElementOf0 @ F @ E )
=> ( aElementOf0 @ F @ B ) )
& ( aSubsetOf0 @ E @ B )
& ( isCountable0 @ E )
& ! [F: $i] :
( ( ( ( ( ( aSet0 @ F )
& ! [G: $i] :
( ( aElementOf0 @ G @ F )
=> ( aElementOf0 @ G @ E ) ) )
| ( aSubsetOf0 @ F @ E ) )
& ( ( sbrdtbr0 @ F )
= A ) )
| ( aElementOf0 @ F @ ( slbdtsldtrb0 @ E @ A ) ) )
=> ( ( sdtlpdtrp0 @ C @ F )
= D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3398) ).
thf(229,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ szNzAzT0 ) ) )
| ( aSubsetOf0 @ B @ szNzAzT0 ) )
& ( isCountable0 @ B ) )
=> ! [C: $i] :
( ( ( aFunction0 @ C )
& ( ! [D: $i] :
( ( ( aElementOf0 @ D @ ( szDzozmdt0 @ C ) )
=> ( ( ( ( aSet0 @ D )
& ! [E: $i] :
( ( aElementOf0 @ E @ D )
=> ( aElementOf0 @ E @ B ) ) )
| ( aSubsetOf0 @ D @ B ) )
& ( ( sbrdtbr0 @ D )
= A ) ) )
& ( ( ( aSet0 @ D )
& ! [E: $i] :
( ( aElementOf0 @ E @ D )
=> ( aElementOf0 @ E @ B ) )
& ( aSubsetOf0 @ D @ B )
& ( ( sbrdtbr0 @ D )
= A ) )
=> ( aElementOf0 @ D @ ( szDzozmdt0 @ C ) ) ) )
| ( ( szDzozmdt0 @ C )
= ( slbdtsldtrb0 @ B @ A ) ) )
& ( ( ( aSet0 @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) )
=> ? [E: $i] :
( ( aElementOf0 @ E @ ( szDzozmdt0 @ C ) )
& ( ( sdtlpdtrp0 @ C @ E )
= D ) ) )
& ( ? [E: $i] :
( ( aElementOf0 @ E @ ( szDzozmdt0 @ C ) )
& ( ( sdtlpdtrp0 @ C @ E )
= D ) )
=> ( aElementOf0 @ D @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) ) ) ) )
=> ( ! [D: $i] :
( ( aElementOf0 @ D @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) )
=> ( aElementOf0 @ D @ xT ) )
| ( aSubsetOf0 @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) @ xT ) ) ) )
=> ( ( iLess0 @ A @ xK )
=> ? [D: $i] :
( ( aElementOf0 @ D @ xT )
& ? [E: $i] :
( ( aSet0 @ E )
& ! [F: $i] :
( ( aElementOf0 @ F @ E )
=> ( aElementOf0 @ F @ B ) )
& ( aSubsetOf0 @ E @ B )
& ( isCountable0 @ E )
& ! [F: $i] :
( ( ( ( ( ( aSet0 @ F )
& ! [G: $i] :
( ( aElementOf0 @ G @ F )
=> ( aElementOf0 @ G @ E ) ) )
| ( aSubsetOf0 @ F @ E ) )
& ( ( sbrdtbr0 @ F )
= A ) )
| ( aElementOf0 @ F @ ( slbdtsldtrb0 @ E @ A ) ) )
=> ( ( sdtlpdtrp0 @ C @ F )
= D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(56,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
thf(484,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ! [C: $i] :
( ( ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ A @ B ) )
& ( isFinite0 @ C ) )
=> ? [D: $i] :
( ( aSubsetOf0 @ D @ A )
& ( isFinite0 @ D )
& ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelExtra) ).
thf(697,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ! [C: $i] :
( ( ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ A @ B ) )
& ( isFinite0 @ C ) )
=> ? [D: $i] :
( ( aSubsetOf0 @ D @ A )
& ( isFinite0 @ D )
& ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(158,plain,
( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ ( sdtlpdtrp0 @ xN @ xi ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ A ) )
& ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
=> ( ( aElement0 @ A )
& ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
& ( A
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) )
& ! [A: $i] :
( ( ( aElement0 @ A )
& ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xi ) )
& ( A
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
=> ( aElementOf0 @ A @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) )
& ( aSet0 @ xQ )
& ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) )
& ( aSubsetOf0 @ xQ @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
& ( ( sbrdtbr0 @ xQ )
= xk )
& ( aElementOf0 @ xQ @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xi ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) @ xk ) ) ),
inference(miniscope,[status(thm)],[157]) ).
thf(169,plain,
aSet0 @ xQ,
inference(cnf,[status(esa)],[158]) ).
thf(57,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ A ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
thf(488,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ A ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(83,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNoScLessZr) ).
thf(686,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(75,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( A = sz00 )
| ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
thf(590,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( A = sz00 )
| ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(96,plain,
aSet0 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ),
inference(cnf,[status(esa)],[91]) ).
thf(3,axiom,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).
thf(108,plain,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(109,plain,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
inference(lifteq,[status(thm)],[108]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtmndt0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
thf(328,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtmndt0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) ) )
& ( ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) ) )
& ( ( ( aElement0 @ D )
& ( aElementOf0 @ D @ A )
& ( D != B ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtmndt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(78,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aSet0 @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( aElementOf0 @ B @ szNzAzT0 ) )
& ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).
thf(647,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aSet0 @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( aElementOf0 @ B @ szNzAzT0 ) )
& ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRel) ).
thf(701,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(11,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( B
= ( slbdtrb0 @ A ) )
<=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
<=> ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).
thf(128,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( B
= ( slbdtrb0 @ A ) )
=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ B )
=> ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) )
& ( ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) )
=> ( aElementOf0 @ C @ B ) ) ) ) )
& ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ B )
=> ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) )
& ( ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) )
=> ( aElementOf0 @ C @ B ) ) ) )
=> ( B
= ( slbdtrb0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
( ( aFunction0 @ xc )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xc ) )
=> ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xS ) )
& ( aSubsetOf0 @ A @ xS )
& ( ( sbrdtbr0 @ A )
= xK ) ) )
& ( ( ( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xS ) ) )
| ( aSubsetOf0 @ A @ xS ) )
& ( ( sbrdtbr0 @ A )
= xK ) )
=> ( aElementOf0 @ A @ ( szDzozmdt0 @ xc ) ) ) )
& ( ( szDzozmdt0 @ xc )
= ( slbdtsldtrb0 @ xS @ xK ) )
& ( aSet0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
<=> ? [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ xc ) )
& ( ( sdtlpdtrp0 @ xc @ B )
= A ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
=> ( aElementOf0 @ A @ xT ) )
& ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) @ xT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
thf(195,plain,
( ( aFunction0 @ xc )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xc ) )
=> ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xS ) )
& ( aSubsetOf0 @ A @ xS )
& ( ( sbrdtbr0 @ A )
= xK ) ) )
& ( ( ( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xS ) ) )
| ( aSubsetOf0 @ A @ xS ) )
& ( ( sbrdtbr0 @ A )
= xK ) )
=> ( aElementOf0 @ A @ ( szDzozmdt0 @ xc ) ) ) )
& ( ( szDzozmdt0 @ xc )
= ( slbdtsldtrb0 @ xS @ xK ) )
& ( aSet0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
=> ? [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ xc ) )
& ( ( sdtlpdtrp0 @ xc @ B )
= A ) ) )
& ( ? [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ xc ) )
& ( ( sdtlpdtrp0 @ xc @ B )
= A ) )
=> ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
=> ( aElementOf0 @ A @ xT ) )
& ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) @ xT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(196,plain,
( ( aFunction0 @ xc )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( szDzozmdt0 @ xc ) )
=> ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xS ) )
& ( aSubsetOf0 @ A @ xS )
& ( ( sbrdtbr0 @ A )
= xK ) ) )
& ! [A: $i] :
( ( ( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xS ) ) )
| ( aSubsetOf0 @ A @ xS ) )
& ( ( sbrdtbr0 @ A )
= xK ) )
=> ( aElementOf0 @ A @ ( szDzozmdt0 @ xc ) ) )
& ( ( szDzozmdt0 @ xc )
= ( slbdtsldtrb0 @ xS @ xK ) )
& ( aSet0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
=> ? [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ xc ) )
& ( ( sdtlpdtrp0 @ xc @ B )
= A ) ) )
& ! [A: $i] :
( ? [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ xc ) )
& ( ( sdtlpdtrp0 @ xc @ B )
= A ) )
=> ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
=> ( aElementOf0 @ A @ xT ) )
& ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) @ xT ) ),
inference(miniscope,[status(thm)],[195]) ).
thf(205,plain,
aFunction0 @ xc,
inference(cnf,[status(esa)],[196]) ).
thf(48,axiom,
( ( aSet0 @ szNzAzT0 )
& ( isCountable0 @ szNzAzT0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
thf(425,plain,
( ( aSet0 @ szNzAzT0 )
& ( isCountable0 @ szNzAzT0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
thf(279,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(46,axiom,
aElementOf0 @ xK @ szNzAzT0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
thf(395,plain,
aElementOf0 @ xK @ szNzAzT0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(769,plain,
( ( aElementOf0 @ sk1 @ xS )
!= ( aElementOf0 @ xK @ szNzAzT0 ) ),
inference(paramod_ordered,[status(thm)],[395,101]) ).
thf(772,plain,
( ( sk1 != xK )
| ( xS != szNzAzT0 ) ),
inference(simp,[status(thm)],[769]) ).
thf(8,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i,C: $i] :
( ( ( aSet0 @ B )
& ( aSet0 @ C )
& ( A != sz00 ) )
=> ( ( ( aSubsetOf0 @ ( slbdtsldtrb0 @ B @ A ) @ ( slbdtsldtrb0 @ C @ A ) )
& ( ( slbdtsldtrb0 @ B @ A )
!= slcrc0 ) )
=> ( aSubsetOf0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelSub) ).
thf(118,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i,C: $i] :
( ( ( aSet0 @ B )
& ( aSet0 @ C )
& ( A != sz00 ) )
=> ( ( ( aSubsetOf0 @ ( slbdtsldtrb0 @ B @ A ) @ ( slbdtsldtrb0 @ C @ A ) )
& ( ( slbdtsldtrb0 @ B @ A )
!= slcrc0 ) )
=> ( aSubsetOf0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(36,axiom,
! [A: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( A != slcrc0 ) )
=> ! [B: $i] :
( ( B
= ( szmzizndt0 @ A ) )
<=> ( ( aElementOf0 @ B @ A )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMin) ).
thf(313,plain,
! [A: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( A != slcrc0 ) )
=> ! [B: $i] :
( ( ( B
= ( szmzizndt0 @ A ) )
=> ( ( aElementOf0 @ B @ A )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ B @ C ) ) ) )
& ( ( ( aElementOf0 @ B @ A )
& ! [C: $i] :
( ( aElementOf0 @ C @ A )
=> ( sdtlseqdt0 @ B @ C ) ) )
=> ( B
= ( szmzizndt0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(14,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( sbrdtbr0 @ A )
= sz00 )
<=> ( A = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
thf(181,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( ( sbrdtbr0 @ A )
= sz00 )
=> ( A = slcrc0 ) )
& ( ( A = slcrc0 )
=> ( ( sbrdtbr0 @ A )
= sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(761,plain,
( ( aElementOf0 @ sk1 @ xS )
!= ( aElementOf0 @ sz00 @ szNzAzT0 ) ),
inference(paramod_ordered,[status(thm)],[307,101]) ).
thf(764,plain,
( ( sk1 != sz00 )
| ( xS != szNzAzT0 ) ),
inference(simp,[status(thm)],[761]) ).
thf(15,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
thf(187,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
isFinite0 @ slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
thf(113,plain,
isFinite0 @ slcrc0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(485,plain,
! [A: $i] :
( ~ ( aSet0 @ A )
| ~ ( isCountable0 @ A )
| ( A != slcrc0 ) ),
inference(cnf,[status(esa)],[484]) ).
thf(486,plain,
! [A: $i] :
( ( A != slcrc0 )
| ~ ( aSet0 @ A )
| ~ ( isCountable0 @ A ) ),
inference(lifteq,[status(thm)],[485]) ).
thf(487,plain,
( ~ ( aSet0 @ slcrc0 )
| ~ ( isCountable0 @ slcrc0 ) ),
inference(simp,[status(thm)],[486]) ).
thf(735,plain,
( ~ $true
| ~ ( isCountable0 @ slcrc0 ) ),
inference(rewrite,[status(thm)],[487,436]) ).
thf(736,plain,
~ ( isCountable0 @ slcrc0 ),
inference(simp,[status(thm)],[735]) ).
thf(63,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
thf(509,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
<=> ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ ( szszuzczcdt0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccLess) ).
thf(387,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
=> ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ ( szszuzczcdt0 @ B ) ) )
& ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ ( szszuzczcdt0 @ B ) )
=> ( sdtlseqdt0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(99,plain,
! [A: $i] :
( ~ ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
| ( aElement0 @ A ) ),
inference(cnf,[status(esa)],[91]) ).
thf(103,plain,
! [A: $i] :
( ~ ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
| ( aElement0 @ A ) ),
inference(simp,[status(thm)],[99]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ! [C: $i] :
( ( C
= ( slbdtsldtrb0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aSubsetOf0 @ D @ A )
& ( ( sbrdtbr0 @ D )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
thf(520,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ! [C: $i] :
( ( ( C
= ( slbdtsldtrb0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aSubsetOf0 @ D @ A )
& ( ( sbrdtbr0 @ D )
= B ) ) )
& ( ( ( aSubsetOf0 @ D @ A )
& ( ( sbrdtbr0 @ D )
= B ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aSubsetOf0 @ D @ A )
& ( ( sbrdtbr0 @ D )
= B ) ) )
& ( ( ( aSubsetOf0 @ D @ A )
& ( ( sbrdtbr0 @ D )
= B ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( slbdtsldtrb0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(82,axiom,
aElementOf0 @ xi @ szNzAzT0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989) ).
thf(685,plain,
aElementOf0 @ xi @ szNzAzT0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(87,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCDiffSet) ).
thf(695,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aSet0 @ B ) )
=> ( ~ ( aElementOf0 @ A @ B )
=> ( ( sdtmndt0 @ ( sdtpldt0 @ B @ A ) @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDiffCons) ).
thf(299,plain,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aSet0 @ B ) )
=> ( ~ ( aElementOf0 @ A @ B )
=> ( ( sdtmndt0 @ ( sdtpldt0 @ B @ A ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aElement0 @ B ) )
=> ( aSubsetOf0 @ ( sdtlbdtrb0 @ A @ B ) @ ( szDzozmdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPttSet) ).
thf(226,plain,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aElement0 @ B ) )
=> ( aSubsetOf0 @ ( sdtlbdtrb0 @ A @ B ) @ ( szDzozmdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(79,axiom,
( ( aFunction0 @ xN )
& ( ( szDzozmdt0 @ xN )
= szNzAzT0 )
& ( ( sdtlpdtrp0 @ xN @ sz00 )
= xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( ( ( ( aSet0 @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( aElementOf0 @ B @ szNzAzT0 ) ) )
| ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 ) )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
=> ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ B ) )
& ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
<=> ( ( aElement0 @ B )
& ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
& ( B
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSet0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) )
=> ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
thf(652,plain,
( ( aFunction0 @ xN )
& ( ( szDzozmdt0 @ xN )
= szNzAzT0 )
& ( ( sdtlpdtrp0 @ xN @ sz00 )
= xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( ( ( ( aSet0 @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( aElementOf0 @ B @ szNzAzT0 ) ) )
| ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 ) )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
=> ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ B ) )
& ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [B: $i] :
( ( ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( ( aElement0 @ B )
& ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
& ( B
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( ( ( aElement0 @ B )
& ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
& ( B
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
& ( aSet0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) )
=> ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(653,plain,
( ( aFunction0 @ xN )
& ( ( szDzozmdt0 @ xN )
= szNzAzT0 )
& ( ( sdtlpdtrp0 @ xN @ sz00 )
= xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( ( ( ( aSet0 @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( aElementOf0 @ B @ szNzAzT0 ) ) )
| ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 ) )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
=> ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ B ) )
& ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( ( aElement0 @ B )
& ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
& ( B
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ! [B: $i] :
( ( ( aElement0 @ B )
& ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
& ( B
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSet0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) )
=> ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[652]) ).
thf(658,plain,
aFunction0 @ xN,
inference(cnf,[status(esa)],[653]) ).
thf(426,plain,
isCountable0 @ szNzAzT0,
inference(cnf,[status(esa)],[425]) ).
thf(80,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
thf(680,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(111,plain,
xK != sz00,
inference(polarity_switch,[status(thm)],[110]) ).
thf(112,plain,
xK != sz00,
inference(lifteq,[status(thm)],[111]) ).
thf(123,plain,
aSubsetOf0 @ xS @ szNzAzT0,
inference(cnf,[status(esa)],[121]) ).
thf(85,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
thf(690,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(28,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRefl) ).
thf(295,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ( ( ( aSubsetOf0 @ A @ B )
& ( aSubsetOf0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubASymm) ).
thf(282,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ( ( ( aSubsetOf0 @ A @ B )
& ( aSubsetOf0 @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(95,plain,
aElementOf0 @ sk1 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ),
inference(cnf,[status(esa)],[91]) ).
thf(37,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(327,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(737,plain,
( ( isCountable0 @ szNzAzT0 )
!= ( isCountable0 @ slcrc0 ) ),
inference(paramod_ordered,[status(thm)],[426,736]) ).
thf(739,plain,
szNzAzT0 != slcrc0,
inference(simp,[status(thm)],[737]) ).
thf(35,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).
thf(310,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(790,plain,
! [A: $i] :
( ( aElement0 @ A )
| ( ( aElementOf0 @ sk1 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
!= ( aElementOf0 @ A @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[95,103]) ).
thf(791,plain,
aElement0 @ sk1,
inference(pattern_uni,[status(thm)],[790:[bind(A,$thf( sk1 ))]]) ).
thf(585,plain,
aElementOf0 @ xk @ szNzAzT0,
inference(cnf,[status(esa)],[583]) ).
thf(162,plain,
( ( sbrdtbr0 @ xQ )
= xk ),
inference(cnf,[status(esa)],[158]) ).
thf(175,plain,
( ( sbrdtbr0 @ xQ )
= xk ),
inference(lifteq,[status(thm)],[162]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 )
& ( A != B ) )
=> ~ ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) ) )
=> ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ B ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ B ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) ) )
| ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3821) ).
thf(571,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 )
& ( A != B ) )
=> ~ ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) ) )
=> ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ B ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ B ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) ) )
| ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtpldt0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
thf(595,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtpldt0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) ) )
& ( ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) ) )
& ( ( ( aElement0 @ D )
& ( ( aElementOf0 @ D @ A )
| ( D = B ) ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtpldt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(60,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
& ( isCountable0 @ B ) )
=> ( ! [C: $i,D: $i] :
( ( ( aElementOf0 @ C @ ( szDzozmdt0 @ A ) )
& ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( C != D ) )
=> ( ( sdtlpdtrp0 @ A @ C )
!= ( sdtlpdtrp0 @ A @ D ) ) )
=> ( isCountable0 @ ( sdtlcdtrc0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgCount) ).
thf(497,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
& ( isCountable0 @ B ) )
=> ( ! [C: $i,D: $i] :
( ( ( aElementOf0 @ C @ ( szDzozmdt0 @ A ) )
& ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( C != D ) )
=> ( ( sdtlpdtrp0 @ A @ C )
!= ( sdtlpdtrp0 @ A @ D ) ) )
=> ( isCountable0 @ ( sdtlcdtrc0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(52,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegFin) ).
thf(450,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(55,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ( aSet0 @ ( szDzozmdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSet) ).
thf(482,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ( aSet0 @ ( szDzozmdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(84,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( ( isFinite0 @ A )
& ( aSubsetOf0 @ B @ A ) )
=> ( sdtlseqdt0 @ ( sbrdtbr0 @ B ) @ ( sbrdtbr0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSub) ).
thf(688,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( ( isFinite0 @ A )
& ( aSubsetOf0 @ B @ A ) )
=> ( sdtlseqdt0 @ ( sbrdtbr0 @ B ) @ ( sbrdtbr0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(59,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
thf(495,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B )
& ( aSet0 @ C ) )
=> ( ( ( aSubsetOf0 @ A @ B )
& ( aSubsetOf0 @ B @ C ) )
=> ( aSubsetOf0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).
thf(390,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B )
& ( aSet0 @ C ) )
=> ( ( ( aSubsetOf0 @ A @ B )
& ( aSubsetOf0 @ B @ C ) )
=> ( aSubsetOf0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(6,axiom,
xK != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
thf(114,plain,
xK != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(70,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ~ ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
=> ( ( slbdtsldtrb0 @ A @ B )
!= slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelNSet) ).
thf(568,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ~ ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
=> ( ( slbdtsldtrb0 @ A @ B )
!= slcrc0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( isFinite0 @ A )
& ( sdtlseqdt0 @ B @ ( sbrdtbr0 @ A ) ) )
=> ? [C: $i] :
( ( aSubsetOf0 @ C @ A )
& ( ( sbrdtbr0 @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSubEx) ).
thf(290,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( isFinite0 @ A )
& ( sdtlseqdt0 @ B @ ( sbrdtbr0 @ A ) ) )
=> ? [C: $i] :
( ( aSubsetOf0 @ C @ A )
& ( ( sbrdtbr0 @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(41,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCConsSet) ).
thf(383,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(67,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessSucc) ).
thf(549,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 )
& ( aElementOf0 @ C @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTrans) ).
thf(305,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 )
& ( aElementOf0 @ C @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(122,plain,
isCountable0 @ xS,
inference(cnf,[status(esa)],[121]) ).
thf(702,plain,
( ~ ( aSet0 @ slcrc0 )
| ( ( isCountable0 @ xS )
!= ( isCountable0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[122,487]) ).
thf(703,plain,
( ~ ( aSet0 @ slcrc0 )
| ( xS != slcrc0 ) ),
inference(simp,[status(thm)],[702]) ).
thf(712,plain,
( ( xS != slcrc0 )
| ( ( aSet0 @ xS )
!= ( aSet0 @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[125,703]) ).
thf(716,plain,
( ( xS != slcrc0 )
| ( xS != slcrc0 ) ),
inference(simp,[status(thm)],[712]) ).
thf(720,plain,
xS != slcrc0,
inference(simp,[status(thm)],[716]) ).
thf(94,plain,
~ ( aSubsetOf0 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) @ xS ),
inference(cnf,[status(esa)],[91]) ).
thf(27,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isFinite0 @ A )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFinRel) ).
thf(294,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).
thf(126,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(724,plain,
( ( aElementOf0 @ sk1 @ ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) ) )
!= ( aElementOf0 @ sk1 @ xS ) ),
inference(paramod_ordered,[status(thm)],[95,101]) ).
thf(726,plain,
( ( sk1 != sk1 )
| ( ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) )
!= xS ) ),
inference(simp,[status(thm)],[724]) ).
thf(728,plain,
( ( sdtpldt0 @ xQ @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) )
!= xS ),
inference(simp,[status(thm)],[726]) ).
thf(427,plain,
aSet0 @ szNzAzT0,
inference(cnf,[status(esa)],[425]) ).
thf(51,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
<=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
thf(442,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( ( aSubsetOf0 @ B @ A )
=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) ) )
& ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) )
=> ( aSubsetOf0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(364,plain,
isFinite0 @ xT,
inference(cnf,[status(esa)],[363]) ).
thf(100,plain,
aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xi ) ) @ ( sdtlpdtrp0 @ xN @ xi ),
inference(cnf,[status(esa)],[91]) ).
thf(1394,plain,
$false,
inference(cvc4,[status(thm)],[385,365,101,518,481,582,308,511,288,565,436,504,110,587,125,157,189,93,228,492,179,121,692,396,428,507,307,452,117,439,366,102,302,392,297,192,630,583,682,551,285,229,484,697,169,488,686,590,96,109,328,647,701,128,205,425,279,772,118,313,181,764,187,113,736,509,387,103,520,108,685,695,299,226,658,426,680,112,123,690,295,282,95,327,739,310,791,585,175,571,595,497,450,363,482,688,495,652,390,114,568,290,383,549,305,195,720,94,294,126,395,728,427,442,90,122,364,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM581+3 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.14/0.33 % Computer : n018.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu May 18 17:12:58 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.86/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.14/1.01 % [INFO] Parsing done (194ms).
% 1.14/1.02 % [INFO] Running in sequential loop mode.
% 1.83/1.24 % [INFO] eprover registered as external prover.
% 1.83/1.24 % [INFO] cvc4 registered as external prover.
% 1.83/1.24 % [INFO] Scanning for conjecture ...
% 1.83/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.83/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.83/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.83/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.05/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.05/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.05/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.05/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.05/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.05/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.05/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.05/1.37 % [INFO] Found a conjecture and 87 axioms. Running axiom selection ...
% 2.23/1.45 % [INFO] Axiom selection finished. Selected 87 axioms (removed 0 axioms).
% 2.23/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.60/1.49 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.60/1.49 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.60/1.49 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.60/1.50 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.60/1.50 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.60/1.50 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.60/1.50 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.60/1.51 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.60/1.51 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.60/1.51 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.69/1.52 % [INFO] Problem is first-order (TPTP FOF).
% 2.72/1.53 % [INFO] Type checking passed.
% 2.72/1.54 % [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 ...
% 12.29/3.61 % External prover 'cvc4' found a proof!
% 12.29/3.61 % [INFO] Killing All external provers ...
% 12.29/3.61 % Time passed: 3113ms (effective reasoning time: 2590ms)
% 12.29/3.61 % 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)>
% 12.29/3.61 % Axioms used in derivation (87): mIHSort, mDefSel, m__3821, mFunSort, mZeroNum, mSubASymm, mCardEmpty, m__3533, mImgRng, mSuccLess, mCountNFin, mSegLess, mCardSubEx, mDefEmp, m__3435, mFinSubSeg, mDefSImg, mDiffCons, mSubRefl, mDefMin, mSubFSet, mEOfElem, m__3398, mDefDiff, mSelCSet, m__3462, mSetSort, mCardS, mSegZero, mSuccEquSucc, mSelNSet, mDomSet, mSegSucc, mLessSucc, mIH, mFDiffSet, m__3754, mCDiffSet, m__4007, mFinRel, mSegFin, mDefCons, mNoScLessZr, mConsDiff, m__3520, mLessRefl, mLessRel, mDefSeg, mCardSub, mCountNFin_01, mCardNum, m__3291, mImgElm, mDefPtt, mImgCount, mLessASymm, mDirichlet, mMinMin, mSelFSet, mNatNSucc, m__3989_02, m__3989, mDefMax, m__3453, m__3671, mEmpFin, mLessTotal, mNATSet, mFConsSet, mElmSort, mCardDiff, mZeroLess, mPttSet, mSelSub, mDefSub, mLessTrans, mNatExtra, mSuccNum, mSubTrans, mCntRel, mSelExtra, m__3418, m__3623, mCardCons, mDefRst, mCConsSet, mCardSeg
% 12.29/3.61 % No. of inferences in proof: 233
% 12.29/3.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3113 ms resp. 2590 ms w/o parsing
% 12.70/3.74 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.70/3.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------