TSTP Solution File: NUM557+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM557+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 11:41:07 EDT 2023
% Result : Theorem 5.64s 2.28s
% Output : Refutation 5.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 99
% Syntax : Number of formulae : 174 ( 21 unt; 26 typ; 0 def)
% Number of atoms : 712 ( 127 equ; 0 cnn)
% Maximal formula atoms : 43 ( 4 avg)
% Number of connectives : 1849 ( 56 ~; 29 |; 271 &;1229 @)
% ( 20 <=>; 244 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 12 con; 0-2 aty)
% Number of variables : 247 ( 0 ^; 236 !; 11 ?; 247 :)
% 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(xP_type,type,
xP: $i ).
thf(xS_type,type,
xS: $i ).
thf(xk_type,type,
xk: $i ).
thf(isCountable0_type,type,
isCountable0: $i > $o ).
thf(sz00_type,type,
sz00: $i ).
thf(xQ_type,type,
xQ: $i ).
thf(xx_type,type,
xx: $i ).
thf(xy_type,type,
xy: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(xT_type,type,
xT: $i ).
thf(39,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/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
thf(238,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)],[39]) ).
thf(8,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isFinite0 @ A )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFinRel) ).
thf(92,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessRel) ).
thf(515,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(15,axiom,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSegZero) ).
thf(105,plain,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(21,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( sbrdtbr0 @ A )
= sz00 )
<=> ( A = slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
thf(148,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( ( sbrdtbr0 @ A )
= sz00 )
=> ( A = slcrc0 ) )
& ( ( A = slcrc0 )
=> ( ( sbrdtbr0 @ A )
= sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(10,axiom,
( ( aSet0 @ szNzAzT0 )
& ( isCountable0 @ szNzAzT0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
thf(95,plain,
( ( aSet0 @ szNzAzT0 )
& ( isCountable0 @ szNzAzT0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
( ( aSet0 @ xQ )
& ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ xS ) )
& ( aSubsetOf0 @ xQ @ xS )
& ( ( sbrdtbr0 @ xQ )
= xk )
& ( aElementOf0 @ xQ @ ( slbdtsldtrb0 @ xS @ xk ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).
thf(138,plain,
( ( aSet0 @ xQ )
& ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ xS ) )
& ( aSubsetOf0 @ xQ @ xS )
& ( ( sbrdtbr0 @ xQ )
= xk )
& ( aElementOf0 @ xQ @ ( slbdtsldtrb0 @ xS @ xk ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(13,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCDiffSet) ).
thf(101,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(58,axiom,
( ( aSet0 @ xQ )
& ( isFinite0 @ xQ )
& ( ( sbrdtbr0 @ xQ )
= xk ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
thf(347,plain,
( ( aSet0 @ xQ )
& ( isFinite0 @ xQ )
& ( ( sbrdtbr0 @ xQ )
= xk ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(7,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
thf(88,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',mDefCons) ).
thf(352,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)],[59]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIHSort) ).
thf(170,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(71,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( aElementOf0 @ ( sbrdtbr0 @ A ) @ szNzAzT0 )
<=> ( isFinite0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
thf(449,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)],[71]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aSet0 @ B ) )
=> ( ( ( aSubsetOf0 @ A @ B )
& ( aSubsetOf0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubASymm) ).
thf(174,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)],[27]) ).
thf(43,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
<=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
thf(257,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)],[43]) ).
thf(9,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCConsSet) ).
thf(93,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(50,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardS) ).
thf(284,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(20,axiom,
aElementOf0 @ xx @ xS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2256) ).
thf(147,plain,
aElementOf0 @ xx @ xS,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(41,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
thf(243,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)],[41]) ).
thf(44,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSegFin) ).
thf(265,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(73,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElement0 @ B )
=> ( ~ ( aElementOf0 @ B @ A )
=> ( ( sbrdtbr0 @ ( sdtpldt0 @ A @ B ) )
= ( szszuzczcdt0 @ ( sbrdtbr0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardCons) ).
thf(512,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)],[73]) ).
thf(46,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardSeg) ).
thf(270,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
<=> ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ ( szszuzczcdt0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccLess) ).
thf(233,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)],[37]) ).
thf(72,axiom,
( ( aSet0 @ ( slbdtsldtrb0 @ xS @ xk ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xS @ xk ) )
=> ( ( 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 @ ( slbdtsldtrb0 @ xS @ xk ) ) ) )
& ( aSet0 @ ( slbdtsldtrb0 @ xT @ xk ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xT @ xk ) )
=> ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xT ) )
& ( aSubsetOf0 @ A @ xT )
& ( ( sbrdtbr0 @ A )
= xk ) ) )
& ( ( ( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xT ) ) )
| ( aSubsetOf0 @ A @ xT ) )
& ( ( sbrdtbr0 @ A )
= xk ) )
=> ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xT @ xk ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xS @ xk ) )
=> ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xT @ xk ) ) )
& ( aSubsetOf0 @ ( slbdtsldtrb0 @ xS @ xk ) @ ( slbdtsldtrb0 @ xT @ xk ) )
& ~ ( ! [A: $i] :
( ( ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xS @ xk ) )
=> ( ( 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 @ ( slbdtsldtrb0 @ xS @ xk ) ) ) )
=> ( ~ ? [A: $i] : ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xS @ xk ) )
| ( ( slbdtsldtrb0 @ xS @ xk )
= slcrc0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
thf(452,plain,
( ( aSet0 @ ( slbdtsldtrb0 @ xS @ xk ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xS @ xk ) )
=> ( ( 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 @ ( slbdtsldtrb0 @ xS @ xk ) ) ) )
& ( aSet0 @ ( slbdtsldtrb0 @ xT @ xk ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xT @ xk ) )
=> ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xT ) )
& ( aSubsetOf0 @ A @ xT )
& ( ( sbrdtbr0 @ A )
= xk ) ) )
& ( ( ( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xT ) ) )
| ( aSubsetOf0 @ A @ xT ) )
& ( ( sbrdtbr0 @ A )
= xk ) )
=> ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xT @ xk ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xS @ xk ) )
=> ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xT @ xk ) ) )
& ( aSubsetOf0 @ ( slbdtsldtrb0 @ xS @ xk ) @ ( slbdtsldtrb0 @ xT @ xk ) )
& ~ ( ! [A: $i] :
( ( ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xS @ xk ) )
=> ( ( 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 @ ( slbdtsldtrb0 @ xS @ xk ) ) ) )
=> ( ~ ? [A: $i] : ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xS @ xk ) )
| ( ( slbdtsldtrb0 @ xS @ xk )
= slcrc0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(4,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSort) ).
thf(85,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSelFSet) ).
thf(201,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(55,axiom,
( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( aElementOf0 @ A @ xS ) )
& ( aSubsetOf0 @ xP @ xS )
& ( ( sbrdtbr0 @ xP )
= xk ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2431) ).
thf(334,plain,
( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( aElementOf0 @ A @ xS ) )
& ( aSubsetOf0 @ xP @ xS )
& ( ( sbrdtbr0 @ xP )
= xk ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(62,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( ( isFinite0 @ A )
& ( aSubsetOf0 @ B @ A ) )
=> ( sdtlseqdt0 @ ( sbrdtbr0 @ B ) @ ( sbrdtbr0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardSub) ).
thf(392,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)],[62]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
thf(407,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)],[68]) ).
thf(48,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(275,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',mDefMax) ).
thf(317,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)],[53]) ).
thf(23,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
thf(156,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',mDefSeg) ).
thf(109,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)],[17]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
<=> ( aSubsetOf0 @ ( slbdtrb0 @ A ) @ ( slbdtrb0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSegLess) ).
thf(339,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)],[56]) ).
thf(66,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ! [B: $i] :
( ( ( aElementOf0 @ B @ szNzAzT0 )
& ( B != sz00 ) )
=> ( isCountable0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSelCSet) ).
thf(402,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)],[66]) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',mDefSel) ).
thf(286,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)],[51]) ).
thf(38,axiom,
~ ( aElementOf0 @ xx @ xQ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2338) ).
thf(236,plain,
~ ( aElementOf0 @ xx @ xQ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(5,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSetSort) ).
thf(86,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
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/sandbox/benchmark/theBenchmark.p',mDefMin) ).
thf(219,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(11,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFDiffSet) ).
thf(98,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(60,axiom,
( ( aElement0 @ xy )
& ( aElementOf0 @ xy @ xQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2304) ).
thf(387,plain,
( ( aElement0 @ xy )
& ( aElementOf0 @ xy @ xQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(14,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
thf(103,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',mLessTrans) ).
thf(213,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)],[33]) ).
thf(40,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/sandbox/benchmark/theBenchmark.p',mMinMin) ).
thf(240,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)],[40]) ).
thf(64,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
thf(399,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(63,axiom,
( ( aSet0 @ xS )
& ( aSet0 @ xT )
& ( xk != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
thf(394,plain,
( ( aSet0 @ xS )
& ( aSet0 @ xT )
& ( xk != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( szszuzczcdt0 @ A )
= ( szszuzczcdt0 @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEquSucc) ).
thf(267,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)],[45]) ).
thf(57,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( A = sz00 )
| ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtra) ).
thf(342,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( A = sz00 )
| ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(19,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubFSet) ).
thf(145,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(28,axiom,
( ( aSet0 @ ( sdtmndt0 @ xQ @ xy ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtmndt0 @ xQ @ xy ) )
<=> ( ( aElement0 @ A )
& ( aElementOf0 @ A @ xQ )
& ( A != xy ) ) )
& ( aSet0 @ xP )
& ! [A: $i] :
( ( aElementOf0 @ A @ xP )
<=> ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ ( sdtmndt0 @ xQ @ xy ) )
| ( A = xx ) ) ) )
& ( xP
= ( sdtpldt0 @ ( sdtmndt0 @ xQ @ xy ) @ xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2357) ).
thf(177,plain,
( ( aSet0 @ ( sdtmndt0 @ xQ @ xy ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtmndt0 @ xQ @ xy ) )
=> ( ( aElement0 @ A )
& ( aElementOf0 @ A @ xQ )
& ( A != xy ) ) )
& ( ( ( aElement0 @ A )
& ( aElementOf0 @ A @ xQ )
& ( A != xy ) )
=> ( aElementOf0 @ A @ ( sdtmndt0 @ xQ @ xy ) ) ) )
& ( aSet0 @ xP )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ xP )
=> ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ ( sdtmndt0 @ xQ @ xy ) )
| ( A = xx ) ) ) )
& ( ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ ( sdtmndt0 @ xQ @ xy ) )
| ( A = xx ) ) )
=> ( aElementOf0 @ A @ xP ) ) )
& ( xP
= ( sdtpldt0 @ ( sdtmndt0 @ xQ @ xy ) @ xx ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(54,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( A
!= ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatNSucc) ).
thf(331,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( A
!= ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(22,axiom,
~ ( aElementOf0 @ xx @ xQ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2323) ).
thf(154,plain,
~ ( aElementOf0 @ xx @ xQ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(70,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ~ ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
=> ( ( slbdtsldtrb0 @ A @ B )
!= slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSelNSet) ).
thf(446,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(6,axiom,
isFinite0 @ slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEmpFin) ).
thf(87,plain,
isFinite0 @ slcrc0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',mCardSubEx) ).
thf(203,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)],[30]) ).
thf(35,axiom,
aElementOf0 @ sz00 @ szNzAzT0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
thf(218,plain,
aElementOf0 @ sz00 @ szNzAzT0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(24,axiom,
( ~ ( aElementOf0 @ xx @ ( sdtmndt0 @ xQ @ xy ) )
& ( aSet0 @ ( sdtmndt0 @ xQ @ xy ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtmndt0 @ xQ @ xy ) )
<=> ( ( aElement0 @ A )
& ( aElementOf0 @ A @ xQ )
& ( A != xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2411) ).
thf(158,plain,
( ~ ( aElementOf0 @ xx @ ( sdtmndt0 @ xQ @ xy ) )
& ( aSet0 @ ( sdtmndt0 @ xQ @ xy ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtmndt0 @ xQ @ xy ) )
=> ( ( aElement0 @ A )
& ( aElementOf0 @ A @ xQ )
& ( A != xy ) ) )
& ( ( ( aElement0 @ A )
& ( aElementOf0 @ A @ xQ )
& ( A != xy ) )
=> ( aElementOf0 @ A @ ( sdtmndt0 @ xQ @ xy ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(61,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNoScLessZr) ).
thf(390,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(65,axiom,
aElementOf0 @ xk @ szNzAzT0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).
thf(401,plain,
aElementOf0 @ xk @ szNzAzT0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).
thf(171,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)],[26]) ).
thf(1,conjecture,
( ( ( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( aElementOf0 @ A @ xS ) )
| ( aSubsetOf0 @ xP @ xS ) )
& ( ( sbrdtbr0 @ xP )
= xk ) )
| ( aElementOf0 @ xP @ ( slbdtsldtrb0 @ xS @ xk ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( aElementOf0 @ A @ xS ) )
| ( aSubsetOf0 @ xP @ xS ) )
& ( ( sbrdtbr0 @ xP )
= xk ) )
| ( aElementOf0 @ xP @ ( slbdtsldtrb0 @ xS @ xk ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(75,plain,
~ ( ( ( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( aElementOf0 @ A @ xS ) )
| ( aSubsetOf0 @ xP @ xS ) )
& ( ( sbrdtbr0 @ xP )
= xk ) )
| ( aElementOf0 @ xP @ ( slbdtsldtrb0 @ xS @ xk ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ( aElement0 @ A )
& ( aSet0 @ B ) )
=> ( ~ ( aElementOf0 @ A @ B )
=> ( ( sdtmndt0 @ ( sdtpldt0 @ B @ A ) @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDiffCons) ).
thf(207,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)],[31]) ).
thf(52,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessSucc) ).
thf(315,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(67,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessRefl) ).
thf(405,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(47,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
thf(273,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(32,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( ( isFinite0 @ A )
& ( aElementOf0 @ B @ A ) )
=> ( ( szszuzczcdt0 @ ( sbrdtbr0 @ ( sdtmndt0 @ A @ B ) ) )
= ( sbrdtbr0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardDiff) ).
thf(210,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)],[32]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessTotal) ).
thf(107,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)],[16]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',mSegSucc) ).
thf(277,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)],[49]) ).
thf(69,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ A ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
thf(442,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ A ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(42,axiom,
! [A: $i] :
( ( ( aSubsetOf0 @ A @ szNzAzT0 )
& ( isFinite0 @ A ) )
=> ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( aSubsetOf0 @ A @ ( slbdtrb0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFinSubSeg) ).
thf(254,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)],[42]) ).
thf(3,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFConsSet) ).
thf(83,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(34,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
thf(215,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(12,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isCountable0 @ A )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCntRel) ).
thf(100,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(516,plain,
$false,
inference(cvc4,[status(thm)],[238,92,515,105,148,95,138,101,347,88,352,170,449,174,257,93,284,147,243,265,512,270,233,452,85,201,334,392,407,275,317,156,109,339,402,286,236,86,219,98,387,103,213,240,399,394,267,342,145,177,331,154,446,87,203,218,158,390,401,171,75,207,315,405,273,210,107,277,442,254,83,215,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : NUM557+3 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 18 17:27:13 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.88/0.76 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/0.92 % [INFO] Parsing done (153ms).
% 1.27/0.92 % [INFO] Running in sequential loop mode.
% 1.67/1.12 % [INFO] eprover registered as external prover.
% 1.67/1.13 % [INFO] cvc4 registered as external prover.
% 1.67/1.13 % [INFO] Scanning for conjecture ...
% 1.67/1.16 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.67/1.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.18 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.92/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.08/1.23 % [INFO] Found a conjecture and 72 axioms. Running axiom selection ...
% 2.17/1.29 % [INFO] Axiom selection finished. Selected 72 axioms (removed 0 axioms).
% 2.17/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.17/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.17/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.17/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.17/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.17/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.17/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 2.47/1.36 % [INFO] Type checking passed.
% 2.47/1.36 % [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 ...
% 5.64/2.28 % External prover 'cvc4' found a proof!
% 5.64/2.28 % [INFO] Killing All external provers ...
% 5.64/2.28 % Time passed: 1792ms (effective reasoning time: 1354ms)
% 5.64/2.28 % 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)>
% 5.64/2.28 % Axioms used in derivation (72): mIHSort, mDiffCons, mDefSel, m__2256, mZeroNum, mSubASymm, mCntRel, mCardEmpty, m__2338, m__2323, mSuccLess, mCountNFin, mSegLess, mCardSubEx, mDefEmp, mFinSubSeg, m__2291, m__2304, mSubRefl, mDefMin, mSubFSet, mEOfElem, mDefDiff, mSelCSet, mSetSort, mCardS, mSegZero, mSuccEquSucc, mSelNSet, m__2270, mSegSucc, mLessSucc, mIH, m__2431, m__2357, mFDiffSet, mCDiffSet, mFinRel, mSegFin, mDefCons, mNoScLessZr, mLessRefl, mLessRel, mConsDiff, m__2411, mDefSeg, mCardSub, mCountNFin_01, mCardNum, mLessASymm, m__2227, m__2202, m__2202_02, mMinMin, mSelFSet, mNatNSucc, mDefMax, mEmpFin, mLessTotal, mNATSet, mFConsSet, mElmSort, mCardDiff, mZeroLess, mDefSub, mLessTrans, mNatExtra, mSuccNum, mSubTrans, mCardCons, mCConsSet, mCardSeg
% 5.64/2.28 % No. of inferences in proof: 148
% 5.64/2.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1792 ms resp. 1354 ms w/o parsing
% 5.64/2.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.64/2.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------