TSTP Solution File: NUM547+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM547+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:41:05 EDT 2023
% Result : Theorem 5.40s 2.37s
% Output : Refutation 5.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 88
% Syntax : Number of formulae : 155 ( 20 unt; 23 typ; 0 def)
% Number of atoms : 538 ( 95 equ; 0 cnn)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 1325 ( 42 ~; 12 |; 174 &; 877 @)
% ( 17 <=>; 203 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 9 con; 0-2 aty)
% Number of variables : 215 ( 0 ^; 203 !; 12 ?; 215 :)
% 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(xS_type,type,
xS: $i ).
thf(xk_type,type,
xk: $i ).
thf(sz00_type,type,
sz00: $i ).
thf(isCountable0_type,type,
isCountable0: $i > $o ).
thf(xx_type,type,
xx: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(xT_type,type,
xT: $i ).
thf(39,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(202,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)],[39]) ).
thf(66,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNoScLessZr) ).
thf(384,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(22,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
thf(110,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(34,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(164,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)],[34]) ).
thf(45,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(243,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)],[45]) ).
thf(13,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(92,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)],[13]) ).
thf(28,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(148,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)],[28]) ).
thf(23,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(112,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)],[23]) ).
thf(25,axiom,
aElementOf0 @ xx @ xS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2256) ).
thf(143,plain,
aElementOf0 @ xx @ xS,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(60,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(363,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)],[60]) ).
thf(3,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubFSet) ).
thf(69,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
thf(88,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(56,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(320,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)],[56]) ).
thf(46,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( A
!= ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatNSucc) ).
thf(257,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( A
!= ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(36,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(189,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)],[36]) ).
thf(58,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(325,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)],[58]) ).
thf(29,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(152,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)],[29]) ).
thf(54,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(316,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)],[54]) ).
thf(64,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(380,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)],[64]) ).
thf(61,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ A ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
thf(366,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ A ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(47,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(260,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)],[47]) ).
thf(32,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(160,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(37,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(192,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)],[37]) ).
thf(5,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFConsSet) ).
thf(77,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(43,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(212,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)],[43]) ).
thf(15,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCConsSet) ).
thf(96,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardS) ).
thf(105,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(59,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(360,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)],[59]) ).
thf(40,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardSeg) ).
thf(205,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(4,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( sbrdtbr0 @ A )
= sz00 )
<=> ( A = slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
thf(71,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( ( sbrdtbr0 @ A )
= sz00 )
=> ( A = slcrc0 ) )
& ( ( A = slcrc0 )
=> ( ( sbrdtbr0 @ A )
= sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(26,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
thf(144,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(10,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(86,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)],[10]) ).
thf(8,axiom,
isFinite0 @ slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEmpFin) ).
thf(81,plain,
isFinite0 @ slcrc0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(63,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(377,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ~ ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
=> ( ( slbdtsldtrb0 @ A @ B )
!= slcrc0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(41,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
thf(208,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(16,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(98,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)],[16]) ).
thf(50,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( aElementOf0 @ ( sbrdtbr0 @ A ) @ szNzAzT0 )
<=> ( isFinite0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
thf(303,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)],[50]) ).
thf(18,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFDiffSet) ).
thf(103,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(57,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessRefl) ).
thf(323,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(30,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(155,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)],[30]) ).
thf(21,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCDiffSet) ).
thf(108,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(51,axiom,
( ( aSubsetOf0 @ ( slbdtsldtrb0 @ xS @ xk ) @ ( slbdtsldtrb0 @ xT @ xk ) )
& ( ( slbdtsldtrb0 @ xS @ xk )
!= slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
thf(306,plain,
( ( aSubsetOf0 @ ( slbdtsldtrb0 @ xS @ xk ) @ ( slbdtsldtrb0 @ xT @ xk ) )
& ( ( slbdtsldtrb0 @ xS @ xk )
!= slcrc0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(44,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessSucc) ).
thf(241,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(7,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSetSort) ).
thf(80,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isFinite0 @ A )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFinRel) ).
thf(95,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(48,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(263,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( A = sz00 )
| ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(52,axiom,
( ( aSet0 @ xS )
& ( aSet0 @ xT )
& ( xk != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
thf(310,plain,
( ( aSet0 @ xS )
& ( aSet0 @ xT )
& ( xk != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1,conjecture,
? [A: $i] : ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xS @ xk ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] : ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xS @ xk ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(67,plain,
~ ? [A: $i] : ( aElementOf0 @ A @ ( slbdtsldtrb0 @ xS @ xk ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(62,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(370,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)],[62]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIHSort) ).
thf(319,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(31,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(158,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)],[31]) ).
thf(24,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(114,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)],[24]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessRel) ).
thf(383,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(9,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
thf(82,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(53,axiom,
aElementOf0 @ xk @ szNzAzT0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).
thf(315,plain,
aElementOf0 @ xk @ szNzAzT0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(27,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(146,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtsldtrb0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(42,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(210,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(20,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isCountable0 @ A )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCntRel) ).
thf(107,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(49,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(268,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)],[49]) ).
thf(6,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSort) ).
thf(79,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
thf(178,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)],[35]) ).
thf(33,axiom,
aElementOf0 @ sz00 @ szNzAzT0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
thf(163,plain,
aElementOf0 @ sz00 @ szNzAzT0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(38,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSegFin) ).
thf(200,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(12,axiom,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSegZero) ).
thf(90,plain,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
( ( aSet0 @ szNzAzT0 )
& ( isCountable0 @ szNzAzT0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
thf(100,plain,
( ( aSet0 @ szNzAzT0 )
& ( isCountable0 @ szNzAzT0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(431,plain,
$false,
inference(cvc4,[status(thm)],[202,384,110,164,243,92,148,112,143,363,69,88,320,257,189,325,152,316,380,366,260,160,192,77,212,96,105,360,205,71,144,86,81,377,208,98,303,103,323,155,108,306,241,80,95,263,310,67,370,319,158,114,383,82,315,146,210,107,268,79,178,163,200,90,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM547+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 17:43:32 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.98/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.34/1.06 % [INFO] Parsing done (167ms).
% 1.34/1.07 % [INFO] Running in sequential loop mode.
% 1.85/1.26 % [INFO] eprover registered as external prover.
% 1.85/1.27 % [INFO] cvc4 registered as external prover.
% 1.85/1.27 % [INFO] Scanning for conjecture ...
% 2.05/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.05/1.31 % [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.
% 2.05/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.05/1.36 % [INFO] Found a conjecture and 64 axioms. Running axiom selection ...
% 2.27/1.41 % [INFO] Axiom selection finished. Selected 64 axioms (removed 0 axioms).
% 2.27/1.43 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.44 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.44 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.44 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.44 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.45 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.45 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.45 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.27/1.46 % [INFO] Problem is first-order (TPTP FOF).
% 2.58/1.47 % [INFO] Type checking passed.
% 2.58/1.47 % [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 ...
% 5.40/2.36 % External prover 'cvc4' found a proof!
% 5.40/2.37 % [INFO] Killing All external provers ...
% 5.40/2.37 % Time passed: 1848ms (effective reasoning time: 1296ms)
% 5.40/2.37 % 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)>
% 5.40/2.37 % Axioms used in derivation (64): mCardEmpty, mSuccLess, mIHSort, mDiffCons, mDefSel, m__2256, mSelNSet, mZeroNum, mSubASymm, mCntRel, mCountNFin, mSegLess, mCardSubEx, mDefEmp, mFinSubSeg, mSubRefl, mDefMin, mSubFSet, mEOfElem, mDefDiff, mSelCSet, mSetSort, mCardS, mSegZero, mSuccEquSucc, mSegSucc, mLessSucc, mIH, mFDiffSet, mCDiffSet, mFinRel, mSegFin, mDefCons, mNoScLessZr, mConsDiff, mLessRefl, mLessRel, 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
% 5.40/2.37 % No. of inferences in proof: 132
% 5.40/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1848 ms resp. 1296 ms w/o parsing
% 5.87/2.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.87/2.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------