TSTP Solution File: NUM542+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM542+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 11:41:03 EDT 2023
% Result : Theorem 7.02s 2.67s
% Output : Refutation 7.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 77
% Syntax : Number of formulae : 193 ( 26 unt; 22 typ; 0 def)
% Number of atoms : 706 ( 113 equ; 0 cnn)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 1814 ( 111 ~; 73 |; 209 &;1182 @)
% ( 22 <=>; 217 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 9 con; 0-2 aty)
% Number of variables : 234 ( 0 ^; 225 !; 9 ?; 234 :)
% 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(xm_type,type,
xm: $i ).
thf(xn_type,type,
xn: $i ).
thf(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
thf(sz00_type,type,
sz00: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(isCountable0_type,type,
isCountable0: $i > $o ).
thf(sk1_type,type,
sk1: $o ).
thf(sk2_type,type,
sk2: $i ).
thf(36,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(217,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)],[36]) ).
thf(1,conjecture,
( ( ( sdtlseqdt0 @ xm @ xn )
=> ( ( ( aSet0 @ ( slbdtrb0 @ xm ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
<=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xm ) ) ) )
=> ( ( ( aSet0 @ ( slbdtrb0 @ xn ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) )
<=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xn ) ) ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) ) )
| ( aSubsetOf0 @ ( slbdtrb0 @ xm ) @ ( slbdtrb0 @ xn ) ) ) ) ) )
& ( ( ( aSet0 @ ( slbdtrb0 @ xm ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
<=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xm ) ) )
& ( aSet0 @ ( slbdtrb0 @ xn ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) )
<=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xn ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) ) )
& ( aSubsetOf0 @ ( slbdtrb0 @ xm ) @ ( slbdtrb0 @ xn ) ) )
=> ( sdtlseqdt0 @ xm @ xn ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( sdtlseqdt0 @ xm @ xn )
=> ( ( ( aSet0 @ ( slbdtrb0 @ xm ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
<=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xm ) ) ) )
=> ( ( ( aSet0 @ ( slbdtrb0 @ xn ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) )
<=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xn ) ) ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) ) )
| ( aSubsetOf0 @ ( slbdtrb0 @ xm ) @ ( slbdtrb0 @ xn ) ) ) ) ) )
& ( ( ( aSet0 @ ( slbdtrb0 @ xm ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
<=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xm ) ) )
& ( aSet0 @ ( slbdtrb0 @ xn ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) )
<=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xn ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) ) )
& ( aSubsetOf0 @ ( slbdtrb0 @ xm ) @ ( slbdtrb0 @ xn ) ) )
=> ( sdtlseqdt0 @ xm @ xn ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(57,plain,
~ ( ( ( sdtlseqdt0 @ xm @ xn )
=> ( ( ( aSet0 @ ( slbdtrb0 @ xm ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xm ) ) )
& ( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xm ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) ) ) ) )
=> ( ( ( aSet0 @ ( slbdtrb0 @ xn ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) )
=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xn ) ) )
& ( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xn ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) ) ) ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) ) )
| ( aSubsetOf0 @ ( slbdtrb0 @ xm ) @ ( slbdtrb0 @ xn ) ) ) ) ) )
& ( ( ( aSet0 @ ( slbdtrb0 @ xm ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xm ) ) )
& ( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xm ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) ) ) )
& ( aSet0 @ ( slbdtrb0 @ xn ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) )
=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xn ) ) )
& ( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xn ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) ) )
& ( aSubsetOf0 @ ( slbdtrb0 @ xm ) @ ( slbdtrb0 @ xn ) ) )
=> ( sdtlseqdt0 @ xm @ xn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(58,plain,
~ ( ( ( sdtlseqdt0 @ xm @ xn )
=> ( ( ( aSet0 @ ( slbdtrb0 @ xm ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xm ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xm ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) ) ) )
=> ( ( ( aSet0 @ ( slbdtrb0 @ xn ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) )
=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xn ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xn ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) ) ) )
=> ( ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) ) )
| ( aSubsetOf0 @ ( slbdtrb0 @ xm ) @ ( slbdtrb0 @ xn ) ) ) ) ) )
& ( ( ( aSet0 @ ( slbdtrb0 @ xm ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xm ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xm ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) ) )
& ( aSet0 @ ( slbdtrb0 @ xn ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) )
=> ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xn ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xn ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
=> ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) ) )
& ( aSubsetOf0 @ ( slbdtrb0 @ xm ) @ ( slbdtrb0 @ xn ) ) )
=> ( sdtlseqdt0 @ xm @ xn ) ) ),
inference(miniscope,[status(thm)],[57]) ).
thf(73,plain,
( ( aElementOf0 @ sk2 @ ( slbdtrb0 @ xm ) )
| ~ sk1 ),
inference(cnf,[status(esa)],[58]) ).
thf(65,plain,
( ~ ( aElementOf0 @ sk2 @ ( slbdtrb0 @ xn ) )
| ~ sk1 ),
inference(cnf,[status(esa)],[58]) ).
thf(405,plain,
( ~ sk1
| ( ( aElementOf0 @ sk2 @ ( slbdtrb0 @ xn ) )
!= ( aElementOf0 @ sk2 @ ( slbdtrb0 @ xm ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,65]) ).
thf(410,plain,
( ~ sk1
| ( sk2 != sk2 )
| ( ( slbdtrb0 @ xn )
!= ( slbdtrb0 @ xm ) ) ),
inference(simp,[status(thm)],[405]) ).
thf(413,plain,
( ~ sk1
| ( ( slbdtrb0 @ xn )
!= ( slbdtrb0 @ xm ) ) ),
inference(simp,[status(thm)],[410]) ).
thf(417,plain,
( ~ sk1
| ( xn != xm ) ),
inference(simp,[status(thm)],[413]) ).
thf(61,plain,
( ( aSet0 @ ( slbdtrb0 @ xm ) )
| ~ sk1 ),
inference(cnf,[status(esa)],[58]) ).
thf(38,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessSucc) ).
thf(226,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(21,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(162,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,axiom,
( ( aElementOf0 @ xm @ szNzAzT0 )
& ( aElementOf0 @ xn @ szNzAzT0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1964) ).
thf(137,plain,
( ( aElementOf0 @ xm @ szNzAzT0 )
& ( aElementOf0 @ xn @ szNzAzT0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(138,plain,
aElementOf0 @ xn @ szNzAzT0,
inference(cnf,[status(esa)],[137]) ).
thf(52,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isCountable0 @ A )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCntRel) ).
thf(347,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(50,axiom,
( ( aSet0 @ szNzAzT0 )
& ( isCountable0 @ szNzAzT0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
thf(333,plain,
( ( aSet0 @ szNzAzT0 )
& ( isCountable0 @ szNzAzT0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(25,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(184,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)],[25]) ).
thf(51,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
thf(336,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)],[51]) ).
thf(337,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)],[336]) ).
thf(339,plain,
! [A: $i] :
( ( A != slcrc0 )
| ( aSet0 @ A ) ),
inference(cnf,[status(esa)],[337]) ).
thf(343,plain,
! [A: $i] :
( ( A != slcrc0 )
| ( aSet0 @ A ) ),
inference(lifteq,[status(thm)],[339]) ).
thf(344,plain,
aSet0 @ slcrc0,
inference(simp,[status(thm)],[343]) ).
thf(30,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
thf(200,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(201,plain,
! [A: $i] :
( ~ ( aSet0 @ A )
| ~ ( isCountable0 @ A )
| ( A != slcrc0 ) ),
inference(cnf,[status(esa)],[200]) ).
thf(202,plain,
! [A: $i] :
( ( A != slcrc0 )
| ~ ( aSet0 @ A )
| ~ ( isCountable0 @ A ) ),
inference(lifteq,[status(thm)],[201]) ).
thf(203,plain,
( ~ ( aSet0 @ slcrc0 )
| ~ ( isCountable0 @ slcrc0 ) ),
inference(simp,[status(thm)],[202]) ).
thf(356,plain,
( ~ $true
| ~ ( isCountable0 @ slcrc0 ) ),
inference(rewrite,[status(thm)],[203,344]) ).
thf(357,plain,
~ ( isCountable0 @ slcrc0 ),
inference(simp,[status(thm)],[356]) ).
thf(18,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(157,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)],[18]) ).
thf(27,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(189,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)],[27]) ).
thf(3,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(93,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(47,axiom,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).
thf(294,plain,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(295,plain,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
inference(lifteq,[status(thm)],[294]) ).
thf(340,plain,
! [B: $i,A: $i] :
( ( A != slcrc0 )
| ~ ( aElementOf0 @ B @ A ) ),
inference(cnf,[status(esa)],[337]) ).
thf(345,plain,
! [B: $i,A: $i] :
( ( A != slcrc0 )
| ~ ( aElementOf0 @ B @ A ) ),
inference(lifteq,[status(thm)],[340]) ).
thf(346,plain,
! [A: $i] :
~ ( aElementOf0 @ A @ slcrc0 ),
inference(simp,[status(thm)],[345]) ).
thf(409,plain,
! [A: $i] :
( ~ sk1
| ( ( aElementOf0 @ sk2 @ ( slbdtrb0 @ xm ) )
!= ( aElementOf0 @ A @ slcrc0 ) ) ),
inference(paramod_ordered,[status(thm)],[73,346]) ).
thf(412,plain,
! [A: $i] :
( ~ sk1
| ( sk2 != A )
| ( ( slbdtrb0 @ xm )
!= slcrc0 ) ),
inference(simp,[status(thm)],[409]) ).
thf(414,plain,
( ~ sk1
| ( ( slbdtrb0 @ xm )
!= slcrc0 ) ),
inference(simp,[status(thm)],[412]) ).
thf(415,plain,
( ~ sk1
| ( ( slbdtrb0 @ sz00 )
!= ( slbdtrb0 @ xm ) ) ),
inference(paramod_ordered,[status(thm)],[295,414]) ).
thf(416,plain,
( ~ sk1
| ( sz00 != xm ) ),
inference(simp,[status(thm)],[415]) ).
thf(39,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(228,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)],[39]) ).
thf(23,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCConsSet) ).
thf(179,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(33,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
thf(211,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(53,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( aElementOf0 @ ( sbrdtbr0 @ A ) @ szNzAzT0 )
<=> ( isFinite0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
thf(348,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)],[53]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRel) ).
thf(353,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(46,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
thf(292,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(60,plain,
( ~ ( aSubsetOf0 @ ( slbdtrb0 @ xm ) @ ( slbdtrb0 @ xn ) )
| ~ sk1 ),
inference(cnf,[status(esa)],[58]) ).
thf(334,plain,
isCountable0 @ szNzAzT0,
inference(cnf,[status(esa)],[333]) ).
thf(20,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).
thf(160,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(70,plain,
( ( aSet0 @ ( slbdtrb0 @ xn ) )
| ~ sk1 ),
inference(cnf,[status(esa)],[58]) ).
thf(66,plain,
! [A: $i] :
( ~ ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xm )
| ~ sk1 ),
inference(cnf,[status(esa)],[58]) ).
thf(406,plain,
! [A: $i] :
( ~ sk1
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ xm )
| ( ( aElementOf0 @ sk2 @ ( slbdtrb0 @ xm ) )
!= ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,66]) ).
thf(407,plain,
( ~ sk1
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ sk2 ) @ xm ) ),
inference(pattern_uni,[status(thm)],[406:[bind(A,$thf( sk2 ))]]) ).
thf(22,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(165,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)],[22]) ).
thf(28,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegFin) ).
thf(197,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(6,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(97,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)],[6]) ).
thf(8,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( sbrdtbr0 @ A )
= sz00 )
<=> ( A = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
thf(128,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( ( sbrdtbr0 @ A )
= sz00 )
=> ( A = slcrc0 ) )
& ( ( A = slcrc0 )
=> ( ( sbrdtbr0 @ A )
= sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(130,plain,
! [A: $i] :
( ~ ( aSet0 @ A )
| ( A != slcrc0 )
| ( ( sbrdtbr0 @ A )
= sz00 ) ),
inference(cnf,[status(esa)],[128]) ).
thf(132,plain,
! [A: $i] :
( ( A != slcrc0 )
| ( ( sbrdtbr0 @ A )
= sz00 )
| ~ ( aSet0 @ A ) ),
inference(lifteq,[status(thm)],[130]) ).
thf(133,plain,
( ( ( sbrdtbr0 @ slcrc0 )
= sz00 )
| ~ ( aSet0 @ slcrc0 ) ),
inference(simp,[status(thm)],[132]) ).
thf(455,plain,
( ( ( sbrdtbr0 @ slcrc0 )
= sz00 )
| ~ $true ),
inference(rewrite,[status(thm)],[133,344]) ).
thf(456,plain,
( ( sbrdtbr0 @ slcrc0 )
= sz00 ),
inference(simp,[status(thm)],[455]) ).
thf(43,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
thf(285,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(37,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardS) ).
thf(224,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(225,plain,
! [A: $i] :
( ~ ( aSet0 @ A )
| ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
inference(cnf,[status(esa)],[224]) ).
thf(77,plain,
( ( sdtlseqdt0 @ xm @ xn )
| ~ sk1 ),
inference(cnf,[status(esa)],[58]) ).
thf(9,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
thf(134,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(49,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(298,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)],[49]) ).
thf(79,plain,
! [A: $i] :
( ~ ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
| ( aElementOf0 @ A @ szNzAzT0 )
| ~ sk1 ),
inference(cnf,[status(esa)],[58]) ).
thf(429,plain,
! [A: $i] :
( ~ sk1
| ( aElementOf0 @ A @ szNzAzT0 )
| ( ( aElementOf0 @ sk2 @ ( slbdtrb0 @ xm ) )
!= ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,79]) ).
thf(430,plain,
( ~ sk1
| ( aElementOf0 @ sk2 @ szNzAzT0 ) ),
inference(pattern_uni,[status(thm)],[429:[bind(A,$thf( sk2 ))]]) ).
thf(48,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRefl) ).
thf(296,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(59,plain,
( sk1
| ( aSet0 @ ( slbdtrb0 @ xm ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(31,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ A ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
thf(204,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ A ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(335,plain,
aSet0 @ szNzAzT0,
inference(cnf,[status(esa)],[333]) ).
thf(24,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(181,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)],[24]) ).
thf(19,axiom,
aElementOf0 @ sz00 @ szNzAzT0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
thf(159,plain,
aElementOf0 @ sz00 @ szNzAzT0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(76,plain,
( sk1
| ~ ( sdtlseqdt0 @ xm @ xn ) ),
inference(cnf,[status(esa)],[58]) ).
thf(41,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(245,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( A = sz00 )
| ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(32,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(208,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)],[32]) ).
thf(12,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(140,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)],[12]) ).
thf(34,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(213,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(15,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isFinite0 @ A )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFinRel) ).
thf(150,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,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(95,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)],[5]) ).
thf(29,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).
thf(199,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(358,plain,
( ( isCountable0 @ szNzAzT0 )
!= ( isCountable0 @ slcrc0 ) ),
inference(paramod_ordered,[status(thm)],[334,357]) ).
thf(359,plain,
szNzAzT0 != slcrc0,
inference(simp,[status(thm)],[358]) ).
thf(17,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(154,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)],[17]) ).
thf(13,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(143,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(42,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(250,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)],[42]) ).
thf(441,plain,
( ~ sk1
| ( ( aElementOf0 @ sk2 @ ( slbdtrb0 @ xn ) )
!= ( aElementOf0 @ sk2 @ szNzAzT0 ) ) ),
inference(paramod_ordered,[status(thm)],[430,65]) ).
thf(445,plain,
( ~ sk1
| ( sk2 != sk2 )
| ( ( slbdtrb0 @ xn )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[441]) ).
thf(450,plain,
( ~ sk1
| ( ( slbdtrb0 @ xn )
!= szNzAzT0 ) ),
inference(simp,[status(thm)],[445]) ).
thf(54,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCDiffSet) ).
thf(351,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(26,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(186,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)],[26]) ).
thf(139,plain,
aElementOf0 @ xm @ szNzAzT0,
inference(cnf,[status(esa)],[137]) ).
thf(75,plain,
( sk1
| ( aSubsetOf0 @ ( slbdtrb0 @ xm ) @ ( slbdtrb0 @ xn ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(45,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(290,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)],[45]) ).
thf(69,plain,
! [A: $i] :
( sk1
| ~ ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
| ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(82,plain,
! [A: $i] :
( sk1
| ~ ( aElementOf0 @ A @ ( slbdtrb0 @ xm ) )
| ( aElementOf0 @ A @ ( slbdtrb0 @ xn ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(44,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(287,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)],[44]) ).
thf(16,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(151,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)],[16]) ).
thf(14,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(146,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)],[14]) ).
thf(40,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( A
!= ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatNSucc) ).
thf(242,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( A
!= ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(4,axiom,
isFinite0 @ slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
thf(94,plain,
isFinite0 @ slcrc0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
thf(126,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIHSort) ).
thf(136,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(62,plain,
( sk1
| ( aSet0 @ ( slbdtrb0 @ xn ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(491,plain,
! [A: $i] :
( ( aElement0 @ ( sbrdtbr0 @ A ) )
| ( ( aSet0 @ slcrc0 )
!= ( aSet0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[344,225]) ).
thf(492,plain,
aElement0 @ ( sbrdtbr0 @ slcrc0 ),
inference(pattern_uni,[status(thm)],[491:[bind(A,$thf( slcrc0 ))]]) ).
thf(501,plain,
aElement0 @ sz00,
inference(rewrite,[status(thm)],[492,456]) ).
thf(56,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNoScLessZr) ).
thf(354,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(35,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
thf(215,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(714,plain,
$false,
inference(cvc4,[status(thm)],[217,417,61,226,162,138,347,333,184,344,357,157,189,93,416,228,57,179,211,348,353,292,60,334,160,70,407,137,165,197,65,97,456,285,224,225,77,134,73,128,298,430,296,59,204,413,335,181,159,76,245,208,140,213,66,295,150,414,95,199,359,336,154,143,250,450,351,186,139,75,290,346,82,287,151,146,242,79,94,294,126,136,200,62,501,354,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM542+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 17:27:58 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.93/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.96 % [INFO] Parsing done (140ms).
% 1.24/0.97 % [INFO] Running in sequential loop mode.
% 1.83/1.17 % [INFO] eprover registered as external prover.
% 1.83/1.17 % [INFO] cvc4 registered as external prover.
% 1.83/1.18 % [INFO] Scanning for conjecture ...
% 1.83/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.83/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.23 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.07/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/1.28 % [INFO] Found a conjecture and 54 axioms. Running axiom selection ...
% 2.43/1.34 % [INFO] Axiom selection finished. Selected 54 axioms (removed 0 axioms).
% 2.43/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.38 % [INFO] Problem is first-order (TPTP FOF).
% 2.55/1.39 % [INFO] Type checking passed.
% 2.55/1.39 % [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 ...
% 7.02/2.66 % External prover 'cvc4' found a proof!
% 7.02/2.66 % [INFO] Killing All external provers ...
% 7.02/2.66 % Time passed: 2164ms (effective reasoning time: 1695ms)
% 7.02/2.66 % 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)>
% 7.02/2.67 % Axioms used in derivation (54): mCardEmpty, mSuccLess, mDefEmp, mIHSort, mDiffCons, mDefDiff, mZeroNum, mMinMin, mNatNSucc, mSubASymm, mCntRel, mCountNFin, mCardSubEx, mSubRefl, mDefMin, mSubFSet, mEOfElem, mSetSort, mCardS, mSegZero, mSuccEquSucc, mSegSucc, mLessSucc, mIH, mFDiffSet, mCDiffSet, mFinRel, mSegFin, mDefCons, mNoScLessZr, mConsDiff, mLessRefl, mLessRel, mDefSeg, mCardSub, mCountNFin_01, mCardNum, mLessASymm, m__1964, mDefMax, mEmpFin, mLessTotal, mNATSet, mFConsSet, mElmSort, mCardDiff, mZeroLess, mDefSub, mLessTrans, mNatExtra, mSuccNum, mSubTrans, mCardCons, mCConsSet
% 7.02/2.67 % No. of inferences in proof: 171
% 7.02/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2164 ms resp. 1695 ms w/o parsing
% 7.02/2.72 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.02/2.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------