TSTP Solution File: NUM630+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM630+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 11:41:32 EDT 2023
% Result : Theorem 9.53s 3.19s
% Output : Refutation 10.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 157
% Syntax : Number of formulae : 275 ( 28 unt; 41 typ; 0 def)
% Number of atoms : 1518 ( 279 equ; 0 cnn)
% Maximal formula atoms : 59 ( 6 avg)
% Number of connectives : 5530 ( 85 ~; 72 |; 670 &;4161 @)
% ( 42 <=>; 500 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 20 con; 0-2 aty)
% Number of variables : 522 ( 0 ^; 473 !; 49 ?; 522 :)
% Comments :
%------------------------------------------------------------------------------
thf(slcrc0_type,type,
slcrc0: $i ).
thf(aSet0_type,type,
aSet0: $i > $o ).
thf(aElementOf0_type,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_type,type,
aSubsetOf0: $i > $i > $o ).
thf(aElement0_type,type,
aElement0: $i > $o ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(sdtmndt0_type,type,
sdtmndt0: $i > $i > $i ).
thf(szNzAzT0_type,type,
szNzAzT0: $i ).
thf(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
thf(sdtlseqdt0_type,type,
sdtlseqdt0: $i > $i > $o ).
thf(isFinite0_type,type,
isFinite0: $i > $o ).
thf(szmzazxdt0_type,type,
szmzazxdt0: $i > $i ).
thf(slbdtrb0_type,type,
slbdtrb0: $i > $i ).
thf(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
thf(slbdtsldtrb0_type,type,
slbdtsldtrb0: $i > $i > $i ).
thf(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
thf(aFunction0_type,type,
aFunction0: $i > $o ).
thf(sdtlbdtrb0_type,type,
sdtlbdtrb0: $i > $i > $i ).
thf(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
thf(sdtlpdtrp0_type,type,
sdtlpdtrp0: $i > $i > $i ).
thf(sdtlcdtrc0_type,type,
sdtlcdtrc0: $i > $i > $i ).
thf(sdtexdt0_type,type,
sdtexdt0: $i > $i > $i ).
thf(xN_type,type,
xN: $i ).
thf(xn_type,type,
xn: $i ).
thf(xP_type,type,
xP: $i ).
thf(xc_type,type,
xc: $i ).
thf(xC_type,type,
xC: $i ).
thf(sz00_type,type,
sz00: $i ).
thf(xK_type,type,
xK: $i ).
thf(xS_type,type,
xS: $i ).
thf(isCountable0_type,type,
isCountable0: $i > $o ).
thf(xO_type,type,
xO: $i ).
thf(xd_type,type,
xd: $i ).
thf(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
thf(xe_type,type,
xe: $i ).
thf(xk_type,type,
xk: $i ).
thf(xT_type,type,
xT: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(xQ_type,type,
xQ: $i ).
thf(xp_type,type,
xp: $i ).
thf(xD_type,type,
xD: $i ).
thf(76,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
& ( isCountable0 @ B ) )
=> ( ! [C: $i,D: $i] :
( ( ( aElementOf0 @ C @ ( szDzozmdt0 @ A ) )
& ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( C != D ) )
=> ( ( sdtlpdtrp0 @ A @ C )
!= ( sdtlpdtrp0 @ A @ D ) ) )
=> ( isCountable0 @ ( sdtlcdtrc0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgCount) ).
thf(746,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
& ( isCountable0 @ B ) )
=> ( ! [C: $i,D: $i] :
( ( ( aElementOf0 @ C @ ( szDzozmdt0 @ A ) )
& ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( C != D ) )
=> ( ( sdtlpdtrp0 @ A @ C )
!= ( sdtlpdtrp0 @ A @ D ) ) )
=> ( isCountable0 @ ( sdtlcdtrc0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(77,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardSeg) ).
thf(753,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(61,axiom,
( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( aElementOf0 @ A @ xO ) )
& ( aSubsetOf0 @ xP @ xO ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5208) ).
thf(573,plain,
( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( aElementOf0 @ A @ xO ) )
& ( aSubsetOf0 @ xP @ xO ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(80,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ? [B: $i] :
( ( aElementOf0 @ B @ xT )
& ? [C: $i] :
( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [D: $i] :
( ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ D ) )
& ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [D: $i] :
( ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
<=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
& ( D
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
=> ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSubsetOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( isCountable0 @ C )
& ! [D: $i] :
( ( ( aSet0 @ D )
& ( ( ( ! [E: $i] :
( ( aElementOf0 @ E @ D )
=> ( aElementOf0 @ E @ C ) )
| ( aSubsetOf0 @ D @ C ) )
& ( ( sbrdtbr0 @ D )
= xk ) )
| ( aElementOf0 @ D @ ( slbdtsldtrb0 @ C @ xk ) ) ) )
=> ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ D )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4411) ).
thf(760,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ? [B: $i] :
( ( aElementOf0 @ B @ xT )
& ? [C: $i] :
( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [D: $i] :
( ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ D ) )
& ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
& ( D
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( ( ( aElement0 @ D )
& ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
& ( D
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
& ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
=> ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSubsetOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( isCountable0 @ C )
& ! [D: $i] :
( ( ( aSet0 @ D )
& ( ( ( ! [E: $i] :
( ( aElementOf0 @ E @ D )
=> ( aElementOf0 @ E @ C ) )
| ( aSubsetOf0 @ D @ C ) )
& ( ( sbrdtbr0 @ D )
= xk ) )
| ( aElementOf0 @ D @ ( slbdtsldtrb0 @ C @ xk ) ) ) )
=> ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ D )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(37,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(333,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)],[37]) ).
thf(55,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) ) )
=> ( ( ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
<=> ( ( aElement0 @ C )
& ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
& ( C
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
=> ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
| ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) ) )
& ( isCountable0 @ B ) )
=> ! [C: $i] :
( ( ( aSet0 @ C )
& ( ( ( ! [D: $i] :
( ( aElementOf0 @ D @ C )
=> ( aElementOf0 @ D @ B ) )
| ( aSubsetOf0 @ C @ B ) )
& ( ( sbrdtbr0 @ C )
= xk ) )
| ( aElementOf0 @ C @ ( slbdtsldtrb0 @ B @ xk ) ) ) )
=> ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [D: $i] :
( ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ D ) )
& ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [D: $i] :
( ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
<=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
& ( D
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
=> ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSubsetOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4331) ).
thf(468,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) ) )
=> ( ( ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( ( aElement0 @ C )
& ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
& ( C
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( ( ( aElement0 @ C )
& ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
& ( C
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) ) )
=> ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
| ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) ) )
& ( isCountable0 @ B ) )
=> ! [C: $i] :
( ( ( aSet0 @ C )
& ( ( ( ! [D: $i] :
( ( aElementOf0 @ D @ C )
=> ( aElementOf0 @ D @ B ) )
| ( aSubsetOf0 @ C @ B ) )
& ( ( sbrdtbr0 @ C )
= xk ) )
| ( aElementOf0 @ C @ ( slbdtsldtrb0 @ B @ xk ) ) ) )
=> ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [D: $i] :
( ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ D ) )
& ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( ( aElement0 @ D )
& ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
& ( D
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( ( ( aElement0 @ D )
& ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
& ( D
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
=> ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSubsetOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(114,axiom,
( ( aFunction0 @ xd )
& ( ( szDzozmdt0 @ xd )
= szNzAzT0 )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( ( ( ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) )
| ( aSubsetOf0 @ B @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) )
& ( ( sbrdtbr0 @ B )
= xk ) )
| ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) ) )
=> ( ( sdtlpdtrp0 @ xd @ A )
= ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4730) ).
thf(1068,plain,
( ( aFunction0 @ xd )
& ( ( szDzozmdt0 @ xd )
= szNzAzT0 )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( ( ( ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) )
| ( aSubsetOf0 @ B @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) )
& ( ( sbrdtbr0 @ B )
= xk ) )
| ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) ) )
=> ( ( sdtlpdtrp0 @ xd @ A )
= ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(93,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(878,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)],[93]) ).
thf(18,axiom,
! [A: $i] :
( ( ? [B: $i] :
( ( aElementOf0 @ B @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ B )
= A ) )
| ( aElementOf0 @ A @ xO ) )
=> ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( ( sdtlpdtrp0 @ xd @ B )
= ( szDzizrdt0 @ xd ) )
& ( aElementOf0 @ B @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4982) ).
thf(202,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( aElementOf0 @ B @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ B )
= A ) )
| ( aElementOf0 @ A @ xO ) )
=> ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( ( sdtlpdtrp0 @ xd @ B )
= ( szDzizrdt0 @ xd ) )
& ( aElementOf0 @ B @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(72,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ A ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
thf(730,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ A ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(21,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(217,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)],[21]) ).
thf(101,axiom,
( ( aSet0 @ ( sdtlcdtrc0 @ xd @ ( szDzozmdt0 @ xd ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xd @ ( szDzozmdt0 @ xd ) ) )
<=> ? [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ B )
= A ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xd @ ( szDzozmdt0 @ xd ) ) )
=> ( aElementOf0 @ A @ xT ) )
& ( aSubsetOf0 @ ( sdtlcdtrc0 @ xd @ ( szDzozmdt0 @ xd ) ) @ xT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4758) ).
thf(973,plain,
( ( aSet0 @ ( sdtlcdtrc0 @ xd @ ( szDzozmdt0 @ xd ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xd @ ( szDzozmdt0 @ xd ) ) )
=> ? [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ B )
= A ) ) )
& ( ? [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ B )
= A ) )
=> ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xd @ ( szDzozmdt0 @ xd ) ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xd @ ( szDzozmdt0 @ xd ) ) )
=> ( aElementOf0 @ A @ xT ) )
& ( aSubsetOf0 @ ( sdtlcdtrc0 @ xd @ ( szDzozmdt0 @ xd ) ) @ xT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(32,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessRefl) ).
thf(320,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(60,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(570,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)],[60]) ).
thf(64,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSegFin) ).
thf(587,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(68,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ( aSet0 @ ( szDzozmdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDomSet) ).
thf(702,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ( aSet0 @ ( szDzozmdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(83,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(802,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)],[83]) ).
thf(59,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ( aSet0 @ A )
& ~ ? [B: $i] : ( aElementOf0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
thf(559,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)],[59]) ).
thf(88,axiom,
( ( aElementOf0 @ xp @ xQ )
& ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( sdtlseqdt0 @ xp @ A ) )
& ( xp
= ( szmzizndt0 @ xQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
thf(853,plain,
( ( aElementOf0 @ xp @ xQ )
& ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( sdtlseqdt0 @ xp @ A ) )
& ( xp
= ( szmzizndt0 @ xQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(14,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubFSet) ).
thf(189,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ A )
=> ( isFinite0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(91,axiom,
( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( aElementOf0 @ A @ xD ) )
& ( aSubsetOf0 @ xP @ xD )
& ( aElementOf0 @ xP @ ( slbdtsldtrb0 @ xD @ xk ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5599) ).
thf(870,plain,
( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( aElementOf0 @ A @ xD ) )
& ( aSubsetOf0 @ xP @ xD )
& ( aElementOf0 @ xP @ ( slbdtsldtrb0 @ xD @ xk ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(94,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(881,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( A = sz00 )
| ? [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(34,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ A @ B ) @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgRng) ).
thf(325,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ A @ B ) @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(10,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(152,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,axiom,
aElementOf0 @ xP @ ( slbdtsldtrb0 @ xO @ xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5270) ).
thf(216,plain,
aElementOf0 @ xP @ ( slbdtsldtrb0 @ xO @ xk ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(78,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
thf(756,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElement0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(109,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(1040,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)],[109]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIHSort) ).
thf(253,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(9,axiom,
( ( aSet0 @ xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ xS )
=> ( aElementOf0 @ A @ szNzAzT0 ) )
& ( aSubsetOf0 @ xS @ szNzAzT0 )
& ( isCountable0 @ xS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
thf(147,plain,
( ( aSet0 @ xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ xS )
=> ( aElementOf0 @ A @ szNzAzT0 ) )
& ( aSubsetOf0 @ xS @ szNzAzT0 )
& ( isCountable0 @ xS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(73,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(734,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)],[73]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtlbdtrb0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPtt) ).
thf(527,plain,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aElement0 @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtlbdtrb0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) ) )
& ( ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) ) )
& ( ( ( aElementOf0 @ D @ ( szDzozmdt0 @ A ) )
& ( ( sdtlpdtrp0 @ A @ D )
= B ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtlbdtrb0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
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(307,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(50,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(439,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)],[50]) ).
thf(81,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(793,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)],[81]) ).
thf(22,axiom,
( ( aFunction0 @ xc )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xc ) )
=> ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xS ) )
& ( aSubsetOf0 @ A @ xS )
& ( ( sbrdtbr0 @ A )
= xK ) ) )
& ( ( ( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xS ) ) )
| ( aSubsetOf0 @ A @ xS ) )
& ( ( sbrdtbr0 @ A )
= xK ) )
=> ( aElementOf0 @ A @ ( szDzozmdt0 @ xc ) ) ) )
& ( ( szDzozmdt0 @ xc )
= ( slbdtsldtrb0 @ xS @ xK ) )
& ( aSet0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
<=> ? [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ xc ) )
& ( ( sdtlpdtrp0 @ xc @ B )
= A ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
=> ( aElementOf0 @ A @ xT ) )
& ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) @ xT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).
thf(220,plain,
( ( aFunction0 @ xc )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xc ) )
=> ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xS ) )
& ( aSubsetOf0 @ A @ xS )
& ( ( sbrdtbr0 @ A )
= xK ) ) )
& ( ( ( ( ( aSet0 @ A )
& ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( aElementOf0 @ B @ xS ) ) )
| ( aSubsetOf0 @ A @ xS ) )
& ( ( sbrdtbr0 @ A )
= xK ) )
=> ( aElementOf0 @ A @ ( szDzozmdt0 @ xc ) ) ) )
& ( ( szDzozmdt0 @ xc )
= ( slbdtsldtrb0 @ xS @ xK ) )
& ( aSet0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
=> ? [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ xc ) )
& ( ( sdtlpdtrp0 @ xc @ B )
= A ) ) )
& ( ? [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ xc ) )
& ( ( sdtlpdtrp0 @ xc @ B )
= A ) )
=> ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) )
=> ( aElementOf0 @ A @ xT ) )
& ( aSubsetOf0 @ ( sdtlcdtrc0 @ xc @ ( szDzozmdt0 @ xc ) ) @ xT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(70,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
thf(714,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ( A != slcrc0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(54,axiom,
aElementOf0 @ xK @ szNzAzT0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3418) ).
thf(467,plain,
aElementOf0 @ xK @ szNzAzT0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(86,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( A
!= ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatNSucc) ).
thf(847,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( A
!= ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(107,axiom,
( ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ xS ) )
& ( aSubsetOf0 @ xQ @ xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ xS ) )
& ( aSubsetOf0 @ xQ @ xS )
& ( aElementOf0 @ xQ @ ( szDzozmdt0 @ xc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5116) ).
thf(1032,plain,
( ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ xS ) )
& ( aSubsetOf0 @ xQ @ xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ xS ) )
& ( aSubsetOf0 @ xQ @ xS )
& ( aElementOf0 @ xQ @ ( szDzozmdt0 @ xc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(16,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
thf(197,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(48,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCConsSet) ).
thf(435,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtpldt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(56,axiom,
( ( aFunction0 @ xe )
& ( ( szDzozmdt0 @ xe )
= szNzAzT0 )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aElementOf0 @ ( sdtlpdtrp0 @ xe @ A ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xe @ A ) @ B ) )
& ( ( sdtlpdtrp0 @ xe @ A )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
thf(519,plain,
( ( aFunction0 @ xe )
& ( ( szDzozmdt0 @ xe )
= szNzAzT0 )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aElementOf0 @ ( sdtlpdtrp0 @ xe @ A ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xe @ A ) @ B ) )
& ( ( sdtlpdtrp0 @ xe @ A )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(92,axiom,
( ( aElementOf0 @ xk @ szNzAzT0 )
& ( ( szszuzczcdt0 @ xk )
= xK ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
thf(874,plain,
( ( aElementOf0 @ xk @ szNzAzT0 )
& ( ( szszuzczcdt0 @ xk )
= xK ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(43,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(356,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)],[43]) ).
thf(90,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isCountable0 @ A )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCntRel) ).
thf(869,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(104,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aSet0 @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( aElementOf0 @ B @ szNzAzT0 ) )
& ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
thf(997,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aSet0 @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( aElementOf0 @ B @ szNzAzT0 ) )
& ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(102,axiom,
( ( sdtlpdtrp0 @ xd @ xn )
= ( szDzizrdt0 @ xd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5321) ).
thf(985,plain,
( ( sdtlpdtrp0 @ xd @ xn )
= ( szDzizrdt0 @ xd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(67,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSetSort) ).
thf(701,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(105,axiom,
( ( aFunction0 @ xN )
& ( ( szDzozmdt0 @ xN )
= szNzAzT0 )
& ( ( sdtlpdtrp0 @ xN @ sz00 )
= xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( ( ( ( aSet0 @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( aElementOf0 @ B @ szNzAzT0 ) ) )
| ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 ) )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
=> ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ B ) )
& ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
<=> ( ( aElement0 @ B )
& ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
& ( B
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSet0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) )
=> ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
thf(1002,plain,
( ( aFunction0 @ xN )
& ( ( szDzozmdt0 @ xN )
= szNzAzT0 )
& ( ( sdtlpdtrp0 @ xN @ sz00 )
= xS )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( ( ( ( aSet0 @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( aElementOf0 @ B @ szNzAzT0 ) ) )
| ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ szNzAzT0 ) )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ A ) ) )
=> ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ B ) )
& ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [B: $i] :
( ( ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( ( aElement0 @ B )
& ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
& ( B
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( ( ( aElement0 @ B )
& ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
& ( B
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
& ( aSet0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) )
=> ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( isCountable0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(3,axiom,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSegZero) ).
thf(134,plain,
( ( slbdtrb0 @ sz00 )
= slcrc0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(71,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aSet0 @ ( sdtlcdtrc0 @ ( sdtlpdtrp0 @ xC @ A ) @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlcdtrc0 @ ( sdtlpdtrp0 @ xC @ A ) @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) )
<=> ? [C: $i] :
( ( aElementOf0 @ C @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) )
& ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ C )
= B ) ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlcdtrc0 @ ( sdtlpdtrp0 @ xC @ A ) @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) )
=> ( aElementOf0 @ B @ xT ) )
& ( aSubsetOf0 @ ( sdtlcdtrc0 @ ( sdtlpdtrp0 @ xC @ A ) @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) @ xT ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4182) ).
thf(718,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aSet0 @ ( sdtlcdtrc0 @ ( sdtlpdtrp0 @ xC @ A ) @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) )
& ! [B: $i] :
( ( ( aElementOf0 @ B @ ( sdtlcdtrc0 @ ( sdtlpdtrp0 @ xC @ A ) @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) )
=> ? [C: $i] :
( ( aElementOf0 @ C @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) )
& ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ C )
= B ) ) )
& ( ? [C: $i] :
( ( aElementOf0 @ C @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) )
& ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ C )
= B ) )
=> ( aElementOf0 @ B @ ( sdtlcdtrc0 @ ( sdtlpdtrp0 @ xC @ A ) @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) ) ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlcdtrc0 @ ( sdtlpdtrp0 @ xC @ A ) @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) )
=> ( aElementOf0 @ B @ xT ) )
& ( aSubsetOf0 @ ( sdtlcdtrc0 @ ( sdtlpdtrp0 @ xC @ A ) @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) @ xT ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(15,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( sbrdtbr0 @ A )
= sz00 )
<=> ( A = slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
thf(191,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( ( ( sbrdtbr0 @ A )
= sz00 )
=> ( A = slcrc0 ) )
& ( ( A = slcrc0 )
=> ( ( sbrdtbr0 @ A )
= sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(63,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(579,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)],[63]) ).
thf(1,conjecture,
( ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xn ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) @ A ) )
=> ( ( ( aSet0 @ ( sdtpldt0 @ xP @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtpldt0 @ xP @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) )
<=> ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ xP )
| ( A
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) ) ) ) )
=> ( ( sdtlpdtrp0 @ xc @ ( sdtpldt0 @ xP @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) )
= ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ xn ) @ xP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xn ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) @ A ) )
=> ( ( ( aSet0 @ ( sdtpldt0 @ xP @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtpldt0 @ xP @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) )
<=> ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ xP )
| ( A
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) ) ) ) )
=> ( ( sdtlpdtrp0 @ xc @ ( sdtpldt0 @ xP @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) )
= ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ xn ) @ xP ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(118,plain,
~ ( ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xn ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) @ A ) )
=> ( ( ( aSet0 @ ( sdtpldt0 @ xP @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtpldt0 @ xP @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) )
=> ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ xP )
| ( A
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) ) ) )
& ( ( ( aElement0 @ A )
& ( ( aElementOf0 @ A @ xP )
| ( A
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) ) )
=> ( aElementOf0 @ A @ ( sdtpldt0 @ xP @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) ) ) ) )
=> ( ( sdtlpdtrp0 @ xc @ ( sdtpldt0 @ xP @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) )
= ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ xn ) @ xP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,axiom,
( ( aSet0 @ xT )
& ( isFinite0 @ xT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).
thf(391,plain,
( ( aSet0 @ xT )
& ( isFinite0 @ xT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
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(313,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(8,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i,C: $i] :
( ( ( aSet0 @ B )
& ( aSet0 @ C )
& ( A != sz00 ) )
=> ( ( ( aSubsetOf0 @ ( slbdtsldtrb0 @ B @ A ) @ ( slbdtsldtrb0 @ C @ A ) )
& ( ( slbdtsldtrb0 @ B @ A )
!= slcrc0 ) )
=> ( aSubsetOf0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSelSub) ).
thf(144,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i,C: $i] :
( ( ( aSet0 @ B )
& ( aSet0 @ C )
& ( A != sz00 ) )
=> ( ( ( aSubsetOf0 @ ( slbdtsldtrb0 @ B @ A ) @ ( slbdtsldtrb0 @ C @ A ) )
& ( ( slbdtsldtrb0 @ B @ A )
!= slcrc0 ) )
=> ( aSubsetOf0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(38,axiom,
aElementOf0 @ sz00 @ szNzAzT0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
thf(335,plain,
aElementOf0 @ sz00 @ szNzAzT0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(69,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ? [B: $i] :
( ( aElementOf0 @ B @ xT )
& ! [C: $i] :
( ( ( aSet0 @ C )
& ( ( ( ! [D: $i] :
( ( aElementOf0 @ D @ C )
=> ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) )
| ( aSubsetOf0 @ C @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) )
& ( ( sbrdtbr0 @ C )
= xk ) )
| ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) ) )
=> ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4618) ).
thf(704,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ? [B: $i] :
( ( aElementOf0 @ B @ xT )
& ! [C: $i] :
( ( ( aSet0 @ C )
& ( ( ( ! [D: $i] :
( ( aElementOf0 @ D @ C )
=> ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) )
| ( aSubsetOf0 @ C @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) ) )
& ( ( sbrdtbr0 @ C )
= xk ) )
| ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ A ) ) @ xk ) ) ) )
=> ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(66,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ! [C: $i] :
( ( C
= ( sdtlcdtrc0 @ A @ B ) )
<=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( aElementOf0 @ D @ C )
<=> ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSImg) ).
thf(672,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ! [C: $i] :
( ( ( C
= ( sdtlcdtrc0 @ A @ B ) )
=> ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) ) )
& ( ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) )
=> ( aElementOf0 @ D @ C ) ) ) ) )
& ( ( ( aSet0 @ C )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ C )
=> ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) ) )
& ( ? [E: $i] :
( ( aElementOf0 @ E @ B )
& ( ( sdtlpdtrp0 @ A @ E )
= D ) )
=> ( aElementOf0 @ D @ C ) ) ) )
=> ( C
= ( sdtlcdtrc0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(84,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessSucc) ).
thf(831,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( sdtlseqdt0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(74,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFDiffSet) ).
thf(737,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtmndt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(110,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(1043,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)],[110]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ! [C: $i] :
( ( ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ A @ B ) )
& ( isFinite0 @ C ) )
=> ? [D: $i] :
( ( aSubsetOf0 @ D @ A )
& ( isFinite0 @ D )
& ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSelExtra) ).
thf(1080,plain,
! [A: $i,B: $i] :
( ( ( aSet0 @ A )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ! [C: $i] :
( ( ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ A @ B ) )
& ( isFinite0 @ C ) )
=> ? [D: $i] :
( ( aSubsetOf0 @ D @ A )
& ( isFinite0 @ D )
& ( aSubsetOf0 @ C @ ( slbdtsldtrb0 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(79,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(758,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 )
& ( A != B ) )
=> ~ ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) ) )
=> ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ B ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ B ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) ) )
| ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3821) ).
thf(858,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 )
& ( A != B ) )
=> ~ ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) ) )
=> ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ B ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ B ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) ) )
| ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(6,axiom,
xK != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
thf(140,plain,
xK != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ B @ A )
=> ( ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ B ) ) )
& ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( sdtlpdtrp0 @ xN @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
thf(213,plain,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ B @ A )
=> ( ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ B ) ) )
& ( aSubsetOf0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( sdtlpdtrp0 @ xN @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aElement0 @ B ) )
=> ( aSubsetOf0 @ ( sdtlbdtrb0 @ A @ B ) @ ( szDzozmdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPttSet) ).
thf(251,plain,
! [A: $i,B: $i] :
( ( ( aFunction0 @ A )
& ( aElement0 @ B ) )
=> ( aSubsetOf0 @ ( sdtlbdtrb0 @ A @ B ) @ ( szDzozmdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(98,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( aElementOf0 @ ( sbrdtbr0 @ A ) @ szNzAzT0 )
<=> ( isFinite0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
thf(964,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)],[98]) ).
thf(36,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(330,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)],[36]) ).
thf(52,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(462,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)],[52]) ).
thf(112,axiom,
( ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ xO ) )
& ~ ( ~ ? [A: $i] : ( aElementOf0 @ A @ xQ )
| ( xQ = slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
thf(1061,plain,
( ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ xO ) )
& ~ ( ~ ? [A: $i] : ( aElementOf0 @ A @ xQ )
| ( xQ = slcrc0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(113,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
thf(1066,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( aSubsetOf0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(45,axiom,
( ( aSet0 @ xP )
& ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ xQ ) @ A ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ xP )
<=> ( ( aElement0 @ A )
& ( aElementOf0 @ A @ xQ )
& ( A
!= ( szmzizndt0 @ xQ ) ) ) )
& ( xP
= ( sdtmndt0 @ xQ @ ( szmzizndt0 @ xQ ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
thf(394,plain,
( ( aSet0 @ xP )
& ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ xQ ) @ A ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ xP )
=> ( ( aElement0 @ A )
& ( aElementOf0 @ A @ xQ )
& ( A
!= ( szmzizndt0 @ xQ ) ) ) )
& ( ( ( aElement0 @ A )
& ( aElementOf0 @ A @ xQ )
& ( A
!= ( szmzizndt0 @ xQ ) ) )
=> ( aElementOf0 @ A @ xP ) ) )
& ( xP
= ( sdtmndt0 @ xQ @ ( szmzizndt0 @ xQ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(97,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) ) )
=> ( ( ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
<=> ( ( aElement0 @ C )
& ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
& ( C
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
=> ( ( ( ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
| ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( ( sbrdtbr0 @ B )
= xk ) )
| ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) ) ) ) )
=> ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) )
& ( aSet0 @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
<=> ( ( aElement0 @ C )
& ( ( aElementOf0 @ C @ B )
| ( C
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( aElementOf0 @ C @ xS ) )
& ( aSubsetOf0 @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xS )
& ( ( sbrdtbr0 @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
= xK )
& ( aElementOf0 @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ ( slbdtsldtrb0 @ xS @ xK ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3965) ).
thf(922,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) ) )
=> ( ( ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( ( aElement0 @ C )
& ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
& ( C
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( ( ( aElement0 @ C )
& ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
& ( C
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) ) )
=> ( ( ( ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
| ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( ( sbrdtbr0 @ B )
= xk ) )
| ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) ) ) ) )
=> ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) )
& ( aSet0 @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( ( aElement0 @ C )
& ( ( aElementOf0 @ C @ B )
| ( C
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
& ( ( ( aElement0 @ C )
& ( ( aElementOf0 @ C @ B )
| ( C
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
=> ( aElementOf0 @ C @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( aElementOf0 @ C @ xS ) )
& ( aSubsetOf0 @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xS )
& ( ( sbrdtbr0 @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
= xK )
& ( aElementOf0 @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ ( slbdtsldtrb0 @ xS @ xK ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(65,axiom,
( ( aFunction0 @ xC )
& ( ( szDzozmdt0 @ xC )
= szNzAzT0 )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aFunction0 @ ( sdtlpdtrp0 @ xC @ A ) )
& ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ B ) )
& ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
<=> ( ( aElement0 @ B )
& ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
& ( B
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ! [B: $i] :
( ( ( aElementOf0 @ B @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) )
=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( ( sbrdtbr0 @ B )
= xk ) ) )
& ( ( ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
| ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( ( sbrdtbr0 @ B )
= xk ) )
=> ( aElementOf0 @ B @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) ) )
& ( ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) )
= ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) )
& ! [B: $i] :
( ( ( aSet0 @ B )
& ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) ) )
=> ( ( ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
<=> ( ( aElement0 @ C )
& ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
& ( C
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
=> ( ( ( ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
| ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( ( sbrdtbr0 @ B )
= xk ) )
| ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) ) ) ) )
=> ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
<=> ( ( aElement0 @ C )
& ( ( aElementOf0 @ C @ B )
| ( C
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
& ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B )
= ( sdtlpdtrp0 @ xc @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4151) ).
thf(589,plain,
( ( aFunction0 @ xC )
& ( ( szDzozmdt0 @ xC )
= szNzAzT0 )
& ! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ( ( aFunction0 @ ( sdtlpdtrp0 @ xC @ A ) )
& ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [B: $i] :
( ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ B ) )
& ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [B: $i] :
( ( ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( ( aElement0 @ B )
& ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
& ( B
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( ( ( aElement0 @ B )
& ( aElementOf0 @ B @ ( sdtlpdtrp0 @ xN @ A ) )
& ( B
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( aElementOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
& ! [B: $i] :
( ( ( aElementOf0 @ B @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) )
=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ( ( sbrdtbr0 @ B )
= xk ) ) )
& ( ( ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
| ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( ( sbrdtbr0 @ B )
= xk ) )
=> ( aElementOf0 @ B @ ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) ) ) ) )
& ( ( szDzozmdt0 @ ( sdtlpdtrp0 @ xC @ A ) )
= ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) )
& ! [B: $i] :
( ( ( aSet0 @ B )
& ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) ) )
=> ( ( ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( ( aElement0 @ C )
& ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
& ( C
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( ( ( aElement0 @ C )
& ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
& ( C
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) ) )
=> ( ( ( ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
| ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
& ( ( sbrdtbr0 @ B )
= xk ) )
| ( aElementOf0 @ B @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) ) ) ) )
=> ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
& ! [C: $i] :
( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
=> ( ( aElement0 @ C )
& ( ( aElementOf0 @ C @ B )
| ( C
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
& ( ( ( aElement0 @ C )
& ( ( aElementOf0 @ C @ B )
| ( C
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
=> ( aElementOf0 @ C @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
& ( ( sdtlpdtrp0 @ ( sdtlpdtrp0 @ xC @ A ) @ B )
= ( sdtlpdtrp0 @ xc @ ( sdtpldt0 @ B @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(42,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSort) ).
thf(355,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(96,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(887,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)],[96]) ).
thf(100,axiom,
( ( sbrdtbr0 @ xP )
= xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5217) ).
thf(971,plain,
( ( sbrdtbr0 @ xP )
= xk ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(35,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(327,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)],[35]) ).
thf(75,axiom,
( ( aSet0 @ xQ )
& ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ xO ) )
& ( aSubsetOf0 @ xQ @ xO )
& ( ( sbrdtbr0 @ xQ )
= xK )
& ( aElementOf0 @ xQ @ ( slbdtsldtrb0 @ xO @ xK ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5078) ).
thf(739,plain,
( ( aSet0 @ xQ )
& ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ xO ) )
& ( aSubsetOf0 @ xQ @ xO )
& ( ( sbrdtbr0 @ xQ )
= xK )
& ( aElementOf0 @ xQ @ ( slbdtsldtrb0 @ xO @ xK ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(28,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ( ( ( isCountable0 @ ( szDzozmdt0 @ A ) )
& ( isFinite0 @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) )
=> ( ( aElement0 @ ( szDzizrdt0 @ A ) )
& ( isCountable0 @ ( sdtlbdtrb0 @ A @ ( szDzizrdt0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDirichlet) ).
thf(310,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ( ( ( isCountable0 @ ( szDzozmdt0 @ A ) )
& ( isFinite0 @ ( sdtlcdtrc0 @ A @ ( szDzozmdt0 @ A ) ) ) )
=> ( ( aElement0 @ ( szDzizrdt0 @ A ) )
& ( isCountable0 @ ( sdtlbdtrb0 @ A @ ( szDzizrdt0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(17,axiom,
( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ xn ) ) ) )
& ( aSubsetOf0 @ xP @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ xn ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5334) ).
thf(199,plain,
( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ xn ) ) ) )
& ( aSubsetOf0 @ xP @ ( sdtlpdtrp0 @ xN @ ( szszuzczcdt0 @ xn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(108,axiom,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
thf(1038,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ( isCountable0 @ A ) )
=> ~ ( isFinite0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(40,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(338,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ A )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ A @ B ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(117,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNoScLessZr) ).
thf(1085,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ A ) @ sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(62,axiom,
( ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ szNzAzT0 ) )
& ( aSubsetOf0 @ xQ @ szNzAzT0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5106) ).
thf(576,plain,
( ! [A: $i] :
( ( aElementOf0 @ A @ xQ )
=> ( aElementOf0 @ A @ szNzAzT0 ) )
& ( aSubsetOf0 @ xQ @ szNzAzT0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(39,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFConsSet) ).
thf(336,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isFinite0 @ B ) )
=> ( isFinite0 @ ( sdtpldt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(11,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( B
= ( slbdtrb0 @ A ) )
<=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
<=> ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSeg) ).
thf(154,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( B
= ( slbdtrb0 @ A ) )
=> ( ( aSet0 @ B )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ B )
=> ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) )
& ( ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) )
=> ( aElementOf0 @ C @ B ) ) ) ) )
& ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( ( aElementOf0 @ C @ B )
=> ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) ) )
& ( ( ( aElementOf0 @ C @ szNzAzT0 )
& ( sdtlseqdt0 @ ( szszuzczcdt0 @ C ) @ A ) )
=> ( aElementOf0 @ C @ B ) ) ) )
=> ( B
= ( slbdtrb0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(7,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFunSort) ).
thf(143,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( ( aElementOf0 @ A @ szNzAzT0 )
& ( aElementOf0 @ B @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessRel) ).
thf(1084,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(58,axiom,
( ( aSet0 @ szNzAzT0 )
& ( isCountable0 @ szNzAzT0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
thf(556,plain,
( ( aSet0 @ szNzAzT0 )
& ( isCountable0 @ szNzAzT0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(31,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( ( isFinite0 @ A )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFinRel) ).
thf(319,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
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(304,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(13,axiom,
( ! [A: $i] :
( ( aElementOf0 @ A @ xO )
=> ( aElementOf0 @ A @ xS ) )
& ( aSubsetOf0 @ xO @ xS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4998) ).
thf(186,plain,
( ! [A: $i] :
( ( aElementOf0 @ A @ xO )
=> ( aElementOf0 @ A @ xS ) )
& ( aSubsetOf0 @ xO @ xS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
isFinite0 @ slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEmpFin) ).
thf(139,plain,
isFinite0 @ slcrc0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(106,axiom,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCDiffSet) ).
thf(1030,plain,
! [A: $i] :
( ( aElement0 @ A )
=> ! [B: $i] :
( ( ( aSet0 @ B )
& ( isCountable0 @ B ) )
=> ( isCountable0 @ ( sdtmndt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(111,axiom,
( ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xn ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) @ A ) )
& ( aSet0 @ xD )
& ! [A: $i] :
( ( aElementOf0 @ A @ xD )
<=> ( ( aElement0 @ A )
& ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xn ) )
& ( A
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) ) )
& ( xD
= ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xn ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5585) ).
thf(1045,plain,
( ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xn ) )
=> ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) @ A ) )
& ( aSet0 @ xD )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ xD )
=> ( ( aElement0 @ A )
& ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xn ) )
& ( A
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) ) )
& ( ( ( aElement0 @ A )
& ( aElementOf0 @ A @ ( sdtlpdtrp0 @ xN @ xn ) )
& ( A
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) )
=> ( aElementOf0 @ A @ xD ) ) )
& ( xD
= ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ xn ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ xn ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(82,axiom,
! [A: $i] :
( ( aSet0 @ A )
=> ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardS) ).
thf(800,plain,
! [A: $i] :
( ( aSet0 @ A )
=> ( aElement0 @ ( sbrdtbr0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
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(315,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(12,axiom,
( ( aSet0 @ xO )
& ( isCountable0 @ xO ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4908) ).
thf(183,plain,
( ( aSet0 @ xO )
& ( isCountable0 @ xO ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(85,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(833,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)],[85]) ).
thf(46,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ! [C: $i] :
( ( C
= ( sdtexdt0 @ A @ B ) )
<=> ( ( aFunction0 @ C )
& ( ( szDzozmdt0 @ C )
= B )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( ( sdtlpdtrp0 @ C @ D )
= ( sdtlpdtrp0 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefRst) ).
thf(410,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aSubsetOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ! [C: $i] :
( ( ( C
= ( sdtexdt0 @ A @ B ) )
=> ( ( aFunction0 @ C )
& ( ( szDzozmdt0 @ C )
= B )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( ( sdtlpdtrp0 @ C @ D )
= ( sdtlpdtrp0 @ A @ D ) ) ) ) )
& ( ( ( aFunction0 @ C )
& ( ( szDzozmdt0 @ C )
= B )
& ! [D: $i] :
( ( aElementOf0 @ D @ B )
=> ( ( sdtlpdtrp0 @ C @ D )
= ( sdtlpdtrp0 @ A @ D ) ) ) )
=> ( C
= ( sdtexdt0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(99,axiom,
? [A: $i] :
( ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ A )
= xp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5182) ).
thf(967,plain,
? [A: $i] :
( ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ A )
= xp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(4,axiom,
xK != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3520) ).
thf(136,plain,
xK != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(41,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(341,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)],[41]) ).
thf(49,axiom,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElement0 @ ( sdtlpdtrp0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgElm) ).
thf(437,plain,
! [A: $i] :
( ( aFunction0 @ A )
=> ! [B: $i] :
( ( aElementOf0 @ B @ ( szDzozmdt0 @ A ) )
=> ( aElement0 @ ( sdtlpdtrp0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(95,axiom,
aElementOf0 @ xp @ xQ,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).
thf(886,plain,
aElementOf0 @ xp @ xQ,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(103,axiom,
( ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT )
& ( aSet0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
<=> ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ A )
= ( szDzizrdt0 @ xd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4854) ).
thf(987,plain,
( ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT )
& ( aSet0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
=> ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ A )
= ( szDzizrdt0 @ xd ) ) ) )
& ( ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ A )
= ( szDzizrdt0 @ xd ) ) )
=> ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(53,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(464,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)],[53]) ).
thf(47,axiom,
( ( aElementOf0 @ xn @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ xn )
= ( szDzizrdt0 @ xd ) )
& ( aElementOf0 @ xn @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( aElementOf0 @ xn @ szNzAzT0 )
& ( ( sdtlpdtrp0 @ xe @ xn )
= xp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
thf(427,plain,
( ( aElementOf0 @ xn @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ xn )
= ( szDzizrdt0 @ xd ) )
& ( aElementOf0 @ xn @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( aElementOf0 @ xn @ szNzAzT0 )
& ( ( sdtlpdtrp0 @ xe @ xn )
= xp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(87,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(850,plain,
! [A: $i] :
( ( ( aSet0 @ A )
& ~ ( isFinite0 @ A ) )
=> ! [B: $i] :
( ( aElementOf0 @ B @ szNzAzT0 )
=> ( ( slbdtsldtrb0 @ A @ B )
!= slcrc0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(51,axiom,
( ( aSet0 @ xO )
& ( aSet0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
<=> ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ A )
= ( szDzizrdt0 @ xd ) ) ) )
& ! [A: $i] :
( ( aElementOf0 @ A @ xO )
<=> ? [B: $i] :
( ( aElementOf0 @ B @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ B )
= A ) ) )
& ( xO
= ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
thf(442,plain,
( ( aSet0 @ xO )
& ( aSet0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
=> ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ A )
= ( szDzizrdt0 @ xd ) ) ) )
& ( ( ( aElementOf0 @ A @ ( szDzozmdt0 @ xd ) )
& ( ( sdtlpdtrp0 @ xd @ A )
= ( szDzizrdt0 @ xd ) ) )
=> ( aElementOf0 @ A @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) )
& ! [A: $i] :
( ( ( aElementOf0 @ A @ xO )
=> ? [B: $i] :
( ( aElementOf0 @ B @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ B )
= A ) ) )
& ( ? [B: $i] :
( ( aElementOf0 @ B @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ B )
= A ) )
=> ( aElementOf0 @ A @ xO ) ) )
& ( xO
= ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(25,axiom,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ szNzAzT0 ) ) )
| ( aSubsetOf0 @ B @ szNzAzT0 ) )
& ( isCountable0 @ B ) )
=> ! [C: $i] :
( ( ( aFunction0 @ C )
& ( ! [D: $i] :
( ( ( aElementOf0 @ D @ ( szDzozmdt0 @ C ) )
=> ( ( ( ( aSet0 @ D )
& ! [E: $i] :
( ( aElementOf0 @ E @ D )
=> ( aElementOf0 @ E @ B ) ) )
| ( aSubsetOf0 @ D @ B ) )
& ( ( sbrdtbr0 @ D )
= A ) ) )
& ( ( ( aSet0 @ D )
& ! [E: $i] :
( ( aElementOf0 @ E @ D )
=> ( aElementOf0 @ E @ B ) )
& ( aSubsetOf0 @ D @ B )
& ( ( sbrdtbr0 @ D )
= A ) )
=> ( aElementOf0 @ D @ ( szDzozmdt0 @ C ) ) ) )
| ( ( szDzozmdt0 @ C )
= ( slbdtsldtrb0 @ B @ A ) ) )
& ( ( ( aSet0 @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) )
& ! [D: $i] :
( ( aElementOf0 @ D @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) )
<=> ? [E: $i] :
( ( aElementOf0 @ E @ ( szDzozmdt0 @ C ) )
& ( ( sdtlpdtrp0 @ C @ E )
= D ) ) ) )
=> ( ! [D: $i] :
( ( aElementOf0 @ D @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) )
=> ( aElementOf0 @ D @ xT ) )
| ( aSubsetOf0 @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) @ xT ) ) ) )
=> ( ( iLess0 @ A @ xK )
=> ? [D: $i] :
( ( aElementOf0 @ D @ xT )
& ? [E: $i] :
( ( aSet0 @ E )
& ! [F: $i] :
( ( aElementOf0 @ F @ E )
=> ( aElementOf0 @ F @ B ) )
& ( aSubsetOf0 @ E @ B )
& ( isCountable0 @ E )
& ! [F: $i] :
( ( ( ( ( ( aSet0 @ F )
& ! [G: $i] :
( ( aElementOf0 @ G @ F )
=> ( aElementOf0 @ G @ E ) ) )
| ( aSubsetOf0 @ F @ E ) )
& ( ( sbrdtbr0 @ F )
= A ) )
| ( aElementOf0 @ F @ ( slbdtsldtrb0 @ E @ A ) ) )
=> ( ( sdtlpdtrp0 @ C @ F )
= D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3398) ).
thf(254,plain,
! [A: $i] :
( ( aElementOf0 @ A @ szNzAzT0 )
=> ! [B: $i] :
( ( ( ( ( aSet0 @ B )
& ! [C: $i] :
( ( aElementOf0 @ C @ B )
=> ( aElementOf0 @ C @ szNzAzT0 ) ) )
| ( aSubsetOf0 @ B @ szNzAzT0 ) )
& ( isCountable0 @ B ) )
=> ! [C: $i] :
( ( ( aFunction0 @ C )
& ( ! [D: $i] :
( ( ( aElementOf0 @ D @ ( szDzozmdt0 @ C ) )
=> ( ( ( ( aSet0 @ D )
& ! [E: $i] :
( ( aElementOf0 @ E @ D )
=> ( aElementOf0 @ E @ B ) ) )
| ( aSubsetOf0 @ D @ B ) )
& ( ( sbrdtbr0 @ D )
= A ) ) )
& ( ( ( aSet0 @ D )
& ! [E: $i] :
( ( aElementOf0 @ E @ D )
=> ( aElementOf0 @ E @ B ) )
& ( aSubsetOf0 @ D @ B )
& ( ( sbrdtbr0 @ D )
= A ) )
=> ( aElementOf0 @ D @ ( szDzozmdt0 @ C ) ) ) )
| ( ( szDzozmdt0 @ C )
= ( slbdtsldtrb0 @ B @ A ) ) )
& ( ( ( aSet0 @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) )
& ! [D: $i] :
( ( ( aElementOf0 @ D @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) )
=> ? [E: $i] :
( ( aElementOf0 @ E @ ( szDzozmdt0 @ C ) )
& ( ( sdtlpdtrp0 @ C @ E )
= D ) ) )
& ( ? [E: $i] :
( ( aElementOf0 @ E @ ( szDzozmdt0 @ C ) )
& ( ( sdtlpdtrp0 @ C @ E )
= D ) )
=> ( aElementOf0 @ D @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) ) ) ) )
=> ( ! [D: $i] :
( ( aElementOf0 @ D @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) )
=> ( aElementOf0 @ D @ xT ) )
| ( aSubsetOf0 @ ( sdtlcdtrc0 @ C @ ( szDzozmdt0 @ C ) ) @ xT ) ) ) )
=> ( ( iLess0 @ A @ xK )
=> ? [D: $i] :
( ( aElementOf0 @ D @ xT )
& ? [E: $i] :
( ( aSet0 @ E )
& ! [F: $i] :
( ( aElementOf0 @ F @ E )
=> ( aElementOf0 @ F @ B ) )
& ( aSubsetOf0 @ E @ B )
& ( isCountable0 @ E )
& ! [F: $i] :
( ( ( ( ( ( aSet0 @ F )
& ! [G: $i] :
( ( aElementOf0 @ G @ F )
=> ( aElementOf0 @ G @ E ) ) )
| ( aSubsetOf0 @ F @ E ) )
& ( ( sbrdtbr0 @ F )
= A ) )
| ( aElementOf0 @ F @ ( slbdtsldtrb0 @ E @ A ) ) )
=> ( ( sdtlpdtrp0 @ C @ F )
= D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(33,axiom,
( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( aElementOf0 @ A @ xQ ) )
& ( aSubsetOf0 @ xP @ xQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5195) ).
thf(322,plain,
( ! [A: $i] :
( ( aElementOf0 @ A @ xP )
=> ( aElementOf0 @ A @ xQ ) )
& ( aSubsetOf0 @ xP @ xQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1144,plain,
$false,
inference(cvc4,[status(thm)],[746,753,573,760,333,468,1068,878,202,730,217,973,320,570,587,702,802,559,853,189,870,881,325,152,216,756,1040,253,147,734,527,307,439,793,220,714,467,847,1032,197,435,519,874,356,869,997,985,701,1002,134,718,191,579,118,391,313,144,335,704,672,831,737,1043,1080,758,858,140,213,251,964,330,462,1061,1066,394,922,589,355,887,971,327,739,310,199,1038,338,1085,576,336,154,143,1084,556,319,304,186,139,1030,1045,800,315,183,833,410,967,136,341,437,886,987,464,427,850,442,254,322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM630+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n011.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 17:02:19 EDT 2023
% 0.15/0.36 % CPUTime :
% 1.00/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.69/1.09 % [INFO] Parsing done (208ms).
% 1.69/1.10 % [INFO] Running in sequential loop mode.
% 2.11/1.30 % [INFO] eprover registered as external prover.
% 2.11/1.30 % [INFO] cvc4 registered as external prover.
% 2.31/1.30 % [INFO] Scanning for conjecture ...
% 2.31/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.49/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.49/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.49/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.49/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.49/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.49/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.49/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.49/1.43 % [INFO] Found a conjecture and 115 axioms. Running axiom selection ...
% 2.92/1.51 % [INFO] Axiom selection finished. Selected 115 axioms (removed 0 axioms).
% 2.92/1.52 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.55 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.56 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.56 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.57 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.57 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.57 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.58 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.59 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.59 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.60 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.11/1.61 % [INFO] Problem is first-order (TPTP FOF).
% 3.11/1.62 % [INFO] Type checking passed.
% 3.11/1.63 % [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 ...
% 9.53/3.18 % External prover 'cvc4' found a proof!
% 9.53/3.18 % [INFO] Killing All external provers ...
% 9.53/3.18 % Time passed: 2669ms (effective reasoning time: 2084ms)
% 9.53/3.18 % 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)>
% 9.53/3.19 % Axioms used in derivation (115): m__5585, mDefSel, mZeroNum, mSubASymm, m__5309, m__5208, mCardEmpty, m__3533, mImgRng, mSuccLess, mCountNFin, mSegLess, m__5195, m__4331, mCardSubEx, mDefEmp, m__3435, mFinSubSeg, m__4660, mIHSort, m__3965, m__5173, mDefSImg, m__4758, mDiffCons, m__4982, mSubRefl, mDefMin, mSubFSet, mEOfElem, m__3398, mDefDiff, mSelCSet, m__4182, m__3462, mSetSort, mCardS, mSegZero, mSuccEquSucc, m__4730, m__5599, m__3821, mFunSort, m__5116, m__5321, mSelNSet, mDomSet, mSegSucc, mLessSucc, mIH, m__5217, mFDiffSet, m__3754, mCDiffSet, mFinRel, m__5106, mSegFin, m__5078, mDefCons, m__5147, mNoScLessZr, m__4854, m__5164, mConsDiff, m__3520, m__4998, mLessRefl, mLessRel, mDefSeg, mCardSub, mCountNFin_01, m__4891, mCardNum, m__3291, mImgElm, mDefPtt, mImgCount, mLessASymm, mDirichlet, mMinMin, m__5182, m__4908, mSelFSet, mNatNSucc, mDefMax, m__3453, m__3671, mEmpFin, mLessTotal, mNATSet, mFConsSet, mElmSort, mCardDiff, mSelSub, m__5270, mZeroLess, m__5093, mPttSet, mDefSub, mLessTrans, mNatExtra, m__4411, mSuccNum, mSubTrans, m__4618, mCntRel, mSelExtra, m__3418, m__3623, m__4151, m__5334, mCardCons, mDefRst, mCConsSet, mCardSeg
% 9.53/3.19 % No. of inferences in proof: 234
% 9.53/3.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2669 ms resp. 2084 ms w/o parsing
% 10.45/3.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.45/3.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------