%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM612+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:35 AM UTC 2025
% Result : Theorem 1.94s 2.11s
% Output : Proof 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 50
% Syntax : Number of formulae : 148 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 793 ( 110 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1021 ( 416 ~; 381 |; 71 &)
% ( 116 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 40 ( 40 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 214 ( 202 !; 0 ?; 214 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(xP_type,type,
xP: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(xO_type,type,
xO: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xK_type,type,
xK: $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(1,plain,
( ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) )
<=> ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != szmzizndt0(xQ) ) ) )
& ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
tff(3,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = sbrdtbr0(xP),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
<=> aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0) ),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
<=> ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( aSet0(xQ)
<=> aSet0(xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO)
& ( sbrdtbr0(xQ) = xK )
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5078) ).
tff(12,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO)
& ( sbrdtbr0(xQ) = xK ) ),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO) ),
inference(and_elim,[status(thm)],[12]) ).
tff(14,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) ) ),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
aSet0(xQ),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
aSet0(xQ),
inference(modus_ponens,[status(thm)],[15,10]) ).
tff(17,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
^ [W0: $i] :
rewrite(( ( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
tff(23,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(xQ)
| ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) ),
inference(unit_resolution,[status(thm)],[29,26,16]) ).
tff(31,plain,
( ( sbrdtbr0(xQ) = xK )
<=> ( sbrdtbr0(xQ) = xK ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
sbrdtbr0(xQ) = xK,
inference(and_elim,[status(thm)],[12]) ).
tff(33,plain,
sbrdtbr0(xQ) = xK,
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> aElementOf0(xK,szNzAzT0) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( aElementOf0(xK,szNzAzT0)
<=> aElementOf0(sbrdtbr0(xQ),szNzAzT0) ),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( aElementOf0(xK,szNzAzT0)
<=> aElementOf0(xK,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3418) ).
tff(38,plain,
aElementOf0(xK,szNzAzT0),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
aElementOf0(sbrdtbr0(xQ),szNzAzT0),
inference(modus_ponens,[status(thm)],[38,35]) ).
tff(40,plain,
( ~ ( aElementOf0(sbrdtbr0(xQ),szNzAzT0)
<=> isFinite0(xQ) )
| ~ aElementOf0(sbrdtbr0(xQ),szNzAzT0)
| isFinite0(xQ) ),
inference(tautology,[status(thm)],[]) ).
tff(41,plain,
isFinite0(xQ),
inference(unit_resolution,[status(thm)],[40,39,30]) ).
tff(42,plain,
( ( xp = szmzizndt0(xQ) )
<=> ( xp = szmzizndt0(xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
( aElementOf0(xp,xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) )
& ( xp = szmzizndt0(xQ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
tff(44,plain,
xp = szmzizndt0(xQ),
inference(and_elim,[status(thm)],[43]) ).
tff(45,plain,
xp = szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[44,42]) ).
tff(46,plain,
szmzizndt0(xQ) = xp,
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( aElementOf0(szmzizndt0(xQ),xQ)
<=> aElementOf0(xp,xQ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( aElementOf0(xp,xQ)
<=> aElementOf0(szmzizndt0(xQ),xQ) ),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( aElementOf0(xp,xQ)
<=> aElementOf0(xp,xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( aElementOf0(xp,xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) ) ),
inference(and_elim,[status(thm)],[43]) ).
tff(51,plain,
aElementOf0(xp,xQ),
inference(and_elim,[status(thm)],[50]) ).
tff(52,plain,
aElementOf0(xp,xQ),
inference(modus_ponens,[status(thm)],[51,49]) ).
tff(53,plain,
aElementOf0(szmzizndt0(xQ),xQ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ) ),
inference(transitivity,[status(thm)],[57,55]) ).
tff(59,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) )
<=> ( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ))),
( ! [W1: $i] :
( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) )
<=> ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ) )),
rewrite(( ( aSet0(W0)
=> ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardDiff) ).
tff(65,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ ( isFinite0(W0)
& aElementOf0(W1,W0) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) ),
inference(modus_ponens,[status(thm)],[68,58]) ).
tff(70,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ( ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ) ) )
<=> ( ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ) ) ),
inference(transitivity,[status(thm)],[72,70]) ).
tff(74,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) )
| ~ isFinite0(W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) ),
inference(unit_resolution,[status(thm)],[75,69,16]) ).
tff(77,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ( ~ aElementOf0(szmzizndt0(xQ),xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) )
<=> ( ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ) ),
inference(transitivity,[status(thm)],[79,77]) ).
tff(81,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,W1))) = sbrdtbr0(xQ) ) )
| ~ isFinite0(xQ)
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( ~ isFinite0(xQ)
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ),
inference(unit_resolution,[status(thm)],[82,76,53]) ).
tff(84,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ),
inference(unit_resolution,[status(thm)],[83,41]) ).
tff(85,plain,
sbrdtbr0(xP) = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(symmetry,[status(thm)],[6]) ).
tff(86,plain,
szszuzczcdt0(sbrdtbr0(xP)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ),
inference(transitivity,[status(thm)],[86,84]) ).
tff(88,plain,
( ~ ~ ( ( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) )
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) )
<=> ( ( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) )
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(xP),szNzAzT0) )
<=> ~ ( ( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) )
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
( ~ ( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(xP),szNzAzT0) )
<=> ~ ~ ( ( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) )
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ~ ( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(xP),szNzAzT0) )
<=> ( ( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) )
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
( ~ ( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(xP),szNzAzT0) )
<=> ~ ( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,axiom,
~ ( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(94,plain,
~ ( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
( ( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) )
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(modus_ponens,[status(thm)],[94,91]) ).
tff(96,plain,
~ aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(unit_resolution,[status(thm)],[95,87]) ).
tff(97,plain,
~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0),
inference(modus_ponens,[status(thm)],[96,9]) ).
tff(98,plain,
( aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
<=> aSet0(xP) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(99,plain,
( aSet0(xP)
<=> aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( aSet0(xP)
<=> aSet0(xP) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != szmzizndt0(xQ) ) ) ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(102,plain,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(and_elim,[status(thm)],[101]) ).
tff(103,plain,
aSet0(xP),
inference(and_elim,[status(thm)],[102]) ).
tff(104,plain,
aSet0(xP),
inference(modus_ponens,[status(thm)],[103,100]) ).
tff(105,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[104,99]) ).
tff(106,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) )
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(unit_resolution,[status(thm)],[108,26]) ).
tff(110,plain,
( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(unit_resolution,[status(thm)],[109,105]) ).
tff(111,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
<=> aSubsetOf0(xP,xQ) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(112,plain,
( aSubsetOf0(xP,xQ)
<=> aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
( aSubsetOf0(xP,xQ)
<=> aSubsetOf0(xP,xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,axiom,
( ! [W0: $i] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xQ) )
& aSubsetOf0(xP,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5195) ).
tff(115,plain,
aSubsetOf0(xP,xQ),
inference(and_elim,[status(thm)],[114]) ).
tff(116,plain,
aSubsetOf0(xP,xQ),
inference(modus_ponens,[status(thm)],[115,113]) ).
tff(117,plain,
aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),
inference(modus_ponens,[status(thm)],[116,112]) ).
tff(118,plain,
^ [W0: $i] :
refl(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
^ [W0: $i] :
rewrite(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(121,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(transitivity,[status(thm)],[121,119]) ).
tff(123,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& isFinite0(W0) )
<=> ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ~ ( aSet0(W0)
& isFinite0(W0) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
rewrite(( ~ ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ~ ( aSet0(W0)
& isFinite0(W0) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
rewrite(( ( ~ aSet0(W0)
| ~ isFinite0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
( ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(124,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aSubsetOf0(W1,W0)
=> isFinite0(W1) )
<=> ( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ))),
( ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) )
<=> ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )),
( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) )
<=> ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
rewrite(( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
<=> ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) )
<=> ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubFSet) ).
tff(129,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[129,125]) ).
tff(131,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[130]) ).
tff(132,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[131,124]) ).
tff(133,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[132,122]) ).
tff(134,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) )
<=> ( ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ) ),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ) ),
inference(transitivity,[status(thm)],[136,134]) ).
tff(138,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
( ~ isFinite0(xQ)
| ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ) ),
inference(unit_resolution,[status(thm)],[139,133,16]) ).
tff(141,plain,
! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) ),
inference(unit_resolution,[status(thm)],[140,41]) ).
tff(142,plain,
( ( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) )
| isFinite0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) )
<=> ( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) )
| isFinite0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,plain,
( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) )
| isFinite0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(144,plain,
( ~ ! [W1: $i] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,xQ) )
| isFinite0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(unit_resolution,[status(thm)],[144,141,117]) ).
tff(146,plain,
( ~ ( aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
<=> isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) )
| aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0)
| ~ isFinite0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(tautology,[status(thm)],[]) ).
tff(147,plain,
aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szNzAzT0),
inference(unit_resolution,[status(thm)],[146,145,110]) ).
tff(148,plain,
$false,
inference(unit_resolution,[status(thm)],[147,97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM612+3 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 01:37:26 EDT 2025
% 0.11/0.32 % CPUTime :
% 1.94/2.11 % SZS status Theorem
% 1.94/2.11 % SZS output start Proof
% See solution above
% 1.95/2.13 % E exiting
%------------------------------------------------------------------------------