%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM623+1 : 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 05:21:37 AM UTC 2025
% Result : Theorem 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 58
% Syntax : Number of formulae : 148 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 1234 ( 200 equ)
% Maximal formula atoms : 36 ( 8 avg)
% Number of connectives : 1977 ( 961 ~; 710 |; 169 &)
% ( 108 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 70 ( 70 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 248 ( 229 !; 0 ?; 248 :)
% Comments :
%------------------------------------------------------------------------------
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xN_type,type,
xN: $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xQ_type,type,
xQ: $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xx_type,type,
xx: $i ).
tff(xp_type,type,
xp: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(xe_type,type,
xe: $i ).
tff(xO_type,type,
xO: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(1,plain,
( ( xx = szmzizndt0(sdtlpdtrp0(xN,xm)) )
<=> ( xx = szmzizndt0(sdtlpdtrp0(xN,xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5401) ).
tff(3,plain,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
szmzizndt0(sdtlpdtrp0(xN,xm)) = xx,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
<=> aElementOf0(xx,xQ) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( aElementOf0(xx,xQ)
<=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( aElementOf0(xx,xQ)
<=> aElementOf0(xx,xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
( aElementOf0(xp,sdtlpdtrp0(xN,xm))
& aElementOf0(xx,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5481) ).
tff(9,plain,
aElementOf0(xx,xQ),
inference(and_elim,[status(thm)],[8]) ).
tff(10,plain,
aElementOf0(xx,xQ),
inference(modus_ponens,[status(thm)],[9,7]) ).
tff(11,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
( ( xp = szmzizndt0(xQ) )
<=> ( xp = szmzizndt0(xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
tff(14,plain,
xp = szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
szmzizndt0(xQ) = xp,
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
<=> aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( aElementOf0(xp,sdtlpdtrp0(xN,xm))
<=> aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( aElementOf0(xp,sdtlpdtrp0(xN,xm))
<=> aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(and_elim,[status(thm)],[8]) ).
tff(20,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,plain,
( aElementOf0(xm,szNzAzT0)
<=> aElementOf0(xm,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
( aElementOf0(xm,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5389) ).
tff(24,plain,
aElementOf0(xm,szNzAzT0),
inference(and_elim,[status(thm)],[23]) ).
tff(25,plain,
aElementOf0(xm,szNzAzT0),
inference(modus_ponens,[status(thm)],[24,22]) ).
tff(26,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).
tff(34,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[37,27]) ).
tff(39,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ),
inference(unit_resolution,[status(thm)],[41,38,25]) ).
tff(43,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(tautology,[status(thm)],[]) ).
tff(44,plain,
aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
( ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) )
<=> ( xp = xx ) ),
inference(monotonicity,[status(thm)],[15,4]) ).
tff(46,plain,
( ( xp = xx )
<=> ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) ) ),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( ( xp != xx )
<=> ( szmzizndt0(xQ) != szmzizndt0(sdtlpdtrp0(xN,xm)) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( xp != xx )
<=> ( xp != xx ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
xp != xx,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(50,plain,
xp != xx,
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
szmzizndt0(xQ) != szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[50,47]) ).
tff(52,plain,
( aSubsetOf0(xQ,szNzAzT0)
<=> aSubsetOf0(xQ,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).
tff(54,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ( xQ != slcrc0 )
<=> ( xQ != slcrc0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
( aSubsetOf0(xQ,xO)
& ( xQ != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).
tff(57,plain,
xQ != slcrc0,
inference(and_elim,[status(thm)],[56]) ).
tff(58,plain,
xQ != slcrc0,
inference(modus_ponens,[status(thm)],[57,55]) ).
tff(59,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) )
<=> ( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [W0: $i,W1: $i] :
( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) )
<=> ! [W0: $i,W1: $i] :
( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
<=> ~ ( ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0) ) )),
( ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
<=> ~ ~ ( ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0) ) )),
rewrite(( ~ ~ ( ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0) )
<=> ( ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0) ) )),
( ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
<=> ( ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0) ) )),
trans(monotonicity(rewrite(( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
<=> ~ ( ( W1 = slcrc0 )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aSubsetOf0(W0,szNzAzT0) ) )),
( ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
<=> ~ ~ ( ( W1 = slcrc0 )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aSubsetOf0(W0,szNzAzT0) ) )),
rewrite(( ~ ~ ( ( W1 = slcrc0 )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aSubsetOf0(W0,szNzAzT0) )
<=> ( ( W1 = slcrc0 )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aSubsetOf0(W0,szNzAzT0) ) )),
( ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
<=> ( ( W1 = slcrc0 )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aSubsetOf0(W0,szNzAzT0) ) )),
( ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) )
<=> ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ( W1 = slcrc0 )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aSubsetOf0(W0,szNzAzT0) ) )),
rewrite(( ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ( W1 = slcrc0 )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aSubsetOf0(W0,szNzAzT0) )
<=> ( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) ) )),
( ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) )
<=> ( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 ) )
<=> ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 ) ) )),
( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
<=> ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) )),
rewrite(( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
<=> ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) )),
( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
<=> ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) )),
rewrite(( ( ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
=> ( szmzizndt0(W0) = szmzizndt0(W1) ) )
<=> ( ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ( szmzizndt0(W0) = szmzizndt0(W1) ) ) )),
( ( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
=> ( szmzizndt0(W0) = szmzizndt0(W1) ) ) )
<=> ( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ( szmzizndt0(W0) = szmzizndt0(W1) ) ) ) )),
rewrite(( ( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ( szmzizndt0(W0) = szmzizndt0(W1) ) ) )
<=> ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) ) )),
( ( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
=> ( szmzizndt0(W0) = szmzizndt0(W1) ) ) )
<=> ( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [W0: $i,W1: $i] :
( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
=> ( szmzizndt0(W0) = szmzizndt0(W1) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,axiom,
! [W0: $i,W1: $i] :
( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
=> ( szmzizndt0(W0) = szmzizndt0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMinMin) ).
tff(67,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(W0) = szmzizndt0(W1) )
| ~ ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
| ~ ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) ) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [W0: $i,W1: $i] :
( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
! [W0: $i,W1: $i] :
( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[70,60]) ).
tff(72,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) )
| ( xQ = slcrc0 )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) )
| ( xQ = slcrc0 )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) )
| ( xQ = slcrc0 )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
| ~ aSubsetOf0(xQ,szNzAzT0) )
<=> ( ( xQ = slcrc0 )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) )
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) )
| ( xQ = slcrc0 )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
| ~ aSubsetOf0(xQ,szNzAzT0) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) )
| ( xQ = slcrc0 )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) )
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) )
| ( xQ = slcrc0 )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
| ~ aSubsetOf0(xQ,szNzAzT0) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) )
| ( xQ = slcrc0 )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) )
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) )
| ( xQ = slcrc0 )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ)
| ~ aSubsetOf0(xQ,szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W1 = slcrc0 )
| ( szmzizndt0(W0) = szmzizndt0(W1) )
| ( W0 = slcrc0 )
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aSubsetOf0(W0,szNzAzT0) )
| ( xQ = slcrc0 )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ) ),
inference(unit_resolution,[status(thm)],[77,71,58,54]) ).
tff(79,plain,
sdtlpdtrp0(xN,xm) = slcrc0,
inference(unit_resolution,[status(thm)],[78,51,44,21,11]) ).
tff(80,plain,
( isFinite0(sdtlpdtrp0(xN,xm))
<=> isFinite0(slcrc0) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( isFinite0(slcrc0)
<=> isFinite0(sdtlpdtrp0(xN,xm)) ),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
( isFinite0(slcrc0)
<=> isFinite0(slcrc0) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
tff(84,plain,
isFinite0(slcrc0),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
isFinite0(sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[84,81]) ).
tff(86,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
tff(88,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[87]) ).
tff(89,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[88,86]) ).
tff(90,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(91,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(transitivity,[status(thm)],[95,93]) ).
tff(97,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(98,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ))),
( ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
rewrite(( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(103,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
tff(105,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[107,100]) ).
tff(109,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[108,98]) ).
tff(110,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[109,96]) ).
tff(111,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[110,91]) ).
tff(112,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ),
inference(unit_resolution,[status(thm)],[114,111,89]) ).
tff(116,plain,
( ~ ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szNzAzT0),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
~ ( ~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szNzAzT0),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szNzAzT0) ) ) ) ),
inference(unit_resolution,[status(thm)],[116,115]) ).
tff(118,plain,
( ~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szNzAzT0),sdtlpdtrp0(xN,xm))
| aElementOf0(tptp_fun_W2_1(sdtlpdtrp0(xN,xm),szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(119,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[118,117]) ).
tff(120,plain,
( ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(121,plain,
( ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[120,44]) ).
tff(122,plain,
~ ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szNzAzT0) ) ),
inference(unit_resolution,[status(thm)],[121,119]) ).
tff(123,plain,
( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,szNzAzT0) )
| aSet0(sdtlpdtrp0(xN,xm)) ),
inference(tautology,[status(thm)],[]) ).
tff(124,plain,
aSet0(sdtlpdtrp0(xN,xm)),
inference(unit_resolution,[status(thm)],[123,122]) ).
tff(125,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| isCountable0(sdtlpdtrp0(xN,xm)) ),
inference(tautology,[status(thm)],[]) ).
tff(126,plain,
isCountable0(sdtlpdtrp0(xN,xm)),
inference(unit_resolution,[status(thm)],[125,42]) ).
tff(127,plain,
^ [W0: $i] :
refl(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(128,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& isCountable0(W0) )
<=> ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ~ ( aSet0(W0)
& isCountable0(W0) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
rewrite(( ~ ~ ( ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ~ ( aSet0(W0)
& isCountable0(W0) )
<=> ( ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
rewrite(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
( ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(130,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,plain,
^ [W0: $i] :
rewrite(( ( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) )
<=> ( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(133,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
tff(135,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ ( aSet0(W0)
& isCountable0(W0) ) ),
inference(skolemize,[status(sab)],[136]) ).
tff(138,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ),
inference(modus_ponens,[status(thm)],[137,130]) ).
tff(139,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) ),
inference(modus_ponens,[status(thm)],[138,128]) ).
tff(140,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ~ isFinite0(sdtlpdtrp0(xN,xm)) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ~ isFinite0(sdtlpdtrp0(xN,xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ( ~ isFinite0(sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm)) )
<=> ( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ~ isFinite0(sdtlpdtrp0(xN,xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm)) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ~ isFinite0(sdtlpdtrp0(xN,xm)) ) ),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm)) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ~ isFinite0(sdtlpdtrp0(xN,xm)) ) ),
inference(transitivity,[status(thm)],[142,140]) ).
tff(144,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ isFinite0(sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ~ isCountable0(W0) )
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isCountable0(sdtlpdtrp0(xN,xm))
| ~ isFinite0(sdtlpdtrp0(xN,xm)) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isFinite0(sdtlpdtrp0(xN,xm)) ),
inference(unit_resolution,[status(thm)],[145,139,126]) ).
tff(147,plain,
~ isFinite0(sdtlpdtrp0(xN,xm)),
inference(unit_resolution,[status(thm)],[146,124]) ).
tff(148,plain,
$false,
inference(unit_resolution,[status(thm)],[147,85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM623+1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.12 % 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 01:38:12 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 % SZS output start Proof
% See solution above
% 0.20/0.55 % E exiting
%------------------------------------------------------------------------------