%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM539+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:21:20 AM UTC 2025
% Result : Theorem 0.11s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 37
% Syntax : Number of formulae : 106 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 601 ( 59 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 757 ( 299 ~; 268 |; 89 &)
% ( 54 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 37 ( 37 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 147 ( 130 !; 3 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xT_type,type,
xT: $i ).
tff(xS_type,type,
xS: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(1,plain,
( aElementOf0(szmzizndt0(xT),xS)
<=> aElementOf0(szmzizndt0(xT),xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aElementOf0(szmzizndt0(xS),xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(szmzizndt0(xS),W0) )
& aElementOf0(szmzizndt0(xS),xT)
& aElementOf0(szmzizndt0(xT),xT)
& ! [W0: $i] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(szmzizndt0(xT),W0) )
& aElementOf0(szmzizndt0(xT),xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1802) ).
tff(3,plain,
aElementOf0(szmzizndt0(xT),xS),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aElementOf0(szmzizndt0(xT),xS),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) )
<=> ( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,xS)
=> sdtlseqdt0(szmzizndt0(xS),W0) )
<=> ( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(szmzizndt0(xS),W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( aElementOf0(szmzizndt0(xS),xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(szmzizndt0(xS),W0) )
& aElementOf0(szmzizndt0(xS),xT)
& aElementOf0(szmzizndt0(xT),xT)
& ! [W0: $i] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(szmzizndt0(xT),W0) ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(11,plain,
( aElementOf0(szmzizndt0(xS),xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(szmzizndt0(xS),W0) )
& aElementOf0(szmzizndt0(xS),xT)
& aElementOf0(szmzizndt0(xT),xT) ),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
( aElementOf0(szmzizndt0(xS),xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(szmzizndt0(xS),W0) )
& aElementOf0(szmzizndt0(xS),xT) ),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
( aElementOf0(szmzizndt0(xS),xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(szmzizndt0(xS),W0) ) ),
inference(and_elim,[status(thm)],[12]) ).
tff(14,plain,
! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(szmzizndt0(xS),W0) ),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) ),
inference(modus_ponens,[status(thm)],[14,9]) ).
tff(16,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) ),
inference(modus_ponens,[status(thm)],[15,7]) ).
tff(17,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) ),
inference(modus_ponens,[status(thm)],[17,6]) ).
tff(19,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) )
| ~ aElementOf0(szmzizndt0(xT),xS)
| sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT)) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) )
| ~ aElementOf0(szmzizndt0(xT),xS)
| sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) )
| ~ aElementOf0(szmzizndt0(xT),xS)
| sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) )
| ~ aElementOf0(szmzizndt0(xT),xS)
| sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT)) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT)),
inference(unit_resolution,[status(thm)],[21,18,4]) ).
tff(23,plain,
( aElementOf0(szmzizndt0(xT),xT)
<=> aElementOf0(szmzizndt0(xT),xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
aElementOf0(szmzizndt0(xT),xT),
inference(and_elim,[status(thm)],[11]) ).
tff(25,plain,
aElementOf0(szmzizndt0(xT),xT),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) )
<=> ( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,xT)
=> aElementOf0(W0,szNzAzT0) )
<=> ( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [W0: $i] :
( aElementOf0(W0,xT)
=> aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
( aSet0(xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& aSet0(xT)
& ! [W0: $i] :
( aElementOf0(W0,xT)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xT,szNzAzT0)
& ~ ( ~ ? [W0: $i] : aElementOf0(W0,xS)
| ( xS = slcrc0 ) )
& ~ ( ~ ? [W0: $i] : aElementOf0(W0,xT)
| ( xT = slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1779) ).
tff(32,plain,
( aSet0(xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& aSet0(xT)
& ! [W0: $i] :
( aElementOf0(W0,xT)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xT,szNzAzT0)
& ~ ( ~ ? [W0: $i] : aElementOf0(W0,xS)
| ( xS = slcrc0 ) ) ),
inference(and_elim,[status(thm)],[31]) ).
tff(33,plain,
( aSet0(xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& aSet0(xT)
& ! [W0: $i] :
( aElementOf0(W0,xT)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xT,szNzAzT0) ),
inference(and_elim,[status(thm)],[32]) ).
tff(34,plain,
( aSet0(xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& aSet0(xT)
& ! [W0: $i] :
( aElementOf0(W0,xT)
=> aElementOf0(W0,szNzAzT0) ) ),
inference(and_elim,[status(thm)],[33]) ).
tff(35,plain,
! [W0: $i] :
( aElementOf0(W0,xT)
=> aElementOf0(W0,szNzAzT0) ),
inference(and_elim,[status(thm)],[34]) ).
tff(36,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[35,30]) ).
tff(37,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[36,28]) ).
tff(38,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[38,27]) ).
tff(40,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xT),xT)
| aElementOf0(szmzizndt0(xT),szNzAzT0) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xT),xT)
| aElementOf0(szmzizndt0(xT),szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xT),xT)
| aElementOf0(szmzizndt0(xT),szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xT),xT)
| aElementOf0(szmzizndt0(xT),szNzAzT0) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
aElementOf0(szmzizndt0(xT),szNzAzT0),
inference(unit_resolution,[status(thm)],[42,39,25]) ).
tff(44,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) )
<=> ( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,xT)
=> sdtlseqdt0(szmzizndt0(xT),W0) )
<=> ( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [W0: $i] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(szmzizndt0(xT),W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
! [W0: $i] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(szmzizndt0(xT),W0) ),
inference(and_elim,[status(thm)],[10]) ).
tff(50,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( aElementOf0(szmzizndt0(xS),xT)
<=> aElementOf0(szmzizndt0(xS),xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
aElementOf0(szmzizndt0(xS),xT),
inference(and_elim,[status(thm)],[12]) ).
tff(56,plain,
aElementOf0(szmzizndt0(xS),xT),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) )
| ~ aElementOf0(szmzizndt0(xS),xT)
| sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) )
| ~ aElementOf0(szmzizndt0(xS),xT)
| sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) )
| ~ aElementOf0(szmzizndt0(xS),xT)
| sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xT),W0) )
| ~ aElementOf0(szmzizndt0(xS),xT)
| sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)),
inference(unit_resolution,[status(thm)],[59,56,53]) ).
tff(61,plain,
( aElementOf0(szmzizndt0(xS),xS)
<=> aElementOf0(szmzizndt0(xS),xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
aElementOf0(szmzizndt0(xS),xS),
inference(and_elim,[status(thm)],[13]) ).
tff(63,plain,
aElementOf0(szmzizndt0(xS),xS),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) )
<=> ( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
<=> ( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( aSet0(xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& aSet0(xT) ),
inference(and_elim,[status(thm)],[34]) ).
tff(70,plain,
( aSet0(xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0) ),
inference(and_elim,[status(thm)],[69]) ).
tff(71,plain,
( aSet0(xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) ) ),
inference(and_elim,[status(thm)],[70]) ).
tff(72,plain,
! [W0: $i] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) ),
inference(and_elim,[status(thm)],[71]) ).
tff(73,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[75,65]) ).
tff(77,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xS),xS)
| aElementOf0(szmzizndt0(xS),szNzAzT0) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xS),xS)
| aElementOf0(szmzizndt0(xS),szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xS),xS)
| aElementOf0(szmzizndt0(xS),szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xS),xS)
| aElementOf0(szmzizndt0(xS),szNzAzT0) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
aElementOf0(szmzizndt0(xS),szNzAzT0),
inference(unit_resolution,[status(thm)],[79,76,63]) ).
tff(81,plain,
( ( szmzizndt0(xS) != szmzizndt0(xT) )
<=> ( szmzizndt0(xS) != szmzizndt0(xT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ~ ( ( aElementOf0(szmzizndt0(xS),xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(szmzizndt0(xS),W0) ) )
=> ( ! [W0: $i] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(szmzizndt0(xS),W0) )
| ( szmzizndt0(xS) = szmzizndt0(xT) ) ) )
<=> ~ ( ( szmzizndt0(xS) = szmzizndt0(xT) )
| ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xS),W0) )
| ~ ( aElementOf0(szmzizndt0(xS),xS)
& ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
~ ( ( aElementOf0(szmzizndt0(xS),xS)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(szmzizndt0(xS),W0) ) )
=> ( ! [W0: $i] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(szmzizndt0(xS),W0) )
| ( szmzizndt0(xS) = szmzizndt0(xT) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(84,plain,
~ ( ( szmzizndt0(xS) = szmzizndt0(xT) )
| ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| sdtlseqdt0(szmzizndt0(xS),W0) )
| ~ ( aElementOf0(szmzizndt0(xS),xS)
& ! [W0: $i] :
( ~ aElementOf0(W0,xS)
| sdtlseqdt0(szmzizndt0(xS),W0) ) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
szmzizndt0(xS) != szmzizndt0(xT),
inference(or_elim,[status(thm)],[84]) ).
tff(86,plain,
szmzizndt0(xS) != szmzizndt0(xT),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ~ ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
rewrite(( ~ ~ ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
trans(monotonicity(rewrite(( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ~ ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
rewrite(( ~ ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
rewrite(( ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) )
<=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) ) )),
rewrite(( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).
tff(95,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ),
inference(modus_ponens,[status(thm)],[98,88]) ).
tff(100,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
| ( szmzizndt0(xS) = szmzizndt0(xT) )
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT))
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
| ( szmzizndt0(xS) = szmzizndt0(xT) )
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT))
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ( ( szmzizndt0(xS) = szmzizndt0(xT) )
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT))
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) )
<=> ( ( szmzizndt0(xS) = szmzizndt0(xT) )
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT))
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
| ( szmzizndt0(xS) = szmzizndt0(xT) )
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT))
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
| ( szmzizndt0(xS) = szmzizndt0(xT) )
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT))
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) ) ),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
| ( szmzizndt0(xS) = szmzizndt0(xT) )
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT))
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
| ( szmzizndt0(xS) = szmzizndt0(xT) )
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT))
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) ) ),
inference(transitivity,[status(thm)],[102,100]) ).
tff(104,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
| ( szmzizndt0(xS) = szmzizndt0(xT) )
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT))
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
| ( szmzizndt0(xS) = szmzizndt0(xT) )
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT))
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
$false,
inference(unit_resolution,[status(thm)],[105,99,86,80,60,43,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM539+2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.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 01:25:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.39 % SZS status Theorem
% 0.11/0.39 % SZS output start Proof
% See solution above
% 0.18/0.41 % E exiting
%------------------------------------------------------------------------------