%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM624+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:38 AM UTC 2025
% Result : Theorem 0.20s 0.54s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 24
% Syntax : Number of formulae : 65 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 498 ( 204 equ)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 654 ( 258 ~; 229 |; 112 &)
% ( 44 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 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 : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 50 ( 44 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xQ_type,type,
xQ: $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xN_type,type,
xN: $i ).
tff(xx_type,type,
xx: $i ).
tff(xp_type,type,
xp: $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(xO_type,type,
xO: $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,
( ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) )
<=> ( xp = xx ) ),
inference(monotonicity,[status(thm)],[15,4]) ).
tff(17,plain,
( ( xp = xx )
<=> ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) ) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( ( xp != xx )
<=> ( szmzizndt0(xQ) != szmzizndt0(sdtlpdtrp0(xN,xm)) ) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ( xp != xx )
<=> ( xp != xx ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
xp != xx,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(21,plain,
xp != xx,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
szmzizndt0(xQ) != szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
( aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
<=> aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(24,plain,
( aElementOf0(xp,sdtlpdtrp0(xN,xm))
<=> aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( aElementOf0(xp,sdtlpdtrp0(xN,xm))
<=> aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(and_elim,[status(thm)],[8]) ).
tff(27,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
( ( sdtlpdtrp0(xN,xm) != slcrc0 )
<=> ( sdtlpdtrp0(xN,xm) != slcrc0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
( aSubsetOf0(xQ,szNzAzT0)
& aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
& ( xQ != slcrc0 )
& ( sdtlpdtrp0(xN,xm) != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5518) ).
tff(31,plain,
sdtlpdtrp0(xN,xm) != slcrc0,
inference(and_elim,[status(thm)],[30]) ).
tff(32,plain,
sdtlpdtrp0(xN,xm) != slcrc0,
inference(modus_ponens,[status(thm)],[31,29]) ).
tff(33,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
<=> aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( aSubsetOf0(xQ,szNzAzT0)
& aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
& ( xQ != slcrc0 ) ),
inference(and_elim,[status(thm)],[30]) ).
tff(35,plain,
( aSubsetOf0(xQ,szNzAzT0)
& aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(and_elim,[status(thm)],[34]) ).
tff(36,plain,
aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0),
inference(and_elim,[status(thm)],[35]) ).
tff(37,plain,
aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0),
inference(modus_ponens,[status(thm)],[36,33]) ).
tff(38,plain,
( aSubsetOf0(xQ,szNzAzT0)
<=> aSubsetOf0(xQ,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).
tff(40,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ( xQ != slcrc0 )
<=> ( xQ != slcrc0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
( aSubsetOf0(xQ,xO)
& ( xQ != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).
tff(43,plain,
xQ != slcrc0,
inference(and_elim,[status(thm)],[42]) ).
tff(44,plain,
xQ != slcrc0,
inference(modus_ponens,[status(thm)],[43,41]) ).
tff(45,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(46,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)],[45]) ).
tff(47,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(48,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)],[47]) ).
tff(49,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(50,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(51,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)],[50]) ).
tff(52,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(53,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)],[52,51]) ).
tff(54,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)],[53,49]) ).
tff(55,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)],[54]) ).
tff(56,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)],[55,48]) ).
tff(57,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)],[56,46]) ).
tff(58,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 )
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ( 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 )
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ( 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(59,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 )
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ( 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(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) )
| ( 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 )
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ( 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)],[59]) ).
tff(61,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 )
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ( 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)],[60,58]) ).
tff(62,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(63,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 )
| ( sdtlpdtrp0(xN,xm) = slcrc0 )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ( 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)],[62,61]) ).
tff(64,plain,
( ( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xm)) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),xQ) ),
inference(unit_resolution,[status(thm)],[63,57,44,40,37,32]) ).
tff(65,plain,
$false,
inference(unit_resolution,[status(thm)],[64,28,22,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM624+1 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:36:57 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.54 % SZS status Theorem
% 0.20/0.54 % SZS output start Proof
% See solution above
% 0.20/0.55 % E exiting
%------------------------------------------------------------------------------