%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM604+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:21:33 AM UTC 2025
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 21
% Syntax : Number of formulae : 56 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 370 ( 64 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 561 ( 265 ~; 194 |; 52 &)
% ( 31 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 108 ( 102 !; 0 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xi_type,type,
xi: $i ).
tff(xN_type,type,
xN: $i ).
tff(xx_type,type,
xx: $i ).
tff(xe_type,type,
xe: $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(xS_type,type,
xS: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(1,plain,
( ( sdtlpdtrp0(xe,xi) = xx )
<=> ( sdtlpdtrp0(xe,xi) = xx ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aElementOf0(xi,szNzAzT0)
& ( sdtlpdtrp0(xe,xi) = xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5034) ).
tff(3,plain,
sdtlpdtrp0(xe,xi) = xx,
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
sdtlpdtrp0(xe,xi) = xx,
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
xx = sdtlpdtrp0(xe,xi),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( aElementOf0(xx,sdtlpdtrp0(xN,xi))
<=> aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi)) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
<=> aElementOf0(xx,sdtlpdtrp0(xN,xi)) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( aElementOf0(xi,szNzAzT0)
<=> aElementOf0(xi,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,plain,
aElementOf0(xi,szNzAzT0),
inference(and_elim,[status(thm)],[2]) ).
tff(10,plain,
aElementOf0(xi,szNzAzT0),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
inference(transitivity,[status(thm)],[14,12]) ).
tff(16,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )),
( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
rewrite(( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
rewrite(( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
( aFunction0(xe)
& ( szDzozmdt0(xe) = szNzAzT0 )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).
tff(22,plain,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(and_elim,[status(thm)],[21]) ).
tff(23,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[22,20]) ).
tff(24,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[23,18]) ).
tff(25,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ),
inference(modus_ponens,[status(thm)],[25,17]) ).
tff(27,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ),
inference(modus_ponens,[status(thm)],[26,15]) ).
tff(28,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(sdtlpdtrp0(xe,xi),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
| ( sdtlpdtrp0(xe,xi) != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(sdtlpdtrp0(xe,xi),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
| ( sdtlpdtrp0(xe,xi) != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( ~ aElementOf0(xi,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,xi) != szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(sdtlpdtrp0(xe,xi),W1) ) ) )
<=> ( ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(sdtlpdtrp0(xe,xi),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
| ( sdtlpdtrp0(xe,xi) != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,xi) != szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(sdtlpdtrp0(xe,xi),W1) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(sdtlpdtrp0(xe,xi),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
| ( sdtlpdtrp0(xe,xi) != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,xi) != szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(sdtlpdtrp0(xe,xi),W1) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(sdtlpdtrp0(xe,xi),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
| ( sdtlpdtrp0(xe,xi) != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,xi) != szmzizndt0(sdtlpdtrp0(xN,xi)) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(sdtlpdtrp0(xe,xi),W1) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xi,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(sdtlpdtrp0(xe,xi),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
| ( sdtlpdtrp0(xe,xi) != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(sdtlpdtrp0(xe,xi),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
| ( sdtlpdtrp0(xe,xi) != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ),
inference(unit_resolution,[status(thm)],[33,27,10]) ).
tff(35,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(sdtlpdtrp0(xe,xi),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
| ( sdtlpdtrp0(xe,xi) != szmzizndt0(sdtlpdtrp0(xN,xi)) )
| aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi)) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi)),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
aElementOf0(xx,sdtlpdtrp0(xN,xi)),
inference(modus_ponens,[status(thm)],[36,7]) ).
tff(38,plain,
( ~ aElementOf0(xx,xS)
<=> ~ aElementOf0(xx,xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
~ aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(40,plain,
~ aElementOf0(xx,xS),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) )
<=> ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,xS) )
<=> ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,xS) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,xS) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5045) ).
tff(47,plain,
! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,xS) ),
inference(and_elim,[status(thm)],[46]) ).
tff(48,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) ),
inference(modus_ponens,[status(thm)],[47,45]) ).
tff(49,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) ),
inference(modus_ponens,[status(thm)],[48,43]) ).
tff(50,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) ),
inference(modus_ponens,[status(thm)],[50,42]) ).
tff(52,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) )
| ~ aElementOf0(xx,sdtlpdtrp0(xN,xi))
| aElementOf0(xx,xS) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) )
| ~ aElementOf0(xx,sdtlpdtrp0(xN,xi))
| aElementOf0(xx,xS) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) )
| ~ aElementOf0(xx,sdtlpdtrp0(xN,xi))
| aElementOf0(xx,xS) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) )
| ~ aElementOf0(xx,sdtlpdtrp0(xN,xi))
| aElementOf0(xx,xS) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
~ aElementOf0(xx,sdtlpdtrp0(xN,xi)),
inference(unit_resolution,[status(thm)],[54,51,40]) ).
tff(56,plain,
$false,
inference(unit_resolution,[status(thm)],[55,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM604+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 01:34:33 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % SZS output start Proof
% See solution above
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------