%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM621+3 : 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 05:21:37 AM UTC 2025
% Result : Theorem 5.36s 5.53s
% Output : Proof 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 53
% Syntax : Number of formulae : 148 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 882 ( 131 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 1218 ( 536 ~; 431 |; 126 &)
% ( 80 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 52 ( 52 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 218 ( 200 !; 1 ?; 218 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(xN_type,type,
xN: $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(xe_type,type,
xe: $i ).
tff(xp_type,type,
xp: $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(xm_type,type,
xm: $i ).
tff(xx_type,type,
xx: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(xP_type,type,
xP: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(1,plain,
( ( sdtlpdtrp0(xe,xn) = xp )
<=> ( sdtlpdtrp0(xe,xn) = xp ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& ( sdtlpdtrp0(xe,xn) = xp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
tff(3,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
xp = sdtlpdtrp0(xe,xn),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( ( xp = szmzizndt0(xQ) )
<=> ( xp = szmzizndt0(xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
( aElementOf0(xp,xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) )
& ( xp = szmzizndt0(xQ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
tff(8,plain,
xp = szmzizndt0(xQ),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
xp = szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[8,6]) ).
tff(10,plain,
szmzizndt0(xQ) = xp,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
szmzizndt0(xQ) = sdtlpdtrp0(xe,xn),
inference(transitivity,[status(thm)],[10,5]) ).
tff(12,plain,
( aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn))
<=> aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn)) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
<=> aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn)) ),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( aElementOf0(xn,szNzAzT0)
<=> aElementOf0(xn,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0) ),
inference(and_elim,[status(thm)],[2]) ).
tff(16,plain,
aElementOf0(xn,szNzAzT0),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
aElementOf0(xn,szNzAzT0),
inference(modus_ponens,[status(thm)],[16,14]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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(21,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)],[20]) ).
tff(22,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)],[21,19]) ).
tff(23,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(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)) ) ) )
<=> ! [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)],[23]) ).
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)) ) ) )
<=> ! [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(26,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(27,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)],[26]) ).
tff(28,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/sandbox/benchmark/theBenchmark.p',m__4660) ).
tff(29,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)],[28]) ).
tff(30,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)],[29,27]) ).
tff(31,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)],[30,25]) ).
tff(32,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)],[31]) ).
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) ) ) ),
inference(modus_ponens,[status(thm)],[32,24]) ).
tff(34,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)],[33,22]) ).
tff(35,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(xn,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
<=> ( ~ ! [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(xn,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ( ~ aElementOf0(xn,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) )
<=> ( ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,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(xn,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),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(xn,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,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(xn,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),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(xn,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ),
inference(transitivity,[status(thm)],[37,35]) ).
tff(39,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(xn,szNzAzT0)
| ~ ( ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,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(xn,szNzAzT0)
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ),
inference(unit_resolution,[status(thm)],[40,34,17]) ).
tff(42,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn)) ),
inference(tautology,[status(thm)],[]) ).
tff(43,plain,
aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn)),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn)),
inference(modus_ponens,[status(thm)],[43,13]) ).
tff(45,plain,
( aElementOf0(szmzizndt0(xQ),xQ)
<=> aElementOf0(xp,xQ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(46,plain,
( aElementOf0(xp,xQ)
<=> aElementOf0(szmzizndt0(xQ),xQ) ),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( aElementOf0(xp,xQ)
<=> aElementOf0(xp,xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( aElementOf0(xp,xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) ) ),
inference(and_elim,[status(thm)],[7]) ).
tff(49,plain,
aElementOf0(xp,xQ),
inference(and_elim,[status(thm)],[48]) ).
tff(50,plain,
aElementOf0(xp,xQ),
inference(modus_ponens,[status(thm)],[49,47]) ).
tff(51,plain,
aElementOf0(szmzizndt0(xQ),xQ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) )
<=> ( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) )
<=> ( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
( ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xQ,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5106) ).
tff(58,plain,
! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) ),
inference(and_elim,[status(thm)],[57]) ).
tff(59,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[58,56]) ).
tff(60,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[59,54]) ).
tff(61,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[61,53]) ).
tff(63,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| aElementOf0(szmzizndt0(xQ),szNzAzT0) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| aElementOf0(szmzizndt0(xQ),szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| aElementOf0(szmzizndt0(xQ),szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| aElementOf0(szmzizndt0(xQ),szNzAzT0) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ aElementOf0(szmzizndt0(xQ),xQ)
| aElementOf0(szmzizndt0(xQ),szNzAzT0) ),
inference(unit_resolution,[status(thm)],[65,62]) ).
tff(67,plain,
aElementOf0(szmzizndt0(xQ),szNzAzT0),
inference(unit_resolution,[status(thm)],[66,51]) ).
tff(68,plain,
( aElementOf0(xx,xQ)
<=> aElementOf0(xx,xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
( aElement0(xx)
& aElementOf0(xx,xQ)
& ( xx != szmzizndt0(xQ) )
& aElementOf0(xx,xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5348) ).
tff(70,plain,
( aElement0(xx)
& aElementOf0(xx,xQ)
& ( xx != szmzizndt0(xQ) ) ),
inference(and_elim,[status(thm)],[69]) ).
tff(71,plain,
( aElement0(xx)
& aElementOf0(xx,xQ) ),
inference(and_elim,[status(thm)],[70]) ).
tff(72,plain,
aElementOf0(xx,xQ),
inference(and_elim,[status(thm)],[71]) ).
tff(73,plain,
aElementOf0(xx,xQ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
<=> ( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
<=> ( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,axiom,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != szmzizndt0(xQ) ) ) )
& ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
tff(80,plain,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != szmzizndt0(xQ) ) ) ) ),
inference(and_elim,[status(thm)],[79]) ).
tff(81,plain,
( aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
inference(and_elim,[status(thm)],[80]) ).
tff(82,plain,
! [W0: $i] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) ),
inference(and_elim,[status(thm)],[81]) ).
tff(83,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) ),
inference(modus_ponens,[status(thm)],[85,75]) ).
tff(87,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
| ~ aElementOf0(xx,xQ)
| sdtlseqdt0(szmzizndt0(xQ),xx) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
| ~ aElementOf0(xx,xQ)
| sdtlseqdt0(szmzizndt0(xQ),xx) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
| ~ aElementOf0(xx,xQ)
| sdtlseqdt0(szmzizndt0(xQ),xx) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
| ~ aElementOf0(xx,xQ)
| sdtlseqdt0(szmzizndt0(xQ),xx) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
sdtlseqdt0(szmzizndt0(xQ),xx),
inference(unit_resolution,[status(thm)],[89,86,73]) ).
tff(91,plain,
( aElementOf0(xx,szNzAzT0)
<=> aElementOf0(xx,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,axiom,
( aElementOf0(xx,szNzAzT0)
& ? [W0: $i] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( sdtlpdtrp0(xe,W0) = xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5365) ).
tff(93,plain,
aElementOf0(xx,szNzAzT0),
inference(and_elim,[status(thm)],[92]) ).
tff(94,plain,
aElementOf0(xx,szNzAzT0),
inference(modus_ponens,[status(thm)],[93,91]) ).
tff(95,plain,
( ( xx != szmzizndt0(xQ) )
<=> ( xx != szmzizndt0(xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
xx != szmzizndt0(xQ),
inference(and_elim,[status(thm)],[70]) ).
tff(97,plain,
xx != szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],[]) ).
tff(99,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,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(W1,W0)
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ~ ~ ( ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ~ ~ ( ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) ) )),
( ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) ) )),
( ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],[]) ).
tff(101,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)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,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(103,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(104,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)],[103]) ).
tff(105,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(106,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[108,101]) ).
tff(110,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[109,99]) ).
tff(111,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,plain,
( ( ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ aElementOf0(xx,szNzAzT0)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) )
<=> ( ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ aElementOf0(xx,szNzAzT0)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) ) ),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ aElementOf0(xx,szNzAzT0)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) ) ),
inference(transitivity,[status(thm)],[113,111]) ).
tff(115,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ aElementOf0(xx,szNzAzT0)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W0,W1) )
| ( xx = szmzizndt0(xQ) )
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
( ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ sdtlseqdt0(xx,szmzizndt0(xQ)) ),
inference(unit_resolution,[status(thm)],[116,110,97,94,90]) ).
tff(118,plain,
~ sdtlseqdt0(xx,szmzizndt0(xQ)),
inference(unit_resolution,[status(thm)],[117,67]) ).
tff(119,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) )
<=> ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(120,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,W0) )
<=> ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,axiom,
! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5401) ).
tff(125,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ),
inference(modus_ponens,[status(thm)],[127,120]) ).
tff(129,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,szmzizndt0(xQ)) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,szmzizndt0(xQ)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,szmzizndt0(xQ)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,szmzizndt0(xQ)) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)),
inference(unit_resolution,[status(thm)],[131,128,118]) ).
tff(133,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
<=> ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ) )),
inference(bind,[status(th)],[]) ).
tff(134,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ) ),
inference(quant_intro,[status(thm)],[133]) ).
tff(135,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ~ ( ( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
& aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
<=> ~ ( ~ ( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
& aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) )
| aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,axiom,
~ ( ( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
& aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(138,plain,
~ ( ~ ( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
& aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) )
| aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
& aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ),
inference(or_elim,[status(thm)],[138]) ).
tff(140,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ),
inference(and_elim,[status(thm)],[139]) ).
tff(141,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ),
inference(modus_ponens,[status(thm)],[140,135]) ).
tff(142,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ),
inference(skolemize,[status(sab)],[141]) ).
tff(143,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ),
inference(modus_ponens,[status(thm)],[142,134]) ).
tff(144,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(145,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(146,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
( ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ),
inference(unit_resolution,[status(thm)],[146,143]) ).
tff(148,plain,
$false,
inference(unit_resolution,[status(thm)],[147,132,44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM621+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.11 % 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 01:37:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 5.36/5.53 % SZS status Theorem
% 5.36/5.53 % SZS output start Proof
% See solution above
% 5.36/5.57 % E exiting
%------------------------------------------------------------------------------