%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM627+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:21:39 AM UTC 2025
% Result : Theorem 5.39s 5.53s
% Output : Proof 5.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 41
% Syntax : Number of formulae : 103 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 969 ( 34 equ)
% Maximal formula atoms : 24 ( 9 avg)
% Number of connectives : 1619 ( 808 ~; 625 |; 82 &)
% ( 75 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 55 ( 55 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 : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 272 ( 253 !; 0 ?; 272 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xN_type,type,
xN: $i ).
tff(xn_type,type,
xn: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(sz00_type,type,
sz00: $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(xp_type,type,
xp: $i ).
tff(xe_type,type,
xe: $i ).
tff(xx_type,type,
xx: $i ).
tff(1,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
<=> ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ ( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
| aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5461) ).
tff(3,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(or_elim,[status(thm)],[2]) ).
tff(4,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) )
| aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ),
inference(tautology,[status(thm)],[]) ).
tff(6,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ),
inference(unit_resolution,[status(thm)],[5,4]) ).
tff(7,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
<=> ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
~ ( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
| aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5442) ).
tff(9,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(or_elim,[status(thm)],[8]) ).
tff(10,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(modus_ponens,[status(thm)],[9,7]) ).
tff(11,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
| aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(tautology,[status(thm)],[]) ).
tff(12,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( aElementOf0(xn,szNzAzT0)
<=> aElementOf0(xn,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,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/sandbox2/benchmark/theBenchmark.p',m__5309) ).
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)],[14]) ).
tff(16,plain,
aElementOf0(xn,szNzAzT0),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
aElementOf0(xn,szNzAzT0),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
| ( szszuzczcdt0(W0) = sz00 ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
| ( szszuzczcdt0(W0) = sz00 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
| ( szszuzczcdt0(W0) = sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
| ( szszuzczcdt0(W0) = sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
| ( szszuzczcdt0(W0) = sz00 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
| ( szszuzczcdt0(W0) = sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
tff(26,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
| ( szszuzczcdt0(W0) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
| ( szszuzczcdt0(W0) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[29,19]) ).
tff(31,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ( szszuzczcdt0(xn) = sz00 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ( szszuzczcdt0(xn) = sz00 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ( szszuzczcdt0(xn) = sz00 ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ( szszuzczcdt0(xn) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ( szszuzczcdt0(xn) = sz00 ) ),
inference(unit_resolution,[status(thm)],[33,30,17]) ).
tff(35,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ( szszuzczcdt0(xn) = sz00 )
| aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
aElementOf0(szszuzczcdt0(xn),szNzAzT0),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
( aElementOf0(xm,szNzAzT0)
<=> aElementOf0(xm,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
( aElementOf0(xm,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5389) ).
tff(39,plain,
aElementOf0(xm,szNzAzT0),
inference(and_elim,[status(thm)],[38]) ).
tff(40,plain,
aElementOf0(xm,szNzAzT0),
inference(modus_ponens,[status(thm)],[39,37]) ).
tff(41,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
<=> ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )),
( ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) ) )),
rewrite(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) ) )),
( ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,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) ) )),
rewrite(( ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
<=> ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )),
( ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
rewrite(( ( ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
( ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
<=> ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )),
( ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
rewrite(( ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
( ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )
<=> ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ) )),
rewrite(( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )
<=> ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )
<=> ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3754) ).
tff(54,plain,
! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
inference(modus_ponens,[status(thm)],[56,49]) ).
tff(58,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
inference(modus_ponens,[status(thm)],[57,47]) ).
tff(59,plain,
! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) ),
inference(modus_ponens,[status(thm)],[58,42]) ).
tff(60,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
<=> ( ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
<=> ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) )
<=> ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) )
<=> ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
<=> ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
<=> ( ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
inference(transitivity,[status(thm)],[65,61]) ).
tff(67,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
inference(transitivity,[status(thm)],[67,60]) ).
tff(69,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
~ sdtlseqdt0(szszuzczcdt0(xn),xm),
inference(unit_resolution,[status(thm)],[70,59,40,36,12]) ).
tff(72,plain,
^ [W0: $i,W1: $i] :
refl(( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,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) ) )),
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
rewrite(( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0) ) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).
tff(80,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[83,73]) ).
tff(85,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| sdtlseqdt0(xm,xn) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| sdtlseqdt0(xm,xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
( ( sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) )
<=> ( ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| sdtlseqdt0(xm,xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| sdtlseqdt0(xm,xn) ) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| sdtlseqdt0(xm,xn) ) ),
inference(transitivity,[status(thm)],[87,85]) ).
tff(89,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| sdtlseqdt0(xm,xn) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
sdtlseqdt0(xm,xn),
inference(unit_resolution,[status(thm)],[90,84,17,40,71]) ).
tff(92,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ( ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) )
<=> ( ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) )
<=> ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) )
<=> ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) )
<=> ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) )
<=> ( ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) ) ),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
( ( ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) )
<=> ( ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) ) ),
inference(transitivity,[status(thm)],[97,93]) ).
tff(99,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) ) ),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) ) ),
inference(transitivity,[status(thm)],[99,92]) ).
tff(101,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W0,szNzAzT0)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
$false,
inference(unit_resolution,[status(thm)],[102,59,17,40,91,6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM627+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:39:01 EDT 2025
% 0.12/0.33 % CPUTime :
% 5.39/5.53 % SZS status Theorem
% 5.39/5.53 % SZS output start Proof
% See solution above
% 5.41/5.58 % E exiting
%------------------------------------------------------------------------------