TSTP Solution File: NUM627+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM627+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Sun Sep 18 13:11:00 EDT 2022
% Result : Theorem 0.48s 0.55s
% Output : Proof 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 56
% Syntax : Number of formulae : 109 ( 26 unt; 17 typ; 0 def)
% Number of atoms : 672 ( 37 equ)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 913 ( 387 ~; 366 |; 79 &)
% ( 64 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 54 ( 54 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 8 >; 5 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 149 ( 129 !; 0 ?; 149 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xn_type,type,
xn: $i ).
tff(xm_type,type,
xm: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xN_type,type,
xN: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(xe_type,type,
xe: $i ).
tff(xx_type,type,
xx: $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(xp_type,type,
xp: $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(sz00_type,type,
sz00: $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,
~ 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(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( aElementOf0(xm,szNzAzT0)
<=> aElementOf0(xm,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( aElementOf0(xm,szNzAzT0)
<=> aElementOf0(xm,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
( aElementOf0(xm,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5389) ).
tff(7,plain,
aElementOf0(xm,szNzAzT0),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
aElementOf0(xm,szNzAzT0),
inference(modus_ponens,[status(thm)],[7,5]) ).
tff(9,plain,
aElementOf0(xm,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
( aElementOf0(xn,szNzAzT0)
<=> aElementOf0(xn,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( aElementOf0(xn,szNzAzT0)
<=> aElementOf0(xn,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
( aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& ( sdtlpdtrp0(xe,xn) = xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).
tff(13,plain,
( aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0) ),
inference(and_elim,[status(thm)],[12]) ).
tff(14,plain,
aElementOf0(xn,szNzAzT0),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
aElementOf0(xn,szNzAzT0),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
aElementOf0(xn,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[15,10]) ).
tff(17,plain,
^ [W0: $i,W1: $i] :
refl(
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )),
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
| ~ sdtlseqdt0(W1,W0) ) )),
rewrite(
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
| ~ sdtlseqdt0(W1,W0) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
<=> ( ~ sdtlseqdt0(W1,W0)
| aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ sdtlseqdt0(W1,W0)
| aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
rewrite(
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ sdtlseqdt0(W1,W0)
| aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3754) ).
tff(27,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(modus_ponens,[status(thm)],[28,22]) ).
tff(30,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[30,20]) ).
tff(32,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[31,18]) ).
tff(33,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ aElementOf0(xn,szDzozmdt0(xN)) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ aElementOf0(xn,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ aElementOf0(xn,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ aElementOf0(xn,szDzozmdt0(xN)) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
~ sdtlseqdt0(xm,xn),
inference(unit_resolution,[status(thm)],[38,32,16,9,3]) ).
tff(40,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,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(47,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(48,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)],[47]) ).
tff(49,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
tff(50,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[51,45]) ).
tff(53,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[53,43]) ).
tff(55,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[54,41]) ).
tff(56,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ),
inference(unit_resolution,[status(thm)],[58,55,16]) ).
tff(60,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 )
| aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN)) ),
inference(tautology,[status(thm)],]) ).
tff(61,plain,
aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN)),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
<=> ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(rewrite,[status(thm)],]) ).
tff(63,axiom,
~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5442) ).
tff(64,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN)) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN)) ),
inference(unit_resolution,[status(thm)],[67,32,9,64]) ).
tff(69,plain,
~ sdtlseqdt0(szszuzczcdt0(xn),xm),
inference(unit_resolution,[status(thm)],[68,61]) ).
tff(70,plain,
^ [W0: $i,W1: $i] :
refl(
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )),
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
rewrite(
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
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(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
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,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(modus_ponens,[status(thm)],[81,75]) ).
tff(83,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[83,73]) ).
tff(85,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[84,71]) ).
tff(86,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN)) )
<=> ( sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ) ),
inference(transitivity,[status(thm)],[88,86]) ).
tff(90,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN)) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
$false,
inference(unit_resolution,[status(thm)],[91,85,16,9,69,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM627+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Sep 2 12:29:46 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.48/0.55 % SZS status Theorem
% 0.48/0.55 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------