TSTP Solution File: NUM582+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM582+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 13:10:40 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 35
% Syntax : Number of formulae : 65 ( 18 unt; 10 typ; 0 def)
% Number of atoms : 342 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 450 ( 194 ~; 172 |; 31 &)
% ( 39 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 31 ( 31 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 79 ( 68 !; 0 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xi_type,type,
xi: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xN_type,type,
xN: $i ).
tff(xS_type,type,
xS: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(1,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
<=> ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
<=> ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(4,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( aElementOf0(xi,szNzAzT0)
<=> aElementOf0(xi,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
( aElementOf0(xi,szNzAzT0)
<=> aElementOf0(xi,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989) ).
tff(9,plain,
aElementOf0(xi,szNzAzT0),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
aElementOf0(xi,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,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(12,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)],[11]) ).
tff(13,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(14,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)],[13]) ).
tff(15,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(16,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)],[15]) ).
tff(17,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(18,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(19,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)],[18]) ).
tff(20,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
tff(21,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)],[20,19]) ).
tff(22,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)],[21,17]) ).
tff(23,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)],[22,16]) ).
tff(24,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)],[23]) ).
tff(25,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)],[24,14]) ).
tff(26,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)],[25,12]) ).
tff(27,plain,
( aElementOf0(sz00,szNzAzT0)
<=> aElementOf0(sz00,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( aElementOf0(sz00,szNzAzT0)
<=> aElementOf0(sz00,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
tff(30,plain,
aElementOf0(sz00,szNzAzT0),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
aElementOf0(sz00,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[30,27]) ).
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)) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(xi,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,xi),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(xi,szDzozmdt0(xN)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00))
| ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ aElementOf0(xi,szDzozmdt0(xN)) )
<=> ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(xi,szDzozmdt0(xN)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,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,xi),sdtlpdtrp0(xN,sz00))
| ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ aElementOf0(xi,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,xi),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(xi,szDzozmdt0(xN)) ) ),
inference(monotonicity,[status(thm)],[33]) ).
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,xi),sdtlpdtrp0(xN,sz00))
| ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ aElementOf0(xi,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,xi),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(xi,szDzozmdt0(xN)) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
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,xi),sdtlpdtrp0(xN,sz00))
| ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ aElementOf0(xi,szDzozmdt0(xN)) ),
inference(quant_inst,[status(thm)],]) ).
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,xi),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szDzozmdt0(xN))
| ~ sdtlseqdt0(sz00,xi)
| ~ aElementOf0(xi,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
~ sdtlseqdt0(sz00,xi),
inference(unit_resolution,[status(thm)],[37,31,26,10,5]) ).
tff(39,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
^ [W0: $i] :
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
tff(47,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[48,42]) ).
tff(50,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) ),
inference(modus_ponens,[status(thm)],[50,40]) ).
tff(52,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(xi,szDzozmdt0(xN))
| sdtlseqdt0(sz00,xi) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(xi,szDzozmdt0(xN))
| sdtlseqdt0(sz00,xi) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(xi,szDzozmdt0(xN))
| sdtlseqdt0(sz00,xi) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| sdtlseqdt0(sz00,W0) )
| ~ aElementOf0(xi,szDzozmdt0(xN))
| sdtlseqdt0(sz00,xi) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
$false,
inference(unit_resolution,[status(thm)],[54,51,10,38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM582+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 12:05:43 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------