TSTP Solution File: NUM622+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM622+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 13:10:58 EDT 2022
% Result : Theorem 0.21s 0.53s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 42
% Syntax : Number of formulae : 85 ( 22 unt; 17 typ; 0 def)
% Number of atoms : 393 ( 71 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 549 ( 244 ~; 180 |; 71 &)
% ( 35 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 9 >; 5 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 112 ( 104 !; 0 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(xN_type,type,
xN: $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(xe_type,type,
xe: $i ).
tff(xp_type,type,
xp: $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(xm_type,type,
xm: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(1,plain,
( ( sdtlpdtrp0(xe,xn) = xp )
<=> ( sdtlpdtrp0(xe,xn) = szmzizndt0(xQ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( sdtlpdtrp0(xe,xn) = xp )
<=> ( sdtlpdtrp0(xe,xn) = xp ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,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(4,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
sdtlpdtrp0(xe,xn) = szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
szmzizndt0(xQ) = sdtlpdtrp0(xe,xn),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn))
<=> aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn)) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
<=> aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn)) ),
inference(symmetry,[status(thm)],[8]) ).
tff(10,plain,
( aElementOf0(xn,szDzozmdt0(xd))
<=> aElementOf0(xn,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( aElementOf0(xn,szDzozmdt0(xd))
<=> aElementOf0(xn,szDzozmdt0(xd)) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0) ),
inference(and_elim,[status(thm)],[3]) ).
tff(13,plain,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(and_elim,[status(thm)],[12]) ).
tff(14,plain,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) ) ),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
aElementOf0(xn,szDzozmdt0(xd)),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
aElementOf0(xn,szDzozmdt0(xd)),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
aElementOf0(xn,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[16,10]) ).
tff(18,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(transitivity,[status(thm)],[23,21]) ).
tff(25,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [W0: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )),
( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
rewrite(
( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
( aFunction0(xe)
& ( szDzozmdt0(xe) = szNzAzT0 )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).
tff(33,plain,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(and_elim,[status(thm)],[32]) ).
tff(34,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[33,31]) ).
tff(35,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[34,29]) ).
tff(36,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[37,26]) ).
tff(39,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[38,24]) ).
tff(40,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ),
inference(modus_ponens,[status(thm)],[39,19]) ).
tff(41,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
| ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
~ ( ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ),
inference(unit_resolution,[status(thm)],[43,40,17]) ).
tff(45,plain,
( ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
| ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
| aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn)) ),
inference(tautology,[status(thm)],]) ).
tff(46,plain,
aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn)),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn)),
inference(modus_ponens,[status(thm)],[46,9]) ).
tff(48,plain,
( ~ aElementOf0(xp,sdtlpdtrp0(xN,xm))
<=> ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ~ aElementOf0(xp,sdtlpdtrp0(xN,xm))
<=> ~ aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(rewrite,[status(thm)],]) ).
tff(50,axiom,
~ aElementOf0(xp,sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(51,plain,
~ aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[51,48]) ).
tff(53,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
<=> ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
^ [W0: $i] :
rewrite(
( ( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
<=> ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,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(59,plain,
! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> aElementOf0(W0,sdtlpdtrp0(xN,xm)) ),
inference(and_elim,[status(thm)],[58]) ).
tff(60,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ),
inference(modus_ponens,[status(thm)],[59,57]) ).
tff(61,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ),
inference(modus_ponens,[status(thm)],[60,55]) ).
tff(62,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) ),
inference(modus_ponens,[status(thm)],[62,54]) ).
tff(64,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
| ~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xm)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
~ aElementOf0(szmzizndt0(xQ),sdtlpdtrp0(xN,xn)),
inference(unit_resolution,[status(thm)],[66,63,52]) ).
tff(68,plain,
$false,
inference(unit_resolution,[status(thm)],[67,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM622+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n028.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 12:36:07 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.
% 0.21/0.53 % SZS status Theorem
% 0.21/0.53 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------