TSTP Solution File: NUM423+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM423+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 13:09:36 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 37
% Syntax : Number of formulae : 84 ( 21 unt; 9 typ; 0 def)
% Number of atoms : 295 ( 167 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 436 ( 233 ~; 123 |; 46 &)
% ( 28 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 47 !; 12 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(xa_type,type,
xa: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(xq_type,type,
xq: $i ).
tff(aInteger0_type,type,
aInteger0: $i > $o ).
tff(aDivisorOf0_type,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(1,plain,
( aInteger0(xa)
<=> aInteger0(xa) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
( aInteger0(xa)
& aInteger0(xq)
& ( xq != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__671) ).
tff(3,plain,
( aInteger0(xa)
& aInteger0(xq) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aInteger0(xa),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aInteger0(xa),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [W0: $i] :
refl(
( ( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [W0: $i] :
rewrite(
( ( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
^ [W0: $i] :
rewrite(
( ( aInteger0(W0)
=> ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,axiom,
! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
tff(14,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[17,7]) ).
tff(19,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xa),xa) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xa),xa) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xa),xa) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xa),xa) ) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xa),xa) ) ),
inference(unit_resolution,[status(thm)],[21,18,5]) ).
tff(23,plain,
( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xa),xa) )
| ( sdtpldt0(xa,smndt0(xa)) = sz00 ) ),
inference(tautology,[status(thm)],]) ).
tff(24,plain,
sdtpldt0(xa,smndt0(xa)) = sz00,
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
sz00 = sdtpldt0(xa,smndt0(xa)),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( aInteger0(xq)
<=> aInteger0(xq) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
aInteger0(xq),
inference(and_elim,[status(thm)],[3]) ).
tff(28,plain,
aInteger0(xq),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
^ [W0: $i] :
refl(
( ( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
^ [W0: $i] :
rewrite(
( ( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
^ [W0: $i] :
rewrite(
( ( aInteger0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
tff(37,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[40,30]) ).
tff(42,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aInteger0(xq)
| ~ ( ( sdtasdt0(xq,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xq) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aInteger0(xq)
| ~ ( ( sdtasdt0(xq,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xq) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aInteger0(xq)
| ~ ( ( sdtasdt0(xq,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xq) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aInteger0(xq)
| ~ ( ( sdtasdt0(xq,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xq) ) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ ( ( sdtasdt0(xq,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xq) ) ),
inference(unit_resolution,[status(thm)],[44,41,28]) ).
tff(46,plain,
( ( sdtasdt0(xq,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xq) )
| ( sdtasdt0(xq,sz00) = sz00 ) ),
inference(tautology,[status(thm)],]) ).
tff(47,plain,
sdtasdt0(xq,sz00) = sz00,
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
sdtasdt0(xq,sz00) = sdtpldt0(xa,smndt0(xa)),
inference(transitivity,[status(thm)],[47,25]) ).
tff(49,plain,
^ [W0: $i] :
refl(
( ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) )
<=> ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) )
<=> ~ ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ) )),
( ~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) )
<=> ~ ~ ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ) )),
rewrite(
( ~ ~ ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) )
<=> ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ) )),
( ~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) )
<=> ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [W0: $i] :
~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) )
<=> ~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,axiom,
~ ( ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(55,plain,
~ ( ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) ),
inference(or_elim,[status(thm)],[54]) ).
tff(56,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
inference(or_elim,[status(thm)],[55]) ).
tff(57,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[56,53]) ).
tff(58,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[58,53]) ).
tff(60,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[59,53]) ).
tff(61,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[61,53]) ).
tff(63,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[62,53]) ).
tff(64,plain,
^ [W0: $i] :
refl(
$oeq(
~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ))),
inference(bind,[status(th)],]) ).
tff(65,plain,
! [W0: $i] :
~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
inference(nnf-neg,[status(sab)],[63,64]) ).
tff(66,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[65,52]) ).
tff(67,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[66,50]) ).
tff(68,plain,
( aInteger0(sz00)
<=> aInteger0(sz00) ),
inference(rewrite,[status(thm)],]) ).
tff(69,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
tff(70,plain,
aInteger0(sz00),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) )
| ~ aInteger0(sz00)
| ( sdtasdt0(xq,sz00) != sdtpldt0(xa,smndt0(xa)) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) )
| ~ aInteger0(sz00)
| ( sdtasdt0(xq,sz00) != sdtpldt0(xa,smndt0(xa)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) )
| ~ aInteger0(sz00)
| ( sdtasdt0(xq,sz00) != sdtpldt0(xa,smndt0(xa)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) )
| ~ aInteger0(sz00)
| ( sdtasdt0(xq,sz00) != sdtpldt0(xa,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
sdtasdt0(xq,sz00) != sdtpldt0(xa,smndt0(xa)),
inference(unit_resolution,[status(thm)],[73,70,67]) ).
tff(75,plain,
$false,
inference(unit_resolution,[status(thm)],[74,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM423+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 10:18:10 EDT 2022
% 0.13/0.34 % 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.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------