TSTP Solution File: NUM612+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM612+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 : 600s
% DateTime : Mon Jul 18 14:28:06 EDT 2022
% Result : Theorem 1.74s 1.96s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of clauses : 34 ( 17 unt; 0 nHn; 34 RR)
% Number of literals : 65 ( 0 equ; 36 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
aFunction0(xc),
file('NUM612+3.p',unknown),
[] ).
cnf(16,axiom,
aSet0(xQ),
file('NUM612+3.p',unknown),
[] ).
cnf(17,axiom,
aSet0(xP),
file('NUM612+3.p',unknown),
[] ).
cnf(19,axiom,
aElementOf0(xK,szNzAzT0),
file('NUM612+3.p',unknown),
[] ).
cnf(29,axiom,
aElementOf0(xp,xQ),
file('NUM612+3.p',unknown),
[] ).
cnf(30,axiom,
aSubsetOf0(xP,xQ),
file('NUM612+3.p',unknown),
[] ).
cnf(46,axiom,
equal(sbrdtbr0(xQ),xK),
file('NUM612+3.p',unknown),
[] ).
cnf(48,axiom,
aElementOf0(xQ,szDzozmdt0(xc)),
file('NUM612+3.p',unknown),
[] ).
cnf(49,axiom,
equal(szmzizndt0(xQ),xp),
file('NUM612+3.p',unknown),
[] ).
cnf(66,axiom,
( ~ aFunction0(u)
| aSet0(szDzozmdt0(u)) ),
file('NUM612+3.p',unknown),
[] ).
cnf(73,axiom,
equal(sdtmndt0(xQ,szmzizndt0(xQ)),xP),
file('NUM612+3.p',unknown),
[] ).
cnf(104,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM612+3.p',unknown),
[] ).
cnf(119,axiom,
( ~ aSet0(u)
| ~ aElementOf0(sbrdtbr0(u),szNzAzT0)
| isFinite0(u) ),
file('NUM612+3.p',unknown),
[] ).
cnf(120,axiom,
( ~ aSet0(u)
| ~ isFinite0(u)
| aElementOf0(sbrdtbr0(u),szNzAzT0) ),
file('NUM612+3.p',unknown),
[] ).
cnf(136,axiom,
( ~ equal(szszuzczcdt0(sbrdtbr0(xP)),sbrdtbr0(xQ))
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
file('NUM612+3.p',unknown),
[] ).
cnf(137,axiom,
( ~ isFinite0(u)
| ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| isFinite0(v) ),
file('NUM612+3.p',unknown),
[] ).
cnf(233,axiom,
( ~ isFinite0(u)
| ~ aSet0(u)
| ~ aElementOf0(v,u)
| equal(szszuzczcdt0(sbrdtbr0(sdtmndt0(u,v))),sbrdtbr0(u)) ),
file('NUM612+3.p',unknown),
[] ).
cnf(402,plain,
equal(sdtmndt0(xQ,xp),xP),
inference(rew,[status(thm),theory(equality)],[49,73]),
[iquote('0:Rew:49.0,73.0')] ).
cnf(412,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ~ equal(szszuzczcdt0(sbrdtbr0(xP)),xK) ),
inference(rew,[status(thm),theory(equality)],[46,136]),
[iquote('0:Rew:46.0,136.0')] ).
cnf(624,plain,
( ~ aSet0(szDzozmdt0(xc))
| aElement0(xQ) ),
inference(res,[status(thm),theory(equality)],[48,104]),
[iquote('0:Res:48.0,104.1')] ).
cnf(643,plain,
aElement0(xQ),
inference(ssi,[status(thm)],[624,66,8]),
[iquote('0:SSi:624.0,66.0,8.1')] ).
cnf(702,plain,
( ~ aSet0(xQ)
| ~ aElementOf0(xK,szNzAzT0)
| isFinite0(xQ) ),
inference(spl,[status(thm),theory(equality)],[46,119]),
[iquote('0:SpL:46.0,119.1')] ).
cnf(708,plain,
( ~ aElementOf0(xK,szNzAzT0)
| isFinite0(xQ) ),
inference(ssi,[status(thm)],[702,16,643]),
[iquote('0:SSi:702.0,16.0,643.0')] ).
cnf(709,plain,
isFinite0(xQ),
inference(mrr,[status(thm)],[708,19]),
[iquote('0:MRR:708.0,19.0')] ).
cnf(773,plain,
( ~ aSet0(xP)
| ~ isFinite0(xP)
| ~ equal(szszuzczcdt0(sbrdtbr0(xP)),xK) ),
inference(res,[status(thm),theory(equality)],[120,412]),
[iquote('0:Res:120.2,412.0')] ).
cnf(774,plain,
( ~ isFinite0(xP)
| ~ equal(szszuzczcdt0(sbrdtbr0(xP)),xK) ),
inference(ssi,[status(thm)],[773,17]),
[iquote('0:SSi:773.0,17.0')] ).
cnf(1217,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| isFinite0(xP) ),
inference(res,[status(thm),theory(equality)],[30,137]),
[iquote('0:Res:30.0,137.2')] ).
cnf(4764,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElementOf0(xp,xQ)
| equal(szszuzczcdt0(sbrdtbr0(xP)),sbrdtbr0(xQ)) ),
inference(spr,[status(thm),theory(equality)],[402,233]),
[iquote('0:SpR:402.0,233.3')] ).
cnf(4791,plain,
isFinite0(xP),
inference(ssi,[status(thm)],[1217,709,643,16]),
[iquote('0:SSi:1217.1,1217.0,709.0,643.0,16.0,709.0,643.0,16.0')] ).
cnf(4792,plain,
~ equal(szszuzczcdt0(sbrdtbr0(xP)),xK),
inference(mrr,[status(thm)],[774,4791]),
[iquote('0:MRR:774.0,4791.0')] ).
cnf(4858,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElementOf0(xp,xQ)
| equal(szszuzczcdt0(sbrdtbr0(xP)),xK) ),
inference(rew,[status(thm),theory(equality)],[46,4764]),
[iquote('0:Rew:46.0,4764.3')] ).
cnf(4859,plain,
( ~ aElementOf0(xp,xQ)
| equal(szszuzczcdt0(sbrdtbr0(xP)),xK) ),
inference(ssi,[status(thm)],[4858,709,643,16]),
[iquote('0:SSi:4858.1,4858.0,709.0,643.0,16.0,709.0,643.0,16.0')] ).
cnf(4860,plain,
equal(szszuzczcdt0(sbrdtbr0(xP)),xK),
inference(mrr,[status(thm)],[4859,29]),
[iquote('0:MRR:4859.0,29.0')] ).
cnf(4861,plain,
$false,
inference(mrr,[status(thm)],[4860,4792]),
[iquote('0:MRR:4860.0,4792.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM612+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jul 5 22:22:52 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.74/1.96
% 1.74/1.96 SPASS V 3.9
% 1.74/1.96 SPASS beiseite: Proof found.
% 1.74/1.96 % SZS status Theorem
% 1.74/1.96 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.74/1.96 SPASS derived 3229 clauses, backtracked 615 clauses, performed 7 splits and kept 2352 clauses.
% 1.74/1.96 SPASS allocated 104656 KBytes.
% 1.74/1.96 SPASS spent 0:00:01.56 on the problem.
% 1.74/1.96 0:00:00.04 for the input.
% 1.74/1.96 0:00:00.69 for the FLOTTER CNF translation.
% 1.74/1.96 0:00:00.05 for inferences.
% 1.74/1.96 0:00:00.01 for the backtracking.
% 1.74/1.96 0:00:00.71 for the reduction.
% 1.74/1.96
% 1.74/1.96
% 1.74/1.96 Here is a proof with depth 1, length 34 :
% 1.74/1.96 % SZS output start Refutation
% See solution above
% 1.74/1.96 Formulae used in the proof : m__3453 m__5116 m__5078 m__5164 m__3418 m__5173 m__5195 m__5147 mDomSet mEOfElem mCardNum m__ mSubFSet mCardDiff
% 1.74/1.96
%------------------------------------------------------------------------------