TSTP Solution File: NUM607+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM607+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 14:28:02 EDT 2022
% Result : Theorem 13.89s 14.07s
% Output : Refutation 13.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of clauses : 41 ( 21 unt; 0 nHn; 41 RR)
% Number of literals : 91 ( 0 equ; 56 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aSet0(szNzAzT0),
file('NUM607+1.p',unknown),
[] ).
cnf(3,axiom,
isCountable0(szNzAzT0),
file('NUM607+1.p',unknown),
[] ).
cnf(6,axiom,
isCountable0(xS),
file('NUM607+1.p',unknown),
[] ).
cnf(8,axiom,
aFunction0(xN),
file('NUM607+1.p',unknown),
[] ).
cnf(13,axiom,
aSet0(xO),
file('NUM607+1.p',unknown),
[] ).
cnf(14,axiom,
isCountable0(xO),
file('NUM607+1.p',unknown),
[] ).
cnf(15,axiom,
aElementOf0(sz00,szNzAzT0),
file('NUM607+1.p',unknown),
[] ).
cnf(16,axiom,
aElementOf0(xK,szNzAzT0),
file('NUM607+1.p',unknown),
[] ).
cnf(17,axiom,
aSubsetOf0(xS,szNzAzT0),
file('NUM607+1.p',unknown),
[] ).
cnf(20,axiom,
aSubsetOf0(xO,xS),
file('NUM607+1.p',unknown),
[] ).
cnf(21,axiom,
aSubsetOf0(xQ,xO),
file('NUM607+1.p',unknown),
[] ).
cnf(29,axiom,
equal(szDzozmdt0(xN),szNzAzT0),
file('NUM607+1.p',unknown),
[] ).
cnf(38,axiom,
~ aElementOf0(xQ,szDzozmdt0(xc)),
file('NUM607+1.p',unknown),
[] ).
cnf(41,axiom,
equal(sdtlpdtrp0(xN,sz00),xS),
file('NUM607+1.p',unknown),
[] ).
cnf(43,axiom,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
file('NUM607+1.p',unknown),
[] ).
cnf(49,axiom,
equal(slbdtsldtrb0(xS,xK),szDzozmdt0(xc)),
file('NUM607+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| aSet0(v) ),
file('NUM607+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ aFunction0(u)
| ~ aElementOf0(v,szDzozmdt0(u))
| aElement0(sdtlpdtrp0(u,v)) ),
file('NUM607+1.p',unknown),
[] ).
cnf(148,axiom,
( ~ aSet0(u)
| ~ aSet0(v)
| ~ aSet0(w)
| ~ aSubsetOf0(u,v)
| ~ aSubsetOf0(v,w)
| aSubsetOf0(u,w) ),
file('NUM607+1.p',unknown),
[] ).
cnf(152,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,w)
| ~ aElementOf0(x,szNzAzT0)
| ~ equal(w,slbdtsldtrb0(u,x))
| equal(sbrdtbr0(v),x) ),
file('NUM607+1.p',unknown),
[] ).
cnf(171,axiom,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| ~ aElementOf0(w,szNzAzT0)
| ~ equal(x,slbdtsldtrb0(u,w))
| ~ equal(sbrdtbr0(v),w)
| aElementOf0(v,x) ),
file('NUM607+1.p',unknown),
[] ).
cnf(207,plain,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| ~ aSubsetOf0(w,v)
| aSubsetOf0(w,u) ),
inference(mrr,[status(thm)],[148,68]),
[iquote('0:MRR:148.0,148.1,68.2,68.2')] ).
cnf(232,plain,
( ~ aSet0(u)
| ~ aElementOf0(v,szNzAzT0)
| ~ aSubsetOf0(xQ,u)
| ~ equal(sbrdtbr0(xQ),v)
| ~ equal(slbdtsldtrb0(u,v),szDzozmdt0(xc)) ),
inference(res,[status(thm),theory(equality)],[171,38]),
[iquote('0:Res:171.5,38.0')] ).
cnf(325,plain,
( ~ aSet0(szNzAzT0)
| aSet0(xS) ),
inference(res,[status(thm),theory(equality)],[17,68]),
[iquote('0:Res:17.0,68.1')] ).
cnf(331,plain,
aSet0(xS),
inference(ssi,[status(thm)],[325,3,2]),
[iquote('0:SSi:325.0,3.0,2.0')] ).
cnf(521,plain,
( ~ aFunction0(xN)
| ~ aElementOf0(u,szNzAzT0)
| aElement0(sdtlpdtrp0(xN,u)) ),
inference(spl,[status(thm),theory(equality)],[29,89]),
[iquote('0:SpL:29.0,89.1')] ).
cnf(526,plain,
( ~ aElementOf0(u,szNzAzT0)
| aElement0(sdtlpdtrp0(xN,u)) ),
inference(ssi,[status(thm)],[521,8]),
[iquote('0:SSi:521.0,8.0')] ).
cnf(569,plain,
( ~ aElementOf0(sz00,szNzAzT0)
| aElement0(xS) ),
inference(spr,[status(thm),theory(equality)],[41,526]),
[iquote('0:SpR:41.0,526.1')] ).
cnf(570,plain,
aElement0(xS),
inference(mrr,[status(thm)],[569,15]),
[iquote('0:MRR:569.0,15.0')] ).
cnf(997,plain,
( ~ aSet0(xS)
| ~ aSubsetOf0(u,xO)
| aSubsetOf0(u,xS) ),
inference(res,[status(thm),theory(equality)],[20,207]),
[iquote('0:Res:20.0,207.1')] ).
cnf(1001,plain,
( ~ aSubsetOf0(u,xO)
| aSubsetOf0(u,xS) ),
inference(ssi,[status(thm)],[997,570,331,6]),
[iquote('0:SSi:997.0,570.0,331.0,6.0')] ).
cnf(1046,plain,
aSubsetOf0(xQ,xS),
inference(res,[status(thm),theory(equality)],[21,1001]),
[iquote('0:Res:21.0,1001.0')] ).
cnf(3505,plain,
( ~ aSet0(u)
| ~ aElementOf0(v,slbdtsldtrb0(u,w))
| ~ aElementOf0(w,szNzAzT0)
| equal(sbrdtbr0(v),w) ),
inference(eqr,[status(thm),theory(equality)],[152]),
[iquote('0:EqR:152.3')] ).
cnf(14022,plain,
( ~ aSet0(xO)
| ~ aElementOf0(xK,szNzAzT0)
| equal(sbrdtbr0(xQ),xK) ),
inference(res,[status(thm),theory(equality)],[43,3505]),
[iquote('0:Res:43.0,3505.1')] ).
cnf(14027,plain,
( ~ aElementOf0(xK,szNzAzT0)
| equal(sbrdtbr0(xQ),xK) ),
inference(ssi,[status(thm)],[14022,13,14]),
[iquote('0:SSi:14022.0,13.0,14.0')] ).
cnf(14028,plain,
equal(sbrdtbr0(xQ),xK),
inference(mrr,[status(thm)],[14027,16]),
[iquote('0:MRR:14027.0,16.0')] ).
cnf(14038,plain,
( ~ aSet0(u)
| ~ aElementOf0(v,szNzAzT0)
| ~ aSubsetOf0(xQ,u)
| ~ equal(xK,v)
| ~ equal(slbdtsldtrb0(u,v),szDzozmdt0(xc)) ),
inference(rew,[status(thm),theory(equality)],[14028,232]),
[iquote('0:Rew:14028.0,232.3')] ).
cnf(22949,plain,
( ~ aSet0(xS)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSubsetOf0(xQ,xS)
| ~ equal(xK,xK)
| ~ equal(szDzozmdt0(xc),szDzozmdt0(xc)) ),
inference(spl,[status(thm),theory(equality)],[49,14038]),
[iquote('0:SpL:49.0,14038.4')] ).
cnf(22950,plain,
( ~ aSet0(xS)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSubsetOf0(xQ,xS) ),
inference(obv,[status(thm),theory(equality)],[22949]),
[iquote('0:Obv:22949.4')] ).
cnf(22951,plain,
( ~ aElementOf0(xK,szNzAzT0)
| ~ aSubsetOf0(xQ,xS) ),
inference(ssi,[status(thm)],[22950,570,331,6]),
[iquote('0:SSi:22950.0,570.0,331.0,6.0')] ).
cnf(22952,plain,
$false,
inference(mrr,[status(thm)],[22951,16,1046]),
[iquote('0:MRR:22951.0,22951.1,16.0,1046.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM607+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 15:15:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 13.89/14.07
% 13.89/14.07 SPASS V 3.9
% 13.89/14.07 SPASS beiseite: Proof found.
% 13.89/14.07 % SZS status Theorem
% 13.89/14.07 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.89/14.07 SPASS derived 17345 clauses, backtracked 2635 clauses, performed 32 splits and kept 9190 clauses.
% 13.89/14.07 SPASS allocated 118991 KBytes.
% 13.89/14.07 SPASS spent 0:0:13.25 on the problem.
% 13.89/14.07 0:00:00.04 for the input.
% 13.89/14.07 0:00:00.29 for the FLOTTER CNF translation.
% 13.89/14.07 0:00:00.30 for inferences.
% 13.89/14.07 0:00:00.50 for the backtracking.
% 13.89/14.07 0:0:11.91 for the reduction.
% 13.89/14.07
% 13.89/14.07
% 13.89/14.07 Here is a proof with depth 2, length 41 :
% 13.89/14.07 % SZS output start Refutation
% See solution above
% 13.89/14.07 Formulae used in the proof : mNATSet m__3435 m__3623 m__4908 mZeroNum m__3418 m__4998 m__5093 m__ m__5078 m__3453 mDefSub mImgElm mSubTrans mDefSel
% 13.89/14.07
%------------------------------------------------------------------------------