TSTP Solution File: NUM580+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM580+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 14:27:44 EDT 2022
% Result : Theorem 2.19s 2.38s
% Output : Refutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 17
% Syntax : Number of clauses : 35 ( 14 unt; 1 nHn; 35 RR)
% Number of literals : 73 ( 0 equ; 41 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
aSet0(xQ),
file('NUM580+3.p',unknown),
[] ).
cnf(14,axiom,
aElementOf0(xk,szNzAzT0),
file('NUM580+3.p',unknown),
[] ).
cnf(15,axiom,
aElementOf0(xi,szNzAzT0),
file('NUM580+3.p',unknown),
[] ).
cnf(21,axiom,
equal(szszuzczcdt0(xk),xK),
file('NUM580+3.p',unknown),
[] ).
cnf(23,axiom,
equal(sbrdtbr0(xQ),xk),
file('NUM580+3.p',unknown),
[] ).
cnf(51,axiom,
( ~ aElementOf0(u,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,u)) ),
file('NUM580+3.p',unknown),
[] ).
cnf(52,axiom,
( ~ aElementOf0(u,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,u)) ),
file('NUM580+3.p',unknown),
[] ).
cnf(53,axiom,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
file('NUM580+3.p',unknown),
[] ).
cnf(54,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM580+3.p',unknown),
[] ).
cnf(65,axiom,
( ~ aElementOf0(u,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,u),szNzAzT0) ),
file('NUM580+3.p',unknown),
[] ).
cnf(67,axiom,
~ equal(sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),xK),
file('NUM580+3.p',unknown),
[] ).
cnf(69,axiom,
( ~ aSet0(u)
| ~ aElementOf0(sbrdtbr0(u),szNzAzT0)
| isFinite0(u) ),
file('NUM580+3.p',unknown),
[] ).
cnf(101,axiom,
( ~ isCountable0(sdtlpdtrp0(xN,u))
| ~ aSubsetOf0(sdtlpdtrp0(xN,u),szNzAzT0)
| skP6(u) ),
file('NUM580+3.p',unknown),
[] ).
cnf(102,axiom,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,sdtlpdtrp0(xN,u))
| aElementOf0(v,szNzAzT0) ),
file('NUM580+3.p',unknown),
[] ).
cnf(113,axiom,
( ~ aElementOf0(u,xQ)
| aElementOf0(u,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
file('NUM580+3.p',unknown),
[] ).
cnf(154,axiom,
( ~ equal(u,szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aElementOf0(u,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
file('NUM580+3.p',unknown),
[] ).
cnf(173,axiom,
( ~ aElement0(u)
| ~ isFinite0(v)
| ~ aSet0(v)
| aElementOf0(u,v)
| equal(sbrdtbr0(sdtpldt0(v,u)),szszuzczcdt0(sbrdtbr0(v))) ),
file('NUM580+3.p',unknown),
[] ).
cnf(430,plain,
( ~ aSet0(sdtlpdtrp0(xN,xi))
| aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))) ),
inference(res,[status(thm),theory(equality)],[53,54]),
[iquote('0:Res:53.0,54.1')] ).
cnf(452,plain,
( ~ aElementOf0(xi,szNzAzT0)
| aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))) ),
inference(sor,[status(thm)],[430,51]),
[iquote('0:SoR:430.0,51.1')] ).
cnf(454,plain,
aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(mrr,[status(thm)],[452,15]),
[iquote('0:MRR:452.0,15.0')] ).
cnf(465,plain,
( ~ aSet0(xQ)
| ~ aElementOf0(xk,szNzAzT0)
| isFinite0(xQ) ),
inference(spl,[status(thm),theory(equality)],[23,69]),
[iquote('0:SpL:23.0,69.1')] ).
cnf(470,plain,
( ~ aElementOf0(xk,szNzAzT0)
| isFinite0(xQ) ),
inference(ssi,[status(thm)],[465,10]),
[iquote('0:SSi:465.0,10.0')] ).
cnf(471,plain,
isFinite0(xQ),
inference(mrr,[status(thm)],[470,14]),
[iquote('0:MRR:470.0,14.0')] ).
cnf(876,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,u))
| skP6(u) ),
inference(res,[status(thm),theory(equality)],[65,101]),
[iquote('0:Res:65.1,101.1')] ).
cnf(879,plain,
( ~ aElementOf0(u,szNzAzT0)
| skP6(u) ),
inference(mrr,[status(thm)],[876,52]),
[iquote('0:MRR:876.1,52.1')] ).
cnf(961,plain,
( ~ aElementOf0(xi,szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),szNzAzT0) ),
inference(res,[status(thm),theory(equality)],[53,102]),
[iquote('0:Res:53.0,102.1')] ).
cnf(965,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),szNzAzT0),
inference(mrr,[status(thm)],[961,15]),
[iquote('0:MRR:961.0,15.0')] ).
cnf(969,plain,
skP6(szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(res,[status(thm),theory(equality)],[965,879]),
[iquote('0:Res:965.0,879.0')] ).
cnf(7459,plain,
( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ equal(szszuzczcdt0(sbrdtbr0(xQ)),xK)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ) ),
inference(spl,[status(thm),theory(equality)],[173,67]),
[iquote('0:SpL:173.4,67.0')] ).
cnf(7480,plain,
( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ equal(xK,xK)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ) ),
inference(rew,[status(thm),theory(equality)],[21,7459,23]),
[iquote('0:Rew:21.0,7459.3,23.0,7459.3')] ).
cnf(7481,plain,
( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ) ),
inference(obv,[status(thm),theory(equality)],[7480]),
[iquote('0:Obv:7480.3')] ).
cnf(7482,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ),
inference(ssi,[status(thm)],[7481,10,471,454,969]),
[iquote('0:SSi:7481.2,7481.1,7481.0,10.0,471.0,10.0,471.0,454.0,969.0')] ).
cnf(8080,plain,
( ~ aElementOf0(u,xQ)
| ~ equal(u,szmzizndt0(sdtlpdtrp0(xN,xi))) ),
inference(res,[status(thm),theory(equality)],[113,154]),
[iquote('0:Res:113.1,154.1')] ).
cnf(9857,plain,
~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ),
inference(eqr,[status(thm),theory(equality)],[8080]),
[iquote('0:EqR:8080.1')] ).
cnf(9858,plain,
$false,
inference(mrr,[status(thm)],[9857,7482]),
[iquote('0:MRR:9857.0,7482.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM580+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.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 15:37:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.19/2.38
% 2.19/2.38 SPASS V 3.9
% 2.19/2.38 SPASS beiseite: Proof found.
% 2.19/2.38 % SZS status Theorem
% 2.19/2.38 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.19/2.38 SPASS derived 7506 clauses, backtracked 1622 clauses, performed 27 splits and kept 4242 clauses.
% 2.19/2.38 SPASS allocated 104303 KBytes.
% 2.19/2.38 SPASS spent 0:00:01.97 on the problem.
% 2.19/2.38 0:00:00.04 for the input.
% 2.19/2.38 0:00:00.53 for the FLOTTER CNF translation.
% 2.19/2.38 0:00:00.11 for inferences.
% 2.19/2.38 0:00:00.03 for the backtracking.
% 2.19/2.38 0:00:01.18 for the reduction.
% 2.19/2.38
% 2.19/2.38
% 2.19/2.38 Here is a proof with depth 2, length 35 :
% 2.19/2.38 % SZS output start Refutation
% See solution above
% 2.19/2.38 Formulae used in the proof : m__3989_02 m__3533 m__3989 m__3671 mEOfElem m__ mCardNum m__3623 mCardCons
% 2.19/2.38
%------------------------------------------------------------------------------