TSTP Solution File: NUM554+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM554+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 14:27:27 EDT 2022
% Result : Theorem 1.04s 1.28s
% Output : Refutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of clauses : 48 ( 27 unt; 9 nHn; 48 RR)
% Number of literals : 92 ( 0 equ; 42 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
aSet0(xS),
file('NUM554+3.p',unknown),
[] ).
cnf(7,axiom,
aSet0(xQ),
file('NUM554+3.p',unknown),
[] ).
cnf(8,axiom,
isFinite0(xQ),
file('NUM554+3.p',unknown),
[] ).
cnf(9,axiom,
aElement0(xy),
file('NUM554+3.p',unknown),
[] ).
cnf(13,axiom,
aElementOf0(xx,xS),
file('NUM554+3.p',unknown),
[] ).
cnf(15,axiom,
aElementOf0(xy,xQ),
file('NUM554+3.p',unknown),
[] ).
cnf(20,axiom,
aSet0(slbdtsldtrb0(xS,xk)),
file('NUM554+3.p',unknown),
[] ).
cnf(23,axiom,
equal(sbrdtbr0(xQ),xk),
file('NUM554+3.p',unknown),
[] ).
cnf(25,axiom,
~ aElementOf0(xx,xQ),
file('NUM554+3.p',unknown),
[] ).
cnf(28,axiom,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('NUM554+3.p',unknown),
[] ).
cnf(42,axiom,
( ~ aElementOf0(u,xQ)
| aElementOf0(u,xS) ),
file('NUM554+3.p',unknown),
[] ).
cnf(43,axiom,
equal(sdtpldt0(sdtmndt0(xQ,xy),xx),xP),
file('NUM554+3.p',unknown),
[] ).
cnf(44,axiom,
( ~ equal(sbrdtbr0(xP),xk)
| aElementOf0(skc2,xP) ),
file('NUM554+3.p',unknown),
[] ).
cnf(53,axiom,
( ~ aElementOf0(skc2,xS)
| ~ equal(sbrdtbr0(xP),xk) ),
file('NUM554+3.p',unknown),
[] ).
cnf(55,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('NUM554+3.p',unknown),
[] ).
cnf(65,axiom,
( ~ aElementOf0(u,sdtmndt0(xQ,xy))
| aElementOf0(u,xQ) ),
file('NUM554+3.p',unknown),
[] ).
cnf(83,axiom,
( ~ aElementOf0(u,xP)
| equal(u,xx)
| aElementOf0(u,sdtmndt0(xQ,xy)) ),
file('NUM554+3.p',unknown),
[] ).
cnf(88,axiom,
( ~ isFinite0(u)
| ~ aSet0(u)
| ~ aElement0(v)
| isFinite0(sdtmndt0(u,v)) ),
file('NUM554+3.p',unknown),
[] ).
cnf(94,axiom,
( ~ aElement0(u)
| ~ aSet0(v)
| ~ equal(w,sdtmndt0(v,u))
| aSet0(w) ),
file('NUM554+3.p',unknown),
[] ).
cnf(121,axiom,
( ~ isFinite0(u)
| ~ aSet0(u)
| ~ aElementOf0(v,u)
| equal(szszuzczcdt0(sbrdtbr0(sdtmndt0(u,v))),sbrdtbr0(u)) ),
file('NUM554+3.p',unknown),
[] ).
cnf(132,axiom,
( ~ aElement0(u)
| ~ isFinite0(v)
| ~ aSet0(v)
| aElementOf0(u,v)
| equal(sbrdtbr0(sdtpldt0(v,u)),szszuzczcdt0(sbrdtbr0(v))) ),
file('NUM554+3.p',unknown),
[] ).
cnf(191,plain,
~ equal(sbrdtbr0(xP),xk),
inference(spt,[spt(split,[position(s1)])],[44]),
[iquote('1:Spt:44.0')] ).
cnf(240,plain,
( ~ aSet0(xS)
| aElement0(xx) ),
inference(res,[status(thm),theory(equality)],[13,55]),
[iquote('0:Res:13.0,55.1')] ).
cnf(246,plain,
( ~ aSet0(slbdtsldtrb0(xS,xk))
| aElement0(xQ) ),
inference(res,[status(thm),theory(equality)],[28,55]),
[iquote('0:Res:28.0,55.1')] ).
cnf(248,plain,
aElement0(xx),
inference(ssi,[status(thm)],[240,4]),
[iquote('0:SSi:240.0,4.0')] ).
cnf(251,plain,
aElement0(xQ),
inference(ssi,[status(thm)],[246,20]),
[iquote('0:SSi:246.0,20.0')] ).
cnf(806,plain,
( ~ aElement0(u)
| ~ aSet0(v)
| aSet0(sdtmndt0(v,u)) ),
inference(eqr,[status(thm),theory(equality)],[94]),
[iquote('0:EqR:94.2')] ).
cnf(2267,plain,
( ~ aElementOf0(u,xP)
| equal(u,xx)
| aElementOf0(u,xQ) ),
inference(res,[status(thm),theory(equality)],[83,65]),
[iquote('0:Res:83.2,65.0')] ).
cnf(2447,plain,
( ~ aElement0(xx)
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy))
| aElementOf0(xx,sdtmndt0(xQ,xy))
| equal(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))),sbrdtbr0(xP)) ),
inference(spr,[status(thm),theory(equality)],[43,132]),
[iquote('0:SpR:43.0,132.4')] ).
cnf(2459,plain,
( aElementOf0(xx,sdtmndt0(xQ,xy))
| equal(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))),sbrdtbr0(xP)) ),
inference(ssi,[status(thm)],[2447,806,8,7,251,9,88,248]),
[iquote('0:SSi:2447.2,2447.1,2447.0,806.0,8.0,7.0,251.0,9.0,88.3,8.0,7.0,251.0,9.0,806.2,8.0,7.0,251.0,9.0,88.3,8.0,7.0,251.0,9.0,248.2')] ).
cnf(4421,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElementOf0(xy,xQ)
| aElementOf0(xx,sdtmndt0(xQ,xy))
| equal(sbrdtbr0(xP),sbrdtbr0(xQ)) ),
inference(spr,[status(thm),theory(equality)],[2459,121]),
[iquote('0:SpR:2459.1,121.3')] ).
cnf(4441,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElementOf0(xy,xQ)
| aElementOf0(xx,sdtmndt0(xQ,xy))
| equal(sbrdtbr0(xP),xk) ),
inference(rew,[status(thm),theory(equality)],[23,4421]),
[iquote('0:Rew:23.0,4421.4')] ).
cnf(4442,plain,
( ~ aElementOf0(xy,xQ)
| aElementOf0(xx,sdtmndt0(xQ,xy))
| equal(sbrdtbr0(xP),xk) ),
inference(ssi,[status(thm)],[4441,8,7,251]),
[iquote('0:SSi:4441.1,4441.0,8.0,7.0,251.0,8.0,7.0,251.0')] ).
cnf(4443,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(mrr,[status(thm)],[4442,15,191]),
[iquote('1:MRR:4442.0,4442.2,15.0,191.0')] ).
cnf(4447,plain,
aElementOf0(xx,xQ),
inference(res,[status(thm),theory(equality)],[4443,65]),
[iquote('1:Res:4443.0,65.0')] ).
cnf(4452,plain,
$false,
inference(mrr,[status(thm)],[4447,25]),
[iquote('1:MRR:4447.0,25.0')] ).
cnf(4453,plain,
equal(sbrdtbr0(xP),xk),
inference(spt,[spt(split,[position(sa)])],[4452,191]),
[iquote('1:Spt:4452.0,44.0,191.0')] ).
cnf(4454,plain,
aElementOf0(skc2,xP),
inference(spt,[spt(split,[position(s2)])],[44]),
[iquote('1:Spt:4452.0,44.1')] ).
cnf(4463,plain,
( ~ aElementOf0(skc2,xS)
| ~ equal(xk,xk) ),
inference(rew,[status(thm),theory(equality)],[4453,53]),
[iquote('1:Rew:4453.0,53.1')] ).
cnf(4464,plain,
~ aElementOf0(skc2,xS),
inference(obv,[status(thm),theory(equality)],[4463]),
[iquote('1:Obv:4463.1')] ).
cnf(4526,plain,
( equal(skc2,xx)
| aElementOf0(skc2,xQ) ),
inference(res,[status(thm),theory(equality)],[4454,2267]),
[iquote('1:Res:4454.0,2267.0')] ).
cnf(4621,plain,
equal(skc2,xx),
inference(spt,[spt(split,[position(s2s1)])],[4526]),
[iquote('2:Spt:4526.0')] ).
cnf(4624,plain,
~ aElementOf0(xx,xS),
inference(rew,[status(thm),theory(equality)],[4621,4464]),
[iquote('2:Rew:4621.0,4464.0')] ).
cnf(4627,plain,
$false,
inference(mrr,[status(thm)],[4624,13]),
[iquote('2:MRR:4624.0,13.0')] ).
cnf(4628,plain,
~ equal(skc2,xx),
inference(spt,[spt(split,[position(s2sa)])],[4627,4621]),
[iquote('2:Spt:4627.0,4526.0,4621.0')] ).
cnf(4629,plain,
aElementOf0(skc2,xQ),
inference(spt,[spt(split,[position(s2s2)])],[4526]),
[iquote('2:Spt:4627.0,4526.1')] ).
cnf(4632,plain,
aElementOf0(skc2,xS),
inference(res,[status(thm),theory(equality)],[4629,42]),
[iquote('2:Res:4629.0,42.0')] ).
cnf(4636,plain,
$false,
inference(mrr,[status(thm)],[4632,4464]),
[iquote('2:MRR:4632.0,4464.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM554+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 08:13:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.04/1.28
% 1.04/1.28 SPASS V 3.9
% 1.04/1.28 SPASS beiseite: Proof found.
% 1.04/1.28 % SZS status Theorem
% 1.04/1.28 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.04/1.28 SPASS derived 3151 clauses, backtracked 371 clauses, performed 24 splits and kept 1984 clauses.
% 1.04/1.28 SPASS allocated 101297 KBytes.
% 1.04/1.28 SPASS spent 0:00:00.91 on the problem.
% 1.04/1.28 0:00:00.03 for the input.
% 1.04/1.28 0:00:00.16 for the FLOTTER CNF translation.
% 1.04/1.28 0:00:00.05 for inferences.
% 1.04/1.28 0:00:00.01 for the backtracking.
% 1.04/1.28 0:00:00.62 for the reduction.
% 1.04/1.28
% 1.04/1.28
% 1.04/1.28 Here is a proof with depth 4, length 48 :
% 1.04/1.28 % SZS output start Refutation
% See solution above
% 1.04/1.28 Formulae used in the proof : m__2202_02 m__2291 m__2304 m__2256 m__2227 m__2338 m__2270 m__2357 m__ mEOfElem mFDiffSet mDefDiff mCardDiff mCardCons
% 1.04/1.28
%------------------------------------------------------------------------------