TSTP Solution File: NUM521+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM521+1 : 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 14:27:04 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of clauses : 31 ( 19 unt; 2 nHn; 31 RR)
% Number of literals : 56 ( 0 equ; 35 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aNaturalNumber0(sz10),
file('NUM521+1.p',unknown),
[] ).
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM521+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM521+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM521+1.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM521+1.p',unknown),
[] ).
cnf(9,axiom,
~ doDivides0(xp,xn),
file('NUM521+1.p',unknown),
[] ).
cnf(14,axiom,
~ sdtlseqdt0(xp,xn),
file('NUM521+1.p',unknown),
[] ).
cnf(15,axiom,
~ sdtlseqdt0(xp,xm),
file('NUM521+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ aNaturalNumber0(u)
| sdtlseqdt0(u,u) ),
file('NUM521+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,sz10),u) ),
file('NUM521+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(v,u)
| sdtlseqdt0(u,v) ),
file('NUM521+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ sdtlseqdt0(xm,xp)
| ~ sdtlseqdt0(xn,xp)
| equal(xp,xm)
| equal(xp,xn) ),
file('NUM521+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM521+1.p',unknown),
[] ).
cnf(89,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ equal(sdtasdt0(xp,u),xn) ),
inference(res,[status(thm),theory(equality)],[51,9]),
[iquote('0:Res:51.4,9.0')] ).
cnf(94,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(xp,u),xn) ),
inference(mrr,[status(thm)],[89,5,3]),
[iquote('0:MRR:89.1,89.2,5.0,3.0')] ).
cnf(115,plain,
equal(xp,xm),
inference(spt,[spt(split,[position(s1)])],[37]),
[iquote('1:Spt:37.2')] ).
cnf(131,plain,
isPrime0(xm),
inference(rew,[status(thm),theory(equality)],[115,6]),
[iquote('1:Rew:115.0,6.0')] ).
cnf(133,plain,
~ sdtlseqdt0(xm,xm),
inference(rew,[status(thm),theory(equality)],[115,15]),
[iquote('1:Rew:115.0,15.0')] ).
cnf(148,plain,
~ aNaturalNumber0(xm),
inference(res,[status(thm),theory(equality)],[17,133]),
[iquote('1:Res:17.1,133.0')] ).
cnf(149,plain,
$false,
inference(ssi,[status(thm)],[148,4,131]),
[iquote('1:SSi:148.0,4.0,131.0')] ).
cnf(150,plain,
~ equal(xp,xm),
inference(spt,[spt(split,[position(sa)])],[149,115]),
[iquote('1:Spt:149.0,37.2,115.0')] ).
cnf(151,plain,
( ~ sdtlseqdt0(xm,xp)
| ~ sdtlseqdt0(xn,xp)
| equal(xp,xn) ),
inference(spt,[spt(split,[position(s2)])],[37]),
[iquote('1:Spt:149.0,37.0,37.1,37.3')] ).
cnf(167,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10)
| ~ equal(xp,xn) ),
inference(spl,[status(thm),theory(equality)],[20,94]),
[iquote('0:SpL:20.1,94.1')] ).
cnf(169,plain,
~ equal(xp,xn),
inference(ssi,[status(thm)],[167,2,5,6]),
[iquote('0:SSi:167.1,167.0,2.0,5.0,6.0')] ).
cnf(170,plain,
( ~ sdtlseqdt0(xm,xp)
| ~ sdtlseqdt0(xn,xp) ),
inference(mrr,[status(thm)],[151,169]),
[iquote('1:MRR:151.2,169.0')] ).
cnf(182,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(xn,xp) ),
inference(res,[status(thm),theory(equality)],[28,14]),
[iquote('0:Res:28.2,14.0')] ).
cnf(185,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(xm,xp) ),
inference(res,[status(thm),theory(equality)],[28,15]),
[iquote('0:Res:28.3,15.0')] ).
cnf(187,plain,
sdtlseqdt0(xn,xp),
inference(ssi,[status(thm)],[182,5,6,3]),
[iquote('0:SSi:182.1,182.0,5.0,6.0,3.0')] ).
cnf(188,plain,
~ sdtlseqdt0(xm,xp),
inference(mrr,[status(thm)],[170,187]),
[iquote('1:MRR:170.1,187.0')] ).
cnf(191,plain,
sdtlseqdt0(xm,xp),
inference(ssi,[status(thm)],[185,4,5,6]),
[iquote('0:SSi:185.1,185.0,4.0,5.0,6.0')] ).
cnf(192,plain,
$false,
inference(mrr,[status(thm)],[191,188]),
[iquote('1:MRR:191.0,188.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM521+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n004.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 : 600
% 0.13/0.34 % DateTime : Thu Jul 7 15:37:52 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 75 clauses, backtracked 24 clauses, performed 1 splits and kept 148 clauses.
% 0.20/0.48 SPASS allocated 97891 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.48 0:00:00.04 for the input.
% 0.20/0.48 0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.00 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.02 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 2, length 31 :
% 0.20/0.48 % SZS output start Refutation
% See solution above
% 0.20/0.48 Formulae used in the proof : mSortsC_01 m__1837 m__1860 m__ m__1870 m__2075 mLERefl m_MulUnit mLETotal m__2287 mDefDiv
% 0.20/0.48
%------------------------------------------------------------------------------