TSTP Solution File: NUM490+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM490+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 14:26:44 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 28 ( 12 unt; 0 nHn; 28 RR)
% Number of literals : 69 ( 0 equ; 50 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM490+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM490+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM490+1.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM490+1.p',unknown),
[] ).
cnf(9,axiom,
sdtlseqdt0(xp,xn),
file('NUM490+1.p',unknown),
[] ).
cnf(16,axiom,
equal(sdtmndt0(xn,xp),xr),
file('NUM490+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM490+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM490+1.p',unknown),
[] ).
cnf(29,axiom,
equal(sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),sdtasdt0(xn,xm)),
file('NUM490+1.p',unknown),
[] ).
cnf(30,axiom,
~ equal(sdtasdt0(xr,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))),
file('NUM490+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM490+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| aNaturalNumber0(w) ),
file('NUM490+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,w)
| ~ equal(sdtpldt0(v,u),w)
| equal(u,sdtmndt0(w,v)) ),
file('NUM490+1.p',unknown),
[] ).
cnf(82,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| equal(w,sdtmndt0(u,v)) ),
inference(mrr,[status(thm)],[74,51]),
[iquote('0:MRR:74.3,51.4')] ).
cnf(88,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ equal(sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),sdtasdt0(xn,xm)) ),
inference(res,[status(thm),theory(equality)],[82,30]),
[iquote('0:Res:82.4,30.0')] ).
cnf(109,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ equal(sdtasdt0(xn,xm),sdtasdt0(xn,xm)) ),
inference(rew,[status(thm),theory(equality)],[29,88]),
[iquote('0:Rew:29.0,88.3')] ).
cnf(110,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm)) ),
inference(obv,[status(thm),theory(equality)],[109]),
[iquote('0:Obv:109.3')] ).
cnf(133,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(spr,[status(thm),theory(equality)],[29,25]),
[iquote('0:SpR:29.0,25.2')] ).
cnf(135,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(ssi,[status(thm)],[133,26,6,5,4]),
[iquote('0:SSi:133.1,26.0,6.0,5.0,4.2')] ).
cnf(136,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm)) ),
inference(mrr,[status(thm)],[110,135]),
[iquote('0:MRR:110.0,135.1')] ).
cnf(137,plain,
~ aNaturalNumber0(sdtasdt0(xr,xm)),
inference(ssi,[status(thm)],[136,26,6,5,4]),
[iquote('0:SSi:136.0,26.0,6.0,5.0,4.2')] ).
cnf(138,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(sor,[status(thm)],[137,26]),
[iquote('0:SoR:137.0,26.2')] ).
cnf(139,plain,
~ aNaturalNumber0(xr),
inference(ssi,[status(thm)],[138,4]),
[iquote('0:SSi:138.1,4.0')] ).
cnf(734,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ~ equal(u,xr)
| aNaturalNumber0(u) ),
inference(spl,[status(thm),theory(equality)],[16,52]),
[iquote('0:SpL:16.0,52.3')] ).
cnf(735,plain,
( ~ sdtlseqdt0(xp,xn)
| ~ equal(u,xr)
| aNaturalNumber0(u) ),
inference(ssi,[status(thm)],[734,6,5,3]),
[iquote('0:SSi:734.1,734.0,6.0,5.0,3.0')] ).
cnf(736,plain,
( ~ equal(u,xr)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[735,9]),
[iquote('0:MRR:735.0,9.0')] ).
cnf(779,plain,
~ equal(xr,xr),
inference(sor,[status(thm)],[139,736]),
[iquote('0:SoR:139.0,736.1')] ).
cnf(780,plain,
$false,
inference(obv,[status(thm),theory(equality)],[779]),
[iquote('0:Obv:779.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM490+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.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 : Tue Jul 5 11:45:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 481 clauses, backtracked 15 clauses, performed 3 splits and kept 224 clauses.
% 0.19/0.49 SPASS allocated 98213 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.49 0:00:00.04 for the input.
% 0.19/0.49 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.01 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.04 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 3, length 28 :
% 0.19/0.49 % SZS output start Refutation
% See solution above
% 0.19/0.49 Formulae used in the proof : m__1837 m__1860 m__1870 m__1883 mSortsB mSortsB_02 m__1951 m__ mDefLE mDefDiff
% 0.19/0.49
%------------------------------------------------------------------------------