TSTP Solution File: NUM505+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM505+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 14:26:54 EDT 2022
% Result : Theorem 0.45s 0.64s
% Output : Refutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of clauses : 43 ( 18 unt; 4 nHn; 43 RR)
% Number of literals : 118 ( 0 equ; 81 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM505+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM505+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM505+1.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM505+1.p',unknown),
[] ).
cnf(15,axiom,
~ sdtlseqdt0(xp,xk),
file('NUM505+1.p',unknown),
[] ).
cnf(17,axiom,
aNaturalNumber0(skf4(u,v)),
file('NUM505+1.p',unknown),
[] ).
cnf(27,axiom,
doDivides0(xp,sdtasdt0(xn,xm)),
file('NUM505+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ aNaturalNumber0(u)
| sdtlseqdt0(u,u) ),
file('NUM505+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ sdtlseqdt0(xk,xp)
| equal(xk,xp) ),
file('NUM505+1.p',unknown),
[] ).
cnf(31,axiom,
equal(sdtsldt0(sdtasdt0(xn,xm),xp),xk),
file('NUM505+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM505+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM505+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ aNaturalNumber0(u)
| ~ isPrime0(u)
| ~ equal(u,sz00) ),
file('NUM505+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(v,u)
| sdtlseqdt0(u,v) ),
file('NUM505+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM505+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| aNaturalNumber0(w) ),
file('NUM505+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| aNaturalNumber0(w)
| equal(v,sz00) ),
file('NUM505+1.p',unknown),
[] ).
cnf(85,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,w)
| ~ equal(sdtpldt0(v,u),w)
| equal(u,sdtmndt0(w,v)) ),
file('NUM505+1.p',unknown),
[] ).
cnf(93,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| equal(w,sdtmndt0(u,v)) ),
inference(mrr,[status(thm)],[85,62]),
[iquote('0:MRR:85.3,62.4')] ).
cnf(96,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(xk,xp) ),
inference(res,[status(thm),theory(equality)],[42,15]),
[iquote('0:Res:42.2,15.0')] ).
cnf(102,plain,
( ~ aNaturalNumber0(xk)
| sdtlseqdt0(xk,xp) ),
inference(mrr,[status(thm)],[96,5]),
[iquote('0:MRR:96.1,5.0')] ).
cnf(107,plain,
equal(xk,xp),
inference(spt,[spt(split,[position(s1)])],[30]),
[iquote('1:Spt:30.1')] ).
cnf(114,plain,
~ sdtlseqdt0(xp,xp),
inference(rew,[status(thm),theory(equality)],[107,15]),
[iquote('1:Rew:107.0,15.0')] ).
cnf(122,plain,
~ aNaturalNumber0(xp),
inference(res,[status(thm),theory(equality)],[29,114]),
[iquote('1:Res:29.1,114.0')] ).
cnf(123,plain,
$false,
inference(ssi,[status(thm)],[122,6,5]),
[iquote('1:SSi:122.0,6.0,5.0')] ).
cnf(124,plain,
~ equal(xk,xp),
inference(spt,[spt(split,[position(sa)])],[123,107]),
[iquote('1:Spt:123.0,30.1,107.0')] ).
cnf(125,plain,
~ sdtlseqdt0(xk,xp),
inference(spt,[spt(split,[position(s2)])],[30]),
[iquote('1:Spt:123.0,30.0')] ).
cnf(126,plain,
~ aNaturalNumber0(xk),
inference(mrr,[status(thm)],[102,125]),
[iquote('1:MRR:102.1,125.0')] ).
cnf(141,plain,
~ equal(xp,sz00),
inference(ems,[status(thm)],[40,5,6]),
[iquote('0:EmS:40.0,40.1,5.0,6.0')] ).
cnf(429,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[62]),
[iquote('0:EqR:62.3')] ).
cnf(435,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(ssi,[status(thm)],[429,38]),
[iquote('0:SSi:429.0,38.2')] ).
cnf(819,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(eqr,[status(thm),theory(equality)],[93]),
[iquote('0:EqR:93.3')] ).
cnf(826,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(ssi,[status(thm)],[819,38]),
[iquote('0:SSi:819.0,38.2')] ).
cnf(845,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,sdtpldt0(u,v))
| ~ equal(w,v)
| aNaturalNumber0(w) ),
inference(spl,[status(thm),theory(equality)],[826,63]),
[iquote('0:SpL:826.2,63.3')] ).
cnf(860,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtpldt0(v,u))
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,sdtpldt0(v,u))
| ~ equal(w,u)
| aNaturalNumber0(w) ),
inference(obv,[status(thm),theory(equality)],[845]),
[iquote('0:Obv:845.0')] ).
cnf(861,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,sdtpldt0(v,u))
| ~ equal(w,u)
| aNaturalNumber0(w) ),
inference(ssi,[status(thm)],[860,38]),
[iquote('0:SSi:860.1,38.2')] ).
cnf(862,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(w,u)
| aNaturalNumber0(w) ),
inference(mrr,[status(thm)],[861,435]),
[iquote('0:MRR:861.2,435.2')] ).
cnf(957,plain,
( ~ aNaturalNumber0(u)
| ~ equal(v,u)
| aNaturalNumber0(v) ),
inference(ems,[status(thm)],[862,17]),
[iquote('0:EmS:862.1,17.0')] ).
cnf(987,plain,
( ~ aNaturalNumber0(u)
| ~ equal(xk,u) ),
inference(sor,[status(thm)],[126,957]),
[iquote('1:SoR:126.0,957.2')] ).
cnf(1257,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(spl,[status(thm),theory(equality)],[31,72]),
[iquote('0:SpL:31.0,72.3')] ).
cnf(1258,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[1257,6,5,39,3,4]),
[iquote('0:SSi:1257.1,1257.0,6.0,5.0,39.2,3.0,4.0')] ).
cnf(1259,plain,
~ equal(u,xk),
inference(mrr,[status(thm)],[1258,27,987,141]),
[iquote('1:MRR:1258.0,1258.2,1258.3,27.0,987.0,141.0')] ).
cnf(1260,plain,
$false,
inference(unc,[status(thm)],[1259,31]),
[iquote('1:UnC:1259.0,31.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM505+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.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 11:49:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.45/0.64
% 0.45/0.64 SPASS V 3.9
% 0.45/0.64 SPASS beiseite: Proof found.
% 0.45/0.64 % SZS status Theorem
% 0.45/0.64 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.64 SPASS derived 748 clauses, backtracked 31 clauses, performed 4 splits and kept 370 clauses.
% 0.45/0.64 SPASS allocated 98725 KBytes.
% 0.45/0.64 SPASS spent 0:00:00.28 on the problem.
% 0.45/0.64 0:00:00.04 for the input.
% 0.45/0.64 0:00:00.04 for the FLOTTER CNF translation.
% 0.45/0.64 0:00:00.01 for inferences.
% 0.45/0.64 0:00:00.00 for the backtracking.
% 0.45/0.64 0:00:00.16 for the reduction.
% 0.45/0.64
% 0.45/0.64
% 0.45/0.64 Here is a proof with depth 4, length 43 :
% 0.45/0.64 % SZS output start Refutation
% See solution above
% 0.45/0.64 Formulae used in the proof : m__1837 m__1860 m__ mDefLE m__2342 mLERefl m__2306 mSortsB mSortsB_02 mDefPrime mLETotal mDefDiff mDefQuot
% 0.45/0.64
%------------------------------------------------------------------------------