TSTP Solution File: NUM495+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM495+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 14:26:47 EDT 2022
% Result : Theorem 1.20s 1.46s
% Output : Refutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of clauses : 39 ( 16 unt; 3 nHn; 39 RR)
% Number of literals : 105 ( 0 equ; 72 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 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('NUM495+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM495+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM495+1.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM495+1.p',unknown),
[] ).
cnf(9,axiom,
sdtlseqdt0(xp,xn),
file('NUM495+1.p',unknown),
[] ).
cnf(11,axiom,
~ doDivides0(xp,xr),
file('NUM495+1.p',unknown),
[] ).
cnf(12,axiom,
~ doDivides0(xp,xm),
file('NUM495+1.p',unknown),
[] ).
cnf(18,axiom,
equal(sdtmndt0(xn,xp),xr),
file('NUM495+1.p',unknown),
[] ).
cnf(19,axiom,
doDivides0(xp,sdtasdt0(xr,xm)),
file('NUM495+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM495+1.p',unknown),
[] ).
cnf(31,axiom,
sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
file('NUM495+1.p',unknown),
[] ).
cnf(35,axiom,
~ equal(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
file('NUM495+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| iLess0(v,u)
| equal(v,u) ),
file('NUM495+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| aNaturalNumber0(w) ),
file('NUM495+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('NUM495+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ isPrime0(w)
| ~ iLess0(sdtpldt0(sdtpldt0(u,v),w),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(w,sdtasdt0(u,v))
| doDivides0(w,u)
| doDivides0(w,v) ),
file('NUM495+1.p',unknown),
[] ).
cnf(86,plain,
( ~ isPrime0(u)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(u,sdtasdt0(w,v))
| ~ iLess0(sdtpldt0(w,sdtpldt0(v,u)),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(u,v)
| doDivides0(u,w) ),
inference(rew,[status(thm),theory(equality)],[62,83]),
[iquote('0:Rew:62.3,83.4')] ).
cnf(91,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ isPrime0(xp)
| ~ iLess0(sdtpldt0(u,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(xp,sdtasdt0(u,xm))
| doDivides0(xp,u) ),
inference(res,[status(thm),theory(equality)],[86,12]),
[iquote('0:Res:86.7,12.0')] ).
cnf(106,plain,
( ~ aNaturalNumber0(u)
| ~ doDivides0(xp,sdtasdt0(u,xm))
| ~ iLess0(sdtpldt0(u,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(xp,u) ),
inference(mrr,[status(thm)],[91,4,5,6]),
[iquote('0:MRR:91.1,91.2,91.3,4.0,5.0,6.0')] ).
cnf(109,plain,
( ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(xp,sdtasdt0(xr,xm)) ),
inference(res,[status(thm),theory(equality)],[106,11]),
[iquote('0:Res:106.3,11.0')] ).
cnf(117,plain,
( ~ aNaturalNumber0(xr)
| ~ iLess0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(mrr,[status(thm)],[109,19]),
[iquote('0:MRR:109.2,19.0')] ).
cnf(713,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| aNaturalNumber0(sdtmndt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[54]),
[iquote('0:EqR:54.3')] ).
cnf(714,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ~ equal(u,xr)
| aNaturalNumber0(u) ),
inference(spl,[status(thm),theory(equality)],[18,54]),
[iquote('0:SpL:18.0,54.3')] ).
cnf(715,plain,
( ~ sdtlseqdt0(xp,xn)
| ~ equal(u,xr)
| aNaturalNumber0(u) ),
inference(ssi,[status(thm)],[714,6,5,3]),
[iquote('0:SSi:714.1,714.0,6.0,5.0,3.0')] ).
cnf(716,plain,
( ~ equal(u,xr)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[715,9]),
[iquote('0:MRR:715.0,9.0')] ).
cnf(851,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(spr,[status(thm),theory(equality)],[62,31]),
[iquote('0:SpR:62.3,31.0')] ).
cnf(862,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xr,sdtpldt0(xm,xp))) ),
inference(spl,[status(thm),theory(equality)],[62,35]),
[iquote('0:SpL:62.3,35.0')] ).
cnf(864,plain,
( ~ aNaturalNumber0(xr)
| sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(ssi,[status(thm)],[851,4,6,5]),
[iquote('0:SSi:851.1,851.0,4.0,6.0,5.0')] ).
cnf(866,plain,
( ~ aNaturalNumber0(xr)
| ~ equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xr,sdtpldt0(xm,xp))) ),
inference(ssi,[status(thm)],[862,4,6,5]),
[iquote('0:SSi:862.1,862.0,4.0,6.0,5.0')] ).
cnf(3382,plain,
( ~ equal(xr,xr)
| sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(sor,[status(thm)],[864,716]),
[iquote('0:SoR:864.0,716.1')] ).
cnf(3384,plain,
sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(obv,[status(thm),theory(equality)],[3382]),
[iquote('0:Obv:3382.0')] ).
cnf(3797,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| aNaturalNumber0(xr) ),
inference(spr,[status(thm),theory(equality)],[18,713]),
[iquote('0:SpR:18.0,713.3')] ).
cnf(3800,plain,
( ~ sdtlseqdt0(xp,xn)
| aNaturalNumber0(xr) ),
inference(ssi,[status(thm)],[3797,6,5,3]),
[iquote('0:SSi:3797.1,3797.0,6.0,5.0,3.0')] ).
cnf(3801,plain,
aNaturalNumber0(xr),
inference(mrr,[status(thm)],[3800,9]),
[iquote('0:MRR:3800.0,9.0')] ).
cnf(3803,plain,
~ equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xr,sdtpldt0(xm,xp))),
inference(mrr,[status(thm)],[866,3801]),
[iquote('0:MRR:866.0,3801.0')] ).
cnf(3804,plain,
~ iLess0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(mrr,[status(thm)],[117,3801]),
[iquote('0:MRR:117.0,3801.0')] ).
cnf(4295,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(xr,sdtpldt0(xm,xp)))
| ~ sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp))
| equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xr,sdtpldt0(xm,xp))) ),
inference(res,[status(thm),theory(equality)],[45,3804]),
[iquote('0:Res:45.3,3804.0')] ).
cnf(4298,plain,
( ~ sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(sdtpldt0(xn,xm),xp))
| equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xr,sdtpldt0(xm,xp))) ),
inference(ssi,[status(thm)],[4295,27,3801,4,6,5,3]),
[iquote('0:SSi:4295.1,4295.0,27.0,3801.0,27.0,4.0,6.2,5.2,27.0,27.0,3.0,4.2,6.0,5.2')] ).
cnf(4299,plain,
$false,
inference(mrr,[status(thm)],[4298,3384,3803]),
[iquote('0:MRR:4298.0,4298.1,3384.0,3803.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM495+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % 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 06:38:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.20/1.46
% 1.20/1.46 SPASS V 3.9
% 1.20/1.46 SPASS beiseite: Proof found.
% 1.20/1.46 % SZS status Theorem
% 1.20/1.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.20/1.46 SPASS derived 2619 clauses, backtracked 252 clauses, performed 6 splits and kept 1342 clauses.
% 1.20/1.46 SPASS allocated 101513 KBytes.
% 1.20/1.46 SPASS spent 0:00:01.02 on the problem.
% 1.20/1.46 0:00:00.04 for the input.
% 1.20/1.46 0:00:00.04 for the FLOTTER CNF translation.
% 1.20/1.46 0:00:00.05 for inferences.
% 1.20/1.46 0:00:00.00 for the backtracking.
% 1.20/1.46 0:00:00.86 for the reduction.
% 1.20/1.46
% 1.20/1.46
% 1.20/1.46 Here is a proof with depth 3, length 39 :
% 1.20/1.46 % SZS output start Refutation
% See solution above
% 1.20/1.46 Formulae used in the proof : m__1837 m__1860 m__1870 m__ m__1883 m__1913 mSortsB m__2062 mIH_03 mDefDiff mAddAsso m__1799
% 1.20/1.46
%------------------------------------------------------------------------------