TSTP Solution File: NUM491+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM491+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 14:26:45 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 6 unt; 0 nHn; 17 RR)
% Number of literals : 43 ( 0 equ; 36 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM491+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM491+1.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM491+1.p',unknown),
[] ).
cnf(18,axiom,
~ doDivides0(xp,sdtasdt0(xp,xm)),
file('NUM491+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM491+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM491+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM491+1.p',unknown),
[] ).
cnf(88,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ equal(sdtasdt0(xp,xm),sdtasdt0(xp,u)) ),
inference(res,[status(thm),theory(equality)],[54,18]),
[iquote('0:Res:54.4,18.0')] ).
cnf(92,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ equal(sdtasdt0(xp,xm),sdtasdt0(xp,u)) ),
inference(mrr,[status(thm)],[88,5]),
[iquote('0:MRR:88.1,5.0')] ).
cnf(249,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ equal(sdtasdt0(xp,xm),sdtasdt0(xp,u)) ),
inference(sor,[status(thm)],[92,27]),
[iquote('0:SoR:92.1,27.2')] ).
cnf(250,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ equal(sdtasdt0(xp,u),sdtasdt0(xm,xp)) ),
inference(rew,[status(thm),theory(equality)],[36,249]),
[iquote('0:Rew:36.2,249.3')] ).
cnf(251,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(xp,u),sdtasdt0(xm,xp)) ),
inference(ssi,[status(thm)],[250,4,6,5]),
[iquote('0:SSi:250.2,250.1,4.0,6.0,5.0')] ).
cnf(252,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(u,xp),sdtasdt0(xm,xp)) ),
inference(spl,[status(thm),theory(equality)],[36,251]),
[iquote('0:SpL:36.2,251.1')] ).
cnf(259,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(u,xp),sdtasdt0(xm,xp)) ),
inference(obv,[status(thm),theory(equality)],[252]),
[iquote('0:Obv:252.0')] ).
cnf(260,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(u,xp),sdtasdt0(xm,xp)) ),
inference(ssi,[status(thm)],[259,6,5]),
[iquote('0:SSi:259.0,6.0,5.0')] ).
cnf(262,plain,
~ aNaturalNumber0(xm),
inference(eqr,[status(thm),theory(equality)],[260]),
[iquote('0:EqR:260.1')] ).
cnf(265,plain,
$false,
inference(ssi,[status(thm)],[262,4]),
[iquote('0:SSi:262.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM491+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 20:00:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 117 clauses, backtracked 0 clauses, performed 0 splits and kept 109 clauses.
% 0.19/0.47 SPASS allocated 97901 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.47 0:00:00.04 for the input.
% 0.19/0.47 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.02 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 4, length 17 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : m__1837 m__1860 m__ mSortsB_02 mMulComm mDefDiv
% 0.19/0.47
%------------------------------------------------------------------------------