TSTP Solution File: NUM476+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM476+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 14:26:35 EDT 2022
% Result : Theorem 6.74s 6.98s
% Output : Refutation 6.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 17
% Syntax : Number of clauses : 46 ( 22 unt; 4 nHn; 46 RR)
% Number of literals : 101 ( 0 equ; 61 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aNaturalNumber0(sz00),
file('NUM476+1.p',unknown),
[] ).
cnf(3,axiom,
aNaturalNumber0(xl),
file('NUM476+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM476+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xn),
file('NUM476+1.p',unknown),
[] ).
cnf(6,axiom,
doDivides0(xl,xm),
file('NUM476+1.p',unknown),
[] ).
cnf(7,axiom,
~ doDivides0(xl,xn),
file('NUM476+1.p',unknown),
[] ).
cnf(10,axiom,
aNaturalNumber0(skf3(u,v)),
file('NUM476+1.p',unknown),
[] ).
cnf(11,axiom,
doDivides0(xl,sdtpldt0(xm,xn)),
file('NUM476+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('NUM476+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(sz00,u),sz00) ),
file('NUM476+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM476+1.p',unknown),
[] ).
cnf(21,axiom,
( equal(xl,sz00)
| sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)) ),
file('NUM476+1.p',unknown),
[] ).
cnf(31,axiom,
( equal(xl,sz00)
| equal(sdtasdt0(xl,sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),xn) ),
file('NUM476+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| equal(sdtasdt0(v,skf3(v,u)),u) ),
file('NUM476+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| aNaturalNumber0(w) ),
file('NUM476+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM476+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| aNaturalNumber0(w)
| equal(v,sz00) ),
file('NUM476+1.p',unknown),
[] ).
cnf(68,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| ~ equal(sdtasdt0(xl,u),xn) ),
inference(res,[status(thm),theory(equality)],[39,7]),
[iquote('0:Res:39.4,7.0')] ).
cnf(70,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(xl,u),xn) ),
inference(mrr,[status(thm)],[68,3,5]),
[iquote('0:MRR:68.1,68.2,3.0,5.0')] ).
cnf(72,plain,
equal(xl,sz00),
inference(spt,[spt(split,[position(s1)])],[21]),
[iquote('1:Spt:21.0')] ).
cnf(74,plain,
doDivides0(sz00,xm),
inference(rew,[status(thm),theory(equality)],[72,6]),
[iquote('1:Rew:72.0,6.0')] ).
cnf(75,plain,
~ doDivides0(sz00,xn),
inference(rew,[status(thm),theory(equality)],[72,7]),
[iquote('1:Rew:72.0,7.0')] ).
cnf(76,plain,
doDivides0(sz00,sdtpldt0(xm,xn)),
inference(rew,[status(thm),theory(equality)],[72,11]),
[iquote('1:Rew:72.0,11.0')] ).
cnf(189,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(skf3(sz00,u))
| ~ doDivides0(sz00,u)
| equal(u,sz00) ),
inference(spr,[status(thm),theory(equality)],[35,18]),
[iquote('0:SpR:35.3,18.1')] ).
cnf(195,plain,
( ~ aNaturalNumber0(u)
| ~ doDivides0(sz00,u)
| equal(u,sz00) ),
inference(ssi,[status(thm)],[189,10,1]),
[iquote('0:SSi:189.2,189.1,10.0,1.0,1.0')] ).
cnf(201,plain,
( ~ aNaturalNumber0(xm)
| equal(xm,sz00) ),
inference(res,[status(thm),theory(equality)],[74,195]),
[iquote('1:Res:74.0,195.1')] ).
cnf(203,plain,
equal(xm,sz00),
inference(ssi,[status(thm)],[201,4]),
[iquote('1:SSi:201.0,4.0')] ).
cnf(206,plain,
doDivides0(sz00,sdtpldt0(sz00,xn)),
inference(rew,[status(thm),theory(equality)],[203,76]),
[iquote('1:Rew:203.0,76.0')] ).
cnf(210,plain,
( ~ aNaturalNumber0(xn)
| doDivides0(sz00,xn) ),
inference(spr,[status(thm),theory(equality)],[14,206]),
[iquote('1:SpR:14.1,206.0')] ).
cnf(212,plain,
doDivides0(sz00,xn),
inference(ssi,[status(thm)],[210,5]),
[iquote('1:SSi:210.0,5.0')] ).
cnf(213,plain,
$false,
inference(mrr,[status(thm)],[212,75]),
[iquote('1:MRR:212.0,75.0')] ).
cnf(216,plain,
~ equal(xl,sz00),
inference(spt,[spt(split,[position(sa)])],[213,72]),
[iquote('1:Spt:213.0,21.0,72.0')] ).
cnf(217,plain,
sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)),
inference(spt,[spt(split,[position(s2)])],[21]),
[iquote('1:Spt:213.0,21.1')] ).
cnf(218,plain,
equal(sdtasdt0(xl,sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),xn),
inference(mrr,[status(thm)],[31,216]),
[iquote('1:MRR:31.0,216.0')] ).
cnf(242,plain,
( ~ aNaturalNumber0(sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl)))
| ~ equal(xn,xn) ),
inference(spl,[status(thm),theory(equality)],[218,70]),
[iquote('1:SpL:218.0,70.1')] ).
cnf(243,plain,
~ aNaturalNumber0(sdtmndt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))),
inference(obv,[status(thm),theory(equality)],[242]),
[iquote('1:Obv:242.1')] ).
cnf(493,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| aNaturalNumber0(sdtmndt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[38]),
[iquote('0:EqR:38.3')] ).
cnf(1078,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| aNaturalNumber0(sdtsldt0(u,v))
| equal(v,sz00) ),
inference(eqr,[status(thm),theory(equality)],[46]),
[iquote('0:EqR:46.3')] ).
cnf(2745,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtpldt0(xm,xn),xl)) ),
inference(sor,[status(thm)],[243,493]),
[iquote('1:SoR:243.0,493.3')] ).
cnf(2757,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl)) ),
inference(mrr,[status(thm)],[2745,217]),
[iquote('1:MRR:2745.2,217.0')] ).
cnf(20433,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| equal(xl,sz00) ),
inference(sor,[status(thm)],[2757,1078]),
[iquote('1:SoR:2757.1,1078.3')] ).
cnf(20452,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| equal(xl,sz00) ),
inference(ssi,[status(thm)],[20433,19,4,5,3]),
[iquote('1:SSi:20433.2,20433.1,19.0,4.0,5.0,3.2')] ).
cnf(20453,plain,
~ aNaturalNumber0(sdtsldt0(xm,xl)),
inference(mrr,[status(thm)],[20452,11,216]),
[iquote('1:MRR:20452.1,20452.2,11.0,216.0')] ).
cnf(20460,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xl,xm)
| equal(xl,sz00) ),
inference(sor,[status(thm)],[20453,1078]),
[iquote('1:SoR:20453.0,1078.3')] ).
cnf(20463,plain,
( ~ doDivides0(xl,xm)
| equal(xl,sz00) ),
inference(ssi,[status(thm)],[20460,4,3]),
[iquote('1:SSi:20460.1,20460.0,4.0,3.0')] ).
cnf(20464,plain,
$false,
inference(mrr,[status(thm)],[20463,6,216]),
[iquote('1:MRR:20463.0,20463.1,6.0,216.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM476+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jul 5 12:36:12 EDT 2022
% 0.14/0.35 % CPUTime :
% 6.74/6.98
% 6.74/6.98 SPASS V 3.9
% 6.74/6.98 SPASS beiseite: Proof found.
% 6.74/6.98 % SZS status Theorem
% 6.74/6.98 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.74/6.98 SPASS derived 11888 clauses, backtracked 3520 clauses, performed 7 splits and kept 5665 clauses.
% 6.74/6.98 SPASS allocated 110974 KBytes.
% 6.74/6.98 SPASS spent 0:00:04.74 on the problem.
% 6.74/6.98 0:00:00.04 for the input.
% 6.74/6.98 0:00:00.04 for the FLOTTER CNF translation.
% 6.74/6.98 0:00:00.12 for inferences.
% 6.74/6.98 0:00:00.02 for the backtracking.
% 6.74/6.98 0:00:04.48 for the reduction.
% 6.74/6.98
% 6.74/6.98
% 6.74/6.98 Here is a proof with depth 5, length 46 :
% 6.74/6.98 % SZS output start Refutation
% See solution above
% 6.74/6.98 Formulae used in the proof : mSortsC m__1324 m__1324_04 m__ mDefDiv m_AddZero m_MulZero mSortsB mDefDiff mDefQuot
% 6.74/6.98
%------------------------------------------------------------------------------