TSTP Solution File: NUM465+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM465+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 14:26:28 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of clauses : 36 ( 18 unt; 9 nHn; 36 RR)
% Number of literals : 81 ( 0 equ; 44 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aNaturalNumber0(sz00),
file('NUM465+1.p',unknown),
[] ).
cnf(2,axiom,
aNaturalNumber0(sz10),
file('NUM465+1.p',unknown),
[] ).
cnf(3,axiom,
aNaturalNumber0(xm),
file('NUM465+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xn),
file('NUM465+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(xm,sz00),
file('NUM465+1.p',unknown),
[] ).
cnf(8,axiom,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
file('NUM465+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ aNaturalNumber0(u)
| sdtlseqdt0(u,u) ),
file('NUM465+1.p',unknown),
[] ).
cnf(10,axiom,
( equal(xm,sz00)
| sdtlseqdt0(sz10,xm) ),
file('NUM465+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,sz10),u) ),
file('NUM465+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(sz00,u),sz00) ),
file('NUM465+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(u,v)
| sdtlseqdt0(v,u) ),
file('NUM465+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(w,u)
| equal(w,u)
| sdtlseqdt0(sdtpldt0(w,v),sdtpldt0(u,v)) ),
file('NUM465+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,u)
| equal(v,u)
| equal(w,sz00)
| sdtlseqdt0(sdtasdt0(w,v),sdtasdt0(w,u)) ),
file('NUM465+1.p',unknown),
[] ).
cnf(51,plain,
sdtlseqdt0(sz10,xm),
inference(mrr,[status(thm)],[10,5]),
[iquote('0:MRR:10.0,5.0')] ).
cnf(59,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(sdtasdt0(u,sz10),sdtasdt0(u,xm))
| equal(u,sz00)
| equal(xm,sz10) ),
inference(res,[status(thm),theory(equality)],[51,48]),
[iquote('0:Res:51.0,48.3')] ).
cnf(63,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(sdtpldt0(sz10,u),sdtpldt0(xm,u))
| equal(xm,sz10) ),
inference(res,[status(thm),theory(equality)],[51,40]),
[iquote('0:Res:51.0,40.3')] ).
cnf(117,plain,
( ~ aNaturalNumber0(u)
| equal(xm,sz10)
| sdtlseqdt0(sdtpldt0(sz10,u),sdtpldt0(xm,u)) ),
inference(mrr,[status(thm)],[63,2,3]),
[iquote('0:MRR:63.0,63.2,2.0,3.0')] ).
cnf(136,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(u,sdtasdt0(u,xm))
| equal(u,sz00)
| equal(xm,sz10) ),
inference(rew,[status(thm),theory(equality)],[13,59]),
[iquote('0:Rew:13.1,59.3')] ).
cnf(137,plain,
( ~ aNaturalNumber0(u)
| equal(u,sz00)
| sdtlseqdt0(u,sdtasdt0(u,xm))
| equal(xm,sz10) ),
inference(mrr,[status(thm)],[136,2,3]),
[iquote('0:MRR:136.1,136.2,2.0,3.0')] ).
cnf(176,plain,
equal(xm,sz10),
inference(spt,[spt(split,[position(s1)])],[117]),
[iquote('1:Spt:117.1')] ).
cnf(177,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,sz10)),
inference(rew,[status(thm),theory(equality)],[176,8]),
[iquote('1:Rew:176.0,8.0')] ).
cnf(243,plain,
( ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xn) ),
inference(spl,[status(thm),theory(equality)],[13,177]),
[iquote('1:SpL:13.1,177.0')] ).
cnf(245,plain,
~ sdtlseqdt0(xn,xn),
inference(ssi,[status(thm)],[243,4]),
[iquote('1:SSi:243.0,4.0')] ).
cnf(246,plain,
~ aNaturalNumber0(xn),
inference(res,[status(thm),theory(equality)],[9,245]),
[iquote('1:Res:9.1,245.0')] ).
cnf(247,plain,
$false,
inference(ssi,[status(thm)],[246,4]),
[iquote('1:SSi:246.0,4.0')] ).
cnf(248,plain,
~ equal(xm,sz10),
inference(spt,[spt(split,[position(sa)])],[247,176]),
[iquote('1:Spt:247.0,117.1,176.0')] ).
cnf(249,plain,
( ~ aNaturalNumber0(u)
| sdtlseqdt0(sdtpldt0(sz10,u),sdtpldt0(xm,u)) ),
inference(spt,[spt(split,[position(s2)])],[117]),
[iquote('1:Spt:247.0,117.0,117.2')] ).
cnf(253,plain,
( ~ aNaturalNumber0(u)
| equal(u,sz00)
| sdtlseqdt0(u,sdtasdt0(u,xm)) ),
inference(mrr,[status(thm)],[137,248]),
[iquote('1:MRR:137.3,248.0')] ).
cnf(478,plain,
( ~ aNaturalNumber0(xn)
| equal(xn,sz00) ),
inference(res,[status(thm),theory(equality)],[253,8]),
[iquote('1:Res:253.2,8.0')] ).
cnf(479,plain,
equal(xn,sz00),
inference(ssi,[status(thm)],[478,4]),
[iquote('1:SSi:478.0,4.0')] ).
cnf(481,plain,
~ sdtlseqdt0(sz00,sdtasdt0(sz00,xm)),
inference(rew,[status(thm),theory(equality)],[479,8]),
[iquote('1:Rew:479.0,8.0')] ).
cnf(497,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sz00,sz00) ),
inference(spl,[status(thm),theory(equality)],[16,481]),
[iquote('1:SpL:16.1,481.0')] ).
cnf(500,plain,
~ sdtlseqdt0(sz00,sz00),
inference(ssi,[status(thm)],[497,3]),
[iquote('1:SSi:497.0,3.0')] ).
cnf(504,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00)
| ~ equal(sz00,sz00) ),
inference(res,[status(thm),theory(equality)],[23,500]),
[iquote('1:Res:23.3,500.0')] ).
cnf(506,plain,
~ aNaturalNumber0(sz00),
inference(obv,[status(thm),theory(equality)],[504]),
[iquote('1:Obv:504.2')] ).
cnf(507,plain,
$false,
inference(ssi,[status(thm)],[506,1]),
[iquote('1:SSi:506.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM465+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jul 5 17:25:28 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 274 clauses, backtracked 42 clauses, performed 1 splits and kept 192 clauses.
% 0.20/0.48 SPASS allocated 97971 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.48 0:00:00.04 for the input.
% 0.20/0.48 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.00 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.02 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 2, length 36 :
% 0.20/0.48 % SZS output start Refutation
% See solution above
% 0.20/0.48 Formulae used in the proof : mSortsC mSortsC_01 m__987 m__ mLERefl m__1007 m_MulUnit m_MulZero mLETotal mMonAdd mMonMul
% 0.20/0.48
%------------------------------------------------------------------------------