TSTP Solution File: NUM527+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM527+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 14:27:08 EDT 2022
% Result : Theorem 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 35 ( 14 unt; 8 nHn; 35 RR)
% Number of literals : 92 ( 0 equ; 54 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM527+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM527+1.p',unknown),
[] ).
cnf(7,axiom,
sdtlseqdt0(xn,xm),
file('NUM527+1.p',unknown),
[] ).
cnf(14,axiom,
~ equal(xn,sz00),
file('NUM527+1.p',unknown),
[] ).
cnf(15,axiom,
~ equal(xm,sz00),
file('NUM527+1.p',unknown),
[] ).
cnf(20,axiom,
~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)),
file('NUM527+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM527+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(v,u)
| sdtlseqdt0(u,v) ),
file('NUM527+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM527+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,u)
| ~ sdtlseqdt0(w,v)
| sdtlseqdt0(w,u) ),
file('NUM527+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,u)
| equal(v,u)
| equal(w,sz00)
| sdtlseqdt0(sdtasdt0(w,v),sdtasdt0(w,u)) ),
file('NUM527+1.p',unknown),
[] ).
cnf(95,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(sdtasdt0(u,xn),sdtasdt0(u,xm))
| equal(u,sz00)
| equal(xm,xn) ),
inference(res,[status(thm),theory(equality)],[7,79]),
[iquote('0:Res:7.0,79.3')] ).
cnf(100,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)) ),
inference(res,[status(thm),theory(equality)],[33,20]),
[iquote('0:Res:33.2,20.0')] ).
cnf(105,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ sdtlseqdt0(u,sdtasdt0(xm,xm))
| ~ sdtlseqdt0(sdtasdt0(xn,xn),u) ),
inference(res,[status(thm),theory(equality)],[58,20]),
[iquote('0:Res:58.5,20.0')] ).
cnf(116,plain,
( ~ aNaturalNumber0(u)
| equal(u,sz00)
| equal(xm,xn)
| sdtlseqdt0(sdtasdt0(u,xn),sdtasdt0(u,xm)) ),
inference(mrr,[status(thm)],[95,3,4]),
[iquote('0:MRR:95.1,95.2,3.0,4.0')] ).
cnf(120,plain,
( ~ aNaturalNumber0(u)
| equal(u,sz00)
| sdtlseqdt0(sdtasdt0(u,xn),sdtasdt0(u,xm)) ),
inference(spt,[spt(split,[position(s1)])],[116]),
[iquote('1:Spt:116.0,116.1,116.3')] ).
cnf(180,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)) ),
inference(ssi,[status(thm)],[100,30,3]),
[iquote('0:SSi:100.0,30.0,3.0,3.2')] ).
cnf(183,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ sdtlseqdt0(u,sdtasdt0(xm,xm))
| ~ sdtlseqdt0(sdtasdt0(xn,xn),u) ),
inference(ssi,[status(thm)],[105,30,3]),
[iquote('0:SSi:105.2,30.0,3.0,3.2')] ).
cnf(259,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)) ),
inference(sor,[status(thm)],[180,30]),
[iquote('0:SoR:180.0,30.2')] ).
cnf(261,plain,
( ~ aNaturalNumber0(xm)
| sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)) ),
inference(obv,[status(thm),theory(equality)],[259]),
[iquote('0:Obv:259.0')] ).
cnf(262,plain,
sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)),
inference(ssi,[status(thm)],[261,4]),
[iquote('0:SSi:261.0,4.0')] ).
cnf(287,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| equal(u,sz00)
| sdtlseqdt0(sdtasdt0(u,xn),sdtasdt0(xm,u)) ),
inference(spr,[status(thm),theory(equality)],[37,120]),
[iquote('1:SpR:37.2,120.2')] ).
cnf(350,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(u)
| equal(u,sz00)
| sdtlseqdt0(sdtasdt0(u,xn),sdtasdt0(xm,u)) ),
inference(obv,[status(thm),theory(equality)],[287]),
[iquote('1:Obv:287.1')] ).
cnf(351,plain,
( ~ aNaturalNumber0(u)
| equal(u,sz00)
| sdtlseqdt0(sdtasdt0(u,xn),sdtasdt0(xm,u)) ),
inference(ssi,[status(thm)],[350,4]),
[iquote('1:SSi:350.0,4.0')] ).
cnf(568,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,sdtasdt0(xm,xm))
| ~ sdtlseqdt0(sdtasdt0(xn,xn),u) ),
inference(ssi,[status(thm)],[183,30,4]),
[iquote('0:SSi:183.1,30.0,4.0,4.2')] ).
cnf(711,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xn))
| equal(xm,sz00) ),
inference(res,[status(thm),theory(equality)],[120,568]),
[iquote('1:Res:120.2,568.1')] ).
cnf(729,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xn))
| equal(xm,sz00) ),
inference(ssi,[status(thm)],[711,30,4,3]),
[iquote('1:SSi:711.1,711.0,30.0,4.0,3.0,4.2')] ).
cnf(730,plain,
~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xn)),
inference(mrr,[status(thm)],[729,15]),
[iquote('1:MRR:729.1,15.0')] ).
cnf(811,plain,
( ~ aNaturalNumber0(xn)
| equal(xn,sz00) ),
inference(res,[status(thm),theory(equality)],[351,730]),
[iquote('1:Res:351.2,730.0')] ).
cnf(814,plain,
equal(xn,sz00),
inference(ssi,[status(thm)],[811,3]),
[iquote('1:SSi:811.0,3.0')] ).
cnf(815,plain,
$false,
inference(mrr,[status(thm)],[814,14]),
[iquote('1:MRR:814.0,14.0')] ).
cnf(819,plain,
equal(xm,xn),
inference(spt,[spt(split,[position(s2)])],[116]),
[iquote('1:Spt:815.0,116.2')] ).
cnf(857,plain,
sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xn,xn)),
inference(rew,[status(thm),theory(equality)],[819,262]),
[iquote('1:Rew:819.0,262.0')] ).
cnf(861,plain,
~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xn,xn)),
inference(rew,[status(thm),theory(equality)],[819,20]),
[iquote('1:Rew:819.0,20.0')] ).
cnf(884,plain,
$false,
inference(mrr,[status(thm)],[861,857]),
[iquote('1:MRR:861.0,857.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM527+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n003.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 08:28:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.51
% 0.18/0.51 SPASS V 3.9
% 0.18/0.51 SPASS beiseite: Proof found.
% 0.18/0.51 % SZS status Theorem
% 0.18/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.51 SPASS derived 504 clauses, backtracked 56 clauses, performed 6 splits and kept 287 clauses.
% 0.18/0.51 SPASS allocated 98224 KBytes.
% 0.18/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.18/0.51 0:00:00.04 for the input.
% 0.18/0.51 0:00:00.04 for the FLOTTER CNF translation.
% 0.18/0.51 0:00:00.01 for inferences.
% 0.18/0.51 0:00:00.00 for the backtracking.
% 0.18/0.51 0:00:00.04 for the reduction.
% 0.18/0.51
% 0.18/0.51
% 0.18/0.51 Here is a proof with depth 4, length 35 :
% 0.18/0.51 % SZS output start Refutation
% See solution above
% 0.18/0.51 Formulae used in the proof : m__2987 m__ mSortsB_02 mLETotal mMulComm mLETran mMonMul
% 0.18/0.51
%------------------------------------------------------------------------------