TSTP Solution File: NUM481+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM481+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 14:26:39 EDT 2022
% Result : Theorem 0.59s 0.87s
% Output : Refutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 23
% Syntax : Number of clauses : 71 ( 22 unt; 18 nHn; 71 RR)
% Number of literals : 193 ( 0 equ; 107 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aNaturalNumber0(skc1),
file('NUM481+3.p',unknown),
[] ).
cnf(2,axiom,
aNaturalNumber0(sz00),
file('NUM481+3.p',unknown),
[] ).
cnf(3,axiom,
aNaturalNumber0(sz10),
file('NUM481+3.p',unknown),
[] ).
cnf(7,axiom,
aNaturalNumber0(skf7(u)),
file('NUM481+3.p',unknown),
[] ).
cnf(8,axiom,
aNaturalNumber0(skf13(u)),
file('NUM481+3.p',unknown),
[] ).
cnf(9,axiom,
~ equal(skc1,sz00),
file('NUM481+3.p',unknown),
[] ).
cnf(10,axiom,
~ equal(skc1,sz10),
file('NUM481+3.p',unknown),
[] ).
cnf(13,axiom,
aNaturalNumber0(skf12(u,v)),
file('NUM481+3.p',unknown),
[] ).
cnf(15,axiom,
( ~ doDivides0(u,v)
| skP0(u,v) ),
file('NUM481+3.p',unknown),
[] ).
cnf(18,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,sz10),u) ),
file('NUM481+3.p',unknown),
[] ).
cnf(21,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(sz00,u),sz00) ),
file('NUM481+3.p',unknown),
[] ).
cnf(22,axiom,
( ~ aNaturalNumber0(u)
| ~ isPrime0(u)
| ~ skP0(u,skc1) ),
file('NUM481+3.p',unknown),
[] ).
cnf(27,axiom,
( ~ aNaturalNumber0(u)
| ~ equal(v,sdtasdt0(w,u))
| skP0(w,v) ),
file('NUM481+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ aNaturalNumber0(u)
| isPrime0(u)
| equal(u,sz10)
| equal(u,sz00)
| doDivides0(skf13(u),u) ),
file('NUM481+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ aNaturalNumber0(u)
| ~ iLess0(u,skc1)
| isPrime0(skf7(u))
| equal(u,sz10)
| equal(u,sz00) ),
file('NUM481+3.p',unknown),
[] ).
cnf(39,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| iLess0(v,u)
| equal(v,u) ),
file('NUM481+3.p',unknown),
[] ).
cnf(40,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| sdtlseqdt0(v,u)
| equal(u,sz00) ),
file('NUM481+3.p',unknown),
[] ).
cnf(41,axiom,
( ~ aNaturalNumber0(u)
| ~ equal(skf13(u),sz10)
| isPrime0(u)
| equal(u,sz10)
| equal(u,sz00) ),
file('NUM481+3.p',unknown),
[] ).
cnf(42,axiom,
( ~ aNaturalNumber0(u)
| ~ equal(skf13(u),u)
| isPrime0(u)
| equal(u,sz10)
| equal(u,sz00) ),
file('NUM481+3.p',unknown),
[] ).
cnf(43,axiom,
( ~ aNaturalNumber0(u)
| ~ iLess0(u,skc1)
| equal(u,sz10)
| equal(u,sz00)
| doDivides0(skf7(u),u) ),
file('NUM481+3.p',unknown),
[] ).
cnf(47,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| equal(sdtasdt0(v,skf12(v,u)),u) ),
file('NUM481+3.p',unknown),
[] ).
cnf(55,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM481+3.p',unknown),
[] ).
cnf(57,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(v,u)
| ~ doDivides0(w,v)
| doDivides0(w,u) ),
file('NUM481+3.p',unknown),
[] ).
cnf(130,plain,
( ~ equal(skf13(skc1),sz10)
| equal(skc1,sz00)
| equal(skc1,sz10)
| isPrime0(skc1) ),
inference(res,[status(thm),theory(equality)],[1,41]),
[iquote('0:Res:1.0,41.0')] ).
cnf(131,plain,
( ~ equal(skf13(skc1),skc1)
| equal(skc1,sz00)
| equal(skc1,sz10)
| isPrime0(skc1) ),
inference(res,[status(thm),theory(equality)],[1,42]),
[iquote('0:Res:1.0,42.0')] ).
cnf(134,plain,
( doDivides0(skf13(skc1),skc1)
| equal(skc1,sz00)
| equal(skc1,sz10)
| isPrime0(skc1) ),
inference(res,[status(thm),theory(equality)],[1,37]),
[iquote('0:Res:1.0,37.0')] ).
cnf(150,plain,
equal(sdtasdt0(skc1,sz10),skc1),
inference(res,[status(thm),theory(equality)],[1,18]),
[iquote('0:Res:1.0,18.0')] ).
cnf(153,plain,
equal(sdtasdt0(sz00,skc1),sz00),
inference(res,[status(thm),theory(equality)],[1,21]),
[iquote('0:Res:1.0,21.0')] ).
cnf(185,plain,
( ~ aNaturalNumber0(u)
| ~ doDivides0(u,skc1)
| equal(sdtasdt0(u,skf12(u,skc1)),skc1) ),
inference(res,[status(thm),theory(equality)],[1,47]),
[iquote('0:Res:1.0,47.1')] ).
cnf(187,plain,
( ~ aNaturalNumber0(u)
| ~ doDivides0(u,skc1)
| sdtlseqdt0(u,skc1)
| equal(skc1,sz00) ),
inference(res,[status(thm),theory(equality)],[1,40]),
[iquote('0:Res:1.0,40.1')] ).
cnf(221,plain,
( isPrime0(skc1)
| doDivides0(skf13(skc1),skc1) ),
inference(mrr,[status(thm)],[134,9,10]),
[iquote('0:MRR:134.1,134.2,9.0,10.0')] ).
cnf(224,plain,
( ~ equal(skf13(skc1),sz10)
| isPrime0(skc1) ),
inference(mrr,[status(thm)],[130,9,10]),
[iquote('0:MRR:130.1,130.2,9.0,10.0')] ).
cnf(225,plain,
( ~ equal(skf13(skc1),skc1)
| isPrime0(skc1) ),
inference(mrr,[status(thm)],[131,9,10]),
[iquote('0:MRR:131.1,131.2,9.0,10.0')] ).
cnf(226,plain,
( ~ aNaturalNumber0(u)
| ~ doDivides0(u,skc1)
| sdtlseqdt0(u,skc1) ),
inference(mrr,[status(thm)],[187,9]),
[iquote('0:MRR:187.3,9.0')] ).
cnf(248,plain,
isPrime0(skc1),
inference(spt,[spt(split,[position(s1)])],[221]),
[iquote('1:Spt:221.0')] ).
cnf(310,plain,
( ~ aNaturalNumber0(u)
| ~ isPrime0(u)
| ~ doDivides0(u,skc1) ),
inference(res,[status(thm),theory(equality)],[15,22]),
[iquote('0:Res:15.1,22.2')] ).
cnf(450,plain,
( ~ aNaturalNumber0(sz10)
| ~ equal(u,skc1)
| skP0(skc1,u) ),
inference(spl,[status(thm),theory(equality)],[150,27]),
[iquote('0:SpL:150.0,27.1')] ).
cnf(457,plain,
( ~ equal(u,skc1)
| skP0(skc1,u) ),
inference(ssi,[status(thm)],[450,3]),
[iquote('0:SSi:450.0,3.0')] ).
cnf(482,plain,
( ~ aNaturalNumber0(skc1)
| ~ isPrime0(skc1)
| ~ equal(skc1,skc1) ),
inference(res,[status(thm),theory(equality)],[457,22]),
[iquote('0:Res:457.1,22.2')] ).
cnf(484,plain,
( ~ aNaturalNumber0(skc1)
| ~ isPrime0(skc1) ),
inference(obv,[status(thm),theory(equality)],[482]),
[iquote('0:Obv:482.2')] ).
cnf(485,plain,
$false,
inference(ssi,[status(thm)],[484,248,1]),
[iquote('1:SSi:484.1,484.0,248.0,1.0,248.0,1.0')] ).
cnf(486,plain,
~ isPrime0(skc1),
inference(spt,[spt(split,[position(sa)])],[485,248]),
[iquote('1:Spt:485.0,221.0,248.0')] ).
cnf(487,plain,
doDivides0(skf13(skc1),skc1),
inference(spt,[spt(split,[position(s2)])],[221]),
[iquote('1:Spt:485.0,221.1')] ).
cnf(488,plain,
~ isPrime0(skc1),
inference(ssi,[status(thm)],[484,1]),
[iquote('0:SSi:484.0,1.0')] ).
cnf(489,plain,
~ equal(skf13(skc1),skc1),
inference(mrr,[status(thm)],[225,488]),
[iquote('0:MRR:225.1,488.0')] ).
cnf(490,plain,
~ equal(skf13(skc1),sz10),
inference(mrr,[status(thm)],[224,488]),
[iquote('0:MRR:224.1,488.0')] ).
cnf(496,plain,
( ~ aNaturalNumber0(skf13(skc1))
| sdtlseqdt0(skf13(skc1),skc1) ),
inference(res,[status(thm),theory(equality)],[487,226]),
[iquote('1:Res:487.0,226.1')] ).
cnf(498,plain,
sdtlseqdt0(skf13(skc1),skc1),
inference(ssi,[status(thm)],[496,8,1]),
[iquote('1:SSi:496.0,8.0,1.0')] ).
cnf(884,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(skf12(sz00,skc1))
| ~ doDivides0(sz00,skc1)
| equal(skc1,sz00) ),
inference(spr,[status(thm),theory(equality)],[185,21]),
[iquote('0:SpR:185.2,21.1')] ).
cnf(894,plain,
( ~ doDivides0(sz00,skc1)
| equal(skc1,sz00) ),
inference(ssi,[status(thm)],[884,13,2,1]),
[iquote('0:SSi:884.1,884.0,13.0,2.0,1.0,2.0')] ).
cnf(895,plain,
~ doDivides0(sz00,skc1),
inference(mrr,[status(thm)],[894,9]),
[iquote('0:MRR:894.1,9.0')] ).
cnf(1397,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(skc1)
| ~ equal(u,sz00)
| doDivides0(sz00,u) ),
inference(spl,[status(thm),theory(equality)],[153,55]),
[iquote('0:SpL:153.0,55.3')] ).
cnf(1414,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sz00)
| doDivides0(sz00,u) ),
inference(ssi,[status(thm)],[1397,1,2]),
[iquote('0:SSi:1397.2,1397.1,1.0,2.0')] ).
cnf(2311,plain,
( ~ aNaturalNumber0(skc1)
| ~ aNaturalNumber0(skf13(skc1))
| ~ aNaturalNumber0(u)
| ~ doDivides0(u,skf13(skc1))
| doDivides0(u,skc1) ),
inference(res,[status(thm),theory(equality)],[487,57]),
[iquote('1:Res:487.0,57.3')] ).
cnf(2330,plain,
( ~ aNaturalNumber0(u)
| ~ doDivides0(u,skf13(skc1))
| doDivides0(u,skc1) ),
inference(ssi,[status(thm)],[2311,8,1]),
[iquote('1:SSi:2311.1,2311.0,8.0,1.0,1.0')] ).
cnf(2581,plain,
( ~ aNaturalNumber0(skf13(skc1))
| ~ aNaturalNumber0(skf7(skf13(skc1)))
| ~ iLess0(skf13(skc1),skc1)
| equal(skf13(skc1),sz10)
| equal(skf13(skc1),sz00)
| doDivides0(skf7(skf13(skc1)),skc1) ),
inference(res,[status(thm),theory(equality)],[43,2330]),
[iquote('1:Res:43.4,2330.1')] ).
cnf(2582,plain,
( ~ aNaturalNumber0(skf13(skc1))
| ~ aNaturalNumber0(sz00)
| ~ equal(skf13(skc1),sz00)
| doDivides0(sz00,skc1) ),
inference(res,[status(thm),theory(equality)],[1414,2330]),
[iquote('1:Res:1414.2,2330.1')] ).
cnf(2586,plain,
( ~ equal(skf13(skc1),sz00)
| doDivides0(sz00,skc1) ),
inference(ssi,[status(thm)],[2582,2,8,1]),
[iquote('1:SSi:2582.1,2582.0,2.0,8.0,1.0')] ).
cnf(2587,plain,
~ equal(skf13(skc1),sz00),
inference(mrr,[status(thm)],[2586,895]),
[iquote('1:MRR:2586.1,895.0')] ).
cnf(2591,plain,
( ~ iLess0(skf13(skc1),skc1)
| equal(skf13(skc1),sz10)
| equal(skf13(skc1),sz00)
| doDivides0(skf7(skf13(skc1)),skc1) ),
inference(ssi,[status(thm)],[2581,7,8,1]),
[iquote('1:SSi:2581.1,2581.0,7.0,8.0,1.0,8.0,1.0')] ).
cnf(2592,plain,
( ~ iLess0(skf13(skc1),skc1)
| equal(skf13(skc1),sz00)
| doDivides0(skf7(skf13(skc1)),skc1) ),
inference(mrr,[status(thm)],[2591,490]),
[iquote('1:MRR:2591.1,490.0')] ).
cnf(2593,plain,
( ~ iLess0(skf13(skc1),skc1)
| doDivides0(skf7(skf13(skc1)),skc1) ),
inference(mrr,[status(thm)],[2592,2587]),
[iquote('1:MRR:2592.1,2587.0')] ).
cnf(2611,plain,
( ~ aNaturalNumber0(skf7(skf13(skc1)))
| ~ isPrime0(skf7(skf13(skc1)))
| ~ iLess0(skf13(skc1),skc1) ),
inference(res,[status(thm),theory(equality)],[2593,310]),
[iquote('1:Res:2593.1,310.2')] ).
cnf(2616,plain,
( ~ isPrime0(skf7(skf13(skc1)))
| ~ iLess0(skf13(skc1),skc1) ),
inference(ssi,[status(thm)],[2611,7,8,1]),
[iquote('1:SSi:2611.0,7.0,8.0,1.0')] ).
cnf(2744,plain,
( ~ aNaturalNumber0(skf13(skc1))
| ~ iLess0(skf13(skc1),skc1)
| ~ iLess0(skf13(skc1),skc1)
| equal(skf13(skc1),sz00)
| equal(skf13(skc1),sz10) ),
inference(sor,[status(thm)],[2616,38]),
[iquote('1:SoR:2616.0,38.2')] ).
cnf(2745,plain,
( ~ aNaturalNumber0(skf13(skc1))
| ~ iLess0(skf13(skc1),skc1)
| equal(skf13(skc1),sz00)
| equal(skf13(skc1),sz10) ),
inference(obv,[status(thm),theory(equality)],[2744]),
[iquote('1:Obv:2744.1')] ).
cnf(2746,plain,
( ~ iLess0(skf13(skc1),skc1)
| equal(skf13(skc1),sz00)
| equal(skf13(skc1),sz10) ),
inference(ssi,[status(thm)],[2745,8,1]),
[iquote('1:SSi:2745.0,8.0,1.0')] ).
cnf(2747,plain,
~ iLess0(skf13(skc1),skc1),
inference(mrr,[status(thm)],[2746,2587,490]),
[iquote('1:MRR:2746.1,2746.2,2587.0,490.0')] ).
cnf(2749,plain,
( ~ aNaturalNumber0(skc1)
| ~ aNaturalNumber0(skf13(skc1))
| ~ sdtlseqdt0(skf13(skc1),skc1)
| equal(skf13(skc1),skc1) ),
inference(res,[status(thm),theory(equality)],[39,2747]),
[iquote('1:Res:39.3,2747.0')] ).
cnf(2752,plain,
( ~ sdtlseqdt0(skf13(skc1),skc1)
| equal(skf13(skc1),skc1) ),
inference(ssi,[status(thm)],[2749,8,1]),
[iquote('1:SSi:2749.1,2749.0,8.0,1.0,1.0')] ).
cnf(2753,plain,
$false,
inference(mrr,[status(thm)],[2752,498,489]),
[iquote('1:MRR:2752.0,2752.1,498.0,489.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM481+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.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 04:02:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.59/0.87
% 0.59/0.87 SPASS V 3.9
% 0.59/0.87 SPASS beiseite: Proof found.
% 0.59/0.87 % SZS status Theorem
% 0.59/0.87 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.59/0.87 SPASS derived 1676 clauses, backtracked 31 clauses, performed 3 splits and kept 661 clauses.
% 0.59/0.87 SPASS allocated 99923 KBytes.
% 0.59/0.87 SPASS spent 0:00:00.50 on the problem.
% 0.59/0.87 0:00:00.03 for the input.
% 0.59/0.87 0:00:00.04 for the FLOTTER CNF translation.
% 0.59/0.87 0:00:00.02 for inferences.
% 0.59/0.87 0:00:00.00 for the backtracking.
% 0.59/0.87 0:00:00.35 for the reduction.
% 0.59/0.87
% 0.59/0.87
% 0.59/0.87 Here is a proof with depth 7, length 71 :
% 0.59/0.87 % SZS output start Refutation
% See solution above
% 0.59/0.87 Formulae used in the proof : m__ mSortsC_01 mSortsC mDefPrime mDefDiv m_MulUnit m_MulZero mIH_03 mDivLE mDivTrans
% 0.59/0.87
%------------------------------------------------------------------------------