TSTP Solution File: NUM477+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM477+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 14:26:36 EDT 2022
% Result : Theorem 15.75s 15.95s
% Output : Refutation 15.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of clauses : 49 ( 9 unt; 1 nHn; 49 RR)
% Number of literals : 184 ( 0 equ; 140 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xm),
file('NUM477+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xn),
file('NUM477+1.p',unknown),
[] ).
cnf(5,axiom,
doDivides0(xm,xn),
file('NUM477+1.p',unknown),
[] ).
cnf(6,axiom,
~ sdtlseqdt0(xm,xn),
file('NUM477+1.p',unknown),
[] ).
cnf(8,axiom,
aNaturalNumber0(skf2(u,v)),
file('NUM477+1.p',unknown),
[] ).
cnf(9,axiom,
aNaturalNumber0(skf3(u,v)),
file('NUM477+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(xn,sz00),
file('NUM477+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,sz00),sz00) ),
file('NUM477+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM477+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM477+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(v,sz00)
| sdtlseqdt0(u,sdtasdt0(u,v)) ),
file('NUM477+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| equal(sdtpldt0(v,skf2(u,v)),u) ),
file('NUM477+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| equal(sdtasdt0(v,skf3(v,u)),u) ),
file('NUM477+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM477+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| aNaturalNumber0(w) ),
file('NUM477+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM477+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,w)
| ~ equal(sdtpldt0(v,u),w)
| equal(u,sdtmndt0(w,v)) ),
file('NUM477+1.p',unknown),
[] ).
cnf(62,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| equal(w,sdtmndt0(u,v)) ),
inference(mrr,[status(thm)],[56,34]),
[iquote('0:MRR:56.3,34.4')] ).
cnf(68,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ equal(sdtpldt0(xm,u),xn) ),
inference(res,[status(thm),theory(equality)],[34,6]),
[iquote('0:Res:34.4,6.0')] ).
cnf(71,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtpldt0(xm,u),xn) ),
inference(mrr,[status(thm)],[68,3,4]),
[iquote('0:MRR:68.1,68.2,3.0,4.0')] ).
cnf(367,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(skf2(u,xm))
| ~ sdtlseqdt0(xm,u)
| ~ equal(u,xn) ),
inference(spl,[status(thm),theory(equality)],[30,71]),
[iquote('0:SpL:30.3,71.1')] ).
cnf(371,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(xm,u)
| ~ equal(u,xn) ),
inference(ssi,[status(thm)],[367,8,3]),
[iquote('0:SSi:367.2,367.1,8.0,3.0,3.0')] ).
cnf(409,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtasdt0(xm,u))
| ~ equal(sdtasdt0(xm,u),xn)
| equal(u,sz00) ),
inference(res,[status(thm),theory(equality)],[26,371]),
[iquote('0:Res:26.3,371.1')] ).
cnf(420,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(xm,u),xn)
| equal(u,sz00) ),
inference(ssi,[status(thm)],[409,19,3]),
[iquote('0:SSi:409.2,409.0,19.0,3.0,3.2')] ).
cnf(456,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(skf3(xm,u))
| ~ doDivides0(xm,u)
| ~ equal(u,xn)
| equal(skf3(xm,u),sz00) ),
inference(spl,[status(thm),theory(equality)],[32,420]),
[iquote('0:SpL:32.3,420.1')] ).
cnf(459,plain,
( ~ aNaturalNumber0(u)
| ~ doDivides0(xm,u)
| ~ equal(u,xn)
| equal(skf3(xm,u),sz00) ),
inference(ssi,[status(thm)],[456,9,3]),
[iquote('0:SSi:456.2,456.1,9.0,3.0,3.0')] ).
cnf(460,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[34]),
[iquote('0:EqR:34.3')] ).
cnf(466,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(ssi,[status(thm)],[460,18]),
[iquote('0:SSi:460.0,18.2')] ).
cnf(505,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(skf3(v,u))
| ~ doDivides0(v,u)
| ~ equal(w,u)
| doDivides0(v,w) ),
inference(spl,[status(thm),theory(equality)],[32,36]),
[iquote('0:SpL:32.3,36.3')] ).
cnf(519,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ aNaturalNumber0(skf3(w,u))
| ~ doDivides0(w,u)
| ~ equal(v,u)
| doDivides0(w,v) ),
inference(obv,[status(thm),theory(equality)],[505]),
[iquote('0:Obv:505.1')] ).
cnf(520,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(w,u)
| ~ equal(v,u)
| doDivides0(w,v) ),
inference(ssi,[status(thm)],[519,9]),
[iquote('0:SSi:519.3,9.0')] ).
cnf(750,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(eqr,[status(thm),theory(equality)],[62]),
[iquote('0:EqR:62.3')] ).
cnf(757,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(ssi,[status(thm)],[750,18]),
[iquote('0:SSi:750.0,18.2')] ).
cnf(854,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,sdtpldt0(u,v))
| ~ equal(w,v)
| aNaturalNumber0(w) ),
inference(spl,[status(thm),theory(equality)],[757,35]),
[iquote('0:SpL:757.2,35.3')] ).
cnf(869,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtpldt0(v,u))
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,sdtpldt0(v,u))
| ~ equal(w,u)
| aNaturalNumber0(w) ),
inference(obv,[status(thm),theory(equality)],[854]),
[iquote('0:Obv:854.0')] ).
cnf(870,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,sdtpldt0(v,u))
| ~ equal(w,u)
| aNaturalNumber0(w) ),
inference(ssi,[status(thm)],[869,18]),
[iquote('0:SSi:869.1,18.2')] ).
cnf(871,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(w,u)
| aNaturalNumber0(w) ),
inference(mrr,[status(thm)],[870,466]),
[iquote('0:MRR:870.2,466.2')] ).
cnf(873,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,w)
| ~ equal(u,w)
| doDivides0(v,u) ),
inference(mrr,[status(thm)],[520,871]),
[iquote('0:MRR:520.0,871.3')] ).
cnf(30530,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ equal(u,xn)
| doDivides0(xm,u) ),
inference(res,[status(thm),theory(equality)],[5,873]),
[iquote('0:Res:5.0,873.2')] ).
cnf(30539,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xn)
| doDivides0(xm,u) ),
inference(ssi,[status(thm)],[30530,3]),
[iquote('0:SSi:30530.1,3.0')] ).
cnf(30540,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xn)
| equal(skf3(xm,u),sz00) ),
inference(mrr,[status(thm)],[459,30539]),
[iquote('0:MRR:459.1,30539.2')] ).
cnf(30599,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ equal(u,xn)
| ~ doDivides0(xm,u)
| equal(sdtasdt0(xm,sz00),u) ),
inference(spr,[status(thm),theory(equality)],[30540,32]),
[iquote('0:SpR:30540.2,32.3')] ).
cnf(30728,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ equal(u,xn)
| ~ doDivides0(xm,u)
| equal(sdtasdt0(xm,sz00),u) ),
inference(obv,[status(thm),theory(equality)],[30599]),
[iquote('0:Obv:30599.0')] ).
cnf(30729,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ equal(u,xn)
| ~ doDivides0(xm,u)
| equal(sz00,u) ),
inference(rew,[status(thm),theory(equality)],[16,30728]),
[iquote('0:Rew:16.1,30728.4')] ).
cnf(30730,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xn)
| ~ doDivides0(xm,u)
| equal(sz00,u) ),
inference(ssi,[status(thm)],[30729,3]),
[iquote('0:SSi:30729.1,3.0')] ).
cnf(30731,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xn)
| equal(sz00,u) ),
inference(mrr,[status(thm)],[30730,30539]),
[iquote('0:MRR:30730.2,30539.2')] ).
cnf(30920,plain,
( ~ equal(xn,xn)
| equal(xn,sz00) ),
inference(ems,[status(thm)],[30731,4]),
[iquote('0:EmS:30731.0,4.0')] ).
cnf(30928,plain,
equal(xn,sz00),
inference(obv,[status(thm),theory(equality)],[30920]),
[iquote('0:Obv:30920.0')] ).
cnf(30929,plain,
$false,
inference(mrr,[status(thm)],[30928,10]),
[iquote('0:MRR:30928.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM477+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jul 5 14:25:28 EDT 2022
% 0.14/0.36 % CPUTime :
% 15.75/15.95
% 15.75/15.95 SPASS V 3.9
% 15.75/15.95 SPASS beiseite: Proof found.
% 15.75/15.95 % SZS status Theorem
% 15.75/15.95 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.75/15.95 SPASS derived 18427 clauses, backtracked 3959 clauses, performed 7 splits and kept 7413 clauses.
% 15.75/15.95 SPASS allocated 118470 KBytes.
% 15.75/15.95 SPASS spent 0:0:10.29 on the problem.
% 15.75/15.95 0:00:00.04 for the input.
% 15.75/15.95 0:00:00.04 for the FLOTTER CNF translation.
% 15.75/15.95 0:00:00.26 for inferences.
% 15.75/15.95 0:00:00.04 for the backtracking.
% 15.75/15.95 0:00:09.84 for the reduction.
% 15.75/15.95
% 15.75/15.95
% 15.75/15.95 Here is a proof with depth 6, length 49 :
% 15.75/15.95 % SZS output start Refutation
% See solution above
% 15.75/15.95 Formulae used in the proof : m__1494 m__1494_04 m__ mDefLE mDefDiv m_MulZero mSortsB mSortsB_02 mMonMul2 mDefDiff
% 15.75/15.95
%------------------------------------------------------------------------------