TSTP Solution File: NUM473+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM473+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 14:26:33 EDT 2022
% Result : Theorem 1.52s 1.75s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 25
% Syntax : Number of clauses : 62 ( 19 unt; 18 nHn; 62 RR)
% Number of literals : 198 ( 0 equ; 129 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xl),
file('NUM473+2.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM473+2.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xn),
file('NUM473+2.p',unknown),
[] ).
cnf(8,axiom,
aNaturalNumber0(xp),
file('NUM473+2.p',unknown),
[] ).
cnf(9,axiom,
aNaturalNumber0(xq),
file('NUM473+2.p',unknown),
[] ).
cnf(11,axiom,
doDivides0(xl,xm),
file('NUM473+2.p',unknown),
[] ).
cnf(12,axiom,
~ sdtlseqdt0(xp,xq),
file('NUM473+2.p',unknown),
[] ).
cnf(14,axiom,
aNaturalNumber0(skf2(u,v)),
file('NUM473+2.p',unknown),
[] ).
cnf(16,axiom,
~ equal(xl,sz00),
file('NUM473+2.p',unknown),
[] ).
cnf(18,axiom,
doDivides0(xl,sdtpldt0(xm,xn)),
file('NUM473+2.p',unknown),
[] ).
cnf(19,axiom,
equal(sdtasdt0(xl,xp),xm),
file('NUM473+2.p',unknown),
[] ).
cnf(20,axiom,
equal(sdtsldt0(xm,xl),xp),
file('NUM473+2.p',unknown),
[] ).
cnf(21,axiom,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
file('NUM473+2.p',unknown),
[] ).
cnf(25,axiom,
equal(sdtsldt0(sdtpldt0(xm,xn),xl),xq),
file('NUM473+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ aNaturalNumber0(u)
| ~ equal(sdtpldt0(xp,u),xq) ),
file('NUM473+2.p',unknown),
[] ).
cnf(34,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM473+2.p',unknown),
[] ).
cnf(36,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(v,u)
| sdtlseqdt0(u,v) ),
file('NUM473+2.p',unknown),
[] ).
cnf(40,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(u,v)
| sdtlseqdt0(v,u) ),
file('NUM473+2.p',unknown),
[] ).
cnf(46,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| equal(sdtpldt0(v,skf2(u,v)),u) ),
file('NUM473+2.p',unknown),
[] ).
cnf(47,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ sdtlseqdt0(u,v)
| equal(v,u) ),
file('NUM473+2.p',unknown),
[] ).
cnf(52,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM473+2.p',unknown),
[] ).
cnf(59,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| aNaturalNumber0(w)
| equal(v,sz00) ),
file('NUM473+2.p',unknown),
[] ).
cnf(68,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| equal(v,sz00)
| equal(u,sdtasdt0(v,w)) ),
file('NUM473+2.p',unknown),
[] ).
cnf(73,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,u)
| equal(v,u)
| equal(w,sz00)
| sdtlseqdt0(sdtasdt0(w,v),sdtasdt0(w,u)) ),
file('NUM473+2.p',unknown),
[] ).
cnf(74,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(v,w)
| ~ equal(w,sdtasdt0(v,u))
| equal(u,sdtsldt0(w,v))
| equal(v,sz00) ),
file('NUM473+2.p',unknown),
[] ).
cnf(78,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| equal(v,sz00)
| equal(w,sdtsldt0(u,v)) ),
inference(mrr,[status(thm)],[74,52]),
[iquote('0:MRR:74.3,52.4')] ).
cnf(80,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq)
| ~ equal(xq,xp) ),
inference(res,[status(thm),theory(equality)],[40,12]),
[iquote('0:Res:40.3,12.0')] ).
cnf(97,plain,
~ equal(xq,xp),
inference(mrr,[status(thm)],[80,8,9]),
[iquote('0:MRR:80.0,80.1,8.0,9.0')] ).
cnf(651,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
| equal(sdtpldt0(xm,xn),xm) ),
inference(res,[status(thm),theory(equality)],[21,47]),
[iquote('0:Res:21.0,47.2')] ).
cnf(652,plain,
( ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
| equal(sdtpldt0(xm,xn),xm) ),
inference(ssi,[status(thm)],[651,4,34,5]),
[iquote('0:SSi:651.1,651.0,4.0,34.0,4.2,5.0')] ).
cnf(865,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(skf2(u,xp))
| ~ sdtlseqdt0(xp,u)
| ~ equal(u,xq) ),
inference(spl,[status(thm),theory(equality)],[46,33]),
[iquote('0:SpL:46.3,33.1')] ).
cnf(869,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(xp,u)
| ~ equal(u,xq) ),
inference(ssi,[status(thm)],[865,14,8]),
[iquote('0:SSi:865.2,865.1,14.0,8.0,8.0')] ).
cnf(1135,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(u)
| ~ equal(u,xp)
| ~ equal(u,xq) ),
inference(res,[status(thm),theory(equality)],[40,869]),
[iquote('0:Res:40.3,869.1')] ).
cnf(1136,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(u)
| ~ equal(u,xq)
| sdtlseqdt0(u,xp) ),
inference(res,[status(thm),theory(equality)],[36,869]),
[iquote('0:Res:36.2,869.1')] ).
cnf(1140,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(u)
| ~ equal(u,xq)
| sdtlseqdt0(u,xp) ),
inference(obv,[status(thm),theory(equality)],[1136]),
[iquote('0:Obv:1136.0')] ).
cnf(1141,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xq)
| sdtlseqdt0(u,xp) ),
inference(ssi,[status(thm)],[1140,8]),
[iquote('0:SSi:1140.0,8.0')] ).
cnf(1143,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(u)
| ~ equal(u,xp)
| ~ equal(u,xq) ),
inference(obv,[status(thm),theory(equality)],[1135]),
[iquote('0:Obv:1135.0')] ).
cnf(1144,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xp)
| ~ equal(u,xq) ),
inference(ssi,[status(thm)],[1143,8]),
[iquote('0:SSi:1143.0,8.0')] ).
cnf(1562,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ~ equal(u,xp)
| aNaturalNumber0(u)
| equal(xl,sz00) ),
inference(spl,[status(thm),theory(equality)],[20,59]),
[iquote('0:SpL:20.0,59.3')] ).
cnf(1563,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ equal(u,xq)
| aNaturalNumber0(u)
| equal(xl,sz00) ),
inference(spl,[status(thm),theory(equality)],[25,59]),
[iquote('0:SpL:25.0,59.3')] ).
cnf(1564,plain,
( ~ doDivides0(xl,xm)
| ~ equal(u,xp)
| aNaturalNumber0(u)
| equal(xl,sz00) ),
inference(ssi,[status(thm)],[1562,3,4]),
[iquote('0:SSi:1562.1,1562.0,3.0,4.0')] ).
cnf(1565,plain,
( ~ equal(u,xp)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[1564,11,16]),
[iquote('0:MRR:1564.0,1564.3,11.0,16.0')] ).
cnf(1566,plain,
( ~ equal(u,xp)
| ~ equal(u,xq) ),
inference(mrr,[status(thm)],[1144,1565]),
[iquote('0:MRR:1144.0,1565.1')] ).
cnf(1567,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ equal(u,xq)
| aNaturalNumber0(u)
| equal(xl,sz00) ),
inference(ssi,[status(thm)],[1563,3,34,4,5]),
[iquote('0:SSi:1563.1,1563.0,3.0,34.0,4.2,5.0')] ).
cnf(1568,plain,
( ~ equal(u,xq)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[1567,18,16]),
[iquote('0:MRR:1567.0,1567.3,18.0,16.0')] ).
cnf(1570,plain,
( ~ equal(u,xq)
| sdtlseqdt0(u,xp) ),
inference(mrr,[status(thm)],[1141,1568]),
[iquote('0:MRR:1141.0,1568.1')] ).
cnf(1828,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xp)
| ~ equal(u,xm)
| equal(xl,sz00)
| equal(sdtsldt0(u,xl),xp) ),
inference(spl,[status(thm),theory(equality)],[19,78]),
[iquote('0:SpL:19.0,78.3')] ).
cnf(1833,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xm)
| equal(xl,sz00)
| equal(sdtsldt0(u,xl),xp) ),
inference(ssi,[status(thm)],[1828,8,3]),
[iquote('0:SSi:1828.2,1828.1,8.0,3.0')] ).
cnf(1834,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xm)
| equal(sdtsldt0(u,xl),xp) ),
inference(mrr,[status(thm)],[1833,16]),
[iquote('0:MRR:1833.2,16.0')] ).
cnf(2317,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ equal(u,xq)
| equal(xl,sz00)
| equal(sdtasdt0(xl,u),sdtpldt0(xm,xn)) ),
inference(spl,[status(thm),theory(equality)],[25,68]),
[iquote('0:SpL:25.0,68.3')] ).
cnf(2320,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ equal(u,xq)
| equal(xl,sz00)
| equal(sdtasdt0(xl,u),sdtpldt0(xm,xn)) ),
inference(ssi,[status(thm)],[2317,3,34,4,5]),
[iquote('0:SSi:2317.1,2317.0,3.0,34.0,4.2,5.0')] ).
cnf(2321,plain,
( ~ equal(u,xq)
| equal(sdtasdt0(xl,u),sdtpldt0(xm,xn)) ),
inference(mrr,[status(thm)],[2320,18,16]),
[iquote('0:MRR:2320.0,2320.2,18.0,16.0')] ).
cnf(2423,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xl)
| ~ sdtlseqdt0(u,xp)
| equal(u,xp)
| equal(xl,sz00)
| sdtlseqdt0(sdtasdt0(xl,u),xm) ),
inference(spr,[status(thm),theory(equality)],[19,73]),
[iquote('0:SpR:19.0,73.6')] ).
cnf(2462,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,xp)
| equal(u,xp)
| equal(xl,sz00)
| sdtlseqdt0(sdtasdt0(xl,u),xm) ),
inference(ssi,[status(thm)],[2423,3,8]),
[iquote('0:SSi:2423.2,2423.0,3.0,8.0')] ).
cnf(2463,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,xp)
| equal(u,xp)
| sdtlseqdt0(sdtasdt0(xl,u),xm) ),
inference(mrr,[status(thm)],[2462,16]),
[iquote('0:MRR:2462.3,16.0')] ).
cnf(2932,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ equal(sdtpldt0(xm,xn),xm)
| equal(xq,xp) ),
inference(spr,[status(thm),theory(equality)],[1834,25]),
[iquote('0:SpR:1834.2,25.0')] ).
cnf(2936,plain,
( ~ equal(sdtpldt0(xm,xn),xm)
| equal(xq,xp) ),
inference(ssi,[status(thm)],[2932,34,4,5]),
[iquote('0:SSi:2932.0,34.0,4.0,5.2')] ).
cnf(2937,plain,
~ equal(sdtpldt0(xm,xn),xm),
inference(mrr,[status(thm)],[2936,97]),
[iquote('0:MRR:2936.1,97.0')] ).
cnf(2938,plain,
~ sdtlseqdt0(sdtpldt0(xm,xn),xm),
inference(mrr,[status(thm)],[652,2937]),
[iquote('0:MRR:652.1,2937.0')] ).
cnf(7067,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xq)
| ~ sdtlseqdt0(u,xp)
| equal(u,xp)
| sdtlseqdt0(sdtpldt0(xm,xn),xm) ),
inference(spr,[status(thm),theory(equality)],[2321,2463]),
[iquote('0:SpR:2321.1,2463.3')] ).
cnf(7075,plain,
~ equal(u,xq),
inference(mrr,[status(thm)],[7067,1568,1570,1566,2938]),
[iquote('0:MRR:7067.0,7067.2,7067.3,7067.4,1568.1,1570.1,1566.0,2938.0')] ).
cnf(7076,plain,
$false,
inference(unc,[status(thm)],[7075,25]),
[iquote('0:UnC:7075.0,25.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07 % Problem : NUM473+2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.07 % Command : run_spass %d %s
% 0.06/0.26 % Computer : n018.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 600
% 0.06/0.26 % DateTime : Wed Jul 6 22:43:38 EDT 2022
% 0.06/0.26 % CPUTime :
% 1.52/1.75
% 1.52/1.75 SPASS V 3.9
% 1.52/1.75 SPASS beiseite: Proof found.
% 1.52/1.75 % SZS status Theorem
% 1.52/1.75 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.52/1.75 SPASS derived 4684 clauses, backtracked 582 clauses, performed 7 splits and kept 2039 clauses.
% 1.52/1.75 SPASS allocated 103144 KBytes.
% 1.52/1.75 SPASS spent 0:00:01.32 on the problem.
% 1.52/1.75 0:00:00.02 for the input.
% 1.52/1.75 0:00:00.02 for the FLOTTER CNF translation.
% 1.52/1.75 0:00:00.05 for inferences.
% 1.52/1.75 0:00:00.01 for the backtracking.
% 1.52/1.75 0:00:01.19 for the reduction.
% 1.52/1.75
% 1.52/1.75
% 1.52/1.75 Here is a proof with depth 2, length 62 :
% 1.52/1.75 % SZS output start Refutation
% See solution above
% 1.52/1.75 Formulae used in the proof : m__1324 m__1360 m__1379 m__1324_04 m__ mDefLE m__1409 m__1347 mSortsB mLETotal mLEAsym mDefDiv mDefQuot mMonMul
% 1.52/1.75
%------------------------------------------------------------------------------