TSTP Solution File: NUM469+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM469+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 14:26:31 EDT 2022
% Result : Theorem 5.44s 5.67s
% Output : Refutation 5.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of clauses : 47 ( 24 unt; 3 nHn; 47 RR)
% Number of literals : 98 ( 0 equ; 58 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aNaturalNumber0(sz00),
file('NUM469+1.p',unknown),
[] ).
cnf(3,axiom,
aNaturalNumber0(xl),
file('NUM469+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM469+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xn),
file('NUM469+1.p',unknown),
[] ).
cnf(6,axiom,
doDivides0(xl,xm),
file('NUM469+1.p',unknown),
[] ).
cnf(7,axiom,
doDivides0(xl,xn),
file('NUM469+1.p',unknown),
[] ).
cnf(10,axiom,
aNaturalNumber0(skf3(u,v)),
file('NUM469+1.p',unknown),
[] ).
cnf(11,axiom,
~ doDivides0(xl,sdtpldt0(xm,xn)),
file('NUM469+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('NUM469+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(sz00,u),sz00) ),
file('NUM469+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM469+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM469+1.p',unknown),
[] ).
cnf(31,axiom,
( equal(xl,sz00)
| equal(sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),sdtpldt0(xm,xn)) ),
file('NUM469+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| equal(sdtasdt0(v,skf3(v,u)),u) ),
file('NUM469+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM469+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| aNaturalNumber0(w)
| equal(v,sz00) ),
file('NUM469+1.p',unknown),
[] ).
cnf(68,plain,
equal(xl,sz00),
inference(spt,[spt(split,[position(s1)])],[31]),
[iquote('1:Spt:31.0')] ).
cnf(70,plain,
doDivides0(sz00,xn),
inference(rew,[status(thm),theory(equality)],[68,7]),
[iquote('1:Rew:68.0,7.0')] ).
cnf(71,plain,
doDivides0(sz00,xm),
inference(rew,[status(thm),theory(equality)],[68,6]),
[iquote('1:Rew:68.0,6.0')] ).
cnf(72,plain,
~ doDivides0(sz00,sdtpldt0(xm,xn)),
inference(rew,[status(thm),theory(equality)],[68,11]),
[iquote('1:Rew:68.0,11.0')] ).
cnf(182,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(skf3(sz00,u))
| ~ doDivides0(sz00,u)
| equal(u,sz00) ),
inference(spr,[status(thm),theory(equality)],[34,18]),
[iquote('0:SpR:34.3,18.1')] ).
cnf(188,plain,
( ~ aNaturalNumber0(u)
| ~ doDivides0(sz00,u)
| equal(u,sz00) ),
inference(ssi,[status(thm)],[182,10,1]),
[iquote('0:SSi:182.2,182.1,10.0,1.0,1.0')] ).
cnf(204,plain,
( ~ aNaturalNumber0(xn)
| equal(xn,sz00) ),
inference(res,[status(thm),theory(equality)],[70,188]),
[iquote('1:Res:70.0,188.1')] ).
cnf(205,plain,
( ~ aNaturalNumber0(xm)
| equal(xm,sz00) ),
inference(res,[status(thm),theory(equality)],[71,188]),
[iquote('1:Res:71.0,188.1')] ).
cnf(206,plain,
equal(xn,sz00),
inference(ssi,[status(thm)],[204,5]),
[iquote('1:SSi:204.0,5.0')] ).
cnf(208,plain,
doDivides0(sz00,sz00),
inference(rew,[status(thm),theory(equality)],[206,70]),
[iquote('1:Rew:206.0,70.0')] ).
cnf(209,plain,
~ doDivides0(sz00,sdtpldt0(xm,sz00)),
inference(rew,[status(thm),theory(equality)],[206,72]),
[iquote('1:Rew:206.0,72.0')] ).
cnf(212,plain,
equal(xm,sz00),
inference(ssi,[status(thm)],[205,4]),
[iquote('1:SSi:205.0,4.0')] ).
cnf(215,plain,
~ doDivides0(sz00,sdtpldt0(sz00,sz00)),
inference(rew,[status(thm),theory(equality)],[212,209]),
[iquote('1:Rew:212.0,209.0')] ).
cnf(223,plain,
( ~ aNaturalNumber0(sz00)
| ~ doDivides0(sz00,sz00) ),
inference(spl,[status(thm),theory(equality)],[13,215]),
[iquote('1:SpL:13.1,215.0')] ).
cnf(227,plain,
~ doDivides0(sz00,sz00),
inference(ssi,[status(thm)],[223,1]),
[iquote('1:SSi:223.0,1.0')] ).
cnf(228,plain,
$false,
inference(mrr,[status(thm)],[227,208]),
[iquote('1:MRR:227.0,208.0')] ).
cnf(231,plain,
~ equal(xl,sz00),
inference(spt,[spt(split,[position(sa)])],[228,68]),
[iquote('1:Spt:228.0,31.0,68.0')] ).
cnf(232,plain,
equal(sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),sdtpldt0(xm,xn)),
inference(spt,[spt(split,[position(s2)])],[31]),
[iquote('1:Spt:228.0,31.1')] ).
cnf(386,plain,
( ~ aNaturalNumber0(sdtasdt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| doDivides0(u,sdtasdt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[38]),
[iquote('0:EqR:38.3')] ).
cnf(395,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| doDivides0(u,sdtasdt0(u,v)) ),
inference(ssi,[status(thm)],[386,20]),
[iquote('0:SSi:386.0,20.2')] ).
cnf(433,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(spr,[status(thm),theory(equality)],[232,395]),
[iquote('1:SpR:232.0,395.2')] ).
cnf(447,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(ssi,[status(thm)],[433,3]),
[iquote('1:SSi:433.0,3.0')] ).
cnf(448,plain,
~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(mrr,[status(thm)],[447,11]),
[iquote('1:MRR:447.1,11.0')] ).
cnf(511,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(xn,xl)) ),
inference(sor,[status(thm)],[448,19]),
[iquote('1:SoR:448.0,19.2')] ).
cnf(939,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| aNaturalNumber0(sdtsldt0(u,v))
| equal(v,sz00) ),
inference(eqr,[status(thm),theory(equality)],[45]),
[iquote('0:EqR:45.3')] ).
cnf(18107,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xl,xm)
| equal(xl,sz00) ),
inference(sor,[status(thm)],[511,939]),
[iquote('1:SoR:511.0,939.3')] ).
cnf(18125,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ doDivides0(xl,xm)
| equal(xl,sz00) ),
inference(ssi,[status(thm)],[18107,4,3]),
[iquote('1:SSi:18107.2,18107.1,4.0,3.0')] ).
cnf(18126,plain,
~ aNaturalNumber0(sdtsldt0(xn,xl)),
inference(mrr,[status(thm)],[18125,6,231]),
[iquote('1:MRR:18125.1,18125.2,6.0,231.0')] ).
cnf(18140,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xl,xn)
| equal(xl,sz00) ),
inference(sor,[status(thm)],[18126,939]),
[iquote('1:SoR:18126.0,939.3')] ).
cnf(18146,plain,
( ~ doDivides0(xl,xn)
| equal(xl,sz00) ),
inference(ssi,[status(thm)],[18140,5,3]),
[iquote('1:SSi:18140.1,18140.0,5.0,3.0')] ).
cnf(18147,plain,
$false,
inference(mrr,[status(thm)],[18146,7,231]),
[iquote('1:MRR:18146.0,18146.1,7.0,231.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM469+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 5 08:36:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 5.44/5.67
% 5.44/5.67 SPASS V 3.9
% 5.44/5.67 SPASS beiseite: Proof found.
% 5.44/5.67 % SZS status Theorem
% 5.44/5.67 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.44/5.67 SPASS derived 10676 clauses, backtracked 3027 clauses, performed 7 splits and kept 5051 clauses.
% 5.44/5.67 SPASS allocated 109709 KBytes.
% 5.44/5.67 SPASS spent 0:00:03.82 on the problem.
% 5.44/5.67 0:00:00.04 for the input.
% 5.44/5.67 0:00:00.04 for the FLOTTER CNF translation.
% 5.44/5.67 0:00:00.10 for inferences.
% 5.44/5.67 0:00:00.02 for the backtracking.
% 5.44/5.67 0:00:03.58 for the reduction.
% 5.44/5.67
% 5.44/5.67
% 5.44/5.67 Here is a proof with depth 5, length 47 :
% 5.44/5.67 % SZS output start Refutation
% See solution above
% 5.44/5.67 Formulae used in the proof : mSortsC m__1240 m__1240_04 mDefDiv m__ m_AddZero m_MulZero mSortsB mSortsB_02 m__1298 mDefQuot
% 5.44/5.67
%------------------------------------------------------------------------------