TSTP Solution File: NUM469+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM469+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 0.18s 0.45s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 32 ( 20 unt; 3 nHn; 32 RR)
% Number of literals : 45 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aNaturalNumber0(sz00),
file('NUM469+2.p',unknown),
[] ).
cnf(6,axiom,
aNaturalNumber0(skc3),
file('NUM469+2.p',unknown),
[] ).
cnf(7,axiom,
aNaturalNumber0(skc2),
file('NUM469+2.p',unknown),
[] ).
cnf(13,axiom,
equal(sdtasdt0(xl,skc2),xm),
file('NUM469+2.p',unknown),
[] ).
cnf(14,axiom,
equal(sdtasdt0(xl,skc3),xn),
file('NUM469+2.p',unknown),
[] ).
cnf(17,axiom,
( aNaturalNumber0(sdtsldt0(xm,xl))
| equal(xl,sz00) ),
file('NUM469+2.p',unknown),
[] ).
cnf(18,axiom,
( aNaturalNumber0(sdtsldt0(xn,xl))
| equal(xl,sz00) ),
file('NUM469+2.p',unknown),
[] ).
cnf(19,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('NUM469+2.p',unknown),
[] ).
cnf(24,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(sz00,u),sz00) ),
file('NUM469+2.p',unknown),
[] ).
cnf(25,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM469+2.p',unknown),
[] ).
cnf(29,axiom,
( ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(xl,u),sdtpldt0(xm,xn)) ),
file('NUM469+2.p',unknown),
[] ).
cnf(40,axiom,
( equal(xl,sz00)
| equal(sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),sdtpldt0(xm,xn)) ),
file('NUM469+2.p',unknown),
[] ).
cnf(81,plain,
~ equal(sdtasdt0(xl,sz00),sdtpldt0(xm,xn)),
inference(res,[status(thm),theory(equality)],[1,29]),
[iquote('0:Res:1.0,29.0')] ).
cnf(87,plain,
equal(xl,sz00),
inference(spt,[spt(split,[position(s1)])],[18]),
[iquote('1:Spt:18.1')] ).
cnf(91,plain,
equal(sdtasdt0(sz00,skc3),xn),
inference(rew,[status(thm),theory(equality)],[87,14]),
[iquote('1:Rew:87.0,14.0')] ).
cnf(92,plain,
equal(sdtasdt0(sz00,skc2),xm),
inference(rew,[status(thm),theory(equality)],[87,13]),
[iquote('1:Rew:87.0,13.0')] ).
cnf(94,plain,
~ equal(sdtasdt0(sz00,sz00),sdtpldt0(xm,xn)),
inference(rew,[status(thm),theory(equality)],[87,81]),
[iquote('1:Rew:87.0,81.0')] ).
cnf(105,plain,
( ~ aNaturalNumber0(skc3)
| equal(xn,sz00) ),
inference(spr,[status(thm),theory(equality)],[24,91]),
[iquote('1:SpR:24.1,91.0')] ).
cnf(106,plain,
( ~ aNaturalNumber0(skc2)
| equal(xm,sz00) ),
inference(spr,[status(thm),theory(equality)],[24,92]),
[iquote('1:SpR:24.1,92.0')] ).
cnf(108,plain,
( ~ aNaturalNumber0(sz00)
| ~ equal(sdtpldt0(xm,xn),sz00) ),
inference(spl,[status(thm),theory(equality)],[24,94]),
[iquote('1:SpL:24.1,94.0')] ).
cnf(110,plain,
equal(xn,sz00),
inference(ssi,[status(thm)],[105,6]),
[iquote('1:SSi:105.0,6.0')] ).
cnf(123,plain,
equal(xm,sz00),
inference(ssi,[status(thm)],[106,7]),
[iquote('1:SSi:106.0,7.0')] ).
cnf(134,plain,
( ~ aNaturalNumber0(sz00)
| ~ equal(sz00,sz00) ),
inference(rew,[status(thm),theory(equality)],[19,108,123,110]),
[iquote('1:Rew:19.1,108.1,123.0,108.1,110.0,108.1')] ).
cnf(135,plain,
~ aNaturalNumber0(sz00),
inference(obv,[status(thm),theory(equality)],[134]),
[iquote('1:Obv:134.1')] ).
cnf(136,plain,
$false,
inference(ssi,[status(thm)],[135,1]),
[iquote('1:SSi:135.0,1.0')] ).
cnf(140,plain,
~ equal(xl,sz00),
inference(spt,[spt(split,[position(sa)])],[136,87]),
[iquote('1:Spt:136.0,18.1,87.0')] ).
cnf(141,plain,
aNaturalNumber0(sdtsldt0(xn,xl)),
inference(spt,[spt(split,[position(s2)])],[18]),
[iquote('1:Spt:136.0,18.0')] ).
cnf(142,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(mrr,[status(thm)],[17,140]),
[iquote('1:MRR:17.1,140.0')] ).
cnf(145,plain,
equal(sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),sdtpldt0(xm,xn)),
inference(mrr,[status(thm)],[40,140]),
[iquote('1:MRR:40.0,140.0')] ).
cnf(184,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ equal(sdtpldt0(xm,xn),sdtpldt0(xm,xn)) ),
inference(spl,[status(thm),theory(equality)],[145,29]),
[iquote('1:SpL:145.0,29.1')] ).
cnf(187,plain,
~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(obv,[status(thm),theory(equality)],[184]),
[iquote('1:Obv:184.1')] ).
cnf(188,plain,
$false,
inference(ssi,[status(thm)],[187,25,142,141]),
[iquote('1:SSi:187.0,25.0,142.0,141.2')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM469+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 04:34:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.45
% 0.18/0.45 SPASS V 3.9
% 0.18/0.45 SPASS beiseite: Proof found.
% 0.18/0.45 % SZS status Theorem
% 0.18/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 SPASS derived 83 clauses, backtracked 23 clauses, performed 1 splits and kept 125 clauses.
% 0.18/0.45 SPASS allocated 97850 KBytes.
% 0.18/0.45 SPASS spent 0:00:00.11 on the problem.
% 0.18/0.45 0:00:00.04 for the input.
% 0.18/0.45 0:00:00.04 for the FLOTTER CNF translation.
% 0.18/0.45 0:00:00.00 for inferences.
% 0.18/0.45 0:00:00.00 for the backtracking.
% 0.18/0.45 0:00:00.01 for the reduction.
% 0.18/0.45
% 0.18/0.45
% 0.18/0.45 Here is a proof with depth 2, length 32 :
% 0.18/0.45 % SZS output start Refutation
% See solution above
% 0.18/0.45 Formulae used in the proof : mSortsC m__1240_04 m__1298 m_AddZero m_MulZero mSortsB m__
% 0.18/0.45
%------------------------------------------------------------------------------