TSTP Solution File: NUM465+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM465+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 14:26:28 EDT 2022
% Result : Theorem 0.37s 0.55s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of clauses : 38 ( 18 unt; 9 nHn; 38 RR)
% Number of literals : 85 ( 0 equ; 48 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aNaturalNumber0(sz00),
file('NUM465+2.p',unknown),
[] ).
cnf(2,axiom,
aNaturalNumber0(sz10),
file('NUM465+2.p',unknown),
[] ).
cnf(3,axiom,
aNaturalNumber0(xm),
file('NUM465+2.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xn),
file('NUM465+2.p',unknown),
[] ).
cnf(6,axiom,
~ equal(xm,sz00),
file('NUM465+2.p',unknown),
[] ).
cnf(9,axiom,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
file('NUM465+2.p',unknown),
[] ).
cnf(11,axiom,
( sdtlseqdt0(sz10,xm)
| equal(xm,sz00) ),
file('NUM465+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('NUM465+2.p',unknown),
[] ).
cnf(14,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,sz10),u) ),
file('NUM465+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(sz00,u),sz00) ),
file('NUM465+2.p',unknown),
[] ).
cnf(21,axiom,
( ~ aNaturalNumber0(u)
| ~ equal(sdtpldt0(xn,u),sdtasdt0(xn,xm)) ),
file('NUM465+2.p',unknown),
[] ).
cnf(26,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(u,v)
| sdtlseqdt0(v,u) ),
file('NUM465+2.p',unknown),
[] ).
cnf(43,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(w,u)
| equal(w,u)
| sdtlseqdt0(sdtpldt0(w,v),sdtpldt0(u,v)) ),
file('NUM465+2.p',unknown),
[] ).
cnf(51,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,u)
| equal(v,u)
| equal(w,sz00)
| sdtlseqdt0(sdtasdt0(w,v),sdtasdt0(w,u)) ),
file('NUM465+2.p',unknown),
[] ).
cnf(54,plain,
sdtlseqdt0(sz10,xm),
inference(mrr,[status(thm)],[11,6]),
[iquote('0:MRR:11.1,6.0')] ).
cnf(63,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(sdtasdt0(u,sz10),sdtasdt0(u,xm))
| equal(u,sz00)
| equal(xm,sz10) ),
inference(res,[status(thm),theory(equality)],[54,51]),
[iquote('0:Res:54.0,51.3')] ).
cnf(67,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(sdtpldt0(sz10,u),sdtpldt0(xm,u))
| equal(xm,sz10) ),
inference(res,[status(thm),theory(equality)],[54,43]),
[iquote('0:Res:54.0,43.3')] ).
cnf(109,plain,
~ equal(sdtasdt0(xn,xm),sdtpldt0(xn,sz00)),
inference(res,[status(thm),theory(equality)],[1,21]),
[iquote('0:Res:1.0,21.0')] ).
cnf(136,plain,
( ~ aNaturalNumber0(u)
| equal(xm,sz10)
| sdtlseqdt0(sdtpldt0(sz10,u),sdtpldt0(xm,u)) ),
inference(mrr,[status(thm)],[67,2,3]),
[iquote('0:MRR:67.0,67.2,2.0,3.0')] ).
cnf(154,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(u,sdtasdt0(u,xm))
| equal(u,sz00)
| equal(xm,sz10) ),
inference(rew,[status(thm),theory(equality)],[14,63]),
[iquote('0:Rew:14.1,63.3')] ).
cnf(155,plain,
( ~ aNaturalNumber0(u)
| equal(u,sz00)
| sdtlseqdt0(u,sdtasdt0(u,xm))
| equal(xm,sz10) ),
inference(mrr,[status(thm)],[154,2,3]),
[iquote('0:MRR:154.1,154.2,2.0,3.0')] ).
cnf(166,plain,
equal(xm,sz10),
inference(spt,[spt(split,[position(s1)])],[136]),
[iquote('1:Spt:136.1')] ).
cnf(168,plain,
~ equal(sdtasdt0(xn,sz10),sdtpldt0(xn,sz00)),
inference(rew,[status(thm),theory(equality)],[166,109]),
[iquote('1:Rew:166.0,109.0')] ).
cnf(234,plain,
( ~ aNaturalNumber0(xn)
| ~ equal(sdtpldt0(xn,sz00),xn) ),
inference(spl,[status(thm),theory(equality)],[14,168]),
[iquote('1:SpL:14.1,168.0')] ).
cnf(239,plain,
( ~ aNaturalNumber0(xn)
| ~ equal(xn,xn) ),
inference(rew,[status(thm),theory(equality)],[12,234]),
[iquote('1:Rew:12.1,234.1')] ).
cnf(240,plain,
~ aNaturalNumber0(xn),
inference(obv,[status(thm),theory(equality)],[239]),
[iquote('1:Obv:239.1')] ).
cnf(241,plain,
$false,
inference(ssi,[status(thm)],[240,4]),
[iquote('1:SSi:240.0,4.0')] ).
cnf(244,plain,
~ equal(xm,sz10),
inference(spt,[spt(split,[position(sa)])],[241,166]),
[iquote('1:Spt:241.0,136.1,166.0')] ).
cnf(245,plain,
( ~ aNaturalNumber0(u)
| sdtlseqdt0(sdtpldt0(sz10,u),sdtpldt0(xm,u)) ),
inference(spt,[spt(split,[position(s2)])],[136]),
[iquote('1:Spt:241.0,136.0,136.2')] ).
cnf(248,plain,
( ~ aNaturalNumber0(u)
| equal(u,sz00)
| sdtlseqdt0(u,sdtasdt0(u,xm)) ),
inference(mrr,[status(thm)],[155,244]),
[iquote('1:MRR:155.3,244.0')] ).
cnf(899,plain,
( ~ aNaturalNumber0(xn)
| equal(xn,sz00) ),
inference(res,[status(thm),theory(equality)],[248,9]),
[iquote('1:Res:248.2,9.0')] ).
cnf(900,plain,
equal(xn,sz00),
inference(ssi,[status(thm)],[899,4]),
[iquote('1:SSi:899.0,4.0')] ).
cnf(903,plain,
~ sdtlseqdt0(sz00,sdtasdt0(sz00,xm)),
inference(rew,[status(thm),theory(equality)],[900,9]),
[iquote('1:Rew:900.0,9.0')] ).
cnf(949,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sz00,sz00) ),
inference(spl,[status(thm),theory(equality)],[17,903]),
[iquote('1:SpL:17.1,903.0')] ).
cnf(952,plain,
~ sdtlseqdt0(sz00,sz00),
inference(ssi,[status(thm)],[949,3]),
[iquote('1:SSi:949.0,3.0')] ).
cnf(955,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00)
| ~ equal(sz00,sz00) ),
inference(res,[status(thm),theory(equality)],[26,952]),
[iquote('1:Res:26.3,952.0')] ).
cnf(957,plain,
~ aNaturalNumber0(sz00),
inference(obv,[status(thm),theory(equality)],[955]),
[iquote('1:Obv:955.2')] ).
cnf(958,plain,
$false,
inference(ssi,[status(thm)],[957,1]),
[iquote('1:SSi:957.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM465+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 00:31:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.37/0.55
% 0.37/0.55 SPASS V 3.9
% 0.37/0.55 SPASS beiseite: Proof found.
% 0.37/0.55 % SZS status Theorem
% 0.37/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/0.55 SPASS derived 560 clauses, backtracked 44 clauses, performed 1 splits and kept 322 clauses.
% 0.37/0.55 SPASS allocated 98399 KBytes.
% 0.37/0.55 SPASS spent 0:00:00.19 on the problem.
% 0.37/0.55 0:00:00.04 for the input.
% 0.37/0.55 0:00:00.04 for the FLOTTER CNF translation.
% 0.37/0.55 0:00:00.01 for inferences.
% 0.37/0.55 0:00:00.00 for the backtracking.
% 0.37/0.55 0:00:00.07 for the reduction.
% 0.37/0.55
% 0.37/0.55
% 0.37/0.55 Here is a proof with depth 2, length 38 :
% 0.37/0.55 % SZS output start Refutation
% See solution above
% 0.37/0.55 Formulae used in the proof : mSortsC mSortsC_01 m__987 m__ m__1007 m_AddZero m_MulUnit m_MulZero mLETotal mMonAdd mMonMul
% 0.37/0.55
%------------------------------------------------------------------------------