TSTP Solution File: NUM463+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM463+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 14:26:27 EDT 2022
% Result : Theorem 2.73s 2.92s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of clauses : 58 ( 15 unt; 9 nHn; 58 RR)
% Number of literals : 180 ( 0 equ; 119 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aNaturalNumber0(sz00),
file('NUM463+2.p',unknown),
[] ).
cnf(2,axiom,
aNaturalNumber0(sz10),
file('NUM463+2.p',unknown),
[] ).
cnf(3,axiom,
aNaturalNumber0(xm),
file('NUM463+2.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xn),
file('NUM463+2.p',unknown),
[] ).
cnf(5,axiom,
~ equal(xm,sz00),
file('NUM463+2.p',unknown),
[] ).
cnf(8,axiom,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
file('NUM463+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ aNaturalNumber0(u)
| sdtlseqdt0(u,u) ),
file('NUM463+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('NUM463+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,sz10),u) ),
file('NUM463+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM463+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM463+2.p',unknown),
[] ).
cnf(18,axiom,
( ~ aNaturalNumber0(u)
| ~ equal(sdtpldt0(xn,u),sdtasdt0(xn,xm)) ),
file('NUM463+2.p',unknown),
[] ).
cnf(20,axiom,
( ~ aNaturalNumber0(u)
| equal(u,sz10)
| equal(u,sz00)
| sdtlseqdt0(sz10,u) ),
file('NUM463+2.p',unknown),
[] ).
cnf(21,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('NUM463+2.p',unknown),
[] ).
cnf(30,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM463+2.p',unknown),
[] ).
cnf(31,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| aNaturalNumber0(w) ),
file('NUM463+2.p',unknown),
[] ).
cnf(37,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| equal(sdtpldt0(v,w),u) ),
file('NUM463+2.p',unknown),
[] ).
cnf(46,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,w)
| ~ equal(sdtpldt0(v,u),w)
| equal(u,sdtmndt0(w,v)) ),
file('NUM463+2.p',unknown),
[] ).
cnf(48,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,u)
| equal(v,u)
| equal(w,sz00)
| sdtlseqdt0(sdtasdt0(w,v),sdtasdt0(w,u)) ),
file('NUM463+2.p',unknown),
[] ).
cnf(51,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| equal(w,sdtmndt0(u,v)) ),
inference(mrr,[status(thm)],[46,30]),
[iquote('0:MRR:46.3,30.4')] ).
cnf(59,plain,
( ~ aNaturalNumber0(xm)
| sdtlseqdt0(sz10,xm)
| equal(xm,sz10) ),
inference(res,[status(thm),theory(equality)],[20,5]),
[iquote('0:Res:20.2,5.0')] ).
cnf(88,plain,
~ equal(sdtasdt0(xn,xm),sdtpldt0(xn,sz00)),
inference(res,[status(thm),theory(equality)],[1,18]),
[iquote('0:Res:1.0,18.0')] ).
cnf(90,plain,
( equal(xm,sz10)
| sdtlseqdt0(sz10,xm) ),
inference(mrr,[status(thm)],[59,3]),
[iquote('0:MRR:59.0,3.0')] ).
cnf(154,plain,
equal(xm,sz10),
inference(spt,[spt(split,[position(s1)])],[90]),
[iquote('1:Spt:90.0')] ).
cnf(156,plain,
~ equal(sdtasdt0(xn,sz10),sdtpldt0(xn,sz00)),
inference(rew,[status(thm),theory(equality)],[154,88]),
[iquote('1:Rew:154.0,88.0')] ).
cnf(217,plain,
( ~ aNaturalNumber0(xn)
| ~ equal(sdtpldt0(xn,sz00),xn) ),
inference(spl,[status(thm),theory(equality)],[12,156]),
[iquote('1:SpL:12.1,156.0')] ).
cnf(222,plain,
( ~ aNaturalNumber0(xn)
| ~ equal(xn,xn) ),
inference(rew,[status(thm),theory(equality)],[10,217]),
[iquote('1:Rew:10.1,217.1')] ).
cnf(223,plain,
~ aNaturalNumber0(xn),
inference(obv,[status(thm),theory(equality)],[222]),
[iquote('1:Obv:222.1')] ).
cnf(224,plain,
$false,
inference(ssi,[status(thm)],[223,4]),
[iquote('1:SSi:223.0,4.0')] ).
cnf(226,plain,
~ equal(xm,sz10),
inference(spt,[spt(split,[position(sa)])],[224,154]),
[iquote('1:Spt:224.0,90.0,154.0')] ).
cnf(227,plain,
sdtlseqdt0(sz10,xm),
inference(spt,[spt(split,[position(s2)])],[90]),
[iquote('1:Spt:224.0,90.1')] ).
cnf(613,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[30]),
[iquote('0:EqR:30.3')] ).
cnf(619,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(ssi,[status(thm)],[613,16]),
[iquote('0:SSi:613.0,16.2')] ).
cnf(628,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(u)
| sdtlseqdt0(v,sdtpldt0(u,v)) ),
inference(spr,[status(thm),theory(equality)],[21,619]),
[iquote('0:SpR:21.2,619.2')] ).
cnf(641,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[628]),
[iquote('0:Obv:628.1')] ).
cnf(884,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(eqr,[status(thm),theory(equality)],[51]),
[iquote('0:EqR:51.3')] ).
cnf(891,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(ssi,[status(thm)],[884,16]),
[iquote('0:SSi:884.0,16.2')] ).
cnf(906,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz00)
| equal(sdtmndt0(u,u),sz00) ),
inference(spr,[status(thm),theory(equality)],[10,891]),
[iquote('0:SpR:10.1,891.2')] ).
cnf(913,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz00)
| equal(sdtmndt0(u,u),sz00) ),
inference(obv,[status(thm),theory(equality)],[906]),
[iquote('0:Obv:906.0')] ).
cnf(914,plain,
( ~ aNaturalNumber0(u)
| equal(sdtmndt0(u,u),sz00) ),
inference(ssi,[status(thm)],[913,1]),
[iquote('0:SSi:913.1,1.0')] ).
cnf(939,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,u)
| ~ equal(v,sz00)
| aNaturalNumber0(v) ),
inference(spl,[status(thm),theory(equality)],[914,31]),
[iquote('0:SpL:914.1,31.3')] ).
cnf(940,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,u)
| ~ equal(v,sz00)
| aNaturalNumber0(v) ),
inference(obv,[status(thm),theory(equality)],[939]),
[iquote('0:Obv:939.1')] ).
cnf(941,plain,
( ~ aNaturalNumber0(u)
| ~ equal(v,sz00)
| aNaturalNumber0(v) ),
inference(mrr,[status(thm)],[940,9]),
[iquote('0:MRR:940.1,9.1')] ).
cnf(947,plain,
( ~ equal(u,sz00)
| aNaturalNumber0(u) ),
inference(ems,[status(thm)],[941,3]),
[iquote('0:EmS:941.0,3.0')] ).
cnf(1219,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,u)
| ~ equal(v,sz00)
| equal(sdtpldt0(u,v),u) ),
inference(spl,[status(thm),theory(equality)],[914,37]),
[iquote('0:SpL:914.1,37.3')] ).
cnf(1221,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,u)
| ~ equal(v,sz00)
| equal(sdtpldt0(u,v),u) ),
inference(obv,[status(thm),theory(equality)],[1219]),
[iquote('0:Obv:1219.1')] ).
cnf(1222,plain,
( ~ aNaturalNumber0(u)
| ~ equal(v,sz00)
| equal(sdtpldt0(u,v),u) ),
inference(mrr,[status(thm)],[1221,9]),
[iquote('0:MRR:1221.1,9.1')] ).
cnf(1409,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(u)
| ~ equal(v,sz00)
| sdtlseqdt0(v,u) ),
inference(spr,[status(thm),theory(equality)],[1222,641]),
[iquote('0:SpR:1222.2,641.2')] ).
cnf(1445,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(u,sz00)
| sdtlseqdt0(u,v) ),
inference(obv,[status(thm),theory(equality)],[1409]),
[iquote('0:Obv:1409.0')] ).
cnf(1446,plain,
( ~ aNaturalNumber0(u)
| ~ equal(v,sz00)
| sdtlseqdt0(v,u) ),
inference(mrr,[status(thm)],[1445,947]),
[iquote('0:MRR:1445.0,947.1')] ).
cnf(1478,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ equal(xn,sz00) ),
inference(res,[status(thm),theory(equality)],[1446,8]),
[iquote('0:Res:1446.2,8.0')] ).
cnf(1490,plain,
~ equal(xn,sz00),
inference(ssi,[status(thm)],[1478,17,4,3]),
[iquote('0:SSi:1478.0,17.0,4.0,3.2')] ).
cnf(2061,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(sz10,v)
| equal(sz10,v)
| equal(u,sz00)
| sdtlseqdt0(u,sdtasdt0(u,v)) ),
inference(spr,[status(thm),theory(equality)],[12,48]),
[iquote('0:SpR:12.1,48.6')] ).
cnf(2079,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(sz10,u)
| equal(sz10,u)
| equal(v,sz00)
| sdtlseqdt0(v,sdtasdt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[2061]),
[iquote('0:Obv:2061.0')] ).
cnf(2080,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(sz10,u)
| equal(sz10,u)
| equal(v,sz00)
| sdtlseqdt0(v,sdtasdt0(v,u)) ),
inference(ssi,[status(thm)],[2079,2]),
[iquote('0:SSi:2079.1,2.0')] ).
cnf(7738,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(sz10,xm)
| equal(xm,sz10)
| equal(xn,sz00) ),
inference(res,[status(thm),theory(equality)],[2080,8]),
[iquote('0:Res:2080.5,8.0')] ).
cnf(7748,plain,
( ~ sdtlseqdt0(sz10,xm)
| equal(xm,sz10)
| equal(xn,sz00) ),
inference(ssi,[status(thm)],[7738,4,3]),
[iquote('0:SSi:7738.1,7738.0,4.0,3.0')] ).
cnf(7749,plain,
$false,
inference(mrr,[status(thm)],[7748,227,226,1490]),
[iquote('1:MRR:7748.0,7748.1,7748.2,227.0,226.0,1490.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM463+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n012.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 : Wed Jul 6 18:51:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.73/2.92
% 2.73/2.92 SPASS V 3.9
% 2.73/2.92 SPASS beiseite: Proof found.
% 2.73/2.92 % SZS status Theorem
% 2.73/2.92 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.73/2.92 SPASS derived 4605 clauses, backtracked 35 clauses, performed 2 splits and kept 1432 clauses.
% 2.73/2.92 SPASS allocated 104647 KBytes.
% 2.73/2.92 SPASS spent 0:00:02.15 on the problem.
% 2.73/2.92 0:00:00.04 for the input.
% 2.73/2.92 0:00:00.03 for the FLOTTER CNF translation.
% 2.73/2.92 0:00:00.06 for inferences.
% 2.73/2.92 0:00:00.02 for the backtracking.
% 2.73/2.92 0:00:01.97 for the reduction.
% 2.73/2.92
% 2.73/2.92
% 2.73/2.92 Here is a proof with depth 5, length 58 :
% 2.73/2.92 % SZS output start Refutation
% See solution above
% 2.73/2.92 Formulae used in the proof : mSortsC mSortsC_01 m__987 m__ mLERefl m_AddZero m_MulUnit mSortsB mSortsB_02 mLENTr mAddComm mDefLE mDefDiff mMonMul
% 2.73/2.92
%------------------------------------------------------------------------------