TSTP Solution File: NUM462+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM462+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 14:26:26 EDT 2022
% Result : Theorem 93.92s 94.16s
% Output : Refutation 93.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of clauses : 62 ( 21 unt; 5 nHn; 62 RR)
% Number of literals : 148 ( 0 equ; 92 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xm),
file('NUM462+2.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xl),
file('NUM462+2.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xn),
file('NUM462+2.p',unknown),
[] ).
cnf(6,axiom,
aNaturalNumber0(skc1),
file('NUM462+2.p',unknown),
[] ).
cnf(10,axiom,
~ equal(xm,sz00),
file('NUM462+2.p',unknown),
[] ).
cnf(11,axiom,
~ equal(xn,xl),
file('NUM462+2.p',unknown),
[] ).
cnf(12,axiom,
equal(sdtpldt0(xl,skc1),xn),
file('NUM462+2.p',unknown),
[] ).
cnf(21,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM462+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM462+2.p',unknown),
[] ).
cnf(25,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM462+2.p',unknown),
[] ).
cnf(27,axiom,
( ~ aNaturalNumber0(u)
| ~ equal(sdtpldt0(sdtasdt0(xm,xl),u),sdtasdt0(xm,xn))
| skC0 ),
file('NUM462+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM462+2.p',unknown),
[] ).
cnf(41,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtasdt0(sdtpldt0(v,u),w),sdtpldt0(sdtasdt0(v,w),sdtasdt0(u,w))) ),
file('NUM462+2.p',unknown),
[] ).
cnf(42,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtasdt0(w,sdtpldt0(v,u)),sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u))) ),
file('NUM462+2.p',unknown),
[] ).
cnf(45,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtasdt0(v,w),sdtasdt0(u,w))
| equal(v,u)
| equal(w,sz00) ),
file('NUM462+2.p',unknown),
[] ).
cnf(50,axiom,
( ~ skC0
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| equal(sdtasdt0(xn,xm),sdtasdt0(xl,xm))
| equal(sdtasdt0(xm,xn),sdtasdt0(xm,xl)) ),
file('NUM462+2.p',unknown),
[] ).
cnf(67,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtpldt0(sdtasdt0(xm,xl),u),sdtasdt0(xm,xn)) ),
inference(spt,[spt(split,[position(s1)])],[27]),
[iquote('1:Spt:27.0,27.1')] ).
cnf(404,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[33]),
[iquote('0:EqR:33.3')] ).
cnf(411,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(ssi,[status(thm)],[404,21]),
[iquote('0:SSi:404.0,21.2')] ).
cnf(1260,plain,
( ~ aNaturalNumber0(skc1)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(u)
| equal(sdtpldt0(sdtasdt0(xl,u),sdtasdt0(skc1,u)),sdtasdt0(xn,u)) ),
inference(spr,[status(thm),theory(equality)],[12,41]),
[iquote('0:SpR:12.0,41.3')] ).
cnf(1262,plain,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(sdtasdt0(xl,u),sdtasdt0(skc1,u)),sdtasdt0(xn,u)) ),
inference(ssi,[status(thm)],[1260,4,6]),
[iquote('0:SSi:1260.1,1260.0,4.0,6.0')] ).
cnf(1349,plain,
( ~ aNaturalNumber0(skc1)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(u)
| equal(sdtpldt0(sdtasdt0(u,xl),sdtasdt0(u,skc1)),sdtasdt0(u,xn)) ),
inference(spr,[status(thm),theory(equality)],[12,42]),
[iquote('0:SpR:12.0,42.3')] ).
cnf(1351,plain,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(sdtasdt0(u,xl),sdtasdt0(u,skc1)),sdtasdt0(u,xn)) ),
inference(ssi,[status(thm)],[1349,4,6]),
[iquote('0:SSi:1349.1,1349.0,4.0,6.0')] ).
cnf(2642,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(skc1)
| ~ aNaturalNumber0(u)
| equal(sdtpldt0(sdtasdt0(u,xl),sdtasdt0(skc1,u)),sdtasdt0(u,xn)) ),
inference(spr,[status(thm),theory(equality)],[25,1351]),
[iquote('0:SpR:25.2,1351.1')] ).
cnf(2652,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xm,skc1))
| ~ equal(sdtasdt0(xm,xn),sdtasdt0(xm,xn)) ),
inference(spl,[status(thm),theory(equality)],[1351,67]),
[iquote('1:SpL:1351.1,67.1')] ).
cnf(2667,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xm,skc1)) ),
inference(obv,[status(thm),theory(equality)],[2652]),
[iquote('1:Obv:2652.2')] ).
cnf(2668,plain,
$false,
inference(ssi,[status(thm)],[2667,22,3,6]),
[iquote('1:SSi:2667.1,2667.0,22.0,3.0,6.0,3.2')] ).
cnf(2673,plain,
( ~ aNaturalNumber0(skc1)
| ~ aNaturalNumber0(u)
| equal(sdtpldt0(sdtasdt0(u,xl),sdtasdt0(skc1,u)),sdtasdt0(u,xn)) ),
inference(obv,[status(thm),theory(equality)],[2642]),
[iquote('0:Obv:2642.0')] ).
cnf(2674,plain,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(sdtasdt0(u,xl),sdtasdt0(skc1,u)),sdtasdt0(u,xn)) ),
inference(ssi,[status(thm)],[2673,6]),
[iquote('0:SSi:2673.0,6.0')] ).
cnf(2704,plain,
skC0,
inference(spt,[spt(split,[position(s2)])],[27]),
[iquote('1:Spt:2668.0,27.2')] ).
cnf(2709,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| equal(sdtasdt0(xn,xm),sdtasdt0(xl,xm))
| equal(sdtasdt0(xm,xn),sdtasdt0(xm,xl)) ),
inference(mrr,[status(thm)],[50,2704]),
[iquote('1:MRR:50.0,2704.0')] ).
cnf(2817,plain,
equal(sdtasdt0(xn,xm),sdtasdt0(xl,xm)),
inference(spt,[spt(split,[position(s2s1)])],[2709]),
[iquote('2:Spt:2709.1')] ).
cnf(2819,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| equal(sdtasdt0(xl,xm),sdtasdt0(xm,xn)) ),
inference(spr,[status(thm),theory(equality)],[2817,25]),
[iquote('2:SpR:2817.0,25.2')] ).
cnf(2832,plain,
equal(sdtasdt0(xl,xm),sdtasdt0(xm,xn)),
inference(ssi,[status(thm)],[2819,5,3]),
[iquote('2:SSi:2819.1,2819.0,5.0,3.0')] ).
cnf(2833,plain,
equal(sdtasdt0(xn,xm),sdtasdt0(xm,xn)),
inference(rew,[status(thm),theory(equality)],[2832,2817]),
[iquote('2:Rew:2832.0,2817.0')] ).
cnf(2918,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| equal(sdtasdt0(xm,xn),sdtasdt0(xm,xl)) ),
inference(spr,[status(thm),theory(equality)],[2832,25]),
[iquote('2:SpR:2832.0,25.2')] ).
cnf(2928,plain,
equal(sdtasdt0(xm,xn),sdtasdt0(xm,xl)),
inference(ssi,[status(thm)],[2918,4,3]),
[iquote('2:SSi:2918.1,2918.0,4.0,3.0')] ).
cnf(2930,plain,
equal(sdtasdt0(xn,xm),sdtasdt0(xm,xl)),
inference(rew,[status(thm),theory(equality)],[2928,2833]),
[iquote('2:Rew:2928.0,2833.0')] ).
cnf(2931,plain,
equal(sdtasdt0(xl,xm),sdtasdt0(xm,xl)),
inference(rew,[status(thm),theory(equality)],[2928,2832]),
[iquote('2:Rew:2928.0,2832.0')] ).
cnf(2977,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ equal(sdtasdt0(xm,xl),sdtasdt0(u,xm))
| equal(xn,u)
| equal(xm,sz00) ),
inference(spl,[status(thm),theory(equality)],[2930,45]),
[iquote('2:SpL:2930.0,45.3')] ).
cnf(2979,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(xm,xl),sdtasdt0(u,xm))
| equal(xn,u)
| equal(xm,sz00) ),
inference(ssi,[status(thm)],[2977,3,5]),
[iquote('2:SSi:2977.2,2977.1,3.0,5.0')] ).
cnf(2980,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(xm,xl),sdtasdt0(u,xm))
| equal(xn,u) ),
inference(mrr,[status(thm)],[2979,10]),
[iquote('2:MRR:2979.3,10.0')] ).
cnf(3015,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtasdt0(xl,u))
| ~ aNaturalNumber0(sdtasdt0(skc1,u))
| sdtlseqdt0(sdtasdt0(xl,u),sdtasdt0(xn,u)) ),
inference(spr,[status(thm),theory(equality)],[1262,411]),
[iquote('0:SpR:1262.1,411.2')] ).
cnf(3030,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| equal(sdtpldt0(sdtasdt0(u,xl),sdtasdt0(skc1,u)),sdtasdt0(xn,u)) ),
inference(spr,[status(thm),theory(equality)],[25,1262]),
[iquote('0:SpR:25.2,1262.1')] ).
cnf(3052,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(u)
| equal(sdtpldt0(sdtasdt0(u,xl),sdtasdt0(skc1,u)),sdtasdt0(xn,u)) ),
inference(obv,[status(thm),theory(equality)],[3030]),
[iquote('0:Obv:3030.1')] ).
cnf(3053,plain,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(sdtasdt0(u,xl),sdtasdt0(skc1,u)),sdtasdt0(xn,u)) ),
inference(ssi,[status(thm)],[3052,4]),
[iquote('0:SSi:3052.0,4.0')] ).
cnf(3054,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(xn,u),sdtasdt0(u,xn)) ),
inference(rew,[status(thm),theory(equality)],[3053,2674]),
[iquote('0:Rew:3053.1,2674.1')] ).
cnf(3060,plain,
( ~ aNaturalNumber0(u)
| sdtlseqdt0(sdtasdt0(xl,u),sdtasdt0(xn,u)) ),
inference(ssi,[status(thm)],[3015,22,6,4]),
[iquote('0:SSi:3015.2,3015.1,22.0,6.2,22.0,4.2')] ).
cnf(39167,plain,
( ~ aNaturalNumber0(xl)
| ~ equal(sdtasdt0(xm,xl),sdtasdt0(xm,xl))
| equal(xn,xl) ),
inference(spl,[status(thm),theory(equality)],[2931,2980]),
[iquote('2:SpL:2931.0,2980.1')] ).
cnf(39169,plain,
( ~ aNaturalNumber0(xl)
| equal(xn,xl) ),
inference(obv,[status(thm),theory(equality)],[39167]),
[iquote('2:Obv:39167.1')] ).
cnf(39170,plain,
equal(xn,xl),
inference(ssi,[status(thm)],[39169,4]),
[iquote('2:SSi:39169.0,4.0')] ).
cnf(39171,plain,
$false,
inference(mrr,[status(thm)],[39170,11]),
[iquote('2:MRR:39170.0,11.0')] ).
cnf(39178,plain,
~ equal(sdtasdt0(xn,xm),sdtasdt0(xl,xm)),
inference(spt,[spt(split,[position(s2sa)])],[39171,2817]),
[iquote('2:Spt:39171.0,2709.1,2817.0')] ).
cnf(39179,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| equal(sdtasdt0(xm,xn),sdtasdt0(xm,xl)) ),
inference(spt,[spt(split,[position(s2s2)])],[2709]),
[iquote('2:Spt:39171.0,2709.0,2709.2')] ).
cnf(39505,plain,
( ~ aNaturalNumber0(xm)
| equal(sdtasdt0(xm,xn),sdtasdt0(xm,xl)) ),
inference(res,[status(thm),theory(equality)],[3060,39179]),
[iquote('2:Res:3060.1,39179.0')] ).
cnf(39506,plain,
equal(sdtasdt0(xm,xn),sdtasdt0(xm,xl)),
inference(ssi,[status(thm)],[39505,3]),
[iquote('2:SSi:39505.0,3.0')] ).
cnf(39557,plain,
( ~ aNaturalNumber0(xm)
| ~ equal(sdtasdt0(xl,xm),sdtasdt0(xm,xn)) ),
inference(spl,[status(thm),theory(equality)],[3054,39178]),
[iquote('2:SpL:3054.1,39178.0')] ).
cnf(39559,plain,
( ~ aNaturalNumber0(xm)
| ~ equal(sdtasdt0(xl,xm),sdtasdt0(xm,xl)) ),
inference(rew,[status(thm),theory(equality)],[39506,39557]),
[iquote('2:Rew:39506.0,39557.1')] ).
cnf(39560,plain,
~ equal(sdtasdt0(xl,xm),sdtasdt0(xm,xl)),
inference(ssi,[status(thm)],[39559,3]),
[iquote('2:SSi:39559.0,3.0')] ).
cnf(40429,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ equal(sdtasdt0(xm,xl),sdtasdt0(xm,xl)) ),
inference(spl,[status(thm),theory(equality)],[25,39560]),
[iquote('2:SpL:25.2,39560.0')] ).
cnf(40432,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(obv,[status(thm),theory(equality)],[40429]),
[iquote('2:Obv:40429.2')] ).
cnf(40433,plain,
$false,
inference(ssi,[status(thm)],[40432,3,4]),
[iquote('2:SSi:40432.1,40432.0,3.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM462+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n011.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 : Thu Jul 7 17:55:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 93.92/94.16
% 93.92/94.16 SPASS V 3.9
% 93.92/94.16 SPASS beiseite: Proof found.
% 93.92/94.16 % SZS status Theorem
% 93.92/94.16 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 93.92/94.16 SPASS derived 22544 clauses, backtracked 1535 clauses, performed 12 splits and kept 7396 clauses.
% 93.92/94.16 SPASS allocated 141011 KBytes.
% 93.92/94.16 SPASS spent 0:1:19.49 on the problem.
% 93.92/94.16 0:00:00.04 for the input.
% 93.92/94.16 0:00:00.03 for the FLOTTER CNF translation.
% 93.92/94.16 0:00:00.28 for inferences.
% 93.92/94.16 0:00:00.22 for the backtracking.
% 93.92/94.16 0:1:18.78 for the reduction.
% 93.92/94.16
% 93.92/94.16
% 93.92/94.16 Here is a proof with depth 4, length 62 :
% 93.92/94.16 % SZS output start Refutation
% See solution above
% 93.92/94.16 Formulae used in the proof : m__897 m__897_03 mSortsB mSortsB_02 mMulComm m__ mDefLE mAMDistr mMulCanc
% 93.92/94.16
%------------------------------------------------------------------------------