TSTP Solution File: NUM459+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM459+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 14:26:24 EDT 2022
% Result : Theorem 0.71s 0.90s
% Output : Refutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of clauses : 59 ( 19 unt; 0 nHn; 59 RR)
% Number of literals : 149 ( 0 equ; 92 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aNaturalNumber0(skc3),
file('NUM459+2.p',unknown),
[] ).
cnf(2,axiom,
aNaturalNumber0(skc2),
file('NUM459+2.p',unknown),
[] ).
cnf(3,axiom,
aNaturalNumber0(sz00),
file('NUM459+2.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xm),
file('NUM459+2.p',unknown),
[] ).
cnf(6,axiom,
aNaturalNumber0(xn),
file('NUM459+2.p',unknown),
[] ).
cnf(8,axiom,
sdtlseqdt0(xn,xm),
file('NUM459+2.p',unknown),
[] ).
cnf(9,axiom,
~ equal(xn,xm),
file('NUM459+2.p',unknown),
[] ).
cnf(12,axiom,
equal(sdtpldt0(xm,skc2),xn),
file('NUM459+2.p',unknown),
[] ).
cnf(13,axiom,
equal(sdtpldt0(xn,skc3),xm),
file('NUM459+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('NUM459+2.p',unknown),
[] ).
cnf(21,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM459+2.p',unknown),
[] ).
cnf(23,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('NUM459+2.p',unknown),
[] ).
cnf(26,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(sdtpldt0(v,u),sz00)
| equal(u,sz00) ),
file('NUM459+2.p',unknown),
[] ).
cnf(29,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM459+2.p',unknown),
[] ).
cnf(34,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('NUM459+2.p',unknown),
[] ).
cnf(35,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| equal(sdtpldt0(v,w),u) ),
file('NUM459+2.p',unknown),
[] ).
cnf(40,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,w)
| ~ equal(sdtpldt0(v,u),w)
| equal(u,sdtmndt0(w,v)) ),
file('NUM459+2.p',unknown),
[] ).
cnf(41,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| equal(w,sdtmndt0(u,v)) ),
inference(mrr,[status(thm)],[40,29]),
[iquote('0:MRR:40.3,29.4')] ).
cnf(58,plain,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(skc2,u),sdtpldt0(u,skc2)) ),
inference(res,[status(thm),theory(equality)],[2,23]),
[iquote('0:Res:2.0,23.0')] ).
cnf(62,plain,
equal(sdtpldt0(skc2,sz00),skc2),
inference(res,[status(thm),theory(equality)],[2,15]),
[iquote('0:Res:2.0,15.0')] ).
cnf(589,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[29]),
[iquote('0:EqR:29.3')] ).
cnf(603,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(ssi,[status(thm)],[589,21]),
[iquote('0:SSi:589.0,21.2')] ).
cnf(678,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(skc3)
| ~ aNaturalNumber0(xn)
| equal(sdtpldt0(xn,sdtpldt0(skc3,u)),sdtpldt0(xm,u)) ),
inference(spr,[status(thm),theory(equality)],[13,34]),
[iquote('0:SpR:13.0,34.3')] ).
cnf(684,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(skc2)
| ~ aNaturalNumber0(xm)
| equal(sdtpldt0(xm,sdtpldt0(skc2,u)),sdtpldt0(xn,u)) ),
inference(spr,[status(thm),theory(equality)],[12,34]),
[iquote('0:SpR:12.0,34.3')] ).
cnf(697,plain,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(xn,sdtpldt0(skc3,u)),sdtpldt0(xm,u)) ),
inference(ssi,[status(thm)],[678,6,1]),
[iquote('0:SSi:678.2,678.1,6.0,1.0')] ).
cnf(699,plain,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(xm,sdtpldt0(skc2,u)),sdtpldt0(xn,u)) ),
inference(ssi,[status(thm)],[684,5,2]),
[iquote('0:SSi:684.2,684.1,5.0,2.0')] ).
cnf(906,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(eqr,[status(thm),theory(equality)],[41]),
[iquote('0:EqR:41.3')] ).
cnf(921,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(ssi,[status(thm)],[906,21]),
[iquote('0:SSi:906.0,21.2')] ).
cnf(974,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(skc3,u))
| sdtlseqdt0(xn,sdtpldt0(xm,u)) ),
inference(spr,[status(thm),theory(equality)],[697,603]),
[iquote('0:SpR:697.1,603.2')] ).
cnf(978,plain,
( ~ aNaturalNumber0(skc3)
| ~ aNaturalNumber0(skc2)
| equal(sdtpldt0(xn,sdtpldt0(skc2,skc3)),sdtpldt0(xm,skc2)) ),
inference(spr,[status(thm),theory(equality)],[58,697]),
[iquote('0:SpR:58.1,697.1')] ).
cnf(990,plain,
( ~ aNaturalNumber0(skc3)
| ~ aNaturalNumber0(skc2)
| equal(sdtpldt0(xn,sdtpldt0(skc2,skc3)),xn) ),
inference(rew,[status(thm),theory(equality)],[12,978]),
[iquote('0:Rew:12.0,978.2')] ).
cnf(991,plain,
equal(sdtpldt0(xn,sdtpldt0(skc2,skc3)),xn),
inference(ssi,[status(thm)],[990,2,1]),
[iquote('0:SSi:990.1,990.0,2.0,1.0')] ).
cnf(992,plain,
( ~ aNaturalNumber0(u)
| sdtlseqdt0(xn,sdtpldt0(xm,u)) ),
inference(ssi,[status(thm)],[974,21,1,6]),
[iquote('0:SSi:974.2,974.1,21.0,1.0,6.2')] ).
cnf(1192,plain,
( ~ aNaturalNumber0(skc2)
| sdtlseqdt0(xn,xn) ),
inference(spr,[status(thm),theory(equality)],[12,992]),
[iquote('0:SpR:12.0,992.1')] ).
cnf(1196,plain,
sdtlseqdt0(xn,xn),
inference(ssi,[status(thm)],[1192,2]),
[iquote('0:SSi:1192.0,2.0')] ).
cnf(1682,plain,
( ~ aNaturalNumber0(sz00)
| equal(sdtpldt0(xn,sz00),sdtpldt0(xm,skc2)) ),
inference(spr,[status(thm),theory(equality)],[62,699]),
[iquote('0:SpR:62.0,699.1')] ).
cnf(1700,plain,
( ~ aNaturalNumber0(sz00)
| equal(sdtpldt0(xn,sz00),xn) ),
inference(rew,[status(thm),theory(equality)],[12,1682]),
[iquote('0:Rew:12.0,1682.1')] ).
cnf(1701,plain,
equal(sdtpldt0(xn,sz00),xn),
inference(ssi,[status(thm)],[1700,3]),
[iquote('0:SSi:1700.0,3.0')] ).
cnf(2180,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(skc3)
| equal(sdtmndt0(xm,xn),skc3) ),
inference(spr,[status(thm),theory(equality)],[13,921]),
[iquote('0:SpR:13.0,921.2')] ).
cnf(2182,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(skc2,skc3))
| equal(sdtmndt0(xn,xn),sdtpldt0(skc2,skc3)) ),
inference(spr,[status(thm),theory(equality)],[991,921]),
[iquote('0:SpR:991.0,921.2')] ).
cnf(2186,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| equal(sdtmndt0(xn,xn),sz00) ),
inference(spr,[status(thm),theory(equality)],[1701,921]),
[iquote('0:SpR:1701.0,921.2')] ).
cnf(2201,plain,
equal(sdtmndt0(xm,xn),skc3),
inference(ssi,[status(thm)],[2180,1,6]),
[iquote('0:SSi:2180.1,2180.0,1.0,6.0')] ).
cnf(2204,plain,
equal(sdtmndt0(xn,xn),sz00),
inference(ssi,[status(thm)],[2186,3,6]),
[iquote('0:SSi:2186.1,2186.0,3.0,6.0')] ).
cnf(2213,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(skc2,skc3))
| equal(sdtpldt0(skc2,skc3),sz00) ),
inference(rew,[status(thm),theory(equality)],[2204,2182]),
[iquote('0:Rew:2204.0,2182.2')] ).
cnf(2214,plain,
equal(sdtpldt0(skc2,skc3),sz00),
inference(ssi,[status(thm)],[2213,21,2,1,6]),
[iquote('0:SSi:2213.1,2213.0,21.0,2.0,1.0,6.2')] ).
cnf(2282,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xm)
| ~ equal(u,skc3)
| equal(sdtpldt0(xn,u),xm) ),
inference(spl,[status(thm),theory(equality)],[2201,35]),
[iquote('0:SpL:2201.0,35.3')] ).
cnf(2286,plain,
( ~ sdtlseqdt0(xn,xm)
| ~ equal(u,skc3)
| equal(sdtpldt0(xn,u),xm) ),
inference(ssi,[status(thm)],[2282,6,5]),
[iquote('0:SSi:2282.1,2282.0,6.0,5.0')] ).
cnf(2287,plain,
( ~ equal(u,skc3)
| equal(sdtpldt0(xn,u),xm) ),
inference(mrr,[status(thm)],[2286,8]),
[iquote('0:MRR:2286.0,8.0')] ).
cnf(2381,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xn)
| ~ equal(u,sz00)
| equal(sdtpldt0(xn,u),xn) ),
inference(spl,[status(thm),theory(equality)],[2204,35]),
[iquote('0:SpL:2204.0,35.3')] ).
cnf(2384,plain,
( ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xn)
| ~ equal(u,sz00)
| equal(sdtpldt0(xn,u),xn) ),
inference(obv,[status(thm),theory(equality)],[2381]),
[iquote('0:Obv:2381.0')] ).
cnf(2385,plain,
( ~ sdtlseqdt0(xn,xn)
| ~ equal(u,sz00)
| equal(sdtpldt0(xn,u),xn) ),
inference(ssi,[status(thm)],[2384,6]),
[iquote('0:SSi:2384.0,6.0')] ).
cnf(2386,plain,
( ~ equal(u,sz00)
| equal(sdtpldt0(xn,u),xn) ),
inference(mrr,[status(thm)],[2385,1196]),
[iquote('0:MRR:2385.0,1196.0')] ).
cnf(2480,plain,
( ~ aNaturalNumber0(skc3)
| ~ aNaturalNumber0(skc2)
| ~ equal(sz00,sz00)
| equal(skc3,sz00) ),
inference(spl,[status(thm),theory(equality)],[2214,26]),
[iquote('0:SpL:2214.0,26.2')] ).
cnf(2503,plain,
( ~ aNaturalNumber0(skc3)
| ~ aNaturalNumber0(skc2)
| equal(skc3,sz00) ),
inference(obv,[status(thm),theory(equality)],[2480]),
[iquote('0:Obv:2480.2')] ).
cnf(2504,plain,
equal(skc3,sz00),
inference(ssi,[status(thm)],[2503,2,1]),
[iquote('0:SSi:2503.1,2503.0,2.0,1.0')] ).
cnf(2558,plain,
( ~ equal(u,sz00)
| equal(sdtpldt0(xn,u),xm) ),
inference(rew,[status(thm),theory(equality)],[2504,2287]),
[iquote('0:Rew:2504.0,2287.0')] ).
cnf(2585,plain,
( ~ equal(u,sz00)
| equal(xn,xm) ),
inference(rew,[status(thm),theory(equality)],[2386,2558]),
[iquote('0:Rew:2386.1,2558.1')] ).
cnf(2586,plain,
~ equal(u,sz00),
inference(mrr,[status(thm)],[2585,9]),
[iquote('0:MRR:2585.1,9.0')] ).
cnf(2587,plain,
$false,
inference(unc,[status(thm)],[2586,2204]),
[iquote('0:UnC:2586.0,2204.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM459+2 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n011.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 17:04:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.71/0.90
% 0.71/0.90 SPASS V 3.9
% 0.71/0.90 SPASS beiseite: Proof found.
% 0.71/0.90 % SZS status Theorem
% 0.71/0.90 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.71/0.90 SPASS derived 1734 clauses, backtracked 58 clauses, performed 3 splits and kept 751 clauses.
% 0.71/0.90 SPASS allocated 100293 KBytes.
% 0.71/0.90 SPASS spent 0:00:00.50 on the problem.
% 0.71/0.90 0:00:00.04 for the input.
% 0.71/0.90 0:00:00.03 for the FLOTTER CNF translation.
% 0.71/0.90 0:00:00.02 for inferences.
% 0.71/0.90 0:00:00.00 for the backtracking.
% 0.71/0.90 0:00:00.37 for the reduction.
% 0.71/0.90
% 0.71/0.90
% 0.71/0.90 Here is a proof with depth 4, length 59 :
% 0.71/0.90 % SZS output start Refutation
% See solution above
% 0.75/0.90 Formulae used in the proof : m__ mSortsC m__745 m_AddZero mSortsB mAddComm mZeroAdd mDefLE mAddAsso mDefDiff
% 0.75/0.90
%------------------------------------------------------------------------------