%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM487+1 : 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 14:26:42 EDT 2022
% Result : Theorem 0.19s 0.56s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of clauses : 62 ( 20 unt; 5 nHn; 62 RR)
% Number of literals : 176 ( 0 equ; 116 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 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('NUM487+1.p',unknown),
[] ).
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM487+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM487+1.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM487+1.p',unknown),
[] ).
cnf(9,axiom,
sdtlseqdt0(xp,xn),
file('NUM487+1.p',unknown),
[] ).
cnf(11,axiom,
aNaturalNumber0(skf4(u,v)),
file('NUM487+1.p',unknown),
[] ).
cnf(14,axiom,
equal(sdtmndt0(xn,xp),xr),
file('NUM487+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ sdtlseqdt0(xr,xn)
| equal(xr,xn) ),
file('NUM487+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('NUM487+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM487+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ aNaturalNumber0(u)
| ~ isPrime0(u)
| ~ equal(u,sz00) ),
file('NUM487+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(v,u)
| sdtlseqdt0(u,v) ),
file('NUM487+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('NUM487+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| equal(sdtpldt0(v,skf4(u,v)),u) ),
file('NUM487+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM487+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| aNaturalNumber0(w) ),
file('NUM487+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,w)
| ~ equal(sdtpldt0(v,u),w)
| equal(u,sdtmndt0(w,v)) ),
file('NUM487+1.p',unknown),
[] ).
cnf(78,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| equal(w,sdtmndt0(u,v)) ),
inference(mrr,[status(thm)],[70,47]),
[iquote('0:MRR:70.3,47.4')] ).
cnf(94,plain,
~ equal(xp,sz00),
inference(ems,[status(thm)],[25,5,6]),
[iquote('0:EmS:25.0,25.1,5.0,6.0')] ).
cnf(104,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| sdtlseqdt0(xn,xr)
| equal(xr,xn) ),
inference(res,[status(thm),theory(equality)],[27,16]),
[iquote('0:Res:27.2,16.0')] ).
cnf(107,plain,
( ~ aNaturalNumber0(xr)
| sdtlseqdt0(xn,xr)
| equal(xr,xn) ),
inference(ssi,[status(thm)],[104,3]),
[iquote('0:SSi:104.0,3.0')] ).
cnf(364,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[47]),
[iquote('0:EqR:47.3')] ).
cnf(370,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(ssi,[status(thm)],[364,23]),
[iquote('0:SSi:364.0,23.2')] ).
cnf(379,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(u)
| sdtlseqdt0(v,sdtpldt0(u,v)) ),
inference(spr,[status(thm),theory(equality)],[30,370]),
[iquote('0:SpR:30.2,370.2')] ).
cnf(389,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[379]),
[iquote('0:Obv:379.1')] ).
cnf(492,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ~ equal(u,xr)
| aNaturalNumber0(u) ),
inference(spl,[status(thm),theory(equality)],[14,48]),
[iquote('0:SpL:14.0,48.3')] ).
cnf(493,plain,
( ~ sdtlseqdt0(xp,xn)
| ~ equal(u,xr)
| aNaturalNumber0(u) ),
inference(ssi,[status(thm)],[492,6,5,3]),
[iquote('0:SSi:492.1,492.0,6.0,5.0,3.0')] ).
cnf(494,plain,
( ~ equal(u,xr)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[493,9]),
[iquote('0:MRR:493.0,9.0')] ).
cnf(510,plain,
( ~ equal(xr,xr)
| sdtlseqdt0(xn,xr)
| equal(xr,xn) ),
inference(sor,[status(thm)],[107,494]),
[iquote('0:SoR:107.0,494.1')] ).
cnf(511,plain,
( sdtlseqdt0(xn,xr)
| equal(xr,xn) ),
inference(obv,[status(thm),theory(equality)],[510]),
[iquote('0:Obv:510.0')] ).
cnf(512,plain,
equal(xr,xn),
inference(spt,[spt(split,[position(s1)])],[511]),
[iquote('1:Spt:511.1')] ).
cnf(513,plain,
equal(sdtmndt0(xn,xp),xn),
inference(rew,[status(thm),theory(equality)],[512,14]),
[iquote('1:Rew:512.0,14.0')] ).
cnf(514,plain,
( ~ equal(u,xn)
| aNaturalNumber0(u) ),
inference(rew,[status(thm),theory(equality)],[512,494]),
[iquote('1:Rew:512.0,494.0')] ).
cnf(735,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(eqr,[status(thm),theory(equality)],[78]),
[iquote('0:EqR:78.3')] ).
cnf(739,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz00)
| ~ equal(u,v)
| equal(sdtmndt0(v,u),sz00) ),
inference(spl,[status(thm),theory(equality)],[17,78]),
[iquote('0:SpL:17.1,78.3')] ).
cnf(742,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(ssi,[status(thm)],[735,23]),
[iquote('0:SSi:735.0,23.2')] ).
cnf(743,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(sz00)
| ~ equal(v,u)
| equal(sdtmndt0(u,v),sz00) ),
inference(obv,[status(thm),theory(equality)],[739]),
[iquote('0:Obv:739.0')] ).
cnf(744,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(v,u)
| equal(sdtmndt0(u,v),sz00) ),
inference(ssi,[status(thm)],[743,1]),
[iquote('0:SSi:743.2,1.0')] ).
cnf(759,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(skf4(u,v))
| ~ sdtlseqdt0(v,u)
| equal(skf4(u,v),sdtmndt0(u,v)) ),
inference(spr,[status(thm),theory(equality)],[43,742]),
[iquote('0:SpR:43.3,742.2')] ).
cnf(768,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(skf4(u,v))
| ~ sdtlseqdt0(v,u)
| equal(skf4(u,v),sdtmndt0(u,v)) ),
inference(obv,[status(thm),theory(equality)],[759]),
[iquote('0:Obv:759.1')] ).
cnf(769,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| equal(skf4(u,v),sdtmndt0(u,v)) ),
inference(ssi,[status(thm)],[768,11]),
[iquote('0:SSi:768.2,11.0')] ).
cnf(770,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| equal(sdtpldt0(v,sdtmndt0(u,v)),u) ),
inference(rew,[status(thm),theory(equality)],[769,43]),
[iquote('0:Rew:769.3,43.3')] ).
cnf(848,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| equal(sdtpldt0(xp,xn),xn) ),
inference(spr,[status(thm),theory(equality)],[513,770]),
[iquote('1:SpR:513.0,770.3')] ).
cnf(854,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| equal(sdtpldt0(xn,xp),xn) ),
inference(rew,[status(thm),theory(equality)],[30,848]),
[iquote('1:Rew:30.2,848.3')] ).
cnf(855,plain,
( ~ sdtlseqdt0(xp,xn)
| equal(sdtpldt0(xn,xp),xn) ),
inference(ssi,[status(thm)],[854,6,5,3]),
[iquote('1:SSi:854.1,854.0,6.0,5.0,3.0')] ).
cnf(856,plain,
equal(sdtpldt0(xn,xp),xn),
inference(mrr,[status(thm)],[855,9]),
[iquote('1:MRR:855.0,9.0')] ).
cnf(874,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ equal(xn,u)
| equal(sdtmndt0(u,xn),xp) ),
inference(spl,[status(thm),theory(equality)],[856,78]),
[iquote('1:SpL:856.0,78.3')] ).
cnf(880,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ equal(xn,u)
| equal(xp,sz00) ),
inference(rew,[status(thm),theory(equality)],[744,874]),
[iquote('1:Rew:744.3,874.4')] ).
cnf(881,plain,
( ~ aNaturalNumber0(u)
| ~ equal(xn,u)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[880,6,5,3]),
[iquote('1:SSi:880.2,880.1,6.0,5.0,3.0')] ).
cnf(882,plain,
~ equal(xn,u),
inference(mrr,[status(thm)],[881,514,94]),
[iquote('1:MRR:881.0,881.2,514.1,94.0')] ).
cnf(883,plain,
$false,
inference(unc,[status(thm)],[882,856]),
[iquote('1:UnC:882.0,856.0')] ).
cnf(884,plain,
~ equal(xr,xn),
inference(spt,[spt(split,[position(sa)])],[883,512]),
[iquote('1:Spt:883.0,511.1,512.0')] ).
cnf(885,plain,
sdtlseqdt0(xn,xr),
inference(spt,[spt(split,[position(s2)])],[511]),
[iquote('1:Spt:883.0,511.0')] ).
cnf(886,plain,
~ sdtlseqdt0(xr,xn),
inference(mrr,[status(thm)],[16,884]),
[iquote('1:MRR:16.1,884.0')] ).
cnf(891,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| equal(sdtpldt0(xp,xr),xn) ),
inference(spr,[status(thm),theory(equality)],[14,770]),
[iquote('0:SpR:14.0,770.3')] ).
cnf(894,plain,
( ~ sdtlseqdt0(xp,xn)
| equal(sdtpldt0(xp,xr),xn) ),
inference(ssi,[status(thm)],[891,6,5,3]),
[iquote('0:SSi:891.1,891.0,6.0,5.0,3.0')] ).
cnf(895,plain,
equal(sdtpldt0(xp,xr),xn),
inference(mrr,[status(thm)],[894,9]),
[iquote('0:MRR:894.0,9.0')] ).
cnf(928,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(xr,xn) ),
inference(spr,[status(thm),theory(equality)],[895,389]),
[iquote('0:SpR:895.0,389.2')] ).
cnf(939,plain,
( ~ aNaturalNumber0(xr)
| sdtlseqdt0(xr,xn) ),
inference(ssi,[status(thm)],[928,6,5]),
[iquote('0:SSi:928.1,6.0,5.0')] ).
cnf(940,plain,
~ aNaturalNumber0(xr),
inference(mrr,[status(thm)],[939,886]),
[iquote('1:MRR:939.1,886.0')] ).
cnf(950,plain,
~ equal(xr,xr),
inference(sor,[status(thm)],[940,494]),
[iquote('1:SoR:940.0,494.1')] ).
cnf(951,plain,
$false,
inference(obv,[status(thm),theory(equality)],[950]),
[iquote('1:Obv:950.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM487+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.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 13:31:21 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.56
% 0.19/0.56 SPASS V 3.9
% 0.19/0.56 SPASS beiseite: Proof found.
% 0.19/0.56 % SZS status Theorem
% 0.19/0.56 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.56 SPASS derived 547 clauses, backtracked 13 clauses, performed 1 splits and kept 261 clauses.
% 0.19/0.56 SPASS allocated 98488 KBytes.
% 0.19/0.56 SPASS spent 0:00:00.20 on the problem.
% 0.19/0.56 0:00:00.04 for the input.
% 0.19/0.56 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.56 0:00:00.01 for inferences.
% 0.19/0.56 0:00:00.00 for the backtracking.
% 0.19/0.56 0:00:00.09 for the reduction.
% 0.19/0.56
% 0.19/0.56
% 0.19/0.56 Here is a proof with depth 4, length 62 :
% 0.19/0.56 % SZS output start Refutation
% See solution above
% 0.19/0.56 Formulae used in the proof : mSortsC m__1837 m__1860 m__1870 mDefLE m__1883 m__ m_AddZero mSortsB mDefPrime mLETotal mAddComm mDefDiff
% 0.19/0.56
%------------------------------------------------------------------------------