%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM492+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 14:26:45 EDT 2022
% Result : Theorem 66.81s 66.97s
% Output : Refutation 66.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of clauses : 61 ( 23 unt; 0 nHn; 61 RR)
% Number of literals : 174 ( 0 equ; 119 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM492+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM492+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM492+1.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM492+1.p',unknown),
[] ).
cnf(9,axiom,
sdtlseqdt0(xp,xn),
file('NUM492+1.p',unknown),
[] ).
cnf(12,axiom,
aNaturalNumber0(skf4(u,v)),
file('NUM492+1.p',unknown),
[] ).
cnf(16,axiom,
equal(sdtmndt0(xn,xp),xr),
file('NUM492+1.p',unknown),
[] ).
cnf(18,axiom,
doDivides0(xp,sdtasdt0(xn,xm)),
file('NUM492+1.p',unknown),
[] ).
cnf(19,axiom,
doDivides0(xp,sdtasdt0(xp,xm)),
file('NUM492+1.p',unknown),
[] ).
cnf(20,axiom,
~ doDivides0(xp,sdtasdt0(xr,xm)),
file('NUM492+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM492+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM492+1.p',unknown),
[] ).
cnf(32,axiom,
equal(sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),sdtasdt0(xn,xm)),
file('NUM492+1.p',unknown),
[] ).
cnf(33,axiom,
equal(sdtasdt0(xr,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))),
file('NUM492+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM492+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| equal(sdtpldt0(v,skf4(u,v)),u) ),
file('NUM492+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM492+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| aNaturalNumber0(w) ),
file('NUM492+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(w,v)
| ~ doDivides0(w,sdtpldt0(v,u))
| doDivides0(w,u) ),
file('NUM492+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,w)
| ~ equal(sdtpldt0(v,u),w)
| equal(u,sdtmndt0(w,v)) ),
file('NUM492+1.p',unknown),
[] ).
cnf(85,plain,
~ doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))),
inference(rew,[status(thm),theory(equality)],[33,20]),
[iquote('0:Rew:33.0,20.0')] ).
cnf(86,plain,
equal(sdtpldt0(sdtasdt0(xp,xm),sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))),sdtasdt0(xn,xm)),
inference(rew,[status(thm),theory(equality)],[33,32]),
[iquote('0:Rew:33.0,32.0')] ).
cnf(87,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| equal(w,sdtmndt0(u,v)) ),
inference(mrr,[status(thm)],[77,54]),
[iquote('0:MRR:77.3,54.4')] ).
cnf(120,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))) ),
inference(spr,[status(thm),theory(equality)],[33,29]),
[iquote('0:SpR:33.0,29.2')] ).
cnf(121,plain,
( ~ aNaturalNumber0(xr)
| aNaturalNumber0(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))) ),
inference(ssi,[status(thm)],[120,4]),
[iquote('0:SSi:120.0,4.0')] ).
cnf(137,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtasdt0(xm,xp)) ),
inference(spr,[status(thm),theory(equality)],[38,19]),
[iquote('0:SpR:38.2,19.0')] ).
cnf(138,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| equal(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),sdtasdt0(xm,xr)) ),
inference(spr,[status(thm),theory(equality)],[38,33]),
[iquote('0:SpR:38.2,33.0')] ).
cnf(155,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp))) ),
inference(spl,[status(thm),theory(equality)],[38,85]),
[iquote('0:SpL:38.2,85.0')] ).
cnf(157,plain,
doDivides0(xp,sdtasdt0(xm,xp)),
inference(ssi,[status(thm)],[137,6,5,4]),
[iquote('0:SSi:137.1,137.0,6.0,5.0,4.0')] ).
cnf(168,plain,
~ doDivides0(xp,sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp))),
inference(ssi,[status(thm)],[155,6,5,4]),
[iquote('0:SSi:155.1,155.0,6.0,5.0,4.0')] ).
cnf(169,plain,
( ~ aNaturalNumber0(xr)
| equal(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),sdtasdt0(xm,xr)) ),
inference(ssi,[status(thm)],[138,4]),
[iquote('0:SSi:138.0,4.0')] ).
cnf(170,plain,
( ~ aNaturalNumber0(xr)
| aNaturalNumber0(sdtasdt0(xm,xr)) ),
inference(rew,[status(thm),theory(equality)],[169,121]),
[iquote('0:Rew:169.1,121.1')] ).
cnf(533,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[54]),
[iquote('0:EqR:54.3')] ).
cnf(541,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(ssi,[status(thm)],[533,28]),
[iquote('0:SSi:533.0,28.2')] ).
cnf(753,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| aNaturalNumber0(sdtmndt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[55]),
[iquote('0:EqR:55.3')] ).
cnf(754,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xn)
| ~ equal(u,xr)
| aNaturalNumber0(u) ),
inference(spl,[status(thm),theory(equality)],[16,55]),
[iquote('0:SpL:16.0,55.3')] ).
cnf(755,plain,
( ~ sdtlseqdt0(xp,xn)
| ~ equal(u,xr)
| aNaturalNumber0(u) ),
inference(ssi,[status(thm)],[754,6,5,3]),
[iquote('0:SSi:754.1,754.0,6.0,5.0,3.0')] ).
cnf(756,plain,
( ~ equal(u,xr)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[755,9]),
[iquote('0:MRR:755.0,9.0')] ).
cnf(821,plain,
( ~ equal(xr,xr)
| aNaturalNumber0(sdtasdt0(xm,xr)) ),
inference(sor,[status(thm)],[170,756]),
[iquote('0:SoR:170.0,756.1')] ).
cnf(822,plain,
aNaturalNumber0(sdtasdt0(xm,xr)),
inference(obv,[status(thm),theory(equality)],[821]),
[iquote('0:Obv:821.0')] ).
cnf(1434,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(eqr,[status(thm),theory(equality)],[87]),
[iquote('0:EqR:87.3')] ).
cnf(1443,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(ssi,[status(thm)],[1434,28]),
[iquote('0:SSi:1434.0,28.2')] ).
cnf(1601,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)],[50,1443]),
[iquote('0:SpR:50.3,1443.2')] ).
cnf(1612,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)],[1601]),
[iquote('0:Obv:1601.1')] ).
cnf(1613,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| equal(skf4(u,v),sdtmndt0(u,v)) ),
inference(ssi,[status(thm)],[1612,12]),
[iquote('0:SSi:1612.2,12.0')] ).
cnf(1614,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| equal(sdtpldt0(v,sdtmndt0(u,v)),u) ),
inference(rew,[status(thm),theory(equality)],[1613,50]),
[iquote('0:Rew:1613.3,50.3')] ).
cnf(2207,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(sdtmndt0(u,v))
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,u)
| ~ doDivides0(w,v)
| ~ doDivides0(w,u)
| doDivides0(w,sdtmndt0(u,v)) ),
inference(spl,[status(thm),theory(equality)],[1614,66]),
[iquote('0:SpL:1614.3,66.4')] ).
cnf(2230,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtmndt0(u,v))
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,u)
| ~ doDivides0(w,v)
| ~ doDivides0(w,u)
| doDivides0(w,sdtmndt0(u,v)) ),
inference(obv,[status(thm),theory(equality)],[2207]),
[iquote('0:Obv:2207.1')] ).
cnf(2231,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,u)
| ~ doDivides0(w,v)
| ~ doDivides0(w,u)
| doDivides0(w,sdtmndt0(u,v)) ),
inference(mrr,[status(thm)],[2230,753]),
[iquote('0:MRR:2230.1,753.3')] ).
cnf(3930,plain,
( ~ equal(xr,xr)
| equal(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),sdtasdt0(xm,xr)) ),
inference(sor,[status(thm)],[169,756]),
[iquote('0:SoR:169.0,756.1')] ).
cnf(3933,plain,
equal(sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),sdtasdt0(xm,xr)),
inference(obv,[status(thm),theory(equality)],[3930]),
[iquote('0:Obv:3930.0')] ).
cnf(3936,plain,
equal(sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xm,xr)),sdtasdt0(xn,xm)),
inference(rew,[status(thm),theory(equality)],[3933,86]),
[iquote('0:Rew:3933.0,86.0')] ).
cnf(4037,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(spr,[status(thm),theory(equality)],[3936,28]),
[iquote('0:SpR:3936.0,28.2')] ).
cnf(4045,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
inference(spr,[status(thm),theory(equality)],[3936,541]),
[iquote('0:SpR:3936.0,541.2')] ).
cnf(4068,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(ssi,[status(thm)],[4037,29,6,5,4,822]),
[iquote('0:SSi:4037.1,4037.0,29.0,6.0,5.0,4.0,822.2')] ).
cnf(4071,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)),
inference(ssi,[status(thm)],[4045,822,29,6,5,4]),
[iquote('0:SSi:4045.1,4045.0,822.0,29.0,6.0,5.2,4.0')] ).
cnf(4110,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(sdtasdt0(xm,xp),sdtasdt0(xn,xm)) ),
inference(spr,[status(thm),theory(equality)],[38,4071]),
[iquote('0:SpR:38.2,4071.0')] ).
cnf(4114,plain,
sdtlseqdt0(sdtasdt0(xm,xp),sdtasdt0(xn,xm)),
inference(ssi,[status(thm)],[4110,6,5,4]),
[iquote('0:SSi:4110.1,4110.0,6.0,5.0,4.0')] ).
cnf(62134,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtasdt0(xm,xp),sdtasdt0(xn,xm))
| ~ doDivides0(xp,sdtasdt0(xm,xp))
| ~ doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(res,[status(thm),theory(equality)],[2231,168]),
[iquote('0:Res:2231.6,168.0')] ).
cnf(62149,plain,
( ~ sdtlseqdt0(sdtasdt0(xm,xp),sdtasdt0(xn,xm))
| ~ doDivides0(xp,sdtasdt0(xm,xp))
| ~ doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(ssi,[status(thm)],[62134,6,5,29,4,4068]),
[iquote('0:SSi:62134.2,62134.1,62134.0,6.0,5.0,29.0,4.0,6.2,5.0,4068.0')] ).
cnf(62150,plain,
$false,
inference(mrr,[status(thm)],[62149,4114,157,18]),
[iquote('0:MRR:62149.0,62149.1,62149.2,4114.0,157.0,18.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM492+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 8 02:11:52 EDT 2022
% 0.14/0.34 % CPUTime :
% 66.81/66.97
% 66.81/66.97 SPASS V 3.9
% 66.81/66.97 SPASS beiseite: Proof found.
% 66.81/66.97 % SZS status Theorem
% 66.81/66.97 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 66.81/66.97 SPASS derived 39715 clauses, backtracked 2553 clauses, performed 20 splits and kept 12938 clauses.
% 66.81/66.97 SPASS allocated 148445 KBytes.
% 66.81/66.97 SPASS spent 0:0:47.52 on the problem.
% 66.81/66.97 0:00:00.04 for the input.
% 66.81/66.97 0:00:00.04 for the FLOTTER CNF translation.
% 66.81/66.97 0:00:00.44 for inferences.
% 66.81/66.97 0:00:00.98 for the backtracking.
% 66.81/66.97 0:0:45.84 for the reduction.
% 66.81/66.97
% 66.81/66.97
% 66.81/66.97 Here is a proof with depth 3, length 61 :
% 66.81/66.97 % SZS output start Refutation
% See solution above
% 66.81/66.97 Formulae used in the proof : m__1837 m__1860 m__1870 mDefLE m__1883 m__2001 m__ mSortsB mSortsB_02 m__1951 m__1978 mMulComm mDefDiff mDivMin
% 66.81/66.97
%------------------------------------------------------------------------------