TSTP Solution File: NUM501+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM501+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 14:26:52 EDT 2022
% Result : Theorem 1.36s 1.54s
% Output : Refutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 28
% Syntax : Number of clauses : 67 ( 23 unt; 26 nHn; 67 RR)
% Number of literals : 197 ( 0 equ; 72 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM501+3.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM501+3.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM501+3.p',unknown),
[] ).
cnf(7,axiom,
isPrime0(xp),
file('NUM501+3.p',unknown),
[] ).
cnf(11,axiom,
aNaturalNumber0(skc7),
file('NUM501+3.p',unknown),
[] ).
cnf(12,axiom,
aNaturalNumber0(xr),
file('NUM501+3.p',unknown),
[] ).
cnf(13,axiom,
isPrime0(xr),
file('NUM501+3.p',unknown),
[] ).
cnf(17,axiom,
aNaturalNumber0(skf11(u)),
file('NUM501+3.p',unknown),
[] ).
cnf(25,axiom,
~ equal(xp,sz00),
file('NUM501+3.p',unknown),
[] ).
cnf(26,axiom,
~ equal(xp,sz10),
file('NUM501+3.p',unknown),
[] ).
cnf(35,axiom,
~ equal(xr,sz00),
file('NUM501+3.p',unknown),
[] ).
cnf(36,axiom,
~ equal(xr,sz10),
file('NUM501+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ isPrime0(u)
| skP1(u) ),
file('NUM501+3.p',unknown),
[] ).
cnf(38,axiom,
doDivides0(xp,sdtasdt0(xn,xm)),
file('NUM501+3.p',unknown),
[] ).
cnf(41,axiom,
equal(sdtasdt0(xr,skc7),xk),
file('NUM501+3.p',unknown),
[] ).
cnf(42,axiom,
~ doDivides0(xr,sdtasdt0(xn,xm)),
file('NUM501+3.p',unknown),
[] ).
cnf(47,axiom,
equal(sdtsldt0(sdtasdt0(xn,xm),xp),xk),
file('NUM501+3.p',unknown),
[] ).
cnf(57,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM501+3.p',unknown),
[] ).
cnf(65,axiom,
( skP1(u)
| equal(u,sz10)
| equal(u,sz00)
| doDivides0(skf11(u),u) ),
file('NUM501+3.p',unknown),
[] ).
cnf(67,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM501+3.p',unknown),
[] ).
cnf(72,axiom,
( ~ equal(skf11(u),sz10)
| skP1(u)
| equal(u,sz10)
| equal(u,sz00) ),
file('NUM501+3.p',unknown),
[] ).
cnf(73,axiom,
( ~ equal(skf11(u),u)
| skP1(u)
| equal(u,sz10)
| equal(u,sz00) ),
file('NUM501+3.p',unknown),
[] ).
cnf(74,axiom,
( ~ aNaturalNumber0(u)
| ~ doDivides0(u,xp)
| equal(u,xp)
| equal(u,sz10) ),
file('NUM501+3.p',unknown),
[] ).
cnf(75,axiom,
( ~ aNaturalNumber0(u)
| ~ doDivides0(u,xr)
| equal(u,xr)
| equal(u,sz10) ),
file('NUM501+3.p',unknown),
[] ).
cnf(91,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM501+3.p',unknown),
[] ).
cnf(100,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
file('NUM501+3.p',unknown),
[] ).
cnf(102,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| aNaturalNumber0(w)
| equal(v,sz00) ),
file('NUM501+3.p',unknown),
[] ).
cnf(112,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| equal(v,sz00)
| equal(u,sdtasdt0(v,w)) ),
file('NUM501+3.p',unknown),
[] ).
cnf(247,plain,
( ~ aNaturalNumber0(skf11(xr))
| skP1(xr)
| equal(xr,sz10)
| equal(xr,sz00)
| equal(skf11(xr),xr)
| equal(skf11(xr),sz10) ),
inference(res,[status(thm),theory(equality)],[65,75]),
[iquote('0:Res:65.3,75.1')] ).
cnf(248,plain,
( skP1(xr)
| equal(xr,sz10)
| equal(xr,sz00)
| equal(skf11(xr),xr)
| equal(skf11(xr),sz10) ),
inference(ssi,[status(thm)],[247,17,13,12]),
[iquote('0:SSi:247.0,17.0,13.0,12.0')] ).
cnf(249,plain,
( skP1(xr)
| equal(skf11(xr),xr)
| equal(skf11(xr),sz10) ),
inference(mrr,[status(thm)],[248,36,35]),
[iquote('0:MRR:248.1,248.2,36.0,35.0')] ).
cnf(252,plain,
( skP1(xr)
| equal(skf11(xr),sz10)
| skP1(xr)
| equal(xr,sz10)
| equal(xr,sz00)
| doDivides0(xr,xr) ),
inference(spr,[status(thm),theory(equality)],[249,65]),
[iquote('0:SpR:249.1,65.3')] ).
cnf(254,plain,
( equal(skf11(xr),sz10)
| skP1(xr)
| equal(xr,sz10)
| equal(xr,sz00)
| doDivides0(xr,xr) ),
inference(obv,[status(thm),theory(equality)],[252]),
[iquote('0:Obv:252.0')] ).
cnf(255,plain,
( equal(skf11(xr),sz10)
| skP1(xr)
| doDivides0(xr,xr) ),
inference(mrr,[status(thm)],[254,36,35]),
[iquote('0:MRR:254.2,254.3,36.0,35.0')] ).
cnf(256,plain,
( ~ aNaturalNumber0(skf11(xp))
| skP1(xp)
| equal(xp,sz10)
| equal(xp,sz00)
| equal(skf11(xp),xp)
| equal(skf11(xp),sz10) ),
inference(res,[status(thm),theory(equality)],[65,74]),
[iquote('0:Res:65.3,74.1')] ).
cnf(257,plain,
( skP1(xp)
| equal(xp,sz10)
| equal(xp,sz00)
| equal(skf11(xp),xp)
| equal(skf11(xp),sz10) ),
inference(ssi,[status(thm)],[256,17,7,5]),
[iquote('0:SSi:256.0,17.0,7.0,5.0')] ).
cnf(258,plain,
( skP1(xp)
| equal(skf11(xp),xp)
| equal(skf11(xp),sz10) ),
inference(mrr,[status(thm)],[257,26,25]),
[iquote('0:MRR:257.1,257.2,26.0,25.0')] ).
cnf(260,plain,
( skP1(xr)
| doDivides0(xr,xr)
| skP1(xr)
| equal(xr,sz10)
| equal(xr,sz00)
| doDivides0(sz10,xr) ),
inference(spr,[status(thm),theory(equality)],[255,65]),
[iquote('0:SpR:255.0,65.3')] ).
cnf(264,plain,
( doDivides0(xr,xr)
| skP1(xr)
| equal(xr,sz10)
| equal(xr,sz00)
| doDivides0(sz10,xr) ),
inference(obv,[status(thm),theory(equality)],[260]),
[iquote('0:Obv:260.0')] ).
cnf(265,plain,
( doDivides0(xr,xr)
| skP1(xr)
| doDivides0(sz10,xr) ),
inference(mrr,[status(thm)],[264,36,35]),
[iquote('0:MRR:264.2,264.3,36.0,35.0')] ).
cnf(266,plain,
skP1(xr),
inference(spt,[spt(split,[position(s1)])],[265]),
[iquote('1:Spt:265.1')] ).
cnf(309,plain,
( ~ equal(xp,xp)
| skP1(xp)
| equal(skf11(xp),sz10)
| skP1(xp)
| equal(xp,sz10)
| equal(xp,sz00) ),
inference(spl,[status(thm),theory(equality)],[258,73]),
[iquote('0:SpL:258.1,73.0')] ).
cnf(310,plain,
( equal(skf11(xp),sz10)
| skP1(xp)
| equal(xp,sz10)
| equal(xp,sz00) ),
inference(obv,[status(thm),theory(equality)],[309]),
[iquote('0:Obv:309.1')] ).
cnf(311,plain,
skP1(xp),
inference(mrr,[status(thm)],[310,72,26,25]),
[iquote('0:MRR:310.0,310.2,310.3,72.0,26.0,25.0')] ).
cnf(1165,plain,
( ~ aNaturalNumber0(sdtasdt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| doDivides0(u,sdtasdt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[91]),
[iquote('0:EqR:91.3')] ).
cnf(1179,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| doDivides0(u,sdtasdt0(u,v)) ),
inference(ssi,[status(thm)],[1165,57]),
[iquote('0:SSi:1165.0,57.2')] ).
cnf(1395,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(skc7)
| ~ aNaturalNumber0(xr)
| equal(sdtasdt0(xr,sdtasdt0(skc7,u)),sdtasdt0(xk,u)) ),
inference(spr,[status(thm),theory(equality)],[41,100]),
[iquote('0:SpR:41.0,100.3')] ).
cnf(1417,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(xr,sdtasdt0(skc7,u)),sdtasdt0(xk,u)) ),
inference(ssi,[status(thm)],[1395,13,12,266,11]),
[iquote('1:SSi:1395.2,1395.1,13.0,12.0,266.0,11.0')] ).
cnf(1761,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(spl,[status(thm),theory(equality)],[47,102]),
[iquote('0:SpL:47.0,102.3')] ).
cnf(1762,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[1761,7,5,311,57,3,4]),
[iquote('0:SSi:1761.1,1761.0,7.0,5.0,311.2,57.0,3.0,4.0')] ).
cnf(1763,plain,
( ~ equal(u,xk)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[1762,38,25]),
[iquote('0:MRR:1762.0,1762.3,38.0,25.0')] ).
cnf(2972,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| equal(xp,sz00)
| equal(sdtasdt0(xp,u),sdtasdt0(xn,xm)) ),
inference(spl,[status(thm),theory(equality)],[47,112]),
[iquote('0:SpL:47.0,112.3')] ).
cnf(2975,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| equal(xp,sz00)
| equal(sdtasdt0(xp,u),sdtasdt0(xn,xm)) ),
inference(ssi,[status(thm)],[2972,7,5,311,57,3,4]),
[iquote('0:SSi:2972.1,2972.0,7.0,5.0,311.2,57.0,3.0,4.0')] ).
cnf(2976,plain,
( ~ equal(u,xk)
| equal(sdtasdt0(xp,u),sdtasdt0(xn,xm)) ),
inference(mrr,[status(thm)],[2975,38,25]),
[iquote('0:MRR:2975.0,2975.2,38.0,25.0')] ).
cnf(3356,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ equal(u,xk)
| equal(sdtasdt0(xn,xm),sdtasdt0(u,xp)) ),
inference(spr,[status(thm),theory(equality)],[2976,67]),
[iquote('0:SpR:2976.1,67.2')] ).
cnf(3393,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xk)
| equal(sdtasdt0(xn,xm),sdtasdt0(u,xp)) ),
inference(ssi,[status(thm)],[3356,7,5,311]),
[iquote('0:SSi:3356.1,7.0,5.0,311.0')] ).
cnf(3394,plain,
( ~ equal(u,xk)
| equal(sdtasdt0(xn,xm),sdtasdt0(u,xp)) ),
inference(mrr,[status(thm)],[3393,1763]),
[iquote('0:MRR:3393.0,1763.1')] ).
cnf(3979,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(skc7,u))
| doDivides0(xr,sdtasdt0(xk,u)) ),
inference(spr,[status(thm),theory(equality)],[1417,1179]),
[iquote('1:SpR:1417.1,1179.2')] ).
cnf(4013,plain,
( ~ aNaturalNumber0(u)
| doDivides0(xr,sdtasdt0(xk,u)) ),
inference(ssi,[status(thm)],[3979,57,11,13,12,266]),
[iquote('1:SSi:3979.2,3979.1,57.0,11.0,13.0,12.0,266.2')] ).
cnf(4209,plain,
( ~ aNaturalNumber0(xp)
| ~ equal(xk,xk)
| doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(spr,[status(thm),theory(equality)],[3394,4013]),
[iquote('1:SpR:3394.1,4013.1')] ).
cnf(4222,plain,
( ~ aNaturalNumber0(xp)
| doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(obv,[status(thm),theory(equality)],[4209]),
[iquote('1:Obv:4209.1')] ).
cnf(4223,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(ssi,[status(thm)],[4222,7,5,311]),
[iquote('1:SSi:4222.0,7.0,5.0,311.0')] ).
cnf(4224,plain,
$false,
inference(mrr,[status(thm)],[4223,42]),
[iquote('1:MRR:4223.0,42.0')] ).
cnf(4236,plain,
~ skP1(xr),
inference(spt,[spt(split,[position(sa)])],[4224,266]),
[iquote('1:Spt:4224.0,265.1,266.0')] ).
cnf(4237,plain,
( doDivides0(xr,xr)
| doDivides0(sz10,xr) ),
inference(spt,[spt(split,[position(s2)])],[265]),
[iquote('1:Spt:4224.0,265.0,265.2')] ).
cnf(4297,plain,
~ isPrime0(xr),
inference(res,[status(thm),theory(equality)],[37,4236]),
[iquote('1:Res:37.1,4236.0')] ).
cnf(4298,plain,
$false,
inference(ssi,[status(thm)],[4297,13,12]),
[iquote('1:SSi:4297.0,13.0,12.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM501+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 00:46:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.36/1.54
% 1.36/1.54 SPASS V 3.9
% 1.36/1.54 SPASS beiseite: Proof found.
% 1.36/1.54 % SZS status Theorem
% 1.36/1.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.36/1.54 SPASS derived 2559 clauses, backtracked 369 clauses, performed 8 splits and kept 1475 clauses.
% 1.36/1.54 SPASS allocated 101619 KBytes.
% 1.36/1.54 SPASS spent 0:00:01.14 on the problem.
% 1.36/1.54 0:00:00.04 for the input.
% 1.36/1.54 0:00:00.05 for the FLOTTER CNF translation.
% 1.36/1.54 0:00:00.04 for inferences.
% 1.36/1.54 0:00:00.01 for the backtracking.
% 1.36/1.54 0:00:00.96 for the reduction.
% 1.36/1.54
% 1.36/1.54
% 1.36/1.54 Here is a proof with depth 4, length 67 :
% 1.36/1.54 % SZS output start Refutation
% See solution above
% 1.36/1.54 Formulae used in the proof : m__1837 m__1860 m__2342 m__1799 m__ m__2306 mSortsB_02 mMulComm mDefDiv mMulAsso mDefQuot
% 1.36/1.54
%------------------------------------------------------------------------------