TSTP Solution File: NUM453+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM453+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 14:26:21 EDT 2022
% Result : Theorem 0.60s 0.80s
% Output : Refutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of clauses : 52 ( 17 unt; 6 nHn; 52 RR)
% Number of literals : 121 ( 0 equ; 65 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aInteger0(sz00),
file('NUM453+1.p',unknown),
[] ).
cnf(2,axiom,
aInteger0(sz10),
file('NUM453+1.p',unknown),
[] ).
cnf(4,axiom,
aInteger0(xp),
file('NUM453+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(xp,sz00),
file('NUM453+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ aInteger0(u)
| aInteger0(smndt0(u)) ),
file('NUM453+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('NUM453+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('NUM453+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ aInteger0(u)
| equal(sdtasdt0(u,sz10),u) ),
file('NUM453+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ aInteger0(u)
| equal(sdtasdt0(u,sz00),sz00) ),
file('NUM453+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(u,smndt0(u)),sz00) ),
file('NUM453+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(smndt0(u),u),sz00) ),
file('NUM453+1.p',unknown),
[] ).
cnf(44,axiom,
( equal(sdtpldt0(sz10,xp),sz10)
| equal(sdtpldt0(sz10,smndt0(xp)),sz10) ),
file('NUM453+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('NUM453+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ aInteger0(u)
| isPrime0(skf15(v))
| equal(u,sz10)
| equal(u,smndt0(sz10)) ),
file('NUM453+1.p',unknown),
[] ).
cnf(85,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('NUM453+1.p',unknown),
[] ).
cnf(114,plain,
( ~ aInteger0(u)
| equal(u,sz10)
| equal(u,smndt0(sz10)) ),
inference(spt,[spt(split,[position(s1)])],[53]),
[iquote('1:Spt:53.0,53.2,53.3')] ).
cnf(166,plain,
( ~ aInteger0(u)
| ~ aInteger0(sz10)
| equal(u,sz10)
| equal(sdtpldt0(sz10,u),sz00) ),
inference(spr,[status(thm),theory(equality)],[114,27]),
[iquote('1:SpR:114.2,27.1')] ).
cnf(167,plain,
( ~ aInteger0(u)
| equal(u,sz10)
| equal(sdtpldt0(sz10,u),sz00) ),
inference(ssi,[status(thm)],[166,2]),
[iquote('1:SSi:166.1,2.0')] ).
cnf(373,plain,
( ~ aInteger0(sz00)
| ~ aInteger0(sz10)
| equal(sz10,sz00)
| equal(sz10,sz00) ),
inference(spr,[status(thm),theory(equality)],[167,18]),
[iquote('1:SpR:167.2,18.1')] ).
cnf(379,plain,
( ~ aInteger0(sz00)
| ~ aInteger0(sz10)
| equal(sz10,sz00) ),
inference(obv,[status(thm),theory(equality)],[373]),
[iquote('1:Obv:373.2')] ).
cnf(380,plain,
equal(sz10,sz00),
inference(ssi,[status(thm)],[379,2,1]),
[iquote('1:SSi:379.1,379.0,2.0,1.0')] ).
cnf(392,plain,
( ~ aInteger0(u)
| equal(sdtasdt0(u,sz00),u) ),
inference(rew,[status(thm),theory(equality)],[380,20]),
[iquote('1:Rew:380.0,20.1')] ).
cnf(429,plain,
( ~ aInteger0(u)
| equal(sz00,u) ),
inference(rew,[status(thm),theory(equality)],[22,392]),
[iquote('1:Rew:22.1,392.1')] ).
cnf(491,plain,
equal(xp,sz00),
inference(ems,[status(thm)],[429,4]),
[iquote('1:EmS:429.0,4.0')] ).
cnf(492,plain,
$false,
inference(mrr,[status(thm)],[491,10]),
[iquote('1:MRR:491.0,10.0')] ).
cnf(515,plain,
isPrime0(skf15(u)),
inference(spt,[spt(split,[position(s2)])],[53]),
[iquote('1:Spt:492.0,53.1')] ).
cnf(551,plain,
equal(sdtpldt0(sz10,xp),sz10),
inference(spt,[spt(split,[position(s2s1)])],[44]),
[iquote('2:Spt:44.0')] ).
cnf(1142,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(smndt0(u))
| ~ aInteger0(u)
| equal(sdtpldt0(u,sdtpldt0(smndt0(u),v)),sdtpldt0(sz00,v)) ),
inference(spr,[status(thm),theory(equality)],[27,85]),
[iquote('0:SpR:27.1,85.3')] ).
cnf(1145,plain,
( ~ aInteger0(u)
| ~ aInteger0(xp)
| ~ aInteger0(sz10)
| equal(sdtpldt0(sz10,sdtpldt0(xp,u)),sdtpldt0(sz10,u)) ),
inference(spr,[status(thm),theory(equality)],[551,85]),
[iquote('2:SpR:551.0,85.3')] ).
cnf(1146,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(xp,u)),sdtpldt0(sz10,u)) ),
inference(ssi,[status(thm)],[1145,2,4]),
[iquote('2:SSi:1145.2,1145.1,2.0,4.0')] ).
cnf(1151,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(v))
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[1142]),
[iquote('0:Obv:1142.0')] ).
cnf(1152,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(v))
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(rew,[status(thm),theory(equality)],[19,1151]),
[iquote('0:Rew:19.1,1151.3')] ).
cnf(1153,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(ssi,[status(thm)],[1152,12]),
[iquote('0:SSi:1152.1,12.1')] ).
cnf(1177,plain,
( ~ aInteger0(u)
| ~ aInteger0(xp)
| ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(u,xp)),sdtpldt0(sz10,u)) ),
inference(spr,[status(thm),theory(equality)],[50,1146]),
[iquote('2:SpR:50.2,1146.1')] ).
cnf(1218,plain,
( ~ aInteger0(xp)
| ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(u,xp)),sdtpldt0(sz10,u)) ),
inference(obv,[status(thm),theory(equality)],[1177]),
[iquote('2:Obv:1177.0')] ).
cnf(1219,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(u,xp)),sdtpldt0(sz10,u)) ),
inference(ssi,[status(thm)],[1218,4]),
[iquote('2:SSi:1218.0,4.0')] ).
cnf(1405,plain,
( ~ aInteger0(xp)
| ~ aInteger0(sz10)
| ~ aInteger0(smndt0(sz10))
| equal(sdtpldt0(sz10,smndt0(sz10)),xp) ),
inference(spr,[status(thm),theory(equality)],[1153,1219]),
[iquote('2:SpR:1153.2,1219.1')] ).
cnf(1420,plain,
( ~ aInteger0(xp)
| ~ aInteger0(sz10)
| ~ aInteger0(smndt0(sz10))
| equal(xp,sz00) ),
inference(rew,[status(thm),theory(equality)],[27,1405]),
[iquote('2:Rew:27.1,1405.3')] ).
cnf(1421,plain,
equal(xp,sz00),
inference(ssi,[status(thm)],[1420,12,2,4]),
[iquote('2:SSi:1420.2,1420.1,1420.0,12.0,2.0,2.0,4.1')] ).
cnf(1422,plain,
$false,
inference(mrr,[status(thm)],[1421,10]),
[iquote('2:MRR:1421.0,10.0')] ).
cnf(1480,plain,
~ equal(sdtpldt0(sz10,xp),sz10),
inference(spt,[spt(split,[position(s2sa)])],[1422,551]),
[iquote('2:Spt:1422.0,44.0,551.0')] ).
cnf(1481,plain,
equal(sdtpldt0(sz10,smndt0(xp)),sz10),
inference(spt,[spt(split,[position(s2s2)])],[44]),
[iquote('2:Spt:1422.0,44.1')] ).
cnf(1509,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz10)
| equal(sdtpldt0(sz10,sdtpldt0(smndt0(xp),u)),sdtpldt0(sz10,u)) ),
inference(spr,[status(thm),theory(equality)],[1481,85]),
[iquote('2:SpR:1481.0,85.3')] ).
cnf(1511,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(smndt0(xp),u)),sdtpldt0(sz10,u)) ),
inference(ssi,[status(thm)],[1509,2,12,4]),
[iquote('2:SSi:1509.2,1509.1,2.0,12.1,4.0')] ).
cnf(1572,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xp)
| equal(sdtpldt0(sz10,xp),sdtpldt0(sz10,sz00)) ),
inference(spr,[status(thm),theory(equality)],[28,1511]),
[iquote('2:SpR:28.1,1511.1')] ).
cnf(1574,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz00)
| equal(sdtpldt0(sz10,smndt0(xp)),sdtpldt0(sz10,sz00)) ),
inference(spr,[status(thm),theory(equality)],[18,1511]),
[iquote('2:SpR:18.1,1511.1')] ).
cnf(1578,plain,
( ~ aInteger0(xp)
| equal(sdtpldt0(sz10,xp),sdtpldt0(sz10,sz00)) ),
inference(obv,[status(thm),theory(equality)],[1572]),
[iquote('2:Obv:1572.0')] ).
cnf(1579,plain,
equal(sdtpldt0(sz10,xp),sdtpldt0(sz10,sz00)),
inference(ssi,[status(thm)],[1578,4]),
[iquote('2:SSi:1578.0,4.0')] ).
cnf(1580,plain,
~ equal(sdtpldt0(sz10,sz00),sz10),
inference(rew,[status(thm),theory(equality)],[1579,1480]),
[iquote('2:Rew:1579.0,1480.0')] ).
cnf(1584,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz00)
| equal(sdtpldt0(sz10,sz00),sz10) ),
inference(rew,[status(thm),theory(equality)],[1481,1574]),
[iquote('2:Rew:1481.0,1574.2')] ).
cnf(1585,plain,
equal(sdtpldt0(sz10,sz00),sz10),
inference(ssi,[status(thm)],[1584,1,12,4]),
[iquote('2:SSi:1584.1,1584.0,1.0,12.1,4.0')] ).
cnf(1586,plain,
$false,
inference(mrr,[status(thm)],[1585,1580]),
[iquote('2:MRR:1585.0,1580.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM453+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Thu Jul 7 06:59:49 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.60/0.80
% 0.60/0.80 SPASS V 3.9
% 0.60/0.80 SPASS beiseite: Proof found.
% 0.60/0.80 % SZS status Theorem
% 0.60/0.80 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.80 SPASS derived 947 clauses, backtracked 149 clauses, performed 9 splits and kept 660 clauses.
% 0.60/0.80 SPASS allocated 100060 KBytes.
% 0.60/0.80 SPASS spent 0:00:00.43 on the problem.
% 0.60/0.80 0:00:00.04 for the input.
% 0.60/0.80 0:00:00.18 for the FLOTTER CNF translation.
% 0.60/0.80 0:00:00.01 for inferences.
% 0.60/0.80 0:00:00.00 for the backtracking.
% 0.60/0.80 0:00:00.16 for the reduction.
% 0.60/0.80
% 0.60/0.80
% 0.60/0.80 Here is a proof with depth 4, length 52 :
% 0.60/0.80 % SZS output start Refutation
% See solution above
% 0.60/0.80 Formulae used in the proof : mIntZero mIntOne m__2171 mIntNeg mAddZero mMulOne mMulZero mAddNeg m__ mAddComm mPrimeDivisor mAddAsso
% 0.60/0.80
%------------------------------------------------------------------------------