TSTP Solution File: NUM452+6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM452+6 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 14:26:20 EDT 2022
% Result : Theorem 6.14s 6.34s
% Output : Refutation 6.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of clauses : 45 ( 11 unt; 0 nHn; 45 RR)
% Number of literals : 112 ( 0 equ; 82 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aInteger0(sz10),
file('NUM452+6.p',unknown),
[] ).
cnf(5,axiom,
aInteger0(xp),
file('NUM452+6.p',unknown),
[] ).
cnf(25,axiom,
equal(stldt0(sbsmnsldt0(xS)),cS2076),
file('NUM452+6.p',unknown),
[] ).
cnf(26,axiom,
( ~ aInteger0(u)
| aInteger0(smndt0(u)) ),
file('NUM452+6.p',unknown),
[] ).
cnf(37,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('NUM452+6.p',unknown),
[] ).
cnf(38,axiom,
( ~ aInteger0(u)
| equal(sdtasdt0(u,sz10),u) ),
file('NUM452+6.p',unknown),
[] ).
cnf(47,axiom,
( ~ aElementOf0(u,stldt0(sbsmnsldt0(xS)))
| aInteger0(u) ),
file('NUM452+6.p',unknown),
[] ).
cnf(49,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(u,smndt0(u)),sz00) ),
file('NUM452+6.p',unknown),
[] ).
cnf(50,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(smndt0(u),u),sz00) ),
file('NUM452+6.p',unknown),
[] ).
cnf(69,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| aInteger0(sdtpldt0(v,u)) ),
file('NUM452+6.p',unknown),
[] ).
cnf(72,axiom,
( ~ aInteger0(u)
| equal(sdtasdt0(u,smndt0(sz10)),smndt0(u)) ),
file('NUM452+6.p',unknown),
[] ).
cnf(80,axiom,
( ~ equal(u,smndt0(sz10))
| aElementOf0(u,stldt0(sbsmnsldt0(xS))) ),
file('NUM452+6.p',unknown),
[] ).
cnf(101,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('NUM452+6.p',unknown),
[] ).
cnf(119,axiom,
( ~ aInteger0(u)
| ~ equal(sdtasdt0(xp,u),sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
| skC0 ),
file('NUM452+6.p',unknown),
[] ).
cnf(138,axiom,
( ~ aInteger0(u)
| ~ skC0
| ~ equal(sdtasdt0(xp,u),sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))) ),
file('NUM452+6.p',unknown),
[] ).
cnf(163,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('NUM452+6.p',unknown),
[] ).
cnf(210,plain,
( ~ aElementOf0(u,cS2076)
| aInteger0(u) ),
inference(rew,[status(thm),theory(equality)],[25,47]),
[iquote('0:Rew:25.0,47.0')] ).
cnf(214,plain,
( ~ equal(u,smndt0(sz10))
| aElementOf0(u,cS2076) ),
inference(rew,[status(thm),theory(equality)],[25,80]),
[iquote('0:Rew:25.0,80.1')] ).
cnf(280,plain,
( ~ aInteger0(u)
| ~ equal(sdtasdt0(xp,u),sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) ),
inference(spt,[spt(split,[position(s1)])],[119]),
[iquote('1:Spt:119.0,119.1')] ).
cnf(450,plain,
aElementOf0(smndt0(sz10),cS2076),
inference(eqr,[status(thm),theory(equality)],[214]),
[iquote('0:EqR:214.0')] ).
cnf(456,plain,
aInteger0(smndt0(sz10)),
inference(res,[status(thm),theory(equality)],[450,210]),
[iquote('0:Res:450.0,210.0')] ).
cnf(477,plain,
( ~ aInteger0(xp)
| ~ aInteger0(sz10)
| ~ equal(sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)),xp) ),
inference(spl,[status(thm),theory(equality)],[38,280]),
[iquote('1:SpL:38.1,280.1')] ).
cnf(480,plain,
~ equal(sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)),xp),
inference(ssi,[status(thm)],[477,2,5]),
[iquote('1:SSi:477.1,477.0,2.0,5.0')] ).
cnf(5923,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(sdtpldt0(sz10,xp))
| ~ equal(sdtpldt0(smndt0(sz10),sdtpldt0(sz10,xp)),xp) ),
inference(spl,[status(thm),theory(equality)],[101,480]),
[iquote('1:SpL:101.2,480.0')] ).
cnf(5945,plain,
~ equal(sdtpldt0(smndt0(sz10),sdtpldt0(sz10,xp)),xp),
inference(ssi,[status(thm)],[5923,69,2,5,456]),
[iquote('1:SSi:5923.1,5923.0,69.0,2.0,5.0,456.2')] ).
cnf(7858,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(u)
| ~ aInteger0(smndt0(u))
| equal(sdtpldt0(smndt0(u),sdtpldt0(u,v)),sdtpldt0(sz00,v)) ),
inference(spr,[status(thm),theory(equality)],[50,163]),
[iquote('0:SpR:50.1,163.3')] ).
cnf(7862,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)],[49,163]),
[iquote('0:SpR:49.1,163.3')] ).
cnf(7988,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(v))
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[7862]),
[iquote('0:Obv:7862.0')] ).
cnf(7989,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(v))
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(rew,[status(thm),theory(equality)],[37,7988]),
[iquote('0:Rew:37.1,7988.3')] ).
cnf(7990,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(ssi,[status(thm)],[7989,26]),
[iquote('0:SSi:7989.1,26.1')] ).
cnf(7991,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[7858]),
[iquote('0:Obv:7858.0')] ).
cnf(7992,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(rew,[status(thm),theory(equality)],[37,7991]),
[iquote('0:Rew:37.1,7991.3')] ).
cnf(7993,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(ssi,[status(thm)],[7992,26]),
[iquote('0:SSi:7992.2,26.1')] ).
cnf(16255,plain,
( ~ aInteger0(xp)
| ~ aInteger0(sz10)
| ~ equal(xp,xp) ),
inference(spl,[status(thm),theory(equality)],[7993,5945]),
[iquote('1:SpL:7993.2,5945.0')] ).
cnf(16261,plain,
( ~ aInteger0(xp)
| ~ aInteger0(sz10) ),
inference(obv,[status(thm),theory(equality)],[16255]),
[iquote('1:Obv:16255.2')] ).
cnf(16262,plain,
$false,
inference(ssi,[status(thm)],[16261,2,5]),
[iquote('1:SSi:16261.1,16261.0,2.0,5.0')] ).
cnf(16288,plain,
skC0,
inference(spt,[spt(split,[position(s2)])],[119]),
[iquote('1:Spt:16262.0,119.2')] ).
cnf(16343,plain,
( ~ aInteger0(u)
| ~ equal(sdtasdt0(xp,u),sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))) ),
inference(mrr,[status(thm)],[138,16288]),
[iquote('1:MRR:138.1,16288.0')] ).
cnf(17217,plain,
( ~ aInteger0(xp)
| ~ aInteger0(smndt0(sz10))
| ~ equal(sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)),smndt0(xp)) ),
inference(spl,[status(thm),theory(equality)],[72,16343]),
[iquote('1:SpL:72.1,16343.1')] ).
cnf(17223,plain,
~ equal(sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)),smndt0(xp)),
inference(ssi,[status(thm)],[17217,456,5]),
[iquote('1:SSi:17217.1,17217.0,456.0,5.0')] ).
cnf(22514,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz10)
| ~ equal(sdtpldt0(sz10,sdtpldt0(smndt0(xp),smndt0(sz10))),smndt0(xp)) ),
inference(spl,[status(thm),theory(equality)],[163,17223]),
[iquote('1:SpL:163.3,17223.0')] ).
cnf(22608,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz10)
| ~ equal(sdtpldt0(sz10,sdtpldt0(smndt0(sz10),smndt0(xp))),smndt0(xp)) ),
inference(rew,[status(thm),theory(equality)],[101,22514]),
[iquote('1:Rew:101.2,22514.3')] ).
cnf(22609,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz10)
| ~ equal(smndt0(xp),smndt0(xp)) ),
inference(rew,[status(thm),theory(equality)],[7990,22608]),
[iquote('1:Rew:7990.2,22608.3')] ).
cnf(22610,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz10) ),
inference(obv,[status(thm),theory(equality)],[22609]),
[iquote('1:Obv:22609.3')] ).
cnf(22611,plain,
$false,
inference(ssi,[status(thm)],[22610,2,26,5,456]),
[iquote('1:SSi:22610.2,22610.1,22610.0,2.0,26.0,5.1,456.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM452+6 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jul 6 03:33:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 6.14/6.34
% 6.14/6.34 SPASS V 3.9
% 6.14/6.34 SPASS beiseite: Proof found.
% 6.14/6.34 % SZS status Theorem
% 6.14/6.34 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.14/6.34 SPASS derived 14130 clauses, backtracked 5242 clauses, performed 78 splits and kept 9452 clauses.
% 6.14/6.34 SPASS allocated 112655 KBytes.
% 6.14/6.34 SPASS spent 0:00:05.30 on the problem.
% 6.14/6.34 0:00:00.04 for the input.
% 6.14/6.34 0:00:00.24 for the FLOTTER CNF translation.
% 6.14/6.34 0:00:00.17 for inferences.
% 6.14/6.34 0:00:00.16 for the backtracking.
% 6.14/6.34 0:00:04.58 for the reduction.
% 6.14/6.34
% 6.14/6.34
% 6.14/6.34 Here is a proof with depth 4, length 45 :
% 6.14/6.34 % SZS output start Refutation
% See solution above
% 6.14/6.34 Formulae used in the proof : mIntOne m__2171 m__2079 mIntNeg mAddZero mMulOne mAddNeg mIntPlus mMulMinOne mAddComm m__ mAddAsso
% 6.14/6.34
%------------------------------------------------------------------------------