TSTP Solution File: NUM454+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM454+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 0.78s 1.01s
% Output : Refutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 17
% Syntax : Number of clauses : 75 ( 19 unt; 4 nHn; 75 RR)
% Number of literals : 187 ( 0 equ; 109 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aInteger0(sz00),
file('NUM454+1.p',unknown),
[] ).
cnf(2,axiom,
aInteger0(sz10),
file('NUM454+1.p',unknown),
[] ).
cnf(4,axiom,
aInteger0(xp),
file('NUM454+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(xp,sz00),
file('NUM454+1.p',unknown),
[] ).
cnf(12,axiom,
equal(sdtpldt0(sz10,xp),smndt0(sz10)),
file('NUM454+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ aInteger0(u)
| aInteger0(smndt0(u)) ),
file('NUM454+1.p',unknown),
[] ).
cnf(16,axiom,
equal(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)),
file('NUM454+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('NUM454+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('NUM454+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ aInteger0(u)
| equal(sdtasdt0(sz10,u),u) ),
file('NUM454+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(u,smndt0(u)),sz00) ),
file('NUM454+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(smndt0(u),u),sz00) ),
file('NUM454+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| aInteger0(sdtpldt0(v,u)) ),
file('NUM454+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('NUM454+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ equal(sdtasdt0(v,u),sz00)
| equal(u,sz00)
| equal(v,sz00) ),
file('NUM454+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('NUM454+1.p',unknown),
[] ).
cnf(98,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtasdt0(sdtpldt0(w,v),u),sdtpldt0(sdtasdt0(w,u),sdtasdt0(v,u))) ),
file('NUM454+1.p',unknown),
[] ).
cnf(1430,plain,
( ~ aInteger0(u)
| ~ aInteger0(xp)
| ~ aInteger0(sz10)
| equal(sdtpldt0(smndt0(sz10),u),sdtpldt0(sz10,sdtpldt0(xp,u))) ),
inference(spr,[status(thm),theory(equality)],[12,88]),
[iquote('0:SpR:12.0,88.3')] ).
cnf(1432,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(smndt0(sz10),u),sdtpldt0(sz10,sdtpldt0(xp,u))) ),
inference(ssi,[status(thm)],[1430,2,4]),
[iquote('0:SSi:1430.2,1430.1,2.0,4.0')] ).
cnf(1465,plain,
( ~ aInteger0(sz10)
| ~ aInteger0(sz10)
| equal(sdtpldt0(sz10,sdtpldt0(xp,sz10)),sz00) ),
inference(spr,[status(thm),theory(equality)],[1432,32]),
[iquote('0:SpR:1432.1,32.1')] ).
cnf(1474,plain,
( ~ aInteger0(sz10)
| equal(sdtpldt0(sz10,sdtpldt0(xp,sz10)),sz00) ),
inference(obv,[status(thm),theory(equality)],[1465]),
[iquote('0:Obv:1465.0')] ).
cnf(1475,plain,
equal(sdtpldt0(sz10,sdtpldt0(xp,sz10)),sz00),
inference(ssi,[status(thm)],[1474,2]),
[iquote('0:SSi:1474.0,2.0')] ).
cnf(1548,plain,
( ~ aInteger0(u)
| ~ aInteger0(sdtpldt0(xp,sz10))
| ~ aInteger0(sz10)
| equal(sdtpldt0(sz10,sdtpldt0(sdtpldt0(xp,sz10),u)),sdtpldt0(sz00,u)) ),
inference(spr,[status(thm),theory(equality)],[1475,88]),
[iquote('0:SpR:1475.0,88.3')] ).
cnf(1553,plain,
( ~ aInteger0(u)
| ~ aInteger0(sdtpldt0(xp,sz10))
| ~ aInteger0(sz10)
| equal(sdtpldt0(sz10,sdtpldt0(sdtpldt0(xp,sz10),u)),u) ),
inference(rew,[status(thm),theory(equality)],[23,1548]),
[iquote('0:Rew:23.1,1548.3')] ).
cnf(1554,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(sdtpldt0(xp,sz10),u)),u) ),
inference(ssi,[status(thm)],[1553,2,38,4]),
[iquote('0:SSi:1553.2,1553.1,2.0,38.0,4.2,2.0')] ).
cnf(1612,plain,
( ~ aInteger0(sz10)
| ~ aInteger0(xp)
| ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(sdtpldt0(sz10,xp),u)),u) ),
inference(spr,[status(thm),theory(equality)],[53,1554]),
[iquote('0:SpR:53.2,1554.1')] ).
cnf(1617,plain,
( ~ aInteger0(sdtpldt0(xp,sz10))
| ~ aInteger0(smndt0(sdtpldt0(xp,sz10)))
| equal(smndt0(sdtpldt0(xp,sz10)),sdtpldt0(sz10,sz00)) ),
inference(spr,[status(thm),theory(equality)],[31,1554]),
[iquote('0:SpR:31.1,1554.1')] ).
cnf(1618,plain,
( ~ aInteger0(sdtpldt0(xp,sz10))
| ~ aInteger0(u)
| ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(u,sdtpldt0(xp,sz10))),u) ),
inference(spr,[status(thm),theory(equality)],[53,1554]),
[iquote('0:SpR:53.2,1554.1')] ).
cnf(1620,plain,
( ~ aInteger0(sz10)
| ~ aInteger0(xp)
| ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(sz10,sdtpldt0(xp,u))),u) ),
inference(rew,[status(thm),theory(equality)],[88,1612]),
[iquote('0:Rew:88.3,1612.3')] ).
cnf(1621,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(sz10,sdtpldt0(xp,u))),u) ),
inference(ssi,[status(thm)],[1620,4,2]),
[iquote('0:SSi:1620.1,1620.0,4.0,2.0')] ).
cnf(1623,plain,
equal(smndt0(sdtpldt0(xp,sz10)),sdtpldt0(sz10,sz00)),
inference(ssi,[status(thm)],[1617,13,38,4,2]),
[iquote('0:SSi:1617.1,1617.0,13.0,38.0,4.2,2.0,38.0,4.2,2.1')] ).
cnf(1624,plain,
( ~ aInteger0(sdtpldt0(xp,sz10))
| ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(u,sdtpldt0(xp,sz10))),u) ),
inference(obv,[status(thm),theory(equality)],[1618]),
[iquote('0:Obv:1618.1')] ).
cnf(1625,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(u,sdtpldt0(xp,sz10))),u) ),
inference(ssi,[status(thm)],[1624,38,4,2]),
[iquote('0:SSi:1624.0,38.0,4.0,2.2')] ).
cnf(1663,plain,
( ~ aInteger0(sdtpldt0(xp,sz10))
| equal(sdtpldt0(sdtpldt0(xp,sz10),sdtpldt0(sz10,sz00)),sz00) ),
inference(spr,[status(thm),theory(equality)],[1623,31]),
[iquote('0:SpR:1623.0,31.1')] ).
cnf(1669,plain,
equal(sdtpldt0(sdtpldt0(xp,sz10),sdtpldt0(sz10,sz00)),sz00),
inference(ssi,[status(thm)],[1663,38,4,2]),
[iquote('0:SSi:1663.0,38.0,4.0,2.2')] ).
cnf(1717,plain,
( ~ aInteger0(sdtpldt0(sz10,sz00))
| ~ aInteger0(sz10)
| ~ aInteger0(xp)
| equal(sdtpldt0(xp,sdtpldt0(sz10,sdtpldt0(sz10,sz00))),sz00) ),
inference(spr,[status(thm),theory(equality)],[1669,88]),
[iquote('0:SpR:1669.0,88.3')] ).
cnf(1732,plain,
( ~ aInteger0(sdtpldt0(sz10,sz00))
| ~ aInteger0(sz10)
| ~ aInteger0(xp)
| equal(sdtpldt0(xp,sdtpldt0(sz10,sz10)),sz00) ),
inference(rew,[status(thm),theory(equality)],[22,1717]),
[iquote('0:Rew:22.1,1717.3')] ).
cnf(1733,plain,
equal(sdtpldt0(xp,sdtpldt0(sz10,sz10)),sz00),
inference(ssi,[status(thm)],[1732,4,2,38,1]),
[iquote('0:SSi:1732.2,1732.1,1732.0,4.0,2.0,38.2,2.0,1.0')] ).
cnf(1754,plain,
( ~ aInteger0(u)
| ~ aInteger0(sdtpldt0(sz10,sz10))
| ~ aInteger0(xp)
| equal(sdtpldt0(xp,sdtpldt0(sdtpldt0(sz10,sz10),u)),sdtpldt0(sz00,u)) ),
inference(spr,[status(thm),theory(equality)],[1733,88]),
[iquote('0:SpR:1733.0,88.3')] ).
cnf(1760,plain,
( ~ aInteger0(u)
| ~ aInteger0(sdtpldt0(sz10,sz10))
| ~ aInteger0(xp)
| equal(sdtpldt0(xp,sdtpldt0(sdtpldt0(sz10,sz10),u)),u) ),
inference(rew,[status(thm),theory(equality)],[23,1754]),
[iquote('0:Rew:23.1,1754.3')] ).
cnf(1761,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(xp,sdtpldt0(sdtpldt0(sz10,sz10),u)),u) ),
inference(ssi,[status(thm)],[1760,4,38,2]),
[iquote('0:SSi:1760.2,1760.1,4.0,38.0,2.2,2.0')] ).
cnf(1788,plain,
( ~ aInteger0(xp)
| ~ aInteger0(smndt0(xp))
| equal(sdtpldt0(sz10,sdtpldt0(sz10,sz00)),smndt0(xp)) ),
inference(spr,[status(thm),theory(equality)],[31,1621]),
[iquote('0:SpR:31.1,1621.1')] ).
cnf(1792,plain,
( ~ aInteger0(sdtpldt0(sz10,sz10))
| equal(sdtpldt0(sz10,sdtpldt0(sz10,sz00)),sdtpldt0(sz10,sz10)) ),
inference(spr,[status(thm),theory(equality)],[1733,1621]),
[iquote('0:SpR:1733.0,1621.1')] ).
cnf(1796,plain,
equal(sdtpldt0(sz10,sdtpldt0(sz10,sz00)),sdtpldt0(sz10,sz10)),
inference(ssi,[status(thm)],[1792,38,2]),
[iquote('0:SSi:1792.0,38.0,2.0,2.2')] ).
cnf(1797,plain,
( ~ aInteger0(xp)
| ~ aInteger0(smndt0(xp))
| equal(sdtpldt0(sz10,sz10),smndt0(xp)) ),
inference(rew,[status(thm),theory(equality)],[1796,1788]),
[iquote('0:Rew:1796.0,1788.2')] ).
cnf(1798,plain,
equal(sdtpldt0(sz10,sz10),smndt0(xp)),
inference(ssi,[status(thm)],[1797,13,4]),
[iquote('0:SSi:1797.1,1797.0,13.0,4.0,4.1')] ).
cnf(1799,plain,
equal(sdtpldt0(xp,smndt0(xp)),sz00),
inference(rew,[status(thm),theory(equality)],[1798,1733]),
[iquote('0:Rew:1798.0,1733.0')] ).
cnf(1800,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(xp,sdtpldt0(smndt0(xp),u)),u) ),
inference(rew,[status(thm),theory(equality)],[1798,1761]),
[iquote('0:Rew:1798.0,1761.1')] ).
cnf(1816,plain,
( ~ aInteger0(u)
| ~ aInteger0(sz10)
| ~ aInteger0(sz10)
| equal(sdtpldt0(smndt0(xp),u),sdtpldt0(sz10,sdtpldt0(sz10,u))) ),
inference(spr,[status(thm),theory(equality)],[1798,88]),
[iquote('0:SpR:1798.0,88.3')] ).
cnf(1822,plain,
( ~ aInteger0(u)
| ~ aInteger0(sz10)
| equal(sdtpldt0(smndt0(xp),u),sdtpldt0(sz10,sdtpldt0(sz10,u))) ),
inference(obv,[status(thm),theory(equality)],[1816]),
[iquote('0:Obv:1816.1')] ).
cnf(1823,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(smndt0(xp),u),sdtpldt0(sz10,sdtpldt0(sz10,u))) ),
inference(ssi,[status(thm)],[1822,2]),
[iquote('0:SSi:1822.1,2.0')] ).
cnf(1825,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(xp,sdtpldt0(sz10,sdtpldt0(sz10,u))),u) ),
inference(rew,[status(thm),theory(equality)],[1823,1800]),
[iquote('0:Rew:1823.1,1800.1')] ).
cnf(2002,plain,
( ~ aInteger0(sz10)
| ~ aInteger0(xp)
| ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(u,sdtpldt0(sz10,xp))),u) ),
inference(spr,[status(thm),theory(equality)],[53,1625]),
[iquote('0:SpR:53.2,1625.1')] ).
cnf(2013,plain,
( ~ aInteger0(sz10)
| ~ aInteger0(xp)
| ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(u,smndt0(sz10))),u) ),
inference(rew,[status(thm),theory(equality)],[12,2002]),
[iquote('0:Rew:12.0,2002.3')] ).
cnf(2014,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(sz10,sdtpldt0(u,smndt0(sz10))),u) ),
inference(ssi,[status(thm)],[2013,4,2]),
[iquote('0:SSi:2013.1,2013.0,4.0,2.0')] ).
cnf(2136,plain,
( ~ aInteger0(sz10)
| equal(sdtpldt0(xp,sdtpldt0(sz10,smndt0(xp))),sz10) ),
inference(spr,[status(thm),theory(equality)],[1798,1825]),
[iquote('0:SpR:1798.0,1825.1')] ).
cnf(2141,plain,
( ~ aInteger0(sz10)
| equal(sdtpldt0(xp,smndt0(sz10)),sz10) ),
inference(rew,[status(thm),theory(equality)],[16,2136]),
[iquote('0:Rew:16.0,2136.1')] ).
cnf(2142,plain,
equal(sdtpldt0(xp,smndt0(sz10)),sz10),
inference(ssi,[status(thm)],[2141,2]),
[iquote('0:SSi:2141.0,2.0')] ).
cnf(2162,plain,
( ~ aInteger0(xp)
| equal(sdtpldt0(sz10,sz10),xp) ),
inference(spr,[status(thm),theory(equality)],[2142,2014]),
[iquote('0:SpR:2142.0,2014.1')] ).
cnf(2165,plain,
( ~ aInteger0(xp)
| equal(smndt0(xp),xp) ),
inference(rew,[status(thm),theory(equality)],[1798,2162]),
[iquote('0:Rew:1798.0,2162.1')] ).
cnf(2166,plain,
equal(smndt0(xp),xp),
inference(ssi,[status(thm)],[2165,4]),
[iquote('0:SSi:2165.0,4.0')] ).
cnf(2168,plain,
equal(sdtpldt0(sz10,sz10),xp),
inference(rew,[status(thm),theory(equality)],[2166,1798]),
[iquote('0:Rew:2166.0,1798.0')] ).
cnf(2170,plain,
equal(sdtpldt0(xp,xp),sz00),
inference(rew,[status(thm),theory(equality)],[2166,1799]),
[iquote('0:Rew:2166.0,1799.0')] ).
cnf(2260,plain,
( ~ aInteger0(u)
| ~ aInteger0(sz10)
| ~ aInteger0(sz10)
| equal(sdtasdt0(xp,u),sdtpldt0(sdtasdt0(sz10,u),sdtasdt0(sz10,u))) ),
inference(spr,[status(thm),theory(equality)],[2168,98]),
[iquote('0:SpR:2168.0,98.3')] ).
cnf(2263,plain,
( ~ aInteger0(u)
| ~ aInteger0(sz10)
| equal(sdtasdt0(xp,u),sdtpldt0(sdtasdt0(sz10,u),sdtasdt0(sz10,u))) ),
inference(obv,[status(thm),theory(equality)],[2260]),
[iquote('0:Obv:2260.1')] ).
cnf(2264,plain,
( ~ aInteger0(u)
| ~ aInteger0(sz10)
| equal(sdtasdt0(xp,u),sdtpldt0(u,u)) ),
inference(rew,[status(thm),theory(equality)],[25,2263]),
[iquote('0:Rew:25.1,2263.2')] ).
cnf(2265,plain,
( ~ aInteger0(u)
| equal(sdtasdt0(xp,u),sdtpldt0(u,u)) ),
inference(ssi,[status(thm)],[2264,2]),
[iquote('0:SSi:2264.1,2.0')] ).
cnf(2345,plain,
( ~ aInteger0(u)
| ~ aInteger0(u)
| ~ aInteger0(xp)
| ~ equal(sdtpldt0(u,u),sz00)
| equal(u,sz00)
| equal(xp,sz00) ),
inference(spl,[status(thm),theory(equality)],[2265,78]),
[iquote('0:SpL:2265.1,78.2')] ).
cnf(2355,plain,
( ~ aInteger0(u)
| ~ aInteger0(xp)
| ~ equal(sdtpldt0(u,u),sz00)
| equal(u,sz00)
| equal(xp,sz00) ),
inference(obv,[status(thm),theory(equality)],[2345]),
[iquote('0:Obv:2345.0')] ).
cnf(2356,plain,
( ~ aInteger0(u)
| ~ equal(sdtpldt0(u,u),sz00)
| equal(u,sz00)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[2355,4]),
[iquote('0:SSi:2355.1,4.0')] ).
cnf(2357,plain,
( ~ aInteger0(u)
| ~ equal(sdtpldt0(u,u),sz00)
| equal(u,sz00) ),
inference(mrr,[status(thm)],[2356,10]),
[iquote('0:MRR:2356.3,10.0')] ).
cnf(3333,plain,
( ~ aInteger0(xp)
| ~ equal(sz00,sz00)
| equal(xp,sz00) ),
inference(spl,[status(thm),theory(equality)],[2170,2357]),
[iquote('0:SpL:2170.0,2357.1')] ).
cnf(3337,plain,
( ~ aInteger0(xp)
| equal(xp,sz00) ),
inference(obv,[status(thm),theory(equality)],[3333]),
[iquote('0:Obv:3333.1')] ).
cnf(3338,plain,
equal(xp,sz00),
inference(ssi,[status(thm)],[3337,4]),
[iquote('0:SSi:3337.0,4.0')] ).
cnf(3339,plain,
$false,
inference(mrr,[status(thm)],[3338,10]),
[iquote('0:MRR:3338.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM454+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 12:58:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.78/1.01
% 0.78/1.01 SPASS V 3.9
% 0.78/1.01 SPASS beiseite: Proof found.
% 0.78/1.01 % SZS status Theorem
% 0.78/1.01 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.78/1.01 SPASS derived 2013 clauses, backtracked 285 clauses, performed 7 splits and kept 1148 clauses.
% 0.78/1.01 SPASS allocated 100753 KBytes.
% 0.78/1.01 SPASS spent 0:00:00.64 on the problem.
% 0.78/1.01 0:00:00.03 for the input.
% 0.78/1.01 0:00:00.18 for the FLOTTER CNF translation.
% 0.78/1.01 0:00:00.03 for inferences.
% 0.78/1.01 0:00:00.01 for the backtracking.
% 0.78/1.01 0:00:00.36 for the reduction.
% 0.78/1.01
% 0.78/1.01
% 0.78/1.01 Here is a proof with depth 9, length 75 :
% 0.78/1.01 % SZS output start Refutation
% See solution above
% 0.78/1.01 Formulae used in the proof : mIntZero mIntOne m__2171 m__ mIntNeg mAddZero mMulOne mAddNeg mIntPlus mAddComm mZeroDiv mAddAsso mDistrib
% 0.78/1.01
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