TSTP Solution File: NUM463+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM463+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 14:26:27 EDT 2022
% Result : Theorem 2.86s 3.08s
% Output : Refutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of clauses : 56 ( 15 unt; 9 nHn; 56 RR)
% Number of literals : 176 ( 0 equ; 115 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aNaturalNumber0(sz00),
file('NUM463+1.p',unknown),
[] ).
cnf(2,axiom,
aNaturalNumber0(sz10),
file('NUM463+1.p',unknown),
[] ).
cnf(3,axiom,
aNaturalNumber0(xm),
file('NUM463+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xn),
file('NUM463+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(xm,sz00),
file('NUM463+1.p',unknown),
[] ).
cnf(8,axiom,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
file('NUM463+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ aNaturalNumber0(u)
| sdtlseqdt0(u,u) ),
file('NUM463+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('NUM463+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,sz10),u) ),
file('NUM463+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM463+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM463+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ aNaturalNumber0(u)
| equal(u,sz10)
| equal(u,sz00)
| sdtlseqdt0(sz10,u) ),
file('NUM463+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('NUM463+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM463+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| aNaturalNumber0(w) ),
file('NUM463+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| equal(sdtpldt0(v,w),u) ),
file('NUM463+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,w)
| ~ equal(sdtpldt0(v,u),w)
| equal(u,sdtmndt0(w,v)) ),
file('NUM463+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,u)
| equal(v,u)
| equal(w,sz00)
| sdtlseqdt0(sdtasdt0(w,v),sdtasdt0(w,u)) ),
file('NUM463+1.p',unknown),
[] ).
cnf(50,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| equal(w,sdtmndt0(u,v)) ),
inference(mrr,[status(thm)],[45,29]),
[iquote('0:MRR:45.3,29.4')] ).
cnf(58,plain,
( ~ aNaturalNumber0(xm)
| sdtlseqdt0(sz10,xm)
| equal(xm,sz10) ),
inference(res,[status(thm),theory(equality)],[19,5]),
[iquote('0:Res:19.2,5.0')] ).
cnf(84,plain,
( equal(xm,sz10)
| sdtlseqdt0(sz10,xm) ),
inference(mrr,[status(thm)],[58,3]),
[iquote('0:MRR:58.0,3.0')] ).
cnf(149,plain,
equal(xm,sz10),
inference(spt,[spt(split,[position(s1)])],[84]),
[iquote('1:Spt:84.0')] ).
cnf(150,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,sz10)),
inference(rew,[status(thm),theory(equality)],[149,8]),
[iquote('1:Rew:149.0,8.0')] ).
cnf(207,plain,
( ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xn) ),
inference(spl,[status(thm),theory(equality)],[12,150]),
[iquote('1:SpL:12.1,150.0')] ).
cnf(209,plain,
~ sdtlseqdt0(xn,xn),
inference(ssi,[status(thm)],[207,4]),
[iquote('1:SSi:207.0,4.0')] ).
cnf(212,plain,
~ aNaturalNumber0(xn),
inference(res,[status(thm),theory(equality)],[9,209]),
[iquote('1:Res:9.1,209.0')] ).
cnf(213,plain,
$false,
inference(ssi,[status(thm)],[212,4]),
[iquote('1:SSi:212.0,4.0')] ).
cnf(214,plain,
~ equal(xm,sz10),
inference(spt,[spt(split,[position(sa)])],[213,149]),
[iquote('1:Spt:213.0,84.0,149.0')] ).
cnf(215,plain,
sdtlseqdt0(sz10,xm),
inference(spt,[spt(split,[position(s2)])],[84]),
[iquote('1:Spt:213.0,84.1')] ).
cnf(525,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[29]),
[iquote('0:EqR:29.3')] ).
cnf(531,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(ssi,[status(thm)],[525,16]),
[iquote('0:SSi:525.0,16.2')] ).
cnf(540,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(u)
| sdtlseqdt0(v,sdtpldt0(u,v)) ),
inference(spr,[status(thm),theory(equality)],[20,531]),
[iquote('0:SpR:20.2,531.2')] ).
cnf(550,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[540]),
[iquote('0:Obv:540.1')] ).
cnf(792,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(eqr,[status(thm),theory(equality)],[50]),
[iquote('0:EqR:50.3')] ).
cnf(799,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(ssi,[status(thm)],[792,16]),
[iquote('0:SSi:792.0,16.2')] ).
cnf(814,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz00)
| equal(sdtmndt0(u,u),sz00) ),
inference(spr,[status(thm),theory(equality)],[10,799]),
[iquote('0:SpR:10.1,799.2')] ).
cnf(821,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz00)
| equal(sdtmndt0(u,u),sz00) ),
inference(obv,[status(thm),theory(equality)],[814]),
[iquote('0:Obv:814.0')] ).
cnf(822,plain,
( ~ aNaturalNumber0(u)
| equal(sdtmndt0(u,u),sz00) ),
inference(ssi,[status(thm)],[821,1]),
[iquote('0:SSi:821.1,1.0')] ).
cnf(847,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,u)
| ~ equal(v,sz00)
| aNaturalNumber0(v) ),
inference(spl,[status(thm),theory(equality)],[822,30]),
[iquote('0:SpL:822.1,30.3')] ).
cnf(848,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,u)
| ~ equal(v,sz00)
| aNaturalNumber0(v) ),
inference(obv,[status(thm),theory(equality)],[847]),
[iquote('0:Obv:847.1')] ).
cnf(849,plain,
( ~ aNaturalNumber0(u)
| ~ equal(v,sz00)
| aNaturalNumber0(v) ),
inference(mrr,[status(thm)],[848,9]),
[iquote('0:MRR:848.1,9.1')] ).
cnf(855,plain,
( ~ equal(u,sz00)
| aNaturalNumber0(u) ),
inference(ems,[status(thm)],[849,3]),
[iquote('0:EmS:849.0,3.0')] ).
cnf(1128,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,u)
| ~ equal(v,sz00)
| equal(sdtpldt0(u,v),u) ),
inference(spl,[status(thm),theory(equality)],[822,36]),
[iquote('0:SpL:822.1,36.3')] ).
cnf(1130,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,u)
| ~ equal(v,sz00)
| equal(sdtpldt0(u,v),u) ),
inference(obv,[status(thm),theory(equality)],[1128]),
[iquote('0:Obv:1128.1')] ).
cnf(1131,plain,
( ~ aNaturalNumber0(u)
| ~ equal(v,sz00)
| equal(sdtpldt0(u,v),u) ),
inference(mrr,[status(thm)],[1130,9]),
[iquote('0:MRR:1130.1,9.1')] ).
cnf(1311,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(u)
| ~ equal(v,sz00)
| sdtlseqdt0(v,u) ),
inference(spr,[status(thm),theory(equality)],[1131,550]),
[iquote('0:SpR:1131.2,550.2')] ).
cnf(1345,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(u,sz00)
| sdtlseqdt0(u,v) ),
inference(obv,[status(thm),theory(equality)],[1311]),
[iquote('0:Obv:1311.0')] ).
cnf(1346,plain,
( ~ aNaturalNumber0(u)
| ~ equal(v,sz00)
| sdtlseqdt0(v,u) ),
inference(mrr,[status(thm)],[1345,855]),
[iquote('0:MRR:1345.0,855.1')] ).
cnf(1380,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ equal(xn,sz00) ),
inference(res,[status(thm),theory(equality)],[1346,8]),
[iquote('0:Res:1346.2,8.0')] ).
cnf(1389,plain,
~ equal(xn,sz00),
inference(ssi,[status(thm)],[1380,17,4,3]),
[iquote('0:SSi:1380.0,17.0,4.0,3.2')] ).
cnf(1926,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(sz10,v)
| equal(sz10,v)
| equal(u,sz00)
| sdtlseqdt0(u,sdtasdt0(u,v)) ),
inference(spr,[status(thm),theory(equality)],[12,47]),
[iquote('0:SpR:12.1,47.6')] ).
cnf(1944,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(sz10,u)
| equal(sz10,u)
| equal(v,sz00)
| sdtlseqdt0(v,sdtasdt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[1926]),
[iquote('0:Obv:1926.0')] ).
cnf(1945,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(sz10,u)
| equal(sz10,u)
| equal(v,sz00)
| sdtlseqdt0(v,sdtasdt0(v,u)) ),
inference(ssi,[status(thm)],[1944,2]),
[iquote('0:SSi:1944.1,2.0')] ).
cnf(7546,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(sz10,xm)
| equal(xm,sz10)
| equal(xn,sz00) ),
inference(res,[status(thm),theory(equality)],[1945,8]),
[iquote('0:Res:1945.5,8.0')] ).
cnf(7550,plain,
( ~ sdtlseqdt0(sz10,xm)
| equal(xm,sz10)
| equal(xn,sz00) ),
inference(ssi,[status(thm)],[7546,4,3]),
[iquote('0:SSi:7546.1,7546.0,4.0,3.0')] ).
cnf(7551,plain,
$false,
inference(mrr,[status(thm)],[7550,215,214,1389]),
[iquote('1:MRR:7550.0,7550.1,7550.2,215.0,214.0,1389.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM463+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 00:07:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.86/3.08
% 2.86/3.08 SPASS V 3.9
% 2.86/3.08 SPASS beiseite: Proof found.
% 2.86/3.08 % SZS status Theorem
% 2.86/3.08 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.86/3.08 SPASS derived 4471 clauses, backtracked 31 clauses, performed 2 splits and kept 1379 clauses.
% 2.86/3.08 SPASS allocated 104518 KBytes.
% 2.86/3.08 SPASS spent 0:00:02.27 on the problem.
% 2.86/3.08 0:00:00.04 for the input.
% 2.86/3.08 0:00:00.03 for the FLOTTER CNF translation.
% 2.86/3.08 0:00:00.06 for inferences.
% 2.86/3.08 0:00:00.02 for the backtracking.
% 2.86/3.08 0:00:02.09 for the reduction.
% 2.86/3.08
% 2.86/3.08
% 2.86/3.08 Here is a proof with depth 5, length 56 :
% 2.86/3.08 % SZS output start Refutation
% See solution above
% 2.86/3.08 Formulae used in the proof : mSortsC mSortsC_01 m__987 m__ mLERefl m_AddZero m_MulUnit mSortsB mSortsB_02 mLENTr mAddComm mDefLE mDefDiff mMonMul
% 2.86/3.08
%------------------------------------------------------------------------------