TSTP Solution File: NUM471+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM471+2 : 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 14:26:32 EDT 2022
% Result : Theorem 1.98s 2.20s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of clauses : 42 ( 16 unt; 11 nHn; 42 RR)
% Number of literals : 124 ( 0 equ; 75 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xl),
file('NUM471+2.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM471+2.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xn),
file('NUM471+2.p',unknown),
[] ).
cnf(8,axiom,
aNaturalNumber0(xp),
file('NUM471+2.p',unknown),
[] ).
cnf(9,axiom,
aNaturalNumber0(xq),
file('NUM471+2.p',unknown),
[] ).
cnf(11,axiom,
~ sdtlseqdt0(xp,xq),
file('NUM471+2.p',unknown),
[] ).
cnf(15,axiom,
~ equal(xl,sz00),
file('NUM471+2.p',unknown),
[] ).
cnf(18,axiom,
equal(sdtasdt0(xl,xp),xm),
file('NUM471+2.p',unknown),
[] ).
cnf(22,axiom,
equal(sdtasdt0(xl,xq),sdtpldt0(xm,xn)),
file('NUM471+2.p',unknown),
[] ).
cnf(23,axiom,
equal(sdtsldt0(sdtpldt0(xm,xn),xl),xq),
file('NUM471+2.p',unknown),
[] ).
cnf(31,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM471+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(v,u)
| sdtlseqdt0(u,v) ),
file('NUM471+2.p',unknown),
[] ).
cnf(37,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(u,v)
| sdtlseqdt0(v,u) ),
file('NUM471+2.p',unknown),
[] ).
cnf(44,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ sdtlseqdt0(u,v)
| equal(v,u) ),
file('NUM471+2.p',unknown),
[] ).
cnf(47,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM471+2.p',unknown),
[] ).
cnf(49,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM471+2.p',unknown),
[] ).
cnf(70,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,u)
| equal(v,u)
| equal(w,sz00)
| sdtlseqdt0(sdtasdt0(w,v),sdtasdt0(w,u)) ),
file('NUM471+2.p',unknown),
[] ).
cnf(71,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(v,w)
| ~ equal(w,sdtasdt0(v,u))
| equal(u,sdtsldt0(w,v))
| equal(v,sz00) ),
file('NUM471+2.p',unknown),
[] ).
cnf(75,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| equal(v,sz00)
| equal(w,sdtsldt0(u,v)) ),
inference(mrr,[status(thm)],[71,49]),
[iquote('0:MRR:71.3,49.4')] ).
cnf(76,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(xq,xp) ),
inference(res,[status(thm),theory(equality)],[33,11]),
[iquote('0:Res:33.2,11.0')] ).
cnf(77,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq)
| ~ equal(xq,xp) ),
inference(res,[status(thm),theory(equality)],[37,11]),
[iquote('0:Res:37.3,11.0')] ).
cnf(92,plain,
sdtlseqdt0(xq,xp),
inference(mrr,[status(thm)],[76,9,8]),
[iquote('0:MRR:76.0,76.1,9.0,8.0')] ).
cnf(93,plain,
~ equal(xq,xp),
inference(mrr,[status(thm)],[77,8,9]),
[iquote('0:MRR:77.0,77.1,8.0,9.0')] ).
cnf(651,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[47]),
[iquote('0:EqR:47.3')] ).
cnf(658,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(ssi,[status(thm)],[651,31]),
[iquote('0:SSi:651.0,31.2')] ).
cnf(1793,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xp)
| ~ equal(u,xm)
| equal(xl,sz00)
| equal(sdtsldt0(u,xl),xp) ),
inference(spl,[status(thm),theory(equality)],[18,75]),
[iquote('0:SpL:18.0,75.3')] ).
cnf(1808,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xm)
| equal(xl,sz00)
| equal(sdtsldt0(u,xl),xp) ),
inference(ssi,[status(thm)],[1793,8,3]),
[iquote('0:SSi:1793.2,1793.1,8.0,3.0')] ).
cnf(1809,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xm)
| equal(sdtsldt0(u,xl),xp) ),
inference(mrr,[status(thm)],[1808,15]),
[iquote('0:MRR:1808.2,15.0')] ).
cnf(2381,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xl)
| ~ sdtlseqdt0(u,xp)
| equal(u,xp)
| equal(xl,sz00)
| sdtlseqdt0(sdtasdt0(xl,u),xm) ),
inference(spr,[status(thm),theory(equality)],[18,70]),
[iquote('0:SpR:18.0,70.6')] ).
cnf(2421,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,xp)
| equal(u,xp)
| equal(xl,sz00)
| sdtlseqdt0(sdtasdt0(xl,u),xm) ),
inference(ssi,[status(thm)],[2381,3,8]),
[iquote('0:SSi:2381.2,2381.0,3.0,8.0')] ).
cnf(2422,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,xp)
| equal(u,xp)
| sdtlseqdt0(sdtasdt0(xl,u),xm) ),
inference(mrr,[status(thm)],[2421,15]),
[iquote('0:MRR:2421.3,15.0')] ).
cnf(2830,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ equal(sdtpldt0(xm,xn),xm)
| equal(xq,xp) ),
inference(spr,[status(thm),theory(equality)],[1809,23]),
[iquote('0:SpR:1809.2,23.0')] ).
cnf(2834,plain,
( ~ equal(sdtpldt0(xm,xn),xm)
| equal(xq,xp) ),
inference(ssi,[status(thm)],[2830,31,4,5]),
[iquote('0:SSi:2830.0,31.0,4.0,5.2')] ).
cnf(2835,plain,
~ equal(sdtpldt0(xm,xn),xm),
inference(mrr,[status(thm)],[2834,93]),
[iquote('0:MRR:2834.1,93.0')] ).
cnf(7974,plain,
( ~ aNaturalNumber0(xq)
| ~ sdtlseqdt0(xq,xp)
| equal(xq,xp)
| sdtlseqdt0(sdtpldt0(xm,xn),xm) ),
inference(spr,[status(thm),theory(equality)],[22,2422]),
[iquote('0:SpR:22.0,2422.3')] ).
cnf(7981,plain,
( ~ sdtlseqdt0(xq,xp)
| equal(xq,xp)
| sdtlseqdt0(sdtpldt0(xm,xn),xm) ),
inference(ssi,[status(thm)],[7974,9]),
[iquote('0:SSi:7974.0,9.0')] ).
cnf(7982,plain,
sdtlseqdt0(sdtpldt0(xm,xn),xm),
inference(mrr,[status(thm)],[7981,92,93]),
[iquote('0:MRR:7981.0,7981.1,92.0,93.0')] ).
cnf(7993,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| equal(sdtpldt0(xm,xn),xm) ),
inference(res,[status(thm),theory(equality)],[7982,44]),
[iquote('0:Res:7982.0,44.2')] ).
cnf(7995,plain,
( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| equal(sdtpldt0(xm,xn),xm) ),
inference(ssi,[status(thm)],[7993,31,4,5]),
[iquote('0:SSi:7993.1,7993.0,31.0,4.0,5.0,4.2')] ).
cnf(7996,plain,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(mrr,[status(thm)],[7995,2835]),
[iquote('0:MRR:7995.1,2835.0')] ).
cnf(7999,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(res,[status(thm),theory(equality)],[658,7996]),
[iquote('0:Res:658.2,7996.0')] ).
cnf(8001,plain,
$false,
inference(ssi,[status(thm)],[7999,5,4]),
[iquote('0:SSi:7999.1,7999.0,5.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM471+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 5 06:47:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.98/2.20
% 1.98/2.20 SPASS V 3.9
% 1.98/2.20 SPASS beiseite: Proof found.
% 1.98/2.20 % SZS status Theorem
% 1.98/2.20 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.98/2.20 SPASS derived 5316 clauses, backtracked 539 clauses, performed 6 splits and kept 2046 clauses.
% 1.98/2.20 SPASS allocated 103865 KBytes.
% 1.98/2.20 SPASS spent 0:00:01.59 on the problem.
% 1.98/2.20 0:00:00.04 for the input.
% 1.98/2.20 0:00:00.04 for the FLOTTER CNF translation.
% 1.98/2.20 0:00:00.06 for inferences.
% 1.98/2.20 0:00:00.02 for the backtracking.
% 1.98/2.20 0:00:01.39 for the reduction.
% 1.98/2.20
% 1.98/2.20
% 1.98/2.20 Here is a proof with depth 4, length 42 :
% 1.98/2.20 % SZS output start Refutation
% See solution above
% 1.98/2.20 Formulae used in the proof : m__1324 m__1360 m__1379 m__ m__1347 mSortsB mLETotal mLEAsym mDefLE mDefDiv mMonMul mDefQuot
% 1.98/2.20
%------------------------------------------------------------------------------