TSTP Solution File: NUM524+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM524+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 14:27:06 EDT 2022
% Result : Theorem 9.07s 9.25s
% Output : Refutation 9.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of clauses : 42 ( 19 unt; 10 nHn; 42 RR)
% Number of literals : 110 ( 0 equ; 66 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM524+3.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM524+3.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM524+3.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM524+3.p',unknown),
[] ).
cnf(8,axiom,
aNaturalNumber0(skc2),
file('NUM524+3.p',unknown),
[] ).
cnf(9,axiom,
aNaturalNumber0(xq),
file('NUM524+3.p',unknown),
[] ).
cnf(14,axiom,
doDivides0(xp,xn),
file('NUM524+3.p',unknown),
[] ).
cnf(20,axiom,
~ equal(xp,sz00),
file('NUM524+3.p',unknown),
[] ).
cnf(24,axiom,
equal(sdtasdt0(xp,xq),xn),
file('NUM524+3.p',unknown),
[] ).
cnf(25,axiom,
equal(sdtsldt0(xn,xp),xq),
file('NUM524+3.p',unknown),
[] ).
cnf(27,axiom,
equal(sdtasdt0(xp,skc2),sdtasdt0(xn,xn)),
file('NUM524+3.p',unknown),
[] ).
cnf(34,axiom,
equal(sdtasdt0(xp,sdtasdt0(xm,xm)),sdtasdt0(xn,xn)),
file('NUM524+3.p',unknown),
[] ).
cnf(35,axiom,
~ equal(sdtasdt0(xp,sdtasdt0(xq,xq)),sdtasdt0(xm,xm)),
file('NUM524+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM524+3.p',unknown),
[] ).
cnf(63,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM524+3.p',unknown),
[] ).
cnf(70,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
file('NUM524+3.p',unknown),
[] ).
cnf(89,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(w,u)
| equal(w,sz00)
| equal(sdtasdt0(v,sdtsldt0(u,w)),sdtsldt0(sdtasdt0(v,u),w)) ),
file('NUM524+3.p',unknown),
[] ).
cnf(90,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(v,w)
| ~ equal(w,sdtasdt0(v,u))
| equal(u,sdtsldt0(w,v))
| equal(v,sz00) ),
file('NUM524+3.p',unknown),
[] ).
cnf(99,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| equal(v,sz00)
| equal(w,sdtsldt0(u,v)) ),
inference(mrr,[status(thm)],[90,63]),
[iquote('0:MRR:90.3,63.4')] ).
cnf(1127,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| equal(sdtasdt0(xp,sdtasdt0(xq,u)),sdtasdt0(xn,u)) ),
inference(spr,[status(thm),theory(equality)],[24,70]),
[iquote('0:SpR:24.0,70.3')] ).
cnf(1141,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(xp,sdtasdt0(xq,u)),sdtasdt0(xn,u)) ),
inference(ssi,[status(thm)],[1127,6,5,9]),
[iquote('0:SSi:1127.2,1127.1,6.0,5.0,9.0')] ).
cnf(5132,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,xn)
| equal(xp,sz00)
| equal(sdtasdt0(u,xq),sdtsldt0(sdtasdt0(u,xn),xp)) ),
inference(spr,[status(thm),theory(equality)],[25,89]),
[iquote('0:SpR:25.0,89.5')] ).
cnf(5138,plain,
( ~ aNaturalNumber0(u)
| ~ doDivides0(xp,xn)
| equal(xp,sz00)
| equal(sdtasdt0(u,xq),sdtsldt0(sdtasdt0(u,xn),xp)) ),
inference(ssi,[status(thm)],[5132,5,6,3]),
[iquote('0:SSi:5132.2,5132.0,5.0,6.0,3.0')] ).
cnf(5139,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,xq),sdtsldt0(sdtasdt0(u,xn),xp)) ),
inference(mrr,[status(thm)],[5138,14,20]),
[iquote('0:MRR:5138.1,5138.2,14.0,20.0')] ).
cnf(5200,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(skc2)
| ~ equal(u,sdtasdt0(xn,xn))
| equal(xp,sz00)
| equal(sdtsldt0(u,xp),skc2) ),
inference(spl,[status(thm),theory(equality)],[27,99]),
[iquote('0:SpL:27.0,99.3')] ).
cnf(5210,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtasdt0(xn,xn))
| equal(xp,sz00)
| equal(sdtsldt0(u,xp),skc2) ),
inference(ssi,[status(thm)],[5200,8,5,6]),
[iquote('0:SSi:5200.2,5200.1,8.0,5.0,6.0')] ).
cnf(5211,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtasdt0(xn,xn))
| equal(sdtsldt0(u,xp),skc2) ),
inference(mrr,[status(thm)],[5210,20]),
[iquote('0:MRR:5210.2,20.0')] ).
cnf(5258,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ equal(u,sdtasdt0(xn,xn))
| equal(xp,sz00)
| equal(sdtasdt0(xm,xm),sdtsldt0(u,xp)) ),
inference(spl,[status(thm),theory(equality)],[34,99]),
[iquote('0:SpL:34.0,99.3')] ).
cnf(5269,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ equal(u,sdtasdt0(xn,xn))
| equal(xp,sz00)
| equal(sdtasdt0(xm,xm),skc2) ),
inference(rew,[status(thm),theory(equality)],[5211,5258]),
[iquote('0:Rew:5211.2,5258.5')] ).
cnf(5270,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtasdt0(xn,xn))
| equal(xp,sz00)
| equal(sdtasdt0(xm,xm),skc2) ),
inference(ssi,[status(thm)],[5269,37,4,5,6]),
[iquote('0:SSi:5269.2,5269.1,37.0,4.0,4.0,5.0,6.2')] ).
cnf(5271,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtasdt0(xn,xn))
| equal(sdtasdt0(xm,xm),skc2) ),
inference(mrr,[status(thm)],[5270,20]),
[iquote('0:MRR:5270.2,20.0')] ).
cnf(12744,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xn))
| equal(sdtasdt0(xm,xm),skc2) ),
inference(eqr,[status(thm),theory(equality)],[5271]),
[iquote('0:EqR:5271.1')] ).
cnf(12747,plain,
equal(sdtasdt0(xm,xm),skc2),
inference(ssi,[status(thm)],[12744,37,3]),
[iquote('0:SSi:12744.0,37.0,3.0,3.2')] ).
cnf(12754,plain,
~ equal(sdtasdt0(xp,sdtasdt0(xq,xq)),skc2),
inference(rew,[status(thm),theory(equality)],[12747,35]),
[iquote('0:Rew:12747.0,35.0')] ).
cnf(12917,plain,
( ~ aNaturalNumber0(xq)
| ~ equal(sdtasdt0(xn,xq),skc2) ),
inference(spl,[status(thm),theory(equality)],[1141,12754]),
[iquote('0:SpL:1141.1,12754.0')] ).
cnf(17692,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xn))
| equal(sdtsldt0(sdtasdt0(xn,xn),xp),skc2) ),
inference(eqr,[status(thm),theory(equality)],[5211]),
[iquote('0:EqR:5211.1')] ).
cnf(17695,plain,
equal(sdtsldt0(sdtasdt0(xn,xn),xp),skc2),
inference(ssi,[status(thm)],[17692,37,3]),
[iquote('0:SSi:17692.0,37.0,3.0,3.2')] ).
cnf(17713,plain,
~ equal(sdtasdt0(xn,xq),skc2),
inference(ssi,[status(thm)],[12917,9]),
[iquote('0:SSi:12917.0,9.0')] ).
cnf(18110,plain,
( ~ aNaturalNumber0(xn)
| ~ equal(sdtsldt0(sdtasdt0(xn,xn),xp),skc2) ),
inference(spl,[status(thm),theory(equality)],[5139,17713]),
[iquote('0:SpL:5139.1,17713.0')] ).
cnf(18111,plain,
( ~ aNaturalNumber0(xn)
| ~ equal(skc2,skc2) ),
inference(rew,[status(thm),theory(equality)],[17695,18110]),
[iquote('0:Rew:17695.0,18110.1')] ).
cnf(18112,plain,
~ aNaturalNumber0(xn),
inference(obv,[status(thm),theory(equality)],[18111]),
[iquote('0:Obv:18111.1')] ).
cnf(18113,plain,
$false,
inference(ssi,[status(thm)],[18112,3]),
[iquote('0:SSi:18112.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : NUM524+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jul 5 21:21:43 EDT 2022
% 0.14/0.36 % CPUTime :
% 9.07/9.25
% 9.07/9.25 SPASS V 3.9
% 9.07/9.25 SPASS beiseite: Proof found.
% 9.07/9.25 % SZS status Theorem
% 9.07/9.25 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.07/9.25 SPASS derived 11828 clauses, backtracked 2961 clauses, performed 25 splits and kept 5314 clauses.
% 9.07/9.25 SPASS allocated 111514 KBytes.
% 9.07/9.25 SPASS spent 0:00:07.24 on the problem.
% 9.07/9.25 0:00:00.04 for the input.
% 9.07/9.25 0:00:00.04 for the FLOTTER CNF translation.
% 9.07/9.25 0:00:00.14 for inferences.
% 9.07/9.25 0:00:00.08 for the backtracking.
% 9.07/9.25 0:00:06.87 for the reduction.
% 9.07/9.25
% 9.07/9.25
% 9.07/9.25 Here is a proof with depth 3, length 42 :
% 9.07/9.25 % SZS output start Refutation
% See solution above
% 9.07/9.25 Formulae used in the proof : m__2987 m__3025 m__3046 m__3059 m__3014 m__ mSortsB_02 mDefDiv mMulAsso mDivAsso mDefQuot
% 9.07/9.25
%------------------------------------------------------------------------------