%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM525+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 14:27:07 EDT 2022
% Result : Theorem 2.60s 2.79s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of clauses : 43 ( 21 unt; 8 nHn; 43 RR)
% Number of literals : 107 ( 0 equ; 67 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 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('NUM525+3.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM525+3.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM525+3.p',unknown),
[] ).
cnf(8,axiom,
aNaturalNumber0(skc2),
file('NUM525+3.p',unknown),
[] ).
cnf(9,axiom,
aNaturalNumber0(xq),
file('NUM525+3.p',unknown),
[] ).
cnf(14,axiom,
doDivides0(xp,xn),
file('NUM525+3.p',unknown),
[] ).
cnf(20,axiom,
~ equal(xp,sz00),
file('NUM525+3.p',unknown),
[] ).
cnf(22,axiom,
doDivides0(xp,sdtasdt0(xn,xn)),
file('NUM525+3.p',unknown),
[] ).
cnf(24,axiom,
equal(sdtasdt0(xp,xq),xn),
file('NUM525+3.p',unknown),
[] ).
cnf(25,axiom,
equal(sdtsldt0(xn,xp),xq),
file('NUM525+3.p',unknown),
[] ).
cnf(27,axiom,
equal(sdtasdt0(xp,skc2),sdtasdt0(xn,xn)),
file('NUM525+3.p',unknown),
[] ).
cnf(34,axiom,
equal(sdtasdt0(xp,sdtasdt0(xm,xm)),sdtasdt0(xn,xn)),
file('NUM525+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM525+3.p',unknown),
[] ).
cnf(48,axiom,
~ equal(sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),sdtasdt0(xp,sdtasdt0(xm,xm))),
file('NUM525+3.p',unknown),
[] ).
cnf(63,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM525+3.p',unknown),
[] ).
cnf(70,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
file('NUM525+3.p',unknown),
[] ).
cnf(83,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| equal(v,sz00)
| equal(u,sdtasdt0(v,w)) ),
file('NUM525+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('NUM525+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('NUM525+3.p',unknown),
[] ).
cnf(98,plain,
~ equal(sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),sdtasdt0(xn,xn)),
inference(rew,[status(thm),theory(equality)],[34,48]),
[iquote('0:Rew:34.0,48.0')] ).
cnf(100,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(125,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ equal(sdtasdt0(xp,sdtasdt0(xq,xq)),sdtsldt0(sdtasdt0(xn,xn),xp))
| equal(xp,sz00) ),
inference(res,[status(thm),theory(equality)],[83,98]),
[iquote('0:Res:83.4,98.0')] ).
cnf(126,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ equal(sdtasdt0(xp,sdtasdt0(xq,xq)),sdtsldt0(sdtasdt0(xn,xn),xp)) ),
inference(mrr,[status(thm)],[125,5,22,20]),
[iquote('0:MRR:125.0,125.2,125.4,5.0,22.0,20.0')] ).
cnf(147,plain,
( ~ aNaturalNumber0(skc2)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(spr,[status(thm),theory(equality)],[27,36]),
[iquote('0:SpR:27.0,36.2')] ).
cnf(153,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(ssi,[status(thm)],[147,6,5,8]),
[iquote('0:SSi:147.1,147.0,6.0,5.0,8.0')] ).
cnf(154,plain,
~ equal(sdtasdt0(xp,sdtasdt0(xq,xq)),sdtsldt0(sdtasdt0(xn,xn),xp)),
inference(mrr,[status(thm)],[126,153]),
[iquote('0:MRR:126.0,153.0')] ).
cnf(1040,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(1054,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(xp,sdtasdt0(xq,u)),sdtasdt0(xn,u)) ),
inference(ssi,[status(thm)],[1040,6,5,9]),
[iquote('0:SSi:1040.2,1040.1,6.0,5.0,9.0')] ).
cnf(3541,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)],[27,100]),
[iquote('0:SpL:27.0,100.3')] ).
cnf(3569,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtasdt0(xn,xn))
| equal(xp,sz00)
| equal(sdtsldt0(u,xp),skc2) ),
inference(ssi,[status(thm)],[3541,8,5,6]),
[iquote('0:SSi:3541.2,3541.1,8.0,5.0,6.0')] ).
cnf(3570,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtasdt0(xn,xn))
| equal(sdtsldt0(u,xp),skc2) ),
inference(mrr,[status(thm)],[3569,20]),
[iquote('0:MRR:3569.2,20.0')] ).
cnf(4587,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(4597,plain,
( ~ aNaturalNumber0(u)
| ~ doDivides0(xp,xn)
| equal(xp,sz00)
| equal(sdtasdt0(u,xq),sdtsldt0(sdtasdt0(u,xn),xp)) ),
inference(ssi,[status(thm)],[4587,5,6,3]),
[iquote('0:SSi:4587.2,4587.0,5.0,6.0,3.0')] ).
cnf(4598,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,xq),sdtsldt0(sdtasdt0(u,xn),xp)) ),
inference(mrr,[status(thm)],[4597,14,20]),
[iquote('0:MRR:4597.1,4597.2,14.0,20.0')] ).
cnf(7336,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xn))
| equal(sdtsldt0(sdtasdt0(xn,xn),xp),skc2) ),
inference(eqr,[status(thm),theory(equality)],[3570]),
[iquote('0:EqR:3570.1')] ).
cnf(7339,plain,
equal(sdtsldt0(sdtasdt0(xn,xn),xp),skc2),
inference(ssi,[status(thm)],[7336,36,3]),
[iquote('0:SSi:7336.0,36.0,3.0,3.2')] ).
cnf(7340,plain,
~ equal(sdtasdt0(xp,sdtasdt0(xq,xq)),skc2),
inference(rew,[status(thm),theory(equality)],[7339,154]),
[iquote('0:Rew:7339.0,154.0')] ).
cnf(7390,plain,
( ~ aNaturalNumber0(xq)
| ~ equal(sdtasdt0(xn,xq),skc2) ),
inference(spl,[status(thm),theory(equality)],[1054,7340]),
[iquote('0:SpL:1054.1,7340.0')] ).
cnf(7417,plain,
~ equal(sdtasdt0(xn,xq),skc2),
inference(ssi,[status(thm)],[7390,9]),
[iquote('0:SSi:7390.0,9.0')] ).
cnf(7887,plain,
( ~ aNaturalNumber0(xn)
| ~ equal(sdtsldt0(sdtasdt0(xn,xn),xp),skc2) ),
inference(spl,[status(thm),theory(equality)],[4598,7417]),
[iquote('0:SpL:4598.1,7417.0')] ).
cnf(7888,plain,
( ~ aNaturalNumber0(xn)
| ~ equal(skc2,skc2) ),
inference(rew,[status(thm),theory(equality)],[7339,7887]),
[iquote('0:Rew:7339.0,7887.1')] ).
cnf(7889,plain,
~ aNaturalNumber0(xn),
inference(obv,[status(thm),theory(equality)],[7888]),
[iquote('0:Obv:7888.1')] ).
cnf(7890,plain,
$false,
inference(ssi,[status(thm)],[7889,3]),
[iquote('0:SSi:7889.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM525+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.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 : Tue Jul 5 16:03:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.60/2.79
% 2.60/2.79 SPASS V 3.9
% 2.60/2.79 SPASS beiseite: Proof found.
% 2.60/2.79 % SZS status Theorem
% 2.60/2.79 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.60/2.79 SPASS derived 4809 clauses, backtracked 819 clauses, performed 15 splits and kept 2259 clauses.
% 2.60/2.79 SPASS allocated 104117 KBytes.
% 2.60/2.79 SPASS spent 0:00:02.22 on the problem.
% 2.60/2.79 0:00:00.04 for the input.
% 2.60/2.79 0:00:00.05 for the FLOTTER CNF translation.
% 2.60/2.79 0:00:00.06 for inferences.
% 2.60/2.79 0:00:00.02 for the backtracking.
% 2.60/2.79 0:00:02.02 for the reduction.
% 2.60/2.79
% 2.60/2.79
% 2.60/2.79 Here is a proof with depth 3, length 43 :
% 2.60/2.79 % SZS output start Refutation
% See solution above
% 2.60/2.79 Formulae used in the proof : m__2987 m__3025 m__3046 m__3059 m__3014 mSortsB_02 m__ mDefDiv mMulAsso mDefQuot mDivAsso
% 2.60/2.79
%------------------------------------------------------------------------------