%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM474+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 14:26:34 EDT 2022
% Result : Theorem 1.36s 1.55s
% Output : Refutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of clauses : 43 ( 19 unt; 10 nHn; 43 RR)
% Number of literals : 113 ( 0 equ; 63 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xl),
file('NUM474+2.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM474+2.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xn),
file('NUM474+2.p',unknown),
[] ).
cnf(6,axiom,
aNaturalNumber0(skc4),
file('NUM474+2.p',unknown),
[] ).
cnf(8,axiom,
aNaturalNumber0(xp),
file('NUM474+2.p',unknown),
[] ).
cnf(9,axiom,
aNaturalNumber0(xq),
file('NUM474+2.p',unknown),
[] ).
cnf(11,axiom,
aNaturalNumber0(xr),
file('NUM474+2.p',unknown),
[] ).
cnf(17,axiom,
~ equal(xl,sz00),
file('NUM474+2.p',unknown),
[] ).
cnf(19,axiom,
doDivides0(xl,sdtpldt0(xm,xn)),
file('NUM474+2.p',unknown),
[] ).
cnf(20,axiom,
equal(sdtasdt0(xl,xp),xm),
file('NUM474+2.p',unknown),
[] ).
cnf(23,axiom,
equal(sdtpldt0(xp,xr),xq),
file('NUM474+2.p',unknown),
[] ).
cnf(26,axiom,
equal(sdtasdt0(xl,skc4),sdtpldt0(xm,xn)),
file('NUM474+2.p',unknown),
[] ).
cnf(27,axiom,
equal(sdtasdt0(xl,xq),sdtpldt0(xm,xn)),
file('NUM474+2.p',unknown),
[] ).
cnf(28,axiom,
equal(sdtsldt0(sdtpldt0(xm,xn),xl),xq),
file('NUM474+2.p',unknown),
[] ).
cnf(35,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM474+2.p',unknown),
[] ).
cnf(43,axiom,
~ equal(sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)),sdtpldt0(sdtasdt0(xl,xp),xn)),
file('NUM474+2.p',unknown),
[] ).
cnf(54,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM474+2.p',unknown),
[] ).
cnf(65,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtasdt0(w,sdtpldt0(v,u)),sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u))) ),
file('NUM474+2.p',unknown),
[] ).
cnf(70,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| equal(v,sz00)
| equal(u,sdtasdt0(v,w)) ),
file('NUM474+2.p',unknown),
[] ).
cnf(76,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(v,w)
| ~ equal(w,sdtasdt0(v,u))
| equal(u,sdtsldt0(w,v))
| equal(v,sz00) ),
file('NUM474+2.p',unknown),
[] ).
cnf(79,plain,
~ equal(sdtpldt0(xm,sdtasdt0(xl,xr)),sdtpldt0(xm,xn)),
inference(rew,[status(thm),theory(equality)],[20,43]),
[iquote('0:Rew:20.0,43.0')] ).
cnf(81,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| equal(v,sz00)
| equal(w,sdtsldt0(u,v)) ),
inference(mrr,[status(thm)],[76,54]),
[iquote('0:MRR:76.3,54.4')] ).
cnf(1551,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,xq),sdtpldt0(sdtasdt0(u,xp),sdtasdt0(u,xr))) ),
inference(spr,[status(thm),theory(equality)],[23,65]),
[iquote('0:SpR:23.0,65.3')] ).
cnf(1558,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,xq),sdtpldt0(sdtasdt0(u,xp),sdtasdt0(u,xr))) ),
inference(ssi,[status(thm)],[1551,8,11]),
[iquote('0:SSi:1551.1,1551.0,8.0,11.0')] ).
cnf(1774,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xq)
| ~ equal(u,sdtpldt0(xm,xn))
| equal(xl,sz00)
| equal(sdtsldt0(u,xl),xq) ),
inference(spl,[status(thm),theory(equality)],[27,81]),
[iquote('0:SpL:27.0,81.3')] ).
cnf(1775,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(skc4)
| ~ equal(u,sdtpldt0(xm,xn))
| equal(xl,sz00)
| equal(sdtsldt0(u,xl),skc4) ),
inference(spl,[status(thm),theory(equality)],[26,81]),
[iquote('0:SpL:26.0,81.3')] ).
cnf(1786,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtpldt0(xm,xn))
| equal(xl,sz00)
| equal(sdtsldt0(u,xl),skc4) ),
inference(ssi,[status(thm)],[1775,6,3]),
[iquote('0:SSi:1775.2,1775.1,6.0,3.0')] ).
cnf(1787,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtpldt0(xm,xn))
| equal(sdtsldt0(u,xl),skc4) ),
inference(mrr,[status(thm)],[1786,17]),
[iquote('0:MRR:1786.2,17.0')] ).
cnf(1788,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xq)
| ~ equal(u,sdtpldt0(xm,xn))
| equal(xl,sz00)
| equal(xq,skc4) ),
inference(rew,[status(thm),theory(equality)],[1787,1774]),
[iquote('0:Rew:1787.2,1774.5')] ).
cnf(1789,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtpldt0(xm,xn))
| equal(xl,sz00)
| equal(xq,skc4) ),
inference(ssi,[status(thm)],[1788,9,3]),
[iquote('0:SSi:1788.2,1788.1,9.0,3.0')] ).
cnf(1790,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtpldt0(xm,xn))
| equal(xq,skc4) ),
inference(mrr,[status(thm)],[1789,17]),
[iquote('0:MRR:1789.2,17.0')] ).
cnf(2219,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ equal(u,xq)
| equal(xl,sz00)
| equal(sdtasdt0(xl,u),sdtpldt0(xm,xn)) ),
inference(spl,[status(thm),theory(equality)],[28,70]),
[iquote('0:SpL:28.0,70.3')] ).
cnf(2222,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ equal(u,xq)
| equal(xl,sz00)
| equal(sdtasdt0(xl,u),sdtpldt0(xm,xn)) ),
inference(ssi,[status(thm)],[2219,3,35,4,5]),
[iquote('0:SSi:2219.1,2219.0,3.0,35.0,4.2,5.0')] ).
cnf(2223,plain,
( ~ equal(u,xq)
| equal(sdtasdt0(xl,u),sdtpldt0(xm,xn)) ),
inference(mrr,[status(thm)],[2222,19,17]),
[iquote('0:MRR:2222.0,2222.2,19.0,17.0')] ).
cnf(2644,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| equal(xq,skc4) ),
inference(eqr,[status(thm),theory(equality)],[1790]),
[iquote('0:EqR:1790.1')] ).
cnf(2648,plain,
equal(xq,skc4),
inference(ssi,[status(thm)],[2644,35,4,5]),
[iquote('0:SSi:2644.0,35.0,4.0,5.2')] ).
cnf(2677,plain,
( ~ equal(u,skc4)
| equal(sdtasdt0(xl,u),sdtpldt0(xm,xn)) ),
inference(rew,[status(thm),theory(equality)],[2648,2223]),
[iquote('0:Rew:2648.0,2223.0')] ).
cnf(2741,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,skc4),sdtpldt0(sdtasdt0(u,xp),sdtasdt0(u,xr))) ),
inference(rew,[status(thm),theory(equality)],[2648,1558]),
[iquote('0:Rew:2648.0,1558.1')] ).
cnf(4797,plain,
( ~ aNaturalNumber0(xl)
| ~ equal(skc4,skc4)
| equal(sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)),sdtpldt0(xm,xn)) ),
inference(spr,[status(thm),theory(equality)],[2741,2677]),
[iquote('0:SpR:2741.1,2677.1')] ).
cnf(4828,plain,
( ~ aNaturalNumber0(xl)
| equal(sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)),sdtpldt0(xm,xn)) ),
inference(obv,[status(thm),theory(equality)],[4797]),
[iquote('0:Obv:4797.1')] ).
cnf(4829,plain,
( ~ aNaturalNumber0(xl)
| equal(sdtpldt0(xm,sdtasdt0(xl,xr)),sdtpldt0(xm,xn)) ),
inference(rew,[status(thm),theory(equality)],[20,4828]),
[iquote('0:Rew:20.0,4828.1')] ).
cnf(4830,plain,
equal(sdtpldt0(xm,sdtasdt0(xl,xr)),sdtpldt0(xm,xn)),
inference(ssi,[status(thm)],[4829,3]),
[iquote('0:SSi:4829.0,3.0')] ).
cnf(4831,plain,
$false,
inference(mrr,[status(thm)],[4830,79]),
[iquote('0:MRR:4830.0,79.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : NUM474+2 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.12 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Thu Jul 7 02:44:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.36/1.55
% 1.36/1.55 SPASS V 3.9
% 1.36/1.55 SPASS beiseite: Proof found.
% 1.36/1.55 % SZS status Theorem
% 1.36/1.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.36/1.55 SPASS derived 2975 clauses, backtracked 70 clauses, performed 5 splits and kept 1255 clauses.
% 1.36/1.55 SPASS allocated 101953 KBytes.
% 1.36/1.55 SPASS spent 0:00:01.14 on the problem.
% 1.36/1.55 0:00:00.04 for the input.
% 1.36/1.55 0:00:00.04 for the FLOTTER CNF translation.
% 1.36/1.55 0:00:00.03 for inferences.
% 1.36/1.55 0:00:00.00 for the backtracking.
% 1.36/1.55 0:00:00.99 for the reduction.
% 1.36/1.55
% 1.36/1.55
% 1.36/1.55 Here is a proof with depth 2, length 43 :
% 1.36/1.55 % SZS output start Refutation
% See solution above
% 1.36/1.56 Formulae used in the proof : m__1324 m__1324_04 m__1360 m__1379 m__1422 m__1347 mSortsB m__ mDefDiv mAMDistr mDefQuot
% 1.36/1.56
%------------------------------------------------------------------------------