TSTP Solution File: NUM508+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM508+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 14:26:56 EDT 2022
% Result : Theorem 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of clauses : 29 ( 15 unt; 3 nHn; 29 RR)
% Number of literals : 78 ( 0 equ; 54 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM508+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM508+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM508+1.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM508+1.p',unknown),
[] ).
cnf(7,axiom,
aNaturalNumber0(xr),
file('NUM508+1.p',unknown),
[] ).
cnf(8,axiom,
isPrime0(xr),
file('NUM508+1.p',unknown),
[] ).
cnf(16,axiom,
~ doDivides0(xr,xn),
file('NUM508+1.p',unknown),
[] ).
cnf(17,axiom,
~ doDivides0(xr,xm),
file('NUM508+1.p',unknown),
[] ).
cnf(31,axiom,
doDivides0(xr,sdtasdt0(xn,xm)),
file('NUM508+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM508+1.p',unknown),
[] ).
cnf(44,axiom,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
file('NUM508+1.p',unknown),
[] ).
cnf(48,axiom,
~ equal(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
file('NUM508+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| iLess0(v,u)
| equal(v,u) ),
file('NUM508+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('NUM508+1.p',unknown),
[] ).
cnf(96,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ isPrime0(w)
| ~ iLess0(sdtpldt0(sdtpldt0(u,v),w),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(w,sdtasdt0(u,v))
| doDivides0(w,u)
| doDivides0(w,v) ),
file('NUM508+1.p',unknown),
[] ).
cnf(99,plain,
( ~ isPrime0(u)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(u,sdtasdt0(w,v))
| ~ iLess0(sdtpldt0(w,sdtpldt0(v,u)),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(u,v)
| doDivides0(u,w) ),
inference(rew,[status(thm),theory(equality)],[75,96]),
[iquote('0:Rew:75.3,96.4')] ).
cnf(105,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xr)
| ~ isPrime0(xr)
| ~ iLess0(sdtpldt0(xn,sdtpldt0(u,xr)),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(xr,sdtasdt0(xn,u))
| doDivides0(xr,u) ),
inference(res,[status(thm),theory(equality)],[99,16]),
[iquote('0:Res:99.6,16.0')] ).
cnf(117,plain,
( ~ aNaturalNumber0(u)
| ~ doDivides0(xr,sdtasdt0(xn,u))
| ~ iLess0(sdtpldt0(xn,sdtpldt0(u,xr)),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(xr,u) ),
inference(mrr,[status(thm)],[105,3,7,8]),
[iquote('0:MRR:105.0,105.2,105.3,3.0,7.0,8.0')] ).
cnf(126,plain,
( ~ aNaturalNumber0(xm)
| ~ iLess0(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(res,[status(thm),theory(equality)],[117,17]),
[iquote('0:Res:117.3,17.0')] ).
cnf(129,plain,
~ iLess0(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(mrr,[status(thm)],[126,4,31]),
[iquote('0:MRR:126.0,126.2,4.0,31.0')] ).
cnf(543,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xr)))
| ~ sdtlseqdt0(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(sdtpldt0(xn,xm),xp))
| equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xr))) ),
inference(res,[status(thm),theory(equality)],[58,129]),
[iquote('0:Res:58.3,129.0')] ).
cnf(546,plain,
( ~ sdtlseqdt0(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(sdtpldt0(xn,xm),xp))
| equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xr))) ),
inference(ssi,[status(thm)],[543,40,3,4,8,7,6,5]),
[iquote('0:SSi:543.1,543.0,40.0,3.0,40.0,4.0,8.2,7.2,40.0,40.0,3.0,4.2,6.0,5.2')] ).
cnf(880,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(spr,[status(thm),theory(equality)],[75,44]),
[iquote('0:SpR:75.3,44.0')] ).
cnf(895,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xr))) ),
inference(spl,[status(thm),theory(equality)],[75,48]),
[iquote('0:SpL:75.3,48.0')] ).
cnf(908,plain,
sdtlseqdt0(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(ssi,[status(thm)],[880,3,4,8,7]),
[iquote('0:SSi:880.2,880.1,880.0,3.0,4.0,8.0,7.0')] ).
cnf(909,plain,
equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xr))),
inference(mrr,[status(thm)],[546,908]),
[iquote('0:MRR:546.0,908.0')] ).
cnf(930,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ equal(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(xn,sdtpldt0(xm,xr))) ),
inference(rew,[status(thm),theory(equality)],[909,895]),
[iquote('0:Rew:909.0,895.3')] ).
cnf(931,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(obv,[status(thm),theory(equality)],[930]),
[iquote('0:Obv:930.3')] ).
cnf(932,plain,
$false,
inference(ssi,[status(thm)],[931,3,4,8,7]),
[iquote('0:SSi:931.2,931.1,931.0,3.0,4.0,8.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM508+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 11:24:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.53
% 0.19/0.53 SPASS V 3.9
% 0.19/0.53 SPASS beiseite: Proof found.
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.53 SPASS derived 542 clauses, backtracked 76 clauses, performed 3 splits and kept 395 clauses.
% 0.19/0.53 SPASS allocated 98431 KBytes.
% 0.19/0.53 SPASS spent 0:00:00.19 on the problem.
% 0.19/0.53 0:00:00.04 for the input.
% 0.19/0.53 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.53 0:00:00.01 for inferences.
% 0.19/0.53 0:00:00.00 for the backtracking.
% 0.19/0.53 0:00:00.07 for the reduction.
% 0.19/0.53
% 0.19/0.53
% 0.19/0.53 Here is a proof with depth 3, length 29 :
% 0.19/0.53 % SZS output start Refutation
% See solution above
% 0.19/0.53 Formulae used in the proof : m__1837 m__1860 m__2342 m__ m__2362 mSortsB m__2478 mIH_03 mAddAsso m__1799
% 0.19/0.53
%------------------------------------------------------------------------------