%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM529+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 14:27:09 EDT 2022
% Result : Theorem 4.83s 5.04s
% Output : Refutation 4.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 22
% Syntax : Number of clauses : 51 ( 19 unt; 18 nHn; 51 RR)
% Number of literals : 162 ( 0 equ; 99 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM529+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM529+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM529+1.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM529+1.p',unknown),
[] ).
cnf(9,axiom,
doDivides0(xp,xn),
file('NUM529+1.p',unknown),
[] ).
cnf(10,axiom,
sdtlseqdt0(xm,xn),
file('NUM529+1.p',unknown),
[] ).
cnf(14,axiom,
~ equal(xn,sz00),
file('NUM529+1.p',unknown),
[] ).
cnf(15,axiom,
~ equal(xm,sz00),
file('NUM529+1.p',unknown),
[] ).
cnf(16,axiom,
~ equal(xp,sz00),
file('NUM529+1.p',unknown),
[] ).
cnf(17,axiom,
~ equal(xm,xn),
file('NUM529+1.p',unknown),
[] ).
cnf(19,axiom,
equal(sdtsldt0(xn,xp),xq),
file('NUM529+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,sz00),sz00) ),
file('NUM529+1.p',unknown),
[] ).
cnf(27,axiom,
equal(sdtasdt0(xp,sdtasdt0(xm,xm)),sdtasdt0(xn,xn)),
file('NUM529+1.p',unknown),
[] ).
cnf(28,axiom,
equal(sdtasdt0(xp,sdtasdt0(xq,xq)),sdtasdt0(xm,xm)),
file('NUM529+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM529+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ aNaturalNumber0(u)
| ~ isPrime0(u)
| ~ equal(u,sz00) ),
file('NUM529+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| iLess0(v,u)
| equal(v,u) ),
file('NUM529+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM529+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| aNaturalNumber0(w)
| equal(v,sz00) ),
file('NUM529+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| equal(v,sz00)
| equal(u,sdtasdt0(v,w)) ),
file('NUM529+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(v,w)
| ~ equal(w,sdtasdt0(v,u))
| equal(u,sdtsldt0(w,v))
| equal(v,sz00) ),
file('NUM529+1.p',unknown),
[] ).
cnf(84,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ isPrime0(w)
| ~ iLess0(u,xn)
| ~ equal(sdtasdt0(w,sdtasdt0(v,v)),sdtasdt0(u,u))
| equal(u,sz00)
| equal(v,sz00)
| equal(w,sz00) ),
file('NUM529+1.p',unknown),
[] ).
cnf(86,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| equal(v,sz00)
| equal(w,sdtsldt0(u,v)) ),
inference(mrr,[status(thm)],[81,55]),
[iquote('0:MRR:81.3,55.4')] ).
cnf(87,plain,
( ~ isPrime0(u)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ iLess0(w,xn)
| ~ equal(sdtasdt0(u,sdtasdt0(v,v)),sdtasdt0(w,w))
| equal(v,sz00)
| equal(w,sz00) ),
inference(mrr,[status(thm)],[84,31]),
[iquote('0:MRR:84.8,31.2')] ).
cnf(1305,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| aNaturalNumber0(sdtsldt0(u,v))
| equal(v,sz00) ),
inference(eqr,[status(thm),theory(equality)],[63]),
[iquote('0:EqR:63.3')] ).
cnf(1956,plain,
( ~ aNaturalNumber0(sdtasdt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(u,sz00)
| equal(sdtsldt0(sdtasdt0(u,v),u),v) ),
inference(eqr,[status(thm),theory(equality)],[86]),
[iquote('0:EqR:86.3')] ).
cnf(1972,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(u,sz00)
| equal(sdtsldt0(sdtasdt0(u,v),u),v) ),
inference(ssi,[status(thm)],[1956,30]),
[iquote('0:SSi:1956.0,30.2')] ).
cnf(8184,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,xn)
| ~ equal(u,xq)
| equal(xp,sz00)
| equal(sdtasdt0(xp,u),xn) ),
inference(spl,[status(thm),theory(equality)],[19,74]),
[iquote('0:SpL:19.0,74.3')] ).
cnf(8186,plain,
( ~ doDivides0(xp,xn)
| ~ equal(u,xq)
| equal(xp,sz00)
| equal(sdtasdt0(xp,u),xn) ),
inference(ssi,[status(thm)],[8184,5,6,3]),
[iquote('0:SSi:8184.1,8184.0,5.0,6.0,3.0')] ).
cnf(8187,plain,
( ~ equal(u,xq)
| equal(sdtasdt0(xp,u),xn) ),
inference(mrr,[status(thm)],[8186,9,16]),
[iquote('0:MRR:8186.0,8186.2,9.0,16.0')] ).
cnf(8209,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| equal(xp,sz00)
| equal(sdtasdt0(xm,xm),sdtsldt0(sdtasdt0(xn,xn),xp)) ),
inference(spr,[status(thm),theory(equality)],[27,1972]),
[iquote('0:SpR:27.0,1972.3')] ).
cnf(8235,plain,
( equal(xp,sz00)
| equal(sdtasdt0(xm,xm),sdtsldt0(sdtasdt0(xn,xn),xp)) ),
inference(ssi,[status(thm)],[8209,30,4,5,6]),
[iquote('0:SSi:8209.1,8209.0,30.0,4.0,4.0,5.0,6.2')] ).
cnf(8236,plain,
equal(sdtasdt0(xm,xm),sdtsldt0(sdtasdt0(xn,xn),xp)),
inference(mrr,[status(thm)],[8235,16]),
[iquote('0:MRR:8235.0,16.0')] ).
cnf(8247,plain,
equal(sdtasdt0(xp,sdtasdt0(xq,xq)),sdtsldt0(sdtasdt0(xn,xn),xp)),
inference(rew,[status(thm),theory(equality)],[8236,28]),
[iquote('0:Rew:8236.0,28.0')] ).
cnf(8611,plain,
( ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(u)
| ~ iLess0(u,xn)
| ~ equal(sdtsldt0(sdtasdt0(xn,xn),xp),sdtasdt0(u,u))
| equal(xq,sz00)
| equal(u,sz00) ),
inference(spl,[status(thm),theory(equality)],[8247,87]),
[iquote('0:SpL:8247.0,87.5')] ).
cnf(8642,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(u)
| ~ iLess0(u,xn)
| ~ equal(sdtsldt0(sdtasdt0(xn,xn),xp),sdtasdt0(u,u))
| equal(xq,sz00)
| equal(u,sz00) ),
inference(ssi,[status(thm)],[8611,5,6]),
[iquote('0:SSi:8611.1,8611.0,5.0,6.0,5.0,6.0')] ).
cnf(8714,plain,
( ~ aNaturalNumber0(xp)
| ~ equal(xq,sz00)
| equal(xn,sz00) ),
inference(spr,[status(thm),theory(equality)],[8187,25]),
[iquote('0:SpR:8187.1,25.1')] ).
cnf(8744,plain,
( ~ equal(xq,sz00)
| equal(xn,sz00) ),
inference(ssi,[status(thm)],[8714,5,6]),
[iquote('0:SSi:8714.0,5.0,6.0')] ).
cnf(8745,plain,
~ equal(xq,sz00),
inference(mrr,[status(thm)],[8744,14]),
[iquote('0:MRR:8744.1,14.0')] ).
cnf(8746,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(u)
| ~ iLess0(u,xn)
| ~ equal(sdtsldt0(sdtasdt0(xn,xn),xp),sdtasdt0(u,u))
| equal(u,sz00) ),
inference(mrr,[status(thm)],[8642,8745]),
[iquote('0:MRR:8642.4,8745.0')] ).
cnf(9849,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,xn)
| aNaturalNumber0(xq)
| equal(xp,sz00) ),
inference(spr,[status(thm),theory(equality)],[19,1305]),
[iquote('0:SpR:19.0,1305.3')] ).
cnf(9854,plain,
( ~ doDivides0(xp,xn)
| aNaturalNumber0(xq)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[9849,5,6,3]),
[iquote('0:SSi:9849.1,9849.0,5.0,6.0,3.0')] ).
cnf(9855,plain,
aNaturalNumber0(xq),
inference(mrr,[status(thm)],[9854,9,16]),
[iquote('0:MRR:9854.0,9854.2,9.0,16.0')] ).
cnf(9856,plain,
( ~ aNaturalNumber0(u)
| ~ iLess0(u,xn)
| ~ equal(sdtsldt0(sdtasdt0(xn,xn),xp),sdtasdt0(u,u))
| equal(u,sz00) ),
inference(mrr,[status(thm)],[8746,9855]),
[iquote('0:MRR:8746.0,9855.0')] ).
cnf(11875,plain,
( ~ aNaturalNumber0(xm)
| ~ iLess0(xm,xn)
| ~ equal(sdtsldt0(sdtasdt0(xn,xn),xp),sdtsldt0(sdtasdt0(xn,xn),xp))
| equal(xm,sz00) ),
inference(spl,[status(thm),theory(equality)],[8236,9856]),
[iquote('0:SpL:8236.0,9856.2')] ).
cnf(11876,plain,
( ~ aNaturalNumber0(xm)
| ~ iLess0(xm,xn)
| equal(xm,sz00) ),
inference(obv,[status(thm),theory(equality)],[11875]),
[iquote('0:Obv:11875.2')] ).
cnf(11877,plain,
( ~ iLess0(xm,xn)
| equal(xm,sz00) ),
inference(ssi,[status(thm)],[11876,4]),
[iquote('0:SSi:11876.0,4.0')] ).
cnf(11878,plain,
~ iLess0(xm,xn),
inference(mrr,[status(thm)],[11877,15]),
[iquote('0:MRR:11877.1,15.0')] ).
cnf(11901,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xm,xn)
| equal(xm,xn) ),
inference(res,[status(thm),theory(equality)],[45,11878]),
[iquote('0:Res:45.3,11878.0')] ).
cnf(11902,plain,
( ~ sdtlseqdt0(xm,xn)
| equal(xm,xn) ),
inference(ssi,[status(thm)],[11901,4,3]),
[iquote('0:SSi:11901.1,11901.0,4.0,3.0')] ).
cnf(11903,plain,
$false,
inference(mrr,[status(thm)],[11902,10,17]),
[iquote('0:MRR:11902.0,11902.1,10.0,17.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM529+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.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 : Thu Jul 7 05:12:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 4.83/5.04
% 4.83/5.04 SPASS V 3.9
% 4.83/5.04 SPASS beiseite: Proof found.
% 4.83/5.04 % SZS status Theorem
% 4.83/5.04 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.83/5.04 SPASS derived 6827 clauses, backtracked 637 clauses, performed 4 splits and kept 3198 clauses.
% 4.83/5.04 SPASS allocated 107682 KBytes.
% 4.83/5.04 SPASS spent 0:00:03.99 on the problem.
% 4.83/5.04 0:00:00.04 for the input.
% 4.83/5.04 0:00:00.04 for the FLOTTER CNF translation.
% 4.83/5.04 0:00:00.08 for inferences.
% 4.83/5.04 0:00:00.03 for the backtracking.
% 4.83/5.04 0:00:03.77 for the reduction.
% 4.83/5.04
% 4.83/5.04
% 4.83/5.04 Here is a proof with depth 4, length 51 :
% 4.83/5.04 % SZS output start Refutation
% See solution above
% 4.83/5.04 Formulae used in the proof : m__2987 m__3025 m__3046 m__3124 m__3059 m_MulZero m__3014 m__3082 mSortsB_02 mDefPrime mIH_03 mDefDiv mDefQuot m__2963
% 4.83/5.04
%------------------------------------------------------------------------------