TSTP Solution File: NUM477+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM477+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 14:26:36 EDT 2022

% Result   : Theorem 15.75s 15.95s
% Output   : Refutation 15.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   49 (   9 unt;   1 nHn;  49 RR)
%            Number of literals    :  184 (   0 equ; 140 neg)
%            Maximal clause size   :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    aNaturalNumber0(xm),
    file('NUM477+1.p',unknown),
    [] ).

cnf(4,axiom,
    aNaturalNumber0(xn),
    file('NUM477+1.p',unknown),
    [] ).

cnf(5,axiom,
    doDivides0(xm,xn),
    file('NUM477+1.p',unknown),
    [] ).

cnf(6,axiom,
    ~ sdtlseqdt0(xm,xn),
    file('NUM477+1.p',unknown),
    [] ).

cnf(8,axiom,
    aNaturalNumber0(skf2(u,v)),
    file('NUM477+1.p',unknown),
    [] ).

cnf(9,axiom,
    aNaturalNumber0(skf3(u,v)),
    file('NUM477+1.p',unknown),
    [] ).

cnf(10,axiom,
    ~ equal(xn,sz00),
    file('NUM477+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ aNaturalNumber0(u)
    | equal(sdtasdt0(u,sz00),sz00) ),
    file('NUM477+1.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | aNaturalNumber0(sdtpldt0(v,u)) ),
    file('NUM477+1.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | aNaturalNumber0(sdtasdt0(v,u)) ),
    file('NUM477+1.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | equal(v,sz00)
    | sdtlseqdt0(u,sdtasdt0(u,v)) ),
    file('NUM477+1.p',unknown),
    [] ).

cnf(30,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ sdtlseqdt0(v,u)
    | equal(sdtpldt0(v,skf2(u,v)),u) ),
    file('NUM477+1.p',unknown),
    [] ).

cnf(32,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ doDivides0(v,u)
    | equal(sdtasdt0(v,skf3(v,u)),u) ),
    file('NUM477+1.p',unknown),
    [] ).

cnf(34,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ equal(sdtpldt0(v,w),u)
    | sdtlseqdt0(v,u) ),
    file('NUM477+1.p',unknown),
    [] ).

cnf(35,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ sdtlseqdt0(v,u)
    | ~ equal(w,sdtmndt0(u,v))
    | aNaturalNumber0(w) ),
    file('NUM477+1.p',unknown),
    [] ).

cnf(36,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ equal(u,sdtasdt0(v,w))
    | doDivides0(v,u) ),
    file('NUM477+1.p',unknown),
    [] ).

cnf(56,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ sdtlseqdt0(v,w)
    | ~ equal(sdtpldt0(v,u),w)
    | equal(u,sdtmndt0(w,v)) ),
    file('NUM477+1.p',unknown),
    [] ).

cnf(62,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ equal(sdtpldt0(v,w),u)
    | equal(w,sdtmndt0(u,v)) ),
    inference(mrr,[status(thm)],[56,34]),
    [iquote('0:MRR:56.3,34.4')] ).

cnf(68,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | ~ equal(sdtpldt0(xm,u),xn) ),
    inference(res,[status(thm),theory(equality)],[34,6]),
    [iquote('0:Res:34.4,6.0')] ).

cnf(71,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(sdtpldt0(xm,u),xn) ),
    inference(mrr,[status(thm)],[68,3,4]),
    [iquote('0:MRR:68.1,68.2,3.0,4.0')] ).

cnf(367,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(skf2(u,xm))
    | ~ sdtlseqdt0(xm,u)
    | ~ equal(u,xn) ),
    inference(spl,[status(thm),theory(equality)],[30,71]),
    [iquote('0:SpL:30.3,71.1')] ).

cnf(371,plain,
    ( ~ aNaturalNumber0(u)
    | ~ sdtlseqdt0(xm,u)
    | ~ equal(u,xn) ),
    inference(ssi,[status(thm)],[367,8,3]),
    [iquote('0:SSi:367.2,367.1,8.0,3.0,3.0')] ).

cnf(409,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(sdtasdt0(xm,u))
    | ~ equal(sdtasdt0(xm,u),xn)
    | equal(u,sz00) ),
    inference(res,[status(thm),theory(equality)],[26,371]),
    [iquote('0:Res:26.3,371.1')] ).

cnf(420,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(sdtasdt0(xm,u),xn)
    | equal(u,sz00) ),
    inference(ssi,[status(thm)],[409,19,3]),
    [iquote('0:SSi:409.2,409.0,19.0,3.0,3.2')] ).

cnf(456,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(skf3(xm,u))
    | ~ doDivides0(xm,u)
    | ~ equal(u,xn)
    | equal(skf3(xm,u),sz00) ),
    inference(spl,[status(thm),theory(equality)],[32,420]),
    [iquote('0:SpL:32.3,420.1')] ).

cnf(459,plain,
    ( ~ aNaturalNumber0(u)
    | ~ doDivides0(xm,u)
    | ~ equal(u,xn)
    | equal(skf3(xm,u),sz00) ),
    inference(ssi,[status(thm)],[456,9,3]),
    [iquote('0:SSi:456.2,456.1,9.0,3.0,3.0')] ).

cnf(460,plain,
    ( ~ aNaturalNumber0(sdtpldt0(u,v))
    | ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | sdtlseqdt0(u,sdtpldt0(u,v)) ),
    inference(eqr,[status(thm),theory(equality)],[34]),
    [iquote('0:EqR:34.3')] ).

cnf(466,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | sdtlseqdt0(u,sdtpldt0(u,v)) ),
    inference(ssi,[status(thm)],[460,18]),
    [iquote('0:SSi:460.0,18.2')] ).

cnf(505,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(skf3(v,u))
    | ~ doDivides0(v,u)
    | ~ equal(w,u)
    | doDivides0(v,w) ),
    inference(spl,[status(thm),theory(equality)],[32,36]),
    [iquote('0:SpL:32.3,36.3')] ).

cnf(519,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ aNaturalNumber0(skf3(w,u))
    | ~ doDivides0(w,u)
    | ~ equal(v,u)
    | doDivides0(w,v) ),
    inference(obv,[status(thm),theory(equality)],[505]),
    [iquote('0:Obv:505.1')] ).

cnf(520,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ doDivides0(w,u)
    | ~ equal(v,u)
    | doDivides0(w,v) ),
    inference(ssi,[status(thm)],[519,9]),
    [iquote('0:SSi:519.3,9.0')] ).

cnf(750,plain,
    ( ~ aNaturalNumber0(sdtpldt0(u,v))
    | ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
    inference(eqr,[status(thm),theory(equality)],[62]),
    [iquote('0:EqR:62.3')] ).

cnf(757,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
    inference(ssi,[status(thm)],[750,18]),
    [iquote('0:SSi:750.0,18.2')] ).

cnf(854,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(sdtpldt0(u,v))
    | ~ aNaturalNumber0(u)
    | ~ sdtlseqdt0(u,sdtpldt0(u,v))
    | ~ equal(w,v)
    | aNaturalNumber0(w) ),
    inference(spl,[status(thm),theory(equality)],[757,35]),
    [iquote('0:SpL:757.2,35.3')] ).

cnf(869,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(sdtpldt0(v,u))
    | ~ aNaturalNumber0(v)
    | ~ sdtlseqdt0(v,sdtpldt0(v,u))
    | ~ equal(w,u)
    | aNaturalNumber0(w) ),
    inference(obv,[status(thm),theory(equality)],[854]),
    [iquote('0:Obv:854.0')] ).

cnf(870,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ sdtlseqdt0(v,sdtpldt0(v,u))
    | ~ equal(w,u)
    | aNaturalNumber0(w) ),
    inference(ssi,[status(thm)],[869,18]),
    [iquote('0:SSi:869.1,18.2')] ).

cnf(871,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ equal(w,u)
    | aNaturalNumber0(w) ),
    inference(mrr,[status(thm)],[870,466]),
    [iquote('0:MRR:870.2,466.2')] ).

cnf(873,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ doDivides0(v,w)
    | ~ equal(u,w)
    | doDivides0(v,u) ),
    inference(mrr,[status(thm)],[520,871]),
    [iquote('0:MRR:520.0,871.3')] ).

cnf(30530,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xm)
    | ~ equal(u,xn)
    | doDivides0(xm,u) ),
    inference(res,[status(thm),theory(equality)],[5,873]),
    [iquote('0:Res:5.0,873.2')] ).

cnf(30539,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(u,xn)
    | doDivides0(xm,u) ),
    inference(ssi,[status(thm)],[30530,3]),
    [iquote('0:SSi:30530.1,3.0')] ).

cnf(30540,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(u,xn)
    | equal(skf3(xm,u),sz00) ),
    inference(mrr,[status(thm)],[459,30539]),
    [iquote('0:MRR:459.1,30539.2')] ).

cnf(30599,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xm)
    | ~ equal(u,xn)
    | ~ doDivides0(xm,u)
    | equal(sdtasdt0(xm,sz00),u) ),
    inference(spr,[status(thm),theory(equality)],[30540,32]),
    [iquote('0:SpR:30540.2,32.3')] ).

cnf(30728,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xm)
    | ~ equal(u,xn)
    | ~ doDivides0(xm,u)
    | equal(sdtasdt0(xm,sz00),u) ),
    inference(obv,[status(thm),theory(equality)],[30599]),
    [iquote('0:Obv:30599.0')] ).

cnf(30729,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xm)
    | ~ equal(u,xn)
    | ~ doDivides0(xm,u)
    | equal(sz00,u) ),
    inference(rew,[status(thm),theory(equality)],[16,30728]),
    [iquote('0:Rew:16.1,30728.4')] ).

cnf(30730,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(u,xn)
    | ~ doDivides0(xm,u)
    | equal(sz00,u) ),
    inference(ssi,[status(thm)],[30729,3]),
    [iquote('0:SSi:30729.1,3.0')] ).

cnf(30731,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(u,xn)
    | equal(sz00,u) ),
    inference(mrr,[status(thm)],[30730,30539]),
    [iquote('0:MRR:30730.2,30539.2')] ).

cnf(30920,plain,
    ( ~ equal(xn,xn)
    | equal(xn,sz00) ),
    inference(ems,[status(thm)],[30731,4]),
    [iquote('0:EmS:30731.0,4.0')] ).

cnf(30928,plain,
    equal(xn,sz00),
    inference(obv,[status(thm),theory(equality)],[30920]),
    [iquote('0:Obv:30920.0')] ).

cnf(30929,plain,
    $false,
    inference(mrr,[status(thm)],[30928,10]),
    [iquote('0:MRR:30928.0,10.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : NUM477+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14  % Command  : run_spass %d %s
% 0.14/0.36  % Computer : n017.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 14:25:28 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 15.75/15.95  
% 15.75/15.95  SPASS V 3.9 
% 15.75/15.95  SPASS beiseite: Proof found.
% 15.75/15.95  % SZS status Theorem
% 15.75/15.95  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 15.75/15.95  SPASS derived 18427 clauses, backtracked 3959 clauses, performed 7 splits and kept 7413 clauses.
% 15.75/15.95  SPASS allocated 118470 KBytes.
% 15.75/15.95  SPASS spent	0:0:10.29 on the problem.
% 15.75/15.95  		0:00:00.04 for the input.
% 15.75/15.95  		0:00:00.04 for the FLOTTER CNF translation.
% 15.75/15.95  		0:00:00.26 for inferences.
% 15.75/15.95  		0:00:00.04 for the backtracking.
% 15.75/15.95  		0:00:09.84 for the reduction.
% 15.75/15.95  
% 15.75/15.95  
% 15.75/15.95  Here is a proof with depth 6, length 49 :
% 15.75/15.95  % SZS output start Refutation
% See solution above
% 15.75/15.95  Formulae used in the proof : m__1494 m__1494_04 m__ mDefLE mDefDiv m_MulZero mSortsB mSortsB_02 mMonMul2 mDefDiff
% 15.75/15.95  
%------------------------------------------------------------------------------