TSTP Solution File: NUM514+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM514+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n004.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 14:26:59 EDT 2022

% Result   : Theorem 18.82s 19.01s
% Output   : Refutation 18.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   49 (  19 unt;   9 nHn;  49 RR)
%            Number of literals    :  127 (   0 equ;  78 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    3 (   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('NUM514+1.p',unknown),
    [] ).

cnf(4,axiom,
    aNaturalNumber0(xm),
    file('NUM514+1.p',unknown),
    [] ).

cnf(5,axiom,
    aNaturalNumber0(xp),
    file('NUM514+1.p',unknown),
    [] ).

cnf(6,axiom,
    isPrime0(xp),
    file('NUM514+1.p',unknown),
    [] ).

cnf(7,axiom,
    aNaturalNumber0(xr),
    file('NUM514+1.p',unknown),
    [] ).

cnf(8,axiom,
    isPrime0(xr),
    file('NUM514+1.p',unknown),
    [] ).

cnf(13,axiom,
    doDivides0(xr,xk),
    file('NUM514+1.p',unknown),
    [] ).

cnf(29,axiom,
    doDivides0(xp,sdtasdt0(xn,xm)),
    file('NUM514+1.p',unknown),
    [] ).

cnf(35,axiom,
    equal(sdtsldt0(sdtasdt0(xn,xm),xp),xk),
    file('NUM514+1.p',unknown),
    [] ).

cnf(36,axiom,
    ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
    file('NUM514+1.p',unknown),
    [] ).

cnf(44,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | aNaturalNumber0(sdtasdt0(v,u)) ),
    file('NUM514+1.p',unknown),
    [] ).

cnf(45,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ isPrime0(u)
    | ~ equal(u,sz00) ),
    file('NUM514+1.p',unknown),
    [] ).

cnf(49,axiom,
    equal(sdtasdt0(sdtsldt0(xn,xr),xm),sdtasdt0(xp,sdtsldt0(xk,xr))),
    file('NUM514+1.p',unknown),
    [] ).

cnf(54,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
    file('NUM514+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ equal(u,sdtasdt0(v,w))
    | doDivides0(v,u) ),
    file('NUM514+1.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ doDivides0(v,u)
    | ~ equal(w,sdtsldt0(u,v))
    | aNaturalNumber0(w)
    | equal(v,sz00) ),
    file('NUM514+1.p',unknown),
    [] ).

cnf(90,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ doDivides0(v,u)
    | ~ equal(w,sdtsldt0(u,v))
    | equal(v,sz00)
    | equal(u,sdtasdt0(v,w)) ),
    file('NUM514+1.p',unknown),
    [] ).

cnf(101,plain,
    ~ doDivides0(xp,sdtasdt0(xp,sdtsldt0(xk,xr))),
    inference(rew,[status(thm),theory(equality)],[49,36]),
    [iquote('0:Rew:49.0,36.0')] ).

cnf(127,plain,
    ~ equal(xp,sz00),
    inference(ems,[status(thm)],[45,5,6]),
    [iquote('0:EmS:45.0,45.1,5.0,6.0')] ).

cnf(128,plain,
    ~ equal(xr,sz00),
    inference(ems,[status(thm)],[45,7,8]),
    [iquote('0:EmS:45.0,45.1,7.0,8.0')] ).

cnf(509,plain,
    ( ~ aNaturalNumber0(sdtasdt0(u,v))
    | ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | doDivides0(u,sdtasdt0(u,v)) ),
    inference(eqr,[status(thm),theory(equality)],[72]),
    [iquote('0:EqR:72.3')] ).

cnf(521,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | doDivides0(u,sdtasdt0(u,v)) ),
    inference(ssi,[status(thm)],[509,44]),
    [iquote('0:SSi:509.0,44.2')] ).

cnf(599,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(sdtsldt0(xk,xr)) ),
    inference(res,[status(thm),theory(equality)],[521,101]),
    [iquote('0:Res:521.2,101.0')] ).

cnf(602,plain,
    ~ aNaturalNumber0(sdtsldt0(xk,xr)),
    inference(ssi,[status(thm)],[599,6,5]),
    [iquote('0:SSi:599.0,6.0,5.0')] ).

cnf(1255,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ doDivides0(v,u)
    | aNaturalNumber0(sdtsldt0(u,v))
    | equal(v,sz00) ),
    inference(eqr,[status(thm),theory(equality)],[80]),
    [iquote('0:EqR:80.3')] ).

cnf(2450,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
    | ~ aNaturalNumber0(xp)
    | ~ doDivides0(xp,sdtasdt0(xn,xm))
    | ~ equal(u,xk)
    | equal(xp,sz00)
    | equal(sdtasdt0(xp,u),sdtasdt0(xn,xm)) ),
    inference(spl,[status(thm),theory(equality)],[35,90]),
    [iquote('0:SpL:35.0,90.3')] ).

cnf(2451,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
    | ~ aNaturalNumber0(xp)
    | ~ doDivides0(xp,sdtasdt0(xn,xm))
    | ~ equal(u,xk)
    | aNaturalNumber0(u)
    | equal(xp,sz00) ),
    inference(spl,[status(thm),theory(equality)],[35,80]),
    [iquote('0:SpL:35.0,80.3')] ).

cnf(2453,plain,
    ( ~ doDivides0(xp,sdtasdt0(xn,xm))
    | ~ equal(u,xk)
    | aNaturalNumber0(u)
    | equal(xp,sz00) ),
    inference(ssi,[status(thm)],[2451,6,5,44,3,4]),
    [iquote('0:SSi:2451.1,2451.0,6.0,5.0,44.2,3.0,4.0')] ).

cnf(2454,plain,
    ( ~ equal(u,xk)
    | aNaturalNumber0(u) ),
    inference(mrr,[status(thm)],[2453,29,127]),
    [iquote('0:MRR:2453.0,2453.3,29.0,127.0')] ).

cnf(2455,plain,
    ( ~ doDivides0(xp,sdtasdt0(xn,xm))
    | ~ equal(u,xk)
    | equal(xp,sz00)
    | equal(sdtasdt0(xp,u),sdtasdt0(xn,xm)) ),
    inference(ssi,[status(thm)],[2450,6,5,44,3,4]),
    [iquote('0:SSi:2450.1,2450.0,6.0,5.0,44.2,3.0,4.0')] ).

cnf(2456,plain,
    ( ~ equal(u,xk)
    | equal(sdtasdt0(xp,u),sdtasdt0(xn,xm)) ),
    inference(mrr,[status(thm)],[2455,29,127]),
    [iquote('0:MRR:2455.0,2455.2,29.0,127.0')] ).

cnf(3540,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xp)
    | ~ equal(u,xk)
    | aNaturalNumber0(sdtasdt0(xn,xm)) ),
    inference(spr,[status(thm),theory(equality)],[2456,44]),
    [iquote('0:SpR:2456.1,44.2')] ).

cnf(3541,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xp)
    | ~ equal(u,xk)
    | equal(sdtasdt0(xn,xm),sdtasdt0(u,xp)) ),
    inference(spr,[status(thm),theory(equality)],[2456,54]),
    [iquote('0:SpR:2456.1,54.2')] ).

cnf(3575,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(u,xk)
    | aNaturalNumber0(sdtasdt0(xn,xm)) ),
    inference(ssi,[status(thm)],[3540,6,5]),
    [iquote('0:SSi:3540.1,6.0,5.0')] ).

cnf(3576,plain,
    ( ~ equal(u,xk)
    | aNaturalNumber0(sdtasdt0(xn,xm)) ),
    inference(mrr,[status(thm)],[3575,2454]),
    [iquote('0:MRR:3575.0,2454.1')] ).

cnf(3580,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(u,xk)
    | equal(sdtasdt0(xn,xm),sdtasdt0(u,xp)) ),
    inference(ssi,[status(thm)],[3541,6,5]),
    [iquote('0:SSi:3541.1,6.0,5.0')] ).

cnf(3581,plain,
    ( ~ equal(u,xk)
    | equal(sdtasdt0(xn,xm),sdtasdt0(u,xp)) ),
    inference(mrr,[status(thm)],[3580,2454]),
    [iquote('0:MRR:3580.0,2454.1')] ).

cnf(3637,plain,
    aNaturalNumber0(sdtasdt0(xn,xm)),
    inference(eqr,[status(thm),theory(equality)],[3576]),
    [iquote('0:EqR:3576.0')] ).

cnf(4205,plain,
    ( ~ equal(u,xk)
    | aNaturalNumber0(sdtasdt0(u,xp)) ),
    inference(spr,[status(thm),theory(equality)],[3581,3637]),
    [iquote('0:SpR:3581.1,3637.0')] ).

cnf(4207,plain,
    ( ~ equal(u,xk)
    | doDivides0(xp,sdtasdt0(u,xp)) ),
    inference(spr,[status(thm),theory(equality)],[3581,29]),
    [iquote('0:SpR:3581.1,29.0')] ).

cnf(4210,plain,
    ( ~ equal(u,xk)
    | equal(sdtsldt0(sdtasdt0(u,xp),xp),xk) ),
    inference(spr,[status(thm),theory(equality)],[3581,35]),
    [iquote('0:SpR:3581.1,35.0')] ).

cnf(36524,plain,
    ( ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xk)
    | ~ doDivides0(xr,xk)
    | equal(xr,sz00) ),
    inference(sor,[status(thm)],[602,1255]),
    [iquote('0:SoR:602.0,1255.3')] ).

cnf(36538,plain,
    ( ~ aNaturalNumber0(sdtasdt0(u,xp))
    | ~ aNaturalNumber0(xp)
    | ~ equal(u,xk)
    | ~ doDivides0(xp,sdtasdt0(u,xp))
    | aNaturalNumber0(xk)
    | equal(xp,sz00) ),
    inference(spr,[status(thm),theory(equality)],[4210,1255]),
    [iquote('0:SpR:4210.1,1255.3')] ).

cnf(36547,plain,
    ( ~ aNaturalNumber0(xk)
    | ~ doDivides0(xr,xk)
    | equal(xr,sz00) ),
    inference(ssi,[status(thm)],[36524,7,8]),
    [iquote('0:SSi:36524.0,7.0,8.0')] ).

cnf(36548,plain,
    ~ aNaturalNumber0(xk),
    inference(mrr,[status(thm)],[36547,13,128]),
    [iquote('0:MRR:36547.1,36547.2,13.0,128.0')] ).

cnf(36556,plain,
    ( ~ aNaturalNumber0(sdtasdt0(u,xp))
    | ~ equal(u,xk)
    | ~ doDivides0(xp,sdtasdt0(u,xp))
    | aNaturalNumber0(xk)
    | equal(xp,sz00) ),
    inference(ssi,[status(thm)],[36538,6,5]),
    [iquote('0:SSi:36538.1,6.0,5.0')] ).

cnf(36557,plain,
    ( ~ equal(u,xk)
    | aNaturalNumber0(xk) ),
    inference(mrr,[status(thm)],[36556,4205,4207,127]),
    [iquote('0:MRR:36556.0,36556.2,36556.4,4205.1,4207.1,127.0')] ).

cnf(36558,plain,
    ~ equal(u,xk),
    inference(mrr,[status(thm)],[36557,36548]),
    [iquote('0:MRR:36557.1,36548.0')] ).

cnf(36559,plain,
    $false,
    inference(unc,[status(thm)],[36558,35]),
    [iquote('0:UnC:36558.0,35.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM514+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n004.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 : Wed Jul  6 18:41:52 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 18.82/19.01  
% 18.82/19.01  SPASS V 3.9 
% 18.82/19.01  SPASS beiseite: Proof found.
% 18.82/19.01  % SZS status Theorem
% 18.82/19.01  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 18.82/19.01  SPASS derived 24693 clauses, backtracked 5055 clauses, performed 17 splits and kept 10632 clauses.
% 18.82/19.01  SPASS allocated 122637 KBytes.
% 18.82/19.01  SPASS spent	0:0:14.21 on the problem.
% 18.82/19.01  		0:00:00.04 for the input.
% 18.82/19.01  		0:00:00.04 for the FLOTTER CNF translation.
% 18.82/19.01  		0:00:00.29 for inferences.
% 18.82/19.01  		0:00:00.21 for the backtracking.
% 18.82/19.01  		0:0:13.48 for the reduction.
% 18.82/19.01  
% 18.82/19.01  
% 18.82/19.01  Here is a proof with depth 4, length 49 :
% 18.82/19.01  % SZS output start Refutation
% See solution above
% 18.82/19.01  Formulae used in the proof : m__1837 m__1860 m__2342 m__2306 m__ mSortsB_02 mDefPrime m__2613 mMulComm mDefDiv mDefQuot
% 18.82/19.01  
%------------------------------------------------------------------------------