TSTP Solution File: NUM434+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM434+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 14:26:09 EDT 2022

% Result   : Theorem 0.96s 1.14s
% Output   : Refutation 0.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   19
% Syntax   : Number of clauses     :   41 (  16 unt;  13 nHn;  41 RR)
%            Number of literals    :  115 (   0 equ;  70 neg)
%            Maximal clause size   :    8 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    aInteger0(xa),
    file('NUM434+1.p',unknown),
    [] ).

cnf(4,axiom,
    aInteger0(xb),
    file('NUM434+1.p',unknown),
    [] ).

cnf(5,axiom,
    aInteger0(xp),
    file('NUM434+1.p',unknown),
    [] ).

cnf(6,axiom,
    aInteger0(xq),
    file('NUM434+1.p',unknown),
    [] ).

cnf(7,axiom,
    aInteger0(skf1(u,v)),
    file('NUM434+1.p',unknown),
    [] ).

cnf(8,axiom,
    ~ equal(xp,sz00),
    file('NUM434+1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ equal(xq,sz00),
    file('NUM434+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ aInteger0(u)
    | aInteger0(smndt0(u)) ),
    file('NUM434+1.p',unknown),
    [] ).

cnf(11,axiom,
    sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
    file('NUM434+1.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ aInteger0(u)
    | ~ aDivisorOf0(v,u)
    | aInteger0(v) ),
    file('NUM434+1.p',unknown),
    [] ).

cnf(21,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | aInteger0(sdtpldt0(v,u)) ),
    file('NUM434+1.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | aInteger0(sdtasdt0(v,u)) ),
    file('NUM434+1.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ aInteger0(u)
    | ~ aDivisorOf0(v,u)
    | ~ equal(v,sz00) ),
    file('NUM434+1.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ aInteger0(u)
    | ~ equal(sdtasdt0(sdtasdt0(xp,xq),u),sdtpldt0(xa,smndt0(xb))) ),
    file('NUM434+1.p',unknown),
    [] ).

cnf(30,axiom,
    ( ~ aInteger0(u)
    | ~ aDivisorOf0(v,u)
    | equal(sdtasdt0(v,skf1(u,v)),u) ),
    file('NUM434+1.p',unknown),
    [] ).

cnf(31,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ equal(sdtasdt0(v,u),sz00)
    | equal(u,sz00)
    | equal(v,sz00) ),
    file('NUM434+1.p',unknown),
    [] ).

cnf(34,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(w)
    | ~ sdteqdtlpzmzozddtrp0(w,v,u)
    | equal(u,sz00)
    | sdteqdtlpzmzozddtrp0(v,w,u) ),
    file('NUM434+1.p',unknown),
    [] ).

cnf(35,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(w)
    | ~ equal(sdtasdt0(w,v),u)
    | aDivisorOf0(w,u)
    | equal(w,sz00) ),
    file('NUM434+1.p',unknown),
    [] ).

cnf(39,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(w)
    | ~ sdteqdtlpzmzozddtrp0(w,v,u)
    | equal(u,sz00)
    | aDivisorOf0(u,sdtpldt0(w,smndt0(v))) ),
    file('NUM434+1.p',unknown),
    [] ).

cnf(47,plain,
    ~ equal(sdtasdt0(sdtasdt0(xp,xq),skf1(u,v)),sdtpldt0(xa,smndt0(xb))),
    inference(res,[status(thm),theory(equality)],[7,29]),
    [iquote('0:Res:7.0,29.0')] ).

cnf(179,plain,
    ( ~ aInteger0(u)
    | ~ aDivisorOf0(sdtasdt0(xp,xq),u)
    | ~ equal(u,sdtpldt0(xa,smndt0(xb))) ),
    inference(spl,[status(thm),theory(equality)],[30,47]),
    [iquote('0:SpL:30.2,47.0')] ).

cnf(458,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(skf1(u,w))
    | ~ aInteger0(w)
    | ~ aDivisorOf0(w,u)
    | ~ equal(u,v)
    | aDivisorOf0(w,v)
    | equal(w,sz00) ),
    inference(spl,[status(thm),theory(equality)],[30,35]),
    [iquote('0:SpL:30.2,35.3')] ).

cnf(472,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(w)
    | ~ aDivisorOf0(w,u)
    | ~ equal(u,v)
    | aDivisorOf0(w,v)
    | equal(w,sz00) ),
    inference(ssi,[status(thm)],[458,7]),
    [iquote('0:SSi:458.2,7.0')] ).

cnf(473,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aDivisorOf0(w,u)
    | ~ equal(u,v)
    | aDivisorOf0(w,v) ),
    inference(mrr,[status(thm)],[472,20,25]),
    [iquote('0:MRR:472.2,472.6,20.2,25.2')] ).

cnf(511,plain,
    ( ~ aInteger0(sdtasdt0(xp,xq))
    | ~ aInteger0(xb)
    | ~ aInteger0(xa)
    | equal(sdtasdt0(xp,xq),sz00)
    | sdteqdtlpzmzozddtrp0(xb,xa,sdtasdt0(xp,xq)) ),
    inference(res,[status(thm),theory(equality)],[11,34]),
    [iquote('0:Res:11.0,34.3')] ).

cnf(513,plain,
    ( equal(sdtasdt0(xp,xq),sz00)
    | sdteqdtlpzmzozddtrp0(xb,xa,sdtasdt0(xp,xq)) ),
    inference(ssi,[status(thm)],[511,3,4,22,5,6]),
    [iquote('0:SSi:511.2,511.1,511.0,3.0,4.0,22.2,5.0,6.0')] ).

cnf(527,plain,
    equal(sdtasdt0(xp,xq),sz00),
    inference(spt,[spt(split,[position(s1)])],[513]),
    [iquote('1:Spt:513.0')] ).

cnf(554,plain,
    ( ~ aInteger0(xq)
    | ~ aInteger0(xp)
    | ~ equal(sz00,sz00)
    | equal(xq,sz00)
    | equal(xp,sz00) ),
    inference(spl,[status(thm),theory(equality)],[527,31]),
    [iquote('1:SpL:527.0,31.2')] ).

cnf(556,plain,
    ( ~ aInteger0(xq)
    | ~ aInteger0(xp)
    | equal(xq,sz00)
    | equal(xp,sz00) ),
    inference(obv,[status(thm),theory(equality)],[554]),
    [iquote('1:Obv:554.2')] ).

cnf(557,plain,
    ( equal(xq,sz00)
    | equal(xp,sz00) ),
    inference(ssi,[status(thm)],[556,5,6]),
    [iquote('1:SSi:556.1,556.0,5.0,6.0')] ).

cnf(558,plain,
    $false,
    inference(mrr,[status(thm)],[557,9,8]),
    [iquote('1:MRR:557.0,557.1,9.0,8.0')] ).

cnf(562,plain,
    ~ equal(sdtasdt0(xp,xq),sz00),
    inference(spt,[spt(split,[position(sa)])],[558,527]),
    [iquote('1:Spt:558.0,513.0,527.0')] ).

cnf(563,plain,
    sdteqdtlpzmzozddtrp0(xb,xa,sdtasdt0(xp,xq)),
    inference(spt,[spt(split,[position(s2)])],[513]),
    [iquote('1:Spt:558.0,513.1')] ).

cnf(816,plain,
    ( ~ aInteger0(sdtasdt0(xp,xq))
    | ~ aInteger0(xb)
    | ~ aInteger0(xa)
    | equal(sdtasdt0(xp,xq),sz00)
    | aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
    inference(res,[status(thm),theory(equality)],[11,39]),
    [iquote('0:Res:11.0,39.3')] ).

cnf(819,plain,
    ( equal(sdtasdt0(xp,xq),sz00)
    | aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
    inference(ssi,[status(thm)],[816,3,4,22,5,6]),
    [iquote('0:SSi:816.2,816.1,816.0,3.0,4.0,22.2,5.0,6.0')] ).

cnf(820,plain,
    aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))),
    inference(mrr,[status(thm)],[819,562]),
    [iquote('1:MRR:819.0,562.0')] ).

cnf(4370,plain,
    ( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
    | ~ aInteger0(u)
    | ~ equal(sdtpldt0(xa,smndt0(xb)),u)
    | aDivisorOf0(sdtasdt0(xp,xq),u) ),
    inference(res,[status(thm),theory(equality)],[820,473]),
    [iquote('1:Res:820.0,473.2')] ).

cnf(4414,plain,
    ( ~ aInteger0(u)
    | ~ equal(sdtpldt0(xa,smndt0(xb)),u)
    | aDivisorOf0(sdtasdt0(xp,xq),u) ),
    inference(ssi,[status(thm)],[4370,21,3,10,4]),
    [iquote('1:SSi:4370.0,21.0,3.1,10.0,4.2')] ).

cnf(4415,plain,
    ( ~ aInteger0(u)
    | ~ equal(sdtpldt0(xa,smndt0(xb)),u) ),
    inference(mrr,[status(thm)],[4414,179]),
    [iquote('1:MRR:4414.2,179.1')] ).

cnf(4425,plain,
    ~ aInteger0(sdtpldt0(xa,smndt0(xb))),
    inference(eqr,[status(thm),theory(equality)],[4415]),
    [iquote('1:EqR:4415.1')] ).

cnf(4428,plain,
    $false,
    inference(ssi,[status(thm)],[4425,21,3,10,4]),
    [iquote('1:SSi:4425.0,21.0,3.1,10.0,4.2')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM434+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n029.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 : Wed Jul  6 08:17:13 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.96/1.14  
% 0.96/1.14  SPASS V 3.9 
% 0.96/1.14  SPASS beiseite: Proof found.
% 0.96/1.14  % SZS status Theorem
% 0.96/1.14  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.96/1.14  SPASS derived 2387 clauses, backtracked 21 clauses, performed 3 splits and kept 544 clauses.
% 0.96/1.14  SPASS allocated 101742 KBytes.
% 0.96/1.14  SPASS spent	0:00:00.61 on the problem.
% 0.96/1.14  		0:00:00.04 for the input.
% 0.96/1.14  		0:00:00.03 for the FLOTTER CNF translation.
% 0.96/1.14  		0:00:00.03 for inferences.
% 0.96/1.14  		0:00:00.00 for the backtracking.
% 0.96/1.14  		0:00:00.49 for the reduction.
% 0.96/1.14  
% 0.96/1.14  
% 0.96/1.14  Here is a proof with depth 3, length 41 :
% 0.96/1.14  % SZS output start Refutation
% See solution above
% 0.96/1.14  Formulae used in the proof : m__979 mDivisor mIntNeg m__1003 mIntPlus mIntMult m__ mZeroDiv mEquModSym mEquMod
% 0.96/1.14  
%------------------------------------------------------------------------------