TSTP Solution File: RNG081+2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG081+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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 20:41:25 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   36 (  14 unt;   1 nHn;  36 RR)
%            Number of literals    :   77 (   0 equ;  55 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    aScalar0(sz0z00),
    file('RNG081+2.p',unknown),
    [] ).

cnf(3,axiom,
    aVector0(xs),
    file('RNG081+2.p',unknown),
    [] ).

cnf(4,axiom,
    aVector0(xt),
    file('RNG081+2.p',unknown),
    [] ).

cnf(7,axiom,
    equal(aDimensionOf0(xt),aDimensionOf0(xs)),
    file('RNG081+2.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ aScalar0(u)
    | equal(sdtasdt0(u,sz0z00),sz0z00) ),
    file('RNG081+2.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ aScalar0(u)
    | equal(sdtasdt0(sz0z00,u),sz0z00) ),
    file('RNG081+2.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ aVector0(u)
    | sdtlseqdt0(sz0z00,sdtasasdt0(u,u)) ),
    file('RNG081+2.p',unknown),
    [] ).

cnf(50,axiom,
    ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
    file('RNG081+2.p',unknown),
    [] ).

cnf(51,axiom,
    ( ~ aVector0(u)
    | ~ aVector0(v)
    | ~ equal(aDimensionOf0(v),aDimensionOf0(u))
    | aScalar0(sdtasasdt0(v,u)) ),
    file('RNG081+2.p',unknown),
    [] ).

cnf(54,axiom,
    ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
    | equal(aDimensionOf0(xs),sz00) ),
    file('RNG081+2.p',unknown),
    [] ).

cnf(63,axiom,
    ( ~ aVector0(u)
    | ~ aVector0(v)
    | ~ equal(aDimensionOf0(u),sz00)
    | ~ equal(aDimensionOf0(v),aDimensionOf0(u))
    | equal(sdtasasdt0(v,u),sz0z00) ),
    file('RNG081+2.p',unknown),
    [] ).

cnf(83,plain,
    equal(aDimensionOf0(xs),sz00),
    inference(mrr,[status(thm)],[54,50]),
    [iquote('0:MRR:54.0,50.0')] ).

cnf(84,plain,
    equal(aDimensionOf0(xt),sz00),
    inference(rew,[status(thm),theory(equality)],[83,7]),
    [iquote('0:Rew:83.0,7.0')] ).

cnf(87,plain,
    ( ~ aVector0(u)
    | ~ aVector0(xt)
    | ~ equal(aDimensionOf0(u),aDimensionOf0(xt))
    | equal(sdtasasdt0(u,xt),sz0z00) ),
    inference(res,[status(thm),theory(equality)],[84,63]),
    [iquote('0:Res:84.0,63.2')] ).

cnf(100,plain,
    ( ~ aVector0(u)
    | ~ aVector0(xt)
    | ~ equal(aDimensionOf0(u),sz00)
    | equal(sdtasasdt0(u,xt),sz0z00) ),
    inference(rew,[status(thm),theory(equality)],[84,87]),
    [iquote('0:Rew:84.0,87.2')] ).

cnf(101,plain,
    ( ~ aVector0(u)
    | ~ equal(aDimensionOf0(u),sz00)
    | equal(sdtasasdt0(u,xt),sz0z00) ),
    inference(mrr,[status(thm)],[100,4]),
    [iquote('0:MRR:100.1,4.0')] ).

cnf(160,plain,
    ( ~ aVector0(xt)
    | ~ aVector0(xt)
    | ~ equal(aDimensionOf0(xt),sz00)
    | sdtlseqdt0(sz0z00,sz0z00) ),
    inference(spr,[status(thm),theory(equality)],[101,23]),
    [iquote('0:SpR:101.2,23.1')] ).

cnf(162,plain,
    ( ~ aVector0(xt)
    | ~ equal(aDimensionOf0(xt),sz00)
    | sdtlseqdt0(sz0z00,sz0z00) ),
    inference(obv,[status(thm),theory(equality)],[160]),
    [iquote('0:Obv:160.0')] ).

cnf(163,plain,
    ( ~ aVector0(xt)
    | ~ equal(sz00,sz00)
    | sdtlseqdt0(sz0z00,sz0z00) ),
    inference(rew,[status(thm),theory(equality)],[84,162]),
    [iquote('0:Rew:84.0,162.1')] ).

cnf(164,plain,
    ( ~ aVector0(xt)
    | sdtlseqdt0(sz0z00,sz0z00) ),
    inference(obv,[status(thm),theory(equality)],[163]),
    [iquote('0:Obv:163.1')] ).

cnf(165,plain,
    sdtlseqdt0(sz0z00,sz0z00),
    inference(ssi,[status(thm)],[164,4]),
    [iquote('0:SSi:164.0,4.0')] ).

cnf(501,plain,
    ( ~ aVector0(xs)
    | ~ equal(aDimensionOf0(xs),sz00)
    | ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(spl,[status(thm),theory(equality)],[101,50]),
    [iquote('0:SpL:101.2,50.0')] ).

cnf(506,plain,
    ( ~ aVector0(xs)
    | ~ equal(sz00,sz00)
    | ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(rew,[status(thm),theory(equality)],[83,501]),
    [iquote('0:Rew:83.0,501.1')] ).

cnf(507,plain,
    ( ~ aVector0(xs)
    | ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(obv,[status(thm),theory(equality)],[506]),
    [iquote('0:Obv:506.1')] ).

cnf(508,plain,
    ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
    inference(ssi,[status(thm)],[507,3]),
    [iquote('0:SSi:507.0,3.0')] ).

cnf(519,plain,
    ( ~ aScalar0(sz0z00)
    | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(spl,[status(thm),theory(equality)],[20,508]),
    [iquote('0:SpL:20.1,508.0')] ).

cnf(523,plain,
    ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
    inference(ssi,[status(thm)],[519,2]),
    [iquote('0:SSi:519.0,2.0')] ).

cnf(532,plain,
    ( ~ aVector0(xt)
    | ~ equal(aDimensionOf0(xt),sz00)
    | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)) ),
    inference(spl,[status(thm),theory(equality)],[101,523]),
    [iquote('0:SpL:101.2,523.0')] ).

cnf(534,plain,
    ( ~ aVector0(xt)
    | ~ equal(sz00,sz00)
    | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)) ),
    inference(rew,[status(thm),theory(equality)],[84,532]),
    [iquote('0:Rew:84.0,532.1')] ).

cnf(535,plain,
    ( ~ aVector0(xt)
    | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)) ),
    inference(obv,[status(thm),theory(equality)],[534]),
    [iquote('0:Obv:534.1')] ).

cnf(536,plain,
    ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)),
    inference(ssi,[status(thm)],[535,4]),
    [iquote('0:SSi:535.0,4.0')] ).

cnf(542,plain,
    ( ~ aScalar0(sdtasasdt0(xs,xs))
    | ~ sdtlseqdt0(sz0z00,sz0z00) ),
    inference(spl,[status(thm),theory(equality)],[19,536]),
    [iquote('0:SpL:19.1,536.0')] ).

cnf(544,plain,
    ~ aScalar0(sdtasasdt0(xs,xs)),
    inference(mrr,[status(thm)],[542,165]),
    [iquote('0:MRR:542.1,165.0')] ).

cnf(548,plain,
    ( ~ aVector0(xs)
    | ~ aVector0(xs)
    | ~ equal(aDimensionOf0(xs),aDimensionOf0(xs)) ),
    inference(sor,[status(thm)],[544,51]),
    [iquote('0:SoR:544.0,51.3')] ).

cnf(551,plain,
    ~ aVector0(xs),
    inference(obv,[status(thm),theory(equality)],[548]),
    [iquote('0:Obv:548.2')] ).

cnf(552,plain,
    $false,
    inference(ssi,[status(thm)],[551,3]),
    [iquote('0:SSi:551.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : RNG081+2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n023.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon May 30 21:24:12 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.20/0.50  
% 0.20/0.50  SPASS V 3.9 
% 0.20/0.50  SPASS beiseite: Proof found.
% 0.20/0.50  % SZS status Theorem
% 0.20/0.50  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.50  SPASS derived 237 clauses, backtracked 0 clauses, performed 0 splits and kept 120 clauses.
% 0.20/0.50  SPASS allocated 98161 KBytes.
% 0.20/0.50  SPASS spent	0:00:00.14 on the problem.
% 0.20/0.50  		0:00:00.04 for the input.
% 0.20/0.50  		0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.50  		0:00:00.00 for inferences.
% 0.20/0.50  		0:00:00.00 for the backtracking.
% 0.20/0.50  		0:00:00.03 for the reduction.
% 0.20/0.50  
% 0.20/0.50  
% 0.20/0.50  Here is a proof with depth 6, length 36 :
% 0.20/0.50  % SZS output start Refutation
% See solution above
% 0.20/0.50  Formulae used in the proof : mSZeroSc m__1678 m__1678_01 mScZero mScSqPos m__ mScPr mDefSPZ
% 0.20/0.50  
%------------------------------------------------------------------------------