TSTP Solution File: RNG081+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG081+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 0.17s 0.47s
% Output   : Refutation 0.17s
% 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+1.p',unknown),
    [] ).

cnf(3,axiom,
    aVector0(xs),
    file('RNG081+1.p',unknown),
    [] ).

cnf(4,axiom,
    aVector0(xt),
    file('RNG081+1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(aDimensionOf0(xt),aDimensionOf0(xs)),
    file('RNG081+1.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ aScalar0(u)
    | equal(sdtasdt0(u,sz0z00),sz0z00) ),
    file('RNG081+1.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ aScalar0(u)
    | equal(sdtasdt0(sz0z00,u),sz0z00) ),
    file('RNG081+1.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ aVector0(u)
    | sdtlseqdt0(sz0z00,sdtasasdt0(u,u)) ),
    file('RNG081+1.p',unknown),
    [] ).

cnf(46,axiom,
    ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
    file('RNG081+1.p',unknown),
    [] ).

cnf(47,axiom,
    ( ~ aVector0(u)
    | ~ aVector0(v)
    | ~ equal(aDimensionOf0(v),aDimensionOf0(u))
    | aScalar0(sdtasasdt0(v,u)) ),
    file('RNG081+1.p',unknown),
    [] ).

cnf(50,axiom,
    ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
    | equal(aDimensionOf0(xs),sz00) ),
    file('RNG081+1.p',unknown),
    [] ).

cnf(59,axiom,
    ( ~ aVector0(u)
    | ~ aVector0(v)
    | ~ equal(aDimensionOf0(u),sz00)
    | ~ equal(aDimensionOf0(v),aDimensionOf0(u))
    | equal(sdtasasdt0(v,u),sz0z00) ),
    file('RNG081+1.p',unknown),
    [] ).

cnf(78,plain,
    equal(aDimensionOf0(xs),sz00),
    inference(mrr,[status(thm)],[50,46]),
    [iquote('0:MRR:50.0,46.0')] ).

cnf(79,plain,
    equal(aDimensionOf0(xt),sz00),
    inference(rew,[status(thm),theory(equality)],[78,7]),
    [iquote('0:Rew:78.0,7.0')] ).

cnf(82,plain,
    ( ~ aVector0(u)
    | ~ aVector0(xt)
    | ~ equal(aDimensionOf0(u),aDimensionOf0(xt))
    | equal(sdtasasdt0(u,xt),sz0z00) ),
    inference(res,[status(thm),theory(equality)],[79,59]),
    [iquote('0:Res:79.0,59.2')] ).

cnf(95,plain,
    ( ~ aVector0(u)
    | ~ aVector0(xt)
    | ~ equal(aDimensionOf0(u),sz00)
    | equal(sdtasasdt0(u,xt),sz0z00) ),
    inference(rew,[status(thm),theory(equality)],[79,82]),
    [iquote('0:Rew:79.0,82.2')] ).

cnf(96,plain,
    ( ~ aVector0(u)
    | ~ equal(aDimensionOf0(u),sz00)
    | equal(sdtasasdt0(u,xt),sz0z00) ),
    inference(mrr,[status(thm)],[95,4]),
    [iquote('0:MRR:95.1,4.0')] ).

cnf(155,plain,
    ( ~ aVector0(xt)
    | ~ aVector0(xt)
    | ~ equal(aDimensionOf0(xt),sz00)
    | sdtlseqdt0(sz0z00,sz0z00) ),
    inference(spr,[status(thm),theory(equality)],[96,23]),
    [iquote('0:SpR:96.2,23.1')] ).

cnf(157,plain,
    ( ~ aVector0(xt)
    | ~ equal(aDimensionOf0(xt),sz00)
    | sdtlseqdt0(sz0z00,sz0z00) ),
    inference(obv,[status(thm),theory(equality)],[155]),
    [iquote('0:Obv:155.0')] ).

cnf(158,plain,
    ( ~ aVector0(xt)
    | ~ equal(sz00,sz00)
    | sdtlseqdt0(sz0z00,sz0z00) ),
    inference(rew,[status(thm),theory(equality)],[79,157]),
    [iquote('0:Rew:79.0,157.1')] ).

cnf(159,plain,
    ( ~ aVector0(xt)
    | sdtlseqdt0(sz0z00,sz0z00) ),
    inference(obv,[status(thm),theory(equality)],[158]),
    [iquote('0:Obv:158.1')] ).

cnf(160,plain,
    sdtlseqdt0(sz0z00,sz0z00),
    inference(ssi,[status(thm)],[159,4]),
    [iquote('0:SSi:159.0,4.0')] ).

cnf(496,plain,
    ( ~ aVector0(xs)
    | ~ equal(aDimensionOf0(xs),sz00)
    | ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(spl,[status(thm),theory(equality)],[96,46]),
    [iquote('0:SpL:96.2,46.0')] ).

cnf(501,plain,
    ( ~ aVector0(xs)
    | ~ equal(sz00,sz00)
    | ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(rew,[status(thm),theory(equality)],[78,496]),
    [iquote('0:Rew:78.0,496.1')] ).

cnf(502,plain,
    ( ~ aVector0(xs)
    | ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(obv,[status(thm),theory(equality)],[501]),
    [iquote('0:Obv:501.1')] ).

cnf(503,plain,
    ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
    inference(ssi,[status(thm)],[502,3]),
    [iquote('0:SSi:502.0,3.0')] ).

cnf(514,plain,
    ( ~ aScalar0(sz0z00)
    | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(spl,[status(thm),theory(equality)],[20,503]),
    [iquote('0:SpL:20.1,503.0')] ).

cnf(518,plain,
    ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
    inference(ssi,[status(thm)],[514,2]),
    [iquote('0:SSi:514.0,2.0')] ).

cnf(527,plain,
    ( ~ aVector0(xt)
    | ~ equal(aDimensionOf0(xt),sz00)
    | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)) ),
    inference(spl,[status(thm),theory(equality)],[96,518]),
    [iquote('0:SpL:96.2,518.0')] ).

cnf(529,plain,
    ( ~ aVector0(xt)
    | ~ equal(sz00,sz00)
    | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)) ),
    inference(rew,[status(thm),theory(equality)],[79,527]),
    [iquote('0:Rew:79.0,527.1')] ).

cnf(530,plain,
    ( ~ aVector0(xt)
    | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)) ),
    inference(obv,[status(thm),theory(equality)],[529]),
    [iquote('0:Obv:529.1')] ).

cnf(531,plain,
    ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)),
    inference(ssi,[status(thm)],[530,4]),
    [iquote('0:SSi:530.0,4.0')] ).

cnf(537,plain,
    ( ~ aScalar0(sdtasasdt0(xs,xs))
    | ~ sdtlseqdt0(sz0z00,sz0z00) ),
    inference(spl,[status(thm),theory(equality)],[19,531]),
    [iquote('0:SpL:19.1,531.0')] ).

cnf(539,plain,
    ~ aScalar0(sdtasasdt0(xs,xs)),
    inference(mrr,[status(thm)],[537,160]),
    [iquote('0:MRR:537.1,160.0')] ).

cnf(543,plain,
    ( ~ aVector0(xs)
    | ~ aVector0(xs)
    | ~ equal(aDimensionOf0(xs),aDimensionOf0(xs)) ),
    inference(sor,[status(thm)],[539,47]),
    [iquote('0:SoR:539.0,47.3')] ).

cnf(546,plain,
    ~ aVector0(xs),
    inference(obv,[status(thm),theory(equality)],[543]),
    [iquote('0:Obv:543.2')] ).

cnf(547,plain,
    $false,
    inference(ssi,[status(thm)],[546,3]),
    [iquote('0:SSi:546.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : RNG081+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n028.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 : Mon May 30 09:10:34 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.17/0.47  
% 0.17/0.47  SPASS V 3.9 
% 0.17/0.47  SPASS beiseite: Proof found.
% 0.17/0.47  % SZS status Theorem
% 0.17/0.47  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.17/0.47  SPASS derived 237 clauses, backtracked 0 clauses, performed 0 splits and kept 116 clauses.
% 0.17/0.47  SPASS allocated 98155 KBytes.
% 0.17/0.47  SPASS spent	0:00:00.13 on the problem.
% 0.17/0.47  		0:00:00.04 for the input.
% 0.17/0.47  		0:00:00.04 for the FLOTTER CNF translation.
% 0.17/0.47  		0:00:00.00 for inferences.
% 0.17/0.47  		0:00:00.00 for the backtracking.
% 0.17/0.47  		0:00:00.02 for the reduction.
% 0.17/0.47  
% 0.17/0.47  
% 0.17/0.47  Here is a proof with depth 6, length 36 :
% 0.17/0.47  % SZS output start Refutation
% See solution above
% 0.17/0.47  Formulae used in the proof : mSZeroSc m__1678 m__1678_01 mScZero mScSqPos m__ mScPr mDefSPZ
% 0.17/0.47  
%------------------------------------------------------------------------------