%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG050+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 20:41:19 EDT 2022

% Result   : Theorem 0.21s 0.46s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   16 (   7 unt;   1 nHn;  16 RR)
%            Number of literals    :   35 (   0 equ;  24 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    aScalar0(sz0z00),
    file('RNG050+1.p',unknown),
    [] ).

cnf(3,axiom,
    aVector0(xs),
    file('RNG050+1.p',unknown),
    [] ).

cnf(6,axiom,
    ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
    file('RNG050+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ aScalar0(u)
    | sdtlseqdt0(u,u) ),
    file('RNG050+1.p',unknown),
    [] ).

cnf(20,axiom,
    ( equal(aDimensionOf0(xs),sz00)
    | sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    file('RNG050+1.p',unknown),
    [] ).

cnf(44,axiom,
    ( ~ aVector0(u)
    | ~ aVector0(v)
    | ~ equal(aDimensionOf0(u),sz00)
    | ~ equal(aDimensionOf0(v),aDimensionOf0(u))
    | equal(sdtasasdt0(v,u),sz0z00) ),
    file('RNG050+1.p',unknown),
    [] ).

cnf(55,plain,
    equal(aDimensionOf0(xs),sz00),
    inference(mrr,[status(thm)],[20,6]),
    [iquote('0:MRR:20.1,6.0')] ).

cnf(57,plain,
    ( ~ aVector0(u)
    | ~ aVector0(xs)
    | ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
    | equal(sdtasasdt0(u,xs),sz0z00) ),
    inference(res,[status(thm),theory(equality)],[55,44]),
    [iquote('0:Res:55.0,44.2')] ).

cnf(69,plain,
    ( ~ aVector0(u)
    | ~ aVector0(xs)
    | ~ equal(aDimensionOf0(u),sz00)
    | equal(sdtasasdt0(u,xs),sz0z00) ),
    inference(rew,[status(thm),theory(equality)],[55,57]),
    [iquote('0:Rew:55.0,57.2')] ).

cnf(70,plain,
    ( ~ aVector0(u)
    | ~ equal(aDimensionOf0(u),sz00)
    | equal(sdtasasdt0(u,xs),sz0z00) ),
    inference(mrr,[status(thm)],[69,3]),
    [iquote('0:MRR:69.1,3.0')] ).

cnf(118,plain,
    ( ~ aVector0(xs)
    | ~ equal(aDimensionOf0(xs),sz00)
    | ~ sdtlseqdt0(sz0z00,sz0z00) ),
    inference(spl,[status(thm),theory(equality)],[70,6]),
    [iquote('0:SpL:70.2,6.0')] ).

cnf(119,plain,
    ( ~ aVector0(xs)
    | ~ equal(sz00,sz00)
    | ~ sdtlseqdt0(sz0z00,sz0z00) ),
    inference(rew,[status(thm),theory(equality)],[55,118]),
    [iquote('0:Rew:55.0,118.1')] ).

cnf(120,plain,
    ( ~ aVector0(xs)
    | ~ sdtlseqdt0(sz0z00,sz0z00) ),
    inference(obv,[status(thm),theory(equality)],[119]),
    [iquote('0:Obv:119.1')] ).

cnf(121,plain,
    ~ sdtlseqdt0(sz0z00,sz0z00),
    inference(ssi,[status(thm)],[120,3]),
    [iquote('0:SSi:120.0,3.0')] ).

cnf(122,plain,
    ~ aScalar0(sz0z00),
    inference(res,[status(thm),theory(equality)],[9,121]),
    [iquote('0:Res:9.1,121.0')] ).

cnf(123,plain,
    $false,
    inference(ssi,[status(thm)],[122,2]),
    [iquote('0:SSi:122.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : RNG050+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13  % Command  : run_spass %d %s
% 0.15/0.34  % Computer : n025.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit : 300
% 0.15/0.34  % WCLimit  : 600
% 0.15/0.34  % DateTime : Mon May 30 15:45:12 EDT 2022
% 0.15/0.35  % CPUTime  : 
% 0.21/0.46  
% 0.21/0.46  SPASS V 3.9 
% 0.21/0.46  SPASS beiseite: Proof found.
% 0.21/0.46  % SZS status Theorem
% 0.21/0.46  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.21/0.46  SPASS derived 48 clauses, backtracked 0 clauses, performed 0 splits and kept 62 clauses.
% 0.21/0.46  SPASS allocated 97874 KBytes.
% 0.21/0.46  SPASS spent	0:00:00.10 on the problem.
% 0.21/0.46  		0:00:00.04 for the input.
% 0.21/0.46  		0:00:00.04 for the FLOTTER CNF translation.
% 0.21/0.46  		0:00:00.00 for inferences.
% 0.21/0.46  		0:00:00.00 for the backtracking.
% 0.21/0.46  		0:00:00.01 for the reduction.
% 0.21/0.46  
% 0.21/0.46  
% 0.21/0.46  Here is a proof with depth 3, length 16 :
% 0.21/0.46  % SZS output start Refutation
% See solution above
% 0.21/0.46  Formulae used in the proof : mSZeroSc m__1542 m__ mLERef mDefSPZ
% 0.21/0.46  
%------------------------------------------------------------------------------