%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG050+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n013.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  : 300s
% DateTime : Thu Aug 31 13:48:44 EDT 2023

% Result   : Theorem 0.20s 0.60s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   38 (   9 unt;  18 typ;   0 def)
%            Number of atoms       :   44 (  17 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   41 (  17   ~;  14   |;   3   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  15   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   3 con; 0-2 aty)
%            Number of variables   :   10 (   0 sgn;   6   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aNaturalNumber0: $i > $o ).

tff(decl_23,type,
    sz00: $i ).

tff(decl_24,type,
    szszuzczcdt0: $i > $i ).

tff(decl_25,type,
    iLess0: ( $i * $i ) > $o ).

tff(decl_26,type,
    aScalar0: $i > $o ).

tff(decl_27,type,
    sz0z00: $i ).

tff(decl_28,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_29,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(decl_30,type,
    smndt0: $i > $i ).

tff(decl_31,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(decl_32,type,
    aVector0: $i > $o ).

tff(decl_33,type,
    aDimensionOf0: $i > $i ).

tff(decl_34,type,
    sdtlbdtrb0: ( $i * $i ) > $i ).

tff(decl_35,type,
    sziznziztdt0: $i > $i ).

tff(decl_36,type,
    sdtasasdt0: ( $i * $i ) > $i ).

tff(decl_37,type,
    xs: $i ).

tff(decl_38,type,
    esk1_1: $i > $i ).

tff(decl_39,type,
    esk2_2: ( $i * $i ) > $i ).

fof(m__,conjecture,
    ( ( aDimensionOf0(xs) != sz00
     => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
   => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(mDefSPZ,axiom,
    ! [X1,X2] :
      ( ( aVector0(X1)
        & aVector0(X2) )
     => ( ( aDimensionOf0(X1) = aDimensionOf0(X2)
          & aDimensionOf0(X2) = sz00 )
       => sdtasasdt0(X1,X2) = sz0z00 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).

fof(m__1542,hypothesis,
    aVector0(xs),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542) ).

fof(mLERef,axiom,
    ! [X1] :
      ( aScalar0(X1)
     => sdtlseqdt0(X1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).

fof(mSZeroSc,axiom,
    aScalar0(sz0z00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).

fof(c_0_5,negated_conjecture,
    ~ ( ( aDimensionOf0(xs) != sz00
       => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
     => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_6,negated_conjecture,
    ( ( aDimensionOf0(xs) = sz00
      | sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
    & ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    inference(fof_nnf,[status(thm)],[c_0_5]) ).

fof(c_0_7,plain,
    ! [X64,X65] :
      ( ~ aVector0(X64)
      | ~ aVector0(X65)
      | aDimensionOf0(X64) != aDimensionOf0(X65)
      | aDimensionOf0(X65) != sz00
      | sdtasasdt0(X64,X65) = sz0z00 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSPZ])]) ).

cnf(c_0_8,negated_conjecture,
    ( aDimensionOf0(xs) = sz00
    | sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,negated_conjecture,
    ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( sdtasasdt0(X1,X2) = sz0z00
    | ~ aVector0(X1)
    | ~ aVector0(X2)
    | aDimensionOf0(X1) != aDimensionOf0(X2)
    | aDimensionOf0(X2) != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,hypothesis,
    aVector0(xs),
    inference(split_conjunct,[status(thm)],[m__1542]) ).

cnf(c_0_12,negated_conjecture,
    aDimensionOf0(xs) = sz00,
    inference(sr,[status(thm)],[c_0_8,c_0_9]) ).

fof(c_0_13,plain,
    ! [X31] :
      ( ~ aScalar0(X31)
      | sdtlseqdt0(X31,X31) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERef])]) ).

cnf(c_0_14,hypothesis,
    ( sdtasasdt0(xs,X1) = sz0z00
    | aDimensionOf0(X1) != sz00
    | ~ aVector0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).

cnf(c_0_15,plain,
    ( sdtlseqdt0(X1,X1)
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_16,plain,
    aScalar0(sz0z00),
    inference(split_conjunct,[status(thm)],[mSZeroSc]) ).

cnf(c_0_17,hypothesis,
    sdtasasdt0(xs,xs) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_11]),c_0_12])]) ).

cnf(c_0_18,plain,
    sdtlseqdt0(sz0z00,sz0z00),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_17]),c_0_18])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem    : RNG050+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n013.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun Aug 27 02:26:02 EDT 2023
% 0.20/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.60  % Version  : CSE_E---1.5
% 0.20/0.60  % Problem  : theBenchmark.p
% 0.20/0.60  % Proof found
% 0.20/0.60  % SZS status Theorem for theBenchmark.p
% 0.20/0.60  % SZS output start Proof
% See solution above
% 0.20/0.60  % Total time : 0.010000 s
% 0.20/0.60  % SZS output end Proof
% 0.20/0.60  % Total time : 0.014000 s
%------------------------------------------------------------------------------