TSTP Solution File: NUM460+2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM460+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n026.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 10:37:42 EDT 2023

% Result   : Theorem 0.20s 0.60s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   39 (   7 unt;  13 typ;   0 def)
%            Number of atoms       :   81 (  23 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :   87 (  32   ~;  25   |;  25   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   36 (   0 sgn;  15   !;   6   ?;   0   :)

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

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

tff(decl_24,type,
    sz10: $i ).

tff(decl_25,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_26,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(decl_27,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(decl_28,type,
    sdtmndt0: ( $i * $i ) > $i ).

tff(decl_29,type,
    xm: $i ).

tff(decl_30,type,
    xn: $i ).

tff(decl_31,type,
    xl: $i ).

tff(decl_32,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_33,type,
    esk2_0: $i ).

tff(decl_34,type,
    esk3_0: $i ).

fof(m__,conjecture,
    ( ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(xm,X1) = xn )
      & sdtlseqdt0(xm,xn)
      & ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(xn,X1) = xl )
      & sdtlseqdt0(xn,xl) )
   => ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(xm,X1) = xl )
      | sdtlseqdt0(xm,xl) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(mAddComm,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).

fof(m__773,hypothesis,
    ( aNaturalNumber0(xm)
    & aNaturalNumber0(xn)
    & aNaturalNumber0(xl) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__773) ).

fof(mAddAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).

fof(mSortsB,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).

fof(c_0_5,negated_conjecture,
    ~ ( ( ? [X1] :
            ( aNaturalNumber0(X1)
            & sdtpldt0(xm,X1) = xn )
        & sdtlseqdt0(xm,xn)
        & ? [X1] :
            ( aNaturalNumber0(X1)
            & sdtpldt0(xn,X1) = xl )
        & sdtlseqdt0(xn,xl) )
     => ( ? [X1] :
            ( aNaturalNumber0(X1)
            & sdtpldt0(xm,X1) = xl )
        | sdtlseqdt0(xm,xl) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_6,negated_conjecture,
    ! [X46] :
      ( aNaturalNumber0(esk2_0)
      & sdtpldt0(xm,esk2_0) = xn
      & sdtlseqdt0(xm,xn)
      & aNaturalNumber0(esk3_0)
      & sdtpldt0(xn,esk3_0) = xl
      & sdtlseqdt0(xn,xl)
      & ( ~ aNaturalNumber0(X46)
        | sdtpldt0(xm,X46) != xl )
      & ~ sdtlseqdt0(xm,xl) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).

fof(c_0_7,plain,
    ! [X8,X9] :
      ( ~ aNaturalNumber0(X8)
      | ~ aNaturalNumber0(X9)
      | sdtpldt0(X8,X9) = sdtpldt0(X9,X8) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).

cnf(c_0_8,negated_conjecture,
    ( ~ aNaturalNumber0(X1)
    | sdtpldt0(xm,X1) != xl ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_10,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__773]) ).

fof(c_0_11,plain,
    ! [X10,X11,X12] :
      ( ~ aNaturalNumber0(X10)
      | ~ aNaturalNumber0(X11)
      | ~ aNaturalNumber0(X12)
      | sdtpldt0(sdtpldt0(X10,X11),X12) = sdtpldt0(X10,sdtpldt0(X11,X12)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).

fof(c_0_12,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | aNaturalNumber0(sdtpldt0(X4,X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).

cnf(c_0_13,negated_conjecture,
    ( sdtpldt0(X1,xm) != xl
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]) ).

cnf(c_0_14,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_16,negated_conjecture,
    ( sdtpldt0(X1,sdtpldt0(X2,xm)) != xl
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_10])]),c_0_15]) ).

cnf(c_0_17,negated_conjecture,
    ( sdtpldt0(X1,sdtpldt0(xm,X2)) != xl
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_9]),c_0_10])]) ).

cnf(c_0_18,negated_conjecture,
    sdtpldt0(xm,esk2_0) = xn,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_19,negated_conjecture,
    aNaturalNumber0(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_20,negated_conjecture,
    ( sdtpldt0(X1,xn) != xl
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).

cnf(c_0_21,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__773]) ).

cnf(c_0_22,negated_conjecture,
    ( sdtpldt0(xn,X1) != xl
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_9]),c_0_21])]) ).

cnf(c_0_23,negated_conjecture,
    sdtpldt0(xn,esk3_0) = xl,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_24,negated_conjecture,
    aNaturalNumber0(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_25,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM460+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.17/0.34  % Computer : n026.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34  % CPULimit   : 300
% 0.17/0.34  % WCLimit    : 300
% 0.17/0.35  % DateTime   : Fri Aug 25 15:59:47 EDT 2023
% 0.17/0.35  % 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
% 0.20/0.61  % Total time : 0.015000 s
% 0.20/0.61  % SZS output end Proof
% 0.20/0.61  % Total time : 0.018000 s
%------------------------------------------------------------------------------