TSTP Solution File: NUM490+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM490+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 : n027.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 10:38:01 EDT 2023

% Result   : Theorem 0.13s 0.63s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   52 (  15 unt;  19 typ;   0 def)
%            Number of atoms       :  104 (  22 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  127 (  56   ~;  52   |;  12   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  13   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :   39 (   0 sgn;  19   !;   1   ?;   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,
    iLess0: ( $i * $i ) > $o ).

tff(decl_30,type,
    doDivides0: ( $i * $i ) > $o ).

tff(decl_31,type,
    sdtsldt0: ( $i * $i ) > $i ).

tff(decl_32,type,
    isPrime0: $i > $o ).

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

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

tff(decl_35,type,
    xp: $i ).

tff(decl_36,type,
    xr: $i ).

tff(decl_37,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk3_1: $i > $i ).

tff(decl_40,type,
    esk4_1: $i > $i ).

fof(mDefLE,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & sdtpldt0(X1,X3) = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).

fof(mSortsB,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).

fof(mDefDiff,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
       => ! [X3] :
            ( X3 = sdtmndt0(X2,X1)
          <=> ( aNaturalNumber0(X3)
              & sdtpldt0(X1,X3) = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).

fof(m__,conjecture,
    sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(m__1951,hypothesis,
    sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1951) ).

fof(mSortsB_02,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

fof(m__1837,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).

fof(m__1870,hypothesis,
    sdtlseqdt0(xp,xn),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).

fof(m__1883,hypothesis,
    xr = sdtmndt0(xn,xp),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).

fof(c_0_9,plain,
    ! [X34,X35,X37] :
      ( ( aNaturalNumber0(esk1_2(X34,X35))
        | ~ sdtlseqdt0(X34,X35)
        | ~ aNaturalNumber0(X34)
        | ~ aNaturalNumber0(X35) )
      & ( sdtpldt0(X34,esk1_2(X34,X35)) = X35
        | ~ sdtlseqdt0(X34,X35)
        | ~ aNaturalNumber0(X34)
        | ~ aNaturalNumber0(X35) )
      & ( ~ aNaturalNumber0(X37)
        | sdtpldt0(X34,X37) != X35
        | sdtlseqdt0(X34,X35)
        | ~ aNaturalNumber0(X34)
        | ~ aNaturalNumber0(X35) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).

fof(c_0_10,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | aNaturalNumber0(sdtpldt0(X4,X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).

fof(c_0_11,plain,
    ! [X38,X39,X40] :
      ( ( aNaturalNumber0(X40)
        | X40 != sdtmndt0(X39,X38)
        | ~ sdtlseqdt0(X38,X39)
        | ~ aNaturalNumber0(X38)
        | ~ aNaturalNumber0(X39) )
      & ( sdtpldt0(X38,X40) = X39
        | X40 != sdtmndt0(X39,X38)
        | ~ sdtlseqdt0(X38,X39)
        | ~ aNaturalNumber0(X38)
        | ~ aNaturalNumber0(X39) )
      & ( ~ aNaturalNumber0(X40)
        | sdtpldt0(X38,X40) != X39
        | X40 = sdtmndt0(X39,X38)
        | ~ sdtlseqdt0(X38,X39)
        | ~ aNaturalNumber0(X38)
        | ~ aNaturalNumber0(X39) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).

cnf(c_0_12,plain,
    ( sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X2,X1) != X3
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    ( X1 = sdtmndt0(X3,X2)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X2,X1) != X3
    | ~ sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_12]),c_0_13]) ).

fof(c_0_16,negated_conjecture,
    sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_17,plain,
    ( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_14]),c_0_13]),c_0_15]) ).

cnf(c_0_18,hypothesis,
    sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
    inference(split_conjunct,[status(thm)],[m__1951]) ).

cnf(c_0_19,negated_conjecture,
    sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_20,plain,
    ! [X6,X7] :
      ( ~ aNaturalNumber0(X6)
      | ~ aNaturalNumber0(X7)
      | aNaturalNumber0(sdtasdt0(X6,X7)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).

cnf(c_0_21,plain,
    ( aNaturalNumber0(X1)
    | X1 != sdtmndt0(X2,X3)
    | ~ sdtlseqdt0(X3,X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_22,hypothesis,
    ( ~ aNaturalNumber0(sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(sdtasdt0(xr,xm)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).

cnf(c_0_23,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_24,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_25,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_26,plain,
    ( aNaturalNumber0(sdtmndt0(X1,X2))
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(er,[status(thm)],[c_0_21]) ).

cnf(c_0_27,hypothesis,
    sdtlseqdt0(xp,xn),
    inference(split_conjunct,[status(thm)],[m__1870]) ).

cnf(c_0_28,hypothesis,
    xr = sdtmndt0(xn,xp),
    inference(split_conjunct,[status(thm)],[m__1883]) ).

cnf(c_0_29,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_30,hypothesis,
    ~ aNaturalNumber0(sdtasdt0(xr,xm)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).

cnf(c_0_31,hypothesis,
    aNaturalNumber0(xr),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_25]),c_0_29])]) ).

cnf(c_0_32,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_23]),c_0_24]),c_0_31])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.17  % Problem    : NUM490+1 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.17  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.36  % Computer : n027.cluster.edu
% 0.08/0.36  % Model    : x86_64 x86_64
% 0.08/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36  % Memory   : 8042.1875MB
% 0.08/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.37  % CPULimit   : 300
% 0.08/0.37  % WCLimit    : 300
% 0.08/0.37  % DateTime   : Fri Aug 25 09:27:33 EDT 2023
% 0.08/0.37  % CPUTime  : 
% 0.13/0.61  start to proof: theBenchmark
% 0.13/0.63  % Version  : CSE_E---1.5
% 0.13/0.63  % Problem  : theBenchmark.p
% 0.13/0.63  % Proof found
% 0.13/0.63  % SZS status Theorem for theBenchmark.p
% 0.13/0.63  % SZS output start Proof
% See solution above
% 0.13/0.64  % Total time : 0.014000 s
% 0.13/0.64  % SZS output end Proof
% 0.13/0.64  % Total time : 0.017000 s
%------------------------------------------------------------------------------