%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM521+1 : 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 : n031.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 10:38:21 EDT 2023

% Result   : Theorem 0.19s 0.57s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   43 (  12 unt;  18 typ;   0 def)
%            Number of atoms       :   57 (  14 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   58 (  26   ~;  22   |;   8   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   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    :   13 (  13 usr;   5 con; 0-2 aty)
%            Number of variables   :    9 (   0 sgn;   6   !;   0   ?;   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,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk3_1: $i > $i ).

tff(decl_39,type,
    esk4_1: $i > $i ).

fof(m__2287,hypothesis,
    ~ ( xn != xp
      & sdtlseqdt0(xn,xp)
      & xm != xp
      & sdtlseqdt0(xm,xp) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).

fof(mLETotal,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
        | ( X2 != X1
          & sdtlseqdt0(X2,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).

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

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

fof(m__2075,hypothesis,
    ~ sdtlseqdt0(xp,xm),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2075) ).

fof(mLERefl,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => sdtlseqdt0(X1,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).

fof(c_0_6,hypothesis,
    ( xn = xp
    | ~ sdtlseqdt0(xn,xp)
    | xm = xp
    | ~ sdtlseqdt0(xm,xp) ),
    inference(fof_nnf,[status(thm)],[m__2287]) ).

fof(c_0_7,plain,
    ! [X47,X48] :
      ( ( X48 != X47
        | sdtlseqdt0(X47,X48)
        | ~ aNaturalNumber0(X47)
        | ~ aNaturalNumber0(X48) )
      & ( sdtlseqdt0(X48,X47)
        | sdtlseqdt0(X47,X48)
        | ~ aNaturalNumber0(X47)
        | ~ aNaturalNumber0(X48) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).

fof(c_0_8,hypothesis,
    ~ sdtlseqdt0(xp,xn),
    inference(fof_simplification,[status(thm)],[m__1870]) ).

cnf(c_0_9,hypothesis,
    ( xn = xp
    | xm = xp
    | ~ sdtlseqdt0(xn,xp)
    | ~ sdtlseqdt0(xm,xp) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( sdtlseqdt0(X1,X2)
    | sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_12,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_13,hypothesis,
    ~ sdtlseqdt0(xp,xn),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_14,hypothesis,
    ~ sdtlseqdt0(xp,xm),
    inference(fof_simplification,[status(thm)],[m__2075]) ).

cnf(c_0_15,hypothesis,
    ( xm = xp
    | xn = xp
    | ~ sdtlseqdt0(xm,xp) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12])]),c_0_13]) ).

cnf(c_0_16,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_17,hypothesis,
    ~ sdtlseqdt0(xp,xm),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,hypothesis,
    ( xn = xp
    | xm = xp ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_10]),c_0_16]),c_0_11])]),c_0_17]) ).

fof(c_0_19,plain,
    ! [X41] :
      ( ~ aNaturalNumber0(X41)
      | sdtlseqdt0(X41,X41) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERefl])]) ).

cnf(c_0_20,hypothesis,
    ( xn = xp
    | ~ sdtlseqdt0(xp,xp) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,plain,
    ( sdtlseqdt0(X1,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_22,hypothesis,
    xn = xp,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_11])]) ).

cnf(c_0_23,hypothesis,
    ~ sdtlseqdt0(xp,xp),
    inference(rw,[status(thm)],[c_0_13,c_0_22]) ).

cnf(c_0_24,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_11])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUM521+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n031.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri Aug 25 16:52:22 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.19/0.57  % Version  : CSE_E---1.5
% 0.19/0.57  % Problem  : theBenchmark.p
% 0.19/0.57  % Proof found
% 0.19/0.57  % SZS status Theorem for theBenchmark.p
% 0.19/0.57  % SZS output start Proof
% See solution above
% 0.19/0.58  % Total time : 0.018000 s
% 0.19/0.58  % SZS output end Proof
% 0.19/0.58  % Total time : 0.021000 s
%------------------------------------------------------------------------------