TSTP Solution File: NUM479+2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM479+2 : 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 : n021.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 10:37:56 EDT 2023

% Result   : Theorem 0.18s 0.63s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   53 (  15 unt;  16 typ;   0 def)
%            Number of atoms       :  106 (  45 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  114 (  45   ~;  37   |;  21   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  10   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :   35 (   0 sgn;  20   !;   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,
    xl: $i ).

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

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

tff(decl_35,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk3_0: $i ).

fof(m__,conjecture,
    ( ( aNaturalNumber0(sdtsldt0(xm,xl))
      & xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
   => ( ( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
        & sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) )
     => sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(mMulCanc,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( X1 != sz00
       => ! [X2,X3] :
            ( ( aNaturalNumber0(X2)
              & aNaturalNumber0(X3) )
           => ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
                | sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
             => X2 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).

fof(m__1524_04,hypothesis,
    ( xl != sz00
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & xm = sdtasdt0(xl,X1) )
    & doDivides0(xl,xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524_04) ).

fof(m__1524,hypothesis,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524) ).

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

fof(mMulAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).

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__1553,hypothesis,
    aNaturalNumber0(xn),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1553) ).

fof(c_0_8,negated_conjecture,
    ~ ( ( aNaturalNumber0(sdtsldt0(xm,xl))
        & xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
     => ( ( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
          & sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) )
       => sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_9,plain,
    ! [X27,X28,X29] :
      ( ( sdtasdt0(X27,X28) != sdtasdt0(X27,X29)
        | X28 = X29
        | ~ aNaturalNumber0(X28)
        | ~ aNaturalNumber0(X29)
        | X27 = sz00
        | ~ aNaturalNumber0(X27) )
      & ( sdtasdt0(X28,X27) != sdtasdt0(X29,X27)
        | X28 = X29
        | ~ aNaturalNumber0(X28)
        | ~ aNaturalNumber0(X29)
        | X27 = sz00
        | ~ aNaturalNumber0(X27) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).

fof(c_0_10,hypothesis,
    ( xl != sz00
    & aNaturalNumber0(esk3_0)
    & xm = sdtasdt0(xl,esk3_0)
    & doDivides0(xl,xm) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1524_04])]) ).

fof(c_0_11,negated_conjecture,
    ( aNaturalNumber0(sdtsldt0(xm,xl))
    & xm = sdtasdt0(xl,sdtsldt0(xm,xl))
    & aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
    & sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))
    & sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) ),
    inference(fof_nnf,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    ( X2 = X3
    | X1 = sz00
    | sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,hypothesis,
    xm = sdtasdt0(xl,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,hypothesis,
    aNaturalNumber0(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,hypothesis,
    aNaturalNumber0(xl),
    inference(split_conjunct,[status(thm)],[m__1524]) ).

cnf(c_0_16,hypothesis,
    xl != sz00,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,negated_conjecture,
    sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,negated_conjecture,
    sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,hypothesis,
    ( X1 = esk3_0
    | sdtasdt0(xl,X1) != xm
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).

cnf(c_0_20,negated_conjecture,
    xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_21,negated_conjecture,
    aNaturalNumber0(sdtsldt0(xm,xl)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_22,negated_conjecture,
    sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xn,xm),
    inference(rw,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    sdtsldt0(xm,xl) = esk3_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

fof(c_0_24,plain,
    ! [X14,X15] :
      ( ~ aNaturalNumber0(X14)
      | ~ aNaturalNumber0(X15)
      | sdtasdt0(X14,X15) = sdtasdt0(X15,X14) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).

fof(c_0_25,plain,
    ! [X16,X17,X18] :
      ( ~ aNaturalNumber0(X16)
      | ~ aNaturalNumber0(X17)
      | ~ aNaturalNumber0(X18)
      | sdtasdt0(sdtasdt0(X16,X17),X18) = sdtasdt0(X16,sdtasdt0(X17,X18)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).

fof(c_0_26,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_27,negated_conjecture,
    sdtasdt0(sdtasdt0(xl,xn),esk3_0) != sdtasdt0(xn,xm),
    inference(rw,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_28,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_29,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_30,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_31,negated_conjecture,
    ( sdtasdt0(esk3_0,sdtasdt0(xl,xn)) != sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(sdtasdt0(xl,xn)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_14])]) ).

cnf(c_0_32,plain,
    ( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).

cnf(c_0_33,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1553]) ).

cnf(c_0_34,negated_conjecture,
    ( sdtasdt0(xn,sdtasdt0(esk3_0,xl)) != sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(sdtasdt0(xl,xn)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_15]),c_0_14])]) ).

cnf(c_0_35,negated_conjecture,
    ~ aNaturalNumber0(sdtasdt0(xl,xn)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_13]),c_0_15]),c_0_14])]) ).

cnf(c_0_36,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_33]),c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : NUM479+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32  % Computer : n021.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Fri Aug 25 17:34:11 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.18/0.55  start to proof: theBenchmark
% 0.18/0.63  % Version  : CSE_E---1.5
% 0.18/0.63  % Problem  : theBenchmark.p
% 0.18/0.63  % Proof found
% 0.18/0.63  % SZS status Theorem for theBenchmark.p
% 0.18/0.63  % SZS output start Proof
% See solution above
% 0.18/0.63  % Total time : 0.073000 s
% 0.18/0.63  % SZS output end Proof
% 0.18/0.64  % Total time : 0.076000 s
%------------------------------------------------------------------------------