TSTP Solution File: NUM480+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM480+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 : n001.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 0.71s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   60 (  14 unt;  15 typ;   0 def)
%            Number of atoms       :  151 (  49 equ)
%            Maximal formula atoms :   19 (   3 avg)
%            Number of connectives :  188 (  82   ~;  83   |;  15   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   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    :   11 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :   56 (   0 sgn;  25   !;   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 ).

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

fof(mDefQuot,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( X1 != sz00
          & doDivides0(X1,X2) )
       => ! [X3] :
            ( X3 = sdtsldt0(X2,X1)
          <=> ( aNaturalNumber0(X3)
              & X2 = sdtasdt0(X1,X3) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).

fof(m__1594,hypothesis,
    sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1594) ).

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

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

fof(mDefDiv,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( doDivides0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & X2 = sdtasdt0(X1,X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).

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__1524_04,hypothesis,
    ( xl != sz00
    & doDivides0(xl,xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524_04) ).

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

fof(c_0_10,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_11,plain,
    ! [X14,X15] :
      ( ~ aNaturalNumber0(X14)
      | ~ aNaturalNumber0(X15)
      | sdtasdt0(X14,X15) = sdtasdt0(X15,X14) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).

cnf(c_0_12,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_13,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_14,plain,
    ! [X64,X65,X66] :
      ( ( aNaturalNumber0(X66)
        | X66 != sdtsldt0(X65,X64)
        | X64 = sz00
        | ~ doDivides0(X64,X65)
        | ~ aNaturalNumber0(X64)
        | ~ aNaturalNumber0(X65) )
      & ( X65 = sdtasdt0(X64,X66)
        | X66 != sdtsldt0(X65,X64)
        | X64 = sz00
        | ~ doDivides0(X64,X65)
        | ~ aNaturalNumber0(X64)
        | ~ aNaturalNumber0(X65) )
      & ( ~ aNaturalNumber0(X66)
        | X65 != sdtasdt0(X64,X66)
        | X66 = sdtsldt0(X65,X64)
        | X64 = sz00
        | ~ doDivides0(X64,X65)
        | ~ aNaturalNumber0(X64)
        | ~ aNaturalNumber0(X65) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).

cnf(c_0_15,hypothesis,
    sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
    inference(split_conjunct,[status(thm)],[m__1594]) ).

cnf(c_0_16,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X2,sdtasdt0(X1,X3))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,hypothesis,
    aNaturalNumber0(xl),
    inference(split_conjunct,[status(thm)],[m__1524]) ).

cnf(c_0_18,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1553]) ).

cnf(c_0_19,plain,
    ( X1 = sdtasdt0(X2,X3)
    | X2 = sz00
    | X3 != sdtsldt0(X1,X2)
    | ~ doDivides0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_20,plain,
    ! [X60,X61,X63] :
      ( ( aNaturalNumber0(esk2_2(X60,X61))
        | ~ doDivides0(X60,X61)
        | ~ aNaturalNumber0(X60)
        | ~ aNaturalNumber0(X61) )
      & ( X61 = sdtasdt0(X60,esk2_2(X60,X61))
        | ~ doDivides0(X60,X61)
        | ~ aNaturalNumber0(X60)
        | ~ aNaturalNumber0(X61) )
      & ( ~ aNaturalNumber0(X63)
        | X61 != sdtasdt0(X60,X63)
        | doDivides0(X60,X61)
        | ~ aNaturalNumber0(X60)
        | ~ aNaturalNumber0(X61) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).

fof(c_0_21,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_22,hypothesis,
    ( sdtasdt0(xn,sdtasdt0(xl,sdtsldt0(xm,xl))) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))
    | ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).

cnf(c_0_23,plain,
    ( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
    | X1 = sz00
    | ~ doDivides0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(er,[status(thm)],[c_0_19]) ).

cnf(c_0_24,hypothesis,
    doDivides0(xl,xm),
    inference(split_conjunct,[status(thm)],[m__1524_04]) ).

cnf(c_0_25,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1524]) ).

cnf(c_0_26,hypothesis,
    xl != sz00,
    inference(split_conjunct,[status(thm)],[m__1524_04]) ).

cnf(c_0_27,plain,
    ( doDivides0(X3,X2)
    | ~ aNaturalNumber0(X1)
    | X2 != sdtasdt0(X3,X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_28,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_29,hypothesis,
    ( sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
    | ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_12]),c_0_18]),c_0_17])]) ).

cnf(c_0_30,hypothesis,
    ( sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) = sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[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_17]),c_0_25])]),c_0_26]) ).

fof(c_0_31,negated_conjecture,
    sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_32,plain,
    ( X1 = sdtsldt0(X2,X3)
    | X3 = sz00
    | ~ aNaturalNumber0(X1)
    | X2 != sdtasdt0(X3,X1)
    | ~ doDivides0(X3,X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_33,plain,
    ( doDivides0(X1,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_27]),c_0_28]) ).

cnf(c_0_34,hypothesis,
    ( sdtasdt0(xl,sdtsldt0(sdtasdt0(xm,xn),xl)) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
    | ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_13]),c_0_25]),c_0_18])]) ).

cnf(c_0_35,hypothesis,
    ( sdtasdt0(xl,sdtsldt0(sdtasdt0(xm,xn),xl)) = sdtasdt0(xm,xn)
    | ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_13]),c_0_25]),c_0_18])]) ).

cnf(c_0_36,negated_conjecture,
    sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_37,plain,
    ( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
    | X1 = sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_32]),c_0_28]),c_0_33]) ).

cnf(c_0_38,hypothesis,
    ( sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) = sdtasdt0(xm,xn)
    | ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_39,negated_conjecture,
    sdtsldt0(sdtasdt0(xm,xn),xl) != sdtasdt0(xn,sdtsldt0(xm,xl)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_13]),c_0_18]),c_0_25])]) ).

cnf(c_0_40,hypothesis,
    ( ~ aNaturalNumber0(sdtasdt0(xn,sdtsldt0(xm,xl)))
    | ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_17])]),c_0_39]),c_0_26]) ).

cnf(c_0_41,plain,
    ( aNaturalNumber0(X1)
    | X3 = sz00
    | X1 != sdtsldt0(X2,X3)
    | ~ doDivides0(X3,X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_42,hypothesis,
    ~ aNaturalNumber0(sdtsldt0(xm,xl)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_28]),c_0_18])]) ).

cnf(c_0_43,plain,
    ( X1 = sz00
    | aNaturalNumber0(sdtsldt0(X2,X1))
    | ~ doDivides0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(er,[status(thm)],[c_0_41]) ).

cnf(c_0_44,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_24]),c_0_17]),c_0_25])]),c_0_26]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM480+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n001.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Aug 25 16:05:29 EDT 2023
% 0.18/0.34  % CPUTime  : 
% 0.18/0.56  start to proof: theBenchmark
% 0.18/0.71  % Version  : CSE_E---1.5
% 0.18/0.71  % Problem  : theBenchmark.p
% 0.18/0.71  % Proof found
% 0.18/0.71  % SZS status Theorem for theBenchmark.p
% 0.18/0.71  % SZS output start Proof
% See solution above
% 0.18/0.72  % Total time : 0.146000 s
% 0.18/0.72  % SZS output end Proof
% 0.18/0.72  % Total time : 0.150000 s
%------------------------------------------------------------------------------