TSTP Solution File: NUM512+3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM512+3 : 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 : 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 10:38:14 EDT 2023

% Result   : Theorem 0.19s 0.66s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   67 (  11 unt;  35 typ;   0 def)
%            Number of atoms       :  125 (  66 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  133 (  40   ~;  34   |;  51   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   34 (  17   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   30 (  30 usr;  18 con; 0-3 aty)
%            Number of variables   :   21 (   0 sgn;  13   !;   3   ?;   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,
    xk: $i ).

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

tff(decl_38,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_40,type,
    esk3_1: $i > $i ).

tff(decl_41,type,
    esk4_1: $i > $i ).

tff(decl_42,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_43,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_44,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_46,type,
    esk9_0: $i ).

tff(decl_47,type,
    esk10_0: $i ).

tff(decl_48,type,
    esk11_0: $i ).

tff(decl_49,type,
    esk12_0: $i ).

tff(decl_50,type,
    esk13_0: $i ).

tff(decl_51,type,
    esk14_0: $i ).

tff(decl_52,type,
    esk15_0: $i ).

tff(decl_53,type,
    esk16_0: $i ).

tff(decl_54,type,
    esk17_0: $i ).

tff(decl_55,type,
    esk18_0: $i ).

tff(decl_56,type,
    esk19_0: $i ).

fof(m__,conjecture,
    ( ( ( aNaturalNumber0(sdtsldt0(xn,xr))
        & xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
     => sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) )
    & ( ( aNaturalNumber0(sdtsldt0(sdtasdt0(xp,xk),xr))
        & sdtasdt0(xp,xk) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xp,xk),xr)) )
     => sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(m__2306,hypothesis,
    ( aNaturalNumber0(xk)
    & sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
    & xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).

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

fof(m__2342,hypothesis,
    ( aNaturalNumber0(xr)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & xk = sdtasdt0(xr,X1) )
    & doDivides0(xr,xk)
    & xr != sz00
    & xr != sz10
    & ! [X1] :
        ( ( aNaturalNumber0(X1)
          & ( ? [X2] :
                ( aNaturalNumber0(X2)
                & xr = sdtasdt0(X1,X2) )
            | doDivides0(X1,xr) ) )
       => ( X1 = sz10
          | X1 = xr ) )
    & isPrime0(xr) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).

fof(m__2504,hypothesis,
    ( ~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
          & xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
       => sdtsldt0(xn,xr) = xn )
    & aNaturalNumber0(sdtsldt0(xn,xr))
    & xn = sdtasdt0(xr,sdtsldt0(xn,xr))
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(sdtsldt0(xn,xr),X1) = xn )
    & sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2504) ).

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

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/sandbox/benchmark/theBenchmark.p',mMulAsso) ).

fof(c_0_7,negated_conjecture,
    ~ ( ( ( aNaturalNumber0(sdtsldt0(xn,xr))
          & xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
       => sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) )
      & ( ( aNaturalNumber0(sdtsldt0(sdtasdt0(xp,xk),xr))
          & sdtasdt0(xp,xk) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xp,xk),xr)) )
       => sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_8,negated_conjecture,
    ( ( aNaturalNumber0(sdtsldt0(sdtasdt0(xp,xk),xr))
      | aNaturalNumber0(sdtsldt0(xn,xr)) )
    & ( sdtasdt0(xp,xk) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xp,xk),xr))
      | aNaturalNumber0(sdtsldt0(xn,xr)) )
    & ( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
      | aNaturalNumber0(sdtsldt0(xn,xr)) )
    & ( aNaturalNumber0(sdtsldt0(sdtasdt0(xp,xk),xr))
      | xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
    & ( sdtasdt0(xp,xk) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xp,xk),xr))
      | xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
    & ( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
      | xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
    & ( aNaturalNumber0(sdtsldt0(sdtasdt0(xp,xk),xr))
      | sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) )
    & ( sdtasdt0(xp,xk) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xp,xk),xr))
      | sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) )
    & ( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
      | sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).

cnf(c_0_9,negated_conjecture,
    ( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
    | sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_10,hypothesis,
    sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

fof(c_0_11,plain,
    ! [X16,X17] :
      ( ~ aNaturalNumber0(X16)
      | ~ aNaturalNumber0(X17)
      | sdtasdt0(X16,X17) = sdtasdt0(X17,X16) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).

fof(c_0_12,hypothesis,
    ! [X104,X105] :
      ( aNaturalNumber0(xr)
      & aNaturalNumber0(esk12_0)
      & xk = sdtasdt0(xr,esk12_0)
      & doDivides0(xr,xk)
      & xr != sz00
      & xr != sz10
      & ( ~ aNaturalNumber0(X105)
        | xr != sdtasdt0(X104,X105)
        | ~ aNaturalNumber0(X104)
        | X104 = sz10
        | X104 = xr )
      & ( ~ doDivides0(X104,xr)
        | ~ aNaturalNumber0(X104)
        | X104 = sz10
        | X104 = xr )
      & isPrime0(xr) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2342])])])])]) ).

cnf(c_0_13,negated_conjecture,
    ( aNaturalNumber0(sdtsldt0(sdtasdt0(xp,xk),xr))
    | sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    ( sdtasdt0(xp,xk) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xp,xk),xr))
    | sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    ( sdtasdt0(sdtsldt0(sdtasdt0(xn,xm),xr),xr) != sdtasdt0(xn,xm)
    | sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
    inference(rw,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_16,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,hypothesis,
    aNaturalNumber0(xr),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,negated_conjecture,
    ( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xr))
    | sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
    inference(rw,[status(thm)],[c_0_13,c_0_10]) ).

cnf(c_0_19,negated_conjecture,
    ( sdtasdt0(xr,sdtsldt0(sdtasdt0(xn,xm),xr)) = sdtasdt0(xn,xm)
    | sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_10]),c_0_10]) ).

fof(c_0_20,hypothesis,
    ( aNaturalNumber0(sdtsldt0(xn,xr))
    & xn = sdtasdt0(xr,sdtsldt0(xn,xr))
    & sdtsldt0(xn,xr) != xn
    & aNaturalNumber0(sdtsldt0(xn,xr))
    & xn = sdtasdt0(xr,sdtsldt0(xn,xr))
    & aNaturalNumber0(esk19_0)
    & sdtpldt0(sdtsldt0(xn,xr),esk19_0) = xn
    & sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2504])])]) ).

cnf(c_0_21,negated_conjecture,
    sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),c_0_18]),c_0_19]) ).

cnf(c_0_22,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_23,hypothesis,
    aNaturalNumber0(sdtsldt0(xn,xr)),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_24,plain,
    ! [X18,X19,X20] :
      ( ~ aNaturalNumber0(X18)
      | ~ aNaturalNumber0(X19)
      | ~ aNaturalNumber0(X20)
      | sdtasdt0(sdtasdt0(X18,X19),X20) = sdtasdt0(X18,sdtasdt0(X19,X20)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).

cnf(c_0_25,negated_conjecture,
    sdtasdt0(sdtasdt0(xm,sdtsldt0(xn,xr)),xr) != sdtasdt0(xn,xm),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_16]),c_0_22]),c_0_23])]) ).

cnf(c_0_26,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_27,negated_conjecture,
    sdtasdt0(xm,sdtasdt0(sdtsldt0(xn,xr),xr)) != sdtasdt0(xn,xm),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_17]),c_0_23]),c_0_22])]) ).

cnf(c_0_28,hypothesis,
    xn = sdtasdt0(xr,sdtsldt0(xn,xr)),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_29,negated_conjecture,
    sdtasdt0(xm,xn) != sdtasdt0(xn,xm),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_16]),c_0_28]),c_0_17]),c_0_23])]) ).

cnf(c_0_30,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_31,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_16]),c_0_30]),c_0_22])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM512+3 : 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
% 0.12/0.34  % Computer : n027.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri Aug 25 09:17:48 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.66  % Version  : CSE_E---1.5
% 0.19/0.66  % Problem  : theBenchmark.p
% 0.19/0.66  % Proof found
% 0.19/0.66  % SZS status Theorem for theBenchmark.p
% 0.19/0.66  % SZS output start Proof
% See solution above
% 0.19/0.66  % Total time : 0.080000 s
% 0.19/0.66  % SZS output end Proof
% 0.19/0.66  % Total time : 0.084000 s
%------------------------------------------------------------------------------