TSTP Solution File: NUM494+3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM494+3 : 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 : n032.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 10:38:03 EDT 2023

% Result   : Theorem 0.13s 0.66s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   70 (  10 unt;  27 typ;   0 def)
%            Number of atoms       :  158 (  57 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  186 (  71   ~;  69   |;  37   &)
%                                         (   1 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 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    :   22 (  22 usr;  10 con; 0-3 aty)
%            Number of variables   :   54 (   0 sgn;  31   !;   5   ?;   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 ).

tff(decl_41,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_42,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_43,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_44,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk9_0: $i ).

tff(decl_46,type,
    esk10_0: $i ).

tff(decl_47,type,
    esk11_0: $i ).

tff(decl_48,type,
    esk12_0: $i ).

fof(m__,conjecture,
    ( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
    & ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X1) = sdtpldt0(sdtpldt0(xn,xm),xp) )
      | sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

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

fof(m__1883,hypothesis,
    ( aNaturalNumber0(xr)
    & sdtpldt0(xp,xr) = xn
    & xr = sdtmndt0(xn,xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).

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

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

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(mAddCanc,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
          | sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
       => X2 = X3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).

fof(m_AddZero,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).

fof(mSortsC,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

fof(m__1860,hypothesis,
    ( xp != sz00
    & xp != sz10
    & ! [X1] :
        ( ( aNaturalNumber0(X1)
          & ( ? [X2] :
                ( aNaturalNumber0(X2)
                & xp = sdtasdt0(X1,X2) )
            | doDivides0(X1,xp) ) )
       => ( X1 = sz10
          | X1 = xp ) )
    & isPrime0(xp)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtasdt0(xn,xm) = sdtasdt0(xp,X1) )
    & doDivides0(xp,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).

fof(c_0_11,negated_conjecture,
    ~ ( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
      & ( ? [X1] :
            ( aNaturalNumber0(X1)
            & sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X1) = sdtpldt0(sdtpldt0(xn,xm),xp) )
        | sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_12,negated_conjecture,
    ! [X102] :
      ( ( ~ aNaturalNumber0(X102)
        | sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X102) != sdtpldt0(sdtpldt0(xn,xm),xp)
        | sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) )
      & ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
        | sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).

fof(c_0_13,plain,
    ! [X10,X11] :
      ( ~ aNaturalNumber0(X10)
      | ~ aNaturalNumber0(X11)
      | sdtpldt0(X10,X11) = sdtpldt0(X11,X10) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).

cnf(c_0_14,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
    | ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_15,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_16,hypothesis,
    aNaturalNumber0(xr),
    inference(split_conjunct,[status(thm)],[m__1883]) ).

cnf(c_0_17,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

fof(c_0_18,plain,
    ! [X12,X13,X14] :
      ( ~ aNaturalNumber0(X12)
      | ~ aNaturalNumber0(X13)
      | ~ aNaturalNumber0(X14)
      | sdtpldt0(sdtpldt0(X12,X13),X14) = sdtpldt0(X12,sdtpldt0(X13,X14)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).

cnf(c_0_19,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
    | ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xr),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).

cnf(c_0_20,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_21,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_22,negated_conjecture,
    ( sdtpldt0(xm,sdtpldt0(xr,xp)) = sdtpldt0(sdtpldt0(xn,xm),xp)
    | ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_16]),c_0_17])]) ).

cnf(c_0_23,hypothesis,
    sdtpldt0(xp,xr) = xn,
    inference(split_conjunct,[status(thm)],[m__1883]) ).

fof(c_0_24,plain,
    ! [X36,X37,X39] :
      ( ( aNaturalNumber0(esk1_2(X36,X37))
        | ~ sdtlseqdt0(X36,X37)
        | ~ aNaturalNumber0(X36)
        | ~ aNaturalNumber0(X37) )
      & ( sdtpldt0(X36,esk1_2(X36,X37)) = X37
        | ~ sdtlseqdt0(X36,X37)
        | ~ aNaturalNumber0(X36)
        | ~ aNaturalNumber0(X37) )
      & ( ~ aNaturalNumber0(X39)
        | sdtpldt0(X36,X39) != X37
        | sdtlseqdt0(X36,X37)
        | ~ aNaturalNumber0(X36)
        | ~ aNaturalNumber0(X37) ) ),
    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_25,plain,
    ! [X6,X7] :
      ( ~ aNaturalNumber0(X6)
      | ~ aNaturalNumber0(X7)
      | aNaturalNumber0(sdtpldt0(X6,X7)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).

fof(c_0_26,plain,
    ! [X26,X27,X28] :
      ( ( sdtpldt0(X26,X27) != sdtpldt0(X26,X28)
        | X27 = X28
        | ~ aNaturalNumber0(X26)
        | ~ aNaturalNumber0(X27)
        | ~ aNaturalNumber0(X28) )
      & ( sdtpldt0(X27,X26) != sdtpldt0(X28,X26)
        | X27 = X28
        | ~ aNaturalNumber0(X26)
        | ~ aNaturalNumber0(X27)
        | ~ aNaturalNumber0(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).

fof(c_0_27,plain,
    ! [X15] :
      ( ( sdtpldt0(X15,sz00) = X15
        | ~ aNaturalNumber0(X15) )
      & ( X15 = sdtpldt0(sz00,X15)
        | ~ aNaturalNumber0(X15) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).

cnf(c_0_28,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xm,xn)
    | ~ sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_15]),c_0_23]),c_0_23]),c_0_21]),c_0_16])]) ).

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

cnf(c_0_30,plain,
    ( sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X2,X1) != X3
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_31,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_32,plain,
    ( X2 = X3
    | sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_33,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_34,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

cnf(c_0_35,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,xm)
    | ~ sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_15]),c_0_29]),c_0_17])]) ).

cnf(c_0_36,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_30]),c_0_31]) ).

fof(c_0_37,hypothesis,
    ! [X96,X97] :
      ( xp != sz00
      & xp != sz10
      & ( ~ aNaturalNumber0(X97)
        | xp != sdtasdt0(X96,X97)
        | ~ aNaturalNumber0(X96)
        | X96 = sz10
        | X96 = xp )
      & ( ~ doDivides0(X96,xp)
        | ~ aNaturalNumber0(X96)
        | X96 = sz10
        | X96 = xp )
      & isPrime0(xp)
      & aNaturalNumber0(esk9_0)
      & sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0)
      & doDivides0(xp,sdtasdt0(xn,xm)) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1860])])])])]) ).

cnf(c_0_38,plain,
    ( X1 = sz00
    | sdtpldt0(X2,X1) != X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).

cnf(c_0_39,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,xm)
    | ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_21])]) ).

cnf(c_0_40,hypothesis,
    xp != sz00,
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_41,negated_conjecture,
    ~ aNaturalNumber0(sdtpldt0(xn,xm)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_21])]),c_0_40]) ).

cnf(c_0_42,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_31]),c_0_17]),c_0_29])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : NUM494+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Fri Aug 25 15:25:43 EDT 2023
% 0.09/0.29  % CPUTime  : 
% 0.13/0.46  start to proof: theBenchmark
% 0.13/0.66  % Version  : CSE_E---1.5
% 0.13/0.66  % Problem  : theBenchmark.p
% 0.13/0.66  % Proof found
% 0.13/0.66  % SZS status Theorem for theBenchmark.p
% 0.13/0.66  % SZS output start Proof
% See solution above
% 0.13/0.66  % Total time : 0.191000 s
% 0.13/0.66  % SZS output end Proof
% 0.13/0.66  % Total time : 0.195000 s
%------------------------------------------------------------------------------