TSTP Solution File: NUM434+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM434+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 : n022.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 10:37:22 EDT 2023

% Result   : Theorem 0.20s 0.55s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   55 (  10 unt;  13 typ;   0 def)
%            Number of atoms       :  138 (  40 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  157 (  61   ~;  66   |;  21   &)
%                                         (   2 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (   7   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   45 (   0 sgn;  27   !;   3   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aInteger0: $i > $o ).

tff(decl_23,type,
    sz00: $i ).

tff(decl_24,type,
    sz10: $i ).

tff(decl_25,type,
    smndt0: $i > $i ).

tff(decl_26,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_27,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(decl_28,type,
    aDivisorOf0: ( $i * $i ) > $o ).

tff(decl_29,type,
    sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).

tff(decl_30,type,
    xa: $i ).

tff(decl_31,type,
    xb: $i ).

tff(decl_32,type,
    xp: $i ).

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

tff(decl_34,type,
    esk1_2: ( $i * $i ) > $i ).

fof(mEquMod,axiom,
    ! [X1,X2,X3] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & aInteger0(X3)
        & X3 != sz00 )
     => ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
      <=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).

fof(m__1003,hypothesis,
    sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1003) ).

fof(m__979,hypothesis,
    ( aInteger0(xa)
    & aInteger0(xb)
    & aInteger0(xp)
    & xp != sz00
    & aInteger0(xq)
    & xq != sz00 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__979) ).

fof(mIntMult,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2) )
     => aInteger0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).

fof(mDivisor,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ! [X2] :
          ( aDivisorOf0(X2,X1)
        <=> ( aInteger0(X2)
            & X2 != sz00
            & ? [X3] :
                ( aInteger0(X3)
                & sdtasdt0(X2,X3) = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).

fof(mIntPlus,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2) )
     => aInteger0(sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).

fof(m__,conjecture,
    ? [X1] :
      ( aInteger0(X1)
      & sdtasdt0(sdtasdt0(xp,xq),X1) = sdtpldt0(xa,smndt0(xb)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(mIntNeg,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => aInteger0(smndt0(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).

fof(mZeroDiv,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2) )
     => ( sdtasdt0(X1,X2) = sz00
       => ( X1 = sz00
          | X2 = sz00 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).

fof(c_0_9,plain,
    ! [X35,X36,X37] :
      ( ( ~ sdteqdtlpzmzozddtrp0(X35,X36,X37)
        | aDivisorOf0(X37,sdtpldt0(X35,smndt0(X36)))
        | ~ aInteger0(X35)
        | ~ aInteger0(X36)
        | ~ aInteger0(X37)
        | X37 = sz00 )
      & ( ~ aDivisorOf0(X37,sdtpldt0(X35,smndt0(X36)))
        | sdteqdtlpzmzozddtrp0(X35,X36,X37)
        | ~ aInteger0(X35)
        | ~ aInteger0(X36)
        | ~ aInteger0(X37)
        | X37 = sz00 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).

cnf(c_0_10,plain,
    ( aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2)))
    | X3 = sz00
    | ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_11,hypothesis,
    sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
    inference(split_conjunct,[status(thm)],[m__1003]) ).

cnf(c_0_12,hypothesis,
    aInteger0(xb),
    inference(split_conjunct,[status(thm)],[m__979]) ).

cnf(c_0_13,hypothesis,
    aInteger0(xa),
    inference(split_conjunct,[status(thm)],[m__979]) ).

fof(c_0_14,plain,
    ! [X8,X9] :
      ( ~ aInteger0(X8)
      | ~ aInteger0(X9)
      | aInteger0(sdtasdt0(X8,X9)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).

fof(c_0_15,plain,
    ! [X30,X31,X33,X34] :
      ( ( aInteger0(X31)
        | ~ aDivisorOf0(X31,X30)
        | ~ aInteger0(X30) )
      & ( X31 != sz00
        | ~ aDivisorOf0(X31,X30)
        | ~ aInteger0(X30) )
      & ( aInteger0(esk1_2(X30,X31))
        | ~ aDivisorOf0(X31,X30)
        | ~ aInteger0(X30) )
      & ( sdtasdt0(X31,esk1_2(X30,X31)) = X30
        | ~ aDivisorOf0(X31,X30)
        | ~ aInteger0(X30) )
      & ( ~ aInteger0(X33)
        | X33 = sz00
        | ~ aInteger0(X34)
        | sdtasdt0(X33,X34) != X30
        | aDivisorOf0(X33,X30)
        | ~ aInteger0(X30) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivisor])])])])])]) ).

cnf(c_0_16,hypothesis,
    ( sdtasdt0(xp,xq) = sz00
    | aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
    | ~ aInteger0(sdtasdt0(xp,xq)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]) ).

cnf(c_0_17,plain,
    ( aInteger0(sdtasdt0(X1,X2))
    | ~ aInteger0(X1)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,hypothesis,
    aInteger0(xq),
    inference(split_conjunct,[status(thm)],[m__979]) ).

cnf(c_0_19,hypothesis,
    aInteger0(xp),
    inference(split_conjunct,[status(thm)],[m__979]) ).

cnf(c_0_20,plain,
    ( sdtasdt0(X1,esk1_2(X2,X1)) = X2
    | ~ aDivisorOf0(X1,X2)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,hypothesis,
    ( sdtasdt0(xp,xq) = sz00
    | aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]) ).

fof(c_0_22,plain,
    ! [X6,X7] :
      ( ~ aInteger0(X6)
      | ~ aInteger0(X7)
      | aInteger0(sdtpldt0(X6,X7)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).

cnf(c_0_23,plain,
    ( aInteger0(esk1_2(X1,X2))
    | ~ aDivisorOf0(X2,X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_24,negated_conjecture,
    ~ ? [X1] :
        ( aInteger0(X1)
        & sdtasdt0(sdtasdt0(xp,xq),X1) = sdtpldt0(xa,smndt0(xb)) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_25,hypothesis,
    ( sdtasdt0(sdtasdt0(xp,xq),esk1_2(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) = sdtpldt0(xa,smndt0(xb))
    | sdtasdt0(xp,xq) = sz00
    | ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,plain,
    ( aInteger0(sdtpldt0(X1,X2))
    | ~ aInteger0(X1)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_27,plain,
    ! [X5] :
      ( ~ aInteger0(X5)
      | aInteger0(smndt0(X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).

cnf(c_0_28,hypothesis,
    ( sdtasdt0(xp,xq) = sz00
    | aInteger0(esk1_2(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq)))
    | ~ aInteger0(sdtpldt0(xa,smndt0(xb))) ),
    inference(spm,[status(thm)],[c_0_23,c_0_21]) ).

fof(c_0_29,negated_conjecture,
    ! [X47] :
      ( ~ aInteger0(X47)
      | sdtasdt0(sdtasdt0(xp,xq),X47) != sdtpldt0(xa,smndt0(xb)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])]) ).

cnf(c_0_30,hypothesis,
    ( sdtasdt0(sdtasdt0(xp,xq),esk1_2(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) = sdtpldt0(xa,smndt0(xb))
    | sdtasdt0(xp,xq) = sz00
    | ~ aInteger0(smndt0(xb)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_13])]) ).

cnf(c_0_31,plain,
    ( aInteger0(smndt0(X1))
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_32,hypothesis,
    ( sdtasdt0(xp,xq) = sz00
    | aInteger0(esk1_2(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq)))
    | ~ aInteger0(smndt0(xb)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_26]),c_0_13])]) ).

fof(c_0_33,plain,
    ! [X28,X29] :
      ( ~ aInteger0(X28)
      | ~ aInteger0(X29)
      | sdtasdt0(X28,X29) != sz00
      | X28 = sz00
      | X29 = sz00 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])]) ).

cnf(c_0_34,negated_conjecture,
    ( ~ aInteger0(X1)
    | sdtasdt0(sdtasdt0(xp,xq),X1) != sdtpldt0(xa,smndt0(xb)) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_35,hypothesis,
    ( sdtasdt0(sdtasdt0(xp,xq),esk1_2(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) = sdtpldt0(xa,smndt0(xb))
    | sdtasdt0(xp,xq) = sz00 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_12])]) ).

cnf(c_0_36,hypothesis,
    ( sdtasdt0(xp,xq) = sz00
    | aInteger0(esk1_2(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_31]),c_0_12])]) ).

cnf(c_0_37,plain,
    ( X1 = sz00
    | X2 = sz00
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | sdtasdt0(X1,X2) != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_38,negated_conjecture,
    sdtasdt0(xp,xq) = sz00,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_39,hypothesis,
    xq != sz00,
    inference(split_conjunct,[status(thm)],[m__979]) ).

cnf(c_0_40,hypothesis,
    xp != sz00,
    inference(split_conjunct,[status(thm)],[m__979]) ).

cnf(c_0_41,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_18]),c_0_19])]),c_0_39]),c_0_40]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM434+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n022.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri Aug 25 11:54:25 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.53  start to proof: theBenchmark
% 0.20/0.55  % Version  : CSE_E---1.5
% 0.20/0.55  % Problem  : theBenchmark.p
% 0.20/0.55  % Proof found
% 0.20/0.55  % SZS status Theorem for theBenchmark.p
% 0.20/0.55  % SZS output start Proof
% See solution above
% 0.20/0.56  % Total time : 0.011000 s
% 0.20/0.56  % SZS output end Proof
% 0.20/0.56  % Total time : 0.013000 s
%------------------------------------------------------------------------------