TSTP Solution File: NUM460+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM460+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 : n006.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 10:37:42 EDT 2023

% Result   : Theorem 0.70s 0.80s
% Output   : CNFRefutation 0.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   67 (  21 unt;  11 typ;   0 def)
%            Number of atoms       :  179 (  47 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  215 (  92   ~;  90   |;  21   &)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   71 (   0 sgn;  31   !;   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,
    xm: $i ).

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

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

tff(decl_32,type,
    esk1_2: ( $i * $i ) > $i ).

fof(mDefDiff,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
       => ! [X3] :
            ( X3 = sdtmndt0(X2,X1)
          <=> ( aNaturalNumber0(X3)
              & sdtpldt0(X1,X3) = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).

fof(m__,conjecture,
    ( ( sdtlseqdt0(xm,xn)
      & sdtlseqdt0(xn,xl) )
   => sdtlseqdt0(xm,xl) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

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

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__773,hypothesis,
    ( aNaturalNumber0(xm)
    & aNaturalNumber0(xn)
    & aNaturalNumber0(xl) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__773) ).

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(c_0_8,plain,
    ! [X38,X39,X40] :
      ( ( aNaturalNumber0(X40)
        | X40 != sdtmndt0(X39,X38)
        | ~ sdtlseqdt0(X38,X39)
        | ~ aNaturalNumber0(X38)
        | ~ aNaturalNumber0(X39) )
      & ( sdtpldt0(X38,X40) = X39
        | X40 != sdtmndt0(X39,X38)
        | ~ sdtlseqdt0(X38,X39)
        | ~ aNaturalNumber0(X38)
        | ~ aNaturalNumber0(X39) )
      & ( ~ aNaturalNumber0(X40)
        | sdtpldt0(X38,X40) != X39
        | X40 = sdtmndt0(X39,X38)
        | ~ sdtlseqdt0(X38,X39)
        | ~ aNaturalNumber0(X38)
        | ~ aNaturalNumber0(X39) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).

fof(c_0_9,negated_conjecture,
    ~ ( ( sdtlseqdt0(xm,xn)
        & sdtlseqdt0(xn,xl) )
     => sdtlseqdt0(xm,xl) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_10,plain,
    ! [X34,X35,X37] :
      ( ( aNaturalNumber0(esk1_2(X34,X35))
        | ~ sdtlseqdt0(X34,X35)
        | ~ aNaturalNumber0(X34)
        | ~ aNaturalNumber0(X35) )
      & ( sdtpldt0(X34,esk1_2(X34,X35)) = X35
        | ~ sdtlseqdt0(X34,X35)
        | ~ aNaturalNumber0(X34)
        | ~ aNaturalNumber0(X35) )
      & ( ~ aNaturalNumber0(X37)
        | sdtpldt0(X34,X37) != X35
        | sdtlseqdt0(X34,X35)
        | ~ aNaturalNumber0(X34)
        | ~ aNaturalNumber0(X35) ) ),
    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_11,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | aNaturalNumber0(sdtpldt0(X4,X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).

cnf(c_0_12,plain,
    ( sdtpldt0(X1,X2) = X3
    | X2 != sdtmndt0(X3,X1)
    | ~ sdtlseqdt0(X1,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_13,negated_conjecture,
    ( sdtlseqdt0(xm,xn)
    & sdtlseqdt0(xn,xl)
    & ~ sdtlseqdt0(xm,xl) ),
    inference(fof_nnf,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( aNaturalNumber0(X1)
    | X1 != sdtmndt0(X2,X3)
    | ~ sdtlseqdt0(X3,X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,plain,
    ( sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X2,X1) != X3
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_17,plain,
    ! [X8,X9] :
      ( ~ aNaturalNumber0(X8)
      | ~ aNaturalNumber0(X9)
      | sdtpldt0(X8,X9) = sdtpldt0(X9,X8) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).

fof(c_0_18,plain,
    ! [X24,X25,X26] :
      ( ( sdtpldt0(X24,X25) != sdtpldt0(X24,X26)
        | X25 = X26
        | ~ aNaturalNumber0(X24)
        | ~ aNaturalNumber0(X25)
        | ~ aNaturalNumber0(X26) )
      & ( sdtpldt0(X25,X24) != sdtpldt0(X26,X24)
        | X25 = X26
        | ~ aNaturalNumber0(X24)
        | ~ aNaturalNumber0(X25)
        | ~ aNaturalNumber0(X26) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).

cnf(c_0_19,plain,
    ( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(er,[status(thm)],[c_0_12]) ).

cnf(c_0_20,negated_conjecture,
    sdtlseqdt0(xm,xn),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__773]) ).

cnf(c_0_22,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__773]) ).

cnf(c_0_23,plain,
    ( aNaturalNumber0(sdtmndt0(X1,X2))
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(er,[status(thm)],[c_0_14]) ).

cnf(c_0_24,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_15]),c_0_16]) ).

cnf(c_0_25,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_26,plain,
    ( X1 = X3
    | sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_27,negated_conjecture,
    sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
    inference(cn,[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_22])]) ).

cnf(c_0_28,negated_conjecture,
    aNaturalNumber0(sdtmndt0(xn,xm)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_20]),c_0_22]),c_0_21])]) ).

cnf(c_0_29,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X2,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_30,negated_conjecture,
    sdtlseqdt0(xn,xl),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_31,hypothesis,
    aNaturalNumber0(xl),
    inference(split_conjunct,[status(thm)],[m__773]) ).

cnf(c_0_32,negated_conjecture,
    ( X1 = xm
    | sdtpldt0(X1,sdtmndt0(xn,xm)) != xn
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_22]),c_0_28])]) ).

cnf(c_0_33,plain,
    ( sdtpldt0(X1,esk1_2(X1,X2)) = X2
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_34,negated_conjecture,
    sdtlseqdt0(sdtmndt0(xn,xm),xn),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_28]),c_0_22])]) ).

cnf(c_0_35,plain,
    ( aNaturalNumber0(esk1_2(X1,X2))
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_36,negated_conjecture,
    sdtpldt0(xn,sdtmndt0(xl,xn)) = xl,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_30]),c_0_31]),c_0_21])]) ).

cnf(c_0_37,negated_conjecture,
    aNaturalNumber0(sdtmndt0(xl,xn)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_30]),c_0_21]),c_0_31])]) ).

fof(c_0_38,plain,
    ! [X10,X11,X12] :
      ( ~ aNaturalNumber0(X10)
      | ~ aNaturalNumber0(X11)
      | ~ aNaturalNumber0(X12)
      | sdtpldt0(sdtpldt0(X10,X11),X12) = sdtpldt0(X10,sdtpldt0(X11,X12)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).

cnf(c_0_39,negated_conjecture,
    ( X1 = xm
    | sdtpldt0(sdtmndt0(xn,xm),X1) != xn
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_28])]) ).

cnf(c_0_40,negated_conjecture,
    sdtpldt0(sdtmndt0(xn,xm),esk1_2(sdtmndt0(xn,xm),xn)) = xn,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_21]),c_0_28])]) ).

cnf(c_0_41,negated_conjecture,
    aNaturalNumber0(esk1_2(sdtmndt0(xn,xm),xn)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_34]),c_0_21]),c_0_28])]) ).

cnf(c_0_42,negated_conjecture,
    ( X1 = xn
    | sdtpldt0(X1,sdtmndt0(xl,xn)) != xl
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_36]),c_0_21]),c_0_37])]) ).

cnf(c_0_43,negated_conjecture,
    sdtlseqdt0(sdtmndt0(xl,xn),xl),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_36]),c_0_37]),c_0_21])]) ).

cnf(c_0_44,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_45,negated_conjecture,
    esk1_2(sdtmndt0(xn,xm),xn) = xm,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).

cnf(c_0_46,negated_conjecture,
    ( X1 = xn
    | sdtpldt0(sdtmndt0(xl,xn),X1) != xl
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_25]),c_0_37])]) ).

cnf(c_0_47,negated_conjecture,
    sdtpldt0(sdtmndt0(xl,xn),esk1_2(sdtmndt0(xl,xn),xl)) = xl,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_43]),c_0_31]),c_0_37])]) ).

cnf(c_0_48,negated_conjecture,
    aNaturalNumber0(esk1_2(sdtmndt0(xl,xn),xl)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_43]),c_0_31]),c_0_37])]) ).

cnf(c_0_49,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X2,sdtpldt0(X3,X1)))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_44]),c_0_16]) ).

cnf(c_0_50,negated_conjecture,
    sdtpldt0(sdtmndt0(xn,xm),xm) = xn,
    inference(rw,[status(thm)],[c_0_40,c_0_45]) ).

cnf(c_0_51,negated_conjecture,
    esk1_2(sdtmndt0(xl,xn),xl) = xn,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).

cnf(c_0_52,negated_conjecture,
    ( sdtlseqdt0(xm,sdtpldt0(X1,xn))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_22]),c_0_28])]) ).

cnf(c_0_53,negated_conjecture,
    sdtpldt0(sdtmndt0(xl,xn),xn) = xl,
    inference(rw,[status(thm)],[c_0_47,c_0_51]) ).

cnf(c_0_54,negated_conjecture,
    ~ sdtlseqdt0(xm,xl),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_55,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_37])]),c_0_54]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM460+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
% 0.14/0.34  % Computer : n006.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Fri Aug 25 14:23:22 EDT 2023
% 0.20/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.70/0.80  % Version  : CSE_E---1.5
% 0.70/0.80  % Problem  : theBenchmark.p
% 0.70/0.80  % Proof found
% 0.70/0.80  % SZS status Theorem for theBenchmark.p
% 0.70/0.80  % SZS output start Proof
% See solution above
% 0.70/0.81  % Total time : 0.234000 s
% 0.70/0.81  % SZS output end Proof
% 0.70/0.81  % Total time : 0.237000 s
%------------------------------------------------------------------------------