TSTP Solution File: RNG091+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG091+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 : n008.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 13:49:04 EDT 2023

% Result   : Theorem 0.59s 0.84s
% Output   : CNFRefutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   62 (  15 unt;  31 typ;   0 def)
%            Number of atoms       :  145 (  21 equ)
%            Maximal formula atoms :   52 (   4 avg)
%            Number of connectives :  188 (  74   ~;  81   |;  26   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   41 (  20   >;  21   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   27 (  27 usr;  11 con; 0-4 aty)
%            Number of variables   :   40 (   0 sgn;  23   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aElement0: $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,
    aSet0: $i > $o ).

tff(decl_29,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(decl_30,type,
    sdtpldt1: ( $i * $i ) > $i ).

tff(decl_31,type,
    sdtasasdt0: ( $i * $i ) > $i ).

tff(decl_32,type,
    aIdeal0: $i > $o ).

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

tff(decl_34,type,
    xJ: $i ).

tff(decl_35,type,
    xx: $i ).

tff(decl_36,type,
    xy: $i ).

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

tff(decl_38,type,
    xk: $i ).

tff(decl_39,type,
    xl: $i ).

tff(decl_40,type,
    xm: $i ).

tff(decl_41,type,
    xn: $i ).

tff(decl_42,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_43,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_44,type,
    esk3_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk4_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_46,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_47,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_48,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_49,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk9_1: $i > $i ).

tff(decl_51,type,
    esk10_1: $i > $i ).

tff(decl_52,type,
    esk11_1: $i > $i ).

fof(mDefSSum,axiom,
    ! [X1,X2] :
      ( ( aSet0(X1)
        & aSet0(X2) )
     => ! [X3] :
          ( X3 = sdtpldt1(X1,X2)
        <=> ( aSet0(X3)
            & ! [X4] :
                ( aElementOf0(X4,X3)
              <=> ? [X5,X6] :
                    ( aElementOf0(X5,X1)
                    & aElementOf0(X6,X2)
                    & sdtpldt0(X5,X6) = X4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).

fof(mDefIdeal,axiom,
    ! [X1] :
      ( aIdeal0(X1)
    <=> ( aSet0(X1)
        & ! [X2] :
            ( aElementOf0(X2,X1)
           => ( ! [X3] :
                  ( aElementOf0(X3,X1)
                 => aElementOf0(sdtpldt0(X2,X3),X1) )
              & ! [X3] :
                  ( aElement0(X3)
                 => aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).

fof(m__870,hypothesis,
    ( aIdeal0(xI)
    & aIdeal0(xJ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).

fof(m__,conjecture,
    ( aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
    & aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(m__1021,hypothesis,
    ( aElementOf0(sdtasdt0(xz,xk),xI)
    & aElementOf0(sdtasdt0(xz,xl),xJ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1021) ).

fof(m__1098,hypothesis,
    sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1098) ).

fof(m__994,hypothesis,
    ( aElementOf0(sdtpldt0(xk,xm),xI)
    & aElementOf0(sdtpldt0(xl,xn),xJ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__994) ).

fof(m__1061,hypothesis,
    sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1061) ).

fof(c_0_8,plain,
    ! [X38,X39,X40,X41,X44,X45,X46,X47,X49,X50] :
      ( ( aSet0(X40)
        | X40 != sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( aElementOf0(esk3_4(X38,X39,X40,X41),X38)
        | ~ aElementOf0(X41,X40)
        | X40 != sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( aElementOf0(esk4_4(X38,X39,X40,X41),X39)
        | ~ aElementOf0(X41,X40)
        | X40 != sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( sdtpldt0(esk3_4(X38,X39,X40,X41),esk4_4(X38,X39,X40,X41)) = X41
        | ~ aElementOf0(X41,X40)
        | X40 != sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( ~ aElementOf0(X45,X38)
        | ~ aElementOf0(X46,X39)
        | sdtpldt0(X45,X46) != X44
        | aElementOf0(X44,X40)
        | X40 != sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( ~ aElementOf0(esk5_3(X38,X39,X47),X47)
        | ~ aElementOf0(X49,X38)
        | ~ aElementOf0(X50,X39)
        | sdtpldt0(X49,X50) != esk5_3(X38,X39,X47)
        | ~ aSet0(X47)
        | X47 = sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( aElementOf0(esk6_3(X38,X39,X47),X38)
        | aElementOf0(esk5_3(X38,X39,X47),X47)
        | ~ aSet0(X47)
        | X47 = sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( aElementOf0(esk7_3(X38,X39,X47),X39)
        | aElementOf0(esk5_3(X38,X39,X47),X47)
        | ~ aSet0(X47)
        | X47 = sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) )
      & ( sdtpldt0(esk6_3(X38,X39,X47),esk7_3(X38,X39,X47)) = esk5_3(X38,X39,X47)
        | aElementOf0(esk5_3(X38,X39,X47),X47)
        | ~ aSet0(X47)
        | X47 = sdtpldt1(X38,X39)
        | ~ aSet0(X38)
        | ~ aSet0(X39) ) ),
    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)],[mDefSSum])])])])])]) ).

fof(c_0_9,plain,
    ! [X60,X61,X62,X63,X64] :
      ( ( aSet0(X60)
        | ~ aIdeal0(X60) )
      & ( ~ aElementOf0(X62,X60)
        | aElementOf0(sdtpldt0(X61,X62),X60)
        | ~ aElementOf0(X61,X60)
        | ~ aIdeal0(X60) )
      & ( ~ aElement0(X63)
        | aElementOf0(sdtasdt0(X63,X61),X60)
        | ~ aElementOf0(X61,X60)
        | ~ aIdeal0(X60) )
      & ( aElementOf0(esk9_1(X64),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) )
      & ( aElement0(esk11_1(X64))
        | aElementOf0(esk10_1(X64),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) )
      & ( ~ aElementOf0(sdtasdt0(esk11_1(X64),esk9_1(X64)),X64)
        | aElementOf0(esk10_1(X64),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) )
      & ( aElement0(esk11_1(X64))
        | ~ aElementOf0(sdtpldt0(esk9_1(X64),esk10_1(X64)),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) )
      & ( ~ aElementOf0(sdtasdt0(esk11_1(X64),esk9_1(X64)),X64)
        | ~ aElementOf0(sdtpldt0(esk9_1(X64),esk10_1(X64)),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) ) ),
    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)],[mDefIdeal])])])])])]) ).

cnf(c_0_10,plain,
    ( aElementOf0(X5,X6)
    | ~ aElementOf0(X1,X2)
    | ~ aElementOf0(X3,X4)
    | sdtpldt0(X1,X3) != X5
    | X6 != sdtpldt1(X2,X4)
    | ~ aSet0(X2)
    | ~ aSet0(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_11,plain,
    ( aSet0(X1)
    | ~ aIdeal0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_12,hypothesis,
    aIdeal0(xJ),
    inference(split_conjunct,[status(thm)],[m__870]) ).

fof(c_0_13,negated_conjecture,
    ~ ( aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
      & aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_14,plain,
    ( aElementOf0(sdtpldt0(X1,X2),sdtpldt1(X3,X4))
    | ~ aElementOf0(X2,X4)
    | ~ aElementOf0(X1,X3)
    | ~ aSet0(X4)
    | ~ aSet0(X3) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10])]) ).

cnf(c_0_15,hypothesis,
    aElementOf0(sdtasdt0(xz,xl),xJ),
    inference(split_conjunct,[status(thm)],[m__1021]) ).

cnf(c_0_16,hypothesis,
    aSet0(xJ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_17,hypothesis,
    aIdeal0(xI),
    inference(split_conjunct,[status(thm)],[m__870]) ).

fof(c_0_18,negated_conjecture,
    ( ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
    | ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ),
    inference(fof_nnf,[status(thm)],[c_0_13]) ).

cnf(c_0_19,hypothesis,
    ( aElementOf0(sdtpldt0(X1,sdtasdt0(xz,xl)),sdtpldt1(X2,xJ))
    | ~ aElementOf0(X1,X2)
    | ~ aSet0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).

cnf(c_0_20,hypothesis,
    aElementOf0(sdtasdt0(xz,xk),xI),
    inference(split_conjunct,[status(thm)],[m__1021]) ).

cnf(c_0_21,hypothesis,
    sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
    inference(split_conjunct,[status(thm)],[m__1098]) ).

cnf(c_0_22,hypothesis,
    aSet0(xI),
    inference(spm,[status(thm)],[c_0_11,c_0_17]) ).

cnf(c_0_23,hypothesis,
    aElementOf0(sdtpldt0(xl,xn),xJ),
    inference(split_conjunct,[status(thm)],[m__994]) ).

cnf(c_0_24,negated_conjecture,
    ( ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
    | ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_25,hypothesis,
    aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)),
    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_26,hypothesis,
    ( aElementOf0(sdtpldt0(X1,sdtpldt0(xl,xn)),sdtpldt1(X2,xJ))
    | ~ aElementOf0(X1,X2)
    | ~ aSet0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_23]),c_0_16])]) ).

cnf(c_0_27,hypothesis,
    aElementOf0(sdtpldt0(xk,xm),xI),
    inference(split_conjunct,[status(thm)],[m__994]) ).

cnf(c_0_28,hypothesis,
    sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
    inference(split_conjunct,[status(thm)],[m__1061]) ).

cnf(c_0_29,negated_conjecture,
    ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).

cnf(c_0_30,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_22])]),c_0_29]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : RNG091+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 : n008.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   : Sun Aug 27 03:02:47 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.59/0.84  % Version  : CSE_E---1.5
% 0.59/0.84  % Problem  : theBenchmark.p
% 0.59/0.84  % Proof found
% 0.59/0.84  % SZS status Theorem for theBenchmark.p
% 0.59/0.84  % SZS output start Proof
% See solution above
% 0.59/0.85  % Total time : 0.274000 s
% 0.59/0.85  % SZS output end Proof
% 0.59/0.85  % Total time : 0.276000 s
%------------------------------------------------------------------------------