TSTP Solution File: RNG088+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG088+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 : n024.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 13:49:03 EDT 2023

% Result   : Theorem 0.20s 0.65s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   67 (  17 unt;  31 typ;   0 def)
%            Number of atoms       :   97 (   5 equ)
%            Maximal formula atoms :   29 (   2 avg)
%            Number of connectives :   97 (  36   ~;  37   |;  17   &)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   3 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   :   27 (   0 sgn;  17   !;   0   ?;   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(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__967,hypothesis,
    ( aElementOf0(xm,xI)
    & aElementOf0(xn,xJ)
    & xy = sdtpldt0(xm,xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__967) ).

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

fof(mEOfElem,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

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

fof(m__934,hypothesis,
    ( aElementOf0(xk,xI)
    & aElementOf0(xl,xJ)
    & xx = sdtpldt0(xk,xl) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).

fof(mAddComm,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).

fof(c_0_7,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_8,plain,
    ( aElementOf0(sdtpldt0(X3,X1),X2)
    | ~ aElementOf0(X1,X2)
    | ~ aElementOf0(X3,X2)
    | ~ aIdeal0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_9,hypothesis,
    aElementOf0(xn,xJ),
    inference(split_conjunct,[status(thm)],[m__967]) ).

cnf(c_0_10,hypothesis,
    aIdeal0(xJ),
    inference(split_conjunct,[status(thm)],[m__870]) ).

fof(c_0_11,plain,
    ! [X32,X33] :
      ( ~ aSet0(X32)
      | ~ aElementOf0(X33,X32)
      | aElement0(X33) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).

cnf(c_0_12,plain,
    ( aSet0(X1)
    | ~ aIdeal0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_13,negated_conjecture,
    ~ ( aElementOf0(sdtpldt0(xk,xm),xI)
      & aElementOf0(sdtpldt0(xl,xn),xJ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_14,hypothesis,
    ( aElementOf0(sdtpldt0(xn,X1),xJ)
    | ~ aElementOf0(X1,xJ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]) ).

cnf(c_0_15,hypothesis,
    aElementOf0(xl,xJ),
    inference(split_conjunct,[status(thm)],[m__934]) ).

fof(c_0_16,plain,
    ! [X12,X13] :
      ( ~ aElement0(X12)
      | ~ aElement0(X13)
      | sdtpldt0(X12,X13) = sdtpldt0(X13,X12) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).

cnf(c_0_17,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,hypothesis,
    aSet0(xJ),
    inference(spm,[status(thm)],[c_0_12,c_0_10]) ).

cnf(c_0_19,hypothesis,
    aElementOf0(xm,xI),
    inference(split_conjunct,[status(thm)],[m__967]) ).

cnf(c_0_20,hypothesis,
    aIdeal0(xI),
    inference(split_conjunct,[status(thm)],[m__870]) ).

fof(c_0_21,negated_conjecture,
    ( ~ aElementOf0(sdtpldt0(xk,xm),xI)
    | ~ aElementOf0(sdtpldt0(xl,xn),xJ) ),
    inference(fof_nnf,[status(thm)],[c_0_13]) ).

cnf(c_0_22,hypothesis,
    aElementOf0(sdtpldt0(xn,xl),xJ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_23,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,hypothesis,
    aElement0(xl),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_18])]) ).

cnf(c_0_25,hypothesis,
    aElement0(xn),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_9]),c_0_18])]) ).

cnf(c_0_26,hypothesis,
    ( aElementOf0(sdtpldt0(xm,X1),xI)
    | ~ aElementOf0(X1,xI) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_19]),c_0_20])]) ).

cnf(c_0_27,hypothesis,
    aElementOf0(xk,xI),
    inference(split_conjunct,[status(thm)],[m__934]) ).

cnf(c_0_28,hypothesis,
    aSet0(xI),
    inference(spm,[status(thm)],[c_0_12,c_0_20]) ).

cnf(c_0_29,negated_conjecture,
    ( ~ aElementOf0(sdtpldt0(xk,xm),xI)
    | ~ aElementOf0(sdtpldt0(xl,xn),xJ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_30,hypothesis,
    aElementOf0(sdtpldt0(xl,xn),xJ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).

cnf(c_0_31,hypothesis,
    aElementOf0(sdtpldt0(xm,xk),xI),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_32,hypothesis,
    aElement0(xk),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_27]),c_0_28])]) ).

cnf(c_0_33,hypothesis,
    aElement0(xm),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_28])]) ).

cnf(c_0_34,negated_conjecture,
    ~ aElementOf0(sdtpldt0(xk,xm),xI),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).

cnf(c_0_35,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_23]),c_0_32]),c_0_33])]),c_0_34]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : RNG088+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun Aug 27 03:08:23 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.20/0.59  start to proof: theBenchmark
% 0.20/0.65  % Version  : CSE_E---1.5
% 0.20/0.65  % Problem  : theBenchmark.p
% 0.20/0.65  % Proof found
% 0.20/0.65  % SZS status Theorem for theBenchmark.p
% 0.20/0.65  % SZS output start Proof
% See solution above
% 0.20/0.66  % Total time : 0.054000 s
% 0.20/0.66  % SZS output end Proof
% 0.20/0.66  % Total time : 0.057000 s
%------------------------------------------------------------------------------