TSTP Solution File: SET801+4 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : SET801+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n021.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  : 600s
% DateTime : Tue Jul 19 00:14:16 EDT 2022

% Result   : Theorem 8.40s 2.46s
% Output   : CNFRefutation 8.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   43 (   7 unt;   0 def)
%            Number of atoms       :  145 (   0 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  169 (  67   ~;  70   |;  20   &)
%                                         (   5 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-4 aty)
%            Number of variables   :   82 (   2 sgn  44   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(thIV13,conjecture,
    ! [X6,X4] :
      ( order(X6,X4)
     => ! [X3] :
          ( subset(X3,X4)
         => ! [X8] :
              ( greatest(X8,X6,X3)
            <=> ( member(X8,X3)
                & least_upper_bound(X8,X3,X6,X4) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV13) ).

fof(greatest,axiom,
    ! [X6,X4,X8] :
      ( greatest(X8,X6,X4)
    <=> ( member(X8,X4)
        & ! [X3] :
            ( member(X3,X4)
           => apply(X6,X3,X8) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',greatest) ).

fof(least_upper_bound,axiom,
    ! [X1,X3,X6,X4] :
      ( least_upper_bound(X1,X3,X6,X4)
    <=> ( member(X1,X3)
        & upper_bound(X1,X6,X3)
        & ! [X8] :
            ( ( member(X8,X4)
              & upper_bound(X8,X6,X3) )
           => apply(X6,X1,X8) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',least_upper_bound) ).

fof(upper_bound,axiom,
    ! [X6,X4,X8] :
      ( upper_bound(X8,X6,X4)
    <=> ! [X3] :
          ( member(X3,X4)
         => apply(X6,X3,X8) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',upper_bound) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X6,X4] :
        ( order(X6,X4)
       => ! [X3] :
            ( subset(X3,X4)
           => ! [X8] :
                ( greatest(X8,X6,X3)
              <=> ( member(X8,X3)
                  & least_upper_bound(X8,X3,X6,X4) ) ) ) ),
    inference(assume_negation,[status(cth)],[thIV13]) ).

fof(c_0_5,plain,
    ! [X72,X73,X74,X75,X76,X77,X78] :
      ( ( member(X74,X73)
        | ~ greatest(X74,X72,X73) )
      & ( ~ member(X75,X73)
        | apply(X72,X75,X74)
        | ~ greatest(X74,X72,X73) )
      & ( member(esk8_3(X76,X77,X78),X77)
        | ~ member(X78,X77)
        | greatest(X78,X76,X77) )
      & ( ~ apply(X76,esk8_3(X76,X77,X78),X78)
        | ~ member(X78,X77)
        | greatest(X78,X76,X77) ) ),
    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)],[greatest])])])])])]) ).

fof(c_0_6,negated_conjecture,
    ( order(esk14_0,esk15_0)
    & subset(esk16_0,esk15_0)
    & ( ~ greatest(esk17_0,esk14_0,esk16_0)
      | ~ member(esk17_0,esk16_0)
      | ~ least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0) )
    & ( member(esk17_0,esk16_0)
      | greatest(esk17_0,esk14_0,esk16_0) )
    & ( least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0)
      | greatest(esk17_0,esk14_0,esk16_0) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).

cnf(c_0_7,plain,
    ( member(X1,X2)
    | ~ greatest(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    ( member(esk17_0,esk16_0)
    | greatest(esk17_0,esk14_0,esk16_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,negated_conjecture,
    ( ~ greatest(esk17_0,esk14_0,esk16_0)
    | ~ member(esk17_0,esk16_0)
    | ~ least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    member(esk17_0,esk16_0),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

fof(c_0_11,plain,
    ! [X104,X105,X106,X107,X108,X109,X110,X111,X112] :
      ( ( member(X104,X105)
        | ~ least_upper_bound(X104,X105,X106,X107) )
      & ( upper_bound(X104,X106,X105)
        | ~ least_upper_bound(X104,X105,X106,X107) )
      & ( ~ member(X108,X107)
        | ~ upper_bound(X108,X106,X105)
        | apply(X106,X104,X108)
        | ~ least_upper_bound(X104,X105,X106,X107) )
      & ( member(esk12_4(X109,X110,X111,X112),X112)
        | ~ member(X109,X110)
        | ~ upper_bound(X109,X111,X110)
        | least_upper_bound(X109,X110,X111,X112) )
      & ( upper_bound(esk12_4(X109,X110,X111,X112),X111,X110)
        | ~ member(X109,X110)
        | ~ upper_bound(X109,X111,X110)
        | least_upper_bound(X109,X110,X111,X112) )
      & ( ~ apply(X111,X109,esk12_4(X109,X110,X111,X112))
        | ~ member(X109,X110)
        | ~ upper_bound(X109,X111,X110)
        | least_upper_bound(X109,X110,X111,X112) ) ),
    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)],[least_upper_bound])])])])])]) ).

cnf(c_0_12,negated_conjecture,
    ( ~ least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0)
    | ~ greatest(esk17_0,esk14_0,esk16_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]) ).

cnf(c_0_13,plain,
    ( upper_bound(esk12_4(X1,X2,X3,X4),X3,X2)
    | least_upper_bound(X1,X2,X3,X4)
    | ~ member(X1,X2)
    | ~ upper_bound(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_14,plain,
    ( apply(X3,X1,X4)
    | ~ member(X1,X2)
    | ~ greatest(X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_15,negated_conjecture,
    ( least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0)
    | greatest(esk17_0,esk14_0,esk16_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_16,plain,
    ! [X56,X57,X58,X59,X60,X61,X62] :
      ( ( ~ upper_bound(X58,X56,X57)
        | ~ member(X59,X57)
        | apply(X56,X59,X58) )
      & ( member(esk6_3(X60,X61,X62),X61)
        | upper_bound(X62,X60,X61) )
      & ( ~ apply(X60,esk6_3(X60,X61,X62),X62)
        | upper_bound(X62,X60,X61) ) ),
    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)],[upper_bound])])])])])]) ).

cnf(c_0_17,negated_conjecture,
    ( upper_bound(esk12_4(esk17_0,esk16_0,esk14_0,esk15_0),esk14_0,esk16_0)
    | ~ greatest(esk17_0,esk14_0,esk16_0)
    | ~ upper_bound(esk17_0,esk14_0,esk16_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_10])]) ).

cnf(c_0_18,plain,
    ( greatest(X3,X1,X2)
    | ~ apply(X1,esk8_3(X1,X2,X3),X3)
    | ~ member(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_19,plain,
    ( upper_bound(X1,X2,X3)
    | ~ least_upper_bound(X1,X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_20,negated_conjecture,
    ( least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0)
    | apply(esk14_0,X1,esk17_0)
    | ~ member(X1,esk16_0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_21,plain,
    ( apply(X2,X4,X1)
    | ~ upper_bound(X1,X2,X3)
    | ~ member(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,plain,
    ( member(esk8_3(X1,X2,X3),X2)
    | greatest(X3,X1,X2)
    | ~ member(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_23,negated_conjecture,
    ( upper_bound(esk12_4(esk17_0,esk16_0,esk14_0,esk15_0),esk14_0,esk16_0)
    | ~ upper_bound(esk17_0,esk14_0,esk16_0)
    | ~ apply(esk14_0,esk8_3(esk14_0,esk16_0,esk17_0),esk17_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_10])]) ).

cnf(c_0_24,negated_conjecture,
    ( apply(esk14_0,X1,esk17_0)
    | ~ member(X1,esk16_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).

cnf(c_0_25,negated_conjecture,
    ( upper_bound(esk12_4(esk17_0,esk16_0,esk14_0,esk15_0),esk14_0,esk16_0)
    | member(esk8_3(esk14_0,esk16_0,esk17_0),esk16_0)
    | ~ upper_bound(esk17_0,esk14_0,esk16_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_22]),c_0_10])]) ).

cnf(c_0_26,negated_conjecture,
    ( upper_bound(esk12_4(esk17_0,esk16_0,esk14_0,esk15_0),esk14_0,esk16_0)
    | ~ upper_bound(esk17_0,esk14_0,esk16_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).

cnf(c_0_27,plain,
    ( upper_bound(X3,X1,X2)
    | ~ apply(X1,esk6_3(X1,X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_28,negated_conjecture,
    ( upper_bound(esk12_4(esk17_0,esk16_0,esk14_0,esk15_0),esk14_0,esk16_0)
    | ~ apply(esk14_0,esk6_3(esk14_0,esk16_0,esk17_0),esk17_0) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_29,plain,
    ( member(esk6_3(X1,X2,X3),X2)
    | upper_bound(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_30,negated_conjecture,
    ( upper_bound(esk12_4(esk17_0,esk16_0,esk14_0,esk15_0),esk14_0,esk16_0)
    | ~ member(esk6_3(esk14_0,esk16_0,esk17_0),esk16_0) ),
    inference(spm,[status(thm)],[c_0_28,c_0_24]) ).

cnf(c_0_31,negated_conjecture,
    upper_bound(esk12_4(esk17_0,esk16_0,esk14_0,esk15_0),esk14_0,esk16_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_29]),c_0_30]) ).

cnf(c_0_32,plain,
    ( least_upper_bound(X2,X3,X1,X4)
    | ~ apply(X1,X2,esk12_4(X2,X3,X1,X4))
    | ~ member(X2,X3)
    | ~ upper_bound(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_33,negated_conjecture,
    ( apply(esk14_0,X1,esk12_4(esk17_0,esk16_0,esk14_0,esk15_0))
    | ~ member(X1,esk16_0) ),
    inference(spm,[status(thm)],[c_0_21,c_0_31]) ).

cnf(c_0_34,negated_conjecture,
    ( ~ greatest(esk17_0,esk14_0,esk16_0)
    | ~ upper_bound(esk17_0,esk14_0,esk16_0)
    | ~ apply(esk14_0,esk17_0,esk12_4(esk17_0,esk16_0,esk14_0,esk15_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_32]),c_0_10])]) ).

cnf(c_0_35,negated_conjecture,
    apply(esk14_0,esk17_0,esk12_4(esk17_0,esk16_0,esk14_0,esk15_0)),
    inference(spm,[status(thm)],[c_0_33,c_0_10]) ).

cnf(c_0_36,negated_conjecture,
    ( ~ greatest(esk17_0,esk14_0,esk16_0)
    | ~ upper_bound(esk17_0,esk14_0,esk16_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).

cnf(c_0_37,negated_conjecture,
    ( ~ upper_bound(esk17_0,esk14_0,esk16_0)
    | ~ apply(esk14_0,esk8_3(esk14_0,esk16_0,esk17_0),esk17_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_18]),c_0_10])]) ).

cnf(c_0_38,negated_conjecture,
    ( ~ upper_bound(esk17_0,esk14_0,esk16_0)
    | ~ member(esk8_3(esk14_0,esk16_0,esk17_0),esk16_0) ),
    inference(spm,[status(thm)],[c_0_37,c_0_24]) ).

cnf(c_0_39,negated_conjecture,
    ~ upper_bound(esk17_0,esk14_0,esk16_0),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_22]),c_0_10])]),c_0_38]) ).

cnf(c_0_40,negated_conjecture,
    ~ apply(esk14_0,esk6_3(esk14_0,esk16_0,esk17_0),esk17_0),
    inference(spm,[status(thm)],[c_0_39,c_0_27]) ).

cnf(c_0_41,negated_conjecture,
    member(esk6_3(esk14_0,esk16_0,esk17_0),esk16_0),
    inference(spm,[status(thm)],[c_0_39,c_0_29]) ).

cnf(c_0_42,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_24]),c_0_41])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET801+4 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : enigmatic-eprover.py %s %d 1
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jul 11 03:28:09 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.44  # ENIGMATIC: Selected SinE mode:
% 0.19/0.45  # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.19/0.45  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.19/0.45  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 8.40/2.46  # ENIGMATIC: Solved by autoschedule:
% 8.40/2.46  # No SInE strategy applied
% 8.40/2.46  # Trying AutoSched0 for 150 seconds
% 8.40/2.46  # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S024I
% 8.40/2.46  # and selection function SelectOptimalRestrPDepth2.
% 8.40/2.46  #
% 8.40/2.46  # Preprocessing time       : 0.017 s
% 8.40/2.46  # Presaturation interreduction done
% 8.40/2.46  
% 8.40/2.46  # Proof found!
% 8.40/2.46  # SZS status Theorem
% 8.40/2.46  # SZS output start CNFRefutation
% See solution above
% 8.40/2.46  # Training examples: 0 positive, 0 negative
% 8.40/2.46  
% 8.40/2.46  # -------------------------------------------------
% 8.40/2.46  # User time                : 0.126 s
% 8.40/2.46  # System time              : 0.012 s
% 8.40/2.46  # Total time               : 0.137 s
% 8.40/2.46  # Maximum resident set size: 7120 pages
% 8.40/2.46  
%------------------------------------------------------------------------------