TSTP Solution File: SET793+4 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET793+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n026.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 14:35:34 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   37
% Syntax   : Number of formulae    :   66 (   7 unt;  32 typ;   0 def)
%            Number of atoms       :  132 (   6 equ)
%            Maximal formula atoms :   19 (   3 avg)
%            Number of connectives :  149 (  51   ~;  65   |;  23   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   79 (  29   >;  50   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-4 aty)
%            Number of functors    :   19 (  19 usr;   3 con; 0-4 aty)
%            Number of variables   :   84 (   1 sgn;  49   !;   0   ?;   0   :)

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

tff(decl_23,type,
    member: ( $i * $i ) > $o ).

tff(decl_24,type,
    apply: ( $i * $i * $i ) > $o ).

tff(decl_25,type,
    total_order: ( $i * $i ) > $o ).

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

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

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

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

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

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

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

tff(decl_33,type,
    greatest_lower_bound: ( $i * $i * $i * $i ) > $o ).

tff(decl_34,type,
    epred1_2: ( $i * $i ) > $o ).

tff(decl_35,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_38,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_39,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_40,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_41,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_42,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_43,type,
    esk9_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_44,type,
    esk10_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk11_0: $i ).

tff(decl_46,type,
    esk12_0: $i ).

tff(decl_47,type,
    esk13_0: $i ).

tff(decl_48,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_49,type,
    esk15_2: ( $i * $i ) > $i ).

tff(decl_50,type,
    esk16_2: ( $i * $i ) > $i ).

tff(decl_51,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk19_2: ( $i * $i ) > $i ).

fof(thIV5,conjecture,
    ! [X1,X2,X6] :
      ( ( total_order(X1,X2)
        & max(X6,X1,X2) )
     => greatest(X6,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV5) ).

fof(total_order,axiom,
    ! [X1,X2] :
      ( total_order(X1,X2)
    <=> ( order(X1,X2)
        & ! [X3,X4] :
            ( ( member(X3,X2)
              & member(X4,X2) )
           => ( apply(X1,X3,X4)
              | apply(X1,X4,X3) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',total_order) ).

fof(max,axiom,
    ! [X1,X2,X6] :
      ( max(X6,X1,X2)
    <=> ( member(X6,X2)
        & ! [X3] :
            ( ( member(X3,X2)
              & apply(X1,X6,X3) )
           => X6 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',max) ).

fof(upper_bound,axiom,
    ! [X1,X2,X6] :
      ( upper_bound(X6,X1,X2)
    <=> ! [X3] :
          ( member(X3,X2)
         => apply(X1,X3,X6) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',upper_bound) ).

fof(greatest,axiom,
    ! [X1,X2,X6] :
      ( greatest(X6,X1,X2)
    <=> ( member(X6,X2)
        & ! [X3] :
            ( member(X3,X2)
           => apply(X1,X3,X6) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',greatest) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X6] :
        ( ( total_order(X1,X2)
          & max(X6,X1,X2) )
       => greatest(X6,X1,X2) ),
    inference(assume_negation,[status(cth)],[thIV5]) ).

fof(c_0_6,plain,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ( order(X10,X11)
        | ~ total_order(X10,X11) )
      & ( ~ member(X12,X11)
        | ~ member(X13,X11)
        | apply(X10,X12,X13)
        | apply(X10,X13,X12)
        | ~ total_order(X10,X11) )
      & ( member(esk1_2(X14,X15),X15)
        | ~ order(X14,X15)
        | total_order(X14,X15) )
      & ( member(esk2_2(X14,X15),X15)
        | ~ order(X14,X15)
        | total_order(X14,X15) )
      & ( ~ apply(X14,esk1_2(X14,X15),esk2_2(X14,X15))
        | ~ order(X14,X15)
        | total_order(X14,X15) )
      & ( ~ apply(X14,esk2_2(X14,X15),esk1_2(X14,X15))
        | ~ order(X14,X15)
        | total_order(X14,X15) ) ),
    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)],[total_order])])])])])]) ).

fof(c_0_7,negated_conjecture,
    ( total_order(esk11_0,esk12_0)
    & max(esk13_0,esk11_0,esk12_0)
    & ~ greatest(esk13_0,esk11_0,esk12_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_8,plain,
    ! [X50,X51,X52,X53,X54,X55,X56] :
      ( ( member(X52,X51)
        | ~ max(X52,X50,X51) )
      & ( ~ member(X53,X51)
        | ~ apply(X50,X52,X53)
        | X52 = X53
        | ~ max(X52,X50,X51) )
      & ( member(esk7_3(X54,X55,X56),X55)
        | ~ member(X56,X55)
        | max(X56,X54,X55) )
      & ( apply(X54,X56,esk7_3(X54,X55,X56))
        | ~ member(X56,X55)
        | max(X56,X54,X55) )
      & ( X56 != esk7_3(X54,X55,X56)
        | ~ member(X56,X55)
        | max(X56,X54,X55) ) ),
    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)],[max])])])])])]) ).

cnf(c_0_9,plain,
    ( apply(X4,X1,X3)
    | apply(X4,X3,X1)
    | ~ member(X1,X2)
    | ~ member(X3,X2)
    | ~ total_order(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    total_order(esk11_0,esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    ( member(X1,X2)
    | ~ max(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    max(esk13_0,esk11_0,esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,negated_conjecture,
    ( apply(esk11_0,X1,X2)
    | apply(esk11_0,X2,X1)
    | ~ member(X2,esk12_0)
    | ~ member(X1,esk12_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    member(esk13_0,esk12_0),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

fof(c_0_15,plain,
    ! [X18,X19,X20,X21,X22,X23,X24] :
      ( ( ~ upper_bound(X20,X18,X19)
        | ~ member(X21,X19)
        | apply(X18,X21,X20) )
      & ( member(esk3_3(X22,X23,X24),X23)
        | upper_bound(X24,X22,X23) )
      & ( ~ apply(X22,esk3_3(X22,X23,X24),X24)
        | upper_bound(X24,X22,X23) ) ),
    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_16,negated_conjecture,
    ( apply(esk11_0,esk13_0,X1)
    | apply(esk11_0,X1,esk13_0)
    | ~ member(X1,esk12_0) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,plain,
    ( member(esk3_3(X1,X2,X3),X2)
    | upper_bound(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_18,plain,
    ( X4 = X1
    | ~ member(X1,X2)
    | ~ apply(X3,X4,X1)
    | ~ max(X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_19,plain,
    ( upper_bound(X3,X1,X2)
    | ~ apply(X1,esk3_3(X1,X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,negated_conjecture,
    ( upper_bound(X1,X2,esk12_0)
    | apply(esk11_0,esk3_3(X2,esk12_0,X1),esk13_0)
    | apply(esk11_0,esk13_0,esk3_3(X2,esk12_0,X1)) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    ( X1 = esk13_0
    | ~ apply(esk11_0,esk13_0,X1)
    | ~ member(X1,esk12_0) ),
    inference(spm,[status(thm)],[c_0_18,c_0_12]) ).

cnf(c_0_22,negated_conjecture,
    ( upper_bound(esk13_0,esk11_0,esk12_0)
    | apply(esk11_0,esk13_0,esk3_3(esk11_0,esk12_0,esk13_0)) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,negated_conjecture,
    ( esk3_3(esk11_0,esk12_0,esk13_0) = esk13_0
    | upper_bound(esk13_0,esk11_0,esk12_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_17]) ).

cnf(c_0_24,negated_conjecture,
    apply(esk11_0,esk13_0,esk13_0),
    inference(spm,[status(thm)],[c_0_16,c_0_14]) ).

fof(c_0_25,plain,
    ! [X34,X35,X36,X37,X38,X39,X40] :
      ( ( member(X36,X35)
        | ~ greatest(X36,X34,X35) )
      & ( ~ member(X37,X35)
        | apply(X34,X37,X36)
        | ~ greatest(X36,X34,X35) )
      & ( member(esk5_3(X38,X39,X40),X39)
        | ~ member(X40,X39)
        | greatest(X40,X38,X39) )
      & ( ~ apply(X38,esk5_3(X38,X39,X40),X40)
        | ~ member(X40,X39)
        | greatest(X40,X38,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)],[greatest])])])])])]) ).

cnf(c_0_26,plain,
    ( apply(X2,X4,X1)
    | ~ upper_bound(X1,X2,X3)
    | ~ member(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_27,negated_conjecture,
    upper_bound(esk13_0,esk11_0,esk12_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_23]),c_0_24])]) ).

cnf(c_0_28,plain,
    ( greatest(X3,X1,X2)
    | ~ apply(X1,esk5_3(X1,X2,X3),X3)
    | ~ member(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_29,negated_conjecture,
    ( apply(esk11_0,X1,esk13_0)
    | ~ member(X1,esk12_0) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    ( greatest(esk13_0,esk11_0,X1)
    | ~ member(esk5_3(esk11_0,X1,esk13_0),esk12_0)
    | ~ member(esk13_0,X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_31,plain,
    ( member(esk5_3(X1,X2,X3),X2)
    | greatest(X3,X1,X2)
    | ~ member(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_32,negated_conjecture,
    ~ greatest(esk13_0,esk11_0,esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_33,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_14])]),c_0_32]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET793+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sat Aug 26 10:30:48 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.59  % Version  : CSE_E---1.5
% 0.19/0.59  % Problem  : theBenchmark.p
% 0.19/0.59  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.60  % Total time : 0.018000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.021000 s
%------------------------------------------------------------------------------