TSTP Solution File: SET867+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET867+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n028.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 14:36:04 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   25 (   6 unt;  10 typ;   0 def)
%            Number of atoms       :   47 (  17 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :   55 (  23   ~;  21   |;   7   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   7   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   29 (   3 sgn;  18   !;   1   ?;   0   :)

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

tff(decl_23,type,
    empty_set: $i ).

tff(decl_24,type,
    union: $i > $i ).

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

tff(decl_26,type,
    esk1_1: $i > $i ).

tff(decl_27,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_28,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_29,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_30,type,
    esk5_0: $i ).

tff(decl_31,type,
    esk6_0: $i ).

fof(d1_xboole_0,axiom,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(d4_tarski,axiom,
    ! [X1,X2] :
      ( X2 = union(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4] :
              ( in(X3,X4)
              & in(X4,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).

fof(t2_zfmisc_1,conjecture,
    union(empty_set) = empty_set,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).

fof(c_0_3,plain,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).

fof(c_0_4,plain,
    ! [X7,X8,X9] :
      ( ( X7 != empty_set
        | ~ in(X8,X7) )
      & ( in(esk1_1(X9),X9)
        | X9 = empty_set ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])]) ).

fof(c_0_5,plain,
    ! [X11,X12,X13,X15,X16,X17,X18,X20] :
      ( ( in(X13,esk2_3(X11,X12,X13))
        | ~ in(X13,X12)
        | X12 != union(X11) )
      & ( in(esk2_3(X11,X12,X13),X11)
        | ~ in(X13,X12)
        | X12 != union(X11) )
      & ( ~ in(X15,X16)
        | ~ in(X16,X11)
        | in(X15,X12)
        | X12 != union(X11) )
      & ( ~ in(esk3_2(X17,X18),X18)
        | ~ in(esk3_2(X17,X18),X20)
        | ~ in(X20,X17)
        | X18 = union(X17) )
      & ( in(esk3_2(X17,X18),esk4_2(X17,X18))
        | in(esk3_2(X17,X18),X18)
        | X18 = union(X17) )
      & ( in(esk4_2(X17,X18),X17)
        | in(esk3_2(X17,X18),X18)
        | X18 = union(X17) ) ),
    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)],[d4_tarski])])])])])]) ).

cnf(c_0_6,plain,
    ( X1 != empty_set
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,plain,
    ( in(esk2_3(X1,X2,X3),X1)
    | ~ in(X3,X2)
    | X2 != union(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,plain,
    ~ in(X1,empty_set),
    inference(er,[status(thm)],[c_0_6]) ).

cnf(c_0_9,plain,
    ( in(esk2_3(X1,union(X1),X2),X1)
    | ~ in(X2,union(X1)) ),
    inference(er,[status(thm)],[c_0_7]) ).

fof(c_0_10,negated_conjecture,
    union(empty_set) != empty_set,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t2_zfmisc_1])]) ).

cnf(c_0_11,plain,
    ~ in(X1,union(empty_set)),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,plain,
    ( in(esk1_1(X1),X1)
    | X1 = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_13,negated_conjecture,
    union(empty_set) != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET867+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n028.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 15:13:07 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.007000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.010000 s
%------------------------------------------------------------------------------