TSTP Solution File: SET929+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET929+1 : 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 : n011.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 14:36:19 EDT 2023

% Result   : Theorem 0.21s 0.61s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   34 (   4 unt;  11 typ;   0 def)
%            Number of atoms       :   60 (  13 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   62 (  25   ~;  25   |;   8   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   5   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   29 (   2 sgn;  16   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    empty_set: $i ).

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

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

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

tff(decl_28,type,
    esk1_0: $i ).

tff(decl_29,type,
    esk2_0: $i ).

tff(decl_30,type,
    esk3_0: $i ).

tff(decl_31,type,
    esk4_0: $i ).

tff(decl_32,type,
    esk5_0: $i ).

fof(t73_zfmisc_1,conjecture,
    ! [X1,X2,X3] :
      ( set_difference(unordered_pair(X1,X2),X3) = empty_set
    <=> ( in(X1,X3)
        & in(X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).

fof(t37_xboole_1,axiom,
    ! [X1,X2] :
      ( set_difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).

fof(t38_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( subset(unordered_pair(X1,X2),X3)
    <=> ( in(X1,X3)
        & in(X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( set_difference(unordered_pair(X1,X2),X3) = empty_set
      <=> ( in(X1,X3)
          & in(X2,X3) ) ),
    inference(assume_negation,[status(cth)],[t73_zfmisc_1]) ).

fof(c_0_4,negated_conjecture,
    ( ( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != empty_set
      | ~ in(esk3_0,esk5_0)
      | ~ in(esk4_0,esk5_0) )
    & ( in(esk3_0,esk5_0)
      | set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = empty_set )
    & ( in(esk4_0,esk5_0)
      | set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = empty_set ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).

fof(c_0_5,plain,
    ! [X11,X12] :
      ( ( set_difference(X11,X12) != empty_set
        | subset(X11,X12) )
      & ( ~ subset(X11,X12)
        | set_difference(X11,X12) = empty_set ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).

cnf(c_0_6,negated_conjecture,
    ( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != empty_set
    | ~ in(esk3_0,esk5_0)
    | ~ in(esk4_0,esk5_0) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,plain,
    ( set_difference(X1,X2) = empty_set
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_8,plain,
    ! [X13,X14,X15] :
      ( ( in(X13,X15)
        | ~ subset(unordered_pair(X13,X14),X15) )
      & ( in(X14,X15)
        | ~ subset(unordered_pair(X13,X14),X15) )
      & ( ~ in(X13,X15)
        | ~ in(X14,X15)
        | subset(unordered_pair(X13,X14),X15) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).

cnf(c_0_9,plain,
    ( subset(X1,X2)
    | set_difference(X1,X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,negated_conjecture,
    ( in(esk4_0,esk5_0)
    | set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_11,negated_conjecture,
    ( ~ subset(unordered_pair(esk3_0,esk4_0),esk5_0)
    | ~ in(esk3_0,esk5_0)
    | ~ in(esk4_0,esk5_0) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_12,plain,
    ( subset(unordered_pair(X1,X3),X2)
    | ~ in(X1,X2)
    | ~ in(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    ( in(X1,X2)
    | ~ subset(unordered_pair(X3,X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    ( subset(unordered_pair(esk3_0,esk4_0),esk5_0)
    | in(esk4_0,esk5_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    ( in(esk3_0,esk5_0)
    | set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_16,negated_conjecture,
    ( ~ in(esk3_0,esk5_0)
    | ~ in(esk4_0,esk5_0) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_17,negated_conjecture,
    in(esk4_0,esk5_0),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    ( subset(unordered_pair(esk3_0,esk4_0),esk5_0)
    | in(esk3_0,esk5_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    ~ in(esk3_0,esk5_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).

cnf(c_0_20,plain,
    ( in(X1,X2)
    | ~ subset(unordered_pair(X1,X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_21,negated_conjecture,
    subset(unordered_pair(esk3_0,esk4_0),esk5_0),
    inference(sr,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_22,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n011.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   : Sat Aug 26 09:22:54 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.59  start to proof: theBenchmark
% 0.21/0.61  % Version  : CSE_E---1.5
% 0.21/0.61  % Problem  : theBenchmark.p
% 0.21/0.61  % Proof found
% 0.21/0.61  % SZS status Theorem for theBenchmark.p
% 0.21/0.61  % SZS output start Proof
% See solution above
% 0.21/0.62  % Total time : 0.005000 s
% 0.21/0.62  % SZS output end Proof
% 0.21/0.62  % Total time : 0.008000 s
%------------------------------------------------------------------------------