%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET591+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n007.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 14:34:40 EDT 2023

% Result   : Theorem 0.19s 0.57s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   34 (  10 unt;   9 typ;   0 def)
%            Number of atoms       :   61 (  10 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   64 (  28   ~;  19   |;  10   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   43 (   5 sgn;  28   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    empty_set: $i ).

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

tff(decl_27,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_28,type,
    esk2_1: $i > $i ).

tff(decl_29,type,
    esk3_0: $i ).

tff(decl_30,type,
    esk4_0: $i ).

fof(empty_set_defn,axiom,
    ! [X1] : ~ member(X1,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).

fof(prove_th50,conjecture,
    ! [X1,X2] :
      ( subset(X1,difference(X2,X1))
     => X1 = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th50) ).

fof(difference_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).

fof(subset_defn,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).

fof(equal_defn,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

fof(c_0_5,plain,
    ! [X1] : ~ member(X1,empty_set),
    inference(fof_simplification,[status(thm)],[empty_set_defn]) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(X1,difference(X2,X1))
       => X1 = empty_set ),
    inference(assume_negation,[status(cth)],[prove_th50]) ).

fof(c_0_7,plain,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    inference(fof_simplification,[status(thm)],[difference_defn]) ).

fof(c_0_8,plain,
    ! [X13] : ~ member(X13,empty_set),
    inference(variable_rename,[status(thm)],[c_0_5]) ).

fof(c_0_9,plain,
    ! [X4,X5,X6,X7,X8] :
      ( ( ~ subset(X4,X5)
        | ~ member(X6,X4)
        | member(X6,X5) )
      & ( member(esk1_2(X7,X8),X7)
        | subset(X7,X8) )
      & ( ~ member(esk1_2(X7,X8),X8)
        | subset(X7,X8) ) ),
    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)],[subset_defn])])])])])]) ).

fof(c_0_10,negated_conjecture,
    ( subset(esk3_0,difference(esk4_0,esk3_0))
    & esk3_0 != empty_set ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

fof(c_0_11,plain,
    ! [X10,X11,X12] :
      ( ( member(X12,X10)
        | ~ member(X12,difference(X10,X11)) )
      & ( ~ member(X12,X11)
        | ~ member(X12,difference(X10,X11)) )
      & ( ~ member(X12,X10)
        | member(X12,X11)
        | member(X12,difference(X10,X11)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_12,plain,
    ! [X14,X15] :
      ( ( subset(X14,X15)
        | X14 != X15 )
      & ( subset(X15,X14)
        | X14 != X15 )
      & ( ~ subset(X14,X15)
        | ~ subset(X15,X14)
        | X14 = X15 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).

cnf(c_0_13,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,negated_conjecture,
    subset(esk3_0,difference(esk4_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,plain,
    ( ~ member(X1,X2)
    | ~ member(X1,difference(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    ( X1 = X2
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    subset(empty_set,X1),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_20,negated_conjecture,
    ~ member(X1,esk3_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).

cnf(c_0_21,plain,
    ( X1 = empty_set
    | ~ subset(X1,empty_set) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_22,negated_conjecture,
    subset(esk3_0,X1),
    inference(spm,[status(thm)],[c_0_20,c_0_14]) ).

cnf(c_0_23,negated_conjecture,
    esk3_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_24,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET591+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat Aug 26 12:07:11 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.19/0.57  % Version  : CSE_E---1.5
% 0.19/0.57  % Problem  : theBenchmark.p
% 0.19/0.57  % Proof found
% 0.19/0.57  % SZS status Theorem for theBenchmark.p
% 0.19/0.57  % SZS output start Proof
% See solution above
% 0.19/0.57  % Total time : 0.008000 s
% 0.19/0.57  % SZS output end Proof
% 0.19/0.57  % Total time : 0.010000 s
%------------------------------------------------------------------------------