%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET603+4 : TPTP v8.1.2. Released v2.2.0.
% 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 14:34:45 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   47 (  13 unt;  16 typ;   0 def)
%            Number of atoms       :   70 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   76 (  37   ~;  25   |;   9   &)
%                                         (   4 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  14   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   2 con; 0-2 aty)
%            Number of variables   :   39 (   2 sgn;  26   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    power_set: $i > $i ).

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

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

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

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

tff(decl_30,type,
    singleton: $i > $i ).

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

tff(decl_32,type,
    sum: $i > $i ).

tff(decl_33,type,
    product: $i > $i ).

tff(decl_34,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk4_0: $i ).

fof(thI30,conjecture,
    ! [X4] : equal_set(difference(X4,empty_set),X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI30) ).

fof(equal_set,axiom,
    ! [X1,X2] :
      ( equal_set(X1,X2)
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).

fof(subset,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).

fof(difference,axiom,
    ! [X2,X1,X4] :
      ( member(X2,difference(X4,X1))
    <=> ( member(X2,X4)
        & ~ member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).

fof(empty_set,axiom,
    ! [X3] : ~ member(X3,empty_set),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X4] : equal_set(difference(X4,empty_set),X4),
    inference(assume_negation,[status(cth)],[thI30]) ).

fof(c_0_6,negated_conjecture,
    ~ equal_set(difference(esk4_0,empty_set),esk4_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_7,plain,
    ! [X12,X13] :
      ( ( subset(X12,X13)
        | ~ equal_set(X12,X13) )
      & ( subset(X13,X12)
        | ~ equal_set(X12,X13) )
      & ( ~ subset(X12,X13)
        | ~ subset(X13,X12)
        | equal_set(X12,X13) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).

cnf(c_0_8,negated_conjecture,
    ~ equal_set(difference(esk4_0,empty_set),esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,plain,
    ( equal_set(X1,X2)
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_10,plain,
    ! [X6,X7,X8,X9,X10] :
      ( ( ~ subset(X6,X7)
        | ~ member(X8,X6)
        | member(X8,X7) )
      & ( member(esk1_2(X9,X10),X9)
        | subset(X9,X10) )
      & ( ~ member(esk1_2(X9,X10),X10)
        | subset(X9,X10) ) ),
    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])])])])])]) ).

cnf(c_0_11,negated_conjecture,
    ( ~ subset(esk4_0,difference(esk4_0,empty_set))
    | ~ subset(difference(esk4_0,empty_set),esk4_0) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_13,plain,
    ! [X2,X1,X4] :
      ( member(X2,difference(X4,X1))
    <=> ( member(X2,X4)
        & ~ member(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[difference]) ).

fof(c_0_14,plain,
    ! [X3] : ~ member(X3,empty_set),
    inference(fof_simplification,[status(thm)],[empty_set]) ).

cnf(c_0_15,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    ( ~ member(esk1_2(difference(esk4_0,empty_set),esk4_0),esk4_0)
    | ~ subset(esk4_0,difference(esk4_0,empty_set)) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

fof(c_0_17,plain,
    ! [X23,X24,X25] :
      ( ( member(X23,X25)
        | ~ member(X23,difference(X25,X24)) )
      & ( ~ member(X23,X24)
        | ~ member(X23,difference(X25,X24)) )
      & ( ~ member(X23,X25)
        | member(X23,X24)
        | member(X23,difference(X25,X24)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).

fof(c_0_18,plain,
    ! [X22] : ~ member(X22,empty_set),
    inference(variable_rename,[status(thm)],[c_0_14]) ).

cnf(c_0_19,negated_conjecture,
    ( member(esk1_2(difference(esk4_0,empty_set),esk4_0),difference(esk4_0,empty_set))
    | ~ subset(esk4_0,difference(esk4_0,empty_set)) ),
    inference(spm,[status(thm)],[c_0_11,c_0_15]) ).

cnf(c_0_20,negated_conjecture,
    ( ~ member(esk1_2(esk4_0,difference(esk4_0,empty_set)),difference(esk4_0,empty_set))
    | ~ member(esk1_2(difference(esk4_0,empty_set),esk4_0),esk4_0) ),
    inference(spm,[status(thm)],[c_0_16,c_0_12]) ).

cnf(c_0_21,plain,
    ( member(X1,X3)
    | member(X1,difference(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_22,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    ( member(esk1_2(esk4_0,difference(esk4_0,empty_set)),esk4_0)
    | ~ member(esk1_2(difference(esk4_0,empty_set),esk4_0),esk4_0) ),
    inference(spm,[status(thm)],[c_0_16,c_0_15]) ).

cnf(c_0_24,plain,
    ( member(X1,X2)
    | ~ member(X1,difference(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,negated_conjecture,
    ( member(esk1_2(difference(esk4_0,empty_set),esk4_0),difference(esk4_0,empty_set))
    | ~ member(esk1_2(esk4_0,difference(esk4_0,empty_set)),difference(esk4_0,empty_set)) ),
    inference(spm,[status(thm)],[c_0_19,c_0_12]) ).

cnf(c_0_26,negated_conjecture,
    ~ member(esk1_2(difference(esk4_0,empty_set),esk4_0),esk4_0),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    ~ member(esk1_2(esk4_0,difference(esk4_0,empty_set)),difference(esk4_0,empty_set)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

cnf(c_0_28,negated_conjecture,
    ~ member(esk1_2(esk4_0,difference(esk4_0,empty_set)),esk4_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_21]),c_0_22]) ).

cnf(c_0_29,negated_conjecture,
    member(esk1_2(difference(esk4_0,empty_set),esk4_0),difference(esk4_0,empty_set)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_15]),c_0_28]) ).

cnf(c_0_30,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_29]),c_0_26]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET603+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n011.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sat Aug 26 13:49:39 EDT 2023
% 0.13/0.35  % 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
% 0.20/0.60  % Total time : 0.009000 s
% 0.20/0.60  % SZS output end Proof
% 0.20/0.60  % Total time : 0.012000 s
%------------------------------------------------------------------------------