%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET639+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 : n005.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 14:35:00 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   24 (   8 unt;  10 typ;   0 def)
%            Number of atoms       :   23 (  15 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   14 (   5   ~;   2   |;   4   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   7   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   16 (   0 sgn;  12   !;   0   ?;   0   :)

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

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

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

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

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_2: ( $i * $i ) > $i ).

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

tff(decl_31,type,
    esk5_0: $i ).

fof(prove_th121,conjecture,
    ! [X1,X2] :
      ( ( subset(X1,X2)
        & intersection(X2,X1) = empty_set )
     => X1 = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th121) ).

fof(commutativity_of_intersection,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

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

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( subset(X1,X2)
          & intersection(X2,X1) = empty_set )
       => X1 = empty_set ),
    inference(assume_negation,[status(cth)],[prove_th121]) ).

fof(c_0_4,negated_conjecture,
    ( subset(esk4_0,esk5_0)
    & intersection(esk5_0,esk4_0) = empty_set
    & esk4_0 != empty_set ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_5,plain,
    ! [X18,X19] : intersection(X18,X19) = intersection(X19,X18),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

cnf(c_0_6,negated_conjecture,
    intersection(esk5_0,esk4_0) = empty_set,
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_8,plain,
    ! [X4,X5] :
      ( ~ subset(X4,X5)
      | intersection(X4,X5) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_intersection])]) ).

cnf(c_0_9,negated_conjecture,
    intersection(esk4_0,esk5_0) = empty_set,
    inference(rw,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,plain,
    ( intersection(X1,X2) = X1
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    subset(esk4_0,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_12,negated_conjecture,
    esk4_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_13,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]),c_0_12]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET639+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
% 0.14/0.34  % Computer : n005.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sat Aug 26 09:11:53 EDT 2023
% 0.14/0.34  % 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 : 0.006000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.009000 s
%------------------------------------------------------------------------------