%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU129+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n002.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 16:22:36 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   42 (  13 unt;  18 typ;   0 def)
%            Number of atoms       :   41 (   3 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   30 (  13   ~;  10   |;   3   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  12   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-3 aty)
%            Number of variables   :   44 (   3 sgn;  26   !;   0   ?;   0   :)

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

tff(decl_23,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_24,type,
    set_intersection2: ( $i * $i ) > $i ).

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

tff(decl_26,type,
    empty_set: $i ).

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

tff(decl_28,type,
    empty: $i > $o ).

tff(decl_29,type,
    esk1_1: $i > $i ).

tff(decl_30,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_31,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_32,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_33,type,
    esk5_0: $i ).

tff(decl_34,type,
    esk6_0: $i ).

tff(decl_35,type,
    esk7_0: $i ).

tff(decl_36,type,
    esk8_0: $i ).

tff(decl_37,type,
    esk9_0: $i ).

tff(decl_38,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk11_2: ( $i * $i ) > $i ).

fof(t26_xboole_1,conjecture,
    ! [X1,X2,X3] :
      ( subset(X1,X2)
     => subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).

fof(t1_xboole_1,lemma,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X2,X3) )
     => subset(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).

fof(t17_xboole_1,lemma,
    ! [X1,X2] : subset(set_intersection2(X1,X2),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).

fof(t19_xboole_1,lemma,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X1,X3) )
     => subset(X1,set_intersection2(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).

fof(commutativity_k3_xboole_0,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( subset(X1,X2)
       => subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
    inference(assume_negation,[status(cth)],[t26_xboole_1]) ).

fof(c_0_6,lemma,
    ! [X62,X63,X64] :
      ( ~ subset(X62,X63)
      | ~ subset(X63,X64)
      | subset(X62,X64) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).

fof(c_0_7,negated_conjecture,
    ( subset(esk7_0,esk8_0)
    & ~ subset(set_intersection2(esk7_0,esk9_0),set_intersection2(esk8_0,esk9_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

cnf(c_0_8,lemma,
    ( subset(X1,X3)
    | ~ subset(X1,X2)
    | ~ subset(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,negated_conjecture,
    subset(esk7_0,esk8_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_10,lemma,
    ! [X56,X57] : subset(set_intersection2(X56,X57),X56),
    inference(variable_rename,[status(thm)],[t17_xboole_1]) ).

fof(c_0_11,lemma,
    ! [X58,X59,X60] :
      ( ~ subset(X58,X59)
      | ~ subset(X58,X60)
      | subset(X58,set_intersection2(X59,X60)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).

cnf(c_0_12,negated_conjecture,
    ( subset(X1,esk8_0)
    | ~ subset(X1,esk7_0) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,lemma,
    subset(set_intersection2(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_14,plain,
    ! [X9,X10] : set_intersection2(X9,X10) = set_intersection2(X10,X9),
    inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).

cnf(c_0_15,lemma,
    ( subset(X1,set_intersection2(X2,X3))
    | ~ subset(X1,X2)
    | ~ subset(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,lemma,
    subset(set_intersection2(esk7_0,X1),esk8_0),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,lemma,
    ( subset(set_intersection2(esk7_0,X1),set_intersection2(X2,esk8_0))
    | ~ subset(set_intersection2(esk7_0,X1),X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,lemma,
    subset(set_intersection2(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_13,c_0_17]) ).

cnf(c_0_20,lemma,
    subset(set_intersection2(esk7_0,X1),set_intersection2(X1,esk8_0)),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_21,negated_conjecture,
    ~ subset(set_intersection2(esk7_0,esk9_0),set_intersection2(esk8_0,esk9_0)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_22,lemma,
    subset(set_intersection2(esk7_0,X1),set_intersection2(esk8_0,X1)),
    inference(spm,[status(thm)],[c_0_20,c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU129+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n002.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   : Wed Aug 23 18:47:16 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.59  % Version  : CSE_E---1.5
% 0.19/0.59  % Problem  : theBenchmark.p
% 0.19/0.59  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.60  % Total time : 0.027000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.030000 s
%------------------------------------------------------------------------------