%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU126+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n021.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 16:22:35 EDT 2023

% Result   : Theorem 0.17s 0.57s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   41 (  14 unt;  17 typ;   0 def)
%            Number of atoms       :   44 (  13 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   35 (  15   ~;  11   |;   5   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   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    :   13 (  13 usr;   5 con; 0-3 aty)
%            Number of variables   :   36 (   2 sgn;  25   !;   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_2: ( $i * $i ) > $i ).

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

fof(t12_xboole_1,conjecture,
    ! [X1,X2] :
      ( subset(X1,X2)
     => set_union2(X1,X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).

fof(t8_xboole_1,lemma,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X3,X2) )
     => subset(set_union2(X1,X3),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).

fof(reflexivity_r1_tarski,axiom,
    ! [X1,X2] : subset(X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(commutativity_k2_xboole_0,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(d10_xboole_0,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).

fof(t7_xboole_1,lemma,
    ! [X1,X2] : subset(X1,set_union2(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(X1,X2)
       => set_union2(X1,X2) = X2 ),
    inference(assume_negation,[status(cth)],[t12_xboole_1]) ).

fof(c_0_7,lemma,
    ! [X81,X82,X83] :
      ( ~ subset(X81,X82)
      | ~ subset(X83,X82)
      | subset(set_union2(X81,X83),X82) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).

fof(c_0_8,negated_conjecture,
    ( subset(esk7_0,esk8_0)
    & set_union2(esk7_0,esk8_0) != esk8_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

cnf(c_0_9,lemma,
    ( subset(set_union2(X1,X3),X2)
    | ~ subset(X1,X2)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    subset(esk7_0,esk8_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_11,plain,
    ! [X51] : subset(X51,X51),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).

fof(c_0_12,plain,
    ! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
    inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).

fof(c_0_13,plain,
    ! [X11,X12] :
      ( ( subset(X11,X12)
        | X11 != X12 )
      & ( subset(X12,X11)
        | X11 != X12 )
      & ( ~ subset(X11,X12)
        | ~ subset(X12,X11)
        | X11 = X12 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).

cnf(c_0_14,negated_conjecture,
    ( subset(set_union2(X1,esk7_0),esk8_0)
    | ~ subset(X1,esk8_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_15,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_16,lemma,
    ! [X77,X78] : subset(X77,set_union2(X77,X78)),
    inference(variable_rename,[status(thm)],[t7_xboole_1]) ).

cnf(c_0_17,negated_conjecture,
    set_union2(esk7_0,esk8_0) != esk8_0,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_18,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    ( X1 = X2
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,negated_conjecture,
    subset(set_union2(esk8_0,esk7_0),esk8_0),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_21,lemma,
    subset(X1,set_union2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,negated_conjecture,
    set_union2(esk8_0,esk7_0) != esk8_0,
    inference(rw,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),c_0_22]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SEU126+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.32  % Computer : n021.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Thu Aug 24 00:10:24 EDT 2023
% 0.12/0.32  % CPUTime  : 
% 0.17/0.55  start to proof: theBenchmark
% 0.17/0.57  % Version  : CSE_E---1.5
% 0.17/0.57  % Problem  : theBenchmark.p
% 0.17/0.57  % Proof found
% 0.17/0.57  % SZS status Theorem for theBenchmark.p
% 0.17/0.57  % SZS output start Proof
% See solution above
% 0.17/0.57  % Total time : 0.011000 s
% 0.17/0.57  % SZS output end Proof
% 0.17/0.57  % Total time : 0.014000 s
%------------------------------------------------------------------------------