%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU140+1 : 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 : 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 16:22:42 EDT 2023

% Result   : Theorem 0.19s 0.57s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   36 (  10 unt;  11 typ;   0 def)
%            Number of atoms       :   45 (  15 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   35 (  15   ~;  10   |;   5   &)
%                                         (   1 <=>;   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  :    9 (   5   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   34 (   0 sgn;  22   !;   0   ?;   0   :)

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

tff(decl_23,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

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

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

tff(decl_28,type,
    esk1_0: $i ).

tff(decl_29,type,
    esk2_0: $i ).

tff(decl_30,type,
    esk3_0: $i ).

tff(decl_31,type,
    esk4_0: $i ).

tff(decl_32,type,
    esk5_0: $i ).

fof(t63_xboole_1,conjecture,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & disjoint(X2,X3) )
     => disjoint(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).

fof(d7_xboole_0,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> set_intersection2(X1,X2) = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).

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

fof(t3_xboole_1,axiom,
    ! [X1] :
      ( subset(X1,empty_set)
     => X1 = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).

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

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( subset(X1,X2)
          & disjoint(X2,X3) )
       => disjoint(X1,X3) ),
    inference(assume_negation,[status(cth)],[t63_xboole_1]) ).

fof(c_0_6,plain,
    ! [X8,X9] :
      ( ( ~ disjoint(X8,X9)
        | set_intersection2(X8,X9) = empty_set )
      & ( set_intersection2(X8,X9) != empty_set
        | disjoint(X8,X9) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).

fof(c_0_7,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    & disjoint(esk4_0,esk5_0)
    & ~ disjoint(esk3_0,esk5_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_8,plain,
    ! [X16,X17,X18] :
      ( ~ subset(X16,X17)
      | subset(set_intersection2(X16,X18),set_intersection2(X17,X18)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_xboole_1])]) ).

cnf(c_0_9,plain,
    ( set_intersection2(X1,X2) = empty_set
    | ~ disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    disjoint(esk4_0,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X20] :
      ( ~ subset(X20,empty_set)
      | X20 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).

cnf(c_0_12,plain,
    ( subset(set_intersection2(X1,X3),set_intersection2(X2,X3))
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    set_intersection2(esk4_0,esk5_0) = empty_set,
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    ~ disjoint(esk3_0,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_15,plain,
    ( disjoint(X1,X2)
    | set_intersection2(X1,X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_16,plain,
    ! [X6,X7] : set_intersection2(X6,X7) = set_intersection2(X7,X6),
    inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).

cnf(c_0_17,plain,
    ( X1 = empty_set
    | ~ subset(X1,empty_set) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,negated_conjecture,
    ( subset(set_intersection2(X1,esk5_0),empty_set)
    | ~ subset(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    set_intersection2(esk3_0,esk5_0) != empty_set,
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    ( set_intersection2(X1,esk5_0) = empty_set
    | ~ subset(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    subset(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_23,negated_conjecture,
    set_intersection2(esk5_0,esk3_0) != empty_set,
    inference(rw,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_20]),c_0_23]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU140+1 : 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
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Wed Aug 23 14:38:21 EDT 2023
% 0.12/0.33  % 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 : 0.006000 s
% 0.19/0.57  % SZS output end Proof
% 0.19/0.57  % Total time : 0.009000 s
%------------------------------------------------------------------------------