%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET575+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 14:34:34 EDT 2023

% Result   : Theorem 0.19s 0.57s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   20 (   3 unt;   5 typ;   0 def)
%            Number of atoms       :   36 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   36 (  15   ~;  11   |;   6   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   27 (   0 sgn;  16   !;   3   ?;   0   :)

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

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

tff(decl_24,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_25,type,
    esk2_0: $i ).

tff(decl_26,type,
    esk3_0: $i ).

fof(prove_th15,conjecture,
    ! [X1,X2] :
      ( intersect(X1,X2)
     => ? [X3] :
          ( member(X3,X1)
          & member(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th15) ).

fof(intersect_defn,axiom,
    ! [X1,X2] :
      ( intersect(X1,X2)
    <=> ? [X3] :
          ( member(X3,X1)
          & member(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).

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

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2] :
        ( intersect(X1,X2)
       => ? [X3] :
            ( member(X3,X1)
            & member(X3,X2) ) ),
    inference(assume_negation,[status(cth)],[prove_th15]) ).

fof(c_0_4,negated_conjecture,
    ! [X14] :
      ( intersect(esk2_0,esk3_0)
      & ( ~ member(X14,esk2_0)
        | ~ member(X14,esk3_0) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).

fof(c_0_5,plain,
    ! [X4,X5,X7,X8,X9] :
      ( ( member(esk1_2(X4,X5),X4)
        | ~ intersect(X4,X5) )
      & ( member(esk1_2(X4,X5),X5)
        | ~ intersect(X4,X5) )
      & ( ~ member(X9,X7)
        | ~ member(X9,X8)
        | intersect(X7,X8) ) ),
    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)],[intersect_defn])])])])])]) ).

fof(c_0_6,plain,
    ! [X10,X11] :
      ( ~ intersect(X10,X11)
      | intersect(X11,X10) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_of_intersect])]) ).

cnf(c_0_7,negated_conjecture,
    ( ~ member(X1,esk2_0)
    | ~ member(X1,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,plain,
    ( member(esk1_2(X1,X2),X2)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( intersect(X2,X1)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    intersect(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_11,negated_conjecture,
    ( ~ member(esk1_2(X1,esk2_0),esk3_0)
    | ~ intersect(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_12,plain,
    ( member(esk1_2(X1,X2),X1)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_13,negated_conjecture,
    intersect(esk3_0,esk2_0),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SET575+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n005.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   : Sat Aug 26 12:37:53 EDT 2023
% 0.13/0.34  % 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 : 0.004000 s
% 0.19/0.57  % SZS output end Proof
% 0.19/0.57  % Total time : 0.007000 s
%------------------------------------------------------------------------------