%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO082+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n004.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 : Wed Aug 30 22:45:59 EDT 2023

% Result   : Theorem 0.66s 0.77s
% Output   : CNFRefutation 0.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   45 (   5 unt;  26 typ;   0 def)
%            Number of atoms       :   52 (  11 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   49 (  16   ~;  20   |;   7   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   40 (  21   >;  19   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   4 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   2 con; 0-3 aty)
%            Number of variables   :   28 (   0 sgn;  17   !;   0   ?;   0   :)

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

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

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

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

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

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

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

tff(decl_29,type,
    open: $i > $o ).

tff(decl_30,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_31,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_32,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_33,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_34,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_35,type,
    esk6_1: $i > $i ).

tff(decl_36,type,
    esk7_1: $i > $i ).

tff(decl_37,type,
    esk8_1: $i > $i ).

tff(decl_38,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_40,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_41,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_42,type,
    esk13_2: ( $i * $i ) > $i ).

tff(decl_43,type,
    esk14_0: $i ).

tff(decl_44,type,
    esk15_0: $i ).

tff(decl_45,type,
    epred1_0: $o ).

tff(decl_46,type,
    epred2_0: $o ).

tff(decl_47,type,
    epred3_0: $o ).

fof(part_of_antisymmetry,conjecture,
    ! [X2,X4] :
      ( ( part_of(X2,X4)
        & part_of(X4,X2) )
     => X2 = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_antisymmetry) ).

fof(part_of_defn,axiom,
    ! [X1,X2] :
      ( part_of(X2,X1)
    <=> ! [X3] :
          ( incident_c(X3,X2)
         => incident_c(X3,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',part_of_defn) ).

fof(c9,axiom,
    ! [X1,X2] :
      ( ! [X3] :
          ( incident_c(X3,X1)
        <=> incident_c(X3,X2) )
     => X1 = X2 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',c9) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X2,X4] :
        ( ( part_of(X2,X4)
          & part_of(X4,X2) )
       => X2 = X4 ),
    inference(assume_negation,[status(cth)],[part_of_antisymmetry]) ).

fof(c_0_4,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ( ~ part_of(X9,X8)
        | ~ incident_c(X10,X9)
        | incident_c(X10,X8) )
      & ( incident_c(esk1_2(X11,X12),X12)
        | part_of(X12,X11) )
      & ( ~ incident_c(esk1_2(X11,X12),X11)
        | part_of(X12,X11) ) ),
    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)],[part_of_defn])])])])])]) ).

fof(c_0_5,negated_conjecture,
    ( part_of(esk14_0,esk15_0)
    & part_of(esk15_0,esk14_0)
    & esk14_0 != esk15_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_6,plain,
    ( incident_c(X3,X2)
    | ~ part_of(X1,X2)
    | ~ incident_c(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    part_of(esk14_0,esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_8,plain,
    ! [X78,X79] :
      ( ( ~ incident_c(esk13_2(X78,X79),X78)
        | ~ incident_c(esk13_2(X78,X79),X79)
        | X78 = X79 )
      & ( incident_c(esk13_2(X78,X79),X78)
        | incident_c(esk13_2(X78,X79),X79)
        | X78 = X79 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c9])])])]) ).

cnf(c_0_9,negated_conjecture,
    part_of(esk15_0,esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,negated_conjecture,
    ( incident_c(X1,esk15_0)
    | ~ incident_c(X1,esk14_0) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_11,plain,
    ( incident_c(esk13_2(X1,X2),X1)
    | incident_c(esk13_2(X1,X2),X2)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    ( X1 = X2
    | ~ incident_c(esk13_2(X1,X2),X1)
    | ~ incident_c(esk13_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    ( incident_c(X1,esk14_0)
    | ~ incident_c(X1,esk15_0) ),
    inference(spm,[status(thm)],[c_0_6,c_0_9]) ).

cnf(c_0_14,negated_conjecture,
    ( esk14_0 = X1
    | incident_c(esk13_2(esk14_0,X1),esk15_0)
    | incident_c(esk13_2(esk14_0,X1),X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    esk14_0 != esk15_0,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_16,negated_conjecture,
    ( esk14_0 = X1
    | ~ incident_c(esk13_2(esk14_0,X1),esk15_0)
    | ~ incident_c(esk13_2(esk14_0,X1),X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    incident_c(esk13_2(esk14_0,esk15_0),esk15_0),
    inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_14]),c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_17])]),c_0_15]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GEO082+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n004.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 29 20:01:37 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.66/0.77  % Version  : CSE_E---1.5
% 0.66/0.77  % Problem  : theBenchmark.p
% 0.66/0.77  % Proof found
% 0.66/0.77  % SZS status Theorem for theBenchmark.p
% 0.66/0.77  % SZS output start Proof
% See solution above
% 0.66/0.77  % Total time : 0.183000 s
% 0.66/0.77  % SZS output end Proof
% 0.66/0.77  % Total time : 0.186000 s
%------------------------------------------------------------------------------