%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO192+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 : 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 : Wed Aug 30 22:46:54 EDT 2023

% Result   : Theorem 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   43 (  15 unt;   9 typ;   0 def)
%            Number of atoms       :   73 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   69 (  30   ~;  26   |;   5   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   51 (   0 sgn;  30   !;   0   ?;   0   :)

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

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

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

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

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

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

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

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

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

fof(apart1,axiom,
    ! [X1] : ~ distinct_points(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).

fof(con,conjecture,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( apart_point_and_line(intersection_point(X1,X2),X3)
       => ( distinct_lines(X1,X3)
          & distinct_lines(X2,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(con2,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( ( apart_point_and_line(X3,X1)
          | apart_point_and_line(X3,X2) )
       => distinct_points(X3,intersection_point(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con2) ).

fof(ceq2,axiom,
    ! [X1,X2,X3] :
      ( apart_point_and_line(X1,X2)
     => ( distinct_lines(X2,X3)
        | apart_point_and_line(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq2) ).

fof(apart2,axiom,
    ! [X1] : ~ distinct_lines(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart2) ).

fof(apart5,axiom,
    ! [X1,X2,X3] :
      ( distinct_lines(X1,X2)
     => ( distinct_lines(X1,X3)
        | distinct_lines(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart5) ).

fof(c_0_6,plain,
    ! [X1] : ~ distinct_points(X1,X1),
    inference(fof_simplification,[status(thm)],[apart1]) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( convergent_lines(X1,X2)
       => ( apart_point_and_line(intersection_point(X1,X2),X3)
         => ( distinct_lines(X1,X3)
            & distinct_lines(X2,X3) ) ) ),
    inference(assume_negation,[status(cth)],[con]) ).

fof(c_0_8,plain,
    ! [X6] : ~ distinct_points(X6,X6),
    inference(variable_rename,[status(thm)],[c_0_6]) ).

fof(c_0_9,plain,
    ! [X21,X22,X23] :
      ( ( ~ apart_point_and_line(X23,X21)
        | distinct_points(X23,intersection_point(X21,X22))
        | ~ convergent_lines(X21,X22) )
      & ( ~ apart_point_and_line(X23,X22)
        | distinct_points(X23,intersection_point(X21,X22))
        | ~ convergent_lines(X21,X22) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con2])])]) ).

fof(c_0_10,plain,
    ! [X31,X32,X33] :
      ( ~ apart_point_and_line(X31,X32)
      | distinct_lines(X32,X33)
      | apart_point_and_line(X31,X33) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).

fof(c_0_11,negated_conjecture,
    ( convergent_lines(esk1_0,esk2_0)
    & apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
    & ( ~ distinct_lines(esk1_0,esk3_0)
      | ~ distinct_lines(esk2_0,esk3_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_12,plain,
    ~ distinct_points(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    ( distinct_points(X1,intersection_point(X3,X2))
    | ~ apart_point_and_line(X1,X2)
    | ~ convergent_lines(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( distinct_lines(X2,X3)
    | apart_point_and_line(X1,X3)
    | ~ apart_point_and_line(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_16,plain,
    ! [X1] : ~ distinct_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[apart2]) ).

fof(c_0_17,plain,
    ! [X12,X13,X14] :
      ( ~ distinct_lines(X12,X13)
      | distinct_lines(X12,X14)
      | distinct_lines(X13,X14) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).

cnf(c_0_18,plain,
    ( ~ apart_point_and_line(intersection_point(X1,X2),X2)
    | ~ convergent_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
    | distinct_lines(esk3_0,X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,negated_conjecture,
    convergent_lines(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_21,plain,
    ( distinct_points(X1,intersection_point(X2,X3))
    | ~ apart_point_and_line(X1,X2)
    | ~ convergent_lines(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_22,plain,
    ! [X7] : ~ distinct_lines(X7,X7),
    inference(variable_rename,[status(thm)],[c_0_16]) ).

cnf(c_0_23,plain,
    ( distinct_lines(X1,X3)
    | distinct_lines(X2,X3)
    | ~ distinct_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_24,negated_conjecture,
    distinct_lines(esk3_0,esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).

cnf(c_0_25,plain,
    ( ~ apart_point_and_line(intersection_point(X1,X2),X1)
    | ~ convergent_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_21]) ).

cnf(c_0_26,plain,
    ~ distinct_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,negated_conjecture,
    ( distinct_lines(esk3_0,X1)
    | distinct_lines(esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_28,negated_conjecture,
    distinct_lines(esk3_0,esk1_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_20])]) ).

cnf(c_0_29,negated_conjecture,
    ( ~ distinct_lines(esk1_0,esk3_0)
    | ~ distinct_lines(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_30,negated_conjecture,
    distinct_lines(esk2_0,esk3_0),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    ( distinct_lines(esk3_0,X1)
    | distinct_lines(esk1_0,X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_28]) ).

cnf(c_0_32,negated_conjecture,
    ~ distinct_lines(esk1_0,esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).

cnf(c_0_33,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_31]),c_0_32]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GEO192+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n002.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   : Tue Aug 29 19:17:20 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.58  % Version  : CSE_E---1.5
% 0.19/0.58  % Problem  : theBenchmark.p
% 0.19/0.58  % Proof found
% 0.19/0.58  % SZS status Theorem for theBenchmark.p
% 0.19/0.58  % SZS output start Proof
% See solution above
% 0.19/0.58  % Total time : 0.006000 s
% 0.19/0.58  % SZS output end Proof
% 0.19/0.58  % Total time : 0.009000 s
%------------------------------------------------------------------------------