%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO183+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 : n016.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 22:46:47 EDT 2023

% Result   : Theorem 0.46s 0.57s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   33 (   5 unt;  10 typ;   0 def)
%            Number of atoms       :   54 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   54 (  23   ~;  15   |;   9   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   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    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   35 (   0 sgn;  26   !;   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 ).

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

fof(con,conjecture,
    ! [X1,X2,X4,X5] :
      ( ( distinct_points(X1,X2)
        & convergent_lines(X4,X5)
        & ~ distinct_lines(X4,line_connecting(X1,X2)) )
     => ( ~ apart_point_and_line(X1,X4)
        & ~ apart_point_and_line(X2,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

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/GEO006+0.ax',ceq2) ).

fof(ci1,axiom,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci1) ).

fof(ci2,axiom,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci2) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2,X4,X5] :
        ( ( distinct_points(X1,X2)
          & convergent_lines(X4,X5)
          & ~ distinct_lines(X4,line_connecting(X1,X2)) )
       => ( ~ apart_point_and_line(X1,X4)
          & ~ apart_point_and_line(X2,X4) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).

fof(c_0_5,plain,
    ! [X33,X34,X35] :
      ( ~ apart_point_and_line(X33,X34)
      | distinct_lines(X34,X35)
      | apart_point_and_line(X33,X35) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).

fof(c_0_6,negated_conjecture,
    ( distinct_points(esk1_0,esk2_0)
    & convergent_lines(esk3_0,esk4_0)
    & ~ distinct_lines(esk3_0,line_connecting(esk1_0,esk2_0))
    & ( apart_point_and_line(esk1_0,esk3_0)
      | apart_point_and_line(esk2_0,esk3_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

fof(c_0_7,plain,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[ci1]) ).

cnf(c_0_8,plain,
    ( distinct_lines(X2,X3)
    | apart_point_and_line(X1,X3)
    | ~ apart_point_and_line(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    ( apart_point_and_line(esk1_0,esk3_0)
    | apart_point_and_line(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_10,plain,
    ! [X18,X19] :
      ( ~ distinct_points(X18,X19)
      | ~ apart_point_and_line(X18,line_connecting(X18,X19)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).

cnf(c_0_11,negated_conjecture,
    ~ distinct_lines(esk3_0,line_connecting(esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,negated_conjecture,
    ( apart_point_and_line(esk2_0,esk3_0)
    | apart_point_and_line(esk1_0,X1)
    | distinct_lines(esk3_0,X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,plain,
    ( ~ distinct_points(X1,X2)
    | ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk2_0,esk3_0) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_15,negated_conjecture,
    distinct_points(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_16,plain,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[ci2]) ).

cnf(c_0_17,negated_conjecture,
    apart_point_and_line(esk2_0,esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).

fof(c_0_18,plain,
    ! [X20,X21] :
      ( ~ distinct_points(X20,X21)
      | ~ apart_point_and_line(X21,line_connecting(X20,X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])]) ).

cnf(c_0_19,negated_conjecture,
    ( apart_point_and_line(esk2_0,X1)
    | distinct_lines(esk3_0,X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_17]) ).

cnf(c_0_20,plain,
    ( ~ distinct_points(X1,X2)
    | ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)),
    inference(spm,[status(thm)],[c_0_11,c_0_19]) ).

cnf(c_0_22,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : GEO183+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n016.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 29 23:09:01 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.46/0.56  start to proof: theBenchmark
% 0.46/0.57  % Version  : CSE_E---1.5
% 0.46/0.57  % Problem  : theBenchmark.p
% 0.46/0.57  % Proof found
% 0.46/0.57  % SZS status Theorem for theBenchmark.p
% 0.46/0.57  % SZS output start Proof
% See solution above
% 0.46/0.58  % Total time : 0.006000 s
% 0.46/0.58  % SZS output end Proof
% 0.46/0.58  % Total time : 0.009000 s
%------------------------------------------------------------------------------