TSTP Solution File: GEO170+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO170+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n027.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 22:46:38 EDT 2023

% Result   : Theorem 0.65s 0.72s
% Output   : CNFRefutation 0.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   61 (  14 unt;  19 typ;   0 def)
%            Number of atoms       :   98 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   94 (  38   ~;  34   |;  10   &)
%                                         (   4 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  16   >;  14   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   66 (   0 sgn;  47   !;   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,
    parallel_through_point: ( $i * $i ) > $i ).

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

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

tff(decl_31,type,
    point: $i > $o ).

tff(decl_32,type,
    line: $i > $o ).

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

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

tff(decl_35,type,
    parallel_lines: ( $i * $i ) > $o ).

tff(decl_36,type,
    incident_point_and_line: ( $i * $i ) > $o ).

tff(decl_37,type,
    orthogonal_lines: ( $i * $i ) > $o ).

tff(decl_38,type,
    esk1_0: $i ).

tff(decl_39,type,
    esk2_0: $i ).

tff(decl_40,type,
    esk3_0: $i ).

fof(con,conjecture,
    ! [X1,X2,X3] :
      ( ( distinct_points(X1,X2)
        & incident_point_and_line(X1,X3)
        & incident_point_and_line(X2,X3) )
     => equal_lines(X3,line_connecting(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

fof(ax2,axiom,
    ! [X1,X2] :
      ( equal_lines(X1,X2)
    <=> ~ distinct_lines(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',ax2) ).

fof(apart1,axiom,
    ! [X1] : ~ distinct_points(X1,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart1) ).

fof(apart4,axiom,
    ! [X1,X2,X3] :
      ( distinct_points(X1,X2)
     => ( distinct_points(X1,X3)
        | distinct_points(X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart4) ).

fof(a4,axiom,
    ! [X1,X2] :
      ( incident_point_and_line(X1,X2)
    <=> ~ apart_point_and_line(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',a4) ).

fof(cu1,axiom,
    ! [X1,X2,X4,X5] :
      ( ( distinct_points(X1,X2)
        & distinct_lines(X4,X5) )
     => ( apart_point_and_line(X1,X4)
        | apart_point_and_line(X1,X5)
        | apart_point_and_line(X2,X4)
        | apart_point_and_line(X2,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',cu1) ).

fof(ci1,axiom,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+0.ax',ci2) ).

fof(c_0_8,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( distinct_points(X1,X2)
          & incident_point_and_line(X1,X3)
          & incident_point_and_line(X2,X3) )
       => equal_lines(X3,line_connecting(X1,X2)) ),
    inference(assume_negation,[status(cth)],[con]) ).

fof(c_0_9,plain,
    ! [X1,X2] :
      ( equal_lines(X1,X2)
    <=> ~ distinct_lines(X1,X2) ),
    inference(fof_simplification,[status(thm)],[ax2]) ).

fof(c_0_10,negated_conjecture,
    ( distinct_points(esk1_0,esk2_0)
    & incident_point_and_line(esk1_0,esk3_0)
    & incident_point_and_line(esk2_0,esk3_0)
    & ~ equal_lines(esk3_0,line_connecting(esk1_0,esk2_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

fof(c_0_11,plain,
    ! [X84,X85] :
      ( ( ~ equal_lines(X84,X85)
        | ~ distinct_lines(X84,X85) )
      & ( distinct_lines(X84,X85)
        | equal_lines(X84,X85) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).

fof(c_0_12,plain,
    ! [X1] : ~ distinct_points(X1,X1),
    inference(fof_simplification,[status(thm)],[apart1]) ).

fof(c_0_13,plain,
    ! [X14,X15,X16] :
      ( ~ distinct_points(X14,X15)
      | distinct_points(X14,X16)
      | distinct_points(X15,X16) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).

fof(c_0_14,plain,
    ! [X1,X2] :
      ( incident_point_and_line(X1,X2)
    <=> ~ apart_point_and_line(X1,X2) ),
    inference(fof_simplification,[status(thm)],[a4]) ).

fof(c_0_15,plain,
    ! [X31,X32,X33,X34] :
      ( ~ distinct_points(X31,X32)
      | ~ distinct_lines(X33,X34)
      | apart_point_and_line(X31,X33)
      | apart_point_and_line(X31,X34)
      | apart_point_and_line(X32,X33)
      | apart_point_and_line(X32,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).

cnf(c_0_16,negated_conjecture,
    ~ equal_lines(esk3_0,line_connecting(esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,plain,
    ( distinct_lines(X1,X2)
    | equal_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_18,plain,
    ! [X11] : ~ distinct_points(X11,X11),
    inference(variable_rename,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    ( distinct_points(X1,X3)
    | distinct_points(X2,X3)
    | ~ distinct_points(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,negated_conjecture,
    distinct_points(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_21,plain,
    ! [X88,X89] :
      ( ( ~ incident_point_and_line(X88,X89)
        | ~ apart_point_and_line(X88,X89) )
      & ( apart_point_and_line(X88,X89)
        | incident_point_and_line(X88,X89) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).

fof(c_0_22,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_23,plain,
    ( apart_point_and_line(X1,X3)
    | apart_point_and_line(X1,X4)
    | apart_point_and_line(X2,X3)
    | apart_point_and_line(X2,X4)
    | ~ distinct_points(X1,X2)
    | ~ distinct_lines(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_24,negated_conjecture,
    distinct_lines(esk3_0,line_connecting(esk1_0,esk2_0)),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_25,plain,
    ~ distinct_points(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_26,negated_conjecture,
    ( distinct_points(esk1_0,X1)
    | distinct_points(esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_27,plain,
    ( ~ incident_point_and_line(X1,X2)
    | ~ apart_point_and_line(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,negated_conjecture,
    incident_point_and_line(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_29,negated_conjecture,
    incident_point_and_line(esk1_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_30,plain,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[ci2]) ).

fof(c_0_31,plain,
    ! [X23,X24] :
      ( ~ distinct_points(X23,X24)
      | ~ apart_point_and_line(X23,line_connecting(X23,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])]) ).

cnf(c_0_32,negated_conjecture,
    ( apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(X2,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(X1,esk3_0)
    | apart_point_and_line(X2,esk3_0)
    | ~ distinct_points(X1,X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_33,negated_conjecture,
    distinct_points(esk2_0,esk1_0),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_34,negated_conjecture,
    ~ apart_point_and_line(esk2_0,esk3_0),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_35,negated_conjecture,
    ~ apart_point_and_line(esk1_0,esk3_0),
    inference(spm,[status(thm)],[c_0_27,c_0_29]) ).

fof(c_0_36,plain,
    ! [X25,X26] :
      ( ~ distinct_points(X25,X26)
      | ~ apart_point_and_line(X26,line_connecting(X25,X26)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])]) ).

cnf(c_0_37,plain,
    ( ~ distinct_points(X1,X2)
    | ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_38,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]) ).

cnf(c_0_39,plain,
    ( ~ distinct_points(X1,X2)
    | ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_40,negated_conjecture,
    apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_20])]) ).

cnf(c_0_41,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_20])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem    : GEO170+3 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n027.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
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 29 23:57:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.65/0.72  % Version  : CSE_E---1.5
% 0.65/0.72  % Problem  : theBenchmark.p
% 0.65/0.72  % Proof found
% 0.65/0.72  % SZS status Theorem for theBenchmark.p
% 0.65/0.72  % SZS output start Proof
% See solution above
% 0.65/0.72  % Total time : 0.128000 s
% 0.65/0.72  % SZS output end Proof
% 0.65/0.72  % Total time : 0.132000 s
%------------------------------------------------------------------------------