TSTP Solution File: GEO202+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO202+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 : 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 22:47:00 EDT 2023

% Result   : Theorem 0.20s 0.63s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   64 (  20 unt;   9 typ;   0 def)
%            Number of atoms       :  124 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  113 (  44   ~;  49   |;   8   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   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   :   88 (   0 sgn;  59   !;   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(con,conjecture,
    ! [X1,X2,X3] :
      ( ( distinct_points(X1,X2)
        & distinct_points(X1,X3)
        & convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3)) )
     => ~ distinct_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(ceq3,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( distinct_lines(X2,X3)
        | convergent_lines(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).

fof(apart3,axiom,
    ! [X1] : ~ convergent_lines(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).

fof(apart5,axiom,
    ! [X1,X2,X3] :
      ( distinct_lines(X1,X2)
     => ( distinct_lines(X1,X3)
        | distinct_lines(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).

fof(apart2,axiom,
    ! [X1] : ~ distinct_lines(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).

fof(apart1,axiom,
    ! [X1] : ~ distinct_points(X1,X1),
    file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',apart4) ).

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/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).

fof(ci4,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci4) ).

fof(ci3,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci3) ).

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(c_0_11,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( distinct_points(X1,X2)
          & distinct_points(X1,X3)
          & convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3)) )
       => ~ distinct_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).

fof(c_0_12,plain,
    ! [X36,X37,X38] :
      ( ~ convergent_lines(X36,X37)
      | distinct_lines(X37,X38)
      | convergent_lines(X36,X38) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).

fof(c_0_13,negated_conjecture,
    ( distinct_points(esk1_0,esk2_0)
    & distinct_points(esk1_0,esk3_0)
    & convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0))
    & distinct_points(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),esk1_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).

fof(c_0_14,plain,
    ! [X1] : ~ convergent_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[apart3]) ).

fof(c_0_15,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_16,plain,
    ( distinct_lines(X2,X3)
    | convergent_lines(X1,X3)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,negated_conjecture,
    convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_18,plain,
    ! [X1] : ~ distinct_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[apart2]) ).

fof(c_0_19,plain,
    ! [X8] : ~ convergent_lines(X8,X8),
    inference(variable_rename,[status(thm)],[c_0_14]) ).

cnf(c_0_20,plain,
    ( distinct_lines(X1,X3)
    | distinct_lines(X2,X3)
    | ~ distinct_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,negated_conjecture,
    ( convergent_lines(line_connecting(esk1_0,esk2_0),X1)
    | distinct_lines(line_connecting(esk1_0,esk3_0),X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

fof(c_0_22,plain,
    ! [X7] : ~ distinct_lines(X7,X7),
    inference(variable_rename,[status(thm)],[c_0_18]) ).

cnf(c_0_23,plain,
    ~ convergent_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_24,negated_conjecture,
    ( convergent_lines(line_connecting(esk1_0,esk2_0),X1)
    | distinct_lines(line_connecting(esk1_0,esk3_0),X2)
    | distinct_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

fof(c_0_25,plain,
    ! [X1] : ~ distinct_points(X1,X1),
    inference(fof_simplification,[status(thm)],[apart1]) ).

fof(c_0_26,plain,
    ! [X9,X10,X11] :
      ( ~ distinct_points(X9,X10)
      | distinct_points(X9,X11)
      | distinct_points(X10,X11) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).

fof(c_0_27,plain,
    ! [X26,X27,X28,X29] :
      ( ~ distinct_points(X26,X27)
      | ~ distinct_lines(X28,X29)
      | apart_point_and_line(X26,X28)
      | apart_point_and_line(X26,X29)
      | apart_point_and_line(X27,X28)
      | apart_point_and_line(X27,X29) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).

cnf(c_0_28,plain,
    ~ distinct_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_29,negated_conjecture,
    ( distinct_lines(line_connecting(esk1_0,esk2_0),X1)
    | distinct_lines(line_connecting(esk1_0,esk3_0),X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

fof(c_0_30,plain,
    ! [X6] : ~ distinct_points(X6,X6),
    inference(variable_rename,[status(thm)],[c_0_25]) ).

cnf(c_0_31,plain,
    ( distinct_points(X1,X3)
    | distinct_points(X2,X3)
    | ~ distinct_points(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_32,negated_conjecture,
    distinct_points(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_33,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[ci4]) ).

cnf(c_0_34,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_27]) ).

cnf(c_0_35,negated_conjecture,
    distinct_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_36,plain,
    ~ distinct_points(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_37,negated_conjecture,
    ( distinct_points(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),X1)
    | distinct_points(esk1_0,X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

fof(c_0_38,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(fof_simplification,[status(thm)],[ci3]) ).

fof(c_0_39,plain,
    ! [X24,X25] :
      ( ~ convergent_lines(X24,X25)
      | ~ apart_point_and_line(intersection_point(X24,X25),X25) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])]) ).

cnf(c_0_40,negated_conjecture,
    ( apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(X1,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(X2,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(X2,line_connecting(esk1_0,esk3_0))
    | ~ distinct_points(X1,X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_41,negated_conjecture,
    distinct_points(esk1_0,intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0))),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

fof(c_0_42,plain,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[ci1]) ).

fof(c_0_43,plain,
    ! [X22,X23] :
      ( ~ convergent_lines(X22,X23)
      | ~ apart_point_and_line(intersection_point(X22,X23),X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])]) ).

cnf(c_0_44,plain,
    ( ~ convergent_lines(X1,X2)
    | ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_45,negated_conjecture,
    ( apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

fof(c_0_46,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_42])]) ).

cnf(c_0_47,plain,
    ( ~ convergent_lines(X1,X2)
    | ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_48,negated_conjecture,
    ( apart_point_and_line(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_17])]) ).

cnf(c_0_49,plain,
    ( ~ distinct_points(X1,X2)
    | ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_50,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_17])]) ).

cnf(c_0_51,negated_conjecture,
    distinct_points(esk1_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_52,negated_conjecture,
    apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).

cnf(c_0_53,negated_conjecture,
    distinct_points(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_54,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_52]),c_0_53])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : GEO202+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n027.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 29 20:24:38 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.63  % Version  : CSE_E---1.5
% 0.20/0.63  % Problem  : theBenchmark.p
% 0.20/0.63  % Proof found
% 0.20/0.63  % SZS status Theorem for theBenchmark.p
% 0.20/0.63  % SZS output start Proof
% See solution above
% 0.20/0.63  % Total time : 0.043000 s
% 0.20/0.63  % SZS output end Proof
% 0.20/0.63  % Total time : 0.046000 s
%------------------------------------------------------------------------------