TSTP Solution File: GEO201+3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO201+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n012.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 0.74s 0.81s
% Output   : CNFRefutation 0.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   77 (  21 unt;  18 typ;   0 def)
%            Number of atoms       :  128 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  111 (  42   ~;  54   |;   3   &)
%                                         (   2 <=>;  10  =>;   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    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   96 (   3 sgn;  60   !;   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 ).

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

fof(ax6,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( convergent_lines(X1,X3)
        | convergent_lines(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).

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

fof(cp1,axiom,
    ! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).

fof(ax1,axiom,
    ! [X1,X2] :
      ( equal_points(X1,X2)
    <=> ~ distinct_points(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax1) ).

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(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(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(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(c_0_11,negated_conjecture,
    ~ ! [X1,X2] :
        ( convergent_lines(X1,X2)
       => equal_points(intersection_point(X1,X2),intersection_point(X2,X1)) ),
    inference(assume_negation,[status(cth)],[con]) ).

fof(c_0_12,plain,
    ! [X20,X21,X22] :
      ( ~ convergent_lines(X20,X21)
      | convergent_lines(X20,X22)
      | convergent_lines(X21,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).

fof(c_0_13,negated_conjecture,
    ( convergent_lines(esk1_0,esk2_0)
    & ~ equal_points(intersection_point(esk1_0,esk2_0),intersection_point(esk2_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]) ).

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

cnf(c_0_16,negated_conjecture,
    convergent_lines(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_17,plain,
    ! [X13] : ~ convergent_lines(X13,X13),
    inference(variable_rename,[status(thm)],[c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    ( convergent_lines(esk1_0,X1)
    | convergent_lines(esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,plain,
    ~ convergent_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_20,negated_conjecture,
    ( convergent_lines(esk2_0,X1)
    | convergent_lines(esk1_0,X2)
    | convergent_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_18]) ).

fof(c_0_21,plain,
    ! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
    inference(fof_simplification,[status(thm)],[cp1]) ).

cnf(c_0_22,negated_conjecture,
    ( convergent_lines(X1,esk1_0)
    | convergent_lines(esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

fof(c_0_23,plain,
    ! [X46,X47] : ~ convergent_lines(parallel_through_point(X47,X46),X47),
    inference(variable_rename,[status(thm)],[c_0_21]) ).

cnf(c_0_24,negated_conjecture,
    ( convergent_lines(X1,esk1_0)
    | convergent_lines(esk2_0,X2)
    | convergent_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_22]) ).

fof(c_0_25,plain,
    ! [X1,X2] :
      ( equal_points(X1,X2)
    <=> ~ distinct_points(X1,X2) ),
    inference(fof_simplification,[status(thm)],[ax1]) ).

fof(c_0_26,plain,
    ! [X41,X42,X43] :
      ( ~ convergent_lines(X41,X42)
      | distinct_lines(X42,X43)
      | convergent_lines(X41,X43) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).

cnf(c_0_27,plain,
    ~ convergent_lines(parallel_through_point(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_28,negated_conjecture,
    ( convergent_lines(X1,esk2_0)
    | convergent_lines(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_19,c_0_24]) ).

fof(c_0_29,plain,
    ! [X82,X83] :
      ( ( ~ equal_points(X82,X83)
        | ~ distinct_points(X82,X83) )
      & ( distinct_points(X82,X83)
        | equal_points(X82,X83) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).

cnf(c_0_30,plain,
    ( distinct_lines(X2,X3)
    | convergent_lines(X1,X3)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_31,negated_conjecture,
    convergent_lines(parallel_through_point(esk1_0,X1),esk2_0),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

fof(c_0_32,plain,
    ! [X1] : ~ distinct_points(X1,X1),
    inference(fof_simplification,[status(thm)],[apart1]) ).

fof(c_0_33,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])]) ).

cnf(c_0_34,negated_conjecture,
    ~ equal_points(intersection_point(esk1_0,esk2_0),intersection_point(esk2_0,esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_35,plain,
    ( distinct_points(X1,X2)
    | equal_points(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

fof(c_0_36,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_37,negated_conjecture,
    ( convergent_lines(parallel_through_point(esk1_0,X1),X2)
    | distinct_lines(esk2_0,X2) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

fof(c_0_38,plain,
    ! [X11] : ~ distinct_points(X11,X11),
    inference(variable_rename,[status(thm)],[c_0_32]) ).

cnf(c_0_39,plain,
    ( distinct_points(X1,X3)
    | distinct_points(X2,X3)
    | ~ distinct_points(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_40,negated_conjecture,
    distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk2_0,esk1_0)),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

fof(c_0_41,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(fof_simplification,[status(thm)],[ci3]) ).

cnf(c_0_42,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_36]) ).

cnf(c_0_43,negated_conjecture,
    distinct_lines(esk2_0,esk1_0),
    inference(spm,[status(thm)],[c_0_27,c_0_37]) ).

cnf(c_0_44,plain,
    ~ distinct_points(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_45,negated_conjecture,
    ( distinct_points(intersection_point(esk1_0,esk2_0),X1)
    | distinct_points(intersection_point(esk2_0,esk1_0),X1) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

fof(c_0_46,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[ci4]) ).

fof(c_0_47,plain,
    ! [X27,X28] :
      ( ~ convergent_lines(X27,X28)
      | ~ apart_point_and_line(intersection_point(X27,X28),X27) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])]) ).

cnf(c_0_48,negated_conjecture,
    ( apart_point_and_line(X1,esk2_0)
    | apart_point_and_line(X1,esk1_0)
    | apart_point_and_line(X2,esk2_0)
    | apart_point_and_line(X2,esk1_0)
    | ~ distinct_points(X1,X2) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_49,negated_conjecture,
    distinct_points(intersection_point(esk2_0,esk1_0),intersection_point(esk1_0,esk2_0)),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

fof(c_0_50,plain,
    ! [X29,X30] :
      ( ~ convergent_lines(X29,X30)
      | ~ apart_point_and_line(intersection_point(X29,X30),X30) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])]) ).

cnf(c_0_51,plain,
    ( ~ convergent_lines(X1,X2)
    | ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_52,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
    | apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
    | apart_point_and_line(intersection_point(esk2_0,esk1_0),esk1_0)
    | apart_point_and_line(intersection_point(esk2_0,esk1_0),esk2_0) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_53,plain,
    ( ~ convergent_lines(X1,X2)
    | ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_54,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk2_0,esk1_0),esk2_0)
    | apart_point_and_line(intersection_point(esk2_0,esk1_0),esk1_0)
    | apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_16])]) ).

cnf(c_0_55,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk2_0,esk1_0),esk1_0)
    | apart_point_and_line(intersection_point(esk2_0,esk1_0),esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_16])]) ).

cnf(c_0_56,negated_conjecture,
    convergent_lines(esk2_0,esk1_0),
    inference(spm,[status(thm)],[c_0_19,c_0_18]) ).

cnf(c_0_57,negated_conjecture,
    apart_point_and_line(intersection_point(esk2_0,esk1_0),esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_55]),c_0_56])]) ).

cnf(c_0_58,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_57]),c_0_56])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GEO201+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n012.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 29 20:42:08 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.74/0.81  % Version  : CSE_E---1.5
% 0.74/0.81  % Problem  : theBenchmark.p
% 0.74/0.81  % Proof found
% 0.74/0.81  % SZS status Theorem for theBenchmark.p
% 0.74/0.81  % SZS output start Proof
% See solution above
% 0.74/0.81  % Total time : 0.244000 s
% 0.74/0.81  % SZS output end Proof
% 0.74/0.81  % Total time : 0.248000 s
%------------------------------------------------------------------------------