TSTP Solution File: GEO224+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO224+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 : n005.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 22:47:16 EDT 2023

% Result   : Theorem 0.17s 0.60s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   52 (   9 unt;  18 typ;   0 def)
%            Number of atoms       :   79 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   84 (  39   ~;  27   |;  10   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   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   :   59 (   3 sgn;  35   !;   2   ?;   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] :
      ( ( point(X1)
        & line(X2) )
     => ? [X3] :
          ( point(X3)
          & incident_point_and_line(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

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(ci4,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).

fof(int1,axiom,
    ! [X6,X7] :
      ( ( line(X6)
        & line(X7)
        & convergent_lines(X6,X7) )
     => point(intersection_point(X6,X7)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+5.ax',int1) ).

fof(ooc1,axiom,
    ! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).

fof(orth1,axiom,
    ! [X6,X9] :
      ( ( line(X6)
        & point(X9) )
     => line(orthogonal_through_point(X6,X9)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+5.ax',orth1) ).

fof(occu1,axiom,
    ! [X6,X7] :
      ( convergent_lines(X6,X7)
      | unorthogonal_lines(X6,X7) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',occu1) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( point(X1)
          & line(X2) )
       => ? [X3] :
            ( point(X3)
            & incident_point_and_line(X3,X2) ) ),
    inference(assume_negation,[status(cth)],[con]) ).

fof(c_0_8,plain,
    ! [X1,X2] :
      ( incident_point_and_line(X1,X2)
    <=> ~ apart_point_and_line(X1,X2) ),
    inference(fof_simplification,[status(thm)],[a4]) ).

fof(c_0_9,negated_conjecture,
    ! [X94] :
      ( point(esk1_0)
      & line(esk2_0)
      & ( ~ point(X94)
        | ~ incident_point_and_line(X94,esk2_0) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).

fof(c_0_10,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_8])]) ).

fof(c_0_11,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_12,negated_conjecture,
    ( ~ point(X1)
    | ~ incident_point_and_line(X1,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

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

fof(c_0_14,plain,
    ! [X76,X77] :
      ( ~ line(X76)
      | ~ line(X77)
      | ~ convergent_lines(X76,X77)
      | point(intersection_point(X76,X77)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int1])]) ).

fof(c_0_15,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_11])]) ).

cnf(c_0_16,negated_conjecture,
    ( apart_point_and_line(X1,esk2_0)
    | ~ point(X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,plain,
    ( point(intersection_point(X1,X2))
    | ~ line(X1)
    | ~ line(X2)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_18,plain,
    ! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
    inference(fof_simplification,[status(thm)],[ooc1]) ).

cnf(c_0_19,plain,
    ( ~ convergent_lines(X1,X2)
    | ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,negated_conjecture,
    ( apart_point_and_line(intersection_point(X1,X2),esk2_0)
    | ~ line(X2)
    | ~ line(X1)
    | ~ convergent_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    line(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_22,plain,
    ! [X80,X81] :
      ( ~ line(X80)
      | ~ point(X81)
      | line(orthogonal_through_point(X80,X81)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[orth1])]) ).

fof(c_0_23,plain,
    ! [X58,X59] : ~ unorthogonal_lines(orthogonal_through_point(X59,X58),X59),
    inference(variable_rename,[status(thm)],[c_0_18]) ).

fof(c_0_24,plain,
    ! [X53,X54] :
      ( convergent_lines(X53,X54)
      | unorthogonal_lines(X53,X54) ),
    inference(variable_rename,[status(thm)],[occu1]) ).

cnf(c_0_25,negated_conjecture,
    ( ~ line(X1)
    | ~ convergent_lines(X1,esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

cnf(c_0_26,plain,
    ( line(orthogonal_through_point(X1,X2))
    | ~ line(X1)
    | ~ point(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

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

cnf(c_0_28,plain,
    ( convergent_lines(X1,X2)
    | unorthogonal_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_29,negated_conjecture,
    ( ~ line(X1)
    | ~ point(X2)
    | ~ convergent_lines(orthogonal_through_point(X1,X2),esk2_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,plain,
    convergent_lines(orthogonal_through_point(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_31,negated_conjecture,
    point(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_32,negated_conjecture,
    ~ point(X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_21])]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem    : GEO224+3 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n005.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
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 29 18:53:52 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.17/0.58  start to proof: theBenchmark
% 0.17/0.60  % Version  : CSE_E---1.5
% 0.17/0.60  % Problem  : theBenchmark.p
% 0.17/0.60  % Proof found
% 0.17/0.60  % SZS status Theorem for theBenchmark.p
% 0.17/0.60  % SZS output start Proof
% See solution above
% 0.17/0.60  % Total time : 0.007000 s
% 0.17/0.60  % SZS output end Proof
% 0.17/0.60  % Total time : 0.009000 s
%------------------------------------------------------------------------------