TSTP Solution File: GEO172+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO172+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 : n002.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 22:46:39 EDT 2023

% Result   : Theorem 0.78s 0.88s
% Output   : CNFRefutation 0.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   74 (  19 unt;  19 typ;   0 def)
%            Number of atoms       :  124 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  113 (  44   ~;  46   |;  10   &)
%                                         (   4 <=>;   9  =>;   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   :   92 (   3 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,
    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] :
      ( ( convergent_lines(X1,X2)
        & incident_point_and_line(X3,X1)
        & incident_point_and_line(X3,X2) )
     => equal_points(X3,intersection_point(X1,X2)) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).

fof(apart3,axiom,
    ! [X1] : ~ convergent_lines(X1,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).

fof(cp1,axiom,
    ! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).

fof(ceq3,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( distinct_lines(X2,X3)
        | convergent_lines(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).

fof(ax1,axiom,
    ! [X1,X2] :
      ( equal_points(X1,X2)
    <=> ~ distinct_points(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',ax1) ).

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(ci3,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( convergent_lines(X1,X2)
          & incident_point_and_line(X3,X1)
          & incident_point_and_line(X3,X2) )
       => equal_points(X3,intersection_point(X1,X2)) ),
    inference(assume_negation,[status(cth)],[con]) ).

fof(c_0_11,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_12,negated_conjecture,
    ( convergent_lines(esk1_0,esk2_0)
    & incident_point_and_line(esk3_0,esk1_0)
    & incident_point_and_line(esk3_0,esk2_0)
    & ~ equal_points(esk3_0,intersection_point(esk1_0,esk2_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_13,plain,
    ! [X1] : ~ convergent_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[apart3]) ).

cnf(c_0_14,plain,
    ( convergent_lines(X1,X3)
    | convergent_lines(X2,X3)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    convergent_lines(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_16,plain,
    ! [X13] : ~ convergent_lines(X13,X13),
    inference(variable_rename,[status(thm)],[c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    ( convergent_lines(esk1_0,X1)
    | convergent_lines(esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,plain,
    ~ convergent_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    ( convergent_lines(esk2_0,X1)
    | convergent_lines(esk1_0,X2)
    | convergent_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_17]) ).

fof(c_0_20,plain,
    ! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
    inference(fof_simplification,[status(thm)],[cp1]) ).

cnf(c_0_21,negated_conjecture,
    ( convergent_lines(X1,esk1_0)
    | convergent_lines(esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

fof(c_0_22,plain,
    ! [X46,X47] : ~ convergent_lines(parallel_through_point(X47,X46),X47),
    inference(variable_rename,[status(thm)],[c_0_20]) ).

cnf(c_0_23,negated_conjecture,
    ( convergent_lines(X1,esk1_0)
    | convergent_lines(esk2_0,X2)
    | convergent_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_21]) ).

fof(c_0_24,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_25,plain,
    ~ convergent_lines(parallel_through_point(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_26,negated_conjecture,
    ( convergent_lines(X1,esk2_0)
    | convergent_lines(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_18,c_0_23]) ).

cnf(c_0_27,plain,
    ( distinct_lines(X2,X3)
    | convergent_lines(X1,X3)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_28,negated_conjecture,
    convergent_lines(parallel_through_point(esk1_0,X1),esk2_0),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

fof(c_0_29,plain,
    ! [X1,X2] :
      ( equal_points(X1,X2)
    <=> ~ distinct_points(X1,X2) ),
    inference(fof_simplification,[status(thm)],[ax1]) ).

fof(c_0_30,plain,
    ! [X1,X2] :
      ( incident_point_and_line(X1,X2)
    <=> ~ apart_point_and_line(X1,X2) ),
    inference(fof_simplification,[status(thm)],[a4]) ).

fof(c_0_31,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_32,negated_conjecture,
    ( convergent_lines(parallel_through_point(esk1_0,X1),X2)
    | distinct_lines(esk2_0,X2) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

fof(c_0_33,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_29])]) ).

fof(c_0_34,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_30])]) ).

fof(c_0_35,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_36,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_31]) ).

cnf(c_0_37,negated_conjecture,
    distinct_lines(esk2_0,esk1_0),
    inference(spm,[status(thm)],[c_0_25,c_0_32]) ).

cnf(c_0_38,negated_conjecture,
    ~ equal_points(esk3_0,intersection_point(esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

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

cnf(c_0_40,plain,
    ( ~ incident_point_and_line(X1,X2)
    | ~ apart_point_and_line(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_41,negated_conjecture,
    incident_point_and_line(esk3_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_42,negated_conjecture,
    incident_point_and_line(esk3_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_43,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_44,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_35])]) ).

cnf(c_0_45,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_36,c_0_37]) ).

cnf(c_0_46,negated_conjecture,
    distinct_points(esk3_0,intersection_point(esk1_0,esk2_0)),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_47,negated_conjecture,
    ~ apart_point_and_line(esk3_0,esk2_0),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_48,negated_conjecture,
    ~ apart_point_and_line(esk3_0,esk1_0),
    inference(spm,[status(thm)],[c_0_40,c_0_42]) ).

fof(c_0_49,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_43])]) ).

cnf(c_0_50,plain,
    ( ~ convergent_lines(X1,X2)
    | ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_51,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) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48]) ).

cnf(c_0_52,plain,
    ( ~ convergent_lines(X1,X2)
    | ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_53,negated_conjecture,
    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_50,c_0_51]),c_0_15])]) ).

cnf(c_0_54,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GEO172+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n002.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 21:02:35 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.78/0.88  % Version  : CSE_E---1.5
% 0.78/0.88  % Problem  : theBenchmark.p
% 0.78/0.88  % Proof found
% 0.78/0.88  % SZS status Theorem for theBenchmark.p
% 0.78/0.88  % SZS output start Proof
% See solution above
% 0.78/0.89  % Total time : 0.298000 s
% 0.78/0.89  % SZS output end Proof
% 0.78/0.89  % Total time : 0.302000 s
%------------------------------------------------------------------------------