TSTP Solution File: GEO196+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO196+2 : 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 : n032.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 22:46:57 EDT 2023

% Result   : Theorem 0.14s 0.51s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   78 (  22 unt;  10 typ;   0 def)
%            Number of atoms       :  179 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  168 (  57   ~;  87   |;  14   &)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   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    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  116 (   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 ).

tff(decl_31,type,
    esk4_0: $i ).

fof(con,conjecture,
    ! [X1,X2,X4,X5] :
      ( ( convergent_lines(X1,X2)
        & convergent_lines(X4,X5)
        & ~ apart_point_and_line(intersection_point(X1,X2),X4)
        & ~ apart_point_and_line(intersection_point(X1,X2),X5) )
     => ( ~ apart_point_and_line(intersection_point(X4,X5),X1)
        & ~ apart_point_and_line(intersection_point(X4,X5),X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(apart6,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( convergent_lines(X1,X3)
        | convergent_lines(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart6) ).

fof(apart3,axiom,
    ! [X1] : ~ convergent_lines(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+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/GEO008+0.ax',apart5) ).

fof(ceq3,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => distinct_lines(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).

fof(apart2,axiom,
    ! [X1] : ~ distinct_lines(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart2) ).

fof(apart1,axiom,
    ! [X1] : ~ distinct_points(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).

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/GEO008+0.ax',cu1) ).

fof(ceq1,axiom,
    ! [X1,X2,X3] :
      ( apart_point_and_line(X1,X2)
     => ( distinct_points(X1,X3)
        | apart_point_and_line(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq1) ).

fof(con2,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( ( apart_point_and_line(X3,X1)
          | apart_point_and_line(X3,X2) )
       => distinct_points(X3,intersection_point(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con2) ).

fof(apart4,axiom,
    ! [X1,X2,X3] :
      ( distinct_points(X1,X2)
     => ( distinct_points(X1,X3)
        | distinct_points(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart4) ).

fof(c_0_11,negated_conjecture,
    ~ ! [X1,X2,X4,X5] :
        ( ( convergent_lines(X1,X2)
          & convergent_lines(X4,X5)
          & ~ apart_point_and_line(intersection_point(X1,X2),X4)
          & ~ apart_point_and_line(intersection_point(X1,X2),X5) )
       => ( ~ apart_point_and_line(intersection_point(X4,X5),X1)
          & ~ apart_point_and_line(intersection_point(X4,X5),X2) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).

fof(c_0_12,plain,
    ! [X15,X16,X17] :
      ( ~ convergent_lines(X15,X16)
      | convergent_lines(X15,X17)
      | convergent_lines(X16,X17) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart6])]) ).

fof(c_0_13,negated_conjecture,
    ( convergent_lines(esk1_0,esk2_0)
    & convergent_lines(esk3_0,esk4_0)
    & ~ apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
    & ~ apart_point_and_line(intersection_point(esk1_0,esk2_0),esk4_0)
    & ( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk1_0)
      | apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_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(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_17,plain,
    ! [X8] : ~ convergent_lines(X8,X8),
    inference(variable_rename,[status(thm)],[c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    ( convergent_lines(esk3_0,X1)
    | convergent_lines(esk4_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(esk3_0,X1)
    | convergent_lines(esk4_0,X2)
    | convergent_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    ( convergent_lines(X1,esk4_0)
    | convergent_lines(esk3_0,X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

fof(c_0_22,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])]) ).

fof(c_0_23,plain,
    ! [X34,X35] :
      ( ~ convergent_lines(X34,X35)
      | distinct_lines(X34,X35) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).

cnf(c_0_24,negated_conjecture,
    ( convergent_lines(X1,esk4_0)
    | convergent_lines(esk3_0,X2)
    | convergent_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_21]) ).

fof(c_0_25,plain,
    ! [X1] : ~ distinct_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[apart2]) ).

cnf(c_0_26,plain,
    ( distinct_lines(X1,X3)
    | distinct_lines(X2,X3)
    | ~ distinct_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

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

cnf(c_0_28,negated_conjecture,
    ( convergent_lines(X1,esk3_0)
    | convergent_lines(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_19,c_0_24]) ).

fof(c_0_29,plain,
    ! [X7] : ~ distinct_lines(X7,X7),
    inference(variable_rename,[status(thm)],[c_0_25]) ).

cnf(c_0_30,plain,
    ( distinct_lines(X1,X2)
    | distinct_lines(X3,X2)
    | ~ convergent_lines(X1,X3) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    convergent_lines(esk4_0,esk3_0),
    inference(spm,[status(thm)],[c_0_19,c_0_28]) ).

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

fof(c_0_33,plain,
    ! [X24,X25,X26,X27] :
      ( ~ distinct_points(X24,X25)
      | ~ distinct_lines(X26,X27)
      | apart_point_and_line(X24,X26)
      | apart_point_and_line(X24,X27)
      | apart_point_and_line(X25,X26)
      | apart_point_and_line(X25,X27) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).

cnf(c_0_34,plain,
    ~ distinct_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_35,negated_conjecture,
    ( distinct_lines(esk3_0,X1)
    | distinct_lines(esk4_0,X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

fof(c_0_36,plain,
    ! [X28,X29,X30] :
      ( ~ apart_point_and_line(X28,X29)
      | distinct_points(X28,X30)
      | apart_point_and_line(X30,X29) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).

fof(c_0_37,plain,
    ! [X6] : ~ distinct_points(X6,X6),
    inference(variable_rename,[status(thm)],[c_0_32]) ).

fof(c_0_38,plain,
    ! [X21,X22,X23] :
      ( ( ~ apart_point_and_line(X23,X21)
        | distinct_points(X23,intersection_point(X21,X22))
        | ~ convergent_lines(X21,X22) )
      & ( ~ apart_point_and_line(X23,X22)
        | distinct_points(X23,intersection_point(X21,X22))
        | ~ convergent_lines(X21,X22) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con2])])]) ).

cnf(c_0_39,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_33]) ).

cnf(c_0_40,negated_conjecture,
    distinct_lines(esk3_0,esk4_0),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_41,plain,
    ( distinct_points(X1,X3)
    | apart_point_and_line(X3,X2)
    | ~ apart_point_and_line(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_42,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk1_0)
    | apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_43,plain,
    ~ distinct_points(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_44,plain,
    ( distinct_points(X1,intersection_point(X3,X2))
    | ~ apart_point_and_line(X1,X2)
    | ~ convergent_lines(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_45,negated_conjecture,
    ( apart_point_and_line(X1,esk3_0)
    | apart_point_and_line(X1,esk4_0)
    | apart_point_and_line(X2,esk3_0)
    | apart_point_and_line(X2,esk4_0)
    | ~ distinct_points(X1,X2) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_46,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0)
    | apart_point_and_line(X1,esk1_0)
    | distinct_points(intersection_point(esk3_0,esk4_0),X1) ),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_47,plain,
    ( distinct_points(X1,intersection_point(X2,X3))
    | ~ apart_point_and_line(X1,X2)
    | ~ convergent_lines(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_48,plain,
    ( ~ apart_point_and_line(intersection_point(X1,X2),X2)
    | ~ convergent_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_49,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0)
    | apart_point_and_line(intersection_point(esk3_0,esk4_0),esk4_0)
    | apart_point_and_line(intersection_point(esk3_0,esk4_0),esk3_0)
    | apart_point_and_line(X1,esk1_0)
    | apart_point_and_line(X1,esk4_0)
    | apart_point_and_line(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_50,plain,
    ( ~ apart_point_and_line(intersection_point(X1,X2),X1)
    | ~ convergent_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_43,c_0_47]) ).

cnf(c_0_51,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk3_0)
    | apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0)
    | apart_point_and_line(X1,esk3_0)
    | apart_point_and_line(X1,esk4_0)
    | apart_point_and_line(X1,esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_16])]) ).

fof(c_0_52,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])]) ).

cnf(c_0_53,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0)
    | apart_point_and_line(X1,esk1_0)
    | apart_point_and_line(X1,esk4_0)
    | apart_point_and_line(X1,esk3_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_16])]) ).

cnf(c_0_54,plain,
    ( distinct_points(X1,X3)
    | distinct_points(X2,X3)
    | ~ distinct_points(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_55,negated_conjecture,
    ~ apart_point_and_line(intersection_point(esk1_0,esk2_0),esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_56,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0)
    | apart_point_and_line(intersection_point(esk1_0,X1),esk3_0)
    | apart_point_and_line(intersection_point(esk1_0,X1),esk4_0)
    | ~ convergent_lines(esk1_0,X1) ),
    inference(spm,[status(thm)],[c_0_50,c_0_53]) ).

cnf(c_0_57,negated_conjecture,
    convergent_lines(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_58,negated_conjecture,
    ~ apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_59,plain,
    ( distinct_points(intersection_point(X1,X2),X3)
    | distinct_points(X4,X3)
    | ~ apart_point_and_line(X4,X2)
    | ~ convergent_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_54,c_0_44]) ).

cnf(c_0_60,negated_conjecture,
    apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]),c_0_58]) ).

cnf(c_0_61,negated_conjecture,
    ( distinct_points(intersection_point(esk3_0,esk4_0),X1)
    | distinct_points(intersection_point(X2,esk2_0),X1)
    | ~ convergent_lines(X2,esk2_0) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_62,negated_conjecture,
    ( convergent_lines(esk1_0,X1)
    | convergent_lines(esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_57]) ).

cnf(c_0_63,negated_conjecture,
    ( distinct_points(intersection_point(esk1_0,esk2_0),X1)
    | distinct_points(intersection_point(esk3_0,esk4_0),X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_19]) ).

cnf(c_0_64,negated_conjecture,
    distinct_points(intersection_point(esk3_0,esk4_0),intersection_point(esk1_0,esk2_0)),
    inference(spm,[status(thm)],[c_0_43,c_0_63]) ).

cnf(c_0_65,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk4_0)
    | apart_point_and_line(intersection_point(esk3_0,esk4_0),esk3_0) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_64]),c_0_58]),c_0_55]) ).

cnf(c_0_66,negated_conjecture,
    apart_point_and_line(intersection_point(esk3_0,esk4_0),esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_65]),c_0_16])]) ).

cnf(c_0_67,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_66]),c_0_16])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : GEO196+2 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.10  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit   : 300
% 0.10/0.29  % WCLimit    : 300
% 0.10/0.29  % DateTime   : Tue Aug 29 21:26:31 EDT 2023
% 0.10/0.29  % CPUTime  : 
% 0.14/0.48  start to proof: theBenchmark
% 0.14/0.51  % Version  : CSE_E---1.5
% 0.14/0.51  % Problem  : theBenchmark.p
% 0.14/0.51  % Proof found
% 0.14/0.51  % SZS status Theorem for theBenchmark.p
% 0.14/0.51  % SZS output start Proof
% See solution above
% 0.14/0.52  % Total time : 0.025000 s
% 0.14/0.52  % SZS output end Proof
% 0.14/0.52  % Total time : 0.028000 s
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