TSTP Solution File: GEO076-4 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : GEO076-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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 : Fri May 19 11:09:14 EDT 2023

% Result   : Unsatisfiable 3.96s 1.89s
% Output   : Refutation 4.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   49
% Syntax   : Number of formulae    :   83 (   5 unt;  16 typ;   0 def)
%            Number of atoms       :  355 (  86 equ;   0 cnn)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  996 ( 208   ~; 288   |;   0   &; 500   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  16 usr;   3 con; 0-3 aty)
%            Number of variables   :  142 (   0   ^; 142   !;   0   ?; 142   :)

% Comments : 
%------------------------------------------------------------------------------
thf(line_type,type,
    line: $i > $o ).

thf(on_type,type,
    on: $i > $i > $o ).

thf(a_point_type,type,
    a_point: $i ).

thf(plane_type,type,
    plane: $i > $o ).

thf(point_type,type,
    point: $i > $o ).

thf(point_not_on_plane_type,type,
    point_not_on_plane: $i > $i ).

thf(point_on_plane_type,type,
    point_on_plane: $i > $i ).

thf(plane_for_points_type,type,
    plane_for_points: $i > $i > $i > $i ).

thf(collinear_type,type,
    collinear: $i > $i > $i > $o ).

thf(line_through_3_points_type,type,
    line_through_3_points: $i > $i > $i > $i ).

thf(line_from_to_type,type,
    line_from_to: $i > $i > $i ).

thf(common_point_on_planes_type,type,
    common_point_on_planes: $i > $i > $i > $i ).

thf(point_1_on_line_type,type,
    point_1_on_line: $i > $i ).

thf(point_not_on_line_type,type,
    point_not_on_line: $i > $i ).

thf(point_2_on_line_type,type,
    point_2_on_line: $i > $i ).

thf(at_least_one_line_type,type,
    at_least_one_line: $i ).

thf(28,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( on @ A @ B )
      | ( A = C )
      | ~ ( on @ C @ B )
      | ( B = D )
      | ~ ( on @ A @ D )
      | ~ ( on @ C @ D )
      | ~ ( point @ A )
      | ~ ( point @ C )
      | ~ ( line @ B )
      | ~ ( line @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G1D) ).

thf(101,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( on @ A @ B )
      | ( A = C )
      | ~ ( on @ C @ B )
      | ( B = D )
      | ~ ( on @ A @ D )
      | ~ ( on @ C @ D )
      | ~ ( point @ A )
      | ~ ( point @ C )
      | ~ ( line @ B )
      | ~ ( line @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(33,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( plane @ A )
      | ~ ( plane @ B )
      | ( A = B )
      | ~ ( on @ C @ A )
      | ~ ( on @ C @ B )
      | ~ ( point @ C )
      | ( on @ ( common_point_on_planes @ A @ B @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G9B) ).

thf(115,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( plane @ A )
      | ~ ( plane @ B )
      | ( A = B )
      | ~ ( on @ C @ A )
      | ~ ( on @ C @ B )
      | ~ ( point @ C )
      | ( on @ ( common_point_on_planes @ A @ B @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( plane @ A )
      | ~ ( plane @ B )
      | ( A = B )
      | ~ ( on @ C @ A )
      | ~ ( on @ C @ B )
      | ~ ( point @ C )
      | ( on @ ( common_point_on_planes @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G9A) ).

thf(84,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( plane @ A )
      | ~ ( plane @ B )
      | ( A = B )
      | ~ ( on @ C @ A )
      | ~ ( on @ C @ B )
      | ~ ( point @ C )
      | ( on @ ( common_point_on_planes @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ~ ( plane @ A )
      | ( point @ ( point_on_plane @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G5B) ).

thf(38,plain,
    ! [A: $i] :
      ( ~ ( plane @ A )
      | ( point @ ( point_on_plane @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( point @ ( point_2_on_line @ A ) )
      | ~ ( line @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G2D) ).

thf(80,plain,
    ! [A: $i] :
      ( ( point @ ( point_2_on_line @ A ) )
      | ~ ( line @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(12,axiom,
    point @ a_point,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',there_is_a_point) ).

thf(63,plain,
    point @ a_point,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( on @ A @ ( plane_for_points @ B @ C @ A ) )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ~ ( point @ A )
      | ( collinear @ B @ C @ A )
      | ( B = C )
      | ( B = A )
      | ( C = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G7C) ).

thf(43,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( on @ A @ ( plane_for_points @ B @ C @ A ) )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ~ ( point @ A )
      | ( collinear @ B @ C @ A )
      | ( B = C )
      | ( B = A )
      | ( C = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(2,axiom,
    ! [A: $i] :
      ( ~ ( plane @ A )
      | ( point @ ( point_not_on_plane @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G6B) ).

thf(36,plain,
    ! [A: $i] :
      ( ~ ( plane @ A )
      | ( point @ ( point_not_on_plane @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C )
      | ( line @ ( line_through_3_points @ A @ B @ C ) )
      | ~ ( collinear @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G10D) ).

thf(107,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C )
      | ( line @ ( line_through_3_points @ A @ B @ C ) )
      | ~ ( collinear @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(15,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( collinear @ A @ B @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C )
      | ~ ( on @ A @ D )
      | ~ ( on @ B @ D )
      | ~ ( on @ C @ D )
      | ~ ( plane @ D )
      | ~ ( on @ A @ E )
      | ~ ( on @ B @ E )
      | ~ ( on @ C @ E )
      | ~ ( plane @ E )
      | ( D = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G7E) ).

thf(68,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( collinear @ A @ B @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C )
      | ~ ( on @ A @ D )
      | ~ ( on @ B @ D )
      | ~ ( on @ C @ D )
      | ~ ( plane @ D )
      | ~ ( on @ A @ E )
      | ~ ( on @ B @ E )
      | ~ ( on @ C @ E )
      | ~ ( plane @ E )
      | ( D = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(23,axiom,
    line @ at_least_one_line,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G4A) ).

thf(90,plain,
    line @ at_least_one_line,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ( on @ A @ ( line_from_to @ A @ B ) )
      | ( A = B )
      | ~ ( point @ A )
      | ~ ( point @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G1A) ).

thf(52,plain,
    ! [B: $i,A: $i] :
      ( ( on @ A @ ( line_from_to @ A @ B ) )
      | ( A = B )
      | ~ ( point @ A )
      | ~ ( point @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(31,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( collinear @ A @ B @ C )
      | ~ ( on @ A @ D )
      | ~ ( on @ B @ D )
      | ~ ( on @ C @ D )
      | ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C )
      | ~ ( line @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G10E) ).

thf(110,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( collinear @ A @ B @ C )
      | ~ ( on @ A @ D )
      | ~ ( on @ B @ D )
      | ~ ( on @ C @ D )
      | ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C )
      | ~ ( line @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C )
      | ( on @ C @ ( line_through_3_points @ A @ B @ C ) )
      | ~ ( collinear @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G10C) ).

thf(46,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C )
      | ( on @ C @ ( line_through_3_points @ A @ B @ C ) )
      | ~ ( collinear @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( on @ A @ B )
      | ~ ( on @ C @ B )
      | ~ ( on @ A @ D )
      | ~ ( on @ C @ D )
      | ~ ( plane @ D )
      | ~ ( point @ A )
      | ~ ( point @ C )
      | ~ ( line @ B )
      | ( A = C )
      | ( on @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G8A) ).

thf(93,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( on @ A @ B )
      | ~ ( on @ C @ B )
      | ~ ( on @ A @ D )
      | ~ ( on @ C @ D )
      | ~ ( plane @ D )
      | ~ ( point @ A )
      | ~ ( point @ C )
      | ~ ( line @ B )
      | ( A = C )
      | ( on @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ~ ( plane @ A )
      | ~ ( on @ ( point_not_on_plane @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G6A) ).

thf(61,plain,
    ! [A: $i] :
      ( ~ ( plane @ A )
      | ~ ( on @ ( point_not_on_plane @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(17,axiom,
    ! [B: $i,A: $i] :
      ( ( line @ ( line_from_to @ A @ B ) )
      | ( A = B )
      | ~ ( point @ A )
      | ~ ( point @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G1C) ).

thf(74,plain,
    ! [B: $i,A: $i] :
      ( ( line @ ( line_from_to @ A @ B ) )
      | ( A = B )
      | ~ ( point @ A )
      | ~ ( point @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( on @ A @ ( plane_for_points @ B @ A @ C ) )
      | ~ ( point @ B )
      | ~ ( point @ A )
      | ~ ( point @ C )
      | ( collinear @ B @ A @ C )
      | ( B = A )
      | ( B = C )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G7B) ).

thf(77,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( on @ A @ ( plane_for_points @ B @ A @ C ) )
      | ~ ( point @ B )
      | ~ ( point @ A )
      | ~ ( point @ C )
      | ( collinear @ B @ A @ C )
      | ( B = A )
      | ( B = C )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( point @ ( point_not_on_line @ A ) )
      | ~ ( line @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G3B) ).

thf(96,plain,
    ! [A: $i] :
      ( ( point @ ( point_not_on_line @ A ) )
      | ~ ( line @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( ~ ( line @ A )
      | ( on @ a_point @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_point_is_not_on_every_line) ).

thf(34,plain,
    ! [A: $i] :
      ( ~ ( line @ A )
      | ( on @ a_point @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( point @ ( point_1_on_line @ A ) )
      | ~ ( line @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G2C) ).

thf(64,plain,
    ! [A: $i] :
      ( ( point @ ( point_1_on_line @ A ) )
      | ~ ( line @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( ( point_1_on_line @ A )
       != ( point_2_on_line @ A ) )
      | ~ ( line @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G2E) ).

thf(71,plain,
    ! [A: $i] :
      ( ( ( point_1_on_line @ A )
       != ( point_2_on_line @ A ) )
      | ~ ( line @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C )
      | ( on @ A @ ( line_through_3_points @ A @ B @ C ) )
      | ~ ( collinear @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G10A) ).

thf(49,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C )
      | ( on @ A @ ( line_through_3_points @ A @ B @ C ) )
      | ~ ( collinear @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ( on @ ( point_1_on_line @ A ) @ A )
      | ~ ( line @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G2A) ).

thf(113,plain,
    ! [A: $i] :
      ( ( on @ ( point_1_on_line @ A ) @ A )
      | ~ ( line @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(27,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( plane @ A )
      | ~ ( plane @ B )
      | ( A = B )
      | ~ ( on @ C @ A )
      | ~ ( on @ C @ B )
      | ~ ( point @ C )
      | ( C
       != ( common_point_on_planes @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G9D) ).

thf(98,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( plane @ A )
      | ~ ( plane @ B )
      | ( A = B )
      | ~ ( on @ C @ A )
      | ~ ( on @ C @ B )
      | ~ ( point @ C )
      | ( C
       != ( common_point_on_planes @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( on @ ( point_2_on_line @ A ) @ A )
      | ~ ( line @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G2B) ).

thf(91,plain,
    ! [A: $i] :
      ( ( on @ ( point_2_on_line @ A ) @ A )
      | ~ ( line @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ~ ( on @ ( point_not_on_line @ A ) @ A )
      | ~ ( line @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G3A) ).

thf(66,plain,
    ! [A: $i] :
      ( ~ ( on @ ( point_not_on_line @ A ) @ A )
      | ~ ( line @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(22,axiom,
    ! [B: $i,A: $i] :
      ( ( on @ A @ ( line_from_to @ B @ A ) )
      | ( B = A )
      | ~ ( point @ B )
      | ~ ( point @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G1B) ).

thf(87,plain,
    ! [B: $i,A: $i] :
      ( ( on @ A @ ( line_from_to @ B @ A ) )
      | ( B = A )
      | ~ ( point @ B )
      | ~ ( point @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( on @ A @ ( plane_for_points @ A @ B @ C ) )
      | ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( collinear @ A @ B @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G7A) ).

thf(104,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( on @ A @ ( plane_for_points @ A @ B @ C ) )
      | ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( collinear @ A @ B @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( plane @ ( plane_for_points @ A @ B @ C ) )
      | ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( collinear @ A @ B @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G7D) ).

thf(40,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( plane @ ( plane_for_points @ A @ B @ C ) )
      | ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( collinear @ A @ B @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( plane @ A )
      | ~ ( plane @ B )
      | ( A = B )
      | ~ ( on @ C @ A )
      | ~ ( on @ C @ B )
      | ~ ( point @ C )
      | ( point @ ( common_point_on_planes @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G9C) ).

thf(55,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( plane @ A )
      | ~ ( plane @ B )
      | ( A = B )
      | ~ ( on @ C @ A )
      | ~ ( on @ C @ B )
      | ~ ( point @ C )
      | ( point @ ( common_point_on_planes @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C )
      | ( on @ B @ ( line_through_3_points @ A @ B @ C ) )
      | ~ ( collinear @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G10B) ).

thf(58,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( point @ A )
      | ~ ( point @ B )
      | ~ ( point @ C )
      | ( A = B )
      | ( A = C )
      | ( B = C )
      | ( on @ B @ ( line_through_3_points @ A @ B @ C ) )
      | ~ ( collinear @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ~ ( plane @ A )
      | ( on @ ( point_on_plane @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_G5A) ).

thf(82,plain,
    ! [A: $i] :
      ( ~ ( plane @ A )
      | ( on @ ( point_on_plane @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(120,plain,
    $false,
    inference(e,[status(thm)],[101,115,84,38,80,63,43,36,107,68,90,52,110,46,93,61,74,77,96,34,64,71,49,113,98,91,66,87,104,40,55,58,82]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GEO076-4 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n010.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 : Fri May 19 04:15:27 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.91/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.21/0.96  % [INFO] 	 Parsing done (123ms). 
% 1.21/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.74/1.16  % [INFO] 	 cvc4 registered as external prover. 
% 1.74/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.74/1.22  % [INFO] 	 Found a conjecture and 32 axioms. Running axiom selection ... 
% 1.92/1.27  % [INFO] 	 Axiom selection finished. Selected 32 axioms (removed 0 axioms). 
% 2.06/1.31  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.06/1.32  % [INFO] 	 Type checking passed. 
% 2.06/1.32  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 3.96/1.88  % External prover 'e' found a proof!
% 3.96/1.88  % [INFO] 	 Killing All external provers ... 
% 3.96/1.89  % Time passed: 1373ms (effective reasoning time: 916ms)
% 3.96/1.89  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.96/1.89  % Axioms used in derivation (32): axiom_G1D, axiom_G2E, axiom_G2A, axiom_G8A, axiom_G7D, axiom_G10A, axiom_G2C, axiom_G7E, axiom_G10D, axiom_G7B, axiom_G1C, axiom_G6A, axiom_G10E, axiom_G2D, axiom_G1A, axiom_G7C, axiom_G6B, there_is_a_point, axiom_G2B, axiom_G3B, axiom_G10C, axiom_G9B, axiom_G5A, axiom_G9C, axiom_G5B, axiom_G1B, axiom_G3A, axiom_G7A, axiom_G10B, axiom_G4A, axiom_G9D, axiom_G9A
% 3.96/1.89  % No. of inferences in proof: 67
% 3.96/1.89  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1373 ms resp. 916 ms w/o parsing
% 4.21/1.94  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.21/1.94  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------