%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO076-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:12:16 AM UTC 2026
% Result : Unsatisfiable 5.20s 22.88s
% Output : Refutation 5.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 33
% Syntax : Number of formulae : 67 ( 5 unt; 0 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 : 0 ( 0 >; 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_decl,type,
line: $i > $o ).
thf(on_decl,type,
on: $i > $i > $o ).
thf(a_point_decl,type,
a_point: $i ).
thf(plane_decl,type,
plane: $i > $o ).
thf(point_decl,type,
point: $i > $o ).
thf(point_not_on_plane_decl,type,
point_not_on_plane: $i > $i ).
thf(point_on_plane_decl,type,
point_on_plane: $i > $i ).
thf(plane_for_points_decl,type,
plane_for_points: $i > $i > $i > $i ).
thf(collinear_decl,type,
collinear: $i > $i > $i > $o ).
thf(line_through_3_points_decl,type,
line_through_3_points: $i > $i > $i > $i ).
thf(line_from_to_decl,type,
line_from_to: $i > $i > $i ).
thf(common_point_on_planes_decl,type,
common_point_on_planes: $i > $i > $i > $i ).
thf(point_1_on_line_decl,type,
point_1_on_line: $i > $i ).
thf(point_not_on_line_decl,type,
point_not_on_line: $i > $i ).
thf(point_2_on_line_decl,type,
point_2_on_line: $i > $i ).
thf(at_least_one_line_decl,type,
at_least_one_line: $i ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ line )
| ~ ( B @ line )
| ~ ( C @ point )
| ~ ( A @ point )
| ~ ( D @ ( C @ on ) )
| ~ ( D @ ( A @ on ) )
| ( B = D )
| ~ ( B @ ( C @ on ) )
| ( A = C )
| ~ ( B @ ( A @ on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G1D) ).
thf(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ line )
| ~ ( B @ line )
| ~ ( C @ point )
| ~ ( A @ point )
| ~ ( D @ ( C @ on ) )
| ~ ( D @ ( A @ on ) )
| ( B = D )
| ~ ( B @ ( C @ on ) )
| ( A = C )
| ~ ( B @ ( A @ on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ common_point_on_planes ) ) @ on ) )
| ~ ( C @ point )
| ~ ( B @ ( C @ on ) )
| ~ ( A @ ( C @ on ) )
| ( A = B )
| ~ ( B @ plane )
| ~ ( A @ plane ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G9B) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ common_point_on_planes ) ) @ on ) )
| ~ ( C @ point )
| ~ ( B @ ( C @ on ) )
| ~ ( A @ ( C @ on ) )
| ( A = B )
| ~ ( B @ plane )
| ~ ( A @ plane ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ common_point_on_planes ) ) @ on ) )
| ~ ( C @ point )
| ~ ( B @ ( C @ on ) )
| ~ ( A @ ( C @ on ) )
| ( A = B )
| ~ ( B @ plane )
| ~ ( A @ plane ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G9A) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ common_point_on_planes ) ) @ on ) )
| ~ ( C @ point )
| ~ ( B @ ( C @ on ) )
| ~ ( A @ ( C @ on ) )
| ( A = B )
| ~ ( B @ plane )
| ~ ( A @ plane ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ point_on_plane @ point )
| ~ ( A @ plane ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G5B) ).
thf(38,plain,
! [A: $i] :
( ( A @ point_on_plane @ point )
| ~ ( A @ plane ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,axiom,
! [A: $i] :
( ~ ( A @ line )
| ( A @ point_2_on_line @ point ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G2D) ).
thf(80,plain,
! [A: $i] :
( ~ ( A @ line )
| ( A @ point_2_on_line @ point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
a_point @ point,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',there_is_a_point) ).
thf(63,plain,
a_point @ point,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( B = A )
| ( B = C )
| ( A @ ( C @ ( B @ collinear ) ) )
| ~ ( A @ point )
| ~ ( C @ point )
| ~ ( B @ point )
| ( A @ ( C @ ( B @ plane_for_points ) ) @ ( A @ on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G7C) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( B = A )
| ( B = C )
| ( A @ ( C @ ( B @ collinear ) ) )
| ~ ( A @ point )
| ~ ( C @ point )
| ~ ( B @ point )
| ( A @ ( C @ ( B @ plane_for_points ) ) @ ( A @ on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ point_not_on_plane @ point )
| ~ ( A @ plane ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G6B) ).
thf(36,plain,
! [A: $i] :
( ( A @ point_not_on_plane @ point )
| ~ ( A @ plane ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ collinear ) ) )
| ( C @ ( B @ ( A @ line_through_3_points ) ) @ line )
| ( B = C )
| ( A = C )
| ( A = B )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G10D) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ collinear ) ) )
| ( C @ ( B @ ( A @ line_through_3_points ) ) @ line )
| ( B = C )
| ( A = C )
| ( A = B )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( E @ plane )
| ~ ( E @ ( C @ on ) )
| ~ ( E @ ( B @ on ) )
| ~ ( E @ ( A @ on ) )
| ~ ( D @ plane )
| ~ ( D @ ( C @ on ) )
| ~ ( D @ ( B @ on ) )
| ~ ( D @ ( A @ on ) )
| ( B = C )
| ( A = C )
| ( A = B )
| ( C @ ( B @ ( A @ collinear ) ) )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G7E) ).
thf(68,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( E @ plane )
| ~ ( E @ ( C @ on ) )
| ~ ( E @ ( B @ on ) )
| ~ ( E @ ( A @ on ) )
| ~ ( D @ plane )
| ~ ( D @ ( C @ on ) )
| ~ ( D @ ( B @ on ) )
| ~ ( D @ ( A @ on ) )
| ( B = C )
| ( A = C )
| ( A = B )
| ( C @ ( B @ ( A @ collinear ) ) )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(23,axiom,
at_least_one_line @ line,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G4A) ).
thf(90,plain,
at_least_one_line @ line,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( B @ point )
| ~ ( A @ point )
| ( A = B )
| ( B @ ( A @ line_from_to ) @ ( A @ on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G1A) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ ( B @ point )
| ~ ( A @ point )
| ( A = B )
| ( B @ ( A @ line_from_to ) @ ( A @ on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ line )
| ( B = C )
| ( A = C )
| ( A = B )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point )
| ~ ( D @ ( C @ on ) )
| ~ ( D @ ( B @ on ) )
| ~ ( D @ ( A @ on ) )
| ( C @ ( B @ ( A @ collinear ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G10E) ).
thf(110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ line )
| ( B = C )
| ( A = C )
| ( A = B )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point )
| ~ ( D @ ( C @ on ) )
| ~ ( D @ ( B @ on ) )
| ~ ( D @ ( A @ on ) )
| ( C @ ( B @ ( A @ collinear ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ collinear ) ) )
| ( C @ ( B @ ( A @ line_through_3_points ) ) @ ( C @ on ) )
| ( B = C )
| ( A = C )
| ( A = B )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G10C) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ collinear ) ) )
| ( C @ ( B @ ( A @ line_through_3_points ) ) @ ( C @ on ) )
| ( B = C )
| ( A = C )
| ( A = B )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ on ) )
| ( A = C )
| ~ ( B @ line )
| ~ ( C @ point )
| ~ ( A @ point )
| ~ ( D @ plane )
| ~ ( D @ ( C @ on ) )
| ~ ( D @ ( A @ on ) )
| ~ ( B @ ( C @ on ) )
| ~ ( B @ ( A @ on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G8A) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ on ) )
| ( A = C )
| ~ ( B @ line )
| ~ ( C @ point )
| ~ ( A @ point )
| ~ ( D @ plane )
| ~ ( D @ ( C @ on ) )
| ~ ( D @ ( A @ on ) )
| ~ ( B @ ( C @ on ) )
| ~ ( B @ ( A @ on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( A @ ( A @ point_not_on_plane @ on ) )
| ~ ( A @ plane ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G6A) ).
thf(61,plain,
! [A: $i] :
( ~ ( A @ ( A @ point_not_on_plane @ on ) )
| ~ ( A @ plane ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( B @ point )
| ~ ( A @ point )
| ( A = B )
| ( B @ ( A @ line_from_to ) @ line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G1C) ).
thf(74,plain,
! [B: $i,A: $i] :
( ~ ( B @ point )
| ~ ( A @ point )
| ( A = B )
| ( B @ ( A @ line_from_to ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ( B = A )
| ( C @ ( A @ ( B @ collinear ) ) )
| ~ ( C @ point )
| ~ ( A @ point )
| ~ ( B @ point )
| ( C @ ( A @ ( B @ plane_for_points ) ) @ ( A @ on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G7B) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( B = C )
| ( B = A )
| ( C @ ( A @ ( B @ collinear ) ) )
| ~ ( C @ point )
| ~ ( A @ point )
| ~ ( B @ point )
| ( C @ ( A @ ( B @ plane_for_points ) ) @ ( A @ on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( A @ line )
| ( A @ point_not_on_line @ point ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G3B) ).
thf(96,plain,
! [A: $i] :
( ~ ( A @ line )
| ( A @ point_not_on_line @ point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ( A @ ( a_point @ on ) )
| ~ ( A @ line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_point_is_not_on_every_line) ).
thf(34,plain,
! [A: $i] :
( ( A @ ( a_point @ on ) )
| ~ ( A @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( A @ line )
| ( A @ point_1_on_line @ point ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G2C) ).
thf(64,plain,
! [A: $i] :
( ~ ( A @ line )
| ( A @ point_1_on_line @ point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(16,axiom,
! [A: $i] :
( ~ ( A @ line )
| ( ( A @ point_1_on_line )
!= ( A @ point_2_on_line ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G2E) ).
thf(71,plain,
! [A: $i] :
( ~ ( A @ line )
| ( ( A @ point_1_on_line )
!= ( A @ point_2_on_line ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ collinear ) ) )
| ( C @ ( B @ ( A @ line_through_3_points ) ) @ ( A @ on ) )
| ( B = C )
| ( A = C )
| ( A = B )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G10A) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ collinear ) ) )
| ( C @ ( B @ ( A @ line_through_3_points ) ) @ ( A @ on ) )
| ( B = C )
| ( A = C )
| ( A = B )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( A @ line )
| ( A @ ( A @ point_1_on_line @ on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G2A) ).
thf(113,plain,
! [A: $i] :
( ~ ( A @ line )
| ( A @ ( A @ point_1_on_line @ on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( C @ ( B @ ( A @ common_point_on_planes ) ) ) )
| ~ ( C @ point )
| ~ ( B @ ( C @ on ) )
| ~ ( A @ ( C @ on ) )
| ( A = B )
| ~ ( B @ plane )
| ~ ( A @ plane ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G9D) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( C @ ( B @ ( A @ common_point_on_planes ) ) ) )
| ~ ( C @ point )
| ~ ( B @ ( C @ on ) )
| ~ ( A @ ( C @ on ) )
| ( A = B )
| ~ ( B @ plane )
| ~ ( A @ plane ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( A @ line )
| ( A @ ( A @ point_2_on_line @ on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G2B) ).
thf(91,plain,
! [A: $i] :
( ~ ( A @ line )
| ( A @ ( A @ point_2_on_line @ on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( A @ line )
| ~ ( A @ ( A @ point_not_on_line @ on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G3A) ).
thf(66,plain,
! [A: $i] :
( ~ ( A @ line )
| ~ ( A @ ( A @ point_not_on_line @ on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( A @ point )
| ~ ( B @ point )
| ( B = A )
| ( A @ ( B @ line_from_to ) @ ( A @ on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G1B) ).
thf(87,plain,
! [B: $i,A: $i] :
( ~ ( A @ point )
| ~ ( B @ point )
| ( B = A )
| ( A @ ( B @ line_from_to ) @ ( A @ on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A = C )
| ( A = B )
| ( C @ ( B @ ( A @ collinear ) ) )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point )
| ( C @ ( B @ ( A @ plane_for_points ) ) @ ( A @ on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G7A) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A = C )
| ( A = B )
| ( C @ ( B @ ( A @ collinear ) ) )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point )
| ( C @ ( B @ ( A @ plane_for_points ) ) @ ( A @ on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A = C )
| ( A = B )
| ( C @ ( B @ ( A @ collinear ) ) )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point )
| ( C @ ( B @ ( A @ plane_for_points ) ) @ plane ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G7D) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A = C )
| ( A = B )
| ( C @ ( B @ ( A @ collinear ) ) )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point )
| ( C @ ( B @ ( A @ plane_for_points ) ) @ plane ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ common_point_on_planes ) ) @ point )
| ~ ( C @ point )
| ~ ( B @ ( C @ on ) )
| ~ ( A @ ( C @ on ) )
| ( A = B )
| ~ ( B @ plane )
| ~ ( A @ plane ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G9C) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ common_point_on_planes ) ) @ point )
| ~ ( C @ point )
| ~ ( B @ ( C @ on ) )
| ~ ( A @ ( C @ on ) )
| ( A = B )
| ~ ( B @ plane )
| ~ ( A @ plane ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ collinear ) ) )
| ( C @ ( B @ ( A @ line_through_3_points ) ) @ ( B @ on ) )
| ( B = C )
| ( A = C )
| ( A = B )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G10B) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ collinear ) ) )
| ( C @ ( B @ ( A @ line_through_3_points ) ) @ ( B @ on ) )
| ( B = C )
| ( A = C )
| ( A = B )
| ~ ( C @ point )
| ~ ( B @ point )
| ~ ( A @ point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ( A @ point_on_plane @ on ) )
| ~ ( A @ plane ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_G5A) ).
thf(82,plain,
! [A: $i] :
( ( A @ ( A @ point_on_plane @ on ) )
| ~ ( A @ plane ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(129,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
% 0.00/0.05 % Problem : GEO076-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.18/20.52 % CPULimit : 300
% 0.18/20.52 % WCLimit : 300
% 0.18/20.52 % DateTime : Fri Sep 25 12:40:23 UTC 2026
% 0.18/20.52 % CPUTime :
% 0.18/20.52 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.16/21.10 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.68/21.32 % [INFO] Parsing done (222ms).
% 1.68/21.34 % [INFO] Running in sequential loop mode.
% 2.45/21.75 % [INFO] eprover registered as external prover.
% 2.45/21.76 % [INFO] Scanning for conjecture ...
% 2.70/21.86 % [INFO] Found a conjecture (or negated_conjecture) and 32 axioms. Running axiom selection ...
% 2.86/21.93 % [INFO] Axiom selection finished. Selected 32 axioms (removed 0 axioms).
% 2.86/22.00 % [INFO] Problem is propositional (TPTP CNF).
% 2.86/22.02 % [INFO] Type checking passed.
% 2.86/22.02 % [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 ...
% 5.20/22.87 % External prover 'e' found a proof!
% 5.20/22.87 % [INFO] Killing All external provers ...
% 5.20/22.87 % Time passed: 2206ms (effective reasoning time: 1526ms)
% 5.20/22.87 % 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
% 5.20/22.88 % No. of inferences in proof: 67
% 5.20/22.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2206 ms resp. 1526 ms w/o parsing
% 5.70/22.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.70/22.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------