%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO077-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.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 : Fri Sep 25 01:19:47 PM UTC 2026
% Result : Unsatisfiable 20.20s 3.81s
% Output : CNFRefutation 20.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 44
% Syntax : Number of formulae : 2475 ( 32 unt; 0 def)
% Number of atoms : 25471 (7977 equ)
% Maximal formula atoms : 25 ( 10 avg)
% Number of connectives : 38854 (15858 ~;22996 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 12 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 4270 ( 0 sgn4270 !; 0 ?;4189 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ point(X1)
| ~ point(X0)
| X0 = X1
| on(X0,line_from_to(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G1A) ).
fof(f2,axiom,
! [X0,X1] :
( ~ point(X0)
| ~ point(X1)
| X1 = X0
| on(X0,line_from_to(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G1B) ).
fof(f3,plain,
! [X0,X1] :
( ~ point(X0)
| ~ point(X1)
| X0 = X1
| on(X0,line_from_to(X1,X0)) ),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X0,X1] :
( ~ point(X1)
| ~ point(X0)
| X0 = X1
| line(line_from_to(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G1C) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( ~ line(X3)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X0,X3)
| X1 = X3
| ~ on(X2,X1)
| X0 = X2
| ~ on(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G1D) ).
fof(f6,axiom,
! [X0] :
( ~ line(X0)
| on(point_1_on_line(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G2A) ).
fof(f7,axiom,
! [X0] :
( ~ line(X0)
| on(point_2_on_line(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G2B) ).
fof(f8,axiom,
! [X0] :
( ~ line(X0)
| point(point_1_on_line(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G2C) ).
fof(f9,axiom,
! [X0] :
( ~ line(X0)
| point(point_2_on_line(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G2D) ).
fof(f10,axiom,
! [X0] :
( ~ line(X0)
| point_1_on_line(X0) != point_2_on_line(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G2E) ).
fof(f11,axiom,
! [X0] :
( ~ line(X0)
| ~ on(point_not_on_line(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G3A) ).
fof(f12,axiom,
! [X0] :
( ~ line(X0)
| point(point_not_on_line(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G3B) ).
fof(f13,axiom,
line(at_least_one_line),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G4A) ).
fof(f14,axiom,
! [X0] :
( on(point_on_plane(X0),X0)
| ~ plane(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G5A) ).
fof(f15,axiom,
! [X0] :
( point(point_on_plane(X0))
| ~ plane(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G5B) ).
fof(f16,axiom,
! [X0] :
( ~ on(point_not_on_plane(X0),X0)
| ~ plane(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G6A) ).
fof(f17,axiom,
! [X0] :
( point(point_not_on_plane(X0))
| ~ plane(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G6B) ).
fof(f18,axiom,
! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| X0 = X1
| collinear(X0,X1,X2)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| on(X0,plane_for_points(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G7A) ).
fof(f19,axiom,
! [X2,X0,X1] :
( X0 = X2
| X1 = X2
| X1 = X0
| collinear(X1,X0,X2)
| ~ point(X2)
| ~ point(X0)
| ~ point(X1)
| on(X0,plane_for_points(X1,X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G7B) ).
fof(f20,plain,
! [X2,X0,X1] :
( X0 = X2
| X1 = X2
| X0 = X1
| collinear(X1,X0,X2)
| ~ point(X2)
| ~ point(X0)
| ~ point(X1)
| on(X0,plane_for_points(X1,X0,X2)) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,axiom,
! [X2,X0,X1] :
( X2 = X0
| X1 = X0
| X1 = X2
| collinear(X1,X2,X0)
| ~ point(X0)
| ~ point(X2)
| ~ point(X1)
| on(X0,plane_for_points(X1,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G7C) ).
fof(f22,plain,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| X1 = X2
| collinear(X1,X2,X0)
| ~ point(X0)
| ~ point(X2)
| ~ point(X1)
| on(X0,plane_for_points(X1,X2,X0)) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,axiom,
! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| X0 = X1
| collinear(X0,X1,X2)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| plane(plane_for_points(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G7D) ).
fof(f24,axiom,
! [X2,X3,X0,X1,X4] :
( X3 = X4
| ~ plane(X4)
| ~ on(X2,X4)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ plane(X3)
| ~ on(X2,X3)
| ~ on(X1,X3)
| ~ on(X0,X3)
| X1 = X2
| X0 = X2
| X0 = X1
| collinear(X0,X1,X2)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G7E) ).
fof(f25,axiom,
! [X2,X3,X0,X1] :
( on(X1,X3)
| X0 = X2
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ plane(X3)
| ~ on(X2,X3)
| ~ on(X0,X3)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G8A) ).
fof(f26,axiom,
! [X2,X0,X1] :
( on(common_point_on_planes(X0,X1,X2),X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| X0 = X1
| ~ plane(X1)
| ~ plane(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G9A) ).
fof(f27,axiom,
! [X2,X0,X1] :
( on(common_point_on_planes(X0,X1,X2),X1)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| X0 = X1
| ~ plane(X1)
| ~ plane(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G9B) ).
fof(f28,axiom,
! [X2,X0,X1] :
( point(common_point_on_planes(X0,X1,X2))
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| X0 = X1
| ~ plane(X1)
| ~ plane(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G9C) ).
fof(f29,axiom,
! [X2,X0,X1] :
( X2 != common_point_on_planes(X0,X1,X2)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| X0 = X1
| ~ plane(X1)
| ~ plane(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G9D) ).
fof(f30,plain,
! [X2,X0,X1] :
( common_point_on_planes(X0,X1,X2) != X2
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| X0 = X1
| ~ plane(X1)
| ~ plane(X0) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,axiom,
! [X2,X0,X1] :
( ~ collinear(X0,X1,X2)
| on(X0,line_through_3_points(X0,X1,X2))
| X1 = X2
| X0 = X2
| X0 = X1
| ~ point(X2)
| ~ point(X1)
| ~ point(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G10A) ).
fof(f32,axiom,
! [X2,X0,X1] :
( ~ collinear(X0,X1,X2)
| on(X1,line_through_3_points(X0,X1,X2))
| X1 = X2
| X0 = X2
| X0 = X1
| ~ point(X2)
| ~ point(X1)
| ~ point(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G10B) ).
fof(f33,axiom,
! [X2,X0,X1] :
( ~ collinear(X0,X1,X2)
| on(X2,line_through_3_points(X0,X1,X2))
| X1 = X2
| X0 = X2
| X0 = X1
| ~ point(X2)
| ~ point(X1)
| ~ point(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G10C) ).
fof(f34,axiom,
! [X2,X0,X1] :
( ~ collinear(X0,X1,X2)
| line(line_through_3_points(X0,X1,X2))
| X1 = X2
| X0 = X2
| X0 = X1
| ~ point(X2)
| ~ point(X1)
| ~ point(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G10D) ).
fof(f35,axiom,
! [X2,X3,X0,X1] :
( ~ line(X3)
| X1 = X2
| X0 = X2
| X0 = X1
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X1,X3)
| ~ on(X0,X3)
| collinear(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G10E) ).
fof(f36,axiom,
point(point1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',point1) ).
fof(f37,axiom,
point(point2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',point2) ).
fof(f38,axiom,
point(point3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',point3) ).
fof(f39,axiom,
line(a_line),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',line) ).
fof(f40,axiom,
on(point1,a_line),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',point1_on_line) ).
fof(f41,axiom,
on(point2,a_line),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',point2_on_line) ).
fof(f42,axiom,
~ on(point3,a_line),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',point3_not_on_line) ).
fof(f43,axiom,
point1 != point2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',point1_not_point2) ).
fof(f44,axiom,
point1 != point3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',point1_not_point3) ).
fof(f45,axiom,
point2 != point3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',point2_not_point3) ).
fof(f46,negated_conjecture,
collinear(point1,point2,point3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_points_noncollinear) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( on(X1,line_from_to(X1,X0))
| ( X0 = X1 )
| ~ point(X1)
| ~ point(X0) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( on(X1,line_from_to(X0,X1))
| ( X0 = X1 )
| ~ point(X1)
| ~ point(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( line(line_from_to(X1,X0))
| ( X0 = X1 )
| ~ point(X1)
| ~ point(X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X0 = X3 )
| ~ line(X2)
| ~ line(X1)
| ~ point(X3)
| ~ point(X0)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X2)
| ~ on(X0,X1) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_95,plain,
! [X0: $i] :
( on(point_1_on_line(X0),X0)
| ~ line(X0) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_96,plain,
! [X0: $i] :
( on(point_2_on_line(X0),X0)
| ~ line(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_97,plain,
! [X0: $i] :
( point(point_1_on_line(X0))
| ~ line(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_98,plain,
! [X0: $i] :
( point(point_2_on_line(X0))
| ~ line(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_99,plain,
! [X0: $i] :
( ~ line(X0)
| ( point_1_on_line(X0) != point_2_on_line(X0) ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_100,plain,
! [X0: $i] :
( ~ line(X0)
| ~ on(point_not_on_line(X0),X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_101,plain,
! [X0: $i] :
( point(point_not_on_line(X0))
| ~ line(X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_102,plain,
line(at_least_one_line),
inference(cnf_transformation,[],[f13]) ).
tcf(c_103,plain,
! [X0: $i] :
( on(point_on_plane(X0),X0)
| ~ plane(X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_104,plain,
! [X0: $i] :
( point(point_on_plane(X0))
| ~ plane(X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_105,plain,
! [X0: $i] :
( ~ plane(X0)
| ~ on(point_not_on_plane(X0),X0) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_106,plain,
! [X0: $i] :
( point(point_not_on_plane(X0))
| ~ plane(X0) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,X0,X1)
| on(X2,plane_for_points(X2,X0,X1))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X2,X1)
| on(X2,plane_for_points(X0,X2,X1))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(X2,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,X0,X1)
| plane(plane_for_points(X2,X0,X1))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X0,X3)
| ( X3 = X4 )
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X3 )
| ~ plane(X2)
| ~ plane(X1)
| ~ point(X4)
| ~ point(X3)
| ~ point(X0)
| ~ on(X4,X2)
| ~ on(X4,X1)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X2)
| ~ on(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X1,X2)
| ( X0 = X3 )
| ~ plane(X2)
| ~ line(X1)
| ~ point(X3)
| ~ point(X0)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X2)
| ~ on(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(common_point_on_planes(X2,X1,X0),X2)
| ( X1 = X2 )
| ~ plane(X2)
| ~ plane(X1)
| ~ point(X0)
| ~ on(X0,X2)
| ~ on(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(common_point_on_planes(X2,X1,X0),X1)
| ( X1 = X2 )
| ~ plane(X2)
| ~ plane(X1)
| ~ point(X0)
| ~ on(X0,X2)
| ~ on(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( point(common_point_on_planes(X2,X1,X0))
| ( X1 = X2 )
| ~ plane(X2)
| ~ plane(X1)
| ~ point(X0)
| ~ on(X0,X2)
| ~ on(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ plane(X1)
| ~ plane(X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ( common_point_on_planes(X0,X1,X2) != X2 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X0,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X2,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,X2) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i] :
( line(line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,X0,X2)
| ( X2 = X3 )
| ( X0 = X3 )
| ( X0 = X2 )
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ on(X3,X1)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_122,plain,
point(point1),
inference(cnf_transformation,[],[f36]) ).
tcf(c_123,plain,
point(point2),
inference(cnf_transformation,[],[f37]) ).
tcf(c_124,plain,
point(point3),
inference(cnf_transformation,[],[f38]) ).
tcf(c_125,plain,
line(a_line),
inference(cnf_transformation,[],[f39]) ).
tcf(c_126,plain,
on(point1,a_line),
inference(cnf_transformation,[],[f40]) ).
tcf(c_127,plain,
on(point2,a_line),
inference(cnf_transformation,[],[f41]) ).
tcf(c_128,plain,
~ on(point3,a_line),
inference(cnf_transformation,[],[f42]) ).
tcf(c_129,plain,
point1 != point2,
inference(cnf_transformation,[],[f43]) ).
tcf(c_130,plain,
point1 != point3,
inference(cnf_transformation,[],[f44]) ).
tcf(c_131,plain,
point2 != point3,
inference(cnf_transformation,[],[f45]) ).
tcf(c_132,negated_conjecture,
collinear(point1,point2,point3),
inference(cnf_transformation,[],[f46]) ).
tcf(c_136,plain,
( point(point_2_on_line(point1))
| ~ line(point1) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_143,plain,
( ~ line(point1)
| ( point_1_on_line(point1) != point_2_on_line(point1) ) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_1799,negated_conjecture,
collinear(point1,point2,point3),
inference(demodulation,[status(thm)],[c_132]) ).
tcf(c_1800,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1802,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1808,plain,
point1 = point1,
inference(instantiation,[status(thm)],[c_1800]) ).
tcf(c_2910,plain,
! [X0: $i,X1: $i] :
( on(X1,a_line)
| ( X0 = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ line(X1)
| ~ point(X0)
| ~ on(point1,X1)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_126,c_112]) ).
tcf(c_2911,plain,
! [X0: $i,X1: $i] :
( on(X1,a_line)
| ( X0 = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ line(X1)
| ~ point(X0)
| ~ on(point2,X1)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_127,c_112]) ).
tcf(c_2912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_from_to(X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X0,X3)
| ~ plane(line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_92,c_112]) ).
tcf(c_2913,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,X0)
| ( point_1_on_line(X0) = X2 )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ point(point_1_on_line(X0))
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_1_on_line(X0),X1) ),
inference(superposition,[status(thm)],[c_95,c_112]) ).
tcf(c_2914,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,X0)
| ( point_2_on_line(X0) = X2 )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ point(point_2_on_line(X0))
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_2_on_line(X0),X1) ),
inference(superposition,[status(thm)],[c_96,c_112]) ).
tcf(c_2915,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,X0)
| ( point_on_plane(X0) = X2 )
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ point(point_on_plane(X0))
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_on_plane(X0),X1) ),
inference(superposition,[status(thm)],[c_103,c_112]) ).
tcf(c_2916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X1,X2,X3)
| on(X4,plane_for_points(X1,X2,X3))
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ~ line(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X4)
| ~ on(X0,X4)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_109,c_112]) ).
tcf(c_2917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on(X4,line_through_3_points(X1,X2,X3))
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X1 )
| ~ line(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_112]) ).
tcf(c_2918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on(X4,line_through_3_points(X1,X2,X3))
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X2 )
| ~ line(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X4)
| ~ on(X0,X4)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_118,c_112]) ).
tcf(c_2919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on(X4,line_through_3_points(X1,X2,X3))
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ~ line(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X4)
| ~ on(X0,X4)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_119,c_112]) ).
tcf(c_2920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_from_to(X1,X2))
| ( X1 = X2 )
| ( X0 = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ on(X0,X3)
| ~ plane(line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_91,c_112]) ).
tcf(c_2921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X1,X2,X3)
| on(X4,plane_for_points(X1,X2,X3))
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X1 )
| ~ line(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_112]) ).
tcf(c_2922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X1,X2,X3)
| on(X4,plane_for_points(X1,X2,X3))
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X2 )
| ~ line(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X4)
| ~ on(X0,X4)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_108,c_112]) ).
tcf(c_2923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on(X3,X0)
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = X4 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X3)
| ~ point(X4)
| ~ point(X2)
| ~ on(X4,X3)
| ~ on(X4,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_113,c_112]) ).
tcf(c_2924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on(X3,X1)
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = X4 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X3)
| ~ point(X4)
| ~ point(X2)
| ~ on(X4,X3)
| ~ on(X4,X1)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_114,c_112]) ).
tcf(c_2925,plain,
! [X0: $i,X1: $i] :
( on(X1,a_line)
| ( X0 = point2 )
| ~ plane(a_line)
| ~ line(X1)
| ~ point(X0)
| ~ on(point2,X1)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2911,c_123]) ).
tcf(c_2934,plain,
! [X0: $i,X1: $i] :
( on(X1,a_line)
| ( X0 = point1 )
| ~ plane(a_line)
| ~ line(X1)
| ~ point(X0)
| ~ on(point1,X1)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2910,c_122]) ).
tcf(c_3128,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point1)
| ~ on(point2,a_line)
| ~ on(point1,a_line) ),
inference(superposition,[status(thm)],[c_126,c_2925]) ).
tcf(c_3130,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X0,X1),a_line)
| ( X1 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(line_from_to(X0,X1))
| ~ on(point2,line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_92,c_2925]) ).
tcf(c_3131,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_1_on_line(X0) = point2 )
| ~ plane(a_line)
| ~ line(X0)
| ~ on(point2,X0)
| ~ point(point_1_on_line(X0))
| ~ on(point_1_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_95,c_2925]) ).
tcf(c_3132,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_2_on_line(X0) = point2 )
| ~ plane(a_line)
| ~ line(X0)
| ~ on(point2,X0)
| ~ point(point_2_on_line(X0))
| ~ on(point_2_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_96,c_2925]) ).
tcf(c_3133,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_on_plane(X0) = point2 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ on(point2,X0)
| ~ point(point_on_plane(X0))
| ~ on(point_on_plane(X0),a_line) ),
inference(superposition,[status(thm)],[c_103,c_2925]) ).
tcf(c_3134,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),a_line)
| ( X2 = point2 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(point2,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_109,c_2925]) ).
tcf(c_3135,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),a_line)
| ( X1 = X2 )
| ( X0 = point2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(point2,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_2925]) ).
tcf(c_3136,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),a_line)
| ( X1 = point2 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(point2,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_118,c_2925]) ).
tcf(c_3137,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),a_line)
| ( X2 = point2 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(point2,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_119,c_2925]) ).
tcf(c_3138,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X0,X1),a_line)
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,X1))
| ~ on(point2,line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_91,c_2925]) ).
tcf(c_3139,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),a_line)
| ( X1 = X2 )
| ( X0 = point2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(point2,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_2925]) ).
tcf(c_3140,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),a_line)
| ( X1 = point2 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(point2,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_108,c_2925]) ).
tcf(c_3141,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X0,a_line)
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = point2 )
| ~ plane(a_line)
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X2)
| ~ on(point2,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_113,c_2925]) ).
tcf(c_3142,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,a_line)
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = point2 )
| ~ plane(a_line)
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ on(point2,X1)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_114,c_2925]) ).
tcf(c_3143,plain,
( on(a_line,a_line)
| ~ plane(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3128,c_129,c_125,c_122,c_127,c_126]) ).
tcf(c_3294,plain,
! [X0: $i,X1: $i] :
( on(X1,a_line)
| ( X0 = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ line(X1)
| ~ point(X0)
| ~ on(a_line,X1)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_3143,c_112]) ).
tcf(c_3305,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_1_on_line(X0) = point2 )
| ~ plane(a_line)
| ~ line(X0)
| ~ on(point2,X0)
| ~ on(point_1_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_3131,c_97,c_3131]) ).
tcf(c_3319,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point2,a_line) ),
inference(superposition,[status(thm)],[c_95,c_3305]) ).
tcf(c_3320,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3319,c_125,c_127]) ).
tcf(c_3356,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point1,X0)
| ( X2 = point1 )
| ( X1 = a_line )
| ( X0 = point1 )
| ( X0 = X2 )
| ~ plane(a_line)
| ~ point(point1)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(point1,X1)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_126,c_111]) ).
tcf(c_3357,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point2,X0)
| ( X2 = point2 )
| ( X1 = a_line )
| ( X0 = point2 )
| ( X0 = X2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(point2,X1)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_127,c_111]) ).
tcf(c_3358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X3,X2,X0)
| ( X2 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( X0 = X2 )
| ( line_from_to(X1,X2) = X4 )
| ~ plane(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X4)
| ~ on(X2,X4)
| ~ on(X0,X4)
| ~ plane(line_from_to(X1,X2))
| ~ on(X3,line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_92,c_111]) ).
tcf(c_3359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_1_on_line(X0),X2)
| ( X2 = X3 )
| ( X0 = X1 )
| ( point_1_on_line(X0) = X3 )
| ( point_1_on_line(X0) = X2 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X3)
| ~ point(X2)
| ~ point(point_1_on_line(X0))
| ~ on(X3,X1)
| ~ on(X3,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_1_on_line(X0),X1) ),
inference(superposition,[status(thm)],[c_95,c_111]) ).
tcf(c_3360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_2_on_line(X0),X2)
| ( X2 = X3 )
| ( X0 = X1 )
| ( point_2_on_line(X0) = X3 )
| ( point_2_on_line(X0) = X2 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X3)
| ~ point(X2)
| ~ point(point_2_on_line(X0))
| ~ on(X3,X1)
| ~ on(X3,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_2_on_line(X0),X1) ),
inference(superposition,[status(thm)],[c_96,c_111]) ).
tcf(c_3361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_on_plane(X0),X2)
| ( X2 = X3 )
| ( X0 = X1 )
| ( point_on_plane(X0) = X3 )
| ( point_on_plane(X0) = X2 )
| ~ plane(X1)
| ~ plane(X0)
| ~ point(X3)
| ~ point(X2)
| ~ point(point_on_plane(X0))
| ~ on(X3,X1)
| ~ on(X3,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_on_plane(X0),X1) ),
inference(superposition,[status(thm)],[c_103,c_111]) ).
tcf(c_3362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X4,X3,X0)
| collinear(X1,X2,X3)
| ( X3 = X4 )
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X3 )
| ( plane_for_points(X1,X2,X3) = X5 )
| ~ plane(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X5)
| ~ on(X3,X5)
| ~ on(X0,X5)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X4,plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_109,c_111]) ).
tcf(c_3363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X4,X1,X0)
| ( X2 = X3 )
| ( X1 = X4 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X1 )
| ( line_through_3_points(X1,X2,X3) = X5 )
| ~ plane(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X5)
| ~ on(X1,X5)
| ~ on(X0,X5)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X4,line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_111]) ).
tcf(c_3364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X4,X2,X0)
| ( X2 = X4 )
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X2 )
| ( line_through_3_points(X1,X2,X3) = X5 )
| ~ plane(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X5)
| ~ on(X2,X5)
| ~ on(X0,X5)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X4,line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_118,c_111]) ).
tcf(c_3365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X4,X3,X0)
| ( X3 = X4 )
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X3 )
| ( line_through_3_points(X1,X2,X3) = X5 )
| ~ plane(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X5)
| ~ on(X3,X5)
| ~ on(X0,X5)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X4,line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_119,c_111]) ).
tcf(c_3366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X3,X1,X0)
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( X0 = X1 )
| ( line_from_to(X1,X2) = X4 )
| ~ plane(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X4)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ plane(line_from_to(X1,X2))
| ~ on(X3,line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_91,c_111]) ).
tcf(c_3367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X4,X1,X0)
| collinear(X1,X2,X3)
| ( X2 = X3 )
| ( X1 = X4 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X1 )
| ( plane_for_points(X1,X2,X3) = X5 )
| ~ plane(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X5)
| ~ on(X1,X5)
| ~ on(X0,X5)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X4,plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_111]) ).
tcf(c_3368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X4,X2,X0)
| collinear(X1,X2,X3)
| ( X2 = X4 )
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X2 )
| ( plane_for_points(X1,X2,X3) = X5 )
| ~ plane(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X5)
| ~ on(X2,X5)
| ~ on(X0,X5)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X4,plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_108,c_111]) ).
tcf(c_3369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X5,common_point_on_planes(X0,X1,X2),X4)
| ( X4 = X5 )
| ( X0 = X3 )
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = X5 )
| ( common_point_on_planes(X0,X1,X2) = X4 )
| ~ plane(X3)
| ~ plane(X1)
| ~ plane(X0)
| ~ point(X5)
| ~ point(X4)
| ~ point(X2)
| ~ on(X5,X3)
| ~ on(X5,X0)
| ~ on(X4,X3)
| ~ on(X4,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_113,c_111]) ).
tcf(c_3370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X5,common_point_on_planes(X0,X1,X2),X4)
| ( X4 = X5 )
| ( X1 = X3 )
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = X5 )
| ( common_point_on_planes(X0,X1,X2) = X4 )
| ~ plane(X3)
| ~ plane(X1)
| ~ plane(X0)
| ~ point(X5)
| ~ point(X4)
| ~ point(X2)
| ~ on(X5,X3)
| ~ on(X5,X1)
| ~ on(X4,X3)
| ~ on(X4,X1)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_114,c_111]) ).
tcf(c_3371,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,a_line,X0)
| ( X2 = a_line )
| ( X1 = a_line )
| ( X0 = a_line )
| ( X0 = X2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(a_line,X1)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_3143,c_111]) ).
tcf(c_3387,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point2,X0)
| ( X2 = point2 )
| ( X1 = a_line )
| ( X0 = point2 )
| ( X0 = X2 )
| ~ plane(a_line)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(point2,X1)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3357,c_123]) ).
tcf(c_3402,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point1,X0)
| ( X2 = point1 )
| ( X1 = a_line )
| ( X0 = point1 )
| ( X0 = X2 )
| ~ plane(a_line)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(point1,X1)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3356,c_122]) ).
tcf(c_3688,plain,
! [X0: $i,X1: $i] :
( ( X1 = a_line )
| ( X0 = point1 )
| ~ line(a_line)
| ~ point(point1)
| ~ line(X1)
| ~ point(X0)
| ~ on(point1,X1)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_126,c_94]) ).
tcf(c_3689,plain,
! [X0: $i,X1: $i] :
( ( X1 = a_line )
| ( X0 = point2 )
| ~ line(a_line)
| ~ point(point2)
| ~ line(X1)
| ~ point(X0)
| ~ on(point2,X1)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_127,c_94]) ).
tcf(c_3690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( line_from_to(X1,X2) = X3 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X0,X3)
| ~ line(line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_92,c_94]) ).
tcf(c_3691,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ( point_1_on_line(X0) = X2 )
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ point(point_1_on_line(X0))
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_1_on_line(X0),X1) ),
inference(superposition,[status(thm)],[c_95,c_94]) ).
tcf(c_3692,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ( point_2_on_line(X0) = X2 )
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ point(point_2_on_line(X0))
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_2_on_line(X0),X1) ),
inference(superposition,[status(thm)],[c_96,c_94]) ).
tcf(c_3693,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ( point_on_plane(X0) = X2 )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ point(point_on_plane(X0))
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_on_plane(X0),X1) ),
inference(superposition,[status(thm)],[c_103,c_94]) ).
tcf(c_3694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X1,X2,X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( plane_for_points(X1,X2,X3) = X4 )
| ~ line(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X4)
| ~ on(X0,X4)
| ~ line(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_109,c_94]) ).
tcf(c_3695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X1,X2,X3) = X4 )
| ~ line(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ collinear(X1,X2,X3)
| ~ line(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_94]) ).
tcf(c_3696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( line_through_3_points(X1,X2,X3) = X4 )
| ~ line(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X4)
| ~ on(X0,X4)
| ~ collinear(X1,X2,X3)
| ~ line(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_118,c_94]) ).
tcf(c_3697,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( line_through_3_points(X1,X2,X3) = X4 )
| ~ line(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X4)
| ~ on(X0,X4)
| ~ collinear(X1,X2,X3)
| ~ line(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_119,c_94]) ).
tcf(c_3698,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X0 = X1 )
| ( line_from_to(X1,X2) = X3 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ on(X0,X3)
| ~ line(line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_91,c_94]) ).
tcf(c_3699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X1,X2,X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X1,X2,X3) = X4 )
| ~ line(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ line(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_94]) ).
tcf(c_3700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X1,X2,X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( plane_for_points(X1,X2,X3) = X4 )
| ~ line(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X4)
| ~ on(X0,X4)
| ~ line(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_108,c_94]) ).
tcf(c_3701,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X3 )
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = X4 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X3)
| ~ line(X0)
| ~ point(X4)
| ~ point(X2)
| ~ on(X4,X3)
| ~ on(X4,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_113,c_94]) ).
tcf(c_3702,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X3 )
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = X4 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X3)
| ~ line(X1)
| ~ point(X4)
| ~ point(X2)
| ~ on(X4,X3)
| ~ on(X4,X1)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_114,c_94]) ).
tcf(c_3703,plain,
! [X0: $i,X1: $i] :
( ( X1 = a_line )
| ( X0 = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ line(X1)
| ~ point(X0)
| ~ on(a_line,X1)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_3143,c_94]) ).
tcf(c_3704,plain,
! [X0: $i,X1: $i] :
( ( X1 = a_line )
| ( X0 = point2 )
| ~ line(X1)
| ~ point(X0)
| ~ on(point2,X1)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3689,c_125,c_123]) ).
tcf(c_3712,plain,
! [X0: $i,X1: $i] :
( ( X1 = a_line )
| ( X0 = point1 )
| ~ line(X1)
| ~ point(X0)
| ~ on(point1,X1)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3688,c_125,c_122]) ).
tcf(c_3720,plain,
! [X0: $i,X1: $i] :
( ( X1 = a_line )
| ( X0 = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ line(X1)
| ~ point(X0)
| ~ on(a_line,X1)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3703,c_125]) ).
tcf(c_3939,plain,
! [X0: $i,X1: $i] :
( collinear(X1,point1,X0)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ~ line(a_line)
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_126,c_121]) ).
tcf(c_3940,plain,
! [X0: $i,X1: $i] :
( collinear(X1,point2,X0)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ line(a_line)
| ~ point(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_127,c_121]) ).
tcf(c_3941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,X2,X0)
| ( X2 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( X0 = X2 )
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ line(line_from_to(X1,X2))
| ~ on(X3,line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_92,c_121]) ).
tcf(c_3942,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point_1_on_line(X1),X0)
| ( X0 = X2 )
| ( point_1_on_line(X1) = X2 )
| ( point_1_on_line(X1) = X0 )
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(X1))
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_95,c_121]) ).
tcf(c_3943,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point_2_on_line(X1),X0)
| ( X0 = X2 )
| ( point_2_on_line(X1) = X2 )
| ( point_2_on_line(X1) = X0 )
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(X1))
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_121]) ).
tcf(c_3944,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point_on_plane(X1),X0)
| ( X0 = X2 )
| ( point_on_plane(X1) = X2 )
| ( point_on_plane(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_on_plane(X1))
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_103,c_121]) ).
tcf(c_3945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X3,X0)
| collinear(X1,X2,X3)
| ( X3 = X4 )
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X3 )
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ line(plane_for_points(X1,X2,X3))
| ~ on(X4,plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_109,c_121]) ).
tcf(c_3946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X1,X0)
| ( X2 = X3 )
| ( X1 = X4 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X1 )
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X1,X2,X3)
| ~ line(line_through_3_points(X1,X2,X3))
| ~ on(X4,line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_121]) ).
tcf(c_3947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X2,X0)
| ( X2 = X4 )
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X2 )
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X1,X2,X3)
| ~ line(line_through_3_points(X1,X2,X3))
| ~ on(X4,line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_118,c_121]) ).
tcf(c_3948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X3,X0)
| ( X3 = X4 )
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X3 )
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X1,X2,X3)
| ~ line(line_through_3_points(X1,X2,X3))
| ~ on(X4,line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_119,c_121]) ).
tcf(c_3949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,X1,X0)
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( X0 = X1 )
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ line(line_from_to(X1,X2))
| ~ on(X3,line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_91,c_121]) ).
tcf(c_3950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X1,X0)
| collinear(X1,X2,X3)
| ( X2 = X3 )
| ( X1 = X4 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X1 )
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ line(plane_for_points(X1,X2,X3))
| ~ on(X4,plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_121]) ).
tcf(c_3951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X2,X0)
| collinear(X1,X2,X3)
| ( X2 = X4 )
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X2 )
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ line(plane_for_points(X1,X2,X3))
| ~ on(X4,plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_108,c_121]) ).
tcf(c_3952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,common_point_on_planes(X0,X1,X2),X3)
| ( X3 = X4 )
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = X4 )
| ( common_point_on_planes(X0,X1,X2) = X3 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ on(X4,X0)
| ~ on(X3,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_113,c_121]) ).
tcf(c_3953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,common_point_on_planes(X0,X1,X2),X3)
| ( X3 = X4 )
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = X4 )
| ( common_point_on_planes(X0,X1,X2) = X3 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X1)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ on(X4,X1)
| ~ on(X3,X1)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_114,c_121]) ).
tcf(c_3954,plain,
! [X0: $i,X1: $i] :
( collinear(X1,a_line,X0)
| ( X1 = a_line )
| ( X0 = a_line )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_3143,c_121]) ).
tcf(c_3955,plain,
! [X0: $i,X1: $i] :
( collinear(X1,point2,X0)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3940,c_125,c_123]) ).
tcf(c_3964,plain,
! [X0: $i,X1: $i] :
( collinear(X1,point1,X0)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3939,c_125,c_122]) ).
tcf(c_3973,plain,
! [X0: $i,X1: $i] :
( collinear(X1,a_line,X0)
| ( X1 = a_line )
| ( X0 = a_line )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3954,c_125]) ).
tcf(c_4200,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(line_from_to(X0,X1))
| ~ on(point2,line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_92,c_3704]) ).
tcf(c_4201,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_1_on_line(X0) = point2 )
| ~ line(X0)
| ~ on(point2,X0)
| ~ point(point_1_on_line(X0))
| ~ on(point_1_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_95,c_3704]) ).
tcf(c_4202,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_2_on_line(X0) = point2 )
| ~ line(X0)
| ~ on(point2,X0)
| ~ point(point_2_on_line(X0))
| ~ on(point_2_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_96,c_3704]) ).
tcf(c_4203,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_on_plane(X0) = point2 )
| ~ plane(X0)
| ~ line(X0)
| ~ on(point2,X0)
| ~ point(point_on_plane(X0))
| ~ on(point_on_plane(X0),a_line) ),
inference(superposition,[status(thm)],[c_103,c_3704]) ).
tcf(c_4204,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X2 = point2 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(point2,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_109,c_3704]) ).
tcf(c_4205,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = point2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(point2,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_3704]) ).
tcf(c_4206,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = point2 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(point2,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_118,c_3704]) ).
tcf(c_4207,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = point2 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(point2,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_119,c_3704]) ).
tcf(c_4208,plain,
! [X0: $i,X1: $i] :
( ( X0 = point2 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,X1))
| ~ on(point2,line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_91,c_3704]) ).
tcf(c_4209,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = point2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(point2,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_3704]) ).
tcf(c_4210,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = point2 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(point2,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_108,c_3704]) ).
tcf(c_4211,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = a_line )
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = point2 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X2)
| ~ on(point2,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_113,c_3704]) ).
tcf(c_4212,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = point2 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ on(point2,X1)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_114,c_3704]) ).
tcf(c_4351,plain,
( point(point_1_on_line(a_line))
| ~ line(a_line) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_4353,plain,
( point(point_2_on_line(a_line))
| ~ line(a_line) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_4355,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_1_on_line(X0) = point2 )
| ~ line(X0)
| ~ on(point2,X0)
| ~ on(point_1_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_4201,c_97,c_4201]) ).
tcf(c_4369,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_2_on_line(X0) = point2 )
| ~ line(X0)
| ~ on(point2,X0)
| ~ on(point_2_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_4202,c_98,c_4202]) ).
tcf(c_4399,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(line_from_to(X0,X1))
| ~ on(point1,line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_92,c_3712]) ).
tcf(c_4400,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_1_on_line(X0) = point1 )
| ~ line(X0)
| ~ on(point1,X0)
| ~ point(point_1_on_line(X0))
| ~ on(point_1_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_95,c_3712]) ).
tcf(c_4401,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_2_on_line(X0) = point1 )
| ~ line(X0)
| ~ on(point1,X0)
| ~ point(point_2_on_line(X0))
| ~ on(point_2_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_96,c_3712]) ).
tcf(c_4402,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_on_plane(X0) = point1 )
| ~ plane(X0)
| ~ line(X0)
| ~ on(point1,X0)
| ~ point(point_on_plane(X0))
| ~ on(point_on_plane(X0),a_line) ),
inference(superposition,[status(thm)],[c_103,c_3712]) ).
tcf(c_4403,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X2 = point1 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(point1,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_109,c_3712]) ).
tcf(c_4404,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = point1 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(point1,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_3712]) ).
tcf(c_4405,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = point1 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(point1,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_118,c_3712]) ).
tcf(c_4406,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = point1 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(point1,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_119,c_3712]) ).
tcf(c_4407,plain,
! [X0: $i,X1: $i] :
( ( X0 = point1 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,X1))
| ~ on(point1,line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_91,c_3712]) ).
tcf(c_4408,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = point1 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(point1,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_3712]) ).
tcf(c_4409,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = point1 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(point1,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_108,c_3712]) ).
tcf(c_4410,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = a_line )
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = point1 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X2)
| ~ on(point1,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_113,c_3712]) ).
tcf(c_4411,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = point1 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ on(point1,X1)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_114,c_3712]) ).
tcf(c_4549,plain,
( on(point_1_on_line(a_line),a_line)
| ~ line(a_line) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_4551,plain,
( on(point_2_on_line(a_line),a_line)
| ~ line(a_line) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_4557,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_1_on_line(X0) = point1 )
| ~ line(X0)
| ~ on(point1,X0)
| ~ on(point_1_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_4400,c_97,c_4400]) ).
tcf(c_4571,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_2_on_line(X0) = point1 )
| ~ line(X0)
| ~ on(point1,X0)
| ~ on(point_2_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_4401,c_98,c_4401]) ).
tcf(c_4589,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_2_on_line(X0) = point2 )
| ~ plane(a_line)
| ~ line(X0)
| ~ on(point2,X0)
| ~ on(point_2_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_3132,c_98,c_3132]) ).
tcf(c_4603,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point2,a_line) ),
inference(superposition,[status(thm)],[c_96,c_4589]) ).
tcf(c_4604,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4603,c_125,c_127]) ).
tcf(c_4627,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ on(point1,a_line) ),
inference(superposition,[status(thm)],[c_127,c_2934]) ).
tcf(c_4628,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X0,X1),a_line)
| ( X1 = point1 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(line_from_to(X0,X1))
| ~ on(point1,line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_92,c_2934]) ).
tcf(c_4629,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_1_on_line(X0) = point1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ on(point1,X0)
| ~ point(point_1_on_line(X0))
| ~ on(point_1_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_95,c_2934]) ).
tcf(c_4630,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_2_on_line(X0) = point1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ on(point1,X0)
| ~ point(point_2_on_line(X0))
| ~ on(point_2_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_96,c_2934]) ).
tcf(c_4631,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_on_plane(X0) = point1 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ on(point1,X0)
| ~ point(point_on_plane(X0))
| ~ on(point_on_plane(X0),a_line) ),
inference(superposition,[status(thm)],[c_103,c_2934]) ).
tcf(c_4632,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),a_line)
| ( X2 = point1 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(point1,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_109,c_2934]) ).
tcf(c_4633,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),a_line)
| ( X1 = X2 )
| ( X0 = point1 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(point1,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_2934]) ).
tcf(c_4634,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),a_line)
| ( X1 = point1 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(point1,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_118,c_2934]) ).
tcf(c_4635,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),a_line)
| ( X2 = point1 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(point1,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_119,c_2934]) ).
tcf(c_4636,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X0,X1),a_line)
| ( X0 = point1 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,X1))
| ~ on(point1,line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_91,c_2934]) ).
tcf(c_4637,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),a_line)
| ( X1 = X2 )
| ( X0 = point1 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(point1,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_2934]) ).
tcf(c_4638,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),a_line)
| ( X1 = point1 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(point1,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_108,c_2934]) ).
tcf(c_4639,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X0,a_line)
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = point1 )
| ~ plane(a_line)
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X2)
| ~ on(point1,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_113,c_2934]) ).
tcf(c_4640,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,a_line)
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = point1 )
| ~ plane(a_line)
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ on(point1,X1)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_114,c_2934]) ).
tcf(c_4799,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_1_on_line(X0) = point1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ on(point1,X0)
| ~ on(point_1_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_4629,c_97,c_4629]) ).
tcf(c_4813,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point1,a_line) ),
inference(superposition,[status(thm)],[c_95,c_4799]) ).
tcf(c_4814,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4813,c_125,c_126]) ).
tcf(c_4823,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_2_on_line(X0) = point1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ on(point1,X0)
| ~ on(point_2_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_4630,c_98,c_4630]) ).
tcf(c_4837,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point1,a_line) ),
inference(superposition,[status(thm)],[c_96,c_4823]) ).
tcf(c_4838,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4837,c_125,c_126]) ).
tcf(c_4874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = X2 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_1_on_line(plane_for_points(X0,X1,X2)))
| ~ on(point_1_on_line(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_95,c_2916]) ).
tcf(c_4875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_2_on_line(plane_for_points(X0,X1,X2)) = X2 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_2_on_line(plane_for_points(X0,X1,X2)))
| ~ on(point_2_on_line(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_96,c_2916]) ).
tcf(c_4876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_on_plane(plane_for_points(X0,X1,X2)) = X2 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ point(point_on_plane(plane_for_points(X0,X1,X2)))
| ~ on(point_on_plane(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_103,c_2916]) ).
tcf(c_4878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_2916]) ).
tcf(c_4879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X1,X3)
| ~ plane(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_108,c_2916]) ).
tcf(c_4880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X0,X1,X2)
| on(X5,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4) = X2 )
| ~ plane(X3)
| ~ line(X5)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X2,X5)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ point(common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4))
| ~ on(common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_113,c_2916]) ).
tcf(c_4881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X1,X2,X3)
| on(X5,plane_for_points(X1,X2,X3))
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,X3) = X0 )
| ( common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4) = X3 )
| ~ plane(X0)
| ~ line(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X4,X0)
| ~ on(X3,X5)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X4,plane_for_points(X1,X2,X3))
| ~ point(common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4))
| ~ on(common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_114,c_2916]) ).
tcf(c_5463,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_on_plane(X0) = point2 )
| ~ plane(X0)
| ~ line(X0)
| ~ on(point2,X0)
| ~ on(point_on_plane(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_4203,c_104,c_4203]) ).
tcf(c_5479,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_on_plane(X0) = point1 )
| ~ plane(X0)
| ~ line(X0)
| ~ on(point1,X0)
| ~ on(point_on_plane(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_4402,c_104,c_4402]) ).
tcf(c_5501,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_on_plane(X0) = point2 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ on(point2,X0)
| ~ on(point_on_plane(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_3133,c_104,c_3133]) ).
tcf(c_5517,plain,
( on(a_line,a_line)
| ( point_on_plane(a_line) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point2,a_line) ),
inference(superposition,[status(thm)],[c_103,c_5501]) ).
tcf(c_5518,plain,
( on(a_line,a_line)
| ( point_on_plane(a_line) = point2 )
| ~ plane(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5517,c_125,c_127]) ).
tcf(c_5556,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_on_plane(X0) = point1 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ on(point1,X0)
| ~ on(point_on_plane(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_4631,c_104,c_4631]) ).
tcf(c_5572,plain,
( on(a_line,a_line)
| ( point_on_plane(a_line) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point1,a_line) ),
inference(superposition,[status(thm)],[c_103,c_5556]) ).
tcf(c_5573,plain,
( on(a_line,a_line)
| ( point_on_plane(a_line) = point1 )
| ~ plane(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5572,c_125,c_126]) ).
tcf(c_5605,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X0,X1),a_line)
| ( X1 = a_line )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(line_from_to(X0,X1))
| ~ on(a_line,line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_92,c_3294]) ).
tcf(c_5606,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_1_on_line(X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ line(X0)
| ~ on(a_line,X0)
| ~ point(point_1_on_line(X0))
| ~ on(point_1_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_95,c_3294]) ).
tcf(c_5607,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_2_on_line(X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ line(X0)
| ~ on(a_line,X0)
| ~ point(point_2_on_line(X0))
| ~ on(point_2_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_96,c_3294]) ).
tcf(c_5608,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_on_plane(X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ on(a_line,X0)
| ~ point(point_on_plane(X0))
| ~ on(point_on_plane(X0),a_line) ),
inference(superposition,[status(thm)],[c_103,c_3294]) ).
tcf(c_5609,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),a_line)
| ( X2 = a_line )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(a_line,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_109,c_3294]) ).
tcf(c_5610,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),a_line)
| ( X1 = X2 )
| ( X0 = a_line )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(a_line,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_3294]) ).
tcf(c_5611,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),a_line)
| ( X1 = a_line )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(a_line,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_118,c_3294]) ).
tcf(c_5612,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),a_line)
| ( X2 = a_line )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(a_line,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_119,c_3294]) ).
tcf(c_5613,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X0,X1),a_line)
| ( X0 = a_line )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,X1))
| ~ on(a_line,line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_91,c_3294]) ).
tcf(c_5614,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),a_line)
| ( X1 = X2 )
| ( X0 = a_line )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(a_line,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_3294]) ).
tcf(c_5615,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),a_line)
| ( X1 = a_line )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(a_line,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_108,c_3294]) ).
tcf(c_5616,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X0,a_line)
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X2)
| ~ on(a_line,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_113,c_3294]) ).
tcf(c_5617,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,a_line)
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ on(a_line,X1)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_114,c_3294]) ).
tcf(c_5788,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_1_on_line(X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ line(X0)
| ~ on(a_line,X0)
| ~ on(point_1_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_5606,c_97,c_5606]) ).
tcf(c_5808,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_2_on_line(X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ line(X0)
| ~ on(a_line,X0)
| ~ on(point_2_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_5607,c_98,c_5607]) ).
tcf(c_5845,plain,
! [X0: $i,X1: $i] :
( ( X1 = a_line )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(line_from_to(X0,X1))
| ~ on(a_line,line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_92,c_3720]) ).
tcf(c_5846,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_1_on_line(X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ line(X0)
| ~ on(a_line,X0)
| ~ point(point_1_on_line(X0))
| ~ on(point_1_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_95,c_3720]) ).
tcf(c_5847,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_2_on_line(X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ line(X0)
| ~ on(a_line,X0)
| ~ point(point_2_on_line(X0))
| ~ on(point_2_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_96,c_3720]) ).
tcf(c_5848,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_on_plane(X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ on(a_line,X0)
| ~ point(point_on_plane(X0))
| ~ on(point_on_plane(X0),a_line) ),
inference(superposition,[status(thm)],[c_103,c_3720]) ).
tcf(c_5849,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X2 = a_line )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(a_line,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_109,c_3720]) ).
tcf(c_5850,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = a_line )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(a_line,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_3720]) ).
tcf(c_5851,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(a_line,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_118,c_3720]) ).
tcf(c_5852,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = a_line )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ on(a_line,line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_119,c_3720]) ).
tcf(c_5853,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,X1))
| ~ on(a_line,line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_91,c_3720]) ).
tcf(c_5854,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = a_line )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(a_line,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_3720]) ).
tcf(c_5855,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = a_line )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(a_line,plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_108,c_3720]) ).
tcf(c_5856,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = a_line )
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X2)
| ~ on(a_line,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_113,c_3720]) ).
tcf(c_5857,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ on(a_line,X1)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_114,c_3720]) ).
tcf(c_6026,plain,
! [X0: $i] :
( line(line_from_to(point2,X0))
| ( X0 = point2 )
| ~ point(point2)
| ~ point(X0) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_6045,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_1_on_line(X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ line(X0)
| ~ on(a_line,X0)
| ~ on(point_1_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_5846,c_97,c_5846]) ).
tcf(c_6063,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_2_on_line(X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ line(X0)
| ~ on(a_line,X0)
| ~ on(point_2_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_5847,c_98,c_5847]) ).
tcf(c_6081,plain,
! [X0: $i] :
( on(X0,a_line)
| ( point_on_plane(X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ on(a_line,X0)
| ~ on(point_on_plane(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_5608,c_104,c_5608]) ).
tcf(c_6100,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,X0)
| ( point_on_plane(X0) = X2 )
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ on(point_on_plane(X0),X1)
| ~ on(X2,X0)
| ~ on(X2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_2915,c_104,c_2915]) ).
tcf(c_6101,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,X0)
| ( point_on_plane(X0) = X2 )
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_on_plane(X0),X1) ),
inference(renaming,[status(thm)],[c_6100]) ).
tcf(c_6118,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_from_to(X1,point_on_plane(X2)),X2)
| ( point_on_plane(X2) = X1 )
| ( point_on_plane(X2) = X0 )
| ~ plane(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X2))
| ~ on(X0,X2)
| ~ line(line_from_to(X1,point_on_plane(X2)))
| ~ on(X0,line_from_to(X1,point_on_plane(X2))) ),
inference(superposition,[status(thm)],[c_92,c_6101]) ).
tcf(c_6119,plain,
! [X0: $i,X1: $i] :
( on(X1,X1)
| ( point_on_plane(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X0)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_103,c_6101]) ).
tcf(c_6120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,X2,point_on_plane(X3))
| on(plane_for_points(X1,X2,point_on_plane(X3)),X3)
| ( X1 = X2 )
| ( point_on_plane(X3) = X2 )
| ( point_on_plane(X3) = X1 )
| ( point_on_plane(X3) = X0 )
| ~ plane(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X3))
| ~ on(X0,X3)
| ~ line(plane_for_points(X1,X2,point_on_plane(X3)))
| ~ on(X0,plane_for_points(X1,X2,point_on_plane(X3))) ),
inference(superposition,[status(thm)],[c_109,c_6101]) ).
tcf(c_6121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(line_through_3_points(point_on_plane(X1),X2,X3),X1)
| ( X2 = X3 )
| ( point_on_plane(X1) = X3 )
| ( point_on_plane(X1) = X2 )
| ( point_on_plane(X1) = X0 )
| ~ plane(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_on_plane(X1))
| ~ on(X0,X1)
| ~ collinear(point_on_plane(X1),X2,X3)
| ~ line(line_through_3_points(point_on_plane(X1),X2,X3))
| ~ on(X0,line_through_3_points(point_on_plane(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_6101]) ).
tcf(c_6122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(line_through_3_points(X1,point_on_plane(X2),X3),X2)
| ( X1 = X3 )
| ( point_on_plane(X2) = X3 )
| ( point_on_plane(X2) = X1 )
| ( point_on_plane(X2) = X0 )
| ~ plane(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X2))
| ~ on(X0,X2)
| ~ collinear(X1,point_on_plane(X2),X3)
| ~ line(line_through_3_points(X1,point_on_plane(X2),X3))
| ~ on(X0,line_through_3_points(X1,point_on_plane(X2),X3)) ),
inference(superposition,[status(thm)],[c_118,c_6101]) ).
tcf(c_6123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(line_through_3_points(X1,X2,point_on_plane(X3)),X3)
| ( X1 = X2 )
| ( point_on_plane(X3) = X2 )
| ( point_on_plane(X3) = X1 )
| ( point_on_plane(X3) = X0 )
| ~ plane(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X3))
| ~ on(X0,X3)
| ~ collinear(X1,X2,point_on_plane(X3))
| ~ line(line_through_3_points(X1,X2,point_on_plane(X3)))
| ~ on(X0,line_through_3_points(X1,X2,point_on_plane(X3))) ),
inference(superposition,[status(thm)],[c_119,c_6101]) ).
tcf(c_6124,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_from_to(point_on_plane(X1),X2),X1)
| ( point_on_plane(X1) = X2 )
| ( point_on_plane(X1) = X0 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_on_plane(X1))
| ~ on(X0,X1)
| ~ line(line_from_to(point_on_plane(X1),X2))
| ~ on(X0,line_from_to(point_on_plane(X1),X2)) ),
inference(superposition,[status(thm)],[c_91,c_6101]) ).
tcf(c_6125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(point_on_plane(X1),X2,X3)
| on(plane_for_points(point_on_plane(X1),X2,X3),X1)
| ( X2 = X3 )
| ( point_on_plane(X1) = X3 )
| ( point_on_plane(X1) = X2 )
| ( point_on_plane(X1) = X0 )
| ~ plane(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_on_plane(X1))
| ~ on(X0,X1)
| ~ line(plane_for_points(point_on_plane(X1),X2,X3))
| ~ on(X0,plane_for_points(point_on_plane(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_6101]) ).
tcf(c_6126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,point_on_plane(X2),X3)
| on(plane_for_points(X1,point_on_plane(X2),X3),X2)
| ( X1 = X3 )
| ( point_on_plane(X2) = X3 )
| ( point_on_plane(X2) = X1 )
| ( point_on_plane(X2) = X0 )
| ~ plane(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X2))
| ~ on(X0,X2)
| ~ line(plane_for_points(X1,point_on_plane(X2),X3))
| ~ on(X0,plane_for_points(X1,point_on_plane(X2),X3)) ),
inference(superposition,[status(thm)],[c_108,c_6101]) ).
tcf(c_6269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = X0 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(point_1_on_line(line_through_3_points(X0,X1,X2)))
| ~ on(point_1_on_line(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_95,c_2917]) ).
tcf(c_6270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_2_on_line(line_through_3_points(X0,X1,X2)) = X0 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(point_2_on_line(line_through_3_points(X0,X1,X2)))
| ~ on(point_2_on_line(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_96,c_2917]) ).
tcf(c_6271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_on_plane(line_through_3_points(X0,X1,X2)) = X0 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ point(point_on_plane(line_through_3_points(X0,X1,X2)))
| ~ on(point_on_plane(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_103,c_2917]) ).
tcf(c_6273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_118,c_2917]) ).
tcf(c_6274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_119,c_2917]) ).
tcf(c_6275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( on(X5,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4) = X0 )
| ~ plane(X3)
| ~ line(X5)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X0,X5)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ point(common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4))
| ~ on(common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_113,c_2917]) ).
tcf(c_6276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( on(X5,line_through_3_points(X1,X2,X3))
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,X3) = X0 )
| ( common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4) = X1 )
| ~ plane(X0)
| ~ line(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X4,X0)
| ~ on(X1,X5)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X4,line_through_3_points(X1,X2,X3))
| ~ point(common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4))
| ~ on(common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_114,c_2917]) ).
tcf(c_6397,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X0,X1),line_from_to(X0,X1))
| ( X0 = X1 )
| ( point_on_plane(line_from_to(X0,X1)) = X1 )
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_92,c_6119]) ).
tcf(c_6398,plain,
! [X0: $i] :
( on(X0,X0)
| ( point_1_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ point(point_1_on_line(X0)) ),
inference(superposition,[status(thm)],[c_95,c_6119]) ).
tcf(c_6399,plain,
! [X0: $i] :
( on(X0,X0)
| ( point_2_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ point(point_2_on_line(X0)) ),
inference(superposition,[status(thm)],[c_96,c_6119]) ).
tcf(c_6401,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_on_plane(plane_for_points(X0,X1,X2)) = X2 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_109,c_6119]) ).
tcf(c_6402,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_on_plane(line_through_3_points(X0,X1,X2)) = X0 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_6119]) ).
tcf(c_6403,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_on_plane(line_through_3_points(X0,X1,X2)) = X1 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_118,c_6119]) ).
tcf(c_6404,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_on_plane(line_through_3_points(X0,X1,X2)) = X2 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_119,c_6119]) ).
tcf(c_6405,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X0,X1),line_from_to(X0,X1))
| ( X0 = X1 )
| ( point_on_plane(line_from_to(X0,X1)) = X0 )
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_91,c_6119]) ).
tcf(c_6406,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_on_plane(plane_for_points(X0,X1,X2)) = X0 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_6119]) ).
tcf(c_6407,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_on_plane(plane_for_points(X0,X1,X2)) = X1 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_108,c_6119]) ).
tcf(c_6408,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X0,X0)
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = point_on_plane(X0) )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_113,c_6119]) ).
tcf(c_6409,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,X1)
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = point_on_plane(X1) )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_114,c_6119]) ).
tcf(c_6410,plain,
( on(a_line,a_line)
| ( point_on_plane(a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_3143,c_6119]) ).
tcf(c_6411,plain,
( on(a_line,a_line)
| ( point_on_plane(a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6410,c_125]) ).
tcf(c_6715,plain,
! [X0: $i] :
( on(X0,X0)
| ( point_1_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0) ),
inference(global_subsumption_just,[status(thm)],[c_6398,c_97,c_6398]) ).
tcf(c_6726,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_6715,c_94]) ).
tcf(c_6727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,X0,X2)
| ( X2 = X3 )
| ( X0 = X3 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(X0) = point_on_plane(X0) )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ on(X3,X1)
| ~ on(X3,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_6715,c_111]) ).
tcf(c_6728,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,X0)
| ( X0 = X2 )
| ( point_1_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_6715,c_112]) ).
tcf(c_6729,plain,
! [X0: $i] :
( on(X0,X0)
| ( point_on_plane(X0) = X0 )
| ( point_1_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0) ),
inference(superposition,[status(thm)],[c_6715,c_6119]) ).
tcf(c_6730,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_1_on_line(X0) = point_on_plane(X0) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0)
| ~ on(a_line,X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_6715,c_3720]) ).
tcf(c_6733,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( X0 = point1 )
| ( point_1_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0)
| ~ on(point1,X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_6715,c_3712]) ).
tcf(c_6734,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( X0 = point2 )
| ( point_1_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0)
| ~ on(point2,X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_6715,c_3704]) ).
tcf(c_6735,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,X1,X0)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(X1) = point_on_plane(X1) )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_6715,c_121]) ).
tcf(c_6737,plain,
! [X0: $i,X1: $i] :
( on(point_on_plane(X1),X1)
| ( point_on_plane(X1) = X0 )
| ( point_1_on_line(point_on_plane(X1)) = point_on_plane(point_on_plane(X1)) )
| ~ plane(X1)
| ~ point(X0)
| ~ plane(point_on_plane(X1))
| ~ line(point_on_plane(X1))
| ~ on(X0,X1)
| ~ on(X0,point_on_plane(X1)) ),
inference(superposition,[status(thm)],[c_6715,c_6101]) ).
tcf(c_6738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X2 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = point_on_plane(plane_for_points(X0,X1,X2)) )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(plane_for_points(X0,X1,X2))
| ~ on(plane_for_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_6715,c_2916]) ).
tcf(c_6739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X0 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = point_on_plane(line_through_3_points(X0,X1,X2)) )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(line_through_3_points(X0,X1,X2))
| ~ on(line_through_3_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_6715,c_2917]) ).
tcf(c_6875,plain,
! [X0: $i] :
( on(X0,X0)
| ( point_2_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0) ),
inference(global_subsumption_just,[status(thm)],[c_6399,c_98,c_6399]) ).
tcf(c_6886,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ( point_2_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_6875,c_94]) ).
tcf(c_6887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,X0,X2)
| ( X2 = X3 )
| ( X0 = X3 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_2_on_line(X0) = point_on_plane(X0) )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ on(X3,X1)
| ~ on(X3,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_6875,c_111]) ).
tcf(c_6888,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,X0)
| ( X0 = X2 )
| ( point_2_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_6875,c_112]) ).
tcf(c_6889,plain,
! [X0: $i] :
( on(X0,X0)
| ( point_on_plane(X0) = X0 )
| ( point_2_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0) ),
inference(superposition,[status(thm)],[c_6875,c_6119]) ).
tcf(c_6890,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_2_on_line(X0) = point_on_plane(X0) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0)
| ~ on(a_line,X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_6875,c_3720]) ).
tcf(c_6893,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( X0 = point1 )
| ( point_2_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0)
| ~ on(point1,X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_6875,c_3712]) ).
tcf(c_6894,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( X0 = point2 )
| ( point_2_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0)
| ~ on(point2,X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_6875,c_3704]) ).
tcf(c_6895,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,X1,X0)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_2_on_line(X1) = point_on_plane(X1) )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_6875,c_121]) ).
tcf(c_6897,plain,
! [X0: $i,X1: $i] :
( on(point_on_plane(X1),X1)
| ( point_on_plane(X1) = X0 )
| ( point_2_on_line(point_on_plane(X1)) = point_on_plane(point_on_plane(X1)) )
| ~ plane(X1)
| ~ point(X0)
| ~ plane(point_on_plane(X1))
| ~ line(point_on_plane(X1))
| ~ on(X0,X1)
| ~ on(X0,point_on_plane(X1)) ),
inference(superposition,[status(thm)],[c_6875,c_6101]) ).
tcf(c_6898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X2 )
| ( point_2_on_line(plane_for_points(X0,X1,X2)) = point_on_plane(plane_for_points(X0,X1,X2)) )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(plane_for_points(X0,X1,X2))
| ~ on(plane_for_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_6875,c_2916]) ).
tcf(c_6899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X0 )
| ( point_2_on_line(line_through_3_points(X0,X1,X2)) = point_on_plane(line_through_3_points(X0,X1,X2)) )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(line_through_3_points(X0,X1,X2))
| ~ on(line_through_3_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_6875,c_2917]) ).
tcf(c_7035,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( point_on_plane(X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ on(a_line,X0)
| ~ on(point_on_plane(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_5848,c_104,c_5848]) ).
tcf(c_7078,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ( line_from_to(X0,point1) = point1 )
| ( point_1_on_line(line_from_to(X0,point1)) = point_on_plane(line_from_to(X0,point1)) )
| ~ point(point1)
| ~ point(X0)
| ~ plane(line_from_to(X0,point1))
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),a_line) ),
inference(superposition,[status(thm)],[c_92,c_6733]) ).
tcf(c_7079,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point1) = a_line )
| ( plane_for_points(X0,X1,point1) = point1 )
| ( point_1_on_line(plane_for_points(X0,X1,point1)) = point_on_plane(plane_for_points(X0,X1,point1)) )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,X1,point1))
| ~ line(plane_for_points(X0,X1,point1))
| ~ point(plane_for_points(X0,X1,point1))
| ~ on(plane_for_points(X0,X1,point1),a_line) ),
inference(superposition,[status(thm)],[c_109,c_6733]) ).
tcf(c_7080,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(point1,X0,X1) = a_line )
| ( line_through_3_points(point1,X0,X1) = point1 )
| ( point_1_on_line(line_through_3_points(point1,X0,X1)) = point_on_plane(line_through_3_points(point1,X0,X1)) )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(point1,X0,X1)
| ~ plane(line_through_3_points(point1,X0,X1))
| ~ line(line_through_3_points(point1,X0,X1))
| ~ point(line_through_3_points(point1,X0,X1))
| ~ on(line_through_3_points(point1,X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_117,c_6733]) ).
tcf(c_7081,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point1,X1) = a_line )
| ( line_through_3_points(X0,point1,X1) = point1 )
| ( point_1_on_line(line_through_3_points(X0,point1,X1)) = point_on_plane(line_through_3_points(X0,point1,X1)) )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,point1,X1)
| ~ plane(line_through_3_points(X0,point1,X1))
| ~ line(line_through_3_points(X0,point1,X1))
| ~ point(line_through_3_points(X0,point1,X1))
| ~ on(line_through_3_points(X0,point1,X1),a_line) ),
inference(superposition,[status(thm)],[c_118,c_6733]) ).
tcf(c_7082,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point1) = a_line )
| ( line_through_3_points(X0,X1,point1) = point1 )
| ( point_1_on_line(line_through_3_points(X0,X1,point1)) = point_on_plane(line_through_3_points(X0,X1,point1)) )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,point1)
| ~ plane(line_through_3_points(X0,X1,point1))
| ~ line(line_through_3_points(X0,X1,point1))
| ~ point(line_through_3_points(X0,X1,point1))
| ~ on(line_through_3_points(X0,X1,point1),a_line) ),
inference(superposition,[status(thm)],[c_119,c_6733]) ).
tcf(c_7083,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ( line_from_to(point1,X0) = point1 )
| ( point_1_on_line(line_from_to(point1,X0)) = point_on_plane(line_from_to(point1,X0)) )
| ~ point(point1)
| ~ point(X0)
| ~ plane(line_from_to(point1,X0))
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),a_line) ),
inference(superposition,[status(thm)],[c_91,c_6733]) ).
tcf(c_7084,plain,
! [X0: $i,X1: $i] :
( collinear(point1,X0,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(point1,X0,X1) = a_line )
| ( plane_for_points(point1,X0,X1) = point1 )
| ( point_1_on_line(plane_for_points(point1,X0,X1)) = point_on_plane(plane_for_points(point1,X0,X1)) )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(point1,X0,X1))
| ~ line(plane_for_points(point1,X0,X1))
| ~ point(plane_for_points(point1,X0,X1))
| ~ on(plane_for_points(point1,X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_107,c_6733]) ).
tcf(c_7085,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point1,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(X0,point1,X1) = a_line )
| ( plane_for_points(X0,point1,X1) = point1 )
| ( point_1_on_line(plane_for_points(X0,point1,X1)) = point_on_plane(plane_for_points(X0,point1,X1)) )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,point1,X1))
| ~ line(plane_for_points(X0,point1,X1))
| ~ point(plane_for_points(X0,point1,X1))
| ~ on(plane_for_points(X0,point1,X1),a_line) ),
inference(superposition,[status(thm)],[c_108,c_6733]) ).
tcf(c_7088,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ( line_from_to(point1,X0) = point1 )
| ( point_1_on_line(line_from_to(point1,X0)) = point_on_plane(line_from_to(point1,X0)) )
| ~ point(X0)
| ~ plane(line_from_to(point1,X0))
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7083,c_122]) ).
tcf(c_7098,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ( line_from_to(X0,point1) = point1 )
| ( point_1_on_line(line_from_to(X0,point1)) = point_on_plane(line_from_to(X0,point1)) )
| ~ point(X0)
| ~ plane(line_from_to(X0,point1))
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7078,c_122]) ).
tcf(c_7108,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point1,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(X0,point1,X1) = a_line )
| ( plane_for_points(X0,point1,X1) = point1 )
| ( point_1_on_line(plane_for_points(X0,point1,X1)) = point_on_plane(plane_for_points(X0,point1,X1)) )
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,point1,X1))
| ~ line(plane_for_points(X0,point1,X1))
| ~ point(plane_for_points(X0,point1,X1))
| ~ on(plane_for_points(X0,point1,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7085,c_122]) ).
tcf(c_7122,plain,
! [X0: $i,X1: $i] :
( collinear(point1,X0,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(point1,X0,X1) = a_line )
| ( plane_for_points(point1,X0,X1) = point1 )
| ( point_1_on_line(plane_for_points(point1,X0,X1)) = point_on_plane(plane_for_points(point1,X0,X1)) )
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(point1,X0,X1))
| ~ line(plane_for_points(point1,X0,X1))
| ~ point(plane_for_points(point1,X0,X1))
| ~ on(plane_for_points(point1,X0,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7084,c_122]) ).
tcf(c_7136,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point1) = a_line )
| ( plane_for_points(X0,X1,point1) = point1 )
| ( point_1_on_line(plane_for_points(X0,X1,point1)) = point_on_plane(plane_for_points(X0,X1,point1)) )
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,X1,point1))
| ~ line(plane_for_points(X0,X1,point1))
| ~ point(plane_for_points(X0,X1,point1))
| ~ on(plane_for_points(X0,X1,point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7079,c_122]) ).
tcf(c_7150,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point1) = a_line )
| ( line_through_3_points(X0,X1,point1) = point1 )
| ( point_1_on_line(line_through_3_points(X0,X1,point1)) = point_on_plane(line_through_3_points(X0,X1,point1)) )
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,point1)
| ~ plane(line_through_3_points(X0,X1,point1))
| ~ line(line_through_3_points(X0,X1,point1))
| ~ point(line_through_3_points(X0,X1,point1))
| ~ on(line_through_3_points(X0,X1,point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7082,c_122]) ).
tcf(c_7164,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point1,X1) = a_line )
| ( line_through_3_points(X0,point1,X1) = point1 )
| ( point_1_on_line(line_through_3_points(X0,point1,X1)) = point_on_plane(line_through_3_points(X0,point1,X1)) )
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,point1,X1)
| ~ plane(line_through_3_points(X0,point1,X1))
| ~ line(line_through_3_points(X0,point1,X1))
| ~ point(line_through_3_points(X0,point1,X1))
| ~ on(line_through_3_points(X0,point1,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7081,c_122]) ).
tcf(c_7178,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(point1,X0,X1) = a_line )
| ( line_through_3_points(point1,X0,X1) = point1 )
| ( point_1_on_line(line_through_3_points(point1,X0,X1)) = point_on_plane(line_through_3_points(point1,X0,X1)) )
| ~ point(X1)
| ~ point(X0)
| ~ collinear(point1,X0,X1)
| ~ plane(line_through_3_points(point1,X0,X1))
| ~ line(line_through_3_points(point1,X0,X1))
| ~ point(line_through_3_points(point1,X0,X1))
| ~ on(line_through_3_points(point1,X0,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7080,c_122]) ).
tcf(c_7208,plain,
( ( point1 = a_line )
| ( point1 = point2 )
| ( point_1_on_line(point1) = point_on_plane(point1) )
| ~ plane(point1)
| ~ line(point1)
| ~ point(point1)
| ~ on(point2,point1) ),
inference(superposition,[status(thm)],[c_126,c_6734]) ).
tcf(c_7210,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(point_1_on_line(a_line)) = point_on_plane(point_1_on_line(a_line)) )
| ~ line(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(point2,point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_95,c_6734]) ).
tcf(c_7211,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( point_1_on_line(point_2_on_line(a_line)) = point_on_plane(point_2_on_line(a_line)) )
| ~ line(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(point2,point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_96,c_6734]) ).
tcf(c_7212,plain,
( ( point_on_plane(a_line) = a_line )
| ( point_on_plane(a_line) = point2 )
| ( point_1_on_line(point_on_plane(a_line)) = point_on_plane(point_on_plane(a_line)) )
| ~ plane(a_line)
| ~ plane(point_on_plane(a_line))
| ~ line(point_on_plane(a_line))
| ~ point(point_on_plane(a_line))
| ~ on(point2,point_on_plane(a_line)) ),
inference(superposition,[status(thm)],[c_103,c_6734]) ).
tcf(c_7213,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = a_line )
| ( common_point_on_planes(a_line,X0,X1) = point2 )
| ( point_1_on_line(common_point_on_planes(a_line,X0,X1)) = point_on_plane(common_point_on_planes(a_line,X0,X1)) )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(a_line,X0,X1))
| ~ line(common_point_on_planes(a_line,X0,X1))
| ~ point(common_point_on_planes(a_line,X0,X1))
| ~ on(point2,common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_6734]) ).
tcf(c_7214,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = a_line )
| ( common_point_on_planes(X0,a_line,X1) = point2 )
| ( point_1_on_line(common_point_on_planes(X0,a_line,X1)) = point_on_plane(common_point_on_planes(X0,a_line,X1)) )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(X0,a_line,X1))
| ~ line(common_point_on_planes(X0,a_line,X1))
| ~ point(common_point_on_planes(X0,a_line,X1))
| ~ on(point2,common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_6734]) ).
tcf(c_7218,plain,
( ( point1 = a_line )
| ( point_1_on_line(point1) = point_on_plane(point1) )
| ~ plane(point1)
| ~ line(point1)
| ~ on(point2,point1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7208,c_129,c_122]) ).
tcf(c_7232,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( point_1_on_line(point_2_on_line(a_line)) = point_on_plane(point_2_on_line(a_line)) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(point2,point_2_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7211,c_125]) ).
tcf(c_7240,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(point_1_on_line(a_line)) = point_on_plane(point_1_on_line(a_line)) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(point2,point_1_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7210,c_125]) ).
tcf(c_7322,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ( line_from_to(X0,point1) = point1 )
| ( point_2_on_line(line_from_to(X0,point1)) = point_on_plane(line_from_to(X0,point1)) )
| ~ point(point1)
| ~ point(X0)
| ~ plane(line_from_to(X0,point1))
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),a_line) ),
inference(superposition,[status(thm)],[c_92,c_6893]) ).
tcf(c_7323,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point1) = a_line )
| ( plane_for_points(X0,X1,point1) = point1 )
| ( point_2_on_line(plane_for_points(X0,X1,point1)) = point_on_plane(plane_for_points(X0,X1,point1)) )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,X1,point1))
| ~ line(plane_for_points(X0,X1,point1))
| ~ point(plane_for_points(X0,X1,point1))
| ~ on(plane_for_points(X0,X1,point1),a_line) ),
inference(superposition,[status(thm)],[c_109,c_6893]) ).
tcf(c_7324,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(point1,X0,X1) = a_line )
| ( line_through_3_points(point1,X0,X1) = point1 )
| ( point_2_on_line(line_through_3_points(point1,X0,X1)) = point_on_plane(line_through_3_points(point1,X0,X1)) )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(point1,X0,X1)
| ~ plane(line_through_3_points(point1,X0,X1))
| ~ line(line_through_3_points(point1,X0,X1))
| ~ point(line_through_3_points(point1,X0,X1))
| ~ on(line_through_3_points(point1,X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_117,c_6893]) ).
tcf(c_7325,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point1,X1) = a_line )
| ( line_through_3_points(X0,point1,X1) = point1 )
| ( point_2_on_line(line_through_3_points(X0,point1,X1)) = point_on_plane(line_through_3_points(X0,point1,X1)) )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,point1,X1)
| ~ plane(line_through_3_points(X0,point1,X1))
| ~ line(line_through_3_points(X0,point1,X1))
| ~ point(line_through_3_points(X0,point1,X1))
| ~ on(line_through_3_points(X0,point1,X1),a_line) ),
inference(superposition,[status(thm)],[c_118,c_6893]) ).
tcf(c_7326,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point1) = a_line )
| ( line_through_3_points(X0,X1,point1) = point1 )
| ( point_2_on_line(line_through_3_points(X0,X1,point1)) = point_on_plane(line_through_3_points(X0,X1,point1)) )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,point1)
| ~ plane(line_through_3_points(X0,X1,point1))
| ~ line(line_through_3_points(X0,X1,point1))
| ~ point(line_through_3_points(X0,X1,point1))
| ~ on(line_through_3_points(X0,X1,point1),a_line) ),
inference(superposition,[status(thm)],[c_119,c_6893]) ).
tcf(c_7327,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ( line_from_to(point1,X0) = point1 )
| ( point_2_on_line(line_from_to(point1,X0)) = point_on_plane(line_from_to(point1,X0)) )
| ~ point(point1)
| ~ point(X0)
| ~ plane(line_from_to(point1,X0))
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),a_line) ),
inference(superposition,[status(thm)],[c_91,c_6893]) ).
tcf(c_7328,plain,
! [X0: $i,X1: $i] :
( collinear(point1,X0,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(point1,X0,X1) = a_line )
| ( plane_for_points(point1,X0,X1) = point1 )
| ( point_2_on_line(plane_for_points(point1,X0,X1)) = point_on_plane(plane_for_points(point1,X0,X1)) )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(point1,X0,X1))
| ~ line(plane_for_points(point1,X0,X1))
| ~ point(plane_for_points(point1,X0,X1))
| ~ on(plane_for_points(point1,X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_107,c_6893]) ).
tcf(c_7329,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point1,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(X0,point1,X1) = a_line )
| ( plane_for_points(X0,point1,X1) = point1 )
| ( point_2_on_line(plane_for_points(X0,point1,X1)) = point_on_plane(plane_for_points(X0,point1,X1)) )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,point1,X1))
| ~ line(plane_for_points(X0,point1,X1))
| ~ point(plane_for_points(X0,point1,X1))
| ~ on(plane_for_points(X0,point1,X1),a_line) ),
inference(superposition,[status(thm)],[c_108,c_6893]) ).
tcf(c_7332,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ( line_from_to(point1,X0) = point1 )
| ( point_2_on_line(line_from_to(point1,X0)) = point_on_plane(line_from_to(point1,X0)) )
| ~ point(X0)
| ~ plane(line_from_to(point1,X0))
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7327,c_122]) ).
tcf(c_7342,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ( line_from_to(X0,point1) = point1 )
| ( point_2_on_line(line_from_to(X0,point1)) = point_on_plane(line_from_to(X0,point1)) )
| ~ point(X0)
| ~ plane(line_from_to(X0,point1))
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7322,c_122]) ).
tcf(c_7352,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point1,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(X0,point1,X1) = a_line )
| ( plane_for_points(X0,point1,X1) = point1 )
| ( point_2_on_line(plane_for_points(X0,point1,X1)) = point_on_plane(plane_for_points(X0,point1,X1)) )
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,point1,X1))
| ~ line(plane_for_points(X0,point1,X1))
| ~ point(plane_for_points(X0,point1,X1))
| ~ on(plane_for_points(X0,point1,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7329,c_122]) ).
tcf(c_7366,plain,
! [X0: $i,X1: $i] :
( collinear(point1,X0,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(point1,X0,X1) = a_line )
| ( plane_for_points(point1,X0,X1) = point1 )
| ( point_2_on_line(plane_for_points(point1,X0,X1)) = point_on_plane(plane_for_points(point1,X0,X1)) )
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(point1,X0,X1))
| ~ line(plane_for_points(point1,X0,X1))
| ~ point(plane_for_points(point1,X0,X1))
| ~ on(plane_for_points(point1,X0,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7328,c_122]) ).
tcf(c_7380,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point1) = a_line )
| ( plane_for_points(X0,X1,point1) = point1 )
| ( point_2_on_line(plane_for_points(X0,X1,point1)) = point_on_plane(plane_for_points(X0,X1,point1)) )
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,X1,point1))
| ~ line(plane_for_points(X0,X1,point1))
| ~ point(plane_for_points(X0,X1,point1))
| ~ on(plane_for_points(X0,X1,point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7323,c_122]) ).
tcf(c_7394,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point1) = a_line )
| ( line_through_3_points(X0,X1,point1) = point1 )
| ( point_2_on_line(line_through_3_points(X0,X1,point1)) = point_on_plane(line_through_3_points(X0,X1,point1)) )
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,point1)
| ~ plane(line_through_3_points(X0,X1,point1))
| ~ line(line_through_3_points(X0,X1,point1))
| ~ point(line_through_3_points(X0,X1,point1))
| ~ on(line_through_3_points(X0,X1,point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7326,c_122]) ).
tcf(c_7408,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point1,X1) = a_line )
| ( line_through_3_points(X0,point1,X1) = point1 )
| ( point_2_on_line(line_through_3_points(X0,point1,X1)) = point_on_plane(line_through_3_points(X0,point1,X1)) )
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,point1,X1)
| ~ plane(line_through_3_points(X0,point1,X1))
| ~ line(line_through_3_points(X0,point1,X1))
| ~ point(line_through_3_points(X0,point1,X1))
| ~ on(line_through_3_points(X0,point1,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7325,c_122]) ).
tcf(c_7422,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(point1,X0,X1) = a_line )
| ( line_through_3_points(point1,X0,X1) = point1 )
| ( point_2_on_line(line_through_3_points(point1,X0,X1)) = point_on_plane(line_through_3_points(point1,X0,X1)) )
| ~ point(X1)
| ~ point(X0)
| ~ collinear(point1,X0,X1)
| ~ plane(line_through_3_points(point1,X0,X1))
| ~ line(line_through_3_points(point1,X0,X1))
| ~ point(line_through_3_points(point1,X0,X1))
| ~ on(line_through_3_points(point1,X0,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7324,c_122]) ).
tcf(c_7482,plain,
( ( point1 = a_line )
| ( point1 = point2 )
| ( point_2_on_line(point1) = point_on_plane(point1) )
| ~ plane(point1)
| ~ line(point1)
| ~ point(point1)
| ~ on(point2,point1) ),
inference(superposition,[status(thm)],[c_126,c_6894]) ).
tcf(c_7484,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( point_2_on_line(point_1_on_line(a_line)) = point_on_plane(point_1_on_line(a_line)) )
| ~ line(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(point2,point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_95,c_6894]) ).
tcf(c_7485,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(point_2_on_line(a_line)) = point_on_plane(point_2_on_line(a_line)) )
| ~ line(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(point2,point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_96,c_6894]) ).
tcf(c_7486,plain,
( ( point_on_plane(a_line) = a_line )
| ( point_on_plane(a_line) = point2 )
| ( point_2_on_line(point_on_plane(a_line)) = point_on_plane(point_on_plane(a_line)) )
| ~ plane(a_line)
| ~ plane(point_on_plane(a_line))
| ~ line(point_on_plane(a_line))
| ~ point(point_on_plane(a_line))
| ~ on(point2,point_on_plane(a_line)) ),
inference(superposition,[status(thm)],[c_103,c_6894]) ).
tcf(c_7487,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = a_line )
| ( common_point_on_planes(a_line,X0,X1) = point2 )
| ( point_2_on_line(common_point_on_planes(a_line,X0,X1)) = point_on_plane(common_point_on_planes(a_line,X0,X1)) )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(a_line,X0,X1))
| ~ line(common_point_on_planes(a_line,X0,X1))
| ~ point(common_point_on_planes(a_line,X0,X1))
| ~ on(point2,common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_6894]) ).
tcf(c_7488,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = a_line )
| ( common_point_on_planes(X0,a_line,X1) = point2 )
| ( point_2_on_line(common_point_on_planes(X0,a_line,X1)) = point_on_plane(common_point_on_planes(X0,a_line,X1)) )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(X0,a_line,X1))
| ~ line(common_point_on_planes(X0,a_line,X1))
| ~ point(common_point_on_planes(X0,a_line,X1))
| ~ on(point2,common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_6894]) ).
tcf(c_7492,plain,
( ( point1 = a_line )
| ( point_2_on_line(point1) = point_on_plane(point1) )
| ~ plane(point1)
| ~ line(point1)
| ~ on(point2,point1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7482,c_129,c_122]) ).
tcf(c_7506,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(point_2_on_line(a_line)) = point_on_plane(point_2_on_line(a_line)) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(point2,point_2_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7485,c_125]) ).
tcf(c_7514,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( point_2_on_line(point_1_on_line(a_line)) = point_on_plane(point_1_on_line(a_line)) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(point2,point_1_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7484,c_125]) ).
tcf(c_7578,plain,
( ( point1 = a_line )
| ( point_1_on_line(point1) = point_on_plane(point1) )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(a_line)
| ~ point(point1)
| ~ on(a_line,point1) ),
inference(superposition,[status(thm)],[c_126,c_6730]) ).
tcf(c_7579,plain,
( ( point2 = a_line )
| ( point_1_on_line(point2) = point_on_plane(point2) )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(a_line)
| ~ point(point2)
| ~ on(a_line,point2) ),
inference(superposition,[status(thm)],[c_127,c_6730]) ).
tcf(c_7580,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(point_1_on_line(a_line)) = point_on_plane(point_1_on_line(a_line)) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(a_line,point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_95,c_6730]) ).
tcf(c_7581,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_1_on_line(point_2_on_line(a_line)) = point_on_plane(point_2_on_line(a_line)) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(a_line,point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_96,c_6730]) ).
tcf(c_7582,plain,
( ( point_on_plane(a_line) = a_line )
| ( point_1_on_line(point_on_plane(a_line)) = point_on_plane(point_on_plane(a_line)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_on_plane(a_line))
| ~ line(point_on_plane(a_line))
| ~ point(point_on_plane(a_line))
| ~ on(a_line,point_on_plane(a_line)) ),
inference(superposition,[status(thm)],[c_103,c_6730]) ).
tcf(c_7583,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = a_line )
| ( point_1_on_line(common_point_on_planes(a_line,X0,X1)) = point_on_plane(common_point_on_planes(a_line,X0,X1)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(a_line,X0,X1))
| ~ line(common_point_on_planes(a_line,X0,X1))
| ~ point(common_point_on_planes(a_line,X0,X1))
| ~ on(a_line,common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_6730]) ).
tcf(c_7584,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = a_line )
| ( point_1_on_line(common_point_on_planes(X0,a_line,X1)) = point_on_plane(common_point_on_planes(X0,a_line,X1)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(X0,a_line,X1))
| ~ line(common_point_on_planes(X0,a_line,X1))
| ~ point(common_point_on_planes(X0,a_line,X1))
| ~ on(a_line,common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_6730]) ).
tcf(c_7588,plain,
( ( point2 = a_line )
| ( point_1_on_line(point2) = point_on_plane(point2) )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(a_line)
| ~ on(a_line,point2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7579,c_123]) ).
tcf(c_7596,plain,
( ( point1 = a_line )
| ( point_1_on_line(point1) = point_on_plane(point1) )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(a_line)
| ~ on(a_line,point1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7578,c_122]) ).
tcf(c_7612,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_1_on_line(point_2_on_line(a_line)) = point_on_plane(point_2_on_line(a_line)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(a_line,point_2_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7581,c_125]) ).
tcf(c_7621,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(point_1_on_line(a_line)) = point_on_plane(point_1_on_line(a_line)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(a_line,point_1_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7580,c_125]) ).
tcf(c_8075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(point_1_on_line(line_through_3_points(X0,X1,X2)))
| ~ on(point_1_on_line(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_95,c_2918]) ).
tcf(c_8076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_2_on_line(line_through_3_points(X0,X1,X2)) = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(point_2_on_line(line_through_3_points(X0,X1,X2)))
| ~ on(point_2_on_line(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_96,c_2918]) ).
tcf(c_8077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_on_plane(line_through_3_points(X0,X1,X2)) = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ point(point_on_plane(line_through_3_points(X0,X1,X2)))
| ~ on(point_on_plane(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_103,c_2918]) ).
tcf(c_8080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X1,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_119,c_2918]) ).
tcf(c_8081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( on(X5,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4) = X1 )
| ~ plane(X3)
| ~ line(X5)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X1,X5)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ point(common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4))
| ~ on(common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_113,c_2918]) ).
tcf(c_8082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( on(X5,line_through_3_points(X1,X2,X3))
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,X3) = X0 )
| ( common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4) = X2 )
| ~ plane(X0)
| ~ line(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X4,X0)
| ~ on(X2,X5)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X4,line_through_3_points(X1,X2,X3))
| ~ point(common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4))
| ~ on(common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_114,c_2918]) ).
tcf(c_8083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X1 )
| ( point_2_on_line(line_through_3_points(X0,X1,X2)) = point_on_plane(line_through_3_points(X0,X1,X2)) )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(line_through_3_points(X0,X1,X2))
| ~ on(line_through_3_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_6875,c_2918]) ).
tcf(c_8084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X1 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = point_on_plane(line_through_3_points(X0,X1,X2)) )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(line_through_3_points(X0,X1,X2))
| ~ on(line_through_3_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_6715,c_2918]) ).
tcf(c_8225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X1 )
| ( line_from_to(X0,X1) = X3 )
| ( line_from_to(X0,X1) = X2 )
| ( point_on_plane(line_from_to(X0,X1)) = X1 )
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X2)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1))
| ~ on(X3,line_from_to(X0,X1))
| ~ on(line_from_to(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6397,c_94]) ).
tcf(c_8226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,line_from_to(X0,X1),X3)
| ( X3 = X4 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = X4 )
| ( line_from_to(X0,X1) = X3 )
| ( line_from_to(X0,X1) = X2 )
| ( point_on_plane(line_from_to(X0,X1)) = X1 )
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1))
| ~ on(X4,line_from_to(X0,X1))
| ~ on(X3,line_from_to(X0,X1))
| ~ on(line_from_to(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6397,c_111]) ).
tcf(c_8227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,line_from_to(X0,X1))
| ( X0 = X1 )
| ( line_from_to(X0,X1) = X3 )
| ( point_on_plane(line_from_to(X0,X1)) = X1 )
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X2)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1))
| ~ on(X3,line_from_to(X0,X1))
| ~ on(line_from_to(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6397,c_112]) ).
tcf(c_8228,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X0,X1),line_from_to(X0,X1))
| ( X0 = X1 )
| ( point_on_plane(line_from_to(X0,X1)) = X1 )
| ( point_on_plane(line_from_to(X0,X1)) = line_from_to(X0,X1) )
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_6397,c_6119]) ).
tcf(c_8229,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ( point_on_plane(line_from_to(X0,X1)) = X1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1))
| ~ on(a_line,line_from_to(X0,X1))
| ~ on(line_from_to(X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_6397,c_3720]) ).
tcf(c_8232,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ( line_from_to(X0,X1) = point1 )
| ( point_on_plane(line_from_to(X0,X1)) = X1 )
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1))
| ~ on(point1,line_from_to(X0,X1))
| ~ on(line_from_to(X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_6397,c_3712]) ).
tcf(c_8233,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ( line_from_to(X0,X1) = point2 )
| ( point_on_plane(line_from_to(X0,X1)) = X1 )
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1))
| ~ on(point2,line_from_to(X0,X1))
| ~ on(line_from_to(X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_6397,c_3704]) ).
tcf(c_8234,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_from_to(X1,X2),X0)
| ( X1 = X2 )
| ( X0 = X3 )
| ( line_from_to(X1,X2) = X3 )
| ( line_from_to(X1,X2) = X0 )
| ( point_on_plane(line_from_to(X1,X2)) = X2 )
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X1,X2))
| ~ line(line_from_to(X1,X2))
| ~ point(line_from_to(X1,X2))
| ~ on(X3,line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_6397,c_121]) ).
tcf(c_8356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X1 )
| ( line_from_to(X0,X1) = X3 )
| ( line_from_to(X0,X1) = X2 )
| ( point_on_plane(line_from_to(X0,X1)) = X0 )
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X2)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1))
| ~ on(X3,line_from_to(X0,X1))
| ~ on(line_from_to(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6405,c_94]) ).
tcf(c_8357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,line_from_to(X0,X1),X3)
| ( X3 = X4 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = X4 )
| ( line_from_to(X0,X1) = X3 )
| ( line_from_to(X0,X1) = X2 )
| ( point_on_plane(line_from_to(X0,X1)) = X0 )
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1))
| ~ on(X4,line_from_to(X0,X1))
| ~ on(X3,line_from_to(X0,X1))
| ~ on(line_from_to(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6405,c_111]) ).
tcf(c_8358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,line_from_to(X0,X1))
| ( X0 = X1 )
| ( line_from_to(X0,X1) = X3 )
| ( point_on_plane(line_from_to(X0,X1)) = X0 )
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X2)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1))
| ~ on(X3,line_from_to(X0,X1))
| ~ on(line_from_to(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6405,c_112]) ).
tcf(c_8359,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X0,X1),line_from_to(X0,X1))
| ( X0 = X1 )
| ( point_on_plane(line_from_to(X0,X1)) = X0 )
| ( point_on_plane(line_from_to(X0,X1)) = line_from_to(X0,X1) )
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_6405,c_6119]) ).
tcf(c_8360,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ( point_on_plane(line_from_to(X0,X1)) = X0 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1))
| ~ on(a_line,line_from_to(X0,X1))
| ~ on(line_from_to(X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_6405,c_3720]) ).
tcf(c_8363,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ( line_from_to(X0,X1) = point1 )
| ( point_on_plane(line_from_to(X0,X1)) = X0 )
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1))
| ~ on(point1,line_from_to(X0,X1))
| ~ on(line_from_to(X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_6405,c_3712]) ).
tcf(c_8364,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ( line_from_to(X0,X1) = point2 )
| ( point_on_plane(line_from_to(X0,X1)) = X0 )
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1))
| ~ on(point2,line_from_to(X0,X1))
| ~ on(line_from_to(X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_6405,c_3704]) ).
tcf(c_8365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_from_to(X1,X2),X0)
| ( X1 = X2 )
| ( X0 = X3 )
| ( line_from_to(X1,X2) = X3 )
| ( line_from_to(X1,X2) = X0 )
| ( point_on_plane(line_from_to(X1,X2)) = X1 )
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X1,X2))
| ~ line(line_from_to(X1,X2))
| ~ point(line_from_to(X1,X2))
| ~ on(X3,line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_6405,c_121]) ).
tcf(c_8501,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ( point_1_on_line(X0) = X2 )
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ on(point_1_on_line(X0),X1)
| ~ on(X2,X0)
| ~ on(X2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_3691,c_97,c_3691]) ).
tcf(c_8502,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ( point_1_on_line(X0) = X2 )
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_1_on_line(X0),X1) ),
inference(renaming,[status(thm)],[c_8501]) ).
tcf(c_8519,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( point_1_on_line(X2) = X1 )
| ( point_1_on_line(X2) = X0 )
| ( line_from_to(X1,point_1_on_line(X2)) = X2 )
| ~ line(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X2))
| ~ on(X0,X2)
| ~ line(line_from_to(X1,point_1_on_line(X2)))
| ~ on(X0,line_from_to(X1,point_1_on_line(X2))) ),
inference(superposition,[status(thm)],[c_92,c_8502]) ).
tcf(c_8521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,X2,point_1_on_line(X3))
| ( X1 = X2 )
| ( point_1_on_line(X3) = X2 )
| ( point_1_on_line(X3) = X1 )
| ( point_1_on_line(X3) = X0 )
| ( plane_for_points(X1,X2,point_1_on_line(X3)) = X3 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X3))
| ~ on(X0,X3)
| ~ line(plane_for_points(X1,X2,point_1_on_line(X3)))
| ~ on(X0,plane_for_points(X1,X2,point_1_on_line(X3))) ),
inference(superposition,[status(thm)],[c_109,c_8502]) ).
tcf(c_8522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( point_1_on_line(X1) = X3 )
| ( point_1_on_line(X1) = X2 )
| ( point_1_on_line(X1) = X0 )
| ( line_through_3_points(point_1_on_line(X1),X2,X3) = X1 )
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ collinear(point_1_on_line(X1),X2,X3)
| ~ line(line_through_3_points(point_1_on_line(X1),X2,X3))
| ~ on(X0,line_through_3_points(point_1_on_line(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_8502]) ).
tcf(c_8523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( point_1_on_line(X2) = X3 )
| ( point_1_on_line(X2) = X1 )
| ( point_1_on_line(X2) = X0 )
| ( line_through_3_points(X1,point_1_on_line(X2),X3) = X2 )
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X2))
| ~ on(X0,X2)
| ~ collinear(X1,point_1_on_line(X2),X3)
| ~ line(line_through_3_points(X1,point_1_on_line(X2),X3))
| ~ on(X0,line_through_3_points(X1,point_1_on_line(X2),X3)) ),
inference(superposition,[status(thm)],[c_118,c_8502]) ).
tcf(c_8524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( point_1_on_line(X3) = X2 )
| ( point_1_on_line(X3) = X1 )
| ( point_1_on_line(X3) = X0 )
| ( line_through_3_points(X1,X2,point_1_on_line(X3)) = X3 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X3))
| ~ on(X0,X3)
| ~ collinear(X1,X2,point_1_on_line(X3))
| ~ line(line_through_3_points(X1,X2,point_1_on_line(X3)))
| ~ on(X0,line_through_3_points(X1,X2,point_1_on_line(X3))) ),
inference(superposition,[status(thm)],[c_119,c_8502]) ).
tcf(c_8525,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( point_1_on_line(X1) = X2 )
| ( point_1_on_line(X1) = X0 )
| ( line_from_to(point_1_on_line(X1),X2) = X1 )
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ line(line_from_to(point_1_on_line(X1),X2))
| ~ on(X0,line_from_to(point_1_on_line(X1),X2)) ),
inference(superposition,[status(thm)],[c_91,c_8502]) ).
tcf(c_8526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(point_1_on_line(X1),X2,X3)
| ( X2 = X3 )
| ( point_1_on_line(X1) = X3 )
| ( point_1_on_line(X1) = X2 )
| ( point_1_on_line(X1) = X0 )
| ( plane_for_points(point_1_on_line(X1),X2,X3) = X1 )
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ line(plane_for_points(point_1_on_line(X1),X2,X3))
| ~ on(X0,plane_for_points(point_1_on_line(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_8502]) ).
tcf(c_8527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,point_1_on_line(X2),X3)
| ( X1 = X3 )
| ( point_1_on_line(X2) = X3 )
| ( point_1_on_line(X2) = X1 )
| ( point_1_on_line(X2) = X0 )
| ( plane_for_points(X1,point_1_on_line(X2),X3) = X2 )
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X2))
| ~ on(X0,X2)
| ~ line(plane_for_points(X1,point_1_on_line(X2),X3))
| ~ on(X0,plane_for_points(X1,point_1_on_line(X2),X3)) ),
inference(superposition,[status(thm)],[c_108,c_8502]) ).
tcf(c_8528,plain,
! [X0: $i,X1: $i] :
( ( point_1_on_line(X1) = X1 )
| ( point_1_on_line(X1) = X0 )
| ( point_2_on_line(point_1_on_line(X1)) = point_on_plane(point_1_on_line(X1)) )
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_1_on_line(X1))
| ~ line(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_1_on_line(X1)) ),
inference(superposition,[status(thm)],[c_6875,c_8502]) ).
tcf(c_8529,plain,
! [X0: $i,X1: $i] :
( ( point_1_on_line(X1) = X1 )
| ( point_1_on_line(X1) = X0 )
| ( point_1_on_line(point_1_on_line(X1)) = point_on_plane(point_1_on_line(X1)) )
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_1_on_line(X1))
| ~ line(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_1_on_line(X1)) ),
inference(superposition,[status(thm)],[c_6715,c_8502]) ).
tcf(c_8656,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ( point_2_on_line(X0) = X2 )
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ on(point_2_on_line(X0),X1)
| ~ on(X2,X0)
| ~ on(X2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_3692,c_98,c_3692]) ).
tcf(c_8657,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ( point_2_on_line(X0) = X2 )
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_2_on_line(X0),X1) ),
inference(renaming,[status(thm)],[c_8656]) ).
tcf(c_8674,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( point_2_on_line(X2) = X1 )
| ( point_2_on_line(X2) = X0 )
| ( line_from_to(X1,point_2_on_line(X2)) = X2 )
| ~ line(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X2))
| ~ on(X0,X2)
| ~ line(line_from_to(X1,point_2_on_line(X2)))
| ~ on(X0,line_from_to(X1,point_2_on_line(X2))) ),
inference(superposition,[status(thm)],[c_92,c_8657]) ).
tcf(c_8676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,X2,point_2_on_line(X3))
| ( X1 = X2 )
| ( point_2_on_line(X3) = X2 )
| ( point_2_on_line(X3) = X1 )
| ( point_2_on_line(X3) = X0 )
| ( plane_for_points(X1,X2,point_2_on_line(X3)) = X3 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X3))
| ~ on(X0,X3)
| ~ line(plane_for_points(X1,X2,point_2_on_line(X3)))
| ~ on(X0,plane_for_points(X1,X2,point_2_on_line(X3))) ),
inference(superposition,[status(thm)],[c_109,c_8657]) ).
tcf(c_8677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( point_2_on_line(X1) = X3 )
| ( point_2_on_line(X1) = X2 )
| ( point_2_on_line(X1) = X0 )
| ( line_through_3_points(point_2_on_line(X1),X2,X3) = X1 )
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(X1))
| ~ on(X0,X1)
| ~ collinear(point_2_on_line(X1),X2,X3)
| ~ line(line_through_3_points(point_2_on_line(X1),X2,X3))
| ~ on(X0,line_through_3_points(point_2_on_line(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_8657]) ).
tcf(c_8678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( point_2_on_line(X2) = X3 )
| ( point_2_on_line(X2) = X1 )
| ( point_2_on_line(X2) = X0 )
| ( line_through_3_points(X1,point_2_on_line(X2),X3) = X2 )
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X2))
| ~ on(X0,X2)
| ~ collinear(X1,point_2_on_line(X2),X3)
| ~ line(line_through_3_points(X1,point_2_on_line(X2),X3))
| ~ on(X0,line_through_3_points(X1,point_2_on_line(X2),X3)) ),
inference(superposition,[status(thm)],[c_118,c_8657]) ).
tcf(c_8679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( point_2_on_line(X3) = X2 )
| ( point_2_on_line(X3) = X1 )
| ( point_2_on_line(X3) = X0 )
| ( line_through_3_points(X1,X2,point_2_on_line(X3)) = X3 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X3))
| ~ on(X0,X3)
| ~ collinear(X1,X2,point_2_on_line(X3))
| ~ line(line_through_3_points(X1,X2,point_2_on_line(X3)))
| ~ on(X0,line_through_3_points(X1,X2,point_2_on_line(X3))) ),
inference(superposition,[status(thm)],[c_119,c_8657]) ).
tcf(c_8680,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( point_2_on_line(X1) = X2 )
| ( point_2_on_line(X1) = X0 )
| ( line_from_to(point_2_on_line(X1),X2) = X1 )
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(X1))
| ~ on(X0,X1)
| ~ line(line_from_to(point_2_on_line(X1),X2))
| ~ on(X0,line_from_to(point_2_on_line(X1),X2)) ),
inference(superposition,[status(thm)],[c_91,c_8657]) ).
tcf(c_8681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(point_2_on_line(X1),X2,X3)
| ( X2 = X3 )
| ( point_2_on_line(X1) = X3 )
| ( point_2_on_line(X1) = X2 )
| ( point_2_on_line(X1) = X0 )
| ( plane_for_points(point_2_on_line(X1),X2,X3) = X1 )
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(X1))
| ~ on(X0,X1)
| ~ line(plane_for_points(point_2_on_line(X1),X2,X3))
| ~ on(X0,plane_for_points(point_2_on_line(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_8657]) ).
tcf(c_8682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,point_2_on_line(X2),X3)
| ( X1 = X3 )
| ( point_2_on_line(X2) = X3 )
| ( point_2_on_line(X2) = X1 )
| ( point_2_on_line(X2) = X0 )
| ( plane_for_points(X1,point_2_on_line(X2),X3) = X2 )
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X2))
| ~ on(X0,X2)
| ~ line(plane_for_points(X1,point_2_on_line(X2),X3))
| ~ on(X0,plane_for_points(X1,point_2_on_line(X2),X3)) ),
inference(superposition,[status(thm)],[c_108,c_8657]) ).
tcf(c_8683,plain,
! [X0: $i,X1: $i] :
( ( point_2_on_line(X1) = X1 )
| ( point_2_on_line(X1) = X0 )
| ( point_2_on_line(point_2_on_line(X1)) = point_on_plane(point_2_on_line(X1)) )
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_2_on_line(X1))
| ~ line(point_2_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_2_on_line(X1)) ),
inference(superposition,[status(thm)],[c_6875,c_8657]) ).
tcf(c_8684,plain,
! [X0: $i,X1: $i] :
( ( point_2_on_line(X1) = X1 )
| ( point_2_on_line(X1) = X0 )
| ( point_1_on_line(point_2_on_line(X1)) = point_on_plane(point_2_on_line(X1)) )
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_2_on_line(X1))
| ~ line(point_2_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_2_on_line(X1)) ),
inference(superposition,[status(thm)],[c_6715,c_8657]) ).
tcf(c_8829,plain,
( ( point1 = a_line )
| ( point_2_on_line(point1) = point_on_plane(point1) )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(a_line)
| ~ point(point1)
| ~ on(a_line,point1) ),
inference(superposition,[status(thm)],[c_126,c_6890]) ).
tcf(c_8830,plain,
( ( point2 = a_line )
| ( point_2_on_line(point2) = point_on_plane(point2) )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(a_line)
| ~ point(point2)
| ~ on(a_line,point2) ),
inference(superposition,[status(thm)],[c_127,c_6890]) ).
tcf(c_8831,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_2_on_line(point_1_on_line(a_line)) = point_on_plane(point_1_on_line(a_line)) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(a_line,point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_95,c_6890]) ).
tcf(c_8832,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(point_2_on_line(a_line)) = point_on_plane(point_2_on_line(a_line)) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(a_line,point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_96,c_6890]) ).
tcf(c_8833,plain,
( ( point_on_plane(a_line) = a_line )
| ( point_2_on_line(point_on_plane(a_line)) = point_on_plane(point_on_plane(a_line)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_on_plane(a_line))
| ~ line(point_on_plane(a_line))
| ~ point(point_on_plane(a_line))
| ~ on(a_line,point_on_plane(a_line)) ),
inference(superposition,[status(thm)],[c_103,c_6890]) ).
tcf(c_8834,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = a_line )
| ( point_2_on_line(common_point_on_planes(a_line,X0,X1)) = point_on_plane(common_point_on_planes(a_line,X0,X1)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(a_line,X0,X1))
| ~ line(common_point_on_planes(a_line,X0,X1))
| ~ point(common_point_on_planes(a_line,X0,X1))
| ~ on(a_line,common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_6890]) ).
tcf(c_8835,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = a_line )
| ( point_2_on_line(common_point_on_planes(X0,a_line,X1)) = point_on_plane(common_point_on_planes(X0,a_line,X1)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(X0,a_line,X1))
| ~ line(common_point_on_planes(X0,a_line,X1))
| ~ point(common_point_on_planes(X0,a_line,X1))
| ~ on(a_line,common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_6890]) ).
tcf(c_8839,plain,
( ( point2 = a_line )
| ( point_2_on_line(point2) = point_on_plane(point2) )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(a_line)
| ~ on(a_line,point2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8830,c_123]) ).
tcf(c_8847,plain,
( ( point1 = a_line )
| ( point_2_on_line(point1) = point_on_plane(point1) )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(a_line)
| ~ on(a_line,point1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8829,c_122]) ).
tcf(c_8863,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(point_2_on_line(a_line)) = point_on_plane(point_2_on_line(a_line)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(a_line,point_2_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8832,c_125]) ).
tcf(c_8872,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_2_on_line(point_1_on_line(a_line)) = point_on_plane(point_1_on_line(a_line)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(a_line,point_1_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8831,c_125]) ).
tcf(c_8934,plain,
! [X0: $i] :
( line(line_from_to(a_line,X0))
| ( X0 = a_line )
| ~ point(a_line)
| ~ point(X0) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_8950,plain,
! [X0: $i,X1: $i] :
( on(common_point_on_planes(a_line,X1,X0),X1)
| ( X1 = a_line )
| ~ plane(a_line)
| ~ plane(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_8952,plain,
! [X0: $i,X1: $i] :
( point(common_point_on_planes(a_line,X1,X0))
| ( X1 = a_line )
| ~ plane(a_line)
| ~ plane(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_8953,plain,
( point(common_point_on_planes(a_line,point1,point1))
| ( point1 = a_line )
| ~ plane(a_line)
| ~ plane(point1)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ on(point1,point1) ),
inference(instantiation,[status(thm)],[c_8952]) ).
tcf(c_8955,plain,
( on(common_point_on_planes(a_line,point1,point1),point1)
| ( point1 = a_line )
| ~ plane(a_line)
| ~ plane(point1)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ on(point1,point1) ),
inference(instantiation,[status(thm)],[c_8950]) ).
tcf(c_8959,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( a_line != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1802]) ).
tcf(c_8960,plain,
( ( point1 = a_line )
| ( a_line != point1 )
| ( point1 != point1 ) ),
inference(instantiation,[status(thm)],[c_8959]) ).
tcf(c_9006,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = a_line )
| ~ point(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_91,c_4200]) ).
tcf(c_9007,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = a_line )
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9006,c_123]) ).
tcf(c_9014,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = a_line )
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(global_subsumption_just,[status(thm)],[c_9007,c_123,c_6026,c_9007]) ).
tcf(c_9025,plain,
( ( point1 = point2 )
| ( line_from_to(point2,point1) = a_line )
| ~ point(point1) ),
inference(superposition,[status(thm)],[c_126,c_9014]) ).
tcf(c_9027,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = a_line )
| ~ line(a_line)
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_95,c_9014]) ).
tcf(c_9028,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = a_line )
| ~ line(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_96,c_9014]) ).
tcf(c_9029,plain,
( ( point_on_plane(a_line) = point2 )
| ( line_from_to(point2,point_on_plane(a_line)) = a_line )
| ~ plane(a_line)
| ~ point(point_on_plane(a_line)) ),
inference(superposition,[status(thm)],[c_103,c_9014]) ).
tcf(c_9030,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_9014]) ).
tcf(c_9031,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = point2 )
| ( line_from_to(point2,common_point_on_planes(X0,a_line,X1)) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_9014]) ).
tcf(c_9032,plain,
( ( point2 = a_line )
| ( line_from_to(point2,a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_3143,c_9014]) ).
tcf(c_9033,plain,
( ( point2 = a_line )
| ( point_2_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(point2,a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_6875,c_9014]) ).
tcf(c_9034,plain,
( ( point2 = a_line )
| ( point_1_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(point2,a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_6715,c_9014]) ).
tcf(c_9035,plain,
line_from_to(point2,point1) = a_line,
inference(forward_subsumption_resolution,[status(thm)],[c_9025,c_129,c_122]) ).
tcf(c_9044,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = a_line )
| ~ point(point_2_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9028,c_125]) ).
tcf(c_9048,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = a_line )
| ~ point(point_1_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9027,c_125]) ).
tcf(c_9052,plain,
( ( point2 = a_line )
| ( point_1_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(point2,a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9034,c_125]) ).
tcf(c_9058,plain,
( ( point2 = a_line )
| ( point_2_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(point2,a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9033,c_125]) ).
tcf(c_9085,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ( point_on_plane(line_from_to(point2,point1)) = point2 )
| ~ point(point2)
| ~ point(point1)
| ~ plane(line_from_to(point2,point1))
| ~ line(line_from_to(point2,point1)) ),
inference(superposition,[status(thm)],[c_9035,c_6405]) ).
tcf(c_9086,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ( point_on_plane(line_from_to(point2,point1)) = point1 )
| ~ point(point2)
| ~ point(point1)
| ~ plane(line_from_to(point2,point1))
| ~ line(line_from_to(point2,point1)) ),
inference(superposition,[status(thm)],[c_9035,c_6397]) ).
tcf(c_9090,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ( point_on_plane(a_line) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point2)
| ~ point(point1) ),
inference(light_normalisation,[status(thm)],[c_9086,c_9035]) ).
tcf(c_9092,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ( point_on_plane(a_line) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point2)
| ~ point(point1) ),
inference(light_normalisation,[status(thm)],[c_9085,c_9035]) ).
tcf(c_9102,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = a_line ) ),
inference(global_subsumption_just,[status(thm)],[c_9044,c_125,c_4353,c_9044]) ).
tcf(c_9109,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_2_on_line(a_line))) = point2 )
| ~ point(point2)
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point2,point_2_on_line(a_line)))
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_6405]) ).
tcf(c_9110,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_2_on_line(a_line))) = point_2_on_line(a_line) )
| ~ point(point2)
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point2,point_2_on_line(a_line)))
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_6397]) ).
tcf(c_9111,plain,
( on(point_2_on_line(a_line),a_line)
| ( point_2_on_line(a_line) = point2 )
| ~ point(point2)
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9102,c_92]) ).
tcf(c_9114,plain,
( on(point_2_on_line(a_line),a_line)
| ( point_2_on_line(a_line) = point2 )
| ~ point(point_2_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9111,c_123]) ).
tcf(c_9118,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_2_on_line(a_line))) = point2 )
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point2,point_2_on_line(a_line)))
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9109,c_123]) ).
tcf(c_9125,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_2_on_line(a_line))) = point_2_on_line(a_line) )
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point2,point_2_on_line(a_line)))
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9110,c_123]) ).
tcf(c_9364,plain,
on(point_2_on_line(a_line),a_line),
inference(global_subsumption_just,[status(thm)],[c_9114,c_125,c_4551]) ).
tcf(c_9366,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_2_on_line(a_line) = X1 )
| ~ line(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ point(point_2_on_line(a_line))
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ on(point_2_on_line(a_line),X0) ),
inference(superposition,[status(thm)],[c_9364,c_94]) ).
tcf(c_9367,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point_2_on_line(a_line),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X1 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X2)
| ~ point(X1)
| ~ point(point_2_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X2,X0)
| ~ on(X1,X0)
| ~ on(point_2_on_line(a_line),X0) ),
inference(superposition,[status(thm)],[c_9364,c_111]) ).
tcf(c_9368,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_2_on_line(a_line) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ point(point_2_on_line(a_line))
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ on(point_2_on_line(a_line),X0) ),
inference(superposition,[status(thm)],[c_9364,c_112]) ).
tcf(c_9369,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9364,c_6119]) ).
tcf(c_9375,plain,
! [X0: $i,X1: $i] :
( collinear(X1,point_2_on_line(a_line),X0)
| ( X0 = X1 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X1,a_line)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_9364,c_121]) ).
tcf(c_9389,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9369,c_125]) ).
tcf(c_9403,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_2_on_line(a_line) = X1 )
| ~ line(X0)
| ~ point(X1)
| ~ point(point_2_on_line(a_line))
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ on(point_2_on_line(a_line),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9366,c_125]) ).
tcf(c_9412,plain,
! [X0: $i,X1: $i] :
( collinear(X1,point_2_on_line(a_line),X0)
| ( X0 = X1 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X1,a_line)
| ~ on(X0,a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9375,c_125]) ).
tcf(c_9438,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = a_line ) ),
inference(global_subsumption_just,[status(thm)],[c_9048,c_125,c_4351,c_9048]) ).
tcf(c_9445,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_1_on_line(a_line))) = point2 )
| ~ point(point2)
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point2,point_1_on_line(a_line)))
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_6405]) ).
tcf(c_9446,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_1_on_line(a_line))) = point_1_on_line(a_line) )
| ~ point(point2)
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point2,point_1_on_line(a_line)))
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_6397]) ).
tcf(c_9447,plain,
( on(point_1_on_line(a_line),a_line)
| ( point_1_on_line(a_line) = point2 )
| ~ point(point2)
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9438,c_92]) ).
tcf(c_9450,plain,
( on(point_1_on_line(a_line),a_line)
| ( point_1_on_line(a_line) = point2 )
| ~ point(point_1_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9447,c_123]) ).
tcf(c_9454,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_1_on_line(a_line))) = point2 )
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point2,point_1_on_line(a_line)))
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9445,c_123]) ).
tcf(c_9461,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_1_on_line(a_line))) = point_1_on_line(a_line) )
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point2,point_1_on_line(a_line)))
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9446,c_123]) ).
tcf(c_9468,plain,
on(point_1_on_line(a_line),a_line),
inference(global_subsumption_just,[status(thm)],[c_9450,c_125,c_4549]) ).
tcf(c_9470,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_1_on_line(a_line) = X1 )
| ~ line(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ point(point_1_on_line(a_line))
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ on(point_1_on_line(a_line),X0) ),
inference(superposition,[status(thm)],[c_9468,c_94]) ).
tcf(c_9471,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point_1_on_line(a_line),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X1 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X2)
| ~ point(X1)
| ~ point(point_1_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X2,X0)
| ~ on(X1,X0)
| ~ on(point_1_on_line(a_line),X0) ),
inference(superposition,[status(thm)],[c_9468,c_111]) ).
tcf(c_9472,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_1_on_line(a_line) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ point(point_1_on_line(a_line))
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ on(point_1_on_line(a_line),X0) ),
inference(superposition,[status(thm)],[c_9468,c_112]) ).
tcf(c_9473,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9468,c_6119]) ).
tcf(c_9479,plain,
! [X0: $i,X1: $i] :
( collinear(X1,point_1_on_line(a_line),X0)
| ( X0 = X1 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X1,a_line)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_9468,c_121]) ).
tcf(c_9493,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ point(point_1_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9473,c_125]) ).
tcf(c_9507,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_1_on_line(a_line) = X1 )
| ~ line(X0)
| ~ point(X1)
| ~ point(point_1_on_line(a_line))
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ on(point_1_on_line(a_line),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9470,c_125]) ).
tcf(c_9516,plain,
! [X0: $i,X1: $i] :
( collinear(X1,point_1_on_line(a_line),X0)
| ( X0 = X1 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X1,a_line)
| ~ on(X0,a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9479,c_125]) ).
tcf(c_9574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = X2 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(point_1_on_line(line_through_3_points(X0,X1,X2)))
| ~ on(point_1_on_line(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_95,c_2919]) ).
tcf(c_9575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_2_on_line(line_through_3_points(X0,X1,X2)) = X2 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(point_2_on_line(line_through_3_points(X0,X1,X2)))
| ~ on(point_2_on_line(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_96,c_2919]) ).
tcf(c_9576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_on_plane(line_through_3_points(X0,X1,X2)) = X2 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ point(point_on_plane(line_through_3_points(X0,X1,X2)))
| ~ on(point_on_plane(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_103,c_2919]) ).
tcf(c_9580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( on(X5,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4) = X2 )
| ~ plane(X3)
| ~ line(X5)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X2,X5)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ point(common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4))
| ~ on(common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_113,c_2919]) ).
tcf(c_9581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( on(X5,line_through_3_points(X1,X2,X3))
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,X3) = X0 )
| ( common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4) = X3 )
| ~ plane(X0)
| ~ line(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X4,X0)
| ~ on(X3,X5)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X4,line_through_3_points(X1,X2,X3))
| ~ point(common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4))
| ~ on(common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_114,c_2919]) ).
tcf(c_9582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X2 )
| ( point_2_on_line(line_through_3_points(X0,X1,X2)) = point_on_plane(line_through_3_points(X0,X1,X2)) )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(line_through_3_points(X0,X1,X2))
| ~ on(line_through_3_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_6875,c_2919]) ).
tcf(c_9583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X2 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = point_on_plane(line_through_3_points(X0,X1,X2)) )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(line_through_3_points(X0,X1,X2))
| ~ on(line_through_3_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_6715,c_2919]) ).
tcf(c_9736,plain,
( ( point_on_plane(a_line) = point2 )
| ( line_from_to(point2,point_on_plane(a_line)) = a_line )
| ~ plane(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9029,c_104]) ).
tcf(c_9746,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_2_on_line(a_line) = X1 )
| ~ line(X0)
| ~ point(X1)
| ~ on(point_2_on_line(a_line),X0)
| ~ on(X1,X0)
| ~ on(X1,a_line) ),
inference(global_subsumption_just,[status(thm)],[c_9403,c_125,c_4353,c_9403]) ).
tcf(c_9747,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_2_on_line(a_line) = X1 )
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ on(point_2_on_line(a_line),X0) ),
inference(renaming,[status(thm)],[c_9746]) ).
tcf(c_9763,plain,
! [X0: $i,X1: $i] :
( ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ( line_from_to(X1,point_2_on_line(a_line)) = a_line )
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(line_from_to(X1,point_2_on_line(a_line)))
| ~ on(X0,line_from_to(X1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_92,c_9747]) ).
tcf(c_9765,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,X2,point_2_on_line(a_line))
| ( X1 = X2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ( plane_for_points(X1,X2,point_2_on_line(a_line)) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(plane_for_points(X1,X2,point_2_on_line(a_line)))
| ~ on(X0,plane_for_points(X1,X2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_109,c_9747]) ).
tcf(c_9766,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ( line_through_3_points(point_2_on_line(a_line),X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ collinear(point_2_on_line(a_line),X1,X2)
| ~ line(line_through_3_points(point_2_on_line(a_line),X1,X2))
| ~ on(X0,line_through_3_points(point_2_on_line(a_line),X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_9747]) ).
tcf(c_9767,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ( line_through_3_points(X1,point_2_on_line(a_line),X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ collinear(X1,point_2_on_line(a_line),X2)
| ~ line(line_through_3_points(X1,point_2_on_line(a_line),X2))
| ~ on(X0,line_through_3_points(X1,point_2_on_line(a_line),X2)) ),
inference(superposition,[status(thm)],[c_118,c_9747]) ).
tcf(c_9768,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ( line_through_3_points(X1,X2,point_2_on_line(a_line)) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ collinear(X1,X2,point_2_on_line(a_line))
| ~ line(line_through_3_points(X1,X2,point_2_on_line(a_line)))
| ~ on(X0,line_through_3_points(X1,X2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_119,c_9747]) ).
tcf(c_9769,plain,
! [X0: $i,X1: $i] :
( ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ( line_from_to(point_2_on_line(a_line),X1) = a_line )
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(line_from_to(point_2_on_line(a_line),X1))
| ~ on(X0,line_from_to(point_2_on_line(a_line),X1)) ),
inference(superposition,[status(thm)],[c_91,c_9747]) ).
tcf(c_9770,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(point_2_on_line(a_line),X1,X2)
| ( X1 = X2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ( plane_for_points(point_2_on_line(a_line),X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(plane_for_points(point_2_on_line(a_line),X1,X2))
| ~ on(X0,plane_for_points(point_2_on_line(a_line),X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_9747]) ).
tcf(c_9771,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,point_2_on_line(a_line),X2)
| ( X1 = X2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ( plane_for_points(X1,point_2_on_line(a_line),X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(plane_for_points(X1,point_2_on_line(a_line),X2))
| ~ on(X0,plane_for_points(X1,point_2_on_line(a_line),X2)) ),
inference(superposition,[status(thm)],[c_108,c_9747]) ).
tcf(c_9773,plain,
! [X0: $i] :
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = X0 )
| ( point_2_on_line(point_2_on_line(a_line)) = point_on_plane(point_2_on_line(a_line)) )
| ~ point(X0)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_6875,c_9747]) ).
tcf(c_9774,plain,
! [X0: $i] :
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = X0 )
| ( point_1_on_line(point_2_on_line(a_line)) = point_on_plane(point_2_on_line(a_line)) )
| ~ point(X0)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_6715,c_9747]) ).
tcf(c_9916,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_1_on_line(a_line) = X1 )
| ~ line(X0)
| ~ point(X1)
| ~ on(point_1_on_line(a_line),X0)
| ~ on(X1,X0)
| ~ on(X1,a_line) ),
inference(global_subsumption_just,[status(thm)],[c_9507,c_125,c_4351,c_9507]) ).
tcf(c_9917,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_1_on_line(a_line) = X1 )
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ on(point_1_on_line(a_line),X0) ),
inference(renaming,[status(thm)],[c_9916]) ).
tcf(c_9933,plain,
! [X0: $i,X1: $i] :
( ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ( line_from_to(X1,point_1_on_line(a_line)) = a_line )
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(line_from_to(X1,point_1_on_line(a_line)))
| ~ on(X0,line_from_to(X1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_92,c_9917]) ).
tcf(c_9935,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,X2,point_1_on_line(a_line))
| ( X1 = X2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ( plane_for_points(X1,X2,point_1_on_line(a_line)) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(plane_for_points(X1,X2,point_1_on_line(a_line)))
| ~ on(X0,plane_for_points(X1,X2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_109,c_9917]) ).
tcf(c_9936,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ( line_through_3_points(point_1_on_line(a_line),X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ collinear(point_1_on_line(a_line),X1,X2)
| ~ line(line_through_3_points(point_1_on_line(a_line),X1,X2))
| ~ on(X0,line_through_3_points(point_1_on_line(a_line),X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_9917]) ).
tcf(c_9937,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ( line_through_3_points(X1,point_1_on_line(a_line),X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ collinear(X1,point_1_on_line(a_line),X2)
| ~ line(line_through_3_points(X1,point_1_on_line(a_line),X2))
| ~ on(X0,line_through_3_points(X1,point_1_on_line(a_line),X2)) ),
inference(superposition,[status(thm)],[c_118,c_9917]) ).
tcf(c_9938,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ( line_through_3_points(X1,X2,point_1_on_line(a_line)) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ collinear(X1,X2,point_1_on_line(a_line))
| ~ line(line_through_3_points(X1,X2,point_1_on_line(a_line)))
| ~ on(X0,line_through_3_points(X1,X2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_119,c_9917]) ).
tcf(c_9939,plain,
! [X0: $i,X1: $i] :
( ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ( line_from_to(point_1_on_line(a_line),X1) = a_line )
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(line_from_to(point_1_on_line(a_line),X1))
| ~ on(X0,line_from_to(point_1_on_line(a_line),X1)) ),
inference(superposition,[status(thm)],[c_91,c_9917]) ).
tcf(c_9940,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(point_1_on_line(a_line),X1,X2)
| ( X1 = X2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ( plane_for_points(point_1_on_line(a_line),X1,X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(plane_for_points(point_1_on_line(a_line),X1,X2))
| ~ on(X0,plane_for_points(point_1_on_line(a_line),X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_9917]) ).
tcf(c_9941,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,point_1_on_line(a_line),X2)
| ( X1 = X2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ( plane_for_points(X1,point_1_on_line(a_line),X2) = a_line )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(plane_for_points(X1,point_1_on_line(a_line),X2))
| ~ on(X0,plane_for_points(X1,point_1_on_line(a_line),X2)) ),
inference(superposition,[status(thm)],[c_108,c_9917]) ).
tcf(c_9943,plain,
! [X0: $i] :
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = X0 )
| ( point_2_on_line(point_1_on_line(a_line)) = point_on_plane(point_1_on_line(a_line)) )
| ~ point(X0)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_6875,c_9917]) ).
tcf(c_9944,plain,
! [X0: $i] :
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = X0 )
| ( point_1_on_line(point_1_on_line(a_line)) = point_on_plane(point_1_on_line(a_line)) )
| ~ point(X0)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_6715,c_9917]) ).
tcf(c_10092,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_2_on_line(a_line) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(point_2_on_line(a_line),X0)
| ~ on(X1,X0)
| ~ on(X1,a_line) ),
inference(global_subsumption_just,[status(thm)],[c_9368,c_125,c_4353,c_9368]) ).
tcf(c_10093,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_2_on_line(a_line) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ on(point_2_on_line(a_line),X0) ),
inference(renaming,[status(thm)],[c_10092]) ).
tcf(c_10110,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X1,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(line_from_to(X1,point_2_on_line(a_line)))
| ~ on(X0,line_from_to(X1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_92,c_10093]) ).
tcf(c_10112,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,X2,point_2_on_line(a_line))
| on(plane_for_points(X1,X2,point_2_on_line(a_line)),a_line)
| ( X1 = X2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(plane_for_points(X1,X2,point_2_on_line(a_line)))
| ~ on(X0,plane_for_points(X1,X2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_109,c_10093]) ).
tcf(c_10113,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(point_2_on_line(a_line),X1,X2),a_line)
| ( X1 = X2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ collinear(point_2_on_line(a_line),X1,X2)
| ~ line(line_through_3_points(point_2_on_line(a_line),X1,X2))
| ~ on(X0,line_through_3_points(point_2_on_line(a_line),X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_10093]) ).
tcf(c_10114,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X1,point_2_on_line(a_line),X2),a_line)
| ( X1 = X2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ collinear(X1,point_2_on_line(a_line),X2)
| ~ line(line_through_3_points(X1,point_2_on_line(a_line),X2))
| ~ on(X0,line_through_3_points(X1,point_2_on_line(a_line),X2)) ),
inference(superposition,[status(thm)],[c_118,c_10093]) ).
tcf(c_10115,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X1,X2,point_2_on_line(a_line)),a_line)
| ( X1 = X2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ collinear(X1,X2,point_2_on_line(a_line))
| ~ line(line_through_3_points(X1,X2,point_2_on_line(a_line)))
| ~ on(X0,line_through_3_points(X1,X2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_119,c_10093]) ).
tcf(c_10116,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(point_2_on_line(a_line),X1),a_line)
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(line_from_to(point_2_on_line(a_line),X1))
| ~ on(X0,line_from_to(point_2_on_line(a_line),X1)) ),
inference(superposition,[status(thm)],[c_91,c_10093]) ).
tcf(c_10117,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(point_2_on_line(a_line),X1,X2)
| on(plane_for_points(point_2_on_line(a_line),X1,X2),a_line)
| ( X1 = X2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(plane_for_points(point_2_on_line(a_line),X1,X2))
| ~ on(X0,plane_for_points(point_2_on_line(a_line),X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_10093]) ).
tcf(c_10118,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,point_2_on_line(a_line),X2)
| on(plane_for_points(X1,point_2_on_line(a_line),X2),a_line)
| ( X1 = X2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(plane_for_points(X1,point_2_on_line(a_line),X2))
| ~ on(X0,plane_for_points(X1,point_2_on_line(a_line),X2)) ),
inference(superposition,[status(thm)],[c_108,c_10093]) ).
tcf(c_10119,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( point_2_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_9364,c_10093]) ).
tcf(c_10122,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( point_2_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10119,c_125]) ).
tcf(c_10526,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_2_on_line(a_line))) = point2 )
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ plane(line_from_to(point2,point_2_on_line(a_line))) ),
inference(global_subsumption_just,[status(thm)],[c_9118,c_125,c_4353,c_9118]) ).
tcf(c_10527,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_2_on_line(a_line))) = point2 )
| ~ plane(line_from_to(point2,point_2_on_line(a_line)))
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(renaming,[status(thm)],[c_10526]) ).
tcf(c_10539,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_2_on_line(a_line))) = point2 )
| ~ line(a_line)
| ~ plane(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_10527]) ).
tcf(c_10540,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_2_on_line(a_line))) = point2 )
| ~ plane(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10539,c_125]) ).
tcf(c_10557,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_2_on_line(a_line))) = point2 )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_9102,c_10540]) ).
tcf(c_10564,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_1_on_line(a_line))) = point2 )
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ plane(line_from_to(point2,point_1_on_line(a_line))) ),
inference(global_subsumption_just,[status(thm)],[c_9454,c_125,c_4351,c_9454]) ).
tcf(c_10565,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_1_on_line(a_line))) = point2 )
| ~ plane(line_from_to(point2,point_1_on_line(a_line)))
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(renaming,[status(thm)],[c_10564]) ).
tcf(c_10577,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_1_on_line(a_line))) = point2 )
| ~ line(a_line)
| ~ plane(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_10565]) ).
tcf(c_10578,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_1_on_line(a_line))) = point2 )
| ~ plane(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10577,c_125]) ).
tcf(c_10595,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_1_on_line(a_line))) = point2 )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_9438,c_10578]) ).
tcf(c_10613,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_2_on_line(a_line))) = point_2_on_line(a_line) )
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ plane(line_from_to(point2,point_2_on_line(a_line))) ),
inference(global_subsumption_just,[status(thm)],[c_9125,c_125,c_4353,c_9125]) ).
tcf(c_10614,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_2_on_line(a_line))) = point_2_on_line(a_line) )
| ~ plane(line_from_to(point2,point_2_on_line(a_line)))
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(renaming,[status(thm)],[c_10613]) ).
tcf(c_10626,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_2_on_line(a_line))) = point_2_on_line(a_line) )
| ~ line(a_line)
| ~ plane(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_10614]) ).
tcf(c_10627,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_2_on_line(a_line))) = point_2_on_line(a_line) )
| ~ plane(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10626,c_125]) ).
tcf(c_10644,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_2_on_line(a_line))) = point_2_on_line(a_line) )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_9102,c_10627]) ).
tcf(c_10679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = X0 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_1_on_line(plane_for_points(X0,X1,X2)))
| ~ on(point_1_on_line(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_95,c_2921]) ).
tcf(c_10680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_2_on_line(plane_for_points(X0,X1,X2)) = X0 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_2_on_line(plane_for_points(X0,X1,X2)))
| ~ on(point_2_on_line(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_96,c_2921]) ).
tcf(c_10681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_on_plane(plane_for_points(X0,X1,X2)) = X0 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ point(point_on_plane(plane_for_points(X0,X1,X2)))
| ~ on(point_on_plane(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_103,c_2921]) ).
tcf(c_10684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_108,c_2921]) ).
tcf(c_10685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X0,X1,X2)
| on(X5,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4) = X0 )
| ~ plane(X3)
| ~ line(X5)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X0,X5)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ point(common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4))
| ~ on(common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_113,c_2921]) ).
tcf(c_10686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X1,X2,X3)
| on(X5,plane_for_points(X1,X2,X3))
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,X3) = X0 )
| ( common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4) = X1 )
| ~ plane(X0)
| ~ line(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X4,X0)
| ~ on(X1,X5)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X4,plane_for_points(X1,X2,X3))
| ~ point(common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4))
| ~ on(common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_114,c_2921]) ).
tcf(c_10687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X0 )
| ( point_2_on_line(plane_for_points(X0,X1,X2)) = point_on_plane(plane_for_points(X0,X1,X2)) )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(plane_for_points(X0,X1,X2))
| ~ on(plane_for_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_6875,c_2921]) ).
tcf(c_10688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X0 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = point_on_plane(plane_for_points(X0,X1,X2)) )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(plane_for_points(X0,X1,X2))
| ~ on(plane_for_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_6715,c_2921]) ).
tcf(c_10825,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_1_on_line(a_line) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(point_1_on_line(a_line),X0)
| ~ on(X1,X0)
| ~ on(X1,a_line) ),
inference(global_subsumption_just,[status(thm)],[c_9472,c_125,c_4351,c_9472]) ).
tcf(c_10826,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_1_on_line(a_line) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ on(point_1_on_line(a_line),X0) ),
inference(renaming,[status(thm)],[c_10825]) ).
tcf(c_10843,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X1,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(line_from_to(X1,point_1_on_line(a_line)))
| ~ on(X0,line_from_to(X1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_92,c_10826]) ).
tcf(c_10845,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,X2,point_1_on_line(a_line))
| on(plane_for_points(X1,X2,point_1_on_line(a_line)),a_line)
| ( X1 = X2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(plane_for_points(X1,X2,point_1_on_line(a_line)))
| ~ on(X0,plane_for_points(X1,X2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_109,c_10826]) ).
tcf(c_10846,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(point_1_on_line(a_line),X1,X2),a_line)
| ( X1 = X2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ collinear(point_1_on_line(a_line),X1,X2)
| ~ line(line_through_3_points(point_1_on_line(a_line),X1,X2))
| ~ on(X0,line_through_3_points(point_1_on_line(a_line),X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_10826]) ).
tcf(c_10847,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X1,point_1_on_line(a_line),X2),a_line)
| ( X1 = X2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ collinear(X1,point_1_on_line(a_line),X2)
| ~ line(line_through_3_points(X1,point_1_on_line(a_line),X2))
| ~ on(X0,line_through_3_points(X1,point_1_on_line(a_line),X2)) ),
inference(superposition,[status(thm)],[c_118,c_10826]) ).
tcf(c_10848,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X1,X2,point_1_on_line(a_line)),a_line)
| ( X1 = X2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ collinear(X1,X2,point_1_on_line(a_line))
| ~ line(line_through_3_points(X1,X2,point_1_on_line(a_line)))
| ~ on(X0,line_through_3_points(X1,X2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_119,c_10826]) ).
tcf(c_10849,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(point_1_on_line(a_line),X1),a_line)
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(line_from_to(point_1_on_line(a_line),X1))
| ~ on(X0,line_from_to(point_1_on_line(a_line),X1)) ),
inference(superposition,[status(thm)],[c_91,c_10826]) ).
tcf(c_10850,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(point_1_on_line(a_line),X1,X2)
| on(plane_for_points(point_1_on_line(a_line),X1,X2),a_line)
| ( X1 = X2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(plane_for_points(point_1_on_line(a_line),X1,X2))
| ~ on(X0,plane_for_points(point_1_on_line(a_line),X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_10826]) ).
tcf(c_10851,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,point_1_on_line(a_line),X2)
| on(plane_for_points(X1,point_1_on_line(a_line),X2),a_line)
| ( X1 = X2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ line(plane_for_points(X1,point_1_on_line(a_line),X2))
| ~ on(X0,plane_for_points(X1,point_1_on_line(a_line),X2)) ),
inference(superposition,[status(thm)],[c_108,c_10826]) ).
tcf(c_10852,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( point_1_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_9468,c_10826]) ).
tcf(c_10855,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( point_1_on_line(a_line) = X0 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10852,c_125]) ).
tcf(c_10993,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = a_line )
| ~ point(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_92,c_4208]) ).
tcf(c_10998,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = a_line )
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10993,c_123]) ).
tcf(c_11015,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = a_line )
| ~ point(point2)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_93,c_10998]) ).
tcf(c_11016,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = a_line )
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11015,c_123]) ).
tcf(c_11034,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = a_line )
| ~ point(point1) ),
inference(superposition,[status(thm)],[c_126,c_11016]) ).
tcf(c_11036,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = a_line )
| ~ line(a_line)
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_95,c_11016]) ).
tcf(c_11037,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = a_line )
| ~ line(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_96,c_11016]) ).
tcf(c_11038,plain,
( ( point_on_plane(a_line) = point2 )
| ( line_from_to(point_on_plane(a_line),point2) = a_line )
| ~ plane(a_line)
| ~ point(point_on_plane(a_line)) ),
inference(superposition,[status(thm)],[c_103,c_11016]) ).
tcf(c_11039,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = point2 )
| ( line_from_to(common_point_on_planes(a_line,X0,X1),point2) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_11016]) ).
tcf(c_11040,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = point2 )
| ( line_from_to(common_point_on_planes(X0,a_line,X1),point2) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_11016]) ).
tcf(c_11041,plain,
( ( point2 = a_line )
| ( line_from_to(a_line,point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_3143,c_11016]) ).
tcf(c_11042,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = a_line )
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9468,c_11016]) ).
tcf(c_11043,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = a_line )
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9364,c_11016]) ).
tcf(c_11044,plain,
( ( point2 = a_line )
| ( point_2_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(a_line,point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_6875,c_11016]) ).
tcf(c_11045,plain,
( ( point2 = a_line )
| ( point_1_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(a_line,point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_6715,c_11016]) ).
tcf(c_11046,plain,
line_from_to(point1,point2) = a_line,
inference(forward_subsumption_resolution,[status(thm)],[c_11034,c_129,c_122]) ).
tcf(c_11063,plain,
( ( point2 = a_line )
| ( point_1_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(a_line,point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11045,c_125]) ).
tcf(c_11069,plain,
( ( point2 = a_line )
| ( point_2_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(a_line,point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11044,c_125]) ).
tcf(c_11107,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ( point_on_plane(line_from_to(point1,point2)) = point1 )
| ~ point(point2)
| ~ point(point1)
| ~ plane(line_from_to(point1,point2))
| ~ line(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_6405]) ).
tcf(c_11108,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ( point_on_plane(line_from_to(point1,point2)) = point2 )
| ~ point(point2)
| ~ point(point1)
| ~ plane(line_from_to(point1,point2))
| ~ line(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_6397]) ).
tcf(c_11124,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = a_line ) ),
inference(global_subsumption_just,[status(thm)],[c_11042,c_125,c_4351,c_11042]) ).
tcf(c_11132,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point2)) = point_1_on_line(a_line) )
| ~ point(point2)
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point_1_on_line(a_line),point2))
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_6405]) ).
tcf(c_11133,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point2)) = point2 )
| ~ point(point2)
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point_1_on_line(a_line),point2))
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_6397]) ).
tcf(c_11137,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point2)) = point2 )
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point_1_on_line(a_line),point2))
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11133,c_123]) ).
tcf(c_11144,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point2)) = point_1_on_line(a_line) )
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point_1_on_line(a_line),point2))
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11132,c_123]) ).
tcf(c_11151,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = a_line ) ),
inference(global_subsumption_just,[status(thm)],[c_11043,c_125,c_4353,c_11043]) ).
tcf(c_11159,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point2)) = point_2_on_line(a_line) )
| ~ point(point2)
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point_2_on_line(a_line),point2))
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_6405]) ).
tcf(c_11160,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point2)) = point2 )
| ~ point(point2)
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point_2_on_line(a_line),point2))
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_6397]) ).
tcf(c_11164,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point2)) = point2 )
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point_2_on_line(a_line),point2))
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11160,c_123]) ).
tcf(c_11171,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point2)) = point_2_on_line(a_line) )
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point_2_on_line(a_line),point2))
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11159,c_123]) ).
tcf(c_11193,plain,
( ( point_on_plane(a_line) = point2 )
| ( line_from_to(point_on_plane(a_line),point2) = a_line )
| ~ plane(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11038,c_104]) ).
tcf(c_11209,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point2)) = point2 )
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ plane(line_from_to(point_1_on_line(a_line),point2)) ),
inference(global_subsumption_just,[status(thm)],[c_11137,c_125,c_4351,c_11137]) ).
tcf(c_11210,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point2)) = point2 )
| ~ plane(line_from_to(point_1_on_line(a_line),point2))
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(renaming,[status(thm)],[c_11209]) ).
tcf(c_11222,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point2)) = point2 )
| ~ line(a_line)
| ~ plane(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_11210]) ).
tcf(c_11223,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point2)) = point2 )
| ~ plane(line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11222,c_125]) ).
tcf(c_11240,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point2)) = point2 )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_11124,c_11223]) ).
tcf(c_11277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_1_on_line(plane_for_points(X0,X1,X2)))
| ~ on(point_1_on_line(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_95,c_2922]) ).
tcf(c_11278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_2_on_line(plane_for_points(X0,X1,X2)) = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_2_on_line(plane_for_points(X0,X1,X2)))
| ~ on(point_2_on_line(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_96,c_2922]) ).
tcf(c_11279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_on_plane(plane_for_points(X0,X1,X2)) = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ point(point_on_plane(plane_for_points(X0,X1,X2)))
| ~ on(point_on_plane(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_103,c_2922]) ).
tcf(c_11283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X0,X1,X2)
| on(X5,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4) = X1 )
| ~ plane(X3)
| ~ line(X5)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X1,X5)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ point(common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4))
| ~ on(common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_113,c_2922]) ).
tcf(c_11284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X1,X2,X3)
| on(X5,plane_for_points(X1,X2,X3))
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,X3) = X0 )
| ( common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4) = X2 )
| ~ plane(X0)
| ~ line(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X4,X0)
| ~ on(X2,X5)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X4,plane_for_points(X1,X2,X3))
| ~ point(common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4))
| ~ on(common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_114,c_2922]) ).
tcf(c_11285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X1 )
| ( point_2_on_line(plane_for_points(X0,X1,X2)) = point_on_plane(plane_for_points(X0,X1,X2)) )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(plane_for_points(X0,X1,X2))
| ~ on(plane_for_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_6875,c_2922]) ).
tcf(c_11286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X1 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = point_on_plane(plane_for_points(X0,X1,X2)) )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(plane_for_points(X0,X1,X2))
| ~ on(plane_for_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_6715,c_2922]) ).
tcf(c_11427,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_91,c_4399]) ).
tcf(c_11430,plain,
( ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point2,point_1_on_line(a_line)) = a_line )
| ~ point(point2)
| ~ on(point1,a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_4399]) ).
tcf(c_11431,plain,
( ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point2,point_2_on_line(a_line)) = a_line )
| ~ point(point2)
| ~ on(point1,a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_4399]) ).
tcf(c_11434,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11427,c_122]) ).
tcf(c_11440,plain,
( ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point2,point_2_on_line(a_line)) = a_line )
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11431,c_123,c_126,c_9364]) ).
tcf(c_11446,plain,
( ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point2,point_1_on_line(a_line)) = a_line )
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11430,c_123,c_126,c_9468]) ).
tcf(c_11469,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_93,c_11434]) ).
tcf(c_11471,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11469,c_122]) ).
tcf(c_11490,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = a_line )
| ~ line(a_line)
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_95,c_11471]) ).
tcf(c_11491,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = a_line )
| ~ line(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_96,c_11471]) ).
tcf(c_11492,plain,
( ( point_on_plane(a_line) = point1 )
| ( line_from_to(point1,point_on_plane(a_line)) = a_line )
| ~ plane(a_line)
| ~ point(point_on_plane(a_line)) ),
inference(superposition,[status(thm)],[c_103,c_11471]) ).
tcf(c_11493,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = point1 )
| ( line_from_to(point1,common_point_on_planes(a_line,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_11471]) ).
tcf(c_11494,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = point1 )
| ( line_from_to(point1,common_point_on_planes(X0,a_line,X1)) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_11471]) ).
tcf(c_11495,plain,
( ( point1 = a_line )
| ( line_from_to(point1,a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_3143,c_11471]) ).
tcf(c_11496,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = a_line )
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9468,c_11471]) ).
tcf(c_11497,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = a_line )
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9364,c_11471]) ).
tcf(c_11498,plain,
( ( point1 = a_line )
| ( point_2_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(point1,a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_6875,c_11471]) ).
tcf(c_11499,plain,
( ( point1 = a_line )
| ( point_1_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(point1,a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_6715,c_11471]) ).
tcf(c_11516,plain,
( ( point1 = a_line )
| ( point_1_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(point1,a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11499,c_125]) ).
tcf(c_11522,plain,
( ( point1 = a_line )
| ( point_2_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(point1,a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11498,c_125]) ).
tcf(c_11736,plain,
( ( point_on_plane(a_line) = point1 )
| ( line_from_to(point1,point_on_plane(a_line)) = a_line )
| ~ plane(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11492,c_104]) ).
tcf(c_11755,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = a_line ) ),
inference(global_subsumption_just,[status(thm)],[c_11496,c_125,c_4351,c_11496]) ).
tcf(c_11764,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_1_on_line(a_line))) = point1 )
| ~ point(point1)
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point1,point_1_on_line(a_line)))
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_6405]) ).
tcf(c_11765,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_1_on_line(a_line))) = point_1_on_line(a_line) )
| ~ point(point1)
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point1,point_1_on_line(a_line)))
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_6397]) ).
tcf(c_11769,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_1_on_line(a_line))) = point1 )
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point1,point_1_on_line(a_line)))
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11764,c_122]) ).
tcf(c_11776,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_1_on_line(a_line))) = point_1_on_line(a_line) )
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point1,point_1_on_line(a_line)))
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11765,c_122]) ).
tcf(c_11783,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = a_line ) ),
inference(global_subsumption_just,[status(thm)],[c_11497,c_125,c_4353,c_11497]) ).
tcf(c_11792,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_2_on_line(a_line))) = point1 )
| ~ point(point1)
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point1,point_2_on_line(a_line)))
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_6405]) ).
tcf(c_11793,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_2_on_line(a_line))) = point_2_on_line(a_line) )
| ~ point(point1)
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point1,point_2_on_line(a_line)))
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_6397]) ).
tcf(c_11797,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_2_on_line(a_line))) = point1 )
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point1,point_2_on_line(a_line)))
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11792,c_122]) ).
tcf(c_11804,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_2_on_line(a_line))) = point_2_on_line(a_line) )
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point1,point_2_on_line(a_line)))
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11793,c_122]) ).
tcf(c_11823,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point2)) = point2 )
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ plane(line_from_to(point_2_on_line(a_line),point2)) ),
inference(global_subsumption_just,[status(thm)],[c_11164,c_125,c_4353,c_11164]) ).
tcf(c_11824,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point2)) = point2 )
| ~ plane(line_from_to(point_2_on_line(a_line),point2))
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(renaming,[status(thm)],[c_11823]) ).
tcf(c_11836,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point2)) = point2 )
| ~ line(a_line)
| ~ plane(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_11824]) ).
tcf(c_11837,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point2)) = point2 )
| ~ plane(line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11836,c_125]) ).
tcf(c_11856,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point2)) = point2 )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_11151,c_11837]) ).
tcf(c_11865,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_1_on_line(a_line))) = point1 )
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ plane(line_from_to(point1,point_1_on_line(a_line))) ),
inference(global_subsumption_just,[status(thm)],[c_11769,c_125,c_4351,c_11769]) ).
tcf(c_11866,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_1_on_line(a_line))) = point1 )
| ~ plane(line_from_to(point1,point_1_on_line(a_line)))
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(renaming,[status(thm)],[c_11865]) ).
tcf(c_11878,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_1_on_line(a_line))) = point1 )
| ~ line(a_line)
| ~ plane(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_11866]) ).
tcf(c_11879,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_1_on_line(a_line))) = point1 )
| ~ plane(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11878,c_125]) ).
tcf(c_11896,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_1_on_line(a_line))) = point1 )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_11755,c_11879]) ).
tcf(c_11958,plain,
! [X0: $i] :
( on(line_from_to(point2,X0),a_line)
| ( X0 = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_91,c_3130]) ).
tcf(c_11959,plain,
( on(line_from_to(point2,point1),a_line)
| ( point1 = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(point1)
| ~ on(point2,a_line)
| ~ on(point1,a_line)
| ~ line(line_from_to(point2,point1)) ),
inference(superposition,[status(thm)],[c_9035,c_3130]) ).
tcf(c_11961,plain,
( on(line_from_to(point2,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_3130]) ).
tcf(c_11962,plain,
( on(line_from_to(point2,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_3130]) ).
tcf(c_11963,plain,
( on(line_from_to(point1,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ on(point2,a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_3130]) ).
tcf(c_11964,plain,
( on(line_from_to(point1,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ on(point2,a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_3130]) ).
tcf(c_11967,plain,
! [X0: $i] :
( on(line_from_to(point2,X0),a_line)
| ( X0 = point2 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11958,c_123]) ).
tcf(c_11974,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point2)
| ~ point(point1)
| ~ on(point2,a_line)
| ~ on(point1,a_line) ),
inference(light_normalisation,[status(thm)],[c_11959,c_9035]) ).
tcf(c_11976,plain,
( on(line_from_to(point2,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11962,c_123,c_127,c_9364]) ).
tcf(c_11982,plain,
( on(line_from_to(point2,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11961,c_123,c_127,c_9468]) ).
tcf(c_11988,plain,
( on(line_from_to(point1,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11964,c_122,c_127,c_9468]) ).
tcf(c_11995,plain,
( on(line_from_to(point1,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11963,c_122,c_127,c_9364]) ).
tcf(c_12003,plain,
! [X0: $i] :
( on(line_from_to(point2,X0),a_line)
| ( X0 = point2 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(global_subsumption_just,[status(thm)],[c_11967,c_123,c_6026,c_11967]) ).
tcf(c_12016,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ~ plane(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(superposition,[status(thm)],[c_9035,c_12003]) ).
tcf(c_12019,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = point2 )
| ( line_from_to(point2,X0) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ point(line_from_to(point2,X0))
| ~ on(line_from_to(point2,X0),X1) ),
inference(superposition,[status(thm)],[c_12003,c_94]) ).
tcf(c_12020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_from_to(point2,X0),X2)
| ( X2 = X3 )
| ( X1 = a_line )
| ( X0 = point2 )
| ( line_from_to(point2,X0) = X3 )
| ( line_from_to(point2,X0) = X2 )
| ~ plane(a_line)
| ~ plane(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X1)
| ~ on(X2,X1)
| ~ point(line_from_to(point2,X0))
| ~ on(line_from_to(point2,X0),X1) ),
inference(superposition,[status(thm)],[c_12003,c_111]) ).
tcf(c_12021,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,a_line)
| ( X0 = point2 )
| ( line_from_to(point2,X0) = X2 )
| ~ plane(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ point(line_from_to(point2,X0))
| ~ on(line_from_to(point2,X0),X1) ),
inference(superposition,[status(thm)],[c_12003,c_112]) ).
tcf(c_12022,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(point2,X0) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_6119]) ).
tcf(c_12025,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(point2,X0) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0))
| ~ on(line_from_to(point2,X0),a_line) ),
inference(superposition,[status(thm)],[c_12003,c_2934]) ).
tcf(c_12028,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(point2,X0),X1)
| ( X1 = X2 )
| ( X0 = point2 )
| ( line_from_to(point2,X0) = X2 )
| ( line_from_to(point2,X0) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_121]) ).
tcf(c_12029,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(point2,X0) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0))
| ~ on(line_from_to(point2,X0),a_line) ),
inference(superposition,[status(thm)],[c_12003,c_2925]) ).
tcf(c_12030,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = point1 )
| ( line_from_to(point1,line_from_to(point2,X0)) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_11471]) ).
tcf(c_12031,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = point2 )
| ( line_from_to(line_from_to(point2,X0),point2) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_11016]) ).
tcf(c_12032,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = point2 )
| ( line_from_to(point2,line_from_to(point2,X0)) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_9014]) ).
tcf(c_12033,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = a_line )
| ( point_2_on_line(line_from_to(point2,X0)) = point_on_plane(line_from_to(point2,X0)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,X0))
| ~ line(line_from_to(point2,X0))
| ~ point(line_from_to(point2,X0))
| ~ on(a_line,line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_6890]) ).
tcf(c_12034,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = a_line )
| ( point_1_on_line(line_from_to(point2,X0)) = point_on_plane(line_from_to(point2,X0)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,X0))
| ~ line(line_from_to(point2,X0))
| ~ point(line_from_to(point2,X0))
| ~ on(a_line,line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_6730]) ).
tcf(c_12035,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = a_line )
| ( line_from_to(point2,X0) = point2 )
| ( point_2_on_line(line_from_to(point2,X0)) = point_on_plane(line_from_to(point2,X0)) )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,X0))
| ~ line(line_from_to(point2,X0))
| ~ point(line_from_to(point2,X0))
| ~ on(point2,line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_6894]) ).
tcf(c_12036,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = a_line )
| ( line_from_to(point2,X0) = point2 )
| ( point_1_on_line(line_from_to(point2,X0)) = point_on_plane(line_from_to(point2,X0)) )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,X0))
| ~ line(line_from_to(point2,X0))
| ~ point(line_from_to(point2,X0))
| ~ on(point2,line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_6734]) ).
tcf(c_12038,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(point2,X0) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12022,c_125]) ).
tcf(c_12067,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(point2,X0) = point2 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0))
| ~ on(line_from_to(point2,X0),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12029,c_125,c_127]) ).
tcf(c_12076,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(point2,X0) = point1 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0))
| ~ on(line_from_to(point2,X0),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12025,c_125,c_126]) ).
tcf(c_12097,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = point2 )
| ( line_from_to(point2,X0) = X2 )
| ~ plane(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ point(line_from_to(point2,X0))
| ~ on(line_from_to(point2,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12019,c_125]) ).
tcf(c_12154,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(point2,X0),X1)
| ( X1 = X2 )
| ( X0 = point2 )
| ( line_from_to(point2,X0) = X2 )
| ( line_from_to(point2,X0) = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12028,c_125]) ).
tcf(c_12206,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_92,c_4407]) ).
tcf(c_12214,plain,
( ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point2) = a_line )
| ~ point(point2)
| ~ on(point1,a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_4407]) ).
tcf(c_12215,plain,
( ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point2) = a_line )
| ~ point(point2)
| ~ on(point1,a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_4407]) ).
tcf(c_12216,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12206,c_122]) ).
tcf(c_12222,plain,
( ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point2) = a_line )
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12215,c_123,c_126,c_9364]) ).
tcf(c_12228,plain,
( ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point2) = a_line )
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12214,c_123,c_126,c_9468]) ).
tcf(c_12244,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_93,c_12216]) ).
tcf(c_12246,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12244,c_122]) ).
tcf(c_12265,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = a_line )
| ~ line(a_line)
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_95,c_12246]) ).
tcf(c_12266,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = a_line )
| ~ line(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_96,c_12246]) ).
tcf(c_12267,plain,
( ( point_on_plane(a_line) = point1 )
| ( line_from_to(point_on_plane(a_line),point1) = a_line )
| ~ plane(a_line)
| ~ point(point_on_plane(a_line)) ),
inference(superposition,[status(thm)],[c_103,c_12246]) ).
tcf(c_12268,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = point1 )
| ( line_from_to(common_point_on_planes(a_line,X0,X1),point1) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_12246]) ).
tcf(c_12269,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = point1 )
| ( line_from_to(common_point_on_planes(X0,a_line,X1),point1) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_12246]) ).
tcf(c_12270,plain,
( ( point1 = a_line )
| ( line_from_to(a_line,point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_3143,c_12246]) ).
tcf(c_12271,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = a_line )
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9468,c_12246]) ).
tcf(c_12272,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = a_line )
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9364,c_12246]) ).
tcf(c_12273,plain,
( ( point1 = a_line )
| ( point_2_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(a_line,point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_6875,c_12246]) ).
tcf(c_12274,plain,
( ( point1 = a_line )
| ( point_1_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(a_line,point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_6715,c_12246]) ).
tcf(c_12275,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = point1 )
| ( line_from_to(line_from_to(point2,X0),point1) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_12246]) ).
tcf(c_12292,plain,
( ( point1 = a_line )
| ( point_1_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(a_line,point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12274,c_125]) ).
tcf(c_12298,plain,
( ( point1 = a_line )
| ( point_2_on_line(a_line) = point_on_plane(a_line) )
| ( line_from_to(a_line,point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12273,c_125]) ).
tcf(c_12340,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = a_line ) ),
inference(global_subsumption_just,[status(thm)],[c_12271,c_125,c_4351,c_12271]) ).
tcf(c_12347,plain,
( on(line_from_to(point_1_on_line(a_line),point1),a_line)
| ( point1 = point2 )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ on(point2,a_line)
| ~ on(point1,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_3130]) ).
tcf(c_12351,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point1)) = point_1_on_line(a_line) )
| ~ point(point1)
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point_1_on_line(a_line),point1))
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_6405]) ).
tcf(c_12352,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point1)) = point1 )
| ~ point(point1)
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point_1_on_line(a_line),point1))
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_6397]) ).
tcf(c_12356,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point1)) = point1 )
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point_1_on_line(a_line),point1))
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12352,c_122]) ).
tcf(c_12363,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point1)) = point_1_on_line(a_line) )
| ~ point(point_1_on_line(a_line))
| ~ plane(line_from_to(point_1_on_line(a_line),point1))
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12351,c_122]) ).
tcf(c_12370,plain,
( on(line_from_to(point_1_on_line(a_line),point1),a_line)
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12347,c_129,c_122,c_127,c_126]) ).
tcf(c_12414,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = a_line ) ),
inference(global_subsumption_just,[status(thm)],[c_12272,c_125,c_4353,c_12272]) ).
tcf(c_12421,plain,
( on(line_from_to(point_2_on_line(a_line),point1),a_line)
| ( point1 = point2 )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ on(point2,a_line)
| ~ on(point1,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_3130]) ).
tcf(c_12425,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point1)) = point_2_on_line(a_line) )
| ~ point(point1)
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point_2_on_line(a_line),point1))
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_6405]) ).
tcf(c_12426,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point1)) = point1 )
| ~ point(point1)
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point_2_on_line(a_line),point1))
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_6397]) ).
tcf(c_12430,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point1)) = point1 )
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point_2_on_line(a_line),point1))
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12426,c_122]) ).
tcf(c_12437,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point1)) = point_2_on_line(a_line) )
| ~ point(point_2_on_line(a_line))
| ~ plane(line_from_to(point_2_on_line(a_line),point1))
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12425,c_122]) ).
tcf(c_12444,plain,
( on(line_from_to(point_2_on_line(a_line),point1),a_line)
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12421,c_129,c_122,c_127,c_126]) ).
tcf(c_12456,plain,
( ( point_on_plane(a_line) = point1 )
| ( line_from_to(point_on_plane(a_line),point1) = a_line )
| ~ plane(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12267,c_104]) ).
tcf(c_12470,plain,
( on(line_from_to(point2,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(global_subsumption_just,[status(thm)],[c_11976,c_125,c_4353,c_11976]) ).
tcf(c_12481,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(line_from_to(point2,point_2_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_12470,c_94]) ).
tcf(c_12482,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(point2,point_2_on_line(a_line)),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X2)
| ~ point(X1)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X2,X0)
| ~ on(X1,X0)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(line_from_to(point2,point_2_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_12470,c_111]) ).
tcf(c_12483,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(line_from_to(point2,point_2_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_12470,c_112]) ).
tcf(c_12484,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12470,c_6119]) ).
tcf(c_12487,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point1,a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(line_from_to(point2,point_2_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_12470,c_2934]) ).
tcf(c_12490,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point2,point_2_on_line(a_line)),X0)
| ( X0 = X1 )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X1 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12470,c_121]) ).
tcf(c_12491,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point2,a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(line_from_to(point2,point_2_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_12470,c_2925]) ).
tcf(c_12492,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point2,point_2_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12470,c_12246]) ).
tcf(c_12493,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point2,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12470,c_11471]) ).
tcf(c_12494,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point2,point_2_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12470,c_11016]) ).
tcf(c_12495,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point2,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12470,c_9014]) ).
tcf(c_12500,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12484,c_125]) ).
tcf(c_12531,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(line_from_to(point2,point_2_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12491,c_125,c_127]) ).
tcf(c_12539,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(line_from_to(point2,point_2_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12487,c_125,c_126]) ).
tcf(c_12558,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(line_from_to(point2,point_2_on_line(a_line)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12481,c_125]) ).
tcf(c_12570,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point2,point_2_on_line(a_line)),X0)
| ( X0 = X1 )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X1 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12490,c_125]) ).
tcf(c_12601,plain,
( on(line_from_to(point2,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(global_subsumption_just,[status(thm)],[c_11982,c_125,c_4351,c_11982]) ).
tcf(c_12612,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(line_from_to(point2,point_1_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_12601,c_94]) ).
tcf(c_12613,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(point2,point_1_on_line(a_line)),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X2)
| ~ point(X1)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X2,X0)
| ~ on(X1,X0)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(line_from_to(point2,point_1_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_12601,c_111]) ).
tcf(c_12614,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(line_from_to(point2,point_1_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_12601,c_112]) ).
tcf(c_12615,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12601,c_6119]) ).
tcf(c_12618,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point1,a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(line_from_to(point2,point_1_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_12601,c_2934]) ).
tcf(c_12621,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point2,point_1_on_line(a_line)),X0)
| ( X0 = X1 )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X1 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12601,c_121]) ).
tcf(c_12622,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point2,a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(line_from_to(point2,point_1_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_12601,c_2925]) ).
tcf(c_12623,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point2,point_1_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12601,c_12246]) ).
tcf(c_12624,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point2,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12601,c_11471]) ).
tcf(c_12625,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point2,point_1_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12601,c_11016]) ).
tcf(c_12626,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point2,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12601,c_9014]) ).
tcf(c_12631,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12615,c_125]) ).
tcf(c_12662,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(line_from_to(point2,point_1_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12622,c_125,c_127]) ).
tcf(c_12670,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(line_from_to(point2,point_1_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12618,c_125,c_126]) ).
tcf(c_12689,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(line_from_to(point2,point_1_on_line(a_line)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12612,c_125]) ).
tcf(c_12701,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point2,point_1_on_line(a_line)),X0)
| ( X0 = X1 )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X1 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12621,c_125]) ).
tcf(c_12919,plain,
( on(line_from_to(point_1_on_line(a_line),point1),a_line)
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(global_subsumption_just,[status(thm)],[c_12370,c_125,c_4351,c_12370]) ).
tcf(c_12930,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1))
| ~ on(line_from_to(point_1_on_line(a_line),point1),X0) ),
inference(superposition,[status(thm)],[c_12919,c_94]) ).
tcf(c_12931,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(point_1_on_line(a_line),point1),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = X2 )
| ( line_from_to(point_1_on_line(a_line),point1) = X1 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X2)
| ~ point(X1)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X2,X0)
| ~ on(X1,X0)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1))
| ~ on(line_from_to(point_1_on_line(a_line),point1),X0) ),
inference(superposition,[status(thm)],[c_12919,c_111]) ).
tcf(c_12932,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1))
| ~ on(line_from_to(point_1_on_line(a_line),point1),X0) ),
inference(superposition,[status(thm)],[c_12919,c_112]) ).
tcf(c_12933,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12919,c_6119]) ).
tcf(c_12936,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point1,a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1))
| ~ on(line_from_to(point_1_on_line(a_line),point1),a_line) ),
inference(superposition,[status(thm)],[c_12919,c_2934]) ).
tcf(c_12939,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point_1_on_line(a_line),point1),X0)
| ( X0 = X1 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = X1 )
| ( line_from_to(point_1_on_line(a_line),point1) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12919,c_121]) ).
tcf(c_12940,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point2,a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1))
| ~ on(line_from_to(point_1_on_line(a_line),point1),a_line) ),
inference(superposition,[status(thm)],[c_12919,c_2925]) ).
tcf(c_12941,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point1 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point1),point1) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12919,c_12246]) ).
tcf(c_12942,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point1 )
| ( line_from_to(point1,line_from_to(point_1_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12919,c_11471]) ).
tcf(c_12943,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point2 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point1),point2) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12919,c_11016]) ).
tcf(c_12944,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point2 )
| ( line_from_to(point2,line_from_to(point_1_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12919,c_9014]) ).
tcf(c_12949,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12933,c_125]) ).
tcf(c_12980,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point2 )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1))
| ~ on(line_from_to(point_1_on_line(a_line),point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12940,c_125,c_127]) ).
tcf(c_12988,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1))
| ~ on(line_from_to(point_1_on_line(a_line),point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12936,c_125,c_126]) ).
tcf(c_13007,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1))
| ~ on(line_from_to(point_1_on_line(a_line),point1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12930,c_125]) ).
tcf(c_13019,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point_1_on_line(a_line),point1),X0)
| ( X0 = X1 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = X1 )
| ( line_from_to(point_1_on_line(a_line),point1) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12939,c_125]) ).
tcf(c_13097,plain,
( on(line_from_to(point_2_on_line(a_line),point1),a_line)
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(global_subsumption_just,[status(thm)],[c_12444,c_125,c_4353,c_12444]) ).
tcf(c_13108,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1))
| ~ on(line_from_to(point_2_on_line(a_line),point1),X0) ),
inference(superposition,[status(thm)],[c_13097,c_94]) ).
tcf(c_13109,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(point_2_on_line(a_line),point1),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = X2 )
| ( line_from_to(point_2_on_line(a_line),point1) = X1 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X2)
| ~ point(X1)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X2,X0)
| ~ on(X1,X0)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1))
| ~ on(line_from_to(point_2_on_line(a_line),point1),X0) ),
inference(superposition,[status(thm)],[c_13097,c_111]) ).
tcf(c_13110,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1))
| ~ on(line_from_to(point_2_on_line(a_line),point1),X0) ),
inference(superposition,[status(thm)],[c_13097,c_112]) ).
tcf(c_13111,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_13097,c_6119]) ).
tcf(c_13114,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point1,a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1))
| ~ on(line_from_to(point_2_on_line(a_line),point1),a_line) ),
inference(superposition,[status(thm)],[c_13097,c_2934]) ).
tcf(c_13117,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point_2_on_line(a_line),point1),X0)
| ( X0 = X1 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = X1 )
| ( line_from_to(point_2_on_line(a_line),point1) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_13097,c_121]) ).
tcf(c_13118,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point2,a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1))
| ~ on(line_from_to(point_2_on_line(a_line),point1),a_line) ),
inference(superposition,[status(thm)],[c_13097,c_2925]) ).
tcf(c_13119,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point1 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point1),point1) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_13097,c_12246]) ).
tcf(c_13120,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point1 )
| ( line_from_to(point1,line_from_to(point_2_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_13097,c_11471]) ).
tcf(c_13121,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point2 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point1),point2) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_13097,c_11016]) ).
tcf(c_13122,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point2 )
| ( line_from_to(point2,line_from_to(point_2_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_13097,c_9014]) ).
tcf(c_13127,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13111,c_125]) ).
tcf(c_13158,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point2 )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1))
| ~ on(line_from_to(point_2_on_line(a_line),point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13118,c_125,c_127]) ).
tcf(c_13166,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1))
| ~ on(line_from_to(point_2_on_line(a_line),point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13114,c_125,c_126]) ).
tcf(c_13185,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1))
| ~ on(line_from_to(point_2_on_line(a_line),point1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13108,c_125]) ).
tcf(c_13197,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point_2_on_line(a_line),point1),X0)
| ( X0 = X1 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = X1 )
| ( line_from_to(point_2_on_line(a_line),point1) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13117,c_125]) ).
tcf(c_13257,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| on(plane_for_points(point2,X0,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_107,c_3134]) ).
tcf(c_13258,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| on(plane_for_points(X0,point2,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_108,c_3134]) ).
tcf(c_13259,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| on(plane_for_points(X0,point2,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13258,c_123]) ).
tcf(c_13270,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| on(plane_for_points(point2,X0,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13257,c_123]) ).
tcf(c_13281,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( point_1_on_line(point_2_on_line(a_line)) = point_on_plane(point_2_on_line(a_line)) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(point2,point_2_on_line(a_line)) ),
inference(global_subsumption_just,[status(thm)],[c_7232,c_125,c_4353,c_7232]) ).
tcf(c_13295,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(point_1_on_line(a_line)) = point_on_plane(point_1_on_line(a_line)) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(point2,point_1_on_line(a_line)) ),
inference(global_subsumption_just,[status(thm)],[c_7240,c_125,c_4351,c_7240]) ).
tcf(c_13309,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(point_2_on_line(a_line)) = point_on_plane(point_2_on_line(a_line)) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(point2,point_2_on_line(a_line)) ),
inference(global_subsumption_just,[status(thm)],[c_7506,c_125,c_4353,c_7506]) ).
tcf(c_13323,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( point_2_on_line(point_1_on_line(a_line)) = point_on_plane(point_1_on_line(a_line)) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(point2,point_1_on_line(a_line)) ),
inference(global_subsumption_just,[status(thm)],[c_7514,c_125,c_4351,c_7514]) ).
tcf(c_13339,plain,
( on(line_from_to(point1,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(global_subsumption_just,[status(thm)],[c_11988,c_125,c_4351,c_11988]) ).
tcf(c_13351,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_13339]) ).
tcf(c_13352,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_13339,c_94]) ).
tcf(c_13353,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(point1,point_1_on_line(a_line)),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X2 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X2)
| ~ point(X1)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X2,X0)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_13339,c_111]) ).
tcf(c_13354,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_13339,c_112]) ).
tcf(c_13355,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_13339,c_6119]) ).
tcf(c_13358,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point1,a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_13339,c_2934]) ).
tcf(c_13361,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point1,point_1_on_line(a_line)),X0)
| ( X0 = X1 )
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_13339,c_121]) ).
tcf(c_13362,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point2,a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_13339,c_2925]) ).
tcf(c_13363,plain,
( ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point1,point_1_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_13339,c_12246]) ).
tcf(c_13364,plain,
( ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point1,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_13339,c_11471]) ).
tcf(c_13365,plain,
( ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point1,point_1_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_13339,c_11016]) ).
tcf(c_13366,plain,
( ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point1,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_13339,c_9014]) ).
tcf(c_13376,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13355,c_125]) ).
tcf(c_13412,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13362,c_125,c_127]) ).
tcf(c_13421,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13358,c_125,c_126]) ).
tcf(c_13442,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13352,c_125]) ).
tcf(c_13455,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point1,point_1_on_line(a_line)),X0)
| ( X0 = X1 )
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13361,c_125]) ).
tcf(c_13548,plain,
( on(line_from_to(point1,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(global_subsumption_just,[status(thm)],[c_11995,c_125,c_4353,c_11995]) ).
tcf(c_13560,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_13548]) ).
tcf(c_13561,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_13548,c_94]) ).
tcf(c_13562,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(point1,point_2_on_line(a_line)),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X2 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X2)
| ~ point(X1)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X2,X0)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_13548,c_111]) ).
tcf(c_13563,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_13548,c_112]) ).
tcf(c_13564,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_13548,c_6119]) ).
tcf(c_13567,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point1,a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_13548,c_2934]) ).
tcf(c_13570,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point1,point_2_on_line(a_line)),X0)
| ( X0 = X1 )
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_13548,c_121]) ).
tcf(c_13571,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point2,a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_13548,c_2925]) ).
tcf(c_13572,plain,
( ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point1,point_2_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_13548,c_12246]) ).
tcf(c_13573,plain,
( ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point1,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_13548,c_11471]) ).
tcf(c_13574,plain,
( ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point1,point_2_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_13548,c_11016]) ).
tcf(c_13575,plain,
( ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point1,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_13548,c_9014]) ).
tcf(c_13585,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13564,c_125]) ).
tcf(c_13621,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13571,c_125,c_127]) ).
tcf(c_13630,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13567,c_125,c_126]) ).
tcf(c_13651,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13561,c_125]) ).
tcf(c_13664,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point1,point_2_on_line(a_line)),X0)
| ( X0 = X1 )
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13570,c_125]) ).
tcf(c_13709,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_2_on_line(a_line))) = point1 )
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ plane(line_from_to(point1,point_2_on_line(a_line))) ),
inference(global_subsumption_just,[status(thm)],[c_11797,c_125,c_4353,c_11797]) ).
tcf(c_13710,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_2_on_line(a_line))) = point1 )
| ~ plane(line_from_to(point1,point_2_on_line(a_line)))
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(renaming,[status(thm)],[c_13709]) ).
tcf(c_13722,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_2_on_line(a_line))) = point1 )
| ~ line(a_line)
| ~ plane(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_13710]) ).
tcf(c_13723,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_2_on_line(a_line))) = point1 )
| ~ plane(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13722,c_125]) ).
tcf(c_13740,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_2_on_line(a_line))) = point1 )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_11783,c_13723]) ).
tcf(c_13745,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),a_line)
| ( X1 = X2 )
| ( X0 = point2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,X2)
| ~ on(point2,line_through_3_points(X0,X1,X2)) ),
inference(global_subsumption_just,[status(thm)],[c_3135,c_120,c_3135]) ).
tcf(c_13772,plain,
! [X0: $i,X1: $i] :
( on(line_through_3_points(X0,point2,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1) ),
inference(superposition,[status(thm)],[c_118,c_13745]) ).
tcf(c_13773,plain,
! [X0: $i,X1: $i] :
( on(line_through_3_points(X0,X1,point2),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2) ),
inference(superposition,[status(thm)],[c_119,c_13745]) ).
tcf(c_13774,plain,
! [X0: $i,X1: $i] :
( on(line_through_3_points(X0,X1,point2),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13773,c_123]) ).
tcf(c_13784,plain,
! [X0: $i,X1: $i] :
( on(line_through_3_points(X0,point2,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13772,c_123]) ).
tcf(c_13822,plain,
( ( point_on_plane(a_line) = a_line )
| ( point_1_on_line(point_on_plane(a_line)) = point_on_plane(point_on_plane(a_line)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_on_plane(a_line))
| ~ line(point_on_plane(a_line))
| ~ on(a_line,point_on_plane(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7582,c_104]) ).
tcf(c_13844,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_1_on_line(point_2_on_line(a_line)) = point_on_plane(point_2_on_line(a_line)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(a_line,point_2_on_line(a_line)) ),
inference(global_subsumption_just,[status(thm)],[c_7612,c_125,c_4353,c_7612]) ).
tcf(c_13860,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(point_1_on_line(a_line)) = point_on_plane(point_1_on_line(a_line)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(a_line,point_1_on_line(a_line)) ),
inference(global_subsumption_just,[status(thm)],[c_7621,c_125,c_4351,c_7621]) ).
tcf(c_13878,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point1)) = point1 )
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ plane(line_from_to(point_1_on_line(a_line),point1)) ),
inference(global_subsumption_just,[status(thm)],[c_12356,c_125,c_4351,c_12356]) ).
tcf(c_13879,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point1)) = point1 )
| ~ plane(line_from_to(point_1_on_line(a_line),point1))
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(renaming,[status(thm)],[c_13878]) ).
tcf(c_13891,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point1)) = point1 )
| ~ line(a_line)
| ~ plane(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_13879]) ).
tcf(c_13892,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point1)) = point1 )
| ~ plane(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13891,c_125]) ).
tcf(c_13909,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point1)) = point1 )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_12340,c_13892]) ).
tcf(c_13916,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point1)) = point1 )
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ plane(line_from_to(point_2_on_line(a_line),point1)) ),
inference(global_subsumption_just,[status(thm)],[c_12430,c_125,c_4353,c_12430]) ).
tcf(c_13917,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point1)) = point1 )
| ~ plane(line_from_to(point_2_on_line(a_line),point1))
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(renaming,[status(thm)],[c_13916]) ).
tcf(c_13929,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point1)) = point1 )
| ~ line(a_line)
| ~ plane(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_13917]) ).
tcf(c_13930,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point1)) = point1 )
| ~ plane(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13929,c_125]) ).
tcf(c_13947,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point1)) = point1 )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_12414,c_13930]) ).
tcf(c_13967,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_1_on_line(a_line))) = point_1_on_line(a_line) )
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ plane(line_from_to(point2,point_1_on_line(a_line))) ),
inference(global_subsumption_just,[status(thm)],[c_9461,c_125,c_4351,c_9461]) ).
tcf(c_13968,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_1_on_line(a_line))) = point_1_on_line(a_line) )
| ~ plane(line_from_to(point2,point_1_on_line(a_line)))
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(renaming,[status(thm)],[c_13967]) ).
tcf(c_13980,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_1_on_line(a_line))) = point_1_on_line(a_line) )
| ~ line(a_line)
| ~ plane(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_13968]) ).
tcf(c_13981,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_1_on_line(a_line))) = point_1_on_line(a_line) )
| ~ plane(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13980,c_125]) ).
tcf(c_13998,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point2,point_1_on_line(a_line))) = point_1_on_line(a_line) )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_9438,c_13981]) ).
tcf(c_14018,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point2)) = point_1_on_line(a_line) )
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ plane(line_from_to(point_1_on_line(a_line),point2)) ),
inference(global_subsumption_just,[status(thm)],[c_11144,c_125,c_4351,c_11144]) ).
tcf(c_14019,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point2)) = point_1_on_line(a_line) )
| ~ plane(line_from_to(point_1_on_line(a_line),point2))
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(renaming,[status(thm)],[c_14018]) ).
tcf(c_14031,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point2)) = point_1_on_line(a_line) )
| ~ line(a_line)
| ~ plane(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_14019]) ).
tcf(c_14032,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point2)) = point_1_on_line(a_line) )
| ~ plane(line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14031,c_125]) ).
tcf(c_14049,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point2)) = point_1_on_line(a_line) )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_11124,c_14032]) ).
tcf(c_14054,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),a_line)
| ( X1 = point2 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,X2)
| ~ on(point2,line_through_3_points(X0,X1,X2)) ),
inference(global_subsumption_just,[status(thm)],[c_3136,c_120,c_3136]) ).
tcf(c_14080,plain,
! [X0: $i,X1: $i] :
( on(line_through_3_points(point2,X0,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1) ),
inference(superposition,[status(thm)],[c_117,c_14054]) ).
tcf(c_14082,plain,
! [X0: $i,X1: $i] :
( on(line_through_3_points(X0,X1,point2),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2) ),
inference(superposition,[status(thm)],[c_119,c_14054]) ).
tcf(c_14083,plain,
! [X0: $i,X1: $i] :
( on(line_through_3_points(X0,X1,point2),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14082,c_123]) ).
tcf(c_14093,plain,
! [X0: $i,X1: $i] :
( on(line_through_3_points(point2,X0,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14080,c_123]) ).
tcf(c_14130,plain,
( ( point_on_plane(a_line) = a_line )
| ( point_2_on_line(point_on_plane(a_line)) = point_on_plane(point_on_plane(a_line)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_on_plane(a_line))
| ~ line(point_on_plane(a_line))
| ~ on(a_line,point_on_plane(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8833,c_104]) ).
tcf(c_14152,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(point_2_on_line(a_line)) = point_on_plane(point_2_on_line(a_line)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(a_line,point_2_on_line(a_line)) ),
inference(global_subsumption_just,[status(thm)],[c_8863,c_125,c_4353,c_8863]) ).
tcf(c_14168,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_2_on_line(point_1_on_line(a_line)) = point_on_plane(point_1_on_line(a_line)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(a_line,point_1_on_line(a_line)) ),
inference(global_subsumption_just,[status(thm)],[c_8872,c_125,c_4351,c_8872]) ).
tcf(c_14381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),X2) ),
inference(superposition,[status(thm)],[c_13774,c_94]) ).
tcf(c_14382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,line_through_3_points(X0,X1,point2),X3)
| ( X3 = X4 )
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = X4 )
| ( line_through_3_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,a_line)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),X2) ),
inference(superposition,[status(thm)],[c_13774,c_111]) ).
tcf(c_14383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),X2) ),
inference(superposition,[status(thm)],[c_13774,c_112]) ).
tcf(c_14384,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_6119]) ).
tcf(c_14387,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),a_line) ),
inference(superposition,[status(thm)],[c_13774,c_2934]) ).
tcf(c_14390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_through_3_points(X0,X1,point2),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = X3 )
| ( line_through_3_points(X0,X1,point2) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_121]) ).
tcf(c_14391,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),a_line) ),
inference(superposition,[status(thm)],[c_13774,c_2925]) ).
tcf(c_14392,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point1 )
| ( line_from_to(line_through_3_points(X0,X1,point2),point1) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_12246]) ).
tcf(c_14393,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point1 )
| ( line_from_to(point1,line_through_3_points(X0,X1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_11471]) ).
tcf(c_14394,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ( line_from_to(line_through_3_points(X0,X1,point2),point2) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_11016]) ).
tcf(c_14395,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ( line_from_to(point2,line_through_3_points(X0,X1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_9014]) ).
tcf(c_14396,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( point_2_on_line(line_through_3_points(X0,X1,point2)) = point_on_plane(line_through_3_points(X0,X1,point2)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(a_line,line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_6890]) ).
tcf(c_14397,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( point_1_on_line(line_through_3_points(X0,X1,point2)) = point_on_plane(line_through_3_points(X0,X1,point2)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(a_line,line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_6730]) ).
tcf(c_14398,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ( point_2_on_line(line_through_3_points(X0,X1,point2)) = point_on_plane(line_through_3_points(X0,X1,point2)) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(point2,line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_6894]) ).
tcf(c_14399,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ( point_1_on_line(line_through_3_points(X0,X1,point2)) = point_on_plane(line_through_3_points(X0,X1,point2)) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(point2,line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_6734]) ).
tcf(c_14400,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14384,c_125]) ).
tcf(c_14456,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14391,c_125,c_127]) ).
tcf(c_14469,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14387,c_125,c_126]) ).
tcf(c_14498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14381,c_125]) ).
tcf(c_14545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_through_3_points(X0,X1,point2),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = X3 )
| ( line_through_3_points(X0,X1,point2) = X2 )
| ~ plane(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14390,c_125]) ).
tcf(c_14617,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point2)) = point_2_on_line(a_line) )
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ plane(line_from_to(point_2_on_line(a_line),point2)) ),
inference(global_subsumption_just,[status(thm)],[c_11171,c_125,c_4353,c_11171]) ).
tcf(c_14618,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point2)) = point_2_on_line(a_line) )
| ~ plane(line_from_to(point_2_on_line(a_line),point2))
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(renaming,[status(thm)],[c_14617]) ).
tcf(c_14630,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point2)) = point_2_on_line(a_line) )
| ~ line(a_line)
| ~ plane(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_14618]) ).
tcf(c_14631,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point2)) = point_2_on_line(a_line) )
| ~ plane(line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14630,c_125]) ).
tcf(c_14648,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point2)) = point_2_on_line(a_line) )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_11151,c_14631]) ).
tcf(c_14655,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_1_on_line(a_line))) = point_1_on_line(a_line) )
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ plane(line_from_to(point1,point_1_on_line(a_line))) ),
inference(global_subsumption_just,[status(thm)],[c_11776,c_125,c_4351,c_11776]) ).
tcf(c_14656,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_1_on_line(a_line))) = point_1_on_line(a_line) )
| ~ plane(line_from_to(point1,point_1_on_line(a_line)))
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(renaming,[status(thm)],[c_14655]) ).
tcf(c_14668,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_1_on_line(a_line))) = point_1_on_line(a_line) )
| ~ line(a_line)
| ~ plane(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_14656]) ).
tcf(c_14669,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_1_on_line(a_line))) = point_1_on_line(a_line) )
| ~ plane(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14668,c_125]) ).
tcf(c_14686,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_1_on_line(a_line))) = point_1_on_line(a_line) )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_11755,c_14669]) ).
tcf(c_14693,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_2_on_line(a_line))) = point_2_on_line(a_line) )
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ plane(line_from_to(point1,point_2_on_line(a_line))) ),
inference(global_subsumption_just,[status(thm)],[c_11804,c_125,c_4353,c_11804]) ).
tcf(c_14694,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_2_on_line(a_line))) = point_2_on_line(a_line) )
| ~ plane(line_from_to(point1,point_2_on_line(a_line)))
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(renaming,[status(thm)],[c_14693]) ).
tcf(c_14706,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_2_on_line(a_line))) = point_2_on_line(a_line) )
| ~ line(a_line)
| ~ plane(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_14694]) ).
tcf(c_14707,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_2_on_line(a_line))) = point_2_on_line(a_line) )
| ~ plane(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14706,c_125]) ).
tcf(c_14724,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point1,point_2_on_line(a_line))) = point_2_on_line(a_line) )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_11783,c_14707]) ).
tcf(c_14745,plain,
( ( point1 = point2 )
| ( line_from_to(point2,point1) = point1 )
| ( line_from_to(point1,line_from_to(point2,point1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(superposition,[status(thm)],[c_9035,c_12030]) ).
tcf(c_14746,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point2,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line) ),
inference(superposition,[status(thm)],[c_9438,c_12030]) ).
tcf(c_14747,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point2,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line) ),
inference(superposition,[status(thm)],[c_9102,c_12030]) ).
tcf(c_14748,plain,
( ( point1 = a_line )
| ( point1 = point2 )
| ( line_from_to(point1,a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(light_normalisation,[status(thm)],[c_14745,c_9035]) ).
tcf(c_14750,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point2,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14747,c_9364]) ).
tcf(c_14757,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point2,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_1_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14746,c_9468]) ).
tcf(c_14764,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point2,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(global_subsumption_just,[status(thm)],[c_14750,c_125,c_4353,c_14750]) ).
tcf(c_14776,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),a_line)
| ( X2 = point2 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ collinear(X0,X1,X2)
| ~ on(point2,line_through_3_points(X0,X1,X2)) ),
inference(global_subsumption_just,[status(thm)],[c_3137,c_120,c_3137]) ).
tcf(c_14802,plain,
! [X0: $i,X1: $i] :
( on(line_through_3_points(point2,X0,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1) ),
inference(superposition,[status(thm)],[c_117,c_14776]) ).
tcf(c_14803,plain,
! [X0: $i,X1: $i] :
( on(line_through_3_points(X0,point2,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1) ),
inference(superposition,[status(thm)],[c_118,c_14776]) ).
tcf(c_14805,plain,
! [X0: $i,X1: $i] :
( on(line_through_3_points(X0,point2,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14803,c_123]) ).
tcf(c_14815,plain,
! [X0: $i,X1: $i] :
( on(line_through_3_points(point2,X0,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14802,c_123]) ).
tcf(c_14843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),X2) ),
inference(superposition,[status(thm)],[c_13784,c_94]) ).
tcf(c_14844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,line_through_3_points(X0,point2,X1),X3)
| ( X3 = X4 )
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = X4 )
| ( line_through_3_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,a_line)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),X2) ),
inference(superposition,[status(thm)],[c_13784,c_111]) ).
tcf(c_14845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),X2) ),
inference(superposition,[status(thm)],[c_13784,c_112]) ).
tcf(c_14846,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_6119]) ).
tcf(c_14849,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),a_line) ),
inference(superposition,[status(thm)],[c_13784,c_2934]) ).
tcf(c_14852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_through_3_points(X0,point2,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = X3 )
| ( line_through_3_points(X0,point2,X1) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_121]) ).
tcf(c_14853,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),a_line) ),
inference(superposition,[status(thm)],[c_13784,c_2925]) ).
tcf(c_14854,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point1 )
| ( line_from_to(line_through_3_points(X0,point2,X1),point1) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_12246]) ).
tcf(c_14855,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point1 )
| ( line_from_to(point1,line_through_3_points(X0,point2,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_11471]) ).
tcf(c_14856,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ( line_from_to(line_through_3_points(X0,point2,X1),point2) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_11016]) ).
tcf(c_14857,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ( line_from_to(point2,line_through_3_points(X0,point2,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_9014]) ).
tcf(c_14858,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( point_2_on_line(line_through_3_points(X0,point2,X1)) = point_on_plane(line_through_3_points(X0,point2,X1)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(a_line,line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_6890]) ).
tcf(c_14859,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( point_1_on_line(line_through_3_points(X0,point2,X1)) = point_on_plane(line_through_3_points(X0,point2,X1)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(a_line,line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_6730]) ).
tcf(c_14860,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ( point_2_on_line(line_through_3_points(X0,point2,X1)) = point_on_plane(line_through_3_points(X0,point2,X1)) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(point2,line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_6894]) ).
tcf(c_14861,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ( point_1_on_line(line_through_3_points(X0,point2,X1)) = point_on_plane(line_through_3_points(X0,point2,X1)) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(point2,line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_6734]) ).
tcf(c_14862,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14846,c_125]) ).
tcf(c_14918,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14853,c_125,c_127]) ).
tcf(c_14931,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14849,c_125,c_126]) ).
tcf(c_14960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14843,c_125]) ).
tcf(c_15007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_through_3_points(X0,point2,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = X3 )
| ( line_through_3_points(X0,point2,X1) = X2 )
| ~ plane(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14852,c_125]) ).
tcf(c_15132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),X2) ),
inference(superposition,[status(thm)],[c_14083,c_94]) ).
tcf(c_15133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,line_through_3_points(X0,X1,point2),X3)
| ( X3 = X4 )
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = X4 )
| ( line_through_3_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,a_line)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),X2) ),
inference(superposition,[status(thm)],[c_14083,c_111]) ).
tcf(c_15134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),X2) ),
inference(superposition,[status(thm)],[c_14083,c_112]) ).
tcf(c_15135,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_6119]) ).
tcf(c_15138,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),a_line) ),
inference(superposition,[status(thm)],[c_14083,c_2934]) ).
tcf(c_15141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_through_3_points(X0,X1,point2),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = X3 )
| ( line_through_3_points(X0,X1,point2) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_121]) ).
tcf(c_15142,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),a_line) ),
inference(superposition,[status(thm)],[c_14083,c_2925]) ).
tcf(c_15143,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point1 )
| ( line_from_to(line_through_3_points(X0,X1,point2),point1) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_12246]) ).
tcf(c_15144,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point1 )
| ( line_from_to(point1,line_through_3_points(X0,X1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_11471]) ).
tcf(c_15145,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ( line_from_to(line_through_3_points(X0,X1,point2),point2) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_11016]) ).
tcf(c_15146,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ( line_from_to(point2,line_through_3_points(X0,X1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_9014]) ).
tcf(c_15147,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( point_2_on_line(line_through_3_points(X0,X1,point2)) = point_on_plane(line_through_3_points(X0,X1,point2)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(a_line,line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_6890]) ).
tcf(c_15148,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( point_1_on_line(line_through_3_points(X0,X1,point2)) = point_on_plane(line_through_3_points(X0,X1,point2)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(a_line,line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_6730]) ).
tcf(c_15149,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ( point_2_on_line(line_through_3_points(X0,X1,point2)) = point_on_plane(line_through_3_points(X0,X1,point2)) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(point2,line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_6894]) ).
tcf(c_15150,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ( point_1_on_line(line_through_3_points(X0,X1,point2)) = point_on_plane(line_through_3_points(X0,X1,point2)) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(point2,line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_6734]) ).
tcf(c_15151,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15135,c_125]) ).
tcf(c_15207,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15142,c_125,c_127]) ).
tcf(c_15220,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15138,c_125,c_126]) ).
tcf(c_15249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15132,c_125]) ).
tcf(c_15296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_through_3_points(X0,X1,point2),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = X3 )
| ( line_through_3_points(X0,X1,point2) = X2 )
| ~ plane(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15141,c_125]) ).
tcf(c_15551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_14093,c_94]) ).
tcf(c_15552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,line_through_3_points(point2,X0,X1),X3)
| ( X3 = X4 )
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = X4 )
| ( line_through_3_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,a_line)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_14093,c_111]) ).
tcf(c_15553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_14093,c_112]) ).
tcf(c_15554,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_6119]) ).
tcf(c_15557,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_14093,c_2934]) ).
tcf(c_15560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_through_3_points(point2,X0,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = X3 )
| ( line_through_3_points(point2,X0,X1) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_121]) ).
tcf(c_15561,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_14093,c_2925]) ).
tcf(c_15562,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point1 )
| ( line_from_to(line_through_3_points(point2,X0,X1),point1) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_12246]) ).
tcf(c_15563,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point1 )
| ( line_from_to(point1,line_through_3_points(point2,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_11471]) ).
tcf(c_15564,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ( line_from_to(line_through_3_points(point2,X0,X1),point2) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_11016]) ).
tcf(c_15565,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ( line_from_to(point2,line_through_3_points(point2,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_9014]) ).
tcf(c_15566,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( point_2_on_line(line_through_3_points(point2,X0,X1)) = point_on_plane(line_through_3_points(point2,X0,X1)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(a_line,line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_6890]) ).
tcf(c_15567,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( point_1_on_line(line_through_3_points(point2,X0,X1)) = point_on_plane(line_through_3_points(point2,X0,X1)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(a_line,line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_6730]) ).
tcf(c_15568,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ( point_2_on_line(line_through_3_points(point2,X0,X1)) = point_on_plane(line_through_3_points(point2,X0,X1)) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(point2,line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_6894]) ).
tcf(c_15569,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ( point_1_on_line(line_through_3_points(point2,X0,X1)) = point_on_plane(line_through_3_points(point2,X0,X1)) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(point2,line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_6734]) ).
tcf(c_15570,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15554,c_125]) ).
tcf(c_15626,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15561,c_125,c_127]) ).
tcf(c_15639,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15557,c_125,c_126]) ).
tcf(c_15668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15551,c_125]) ).
tcf(c_15715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_through_3_points(point2,X0,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = X3 )
| ( line_through_3_points(point2,X0,X1) = X2 )
| ~ plane(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15560,c_125]) ).
tcf(c_15829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),X2) ),
inference(superposition,[status(thm)],[c_14805,c_94]) ).
tcf(c_15830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,line_through_3_points(X0,point2,X1),X3)
| ( X3 = X4 )
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = X4 )
| ( line_through_3_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,a_line)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),X2) ),
inference(superposition,[status(thm)],[c_14805,c_111]) ).
tcf(c_15831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),X2) ),
inference(superposition,[status(thm)],[c_14805,c_112]) ).
tcf(c_15832,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_6119]) ).
tcf(c_15835,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),a_line) ),
inference(superposition,[status(thm)],[c_14805,c_2934]) ).
tcf(c_15838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_through_3_points(X0,point2,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = X3 )
| ( line_through_3_points(X0,point2,X1) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_121]) ).
tcf(c_15839,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),a_line) ),
inference(superposition,[status(thm)],[c_14805,c_2925]) ).
tcf(c_15840,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point1 )
| ( line_from_to(line_through_3_points(X0,point2,X1),point1) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_12246]) ).
tcf(c_15841,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point1 )
| ( line_from_to(point1,line_through_3_points(X0,point2,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_11471]) ).
tcf(c_15842,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ( line_from_to(line_through_3_points(X0,point2,X1),point2) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_11016]) ).
tcf(c_15843,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ( line_from_to(point2,line_through_3_points(X0,point2,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_9014]) ).
tcf(c_15844,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( point_2_on_line(line_through_3_points(X0,point2,X1)) = point_on_plane(line_through_3_points(X0,point2,X1)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(a_line,line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_6890]) ).
tcf(c_15845,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( point_1_on_line(line_through_3_points(X0,point2,X1)) = point_on_plane(line_through_3_points(X0,point2,X1)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(a_line,line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_6730]) ).
tcf(c_15846,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ( point_2_on_line(line_through_3_points(X0,point2,X1)) = point_on_plane(line_through_3_points(X0,point2,X1)) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(point2,line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_6894]) ).
tcf(c_15847,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ( point_1_on_line(line_through_3_points(X0,point2,X1)) = point_on_plane(line_through_3_points(X0,point2,X1)) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(point2,line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_6734]) ).
tcf(c_15848,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15832,c_125]) ).
tcf(c_15904,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15839,c_125,c_127]) ).
tcf(c_15917,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15835,c_125,c_126]) ).
tcf(c_15946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15829,c_125]) ).
tcf(c_15993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_through_3_points(X0,point2,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = X3 )
| ( line_through_3_points(X0,point2,X1) = X2 )
| ~ plane(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15838,c_125]) ).
tcf(c_16093,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point2,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(global_subsumption_just,[status(thm)],[c_14757,c_125,c_4351,c_14757]) ).
tcf(c_16140,plain,
( ( point1 = point2 )
| ( line_from_to(point2,point1) = point2 )
| ( line_from_to(line_from_to(point2,point1),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(superposition,[status(thm)],[c_9035,c_12031]) ).
tcf(c_16141,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point2,point_1_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line) ),
inference(superposition,[status(thm)],[c_9438,c_12031]) ).
tcf(c_16142,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point2,point_2_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line) ),
inference(superposition,[status(thm)],[c_9102,c_12031]) ).
tcf(c_16143,plain,
( ( point2 = a_line )
| ( point1 = point2 )
| ( line_from_to(a_line,point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(light_normalisation,[status(thm)],[c_16140,c_9035]) ).
tcf(c_16145,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point2,point_2_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16142,c_9364]) ).
tcf(c_16152,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point2,point_1_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_1_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16141,c_9468]) ).
tcf(c_16159,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point2,point_2_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(global_subsumption_just,[status(thm)],[c_16145,c_125,c_4353,c_16145]) ).
tcf(c_16171,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point2,point_1_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(global_subsumption_just,[status(thm)],[c_16152,c_125,c_4351,c_16152]) ).
tcf(c_16197,plain,
( ( point1 = point2 )
| ( line_from_to(point2,point1) = point2 )
| ( line_from_to(point2,line_from_to(point2,point1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(superposition,[status(thm)],[c_9035,c_12032]) ).
tcf(c_16198,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point2,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line) ),
inference(superposition,[status(thm)],[c_9438,c_12032]) ).
tcf(c_16199,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point2,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line) ),
inference(superposition,[status(thm)],[c_9102,c_12032]) ).
tcf(c_16200,plain,
( ( point2 = a_line )
| ( point1 = point2 )
| ( line_from_to(point2,a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(light_normalisation,[status(thm)],[c_16197,c_9035]) ).
tcf(c_16202,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point2,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16199,c_9364]) ).
tcf(c_16209,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point2,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_1_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16198,c_9468]) ).
tcf(c_16271,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point2,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(global_subsumption_just,[status(thm)],[c_16202,c_125,c_4353,c_16202]) ).
tcf(c_16283,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point2,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(global_subsumption_just,[status(thm)],[c_16209,c_125,c_4351,c_16209]) ).
tcf(c_16309,plain,
( ( point1 = point2 )
| ( line_from_to(point2,point1) = point1 )
| ( line_from_to(line_from_to(point2,point1),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(superposition,[status(thm)],[c_9035,c_12275]) ).
tcf(c_16310,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point2,point_1_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line) ),
inference(superposition,[status(thm)],[c_9438,c_12275]) ).
tcf(c_16311,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point2,point_2_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line) ),
inference(superposition,[status(thm)],[c_9102,c_12275]) ).
tcf(c_16312,plain,
( ( point1 = a_line )
| ( point1 = point2 )
| ( line_from_to(a_line,point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(light_normalisation,[status(thm)],[c_16309,c_9035]) ).
tcf(c_16314,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point2,point_2_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16311,c_9364]) ).
tcf(c_16321,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point2,point_1_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_1_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16310,c_9468]) ).
tcf(c_16370,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point2,point_2_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(global_subsumption_just,[status(thm)],[c_16314,c_125,c_4353,c_16314]) ).
tcf(c_16382,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point2,point_1_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(global_subsumption_just,[status(thm)],[c_16321,c_125,c_4351,c_16321]) ).
tcf(c_16394,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point1)) = point_1_on_line(a_line) )
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ plane(line_from_to(point_1_on_line(a_line),point1)) ),
inference(global_subsumption_just,[status(thm)],[c_12363,c_125,c_4351,c_12363]) ).
tcf(c_16395,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point1)) = point_1_on_line(a_line) )
| ~ plane(line_from_to(point_1_on_line(a_line),point1))
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(renaming,[status(thm)],[c_16394]) ).
tcf(c_16407,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point1)) = point_1_on_line(a_line) )
| ~ line(a_line)
| ~ plane(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_16395]) ).
tcf(c_16408,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point1)) = point_1_on_line(a_line) )
| ~ plane(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16407,c_125]) ).
tcf(c_16618,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_1_on_line(a_line),point1)) = point_1_on_line(a_line) )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_12340,c_16408]) ).
tcf(c_16641,plain,
! [X0: $i] :
( on(line_from_to(X0,point2),a_line)
| ( X0 = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_92,c_3138]) ).
tcf(c_16644,plain,
( on(line_from_to(point1,point2),a_line)
| ( point1 = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(point1)
| ~ on(point2,a_line)
| ~ on(point1,a_line)
| ~ line(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_3138]) ).
tcf(c_16647,plain,
( on(line_from_to(point_2_on_line(a_line),point1),a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ on(point2,a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_3138]) ).
tcf(c_16648,plain,
( on(line_from_to(point1,point_2_on_line(a_line)),a_line)
| ( point1 = point2 )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ on(point2,a_line)
| ~ on(point1,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_3138]) ).
tcf(c_16649,plain,
( on(line_from_to(point_1_on_line(a_line),point1),a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ on(point2,a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_3138]) ).
tcf(c_16650,plain,
( on(line_from_to(point1,point_1_on_line(a_line)),a_line)
| ( point1 = point2 )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ on(point2,a_line)
| ~ on(point1,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_3138]) ).
tcf(c_16651,plain,
( on(line_from_to(point_1_on_line(a_line),point2),a_line)
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_3138]) ).
tcf(c_16652,plain,
( on(line_from_to(point_2_on_line(a_line),point2),a_line)
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_3138]) ).
tcf(c_16653,plain,
! [X0: $i] :
( on(line_from_to(X0,point2),a_line)
| ( X0 = point2 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16641,c_123]) ).
tcf(c_16662,plain,
( on(line_from_to(point_2_on_line(a_line),point2),a_line)
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16652,c_123,c_127,c_9364]) ).
tcf(c_16668,plain,
( on(line_from_to(point_1_on_line(a_line),point2),a_line)
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16651,c_123,c_127,c_9468]) ).
tcf(c_16674,plain,
( on(line_from_to(point1,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16650,c_129,c_122,c_127,c_126]) ).
tcf(c_16680,plain,
( on(line_from_to(point1,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16648,c_129,c_122,c_127,c_126]) ).
tcf(c_16686,plain,
( on(line_from_to(point_1_on_line(a_line),point1),a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16649,c_122,c_127,c_9468]) ).
tcf(c_16693,plain,
( on(line_from_to(point_2_on_line(a_line),point1),a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16647,c_122,c_127,c_9364]) ).
tcf(c_16713,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ~ plane(a_line)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ line(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_16653]) ).
tcf(c_16716,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = point2 )
| ( line_from_to(X0,point2) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(line_from_to(X0,point2),X1) ),
inference(superposition,[status(thm)],[c_16653,c_94]) ).
tcf(c_16717,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_from_to(X0,point2),X2)
| ( X2 = X3 )
| ( X1 = a_line )
| ( X0 = point2 )
| ( line_from_to(X0,point2) = X3 )
| ( line_from_to(X0,point2) = X2 )
| ~ plane(a_line)
| ~ plane(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X1)
| ~ on(X2,X1)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(line_from_to(X0,point2),X1) ),
inference(superposition,[status(thm)],[c_16653,c_111]) ).
tcf(c_16718,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,a_line)
| ( X0 = point2 )
| ( line_from_to(X0,point2) = X2 )
| ~ plane(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(line_from_to(X0,point2),X1) ),
inference(superposition,[status(thm)],[c_16653,c_112]) ).
tcf(c_16719,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(X0,point2) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_6119]) ).
tcf(c_16722,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(X0,point2) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(line_from_to(X0,point2),a_line) ),
inference(superposition,[status(thm)],[c_16653,c_2934]) ).
tcf(c_16725,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(X0,point2),X1)
| ( X1 = X2 )
| ( X0 = point2 )
| ( line_from_to(X0,point2) = X2 )
| ( line_from_to(X0,point2) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_121]) ).
tcf(c_16726,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(X0,point2) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(line_from_to(X0,point2),a_line) ),
inference(superposition,[status(thm)],[c_16653,c_2925]) ).
tcf(c_16727,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = point1 )
| ( line_from_to(line_from_to(X0,point2),point1) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_12246]) ).
tcf(c_16728,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = point1 )
| ( line_from_to(point1,line_from_to(X0,point2)) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_11471]) ).
tcf(c_16729,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = point2 )
| ( line_from_to(line_from_to(X0,point2),point2) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_11016]) ).
tcf(c_16730,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = point2 )
| ( line_from_to(point2,line_from_to(X0,point2)) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_9014]) ).
tcf(c_16731,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = a_line )
| ( point_2_on_line(line_from_to(X0,point2)) = point_on_plane(line_from_to(X0,point2)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,point2))
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(a_line,line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_6890]) ).
tcf(c_16732,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = a_line )
| ( point_1_on_line(line_from_to(X0,point2)) = point_on_plane(line_from_to(X0,point2)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,point2))
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(a_line,line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_6730]) ).
tcf(c_16733,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = a_line )
| ( line_from_to(X0,point2) = point2 )
| ( point_2_on_line(line_from_to(X0,point2)) = point_on_plane(line_from_to(X0,point2)) )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,point2))
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(point2,line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_6894]) ).
tcf(c_16734,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = a_line )
| ( line_from_to(X0,point2) = point2 )
| ( point_1_on_line(line_from_to(X0,point2)) = point_on_plane(line_from_to(X0,point2)) )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,point2))
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(point2,line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_6734]) ).
tcf(c_16735,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(light_normalisation,[status(thm)],[c_16713,c_11046]) ).
tcf(c_16737,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(X0,point2) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16719,c_125]) ).
tcf(c_16778,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(X0,point2) = point2 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(line_from_to(X0,point2),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16726,c_125,c_127]) ).
tcf(c_16788,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(X0,point2) = point1 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(line_from_to(X0,point2),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16722,c_125,c_126]) ).
tcf(c_16855,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = point2 )
| ( line_from_to(X0,point2) = X2 )
| ~ plane(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(line_from_to(X0,point2),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16716,c_125]) ).
tcf(c_16869,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(X0,point2),X1)
| ( X1 = X2 )
| ( X0 = point2 )
| ( line_from_to(X0,point2) = X2 )
| ( line_from_to(X0,point2) = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16725,c_125]) ).
tcf(c_16956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_14815,c_94]) ).
tcf(c_16957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,line_through_3_points(point2,X0,X1),X3)
| ( X3 = X4 )
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = X4 )
| ( line_through_3_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,a_line)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_14815,c_111]) ).
tcf(c_16958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_14815,c_112]) ).
tcf(c_16959,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_6119]) ).
tcf(c_16962,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_14815,c_2934]) ).
tcf(c_16965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_through_3_points(point2,X0,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = X3 )
| ( line_through_3_points(point2,X0,X1) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_121]) ).
tcf(c_16966,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_14815,c_2925]) ).
tcf(c_16967,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point1 )
| ( line_from_to(line_through_3_points(point2,X0,X1),point1) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_12246]) ).
tcf(c_16968,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point1 )
| ( line_from_to(point1,line_through_3_points(point2,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_11471]) ).
tcf(c_16969,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ( line_from_to(line_through_3_points(point2,X0,X1),point2) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_11016]) ).
tcf(c_16970,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ( line_from_to(point2,line_through_3_points(point2,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_9014]) ).
tcf(c_16971,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( point_2_on_line(line_through_3_points(point2,X0,X1)) = point_on_plane(line_through_3_points(point2,X0,X1)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(a_line,line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_6890]) ).
tcf(c_16972,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( point_1_on_line(line_through_3_points(point2,X0,X1)) = point_on_plane(line_through_3_points(point2,X0,X1)) )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(a_line,line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_6730]) ).
tcf(c_16973,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ( point_2_on_line(line_through_3_points(point2,X0,X1)) = point_on_plane(line_through_3_points(point2,X0,X1)) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(point2,line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_6894]) ).
tcf(c_16974,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ( point_1_on_line(line_through_3_points(point2,X0,X1)) = point_on_plane(line_through_3_points(point2,X0,X1)) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(point2,line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_6734]) ).
tcf(c_16975,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point_on_plane(a_line) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16959,c_125]) ).
tcf(c_17031,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16966,c_125,c_127]) ).
tcf(c_17044,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16962,c_125,c_126]) ).
tcf(c_17073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16956,c_125]) ).
tcf(c_17120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_through_3_points(point2,X0,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = X3 )
| ( line_through_3_points(point2,X0,X1) = X2 )
| ~ plane(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16965,c_125]) ).
tcf(c_17220,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,X0)
| ( point_1_on_line(X0) = X2 )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ on(point_1_on_line(X0),X1)
| ~ on(X2,X0)
| ~ on(X2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_2913,c_97,c_2913]) ).
tcf(c_17221,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,X0)
| ( point_1_on_line(X0) = X2 )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_1_on_line(X0),X1) ),
inference(renaming,[status(thm)],[c_17220]) ).
tcf(c_17240,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_from_to(X1,point_1_on_line(X2)),X2)
| ( point_1_on_line(X2) = X1 )
| ( point_1_on_line(X2) = X0 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X2))
| ~ on(X0,X2)
| ~ line(line_from_to(X1,point_1_on_line(X2)))
| ~ on(X0,line_from_to(X1,point_1_on_line(X2))) ),
inference(superposition,[status(thm)],[c_92,c_17221]) ).
tcf(c_17241,plain,
! [X0: $i,X1: $i] :
( on(X1,X1)
| ( point_1_on_line(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X0)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_95,c_17221]) ).
tcf(c_17242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,X2,point_1_on_line(X3))
| on(plane_for_points(X1,X2,point_1_on_line(X3)),X3)
| ( X1 = X2 )
| ( point_1_on_line(X3) = X2 )
| ( point_1_on_line(X3) = X1 )
| ( point_1_on_line(X3) = X0 )
| ~ plane(X3)
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X3))
| ~ on(X0,X3)
| ~ line(plane_for_points(X1,X2,point_1_on_line(X3)))
| ~ on(X0,plane_for_points(X1,X2,point_1_on_line(X3))) ),
inference(superposition,[status(thm)],[c_109,c_17221]) ).
tcf(c_17243,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(line_through_3_points(point_1_on_line(X1),X2,X3),X1)
| ( X2 = X3 )
| ( point_1_on_line(X1) = X3 )
| ( point_1_on_line(X1) = X2 )
| ( point_1_on_line(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ collinear(point_1_on_line(X1),X2,X3)
| ~ line(line_through_3_points(point_1_on_line(X1),X2,X3))
| ~ on(X0,line_through_3_points(point_1_on_line(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_17221]) ).
tcf(c_17244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(line_through_3_points(X1,point_1_on_line(X2),X3),X2)
| ( X1 = X3 )
| ( point_1_on_line(X2) = X3 )
| ( point_1_on_line(X2) = X1 )
| ( point_1_on_line(X2) = X0 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X2))
| ~ on(X0,X2)
| ~ collinear(X1,point_1_on_line(X2),X3)
| ~ line(line_through_3_points(X1,point_1_on_line(X2),X3))
| ~ on(X0,line_through_3_points(X1,point_1_on_line(X2),X3)) ),
inference(superposition,[status(thm)],[c_118,c_17221]) ).
tcf(c_17245,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(line_through_3_points(X1,X2,point_1_on_line(X3)),X3)
| ( X1 = X2 )
| ( point_1_on_line(X3) = X2 )
| ( point_1_on_line(X3) = X1 )
| ( point_1_on_line(X3) = X0 )
| ~ plane(X3)
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X3))
| ~ on(X0,X3)
| ~ collinear(X1,X2,point_1_on_line(X3))
| ~ line(line_through_3_points(X1,X2,point_1_on_line(X3)))
| ~ on(X0,line_through_3_points(X1,X2,point_1_on_line(X3))) ),
inference(superposition,[status(thm)],[c_119,c_17221]) ).
tcf(c_17246,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_from_to(point_1_on_line(X1),X2),X1)
| ( point_1_on_line(X1) = X2 )
| ( point_1_on_line(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ line(line_from_to(point_1_on_line(X1),X2))
| ~ on(X0,line_from_to(point_1_on_line(X1),X2)) ),
inference(superposition,[status(thm)],[c_91,c_17221]) ).
tcf(c_17247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(point_1_on_line(X1),X2,X3)
| on(plane_for_points(point_1_on_line(X1),X2,X3),X1)
| ( X2 = X3 )
| ( point_1_on_line(X1) = X3 )
| ( point_1_on_line(X1) = X2 )
| ( point_1_on_line(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ line(plane_for_points(point_1_on_line(X1),X2,X3))
| ~ on(X0,plane_for_points(point_1_on_line(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_17221]) ).
tcf(c_17248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,point_1_on_line(X2),X3)
| on(plane_for_points(X1,point_1_on_line(X2),X3),X2)
| ( X1 = X3 )
| ( point_1_on_line(X2) = X3 )
| ( point_1_on_line(X2) = X1 )
| ( point_1_on_line(X2) = X0 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X2))
| ~ on(X0,X2)
| ~ line(plane_for_points(X1,point_1_on_line(X2),X3))
| ~ on(X0,plane_for_points(X1,point_1_on_line(X2),X3)) ),
inference(superposition,[status(thm)],[c_108,c_17221]) ).
tcf(c_17250,plain,
! [X0: $i,X1: $i] :
( on(point_1_on_line(X1),X1)
| ( point_1_on_line(X1) = X0 )
| ( point_2_on_line(point_1_on_line(X1)) = point_on_plane(point_1_on_line(X1)) )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_1_on_line(X1))
| ~ line(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_1_on_line(X1)) ),
inference(superposition,[status(thm)],[c_6875,c_17221]) ).
tcf(c_17251,plain,
! [X0: $i,X1: $i] :
( on(point_1_on_line(X1),X1)
| ( point_1_on_line(X1) = X0 )
| ( point_1_on_line(point_1_on_line(X1)) = point_on_plane(point_1_on_line(X1)) )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_1_on_line(X1))
| ~ line(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_1_on_line(X1)) ),
inference(superposition,[status(thm)],[c_6715,c_17221]) ).
tcf(c_17438,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X0,X1),line_from_to(X0,X1))
| ( X0 = X1 )
| ( point_1_on_line(line_from_to(X0,X1)) = X1 )
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_92,c_17241]) ).
tcf(c_17440,plain,
! [X0: $i] :
( on(X0,X0)
| ( point_1_on_line(X0) = point_2_on_line(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ point(point_2_on_line(X0)) ),
inference(superposition,[status(thm)],[c_96,c_17241]) ).
tcf(c_17442,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = X2 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_109,c_17241]) ).
tcf(c_17443,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = X0 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_17241]) ).
tcf(c_17444,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = X1 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_118,c_17241]) ).
tcf(c_17445,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_through_3_points(X0,X1,X2),line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = X2 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_119,c_17241]) ).
tcf(c_17446,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X0,X1),line_from_to(X0,X1))
| ( X0 = X1 )
| ( point_1_on_line(line_from_to(X0,X1)) = X0 )
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_91,c_17241]) ).
tcf(c_17447,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = X0 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_17241]) ).
tcf(c_17448,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| on(plane_for_points(X0,X1,X2),plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = X1 )
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_108,c_17241]) ).
tcf(c_17449,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X0,X0)
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = point_1_on_line(X0) )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_113,c_17241]) ).
tcf(c_17450,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,X1)
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = point_1_on_line(X1) )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_114,c_17241]) ).
tcf(c_17451,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_3143,c_17241]) ).
tcf(c_17453,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point_2_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9364,c_17241]) ).
tcf(c_17454,plain,
! [X0: $i] :
( on(X0,X0)
| ( point_2_on_line(X0) = point_on_plane(X0) )
| ( point_1_on_line(X0) = X0 )
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0) ),
inference(superposition,[status(thm)],[c_6875,c_17241]) ).
tcf(c_17455,plain,
! [X0: $i] :
( on(X0,X0)
| ( point_1_on_line(X0) = X0 )
| ( point_1_on_line(X0) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0) ),
inference(superposition,[status(thm)],[c_6715,c_17241]) ).
tcf(c_17456,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X0,X1),line_from_to(X0,X1))
| ( X0 = X1 )
| ( point_on_plane(line_from_to(X0,X1)) = X0 )
| ( point_1_on_line(line_from_to(X0,X1)) = line_from_to(X0,X1) )
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_6405,c_17241]) ).
tcf(c_17457,plain,
! [X0: $i,X1: $i] :
( on(line_from_to(X0,X1),line_from_to(X0,X1))
| ( X0 = X1 )
| ( point_on_plane(line_from_to(X0,X1)) = X1 )
| ( point_1_on_line(line_from_to(X0,X1)) = line_from_to(X0,X1) )
| ~ point(X1)
| ~ point(X0)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_6397,c_17241]) ).
tcf(c_17458,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_13097,c_17241]) ).
tcf(c_17459,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_13548,c_17241]) ).
tcf(c_17460,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12919,c_17241]) ).
tcf(c_17461,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_13339,c_17241]) ).
tcf(c_17462,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(X0,point2) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_17241]) ).
tcf(c_17463,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(point2,X0) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_17241]) ).
tcf(c_17464,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12601,c_17241]) ).
tcf(c_17465,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12470,c_17241]) ).
tcf(c_17466,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_17241]) ).
tcf(c_17467,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_17241]) ).
tcf(c_17468,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_17241]) ).
tcf(c_17469,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_17241]) ).
tcf(c_17470,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_17241]) ).
tcf(c_17471,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_17241]) ).
tcf(c_17472,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17451,c_125]) ).
tcf(c_17477,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point_2_on_line(a_line) )
| ~ plane(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17453,c_125]) ).
tcf(c_17499,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(point2,X0) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17463,c_125]) ).
tcf(c_17507,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17465,c_125]) ).
tcf(c_17514,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17464,c_125]) ).
tcf(c_17521,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17460,c_125]) ).
tcf(c_17528,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17458,c_125]) ).
tcf(c_17549,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point2 )
| ( line_from_to(X0,point2) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17462,c_125]) ).
tcf(c_17558,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17461,c_125]) ).
tcf(c_17566,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17459,c_125]) ).
tcf(c_17612,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17471,c_125]) ).
tcf(c_17624,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17470,c_125]) ).
tcf(c_17636,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17469,c_125]) ).
tcf(c_17648,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17468,c_125]) ).
tcf(c_17660,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17467,c_125]) ).
tcf(c_17672,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point_1_on_line(a_line) )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17466,c_125]) ).
tcf(c_17750,plain,
( on(point1,point1)
| ( point_1_on_line(point1) = point_2_on_line(point1) )
| ~ plane(point1)
| ~ line(point1)
| ~ point(point_2_on_line(point1)) ),
inference(instantiation,[status(thm)],[c_17440]) ).
tcf(c_18001,plain,
! [X0: $i] :
( on(X0,X0)
| ~ line(X0)
| ~ plane(X0) ),
inference(global_subsumption_just,[status(thm)],[c_17440,c_98,c_99,c_17440]) ).
tcf(c_18002,plain,
! [X0: $i] :
( on(X0,X0)
| ~ plane(X0)
| ~ line(X0) ),
inference(renaming,[status(thm)],[c_18001]) ).
tcf(c_18010,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_18002,c_94]) ).
tcf(c_18011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,X0,X2)
| ( X2 = X3 )
| ( X0 = X3 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ on(X3,X1)
| ~ on(X3,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_18002,c_111]) ).
tcf(c_18012,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,X0)
| ( X0 = X2 )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_18002,c_112]) ).
tcf(c_18013,plain,
! [X0: $i] :
( ( X0 = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0)
| ~ on(a_line,X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_18002,c_3720]) ).
tcf(c_18016,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( X0 = point1 )
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0)
| ~ on(point1,X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_18002,c_3712]) ).
tcf(c_18017,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( X0 = point2 )
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0)
| ~ on(point2,X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_18002,c_3704]) ).
tcf(c_18018,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,X1,X0)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_18002,c_121]) ).
tcf(c_18022,plain,
( ( point1 = a_line )
| ( line_from_to(a_line,point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_18002,c_12246]) ).
tcf(c_18023,plain,
( ( point1 = a_line )
| ( line_from_to(point1,a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_18002,c_11471]) ).
tcf(c_18024,plain,
( ( point2 = a_line )
| ( line_from_to(a_line,point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_18002,c_11016]) ).
tcf(c_18025,plain,
( ( point2 = a_line )
| ( line_from_to(point2,a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_18002,c_9014]) ).
tcf(c_18030,plain,
! [X0: $i,X1: $i] :
( on(point_1_on_line(X1),X1)
| ( point_1_on_line(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_1_on_line(X1))
| ~ line(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_1_on_line(X1)) ),
inference(superposition,[status(thm)],[c_18002,c_17221]) ).
tcf(c_18031,plain,
! [X0: $i,X1: $i] :
( ( point_1_on_line(X1) = X1 )
| ( point_1_on_line(X1) = X0 )
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_1_on_line(X1))
| ~ line(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_1_on_line(X1)) ),
inference(superposition,[status(thm)],[c_18002,c_8502]) ).
tcf(c_18032,plain,
! [X0: $i,X1: $i] :
( ( point_2_on_line(X1) = X1 )
| ( point_2_on_line(X1) = X0 )
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_2_on_line(X1))
| ~ line(point_2_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_2_on_line(X1)) ),
inference(superposition,[status(thm)],[c_18002,c_8657]) ).
tcf(c_18033,plain,
! [X0: $i,X1: $i] :
( on(point_on_plane(X1),X1)
| ( point_on_plane(X1) = X0 )
| ~ plane(X1)
| ~ point(X0)
| ~ plane(point_on_plane(X1))
| ~ line(point_on_plane(X1))
| ~ on(X0,X1)
| ~ on(X0,point_on_plane(X1)) ),
inference(superposition,[status(thm)],[c_18002,c_6101]) ).
tcf(c_18034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(plane_for_points(X0,X1,X2))
| ~ on(plane_for_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_18002,c_2922]) ).
tcf(c_18035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X0 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(plane_for_points(X0,X1,X2))
| ~ on(plane_for_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_18002,c_2921]) ).
tcf(c_18036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| on(X3,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X2 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(plane_for_points(X0,X1,X2))
| ~ on(plane_for_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_18002,c_2916]) ).
tcf(c_18037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X2 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(line_through_3_points(X0,X1,X2))
| ~ on(line_through_3_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_18002,c_2919]) ).
tcf(c_18038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X1 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(line_through_3_points(X0,X1,X2))
| ~ on(line_through_3_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_18002,c_2918]) ).
tcf(c_18039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X3,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X0 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(line_through_3_points(X0,X1,X2))
| ~ on(line_through_3_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_18002,c_2917]) ).
tcf(c_18041,plain,
! [X0: $i] :
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = X0 )
| ~ point(X0)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_18002,c_9747]) ).
tcf(c_18043,plain,
! [X0: $i] :
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = X0 )
| ~ point(X0)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_18002,c_9917]) ).
tcf(c_18280,plain,
( on(line_from_to(point_2_on_line(a_line),point2),a_line)
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(global_subsumption_just,[status(thm)],[c_16662,c_125,c_4353,c_16662]) ).
tcf(c_18291,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2))
| ~ on(line_from_to(point_2_on_line(a_line),point2),X0) ),
inference(superposition,[status(thm)],[c_18280,c_94]) ).
tcf(c_18292,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(point_2_on_line(a_line),point2),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = X2 )
| ( line_from_to(point_2_on_line(a_line),point2) = X1 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X2)
| ~ point(X1)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X2,X0)
| ~ on(X1,X0)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2))
| ~ on(line_from_to(point_2_on_line(a_line),point2),X0) ),
inference(superposition,[status(thm)],[c_18280,c_111]) ).
tcf(c_18293,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2))
| ~ on(line_from_to(point_2_on_line(a_line),point2),X0) ),
inference(superposition,[status(thm)],[c_18280,c_112]) ).
tcf(c_18296,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point1,a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2))
| ~ on(line_from_to(point_2_on_line(a_line),point2),a_line) ),
inference(superposition,[status(thm)],[c_18280,c_2934]) ).
tcf(c_18299,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point_2_on_line(a_line),point2),X0)
| ( X0 = X1 )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = X1 )
| ( line_from_to(point_2_on_line(a_line),point2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_18280,c_121]) ).
tcf(c_18300,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point2,a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2))
| ~ on(line_from_to(point_2_on_line(a_line),point2),a_line) ),
inference(superposition,[status(thm)],[c_18280,c_2925]) ).
tcf(c_18301,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point1 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point2),point1) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_18280,c_12246]) ).
tcf(c_18302,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point1 )
| ( line_from_to(point1,line_from_to(point_2_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_18280,c_11471]) ).
tcf(c_18303,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point2 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point2),point2) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_18280,c_11016]) ).
tcf(c_18304,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point2 )
| ( line_from_to(point2,line_from_to(point_2_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_18280,c_9014]) ).
tcf(c_18333,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point2 )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2))
| ~ on(line_from_to(point_2_on_line(a_line),point2),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18300,c_125,c_127]) ).
tcf(c_18341,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2))
| ~ on(line_from_to(point_2_on_line(a_line),point2),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18296,c_125,c_126]) ).
tcf(c_18360,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2))
| ~ on(line_from_to(point_2_on_line(a_line),point2),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18291,c_125]) ).
tcf(c_18372,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point_2_on_line(a_line),point2),X0)
| ( X0 = X1 )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = X1 )
| ( line_from_to(point_2_on_line(a_line),point2) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18299,c_125]) ).
tcf(c_18420,plain,
( on(line_from_to(point_1_on_line(a_line),point2),a_line)
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(global_subsumption_just,[status(thm)],[c_16668,c_125,c_4351,c_16668]) ).
tcf(c_18431,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2))
| ~ on(line_from_to(point_1_on_line(a_line),point2),X0) ),
inference(superposition,[status(thm)],[c_18420,c_94]) ).
tcf(c_18432,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(point_1_on_line(a_line),point2),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = X2 )
| ( line_from_to(point_1_on_line(a_line),point2) = X1 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X2)
| ~ point(X1)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X2,X0)
| ~ on(X1,X0)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2))
| ~ on(line_from_to(point_1_on_line(a_line),point2),X0) ),
inference(superposition,[status(thm)],[c_18420,c_111]) ).
tcf(c_18433,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2))
| ~ on(line_from_to(point_1_on_line(a_line),point2),X0) ),
inference(superposition,[status(thm)],[c_18420,c_112]) ).
tcf(c_18436,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point1,a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2))
| ~ on(line_from_to(point_1_on_line(a_line),point2),a_line) ),
inference(superposition,[status(thm)],[c_18420,c_2934]) ).
tcf(c_18439,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point_1_on_line(a_line),point2),X0)
| ( X0 = X1 )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = X1 )
| ( line_from_to(point_1_on_line(a_line),point2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_18420,c_121]) ).
tcf(c_18440,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point2,a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2))
| ~ on(line_from_to(point_1_on_line(a_line),point2),a_line) ),
inference(superposition,[status(thm)],[c_18420,c_2925]) ).
tcf(c_18441,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point1 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point2),point1) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_18420,c_12246]) ).
tcf(c_18442,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point1 )
| ( line_from_to(point1,line_from_to(point_1_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_18420,c_11471]) ).
tcf(c_18443,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point2 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point2),point2) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_18420,c_11016]) ).
tcf(c_18444,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point2 )
| ( line_from_to(point2,line_from_to(point_1_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_18420,c_9014]) ).
tcf(c_18473,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point2 )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2))
| ~ on(line_from_to(point_1_on_line(a_line),point2),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18440,c_125,c_127]) ).
tcf(c_18481,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2))
| ~ on(line_from_to(point_1_on_line(a_line),point2),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18436,c_125,c_126]) ).
tcf(c_18500,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2))
| ~ on(line_from_to(point_1_on_line(a_line),point2),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18431,c_125]) ).
tcf(c_18512,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point_1_on_line(a_line),point2),X0)
| ( X0 = X1 )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = X1 )
| ( line_from_to(point_1_on_line(a_line),point2) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18439,c_125]) ).
tcf(c_18610,plain,
( on(line_from_to(point1,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(global_subsumption_just,[status(thm)],[c_16674,c_125,c_4351,c_16674]) ).
tcf(c_18621,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_18610,c_94]) ).
tcf(c_18622,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(point1,point_1_on_line(a_line)),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X2 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X2)
| ~ point(X1)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X2,X0)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_18610,c_111]) ).
tcf(c_18623,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_18610,c_112]) ).
tcf(c_18626,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point1,a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_18610,c_2934]) ).
tcf(c_18629,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point1,point_1_on_line(a_line)),X0)
| ( X0 = X1 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_18610,c_121]) ).
tcf(c_18630,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point2,a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_18610,c_2925]) ).
tcf(c_18631,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point1,point_1_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_18610,c_12246]) ).
tcf(c_18632,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point1,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_18610,c_11471]) ).
tcf(c_18633,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point1,point_1_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_18610,c_11016]) ).
tcf(c_18634,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point1,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_18610,c_9014]) ).
tcf(c_18663,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18630,c_125,c_127]) ).
tcf(c_18671,plain,
( on(a_line,a_line)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18626,c_125,c_126]) ).
tcf(c_18690,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18621,c_125]) ).
tcf(c_18702,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point1,point_1_on_line(a_line)),X0)
| ( X0 = X1 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18629,c_125]) ).
tcf(c_18782,plain,
( on(line_from_to(point1,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(global_subsumption_just,[status(thm)],[c_16680,c_125,c_4353,c_16680]) ).
tcf(c_18793,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_18782,c_94]) ).
tcf(c_18794,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(point1,point_2_on_line(a_line)),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X2 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X2)
| ~ point(X1)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X2,X0)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_18782,c_111]) ).
tcf(c_18795,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),X0) ),
inference(superposition,[status(thm)],[c_18782,c_112]) ).
tcf(c_18798,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point1,a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_18782,c_2934]) ).
tcf(c_18801,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point1,point_2_on_line(a_line)),X0)
| ( X0 = X1 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_18782,c_121]) ).
tcf(c_18802,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ on(point2,a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_18782,c_2925]) ).
tcf(c_18803,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point1,point_2_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_18782,c_12246]) ).
tcf(c_18804,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point1,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_18782,c_11471]) ).
tcf(c_18805,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point1,point_2_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_18782,c_11016]) ).
tcf(c_18806,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point1,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_18782,c_9014]) ).
tcf(c_18835,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18802,c_125,c_127]) ).
tcf(c_18843,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18798,c_125,c_126]) ).
tcf(c_18862,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ~ plane(a_line)
| ~ line(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18793,c_125]) ).
tcf(c_18874,plain,
! [X0: $i,X1: $i] :
( collinear(X1,line_from_to(point1,point_2_on_line(a_line)),X0)
| ( X0 = X1 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18801,c_125]) ).
tcf(c_18920,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ( line_from_to(X0,point1) = point1 )
| ~ point(point1)
| ~ point(X0)
| ~ plane(line_from_to(X0,point1))
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),a_line) ),
inference(superposition,[status(thm)],[c_92,c_18016]) ).
tcf(c_18921,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point1) = a_line )
| ( plane_for_points(X0,X1,point1) = point1 )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,X1,point1))
| ~ line(plane_for_points(X0,X1,point1))
| ~ point(plane_for_points(X0,X1,point1))
| ~ on(plane_for_points(X0,X1,point1),a_line) ),
inference(superposition,[status(thm)],[c_109,c_18016]) ).
tcf(c_18922,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(point1,X0,X1) = a_line )
| ( line_through_3_points(point1,X0,X1) = point1 )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(point1,X0,X1)
| ~ plane(line_through_3_points(point1,X0,X1))
| ~ line(line_through_3_points(point1,X0,X1))
| ~ point(line_through_3_points(point1,X0,X1))
| ~ on(line_through_3_points(point1,X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_117,c_18016]) ).
tcf(c_18923,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point1,X1) = a_line )
| ( line_through_3_points(X0,point1,X1) = point1 )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,point1,X1)
| ~ plane(line_through_3_points(X0,point1,X1))
| ~ line(line_through_3_points(X0,point1,X1))
| ~ point(line_through_3_points(X0,point1,X1))
| ~ on(line_through_3_points(X0,point1,X1),a_line) ),
inference(superposition,[status(thm)],[c_118,c_18016]) ).
tcf(c_18924,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point1) = a_line )
| ( line_through_3_points(X0,X1,point1) = point1 )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,point1)
| ~ plane(line_through_3_points(X0,X1,point1))
| ~ line(line_through_3_points(X0,X1,point1))
| ~ point(line_through_3_points(X0,X1,point1))
| ~ on(line_through_3_points(X0,X1,point1),a_line) ),
inference(superposition,[status(thm)],[c_119,c_18016]) ).
tcf(c_18925,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ( line_from_to(point1,X0) = point1 )
| ~ point(point1)
| ~ point(X0)
| ~ plane(line_from_to(point1,X0))
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),a_line) ),
inference(superposition,[status(thm)],[c_91,c_18016]) ).
tcf(c_18926,plain,
! [X0: $i,X1: $i] :
( collinear(point1,X0,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(point1,X0,X1) = a_line )
| ( plane_for_points(point1,X0,X1) = point1 )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(point1,X0,X1))
| ~ line(plane_for_points(point1,X0,X1))
| ~ point(plane_for_points(point1,X0,X1))
| ~ on(plane_for_points(point1,X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_107,c_18016]) ).
tcf(c_18927,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point1,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(X0,point1,X1) = a_line )
| ( plane_for_points(X0,point1,X1) = point1 )
| ~ point(point1)
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,point1,X1))
| ~ line(plane_for_points(X0,point1,X1))
| ~ point(plane_for_points(X0,point1,X1))
| ~ on(plane_for_points(X0,point1,X1),a_line) ),
inference(superposition,[status(thm)],[c_108,c_18016]) ).
tcf(c_18929,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ( line_from_to(point1,X0) = point1 )
| ~ point(X0)
| ~ plane(line_from_to(point1,X0))
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18925,c_122]) ).
tcf(c_18938,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ( line_from_to(X0,point1) = point1 )
| ~ point(X0)
| ~ plane(line_from_to(X0,point1))
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18920,c_122]) ).
tcf(c_18947,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point1,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(X0,point1,X1) = a_line )
| ( plane_for_points(X0,point1,X1) = point1 )
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,point1,X1))
| ~ line(plane_for_points(X0,point1,X1))
| ~ point(plane_for_points(X0,point1,X1))
| ~ on(plane_for_points(X0,point1,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18927,c_122]) ).
tcf(c_18960,plain,
! [X0: $i,X1: $i] :
( collinear(point1,X0,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(point1,X0,X1) = a_line )
| ( plane_for_points(point1,X0,X1) = point1 )
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(point1,X0,X1))
| ~ line(plane_for_points(point1,X0,X1))
| ~ point(plane_for_points(point1,X0,X1))
| ~ on(plane_for_points(point1,X0,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18926,c_122]) ).
tcf(c_18973,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point1) = a_line )
| ( plane_for_points(X0,X1,point1) = point1 )
| ~ point(X1)
| ~ point(X0)
| ~ plane(plane_for_points(X0,X1,point1))
| ~ line(plane_for_points(X0,X1,point1))
| ~ point(plane_for_points(X0,X1,point1))
| ~ on(plane_for_points(X0,X1,point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18921,c_122]) ).
tcf(c_18986,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point1) = a_line )
| ( line_through_3_points(X0,X1,point1) = point1 )
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,X1,point1)
| ~ plane(line_through_3_points(X0,X1,point1))
| ~ line(line_through_3_points(X0,X1,point1))
| ~ point(line_through_3_points(X0,X1,point1))
| ~ on(line_through_3_points(X0,X1,point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18924,c_122]) ).
tcf(c_18999,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point1,X1) = a_line )
| ( line_through_3_points(X0,point1,X1) = point1 )
| ~ point(X1)
| ~ point(X0)
| ~ collinear(X0,point1,X1)
| ~ plane(line_through_3_points(X0,point1,X1))
| ~ line(line_through_3_points(X0,point1,X1))
| ~ point(line_through_3_points(X0,point1,X1))
| ~ on(line_through_3_points(X0,point1,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18923,c_122]) ).
tcf(c_19012,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_through_3_points(point1,X0,X1) = a_line )
| ( line_through_3_points(point1,X0,X1) = point1 )
| ~ point(X1)
| ~ point(X0)
| ~ collinear(point1,X0,X1)
| ~ plane(line_through_3_points(point1,X0,X1))
| ~ line(line_through_3_points(point1,X0,X1))
| ~ point(line_through_3_points(point1,X0,X1))
| ~ on(line_through_3_points(point1,X0,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18922,c_122]) ).
tcf(c_19039,plain,
( ( point1 = a_line )
| ( point1 = point2 )
| ~ plane(point1)
| ~ line(point1)
| ~ point(point1)
| ~ on(point2,point1) ),
inference(superposition,[status(thm)],[c_126,c_18017]) ).
tcf(c_19041,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point2 )
| ~ line(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(point2,point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_95,c_18017]) ).
tcf(c_19042,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point2 )
| ~ line(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(point2,point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_96,c_18017]) ).
tcf(c_19043,plain,
( ( point_on_plane(a_line) = a_line )
| ( point_on_plane(a_line) = point2 )
| ~ plane(a_line)
| ~ plane(point_on_plane(a_line))
| ~ line(point_on_plane(a_line))
| ~ point(point_on_plane(a_line))
| ~ on(point2,point_on_plane(a_line)) ),
inference(superposition,[status(thm)],[c_103,c_18017]) ).
tcf(c_19044,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = a_line )
| ( common_point_on_planes(a_line,X0,X1) = point2 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(a_line,X0,X1))
| ~ line(common_point_on_planes(a_line,X0,X1))
| ~ point(common_point_on_planes(a_line,X0,X1))
| ~ on(point2,common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_18017]) ).
tcf(c_19045,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = a_line )
| ( common_point_on_planes(X0,a_line,X1) = point2 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(X0,a_line,X1))
| ~ line(common_point_on_planes(X0,a_line,X1))
| ~ point(common_point_on_planes(X0,a_line,X1))
| ~ on(point2,common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_18017]) ).
tcf(c_19047,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(point2,point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9468,c_18017]) ).
tcf(c_19048,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(point2,point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9364,c_18017]) ).
tcf(c_19054,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = a_line )
| ( line_from_to(X0,point2) = point2 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,point2))
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(point2,line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_18017]) ).
tcf(c_19055,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = a_line )
| ( line_from_to(point2,X0) = point2 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,X0))
| ~ line(line_from_to(point2,X0))
| ~ point(line_from_to(point2,X0))
| ~ on(point2,line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_18017]) ).
tcf(c_19060,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(point2,line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_18017]) ).
tcf(c_19061,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(point2,line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_18017]) ).
tcf(c_19062,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(point2,line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_18017]) ).
tcf(c_19063,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(point2,line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_18017]) ).
tcf(c_19064,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(point2,line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_18017]) ).
tcf(c_19065,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(point2,line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_18017]) ).
tcf(c_19066,plain,
( ( point1 = a_line )
| ~ plane(point1)
| ~ line(point1)
| ~ on(point2,point1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19039,c_129,c_122]) ).
tcf(c_19385,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| on(plane_for_points(X0,X1,point2),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_109,c_3139]) ).
tcf(c_19387,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| on(plane_for_points(X0,point2,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_108,c_3139]) ).
tcf(c_19388,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| on(plane_for_points(X0,point2,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19387,c_123]) ).
tcf(c_19399,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| on(plane_for_points(X0,X1,point2),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19385,c_123]) ).
tcf(c_19425,plain,
( ( point_on_plane(a_line) = a_line )
| ( point_on_plane(a_line) = point2 )
| ~ plane(a_line)
| ~ plane(point_on_plane(a_line))
| ~ line(point_on_plane(a_line))
| ~ on(point2,point_on_plane(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19043,c_104]) ).
tcf(c_19460,plain,
( ( point1 = a_line )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(a_line)
| ~ point(point1)
| ~ on(a_line,point1) ),
inference(superposition,[status(thm)],[c_126,c_18013]) ).
tcf(c_19461,plain,
( ( point2 = a_line )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(a_line)
| ~ point(point2)
| ~ on(a_line,point2) ),
inference(superposition,[status(thm)],[c_127,c_18013]) ).
tcf(c_19462,plain,
( ( point_1_on_line(a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(a_line,point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_95,c_18013]) ).
tcf(c_19463,plain,
( ( point_2_on_line(a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(a_line,point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_96,c_18013]) ).
tcf(c_19464,plain,
( ( point_on_plane(a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_on_plane(a_line))
| ~ line(point_on_plane(a_line))
| ~ point(point_on_plane(a_line))
| ~ on(a_line,point_on_plane(a_line)) ),
inference(superposition,[status(thm)],[c_103,c_18013]) ).
tcf(c_19465,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(a_line,X0,X1))
| ~ line(common_point_on_planes(a_line,X0,X1))
| ~ point(common_point_on_planes(a_line,X0,X1))
| ~ on(a_line,common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_18013]) ).
tcf(c_19466,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(X0,a_line,X1))
| ~ line(common_point_on_planes(X0,a_line,X1))
| ~ point(common_point_on_planes(X0,a_line,X1))
| ~ on(a_line,common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_18013]) ).
tcf(c_19468,plain,
( ( point_1_on_line(a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(a_line,point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9468,c_18013]) ).
tcf(c_19469,plain,
( ( point_2_on_line(a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(a_line,point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9364,c_18013]) ).
tcf(c_19475,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,point2))
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(a_line,line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_18013]) ).
tcf(c_19476,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,X0))
| ~ line(line_from_to(point2,X0))
| ~ point(line_from_to(point2,X0))
| ~ on(a_line,line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_18013]) ).
tcf(c_19481,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(a_line,line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_18013]) ).
tcf(c_19482,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(a_line,line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_18013]) ).
tcf(c_19483,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(a_line,line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_18013]) ).
tcf(c_19484,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(a_line,line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_18013]) ).
tcf(c_19485,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(a_line,line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_18013]) ).
tcf(c_19486,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(a_line,line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_18013]) ).
tcf(c_19487,plain,
( ( point2 = a_line )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(a_line)
| ~ on(a_line,point2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19461,c_123]) ).
tcf(c_19494,plain,
( ( point1 = a_line )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(a_line)
| ~ on(a_line,point1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19460,c_122]) ).
tcf(c_19678,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(point2,point_1_on_line(a_line)) ),
inference(global_subsumption_just,[status(thm)],[c_19047,c_125,c_4351,c_19047]) ).
tcf(c_19690,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(point2,point_2_on_line(a_line)) ),
inference(global_subsumption_just,[status(thm)],[c_19048,c_125,c_4353,c_19048]) ).
tcf(c_19709,plain,
( ( point_on_plane(a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_on_plane(a_line))
| ~ line(point_on_plane(a_line))
| ~ on(a_line,point_on_plane(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19464,c_104]) ).
tcf(c_19728,plain,
( ( point_1_on_line(a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(a_line,point_1_on_line(a_line)) ),
inference(global_subsumption_just,[status(thm)],[c_19468,c_125,c_4351,c_19468]) ).
tcf(c_19742,plain,
( ( point_2_on_line(a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(a_line,point_2_on_line(a_line)) ),
inference(global_subsumption_just,[status(thm)],[c_19469,c_125,c_4353,c_19469]) ).
tcf(c_19776,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_1_on_line(point_2_on_line(a_line)) = point_2_on_line(a_line) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_1_on_line(point_2_on_line(a_line)))
| ~ on(point_1_on_line(point_2_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_95,c_18041]) ).
tcf(c_19777,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(point_2_on_line(a_line)) = point_2_on_line(a_line) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(point_2_on_line(a_line)))
| ~ on(point_2_on_line(point_2_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_96,c_18041]) ).
tcf(c_19778,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_on_plane(point_2_on_line(a_line)) = point_2_on_line(a_line) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_on_plane(point_2_on_line(a_line)))
| ~ on(point_on_plane(point_2_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_103,c_18041]) ).
tcf(c_19779,plain,
! [X0: $i,X1: $i] :
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = X0 )
| ( common_point_on_planes(point_2_on_line(a_line),X0,X1) = point_2_on_line(a_line) )
| ~ plane(X0)
| ~ point(X1)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(X1,X0)
| ~ on(X1,point_2_on_line(a_line))
| ~ point(common_point_on_planes(point_2_on_line(a_line),X0,X1))
| ~ on(common_point_on_planes(point_2_on_line(a_line),X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_113,c_18041]) ).
tcf(c_19780,plain,
! [X0: $i,X1: $i] :
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = X0 )
| ( common_point_on_planes(X0,point_2_on_line(a_line),X1) = point_2_on_line(a_line) )
| ~ plane(X0)
| ~ point(X1)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(X1,X0)
| ~ on(X1,point_2_on_line(a_line))
| ~ point(common_point_on_planes(X0,point_2_on_line(a_line),X1))
| ~ on(common_point_on_planes(X0,point_2_on_line(a_line),X1),a_line) ),
inference(superposition,[status(thm)],[c_114,c_18041]) ).
tcf(c_19850,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| on(plane_for_points(X0,X1,point2),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_109,c_3140]) ).
tcf(c_19851,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| on(plane_for_points(point2,X0,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_107,c_3140]) ).
tcf(c_19853,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| on(plane_for_points(point2,X0,X1),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19851,c_123]) ).
tcf(c_19864,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| on(plane_for_points(X0,X1,point2),a_line)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19850,c_123]) ).
tcf(c_19881,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_1_on_line(point_2_on_line(a_line)) = point_2_on_line(a_line) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(point_1_on_line(point_2_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19776,c_97]) ).
tcf(c_19903,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(point_2_on_line(a_line)) = point_2_on_line(a_line) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(point_2_on_line(point_2_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19777,c_98]) ).
tcf(c_19925,plain,
( ( point_2_on_line(a_line) = a_line )
| ( point_on_plane(point_2_on_line(a_line)) = point_2_on_line(a_line) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(point_on_plane(point_2_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19778,c_104]) ).
tcf(c_19961,plain,
! [X0: $i] :
( on(a_line,point1)
| ( X0 = point1 )
| ~ plane(point1)
| ~ line(a_line)
| ~ line(point1)
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X0,point1) ),
inference(superposition,[status(thm)],[c_126,c_18012]) ).
tcf(c_19962,plain,
! [X0: $i] :
( on(a_line,point2)
| ( X0 = point2 )
| ~ plane(point2)
| ~ line(a_line)
| ~ line(point2)
| ~ point(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X0,point2) ),
inference(superposition,[status(thm)],[c_127,c_18012]) ).
tcf(c_19963,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_from_to(X1,X2),X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X2)
| ~ line(line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_92,c_18012]) ).
tcf(c_19964,plain,
! [X0: $i,X1: $i] :
( on(X1,point_1_on_line(X1))
| ( point_1_on_line(X1) = X0 )
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_1_on_line(X1))
| ~ line(point_1_on_line(X1))
| ~ point(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_1_on_line(X1)) ),
inference(superposition,[status(thm)],[c_95,c_18012]) ).
tcf(c_19965,plain,
! [X0: $i,X1: $i] :
( on(X1,point_2_on_line(X1))
| ( point_2_on_line(X1) = X0 )
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_2_on_line(X1))
| ~ line(point_2_on_line(X1))
| ~ point(point_2_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_2_on_line(X1)) ),
inference(superposition,[status(thm)],[c_96,c_18012]) ).
tcf(c_19966,plain,
! [X0: $i,X1: $i] :
( on(X1,point_on_plane(X1))
| ( point_on_plane(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_on_plane(X1))
| ~ line(point_on_plane(X1))
| ~ point(point_on_plane(X1))
| ~ on(X0,X1)
| ~ on(X0,point_on_plane(X1)) ),
inference(superposition,[status(thm)],[c_103,c_18012]) ).
tcf(c_19967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,X2,X3)
| on(plane_for_points(X1,X2,X3),X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ~ plane(X3)
| ~ line(X3)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ line(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_109,c_18012]) ).
tcf(c_19968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(line_through_3_points(X1,X2,X3),X1)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X1)
| ~ collinear(X1,X2,X3)
| ~ line(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_18012]) ).
tcf(c_19969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(line_through_3_points(X1,X2,X3),X2)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X2)
| ~ collinear(X1,X2,X3)
| ~ line(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_118,c_18012]) ).
tcf(c_19970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(line_through_3_points(X1,X2,X3),X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ~ plane(X3)
| ~ line(X3)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ collinear(X1,X2,X3)
| ~ line(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_119,c_18012]) ).
tcf(c_19971,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_from_to(X1,X2),X1)
| ( X1 = X2 )
| ( X0 = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X1)
| ~ line(line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_91,c_18012]) ).
tcf(c_19972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,X2,X3)
| on(plane_for_points(X1,X2,X3),X1)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X1)
| ~ line(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_18012]) ).
tcf(c_19973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,X2,X3)
| on(plane_for_points(X1,X2,X3),X2)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X2)
| ~ line(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_108,c_18012]) ).
tcf(c_19974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X1,common_point_on_planes(X1,X2,X3))
| ( X1 = X2 )
| ( common_point_on_planes(X1,X2,X3) = X0 )
| ~ plane(X2)
| ~ plane(X1)
| ~ line(X1)
| ~ point(X3)
| ~ point(X0)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X1)
| ~ plane(common_point_on_planes(X1,X2,X3))
| ~ line(common_point_on_planes(X1,X2,X3))
| ~ point(common_point_on_planes(X1,X2,X3))
| ~ on(X0,common_point_on_planes(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_113,c_18012]) ).
tcf(c_19975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,common_point_on_planes(X1,X2,X3))
| ( X1 = X2 )
| ( common_point_on_planes(X1,X2,X3) = X0 )
| ~ plane(X2)
| ~ plane(X1)
| ~ line(X2)
| ~ point(X3)
| ~ point(X0)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X2)
| ~ plane(common_point_on_planes(X1,X2,X3))
| ~ line(common_point_on_planes(X1,X2,X3))
| ~ point(common_point_on_planes(X1,X2,X3))
| ~ on(X0,common_point_on_planes(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_114,c_18012]) ).
tcf(c_19976,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_3143,c_18012]) ).
tcf(c_19977,plain,
! [X0: $i] :
( on(a_line,point_1_on_line(a_line))
| ( point_1_on_line(a_line) = X0 )
| ~ line(a_line)
| ~ point(X0)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9468,c_18012]) ).
tcf(c_19978,plain,
! [X0: $i] :
( on(a_line,point_2_on_line(a_line))
| ( point_2_on_line(a_line) = X0 )
| ~ line(a_line)
| ~ point(X0)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9364,c_18012]) ).
tcf(c_19979,plain,
! [X0: $i,X1: $i] :
( on(X1,X1)
| ( X0 = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_18002,c_18012]) ).
tcf(c_19980,plain,
! [X0: $i] :
( on(a_line,line_from_to(point_2_on_line(a_line),point1))
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point_2_on_line(a_line),point1))
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1))
| ~ on(X0,line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_13097,c_18012]) ).
tcf(c_19981,plain,
! [X0: $i] :
( on(a_line,line_from_to(point1,point_2_on_line(a_line)))
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point1,point_2_on_line(a_line)))
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(X0,line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_18782,c_18012]) ).
tcf(c_19982,plain,
! [X0: $i] :
( on(a_line,line_from_to(point_1_on_line(a_line),point1))
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point_1_on_line(a_line),point1))
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1))
| ~ on(X0,line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12919,c_18012]) ).
tcf(c_19983,plain,
! [X0: $i] :
( on(a_line,line_from_to(point1,point_1_on_line(a_line)))
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point1,point_1_on_line(a_line)))
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(X0,line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_18610,c_18012]) ).
tcf(c_19984,plain,
! [X0: $i,X1: $i] :
( on(a_line,line_from_to(X1,point2))
| ( X1 = point2 )
| ( line_from_to(X1,point2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X1,point2))
| ~ line(line_from_to(X1,point2))
| ~ point(line_from_to(X1,point2))
| ~ on(X0,line_from_to(X1,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_18012]) ).
tcf(c_19985,plain,
! [X0: $i,X1: $i] :
( on(a_line,line_from_to(point2,X1))
| ( X1 = point2 )
| ( line_from_to(point2,X1) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,X1))
| ~ line(line_from_to(point2,X1))
| ~ point(line_from_to(point2,X1))
| ~ on(X0,line_from_to(point2,X1)) ),
inference(superposition,[status(thm)],[c_12003,c_18012]) ).
tcf(c_19986,plain,
! [X0: $i] :
( on(a_line,line_from_to(point2,point_1_on_line(a_line)))
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,point_1_on_line(a_line)))
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(X0,line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12601,c_18012]) ).
tcf(c_19987,plain,
! [X0: $i] :
( on(a_line,line_from_to(point2,point_2_on_line(a_line)))
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,point_2_on_line(a_line)))
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(X0,line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_12470,c_18012]) ).
tcf(c_19988,plain,
! [X0: $i] :
( on(a_line,line_from_to(point_1_on_line(a_line),point2))
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point_1_on_line(a_line),point2))
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2))
| ~ on(X0,line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_18420,c_18012]) ).
tcf(c_19989,plain,
! [X0: $i] :
( on(a_line,line_from_to(point_2_on_line(a_line),point2))
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point_2_on_line(a_line),point2))
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2))
| ~ on(X0,line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_18280,c_18012]) ).
tcf(c_19990,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(a_line,line_through_3_points(point2,X1,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(point2,X1,X2)
| ~ plane(line_through_3_points(point2,X1,X2))
| ~ line(line_through_3_points(point2,X1,X2))
| ~ point(line_through_3_points(point2,X1,X2))
| ~ on(X0,line_through_3_points(point2,X1,X2)) ),
inference(superposition,[status(thm)],[c_14815,c_18012]) ).
tcf(c_19991,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(a_line,line_through_3_points(point2,X1,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ collinear(point2,X1,X2)
| ~ plane(line_through_3_points(point2,X1,X2))
| ~ line(line_through_3_points(point2,X1,X2))
| ~ point(line_through_3_points(point2,X1,X2))
| ~ on(X0,line_through_3_points(point2,X1,X2)) ),
inference(superposition,[status(thm)],[c_14093,c_18012]) ).
tcf(c_19992,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(a_line,line_through_3_points(X1,point2,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,point2,X2)
| ~ plane(line_through_3_points(X1,point2,X2))
| ~ line(line_through_3_points(X1,point2,X2))
| ~ point(line_through_3_points(X1,point2,X2))
| ~ on(X0,line_through_3_points(X1,point2,X2)) ),
inference(superposition,[status(thm)],[c_14805,c_18012]) ).
tcf(c_19993,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(a_line,line_through_3_points(X1,point2,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,point2,X2)
| ~ plane(line_through_3_points(X1,point2,X2))
| ~ line(line_through_3_points(X1,point2,X2))
| ~ point(line_through_3_points(X1,point2,X2))
| ~ on(X0,line_through_3_points(X1,point2,X2)) ),
inference(superposition,[status(thm)],[c_13784,c_18012]) ).
tcf(c_19994,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(a_line,line_through_3_points(X1,X2,point2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,X2,point2)
| ~ plane(line_through_3_points(X1,X2,point2))
| ~ line(line_through_3_points(X1,X2,point2))
| ~ point(line_through_3_points(X1,X2,point2))
| ~ on(X0,line_through_3_points(X1,X2,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_18012]) ).
tcf(c_19995,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(a_line,line_through_3_points(X1,X2,point2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,X2,point2)
| ~ plane(line_through_3_points(X1,X2,point2))
| ~ line(line_through_3_points(X1,X2,point2))
| ~ point(line_through_3_points(X1,X2,point2))
| ~ on(X0,line_through_3_points(X1,X2,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_18012]) ).
tcf(c_20003,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19976,c_125]) ).
tcf(c_20010,plain,
! [X0: $i] :
( on(a_line,point2)
| ( X0 = point2 )
| ~ plane(point2)
| ~ line(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X0,point2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19962,c_125,c_123]) ).
tcf(c_20018,plain,
! [X0: $i] :
( on(a_line,point1)
| ( X0 = point1 )
| ~ plane(point1)
| ~ line(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X0,point1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19961,c_125,c_122]) ).
tcf(c_20026,plain,
! [X0: $i] :
( on(a_line,point_2_on_line(a_line))
| ( point_2_on_line(a_line) = X0 )
| ~ point(X0)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_2_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19978,c_125]) ).
tcf(c_20035,plain,
! [X0: $i] :
( on(a_line,point_1_on_line(a_line))
| ( point_1_on_line(a_line) = X0 )
| ~ point(X0)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_1_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19977,c_125]) ).
tcf(c_20094,plain,
! [X0: $i] :
( on(a_line,line_from_to(point_2_on_line(a_line),point2))
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = X0 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point_2_on_line(a_line),point2))
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2))
| ~ on(X0,line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19989,c_125]) ).
tcf(c_20105,plain,
! [X0: $i] :
( on(a_line,line_from_to(point_1_on_line(a_line),point2))
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = X0 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point_1_on_line(a_line),point2))
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2))
| ~ on(X0,line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19988,c_125]) ).
tcf(c_20116,plain,
! [X0: $i] :
( on(a_line,line_from_to(point2,point_2_on_line(a_line)))
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,point_2_on_line(a_line)))
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(X0,line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19987,c_125]) ).
tcf(c_20127,plain,
! [X0: $i] :
( on(a_line,line_from_to(point2,point_1_on_line(a_line)))
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,point_1_on_line(a_line)))
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(X0,line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19986,c_125]) ).
tcf(c_20138,plain,
! [X0: $i,X1: $i] :
( on(a_line,line_from_to(point2,X1))
| ( X1 = point2 )
| ( line_from_to(point2,X1) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,X1))
| ~ line(line_from_to(point2,X1))
| ~ point(line_from_to(point2,X1))
| ~ on(X0,line_from_to(point2,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19985,c_125]) ).
tcf(c_20151,plain,
! [X0: $i,X1: $i] :
( on(a_line,line_from_to(X1,point2))
| ( X1 = point2 )
| ( line_from_to(X1,point2) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X1,point2))
| ~ line(line_from_to(X1,point2))
| ~ point(line_from_to(X1,point2))
| ~ on(X0,line_from_to(X1,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19984,c_125]) ).
tcf(c_20164,plain,
! [X0: $i] :
( on(a_line,line_from_to(point1,point_1_on_line(a_line)))
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point1,point_1_on_line(a_line)))
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(X0,line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19983,c_125]) ).
tcf(c_20175,plain,
! [X0: $i] :
( on(a_line,line_from_to(point_1_on_line(a_line),point1))
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = X0 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point_1_on_line(a_line),point1))
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1))
| ~ on(X0,line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19982,c_125]) ).
tcf(c_20186,plain,
! [X0: $i] :
( on(a_line,line_from_to(point1,point_2_on_line(a_line)))
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X0 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point1,point_2_on_line(a_line)))
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(X0,line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19981,c_125]) ).
tcf(c_20197,plain,
! [X0: $i] :
( on(a_line,line_from_to(point_2_on_line(a_line),point1))
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = X0 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point_2_on_line(a_line),point1))
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1))
| ~ on(X0,line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19980,c_125]) ).
tcf(c_20328,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(a_line,line_through_3_points(X1,X2,point2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,X2,point2)
| ~ plane(line_through_3_points(X1,X2,point2))
| ~ line(line_through_3_points(X1,X2,point2))
| ~ point(line_through_3_points(X1,X2,point2))
| ~ on(X0,line_through_3_points(X1,X2,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19995,c_125]) ).
tcf(c_20345,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(a_line,line_through_3_points(X1,X2,point2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,X2,point2)
| ~ plane(line_through_3_points(X1,X2,point2))
| ~ line(line_through_3_points(X1,X2,point2))
| ~ point(line_through_3_points(X1,X2,point2))
| ~ on(X0,line_through_3_points(X1,X2,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19994,c_125]) ).
tcf(c_20362,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(a_line,line_through_3_points(X1,point2,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,point2,X2)
| ~ plane(line_through_3_points(X1,point2,X2))
| ~ line(line_through_3_points(X1,point2,X2))
| ~ point(line_through_3_points(X1,point2,X2))
| ~ on(X0,line_through_3_points(X1,point2,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19993,c_125]) ).
tcf(c_20379,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(a_line,line_through_3_points(X1,point2,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,point2,X2)
| ~ plane(line_through_3_points(X1,point2,X2))
| ~ line(line_through_3_points(X1,point2,X2))
| ~ point(line_through_3_points(X1,point2,X2))
| ~ on(X0,line_through_3_points(X1,point2,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19992,c_125]) ).
tcf(c_20396,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(a_line,line_through_3_points(point2,X1,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ collinear(point2,X1,X2)
| ~ plane(line_through_3_points(point2,X1,X2))
| ~ line(line_through_3_points(point2,X1,X2))
| ~ point(line_through_3_points(point2,X1,X2))
| ~ on(X0,line_through_3_points(point2,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19991,c_125]) ).
tcf(c_20413,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(a_line,line_through_3_points(point2,X1,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(point2,X1,X2)
| ~ plane(line_through_3_points(point2,X1,X2))
| ~ line(line_through_3_points(point2,X1,X2))
| ~ point(line_through_3_points(point2,X1,X2))
| ~ on(X0,line_through_3_points(point2,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19990,c_125]) ).
tcf(c_20656,plain,
( on(a_line,point2)
| ( point1 = point2 )
| ~ plane(point2)
| ~ line(point2)
| ~ point(point1)
| ~ on(point1,point2) ),
inference(superposition,[status(thm)],[c_126,c_20010]) ).
tcf(c_20658,plain,
( on(a_line,point2)
| ( point_1_on_line(a_line) = point2 )
| ~ plane(point2)
| ~ line(a_line)
| ~ line(point2)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),point2) ),
inference(superposition,[status(thm)],[c_95,c_20010]) ).
tcf(c_20659,plain,
( on(a_line,point2)
| ( point_2_on_line(a_line) = point2 )
| ~ plane(point2)
| ~ line(a_line)
| ~ line(point2)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),point2) ),
inference(superposition,[status(thm)],[c_96,c_20010]) ).
tcf(c_20660,plain,
( on(a_line,point2)
| ( point_on_plane(a_line) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(point_on_plane(a_line))
| ~ on(point_on_plane(a_line),point2) ),
inference(superposition,[status(thm)],[c_103,c_20010]) ).
tcf(c_20661,plain,
! [X0: $i,X1: $i] :
( on(a_line,point2)
| ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(a_line,X0,X1))
| ~ on(common_point_on_planes(a_line,X0,X1),point2) ),
inference(superposition,[status(thm)],[c_113,c_20010]) ).
tcf(c_20662,plain,
! [X0: $i,X1: $i] :
( on(a_line,point2)
| ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(X0,a_line,X1))
| ~ on(common_point_on_planes(X0,a_line,X1),point2) ),
inference(superposition,[status(thm)],[c_114,c_20010]) ).
tcf(c_20664,plain,
( on(a_line,point2)
| ( point_1_on_line(a_line) = point2 )
| ~ plane(point2)
| ~ line(point2)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),point2) ),
inference(superposition,[status(thm)],[c_9468,c_20010]) ).
tcf(c_20665,plain,
( on(a_line,point2)
| ( point_2_on_line(a_line) = point2 )
| ~ plane(point2)
| ~ line(point2)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),point2) ),
inference(superposition,[status(thm)],[c_9364,c_20010]) ).
tcf(c_20667,plain,
( on(a_line,point2)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1))
| ~ on(line_from_to(point_2_on_line(a_line),point1),point2) ),
inference(superposition,[status(thm)],[c_13097,c_20010]) ).
tcf(c_20668,plain,
( on(a_line,point2)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),point2) ),
inference(superposition,[status(thm)],[c_18782,c_20010]) ).
tcf(c_20669,plain,
( on(a_line,point2)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1))
| ~ on(line_from_to(point_1_on_line(a_line),point1),point2) ),
inference(superposition,[status(thm)],[c_12919,c_20010]) ).
tcf(c_20670,plain,
( on(a_line,point2)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),point2) ),
inference(superposition,[status(thm)],[c_18610,c_20010]) ).
tcf(c_20671,plain,
! [X0: $i] :
( on(a_line,point2)
| ( X0 = point2 )
| ( line_from_to(X0,point2) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(line_from_to(X0,point2),point2) ),
inference(superposition,[status(thm)],[c_16653,c_20010]) ).
tcf(c_20672,plain,
! [X0: $i] :
( on(a_line,point2)
| ( X0 = point2 )
| ( line_from_to(point2,X0) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0))
| ~ on(line_from_to(point2,X0),point2) ),
inference(superposition,[status(thm)],[c_12003,c_20010]) ).
tcf(c_20673,plain,
( on(a_line,point2)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(line_from_to(point2,point_1_on_line(a_line)),point2) ),
inference(superposition,[status(thm)],[c_12601,c_20010]) ).
tcf(c_20674,plain,
( on(a_line,point2)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(line_from_to(point2,point_2_on_line(a_line)),point2) ),
inference(superposition,[status(thm)],[c_12470,c_20010]) ).
tcf(c_20675,plain,
( on(a_line,point2)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2))
| ~ on(line_from_to(point_1_on_line(a_line),point2),point2) ),
inference(superposition,[status(thm)],[c_18420,c_20010]) ).
tcf(c_20676,plain,
( on(a_line,point2)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2))
| ~ on(line_from_to(point_2_on_line(a_line),point2),point2) ),
inference(superposition,[status(thm)],[c_18280,c_20010]) ).
tcf(c_20677,plain,
! [X0: $i,X1: $i] :
( on(a_line,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),point2) ),
inference(superposition,[status(thm)],[c_14815,c_20010]) ).
tcf(c_20678,plain,
! [X0: $i,X1: $i] :
( on(a_line,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),point2) ),
inference(superposition,[status(thm)],[c_14093,c_20010]) ).
tcf(c_20679,plain,
! [X0: $i,X1: $i] :
( on(a_line,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),point2) ),
inference(superposition,[status(thm)],[c_14805,c_20010]) ).
tcf(c_20680,plain,
! [X0: $i,X1: $i] :
( on(a_line,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),point2) ),
inference(superposition,[status(thm)],[c_13784,c_20010]) ).
tcf(c_20681,plain,
! [X0: $i,X1: $i] :
( on(a_line,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),point2) ),
inference(superposition,[status(thm)],[c_14083,c_20010]) ).
tcf(c_20682,plain,
! [X0: $i,X1: $i] :
( on(a_line,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),point2) ),
inference(superposition,[status(thm)],[c_13774,c_20010]) ).
tcf(c_20683,plain,
( on(a_line,point2)
| ~ plane(point2)
| ~ line(point2)
| ~ on(point1,point2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20656,c_129,c_122]) ).
tcf(c_21065,plain,
( on(a_line,point2)
| ( point_1_on_line(a_line) = point2 )
| ~ plane(point2)
| ~ line(point2)
| ~ on(point_1_on_line(a_line),point2) ),
inference(global_subsumption_just,[status(thm)],[c_20664,c_125,c_4351,c_20664]) ).
tcf(c_21077,plain,
( on(a_line,point2)
| ( point_2_on_line(a_line) = point2 )
| ~ plane(point2)
| ~ line(point2)
| ~ on(point_2_on_line(a_line),point2) ),
inference(global_subsumption_just,[status(thm)],[c_20665,c_125,c_4353,c_20665]) ).
tcf(c_21104,plain,
( on(a_line,point1)
| ( point1 = point2 )
| ~ plane(point1)
| ~ line(point1)
| ~ point(point2)
| ~ on(point2,point1) ),
inference(superposition,[status(thm)],[c_127,c_20018]) ).
tcf(c_21105,plain,
( on(a_line,point1)
| ( point_1_on_line(a_line) = point1 )
| ~ plane(point1)
| ~ line(a_line)
| ~ line(point1)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),point1) ),
inference(superposition,[status(thm)],[c_95,c_20018]) ).
tcf(c_21106,plain,
( on(a_line,point1)
| ( point_2_on_line(a_line) = point1 )
| ~ plane(point1)
| ~ line(a_line)
| ~ line(point1)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),point1) ),
inference(superposition,[status(thm)],[c_96,c_20018]) ).
tcf(c_21107,plain,
( on(a_line,point1)
| ( point_on_plane(a_line) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(point_on_plane(a_line))
| ~ on(point_on_plane(a_line),point1) ),
inference(superposition,[status(thm)],[c_103,c_20018]) ).
tcf(c_21108,plain,
! [X0: $i,X1: $i] :
( on(a_line,point1)
| ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(a_line,X0,X1))
| ~ on(common_point_on_planes(a_line,X0,X1),point1) ),
inference(superposition,[status(thm)],[c_113,c_20018]) ).
tcf(c_21109,plain,
! [X0: $i,X1: $i] :
( on(a_line,point1)
| ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(X0,a_line,X1))
| ~ on(common_point_on_planes(X0,a_line,X1),point1) ),
inference(superposition,[status(thm)],[c_114,c_20018]) ).
tcf(c_21111,plain,
( on(a_line,point1)
| ( point_1_on_line(a_line) = point1 )
| ~ plane(point1)
| ~ line(point1)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),point1) ),
inference(superposition,[status(thm)],[c_9468,c_20018]) ).
tcf(c_21112,plain,
( on(a_line,point1)
| ( point_2_on_line(a_line) = point1 )
| ~ plane(point1)
| ~ line(point1)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),point1) ),
inference(superposition,[status(thm)],[c_9364,c_20018]) ).
tcf(c_21114,plain,
( on(a_line,point1)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1))
| ~ on(line_from_to(point_2_on_line(a_line),point1),point1) ),
inference(superposition,[status(thm)],[c_13097,c_20018]) ).
tcf(c_21115,plain,
( on(a_line,point1)
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),point1) ),
inference(superposition,[status(thm)],[c_18782,c_20018]) ).
tcf(c_21116,plain,
( on(a_line,point1)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1))
| ~ on(line_from_to(point_1_on_line(a_line),point1),point1) ),
inference(superposition,[status(thm)],[c_12919,c_20018]) ).
tcf(c_21117,plain,
( on(a_line,point1)
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),point1) ),
inference(superposition,[status(thm)],[c_18610,c_20018]) ).
tcf(c_21118,plain,
! [X0: $i] :
( on(a_line,point1)
| ( X0 = point2 )
| ( line_from_to(X0,point2) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(line_from_to(X0,point2),point1) ),
inference(superposition,[status(thm)],[c_16653,c_20018]) ).
tcf(c_21119,plain,
! [X0: $i] :
( on(a_line,point1)
| ( X0 = point2 )
| ( line_from_to(point2,X0) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0))
| ~ on(line_from_to(point2,X0),point1) ),
inference(superposition,[status(thm)],[c_12003,c_20018]) ).
tcf(c_21120,plain,
( on(a_line,point1)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(line_from_to(point2,point_1_on_line(a_line)),point1) ),
inference(superposition,[status(thm)],[c_12601,c_20018]) ).
tcf(c_21121,plain,
( on(a_line,point1)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(line_from_to(point2,point_2_on_line(a_line)),point1) ),
inference(superposition,[status(thm)],[c_12470,c_20018]) ).
tcf(c_21122,plain,
( on(a_line,point1)
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2))
| ~ on(line_from_to(point_1_on_line(a_line),point2),point1) ),
inference(superposition,[status(thm)],[c_18420,c_20018]) ).
tcf(c_21123,plain,
( on(a_line,point1)
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2))
| ~ on(line_from_to(point_2_on_line(a_line),point2),point1) ),
inference(superposition,[status(thm)],[c_18280,c_20018]) ).
tcf(c_21124,plain,
! [X0: $i,X1: $i] :
( on(a_line,point1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),point1) ),
inference(superposition,[status(thm)],[c_14815,c_20018]) ).
tcf(c_21125,plain,
! [X0: $i,X1: $i] :
( on(a_line,point1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),point1) ),
inference(superposition,[status(thm)],[c_14093,c_20018]) ).
tcf(c_21126,plain,
! [X0: $i,X1: $i] :
( on(a_line,point1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),point1) ),
inference(superposition,[status(thm)],[c_14805,c_20018]) ).
tcf(c_21127,plain,
! [X0: $i,X1: $i] :
( on(a_line,point1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),point1) ),
inference(superposition,[status(thm)],[c_13784,c_20018]) ).
tcf(c_21128,plain,
! [X0: $i,X1: $i] :
( on(a_line,point1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),point1) ),
inference(superposition,[status(thm)],[c_14083,c_20018]) ).
tcf(c_21129,plain,
! [X0: $i,X1: $i] :
( on(a_line,point1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),point1) ),
inference(superposition,[status(thm)],[c_13774,c_20018]) ).
tcf(c_21130,plain,
( on(a_line,point1)
| ~ plane(point1)
| ~ line(point1)
| ~ on(point2,point1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21104,c_129,c_123]) ).
tcf(c_21422,plain,
( on(a_line,point1)
| ( point_1_on_line(a_line) = point1 )
| ~ plane(point1)
| ~ line(point1)
| ~ on(point_1_on_line(a_line),point1) ),
inference(global_subsumption_just,[status(thm)],[c_21111,c_125,c_4351,c_21111]) ).
tcf(c_21434,plain,
( on(a_line,point1)
| ( point_2_on_line(a_line) = point1 )
| ~ plane(point1)
| ~ line(point1)
| ~ on(point_2_on_line(a_line),point1) ),
inference(global_subsumption_just,[status(thm)],[c_21112,c_125,c_4353,c_21112]) ).
tcf(c_21453,plain,
( on(a_line,point2)
| ( point_on_plane(a_line) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ on(point_on_plane(a_line),point2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20660,c_104]) ).
tcf(c_21479,plain,
( on(a_line,point1)
| ( point_on_plane(a_line) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ on(point_on_plane(a_line),point1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21107,c_104]) ).
tcf(c_21524,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(point2,a_line)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_3141]) ).
tcf(c_21525,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = point2 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X1)
| ~ on(point2,X0)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_3141]) ).
tcf(c_21537,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = point2 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(a_line,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21524,c_125,c_127]) ).
tcf(c_21567,plain,
! [X0: $i] :
( ( point1 = a_line )
| ( X0 = point1 )
| ~ plane(point1)
| ~ line(a_line)
| ~ line(point1)
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X0,point1) ),
inference(superposition,[status(thm)],[c_126,c_18010]) ).
tcf(c_21568,plain,
! [X0: $i] :
( ( point2 = a_line )
| ( X0 = point2 )
| ~ plane(point2)
| ~ line(a_line)
| ~ line(point2)
| ~ point(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X0,point2) ),
inference(superposition,[status(thm)],[c_127,c_18010]) ).
tcf(c_21569,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( line_from_to(X1,X2) = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X2)
| ~ line(line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_92,c_18010]) ).
tcf(c_21570,plain,
! [X0: $i,X1: $i] :
( ( point_1_on_line(X1) = X1 )
| ( point_1_on_line(X1) = X0 )
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_1_on_line(X1))
| ~ line(point_1_on_line(X1))
| ~ point(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_1_on_line(X1)) ),
inference(superposition,[status(thm)],[c_95,c_18010]) ).
tcf(c_21571,plain,
! [X0: $i,X1: $i] :
( ( point_2_on_line(X1) = X1 )
| ( point_2_on_line(X1) = X0 )
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_2_on_line(X1))
| ~ line(point_2_on_line(X1))
| ~ point(point_2_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_2_on_line(X1)) ),
inference(superposition,[status(thm)],[c_96,c_18010]) ).
tcf(c_21572,plain,
! [X0: $i,X1: $i] :
( ( point_on_plane(X1) = X1 )
| ( point_on_plane(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_on_plane(X1))
| ~ line(point_on_plane(X1))
| ~ point(point_on_plane(X1))
| ~ on(X0,X1)
| ~ on(X0,point_on_plane(X1)) ),
inference(superposition,[status(thm)],[c_103,c_18010]) ).
tcf(c_21573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,X2,X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( plane_for_points(X1,X2,X3) = X3 )
| ~ plane(X3)
| ~ line(X3)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ line(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_109,c_18010]) ).
tcf(c_21574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X1,X2,X3) = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X1)
| ~ collinear(X1,X2,X3)
| ~ line(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_18010]) ).
tcf(c_21575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( line_through_3_points(X1,X2,X3) = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X2)
| ~ collinear(X1,X2,X3)
| ~ line(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_118,c_18010]) ).
tcf(c_21576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( line_through_3_points(X1,X2,X3) = X3 )
| ~ plane(X3)
| ~ line(X3)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ collinear(X1,X2,X3)
| ~ line(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_119,c_18010]) ).
tcf(c_21577,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X1 )
| ( line_from_to(X1,X2) = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X1)
| ~ line(line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_91,c_18010]) ).
tcf(c_21578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,X2,X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X1,X2,X3) = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X1)
| ~ line(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_18010]) ).
tcf(c_21579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,X2,X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( plane_for_points(X1,X2,X3) = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X2)
| ~ line(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_108,c_18010]) ).
tcf(c_21580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( common_point_on_planes(X1,X2,X3) = X1 )
| ( common_point_on_planes(X1,X2,X3) = X0 )
| ~ plane(X2)
| ~ plane(X1)
| ~ line(X1)
| ~ point(X3)
| ~ point(X0)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X1)
| ~ plane(common_point_on_planes(X1,X2,X3))
| ~ line(common_point_on_planes(X1,X2,X3))
| ~ point(common_point_on_planes(X1,X2,X3))
| ~ on(X0,common_point_on_planes(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_113,c_18010]) ).
tcf(c_21581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( common_point_on_planes(X1,X2,X3) = X2 )
| ( common_point_on_planes(X1,X2,X3) = X0 )
| ~ plane(X2)
| ~ plane(X1)
| ~ line(X2)
| ~ point(X3)
| ~ point(X0)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X2)
| ~ plane(common_point_on_planes(X1,X2,X3))
| ~ line(common_point_on_planes(X1,X2,X3))
| ~ point(common_point_on_planes(X1,X2,X3))
| ~ on(X0,common_point_on_planes(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_114,c_18010]) ).
tcf(c_21583,plain,
! [X0: $i] :
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = X0 )
| ~ line(a_line)
| ~ point(X0)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9468,c_18010]) ).
tcf(c_21584,plain,
! [X0: $i] :
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = X0 )
| ~ line(a_line)
| ~ point(X0)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9364,c_18010]) ).
tcf(c_21590,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( line_from_to(X1,point2) = a_line )
| ( line_from_to(X1,point2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X1,point2))
| ~ line(line_from_to(X1,point2))
| ~ point(line_from_to(X1,point2))
| ~ on(X0,line_from_to(X1,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_18010]) ).
tcf(c_21591,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( line_from_to(point2,X1) = a_line )
| ( line_from_to(point2,X1) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,X1))
| ~ line(line_from_to(point2,X1))
| ~ point(line_from_to(point2,X1))
| ~ on(X0,line_from_to(point2,X1)) ),
inference(superposition,[status(thm)],[c_12003,c_18010]) ).
tcf(c_21596,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(point2,X1,X2) = a_line )
| ( line_through_3_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(point2,X1,X2)
| ~ plane(line_through_3_points(point2,X1,X2))
| ~ line(line_through_3_points(point2,X1,X2))
| ~ point(line_through_3_points(point2,X1,X2))
| ~ on(X0,line_through_3_points(point2,X1,X2)) ),
inference(superposition,[status(thm)],[c_14815,c_18010]) ).
tcf(c_21597,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(point2,X1,X2) = a_line )
| ( line_through_3_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ collinear(point2,X1,X2)
| ~ plane(line_through_3_points(point2,X1,X2))
| ~ line(line_through_3_points(point2,X1,X2))
| ~ point(line_through_3_points(point2,X1,X2))
| ~ on(X0,line_through_3_points(point2,X1,X2)) ),
inference(superposition,[status(thm)],[c_14093,c_18010]) ).
tcf(c_21598,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,point2,X2) = a_line )
| ( line_through_3_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,point2,X2)
| ~ plane(line_through_3_points(X1,point2,X2))
| ~ line(line_through_3_points(X1,point2,X2))
| ~ point(line_through_3_points(X1,point2,X2))
| ~ on(X0,line_through_3_points(X1,point2,X2)) ),
inference(superposition,[status(thm)],[c_14805,c_18010]) ).
tcf(c_21599,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,point2,X2) = a_line )
| ( line_through_3_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,point2,X2)
| ~ plane(line_through_3_points(X1,point2,X2))
| ~ line(line_through_3_points(X1,point2,X2))
| ~ point(line_through_3_points(X1,point2,X2))
| ~ on(X0,line_through_3_points(X1,point2,X2)) ),
inference(superposition,[status(thm)],[c_13784,c_18010]) ).
tcf(c_21600,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,point2) = a_line )
| ( line_through_3_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,X2,point2)
| ~ plane(line_through_3_points(X1,X2,point2))
| ~ line(line_through_3_points(X1,X2,point2))
| ~ point(line_through_3_points(X1,X2,point2))
| ~ on(X0,line_through_3_points(X1,X2,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_18010]) ).
tcf(c_21601,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,point2) = a_line )
| ( line_through_3_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,X2,point2)
| ~ plane(line_through_3_points(X1,X2,point2))
| ~ line(line_through_3_points(X1,X2,point2))
| ~ point(line_through_3_points(X1,X2,point2))
| ~ on(X0,line_through_3_points(X1,X2,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_18010]) ).
tcf(c_21602,plain,
! [X0: $i] :
( ( point2 = a_line )
| ( X0 = point2 )
| ~ plane(point2)
| ~ line(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X0,point2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21568,c_125,c_123]) ).
tcf(c_21610,plain,
! [X0: $i] :
( ( point1 = a_line )
| ( X0 = point1 )
| ~ plane(point1)
| ~ line(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X0,point1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21567,c_125,c_122]) ).
tcf(c_21618,plain,
! [X0: $i] :
( ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = X0 )
| ~ point(X0)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_2_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21584,c_125]) ).
tcf(c_21627,plain,
! [X0: $i] :
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = X0 )
| ~ point(X0)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_1_on_line(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21583,c_125]) ).
tcf(c_21686,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( line_from_to(point2,X1) = a_line )
| ( line_from_to(point2,X1) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,X1))
| ~ line(line_from_to(point2,X1))
| ~ point(line_from_to(point2,X1))
| ~ on(X0,line_from_to(point2,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21591,c_125]) ).
tcf(c_21699,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( line_from_to(X1,point2) = a_line )
| ( line_from_to(X1,point2) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X1,point2))
| ~ line(line_from_to(X1,point2))
| ~ point(line_from_to(X1,point2))
| ~ on(X0,line_from_to(X1,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21590,c_125]) ).
tcf(c_21832,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,point2) = a_line )
| ( line_through_3_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,X2,point2)
| ~ plane(line_through_3_points(X1,X2,point2))
| ~ line(line_through_3_points(X1,X2,point2))
| ~ point(line_through_3_points(X1,X2,point2))
| ~ on(X0,line_through_3_points(X1,X2,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21601,c_125]) ).
tcf(c_21849,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,point2) = a_line )
| ( line_through_3_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,X2,point2)
| ~ plane(line_through_3_points(X1,X2,point2))
| ~ line(line_through_3_points(X1,X2,point2))
| ~ point(line_through_3_points(X1,X2,point2))
| ~ on(X0,line_through_3_points(X1,X2,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21600,c_125]) ).
tcf(c_21866,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,point2,X2) = a_line )
| ( line_through_3_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,point2,X2)
| ~ plane(line_through_3_points(X1,point2,X2))
| ~ line(line_through_3_points(X1,point2,X2))
| ~ point(line_through_3_points(X1,point2,X2))
| ~ on(X0,line_through_3_points(X1,point2,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21599,c_125]) ).
tcf(c_21883,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(X1,point2,X2) = a_line )
| ( line_through_3_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(X1,point2,X2)
| ~ plane(line_through_3_points(X1,point2,X2))
| ~ line(line_through_3_points(X1,point2,X2))
| ~ point(line_through_3_points(X1,point2,X2))
| ~ on(X0,line_through_3_points(X1,point2,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21598,c_125]) ).
tcf(c_21900,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(point2,X1,X2) = a_line )
| ( line_through_3_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ collinear(point2,X1,X2)
| ~ plane(line_through_3_points(point2,X1,X2))
| ~ line(line_through_3_points(point2,X1,X2))
| ~ point(line_through_3_points(point2,X1,X2))
| ~ on(X0,line_through_3_points(point2,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21597,c_125]) ).
tcf(c_21917,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( line_through_3_points(point2,X1,X2) = a_line )
| ( line_through_3_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ collinear(point2,X1,X2)
| ~ plane(line_through_3_points(point2,X1,X2))
| ~ line(line_through_3_points(point2,X1,X2))
| ~ point(line_through_3_points(point2,X1,X2))
| ~ on(X0,line_through_3_points(point2,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21596,c_125]) ).
tcf(c_22082,plain,
( ( point2 = a_line )
| ( point1 = point2 )
| ~ plane(point2)
| ~ line(point2)
| ~ point(point1)
| ~ on(point1,point2) ),
inference(superposition,[status(thm)],[c_126,c_21602]) ).
tcf(c_22084,plain,
( ( point2 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(point2)
| ~ line(a_line)
| ~ line(point2)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),point2) ),
inference(superposition,[status(thm)],[c_95,c_21602]) ).
tcf(c_22085,plain,
( ( point2 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(point2)
| ~ line(a_line)
| ~ line(point2)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),point2) ),
inference(superposition,[status(thm)],[c_96,c_21602]) ).
tcf(c_22086,plain,
( ( point2 = a_line )
| ( point_on_plane(a_line) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(point_on_plane(a_line))
| ~ on(point_on_plane(a_line),point2) ),
inference(superposition,[status(thm)],[c_103,c_21602]) ).
tcf(c_22087,plain,
! [X0: $i,X1: $i] :
( ( point2 = a_line )
| ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(a_line,X0,X1))
| ~ on(common_point_on_planes(a_line,X0,X1),point2) ),
inference(superposition,[status(thm)],[c_113,c_21602]) ).
tcf(c_22088,plain,
! [X0: $i,X1: $i] :
( ( point2 = a_line )
| ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(X0,a_line,X1))
| ~ on(common_point_on_planes(X0,a_line,X1),point2) ),
inference(superposition,[status(thm)],[c_114,c_21602]) ).
tcf(c_22090,plain,
( ( point2 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(point2)
| ~ line(point2)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),point2) ),
inference(superposition,[status(thm)],[c_9468,c_21602]) ).
tcf(c_22091,plain,
( ( point2 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(point2)
| ~ line(point2)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),point2) ),
inference(superposition,[status(thm)],[c_9364,c_21602]) ).
tcf(c_22092,plain,
( ( point2 = a_line )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(a_line)
| ~ line(point2)
| ~ point(a_line)
| ~ on(a_line,point2) ),
inference(superposition,[status(thm)],[c_18002,c_21602]) ).
tcf(c_22093,plain,
( ( point2 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1))
| ~ on(line_from_to(point_2_on_line(a_line),point1),point2) ),
inference(superposition,[status(thm)],[c_13097,c_21602]) ).
tcf(c_22094,plain,
( ( point2 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),point2) ),
inference(superposition,[status(thm)],[c_18782,c_21602]) ).
tcf(c_22095,plain,
( ( point2 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1))
| ~ on(line_from_to(point_1_on_line(a_line),point1),point2) ),
inference(superposition,[status(thm)],[c_12919,c_21602]) ).
tcf(c_22096,plain,
( ( point2 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),point2) ),
inference(superposition,[status(thm)],[c_18610,c_21602]) ).
tcf(c_22097,plain,
! [X0: $i] :
( ( point2 = a_line )
| ( X0 = point2 )
| ( line_from_to(X0,point2) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(line_from_to(X0,point2),point2) ),
inference(superposition,[status(thm)],[c_16653,c_21602]) ).
tcf(c_22098,plain,
! [X0: $i] :
( ( point2 = a_line )
| ( X0 = point2 )
| ( line_from_to(point2,X0) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0))
| ~ on(line_from_to(point2,X0),point2) ),
inference(superposition,[status(thm)],[c_12003,c_21602]) ).
tcf(c_22099,plain,
( ( point2 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(line_from_to(point2,point_1_on_line(a_line)),point2) ),
inference(superposition,[status(thm)],[c_12601,c_21602]) ).
tcf(c_22100,plain,
( ( point2 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(line_from_to(point2,point_2_on_line(a_line)),point2) ),
inference(superposition,[status(thm)],[c_12470,c_21602]) ).
tcf(c_22101,plain,
( ( point2 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2))
| ~ on(line_from_to(point_1_on_line(a_line),point2),point2) ),
inference(superposition,[status(thm)],[c_18420,c_21602]) ).
tcf(c_22102,plain,
( ( point2 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2))
| ~ on(line_from_to(point_2_on_line(a_line),point2),point2) ),
inference(superposition,[status(thm)],[c_18280,c_21602]) ).
tcf(c_22103,plain,
! [X0: $i,X1: $i] :
( ( point2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),point2) ),
inference(superposition,[status(thm)],[c_14815,c_21602]) ).
tcf(c_22104,plain,
! [X0: $i,X1: $i] :
( ( point2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),point2) ),
inference(superposition,[status(thm)],[c_14093,c_21602]) ).
tcf(c_22105,plain,
! [X0: $i,X1: $i] :
( ( point2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),point2) ),
inference(superposition,[status(thm)],[c_14805,c_21602]) ).
tcf(c_22106,plain,
! [X0: $i,X1: $i] :
( ( point2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),point2) ),
inference(superposition,[status(thm)],[c_13784,c_21602]) ).
tcf(c_22107,plain,
! [X0: $i,X1: $i] :
( ( point2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),point2) ),
inference(superposition,[status(thm)],[c_14083,c_21602]) ).
tcf(c_22108,plain,
! [X0: $i,X1: $i] :
( ( point2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),point2) ),
inference(superposition,[status(thm)],[c_13774,c_21602]) ).
tcf(c_22109,plain,
( ( point2 = a_line )
| ~ plane(point2)
| ~ line(point2)
| ~ on(point1,point2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22082,c_129,c_122]) ).
tcf(c_22507,plain,
( ( point1 = a_line )
| ( point1 = point2 )
| ~ plane(point1)
| ~ line(point1)
| ~ point(point2)
| ~ on(point2,point1) ),
inference(superposition,[status(thm)],[c_127,c_21610]) ).
tcf(c_22508,plain,
( ( point1 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(point1)
| ~ line(a_line)
| ~ line(point1)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),point1) ),
inference(superposition,[status(thm)],[c_95,c_21610]) ).
tcf(c_22509,plain,
( ( point1 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(point1)
| ~ line(a_line)
| ~ line(point1)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),point1) ),
inference(superposition,[status(thm)],[c_96,c_21610]) ).
tcf(c_22510,plain,
( ( point1 = a_line )
| ( point_on_plane(a_line) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(point_on_plane(a_line))
| ~ on(point_on_plane(a_line),point1) ),
inference(superposition,[status(thm)],[c_103,c_21610]) ).
tcf(c_22511,plain,
! [X0: $i,X1: $i] :
( ( point1 = a_line )
| ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(a_line,X0,X1))
| ~ on(common_point_on_planes(a_line,X0,X1),point1) ),
inference(superposition,[status(thm)],[c_113,c_21610]) ).
tcf(c_22512,plain,
! [X0: $i,X1: $i] :
( ( point1 = a_line )
| ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(X0,a_line,X1))
| ~ on(common_point_on_planes(X0,a_line,X1),point1) ),
inference(superposition,[status(thm)],[c_114,c_21610]) ).
tcf(c_22514,plain,
( ( point1 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(point1)
| ~ line(point1)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),point1) ),
inference(superposition,[status(thm)],[c_9468,c_21610]) ).
tcf(c_22515,plain,
( ( point1 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(point1)
| ~ line(point1)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),point1) ),
inference(superposition,[status(thm)],[c_9364,c_21610]) ).
tcf(c_22516,plain,
( ( point1 = a_line )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(a_line)
| ~ line(point1)
| ~ point(a_line)
| ~ on(a_line,point1) ),
inference(superposition,[status(thm)],[c_18002,c_21610]) ).
tcf(c_22517,plain,
( ( point1 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ point(line_from_to(point_2_on_line(a_line),point1))
| ~ on(line_from_to(point_2_on_line(a_line),point1),point1) ),
inference(superposition,[status(thm)],[c_13097,c_21610]) ).
tcf(c_22518,plain,
( ( point1 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point1,point_2_on_line(a_line)))
| ~ point(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(line_from_to(point1,point_2_on_line(a_line)),point1) ),
inference(superposition,[status(thm)],[c_18782,c_21610]) ).
tcf(c_22519,plain,
( ( point1 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point_1_on_line(a_line),point1))
| ~ point(line_from_to(point_1_on_line(a_line),point1))
| ~ on(line_from_to(point_1_on_line(a_line),point1),point1) ),
inference(superposition,[status(thm)],[c_12919,c_21610]) ).
tcf(c_22520,plain,
( ( point1 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point1,point_1_on_line(a_line)))
| ~ point(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(line_from_to(point1,point_1_on_line(a_line)),point1) ),
inference(superposition,[status(thm)],[c_18610,c_21610]) ).
tcf(c_22521,plain,
! [X0: $i] :
( ( point1 = a_line )
| ( X0 = point2 )
| ( line_from_to(X0,point2) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2))
| ~ on(line_from_to(X0,point2),point1) ),
inference(superposition,[status(thm)],[c_16653,c_21610]) ).
tcf(c_22522,plain,
! [X0: $i] :
( ( point1 = a_line )
| ( X0 = point2 )
| ( line_from_to(point2,X0) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0))
| ~ on(line_from_to(point2,X0),point1) ),
inference(superposition,[status(thm)],[c_12003,c_21610]) ).
tcf(c_22523,plain,
( ( point1 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point2,point_1_on_line(a_line)))
| ~ point(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(line_from_to(point2,point_1_on_line(a_line)),point1) ),
inference(superposition,[status(thm)],[c_12601,c_21610]) ).
tcf(c_22524,plain,
( ( point1 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point2,point_2_on_line(a_line)))
| ~ point(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(line_from_to(point2,point_2_on_line(a_line)),point1) ),
inference(superposition,[status(thm)],[c_12470,c_21610]) ).
tcf(c_22525,plain,
( ( point1 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point_1_on_line(a_line),point2))
| ~ point(line_from_to(point_1_on_line(a_line),point2))
| ~ on(line_from_to(point_1_on_line(a_line),point2),point1) ),
inference(superposition,[status(thm)],[c_18420,c_21610]) ).
tcf(c_22526,plain,
( ( point1 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ line(line_from_to(point_2_on_line(a_line),point2))
| ~ point(line_from_to(point_2_on_line(a_line),point2))
| ~ on(line_from_to(point_2_on_line(a_line),point2),point1) ),
inference(superposition,[status(thm)],[c_18280,c_21610]) ).
tcf(c_22527,plain,
! [X0: $i,X1: $i] :
( ( point1 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),point1) ),
inference(superposition,[status(thm)],[c_14815,c_21610]) ).
tcf(c_22528,plain,
! [X0: $i,X1: $i] :
( ( point1 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1))
| ~ on(line_through_3_points(point2,X0,X1),point1) ),
inference(superposition,[status(thm)],[c_14093,c_21610]) ).
tcf(c_22529,plain,
! [X0: $i,X1: $i] :
( ( point1 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),point1) ),
inference(superposition,[status(thm)],[c_14805,c_21610]) ).
tcf(c_22530,plain,
! [X0: $i,X1: $i] :
( ( point1 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1))
| ~ on(line_through_3_points(X0,point2,X1),point1) ),
inference(superposition,[status(thm)],[c_13784,c_21610]) ).
tcf(c_22531,plain,
! [X0: $i,X1: $i] :
( ( point1 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),point1) ),
inference(superposition,[status(thm)],[c_14083,c_21610]) ).
tcf(c_22532,plain,
! [X0: $i,X1: $i] :
( ( point1 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2))
| ~ on(line_through_3_points(X0,X1,point2),point1) ),
inference(superposition,[status(thm)],[c_13774,c_21610]) ).
tcf(c_22760,plain,
( ( point1 = a_line )
| ( common_point_on_planes(a_line,point1,point1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ on(point1,point1)
| ~ point(common_point_on_planes(a_line,point1,point1))
| ~ on(common_point_on_planes(a_line,point1,point1),point1) ),
inference(instantiation,[status(thm)],[c_22511]) ).
tcf(c_22787,plain,
( ( point2 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(point2)
| ~ line(point2)
| ~ on(point_1_on_line(a_line),point2) ),
inference(global_subsumption_just,[status(thm)],[c_22090,c_125,c_4351,c_22090]) ).
tcf(c_22799,plain,
( ( point2 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(point2)
| ~ line(point2)
| ~ on(point_2_on_line(a_line),point2) ),
inference(global_subsumption_just,[status(thm)],[c_22091,c_125,c_4353,c_22091]) ).
tcf(c_22811,plain,
( ( point1 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(point1)
| ~ line(point1)
| ~ on(point_1_on_line(a_line),point1) ),
inference(global_subsumption_just,[status(thm)],[c_22514,c_125,c_4351,c_22514]) ).
tcf(c_22823,plain,
( ( point1 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(point1)
| ~ line(point1)
| ~ on(point_2_on_line(a_line),point1) ),
inference(global_subsumption_just,[status(thm)],[c_22515,c_125,c_4353,c_22515]) ).
tcf(c_22842,plain,
( ( point2 = a_line )
| ( point_on_plane(a_line) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ on(point_on_plane(a_line),point2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22086,c_104]) ).
tcf(c_22868,plain,
( ( point1 = a_line )
| ( point_on_plane(a_line) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ on(point_on_plane(a_line),point1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22510,c_104]) ).
tcf(c_22901,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(point_1_on_line(a_line)))
| ~ on(point_1_on_line(point_1_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_95,c_18043]) ).
tcf(c_22902,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_2_on_line(point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_2_on_line(point_1_on_line(a_line)))
| ~ on(point_2_on_line(point_1_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_96,c_18043]) ).
tcf(c_22903,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_on_plane(point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_on_plane(point_1_on_line(a_line)))
| ~ on(point_on_plane(point_1_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_103,c_18043]) ).
tcf(c_22904,plain,
! [X0: $i,X1: $i] :
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = X0 )
| ( common_point_on_planes(point_1_on_line(a_line),X0,X1) = point_1_on_line(a_line) )
| ~ plane(X0)
| ~ point(X1)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(X1,X0)
| ~ on(X1,point_1_on_line(a_line))
| ~ point(common_point_on_planes(point_1_on_line(a_line),X0,X1))
| ~ on(common_point_on_planes(point_1_on_line(a_line),X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_113,c_18043]) ).
tcf(c_22905,plain,
! [X0: $i,X1: $i] :
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = X0 )
| ( common_point_on_planes(X0,point_1_on_line(a_line),X1) = point_1_on_line(a_line) )
| ~ plane(X0)
| ~ point(X1)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(X1,X0)
| ~ on(X1,point_1_on_line(a_line))
| ~ point(common_point_on_planes(X0,point_1_on_line(a_line),X1))
| ~ on(common_point_on_planes(X0,point_1_on_line(a_line),X1),a_line) ),
inference(superposition,[status(thm)],[c_114,c_18043]) ).
tcf(c_22967,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(point_1_on_line(point_1_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22901,c_97]) ).
tcf(c_23009,plain,
! [X0: $i,X1: $i] :
( on(X0,a_line)
| ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = point2 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X1)
| ~ on(point2,X0)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_3142]) ).
tcf(c_23010,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(point2,a_line)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_3142]) ).
tcf(c_23011,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = point2 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(X0,a_line,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23010,c_125,c_127]) ).
tcf(c_23111,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_2_on_line(point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(point_2_on_line(point_1_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22902,c_98]) ).
tcf(c_23135,plain,
( ( point_1_on_line(a_line) = a_line )
| ( point_on_plane(point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(point_on_plane(point_1_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22903,c_104]) ).
tcf(c_23161,plain,
! [X0: $i,X1: $i] :
( on(X1,point_1_on_line(X1))
| ( point_1_on_line(X1) = X0 )
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_1_on_line(X1))
| ~ line(point_1_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_1_on_line(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19964,c_97]) ).
tcf(c_23186,plain,
! [X0: $i] :
( on(X0,point_1_on_line(X0))
| ( point_1_on_line(point_1_on_line(X0)) = point_1_on_line(X0) )
| ~ line(X0)
| ~ plane(point_1_on_line(X0))
| ~ line(point_1_on_line(X0))
| ~ point(point_1_on_line(point_1_on_line(X0)))
| ~ on(point_1_on_line(point_1_on_line(X0)),X0) ),
inference(superposition,[status(thm)],[c_95,c_23161]) ).
tcf(c_23187,plain,
! [X0: $i] :
( on(X0,point_1_on_line(X0))
| ( point_2_on_line(point_1_on_line(X0)) = point_1_on_line(X0) )
| ~ line(X0)
| ~ plane(point_1_on_line(X0))
| ~ line(point_1_on_line(X0))
| ~ point(point_2_on_line(point_1_on_line(X0)))
| ~ on(point_2_on_line(point_1_on_line(X0)),X0) ),
inference(superposition,[status(thm)],[c_96,c_23161]) ).
tcf(c_23188,plain,
! [X0: $i] :
( on(X0,point_1_on_line(X0))
| ( point_on_plane(point_1_on_line(X0)) = point_1_on_line(X0) )
| ~ line(X0)
| ~ plane(point_1_on_line(X0))
| ~ line(point_1_on_line(X0))
| ~ point(point_on_plane(point_1_on_line(X0)))
| ~ on(point_on_plane(point_1_on_line(X0)),X0) ),
inference(superposition,[status(thm)],[c_103,c_23161]) ).
tcf(c_23189,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X0,point_1_on_line(X0))
| ( point_1_on_line(X0) = X1 )
| ( common_point_on_planes(point_1_on_line(X0),X1,X2) = point_1_on_line(X0) )
| ~ plane(X1)
| ~ line(X0)
| ~ point(X2)
| ~ plane(point_1_on_line(X0))
| ~ line(point_1_on_line(X0))
| ~ on(X2,X1)
| ~ on(X2,point_1_on_line(X0))
| ~ point(common_point_on_planes(point_1_on_line(X0),X1,X2))
| ~ on(common_point_on_planes(point_1_on_line(X0),X1,X2),X0) ),
inference(superposition,[status(thm)],[c_113,c_23161]) ).
tcf(c_23190,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,point_1_on_line(X1))
| ( point_1_on_line(X1) = X0 )
| ( common_point_on_planes(X0,point_1_on_line(X1),X2) = point_1_on_line(X1) )
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ plane(point_1_on_line(X1))
| ~ line(point_1_on_line(X1))
| ~ on(X2,X0)
| ~ on(X2,point_1_on_line(X1))
| ~ point(common_point_on_planes(X0,point_1_on_line(X1),X2))
| ~ on(common_point_on_planes(X0,point_1_on_line(X1),X2),X1) ),
inference(superposition,[status(thm)],[c_114,c_23161]) ).
tcf(c_23365,plain,
! [X0: $i] :
( on(X0,point_1_on_line(X0))
| ( point_1_on_line(point_1_on_line(X0)) = point_1_on_line(X0) )
| ~ line(X0)
| ~ plane(point_1_on_line(X0))
| ~ line(point_1_on_line(X0))
| ~ on(point_1_on_line(point_1_on_line(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23186,c_97]) ).
tcf(c_23385,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point1)) = point_2_on_line(a_line) )
| ~ line(line_from_to(point_2_on_line(a_line),point1))
| ~ plane(line_from_to(point_2_on_line(a_line),point1)) ),
inference(global_subsumption_just,[status(thm)],[c_12437,c_125,c_4353,c_12437]) ).
tcf(c_23386,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point1)) = point_2_on_line(a_line) )
| ~ plane(line_from_to(point_2_on_line(a_line),point1))
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(renaming,[status(thm)],[c_23385]) ).
tcf(c_23398,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point1)) = point_2_on_line(a_line) )
| ~ line(a_line)
| ~ plane(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_23386]) ).
tcf(c_23399,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point1)) = point_2_on_line(a_line) )
| ~ plane(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23398,c_125]) ).
tcf(c_23416,plain,
( on(a_line,a_line)
| ( point_2_on_line(a_line) = point1 )
| ( point_on_plane(line_from_to(point_2_on_line(a_line),point1)) = point_2_on_line(a_line) )
| ~ plane(a_line) ),
inference(superposition,[status(thm)],[c_12414,c_23399]) ).
tcf(c_23439,plain,
! [X0: $i] :
( ( point_1_on_line(X0) = X0 )
| ( point_1_on_line(point_1_on_line(X0)) = point_1_on_line(X0) )
| ~ line(X0)
| ~ plane(point_1_on_line(X0))
| ~ line(point_1_on_line(X0))
| ~ point(point_1_on_line(point_1_on_line(X0)))
| ~ on(point_1_on_line(point_1_on_line(X0)),X0) ),
inference(superposition,[status(thm)],[c_95,c_18031]) ).
tcf(c_23440,plain,
! [X0: $i] :
( ( point_1_on_line(X0) = X0 )
| ( point_2_on_line(point_1_on_line(X0)) = point_1_on_line(X0) )
| ~ line(X0)
| ~ plane(point_1_on_line(X0))
| ~ line(point_1_on_line(X0))
| ~ point(point_2_on_line(point_1_on_line(X0)))
| ~ on(point_2_on_line(point_1_on_line(X0)),X0) ),
inference(superposition,[status(thm)],[c_96,c_18031]) ).
tcf(c_23441,plain,
! [X0: $i] :
( ( point_1_on_line(X0) = X0 )
| ( point_on_plane(point_1_on_line(X0)) = point_1_on_line(X0) )
| ~ line(X0)
| ~ plane(point_1_on_line(X0))
| ~ line(point_1_on_line(X0))
| ~ point(point_on_plane(point_1_on_line(X0)))
| ~ on(point_on_plane(point_1_on_line(X0)),X0) ),
inference(superposition,[status(thm)],[c_103,c_18031]) ).
tcf(c_23442,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( point_1_on_line(X0) = X1 )
| ( point_1_on_line(X0) = X0 )
| ( common_point_on_planes(point_1_on_line(X0),X1,X2) = point_1_on_line(X0) )
| ~ plane(X1)
| ~ line(X0)
| ~ point(X2)
| ~ plane(point_1_on_line(X0))
| ~ line(point_1_on_line(X0))
| ~ on(X2,X1)
| ~ on(X2,point_1_on_line(X0))
| ~ point(common_point_on_planes(point_1_on_line(X0),X1,X2))
| ~ on(common_point_on_planes(point_1_on_line(X0),X1,X2),X0) ),
inference(superposition,[status(thm)],[c_113,c_18031]) ).
tcf(c_23443,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( point_1_on_line(X1) = X1 )
| ( point_1_on_line(X1) = X0 )
| ( common_point_on_planes(X0,point_1_on_line(X1),X2) = point_1_on_line(X1) )
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ plane(point_1_on_line(X1))
| ~ line(point_1_on_line(X1))
| ~ on(X2,X0)
| ~ on(X2,point_1_on_line(X1))
| ~ point(common_point_on_planes(X0,point_1_on_line(X1),X2))
| ~ on(common_point_on_planes(X0,point_1_on_line(X1),X2),X1) ),
inference(superposition,[status(thm)],[c_114,c_18031]) ).
tcf(c_23589,plain,
! [X0: $i] :
( ( point_2_on_line(X0) = X0 )
| ( point_1_on_line(point_2_on_line(X0)) = point_2_on_line(X0) )
| ~ line(X0)
| ~ plane(point_2_on_line(X0))
| ~ line(point_2_on_line(X0))
| ~ point(point_1_on_line(point_2_on_line(X0)))
| ~ on(point_1_on_line(point_2_on_line(X0)),X0) ),
inference(superposition,[status(thm)],[c_95,c_18032]) ).
tcf(c_23590,plain,
! [X0: $i] :
( ( point_2_on_line(X0) = X0 )
| ( point_2_on_line(point_2_on_line(X0)) = point_2_on_line(X0) )
| ~ line(X0)
| ~ plane(point_2_on_line(X0))
| ~ line(point_2_on_line(X0))
| ~ point(point_2_on_line(point_2_on_line(X0)))
| ~ on(point_2_on_line(point_2_on_line(X0)),X0) ),
inference(superposition,[status(thm)],[c_96,c_18032]) ).
tcf(c_23591,plain,
! [X0: $i] :
( ( point_2_on_line(X0) = X0 )
| ( point_on_plane(point_2_on_line(X0)) = point_2_on_line(X0) )
| ~ line(X0)
| ~ plane(point_2_on_line(X0))
| ~ line(point_2_on_line(X0))
| ~ point(point_on_plane(point_2_on_line(X0)))
| ~ on(point_on_plane(point_2_on_line(X0)),X0) ),
inference(superposition,[status(thm)],[c_103,c_18032]) ).
tcf(c_23592,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( point_2_on_line(X0) = X1 )
| ( point_2_on_line(X0) = X0 )
| ( common_point_on_planes(point_2_on_line(X0),X1,X2) = point_2_on_line(X0) )
| ~ plane(X1)
| ~ line(X0)
| ~ point(X2)
| ~ plane(point_2_on_line(X0))
| ~ line(point_2_on_line(X0))
| ~ on(X2,X1)
| ~ on(X2,point_2_on_line(X0))
| ~ point(common_point_on_planes(point_2_on_line(X0),X1,X2))
| ~ on(common_point_on_planes(point_2_on_line(X0),X1,X2),X0) ),
inference(superposition,[status(thm)],[c_113,c_18032]) ).
tcf(c_23593,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( point_2_on_line(X1) = X1 )
| ( point_2_on_line(X1) = X0 )
| ( common_point_on_planes(X0,point_2_on_line(X1),X2) = point_2_on_line(X1) )
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ plane(point_2_on_line(X1))
| ~ line(point_2_on_line(X1))
| ~ on(X2,X0)
| ~ on(X2,point_2_on_line(X1))
| ~ point(common_point_on_planes(X0,point_2_on_line(X1),X2))
| ~ on(common_point_on_planes(X0,point_2_on_line(X1),X2),X1) ),
inference(superposition,[status(thm)],[c_114,c_18032]) ).
tcf(c_23645,plain,
! [X0: $i] :
( on(a_line,point_2_on_line(a_line))
| ( point_2_on_line(a_line) = X0 )
| ~ point(X0)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(X0,point_2_on_line(a_line))
| ~ on(X0,a_line) ),
inference(global_subsumption_just,[status(thm)],[c_20026,c_125,c_4353,c_20026]) ).
tcf(c_23646,plain,
! [X0: $i] :
( on(a_line,point_2_on_line(a_line))
| ( point_2_on_line(a_line) = X0 )
| ~ point(X0)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_2_on_line(a_line)) ),
inference(renaming,[status(thm)],[c_23645]) ).
tcf(c_23662,plain,
( on(a_line,point_2_on_line(a_line))
| ( point_1_on_line(point_2_on_line(a_line)) = point_2_on_line(a_line) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_1_on_line(point_2_on_line(a_line)))
| ~ on(point_1_on_line(point_2_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_95,c_23646]) ).
tcf(c_23663,plain,
( on(a_line,point_2_on_line(a_line))
| ( point_2_on_line(point_2_on_line(a_line)) = point_2_on_line(a_line) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(point_2_on_line(a_line)))
| ~ on(point_2_on_line(point_2_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_96,c_23646]) ).
tcf(c_23664,plain,
( on(a_line,point_2_on_line(a_line))
| ( point_on_plane(point_2_on_line(a_line)) = point_2_on_line(a_line) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_on_plane(point_2_on_line(a_line)))
| ~ on(point_on_plane(point_2_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_103,c_23646]) ).
tcf(c_23665,plain,
! [X0: $i,X1: $i] :
( on(a_line,point_2_on_line(a_line))
| ( point_2_on_line(a_line) = X0 )
| ( common_point_on_planes(point_2_on_line(a_line),X0,X1) = point_2_on_line(a_line) )
| ~ plane(X0)
| ~ point(X1)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(X1,X0)
| ~ on(X1,point_2_on_line(a_line))
| ~ point(common_point_on_planes(point_2_on_line(a_line),X0,X1))
| ~ on(common_point_on_planes(point_2_on_line(a_line),X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_113,c_23646]) ).
tcf(c_23666,plain,
! [X0: $i,X1: $i] :
( on(a_line,point_2_on_line(a_line))
| ( point_2_on_line(a_line) = X0 )
| ( common_point_on_planes(X0,point_2_on_line(a_line),X1) = point_2_on_line(a_line) )
| ~ plane(X0)
| ~ point(X1)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(X1,X0)
| ~ on(X1,point_2_on_line(a_line))
| ~ point(common_point_on_planes(X0,point_2_on_line(a_line),X1))
| ~ on(common_point_on_planes(X0,point_2_on_line(a_line),X1),a_line) ),
inference(superposition,[status(thm)],[c_114,c_23646]) ).
tcf(c_23716,plain,
( on(a_line,point_2_on_line(a_line))
| ( point_1_on_line(point_2_on_line(a_line)) = point_2_on_line(a_line) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(point_1_on_line(point_2_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23662,c_97]) ).
tcf(c_23738,plain,
( on(a_line,point_2_on_line(a_line))
| ( point_2_on_line(point_2_on_line(a_line)) = point_2_on_line(a_line) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(point_2_on_line(point_2_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23663,c_98]) ).
tcf(c_23760,plain,
( on(a_line,point_2_on_line(a_line))
| ( point_on_plane(point_2_on_line(a_line)) = point_2_on_line(a_line) )
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ on(point_on_plane(point_2_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23664,c_104]) ).
tcf(c_23776,plain,
! [X0: $i] :
( on(a_line,point_1_on_line(a_line))
| ( point_1_on_line(a_line) = X0 )
| ~ point(X0)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(X0,point_1_on_line(a_line))
| ~ on(X0,a_line) ),
inference(global_subsumption_just,[status(thm)],[c_20035,c_125,c_4351,c_20035]) ).
tcf(c_23777,plain,
! [X0: $i] :
( on(a_line,point_1_on_line(a_line))
| ( point_1_on_line(a_line) = X0 )
| ~ point(X0)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(X0,a_line)
| ~ on(X0,point_1_on_line(a_line)) ),
inference(renaming,[status(thm)],[c_23776]) ).
tcf(c_23793,plain,
( on(a_line,point_1_on_line(a_line))
| ( point_1_on_line(point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(point_1_on_line(a_line)))
| ~ on(point_1_on_line(point_1_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_95,c_23777]) ).
tcf(c_23794,plain,
( on(a_line,point_1_on_line(a_line))
| ( point_2_on_line(point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_2_on_line(point_1_on_line(a_line)))
| ~ on(point_2_on_line(point_1_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_96,c_23777]) ).
tcf(c_23795,plain,
( on(a_line,point_1_on_line(a_line))
| ( point_on_plane(point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_on_plane(point_1_on_line(a_line)))
| ~ on(point_on_plane(point_1_on_line(a_line)),a_line) ),
inference(superposition,[status(thm)],[c_103,c_23777]) ).
tcf(c_23796,plain,
! [X0: $i,X1: $i] :
( on(a_line,point_1_on_line(a_line))
| ( point_1_on_line(a_line) = X0 )
| ( common_point_on_planes(point_1_on_line(a_line),X0,X1) = point_1_on_line(a_line) )
| ~ plane(X0)
| ~ point(X1)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(X1,X0)
| ~ on(X1,point_1_on_line(a_line))
| ~ point(common_point_on_planes(point_1_on_line(a_line),X0,X1))
| ~ on(common_point_on_planes(point_1_on_line(a_line),X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_113,c_23777]) ).
tcf(c_23797,plain,
! [X0: $i,X1: $i] :
( on(a_line,point_1_on_line(a_line))
| ( point_1_on_line(a_line) = X0 )
| ( common_point_on_planes(X0,point_1_on_line(a_line),X1) = point_1_on_line(a_line) )
| ~ plane(X0)
| ~ point(X1)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(X1,X0)
| ~ on(X1,point_1_on_line(a_line))
| ~ point(common_point_on_planes(X0,point_1_on_line(a_line),X1))
| ~ on(common_point_on_planes(X0,point_1_on_line(a_line),X1),a_line) ),
inference(superposition,[status(thm)],[c_114,c_23777]) ).
tcf(c_23847,plain,
( on(a_line,point_1_on_line(a_line))
| ( point_1_on_line(point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(point_1_on_line(point_1_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23793,c_97]) ).
tcf(c_23898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,X1,point_1_on_line(line_from_to(X0,X1)))
| ( X1 = X3 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = X2 )
| ( point_1_on_line(line_from_to(X0,X1)) = X3 )
| ( point_1_on_line(line_from_to(X0,X1)) = X1 )
| ~ plane(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X2)
| ~ on(X1,X2)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(point_1_on_line(line_from_to(X0,X1)))
| ~ on(X3,line_from_to(X0,X1))
| ~ on(point_1_on_line(line_from_to(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_95,c_3358]) ).
tcf(c_23899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,X1,point_2_on_line(line_from_to(X0,X1)))
| ( X1 = X3 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = X2 )
| ( point_2_on_line(line_from_to(X0,X1)) = X3 )
| ( point_2_on_line(line_from_to(X0,X1)) = X1 )
| ~ plane(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X2)
| ~ on(X1,X2)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(point_2_on_line(line_from_to(X0,X1)))
| ~ on(X3,line_from_to(X0,X1))
| ~ on(point_2_on_line(line_from_to(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_96,c_3358]) ).
tcf(c_23900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,X1,point_on_plane(line_from_to(X0,X1)))
| ( X1 = X3 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = X2 )
| ( point_on_plane(line_from_to(X0,X1)) = X3 )
| ( point_on_plane(line_from_to(X0,X1)) = X1 )
| ~ plane(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X2)
| ~ on(X1,X2)
| ~ plane(line_from_to(X0,X1))
| ~ point(point_on_plane(line_from_to(X0,X1)))
| ~ on(X3,line_from_to(X0,X1))
| ~ on(point_on_plane(line_from_to(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_103,c_3358]) ).
tcf(c_23901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X2,X1)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_from_to(X1,X2) = X3 )
| ~ plane(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X1,X3)
| ~ on(X0,X3)
| ~ plane(line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_91,c_3358]) ).
tcf(c_23902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X5,X1,common_point_on_planes(line_from_to(X0,X1),X2,X3))
| ( X1 = X5 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = X4 )
| ( line_from_to(X0,X1) = X2 )
| ( common_point_on_planes(line_from_to(X0,X1),X2,X3) = X5 )
| ( common_point_on_planes(line_from_to(X0,X1),X2,X3) = X1 )
| ~ plane(X4)
| ~ plane(X2)
| ~ point(X5)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X5,X4)
| ~ on(X3,X2)
| ~ on(X1,X4)
| ~ plane(line_from_to(X0,X1))
| ~ on(X5,line_from_to(X0,X1))
| ~ on(X3,line_from_to(X0,X1))
| ~ point(common_point_on_planes(line_from_to(X0,X1),X2,X3))
| ~ on(common_point_on_planes(line_from_to(X0,X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_113,c_3358]) ).
tcf(c_23903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X5,X2,common_point_on_planes(X0,line_from_to(X1,X2),X3))
| ( X2 = X5 )
| ( X1 = X2 )
| ( line_from_to(X1,X2) = X4 )
| ( line_from_to(X1,X2) = X0 )
| ( common_point_on_planes(X0,line_from_to(X1,X2),X3) = X5 )
| ( common_point_on_planes(X0,line_from_to(X1,X2),X3) = X2 )
| ~ plane(X4)
| ~ plane(X0)
| ~ point(X5)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X5,X4)
| ~ on(X3,X0)
| ~ on(X2,X4)
| ~ plane(line_from_to(X1,X2))
| ~ on(X5,line_from_to(X1,X2))
| ~ on(X3,line_from_to(X1,X2))
| ~ point(common_point_on_planes(X0,line_from_to(X1,X2),X3))
| ~ on(common_point_on_planes(X0,line_from_to(X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_114,c_3358]) ).
tcf(c_23904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,X1,line_from_to(X0,X1))
| ( X1 = X3 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = X3 )
| ( line_from_to(X0,X1) = X2 )
| ( line_from_to(X0,X1) = X1 )
| ~ plane(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X2)
| ~ on(X1,X2)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1))
| ~ on(X3,line_from_to(X0,X1))
| ~ on(line_from_to(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_18002,c_3358]) ).
tcf(c_23905,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point1,X1)
| ( point1 = point2 )
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_from_to(point2,point1) = X2 )
| ~ point(point2)
| ~ point(point1)
| ~ plane(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(point1,X2)
| ~ on(X1,a_line)
| ~ on(X1,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(point2,point1))
| ~ on(X0,line_from_to(point2,point1)) ),
inference(superposition,[status(thm)],[c_9035,c_3358]) ).
tcf(c_23906,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point2,X1)
| ( point1 = point2 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_from_to(point1,point2) = X2 )
| ~ point(point2)
| ~ point(point1)
| ~ plane(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(point2,X2)
| ~ on(X1,a_line)
| ~ on(X1,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(point1,point2))
| ~ on(X0,line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_3358]) ).
tcf(c_23907,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_1_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X0 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X1 )
| ~ point(point2)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_1_on_line(a_line),X1)
| ~ plane(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(X0,line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_3358]) ).
tcf(c_23908,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_2_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X0 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X1 )
| ~ point(point2)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_2_on_line(a_line),X1)
| ~ plane(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(X0,line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_3358]) ).
tcf(c_23909,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point1,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = X2 )
| ~ point(point1)
| ~ plane(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(point1,X2)
| ~ on(X1,a_line)
| ~ on(X1,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(point_2_on_line(a_line),point1))
| ~ on(X0,line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_3358]) ).
tcf(c_23910,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_2_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_2_on_line(a_line) = point1 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X0 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ~ point(point1)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_2_on_line(a_line),X1)
| ~ plane(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(X0,line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_3358]) ).
tcf(c_23911,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point1,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = X2 )
| ~ point(point1)
| ~ plane(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(point1,X2)
| ~ on(X1,a_line)
| ~ on(X1,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(point_1_on_line(a_line),point1))
| ~ on(X0,line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_3358]) ).
tcf(c_23912,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_1_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_1_on_line(a_line) = point1 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X0 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ~ point(point1)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_1_on_line(a_line),X1)
| ~ plane(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(X0,line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_3358]) ).
tcf(c_23913,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = X2 )
| ~ point(point2)
| ~ plane(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(point2,X2)
| ~ on(X1,a_line)
| ~ on(X1,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(point_1_on_line(a_line),point2))
| ~ on(X0,line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_3358]) ).
tcf(c_23914,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = X2 )
| ~ point(point2)
| ~ plane(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(point2,X2)
| ~ on(X1,a_line)
| ~ on(X1,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(point_2_on_line(a_line),point2))
| ~ on(X0,line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_3358]) ).
tcf(c_23929,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point2,X2)
| ( point1 = point2 )
| ( X2 = point2 )
| ( X1 = a_line )
| ( X0 = point2 )
| ( X0 = X2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(point1)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(point2,X1)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_23906,c_11046]) ).
tcf(c_23930,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point2,X2)
| ( X2 = point2 )
| ( X1 = a_line )
| ( X0 = point2 )
| ( X0 = X2 )
| ~ plane(a_line)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(point2,X1)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23929,c_129,c_123,c_122]) ).
tcf(c_23945,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point1,X2)
| ( point1 = point2 )
| ( X2 = point1 )
| ( X1 = a_line )
| ( X0 = point1 )
| ( X0 = X2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(point1)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(point1,X1)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_23905,c_9035]) ).
tcf(c_23946,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point1,X2)
| ( X2 = point1 )
| ( X1 = a_line )
| ( X0 = point1 )
| ( X0 = X2 )
| ~ plane(a_line)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(point1,X1)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23945,c_129,c_123,c_122]) ).
tcf(c_23961,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point2,X2)
| ( X2 = point2 )
| ( X0 = point2 )
| ( X0 = X2 )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(point2,X1)
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ plane(line_from_to(point_2_on_line(a_line),point2))
| ~ on(X0,line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23914,c_123]) ).
tcf(c_23978,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point2,X2)
| ( X2 = point2 )
| ( X0 = point2 )
| ( X0 = X2 )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(point2,X1)
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ plane(line_from_to(point_1_on_line(a_line),point2))
| ~ on(X0,line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23913,c_123]) ).
tcf(c_23995,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point1,X2)
| ( X2 = point1 )
| ( X0 = point1 )
| ( X0 = X2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(point1,X1)
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ plane(line_from_to(point_1_on_line(a_line),point1))
| ~ on(X0,line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23911,c_122]) ).
tcf(c_24012,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point1,X2)
| ( X2 = point1 )
| ( X0 = point1 )
| ( X0 = X2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(point1,X1)
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ plane(line_from_to(point_2_on_line(a_line),point1))
| ~ on(X0,line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23909,c_122]) ).
tcf(c_24029,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_1_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_1_on_line(a_line) = point1 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X0 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_1_on_line(a_line),X1)
| ~ plane(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(X0,line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23912,c_122]) ).
tcf(c_24046,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_2_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_2_on_line(a_line) = point1 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X0 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_2_on_line(a_line),X1)
| ~ plane(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(X0,line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23910,c_122]) ).
tcf(c_24063,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_2_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X0 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_2_on_line(a_line),X1)
| ~ plane(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(X0,line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23908,c_123]) ).
tcf(c_24080,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_1_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X0 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_1_on_line(a_line),X1)
| ~ plane(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(X0,line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23907,c_123]) ).
tcf(c_24212,plain,
( on(a_line,point_1_on_line(a_line))
| ( point_2_on_line(point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(point_2_on_line(point_1_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23794,c_98]) ).
tcf(c_24234,plain,
( on(a_line,point_1_on_line(a_line))
| ( point_on_plane(point_1_on_line(a_line)) = point_1_on_line(a_line) )
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ on(point_on_plane(point_1_on_line(a_line)),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23795,c_104]) ).
tcf(c_24257,plain,
! [X0: $i] :
( on(X0,point_1_on_line(X0))
| ( point_2_on_line(point_1_on_line(X0)) = point_1_on_line(X0) )
| ~ line(X0)
| ~ plane(point_1_on_line(X0))
| ~ line(point_1_on_line(X0))
| ~ on(point_2_on_line(point_1_on_line(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23187,c_98]) ).
tcf(c_24283,plain,
! [X0: $i] :
( on(X0,point_1_on_line(X0))
| ( point_on_plane(point_1_on_line(X0)) = point_1_on_line(X0) )
| ~ line(X0)
| ~ plane(point_1_on_line(X0))
| ~ line(point_1_on_line(X0))
| ~ on(point_on_plane(point_1_on_line(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23188,c_104]) ).
tcf(c_24321,plain,
! [X0: $i] :
( ( point_1_on_line(X0) = X0 )
| ( point_1_on_line(point_1_on_line(X0)) = point_1_on_line(X0) )
| ~ line(X0)
| ~ plane(point_1_on_line(X0))
| ~ line(point_1_on_line(X0))
| ~ on(point_1_on_line(point_1_on_line(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23439,c_97]) ).
tcf(c_24347,plain,
! [X0: $i] :
( ( point_1_on_line(X0) = X0 )
| ( point_2_on_line(point_1_on_line(X0)) = point_1_on_line(X0) )
| ~ line(X0)
| ~ plane(point_1_on_line(X0))
| ~ line(point_1_on_line(X0))
| ~ on(point_2_on_line(point_1_on_line(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23440,c_98]) ).
tcf(c_24373,plain,
! [X0: $i] :
( ( point_1_on_line(X0) = X0 )
| ( point_on_plane(point_1_on_line(X0)) = point_1_on_line(X0) )
| ~ line(X0)
| ~ plane(point_1_on_line(X0))
| ~ line(point_1_on_line(X0))
| ~ on(point_on_plane(point_1_on_line(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23441,c_104]) ).
tcf(c_24399,plain,
! [X0: $i] :
( ( point_2_on_line(X0) = X0 )
| ( point_1_on_line(point_2_on_line(X0)) = point_2_on_line(X0) )
| ~ line(X0)
| ~ plane(point_2_on_line(X0))
| ~ line(point_2_on_line(X0))
| ~ on(point_1_on_line(point_2_on_line(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23589,c_97]) ).
tcf(c_24425,plain,
! [X0: $i] :
( ( point_2_on_line(X0) = X0 )
| ( point_2_on_line(point_2_on_line(X0)) = point_2_on_line(X0) )
| ~ line(X0)
| ~ plane(point_2_on_line(X0))
| ~ line(point_2_on_line(X0))
| ~ on(point_2_on_line(point_2_on_line(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23590,c_98]) ).
tcf(c_24451,plain,
! [X0: $i] :
( ( point_2_on_line(X0) = X0 )
| ( point_on_plane(point_2_on_line(X0)) = point_2_on_line(X0) )
| ~ line(X0)
| ~ plane(point_2_on_line(X0))
| ~ line(point_2_on_line(X0))
| ~ on(point_on_plane(point_2_on_line(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23591,c_104]) ).
tcf(c_24470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_1_on_line(X0),X2)
| ( X2 = X3 )
| ( X0 = X1 )
| ( point_1_on_line(X0) = X3 )
| ( point_1_on_line(X0) = X2 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X3)
| ~ point(X2)
| ~ on(point_1_on_line(X0),X1)
| ~ on(X2,X0)
| ~ on(X2,X1)
| ~ on(X3,X0)
| ~ on(X3,X1) ),
inference(global_subsumption_just,[status(thm)],[c_3359,c_97,c_3359]) ).
tcf(c_24471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_1_on_line(X0),X2)
| ( X2 = X3 )
| ( X0 = X1 )
| ( point_1_on_line(X0) = X3 )
| ( point_1_on_line(X0) = X2 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X3)
| ~ point(X2)
| ~ on(X3,X1)
| ~ on(X3,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_1_on_line(X0),X1) ),
inference(renaming,[status(thm)],[c_24470]) ).
tcf(c_24502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_1_on_line(X2),X0)
| ( X0 = X3 )
| ( point_1_on_line(X2) = X3 )
| ( point_1_on_line(X2) = X1 )
| ( point_1_on_line(X2) = X0 )
| ( line_from_to(X1,point_1_on_line(X2)) = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X2))
| ~ on(X3,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(X1,point_1_on_line(X2)))
| ~ on(X3,line_from_to(X1,point_1_on_line(X2)))
| ~ on(X0,line_from_to(X1,point_1_on_line(X2))) ),
inference(superposition,[status(thm)],[c_92,c_24471]) ).
tcf(c_24504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_1_on_line(X3),X0)
| collinear(X1,X2,point_1_on_line(X3))
| ( X1 = X2 )
| ( X0 = X4 )
| ( point_1_on_line(X3) = X4 )
| ( point_1_on_line(X3) = X2 )
| ( point_1_on_line(X3) = X1 )
| ( point_1_on_line(X3) = X0 )
| ( plane_for_points(X1,X2,point_1_on_line(X3)) = X3 )
| ~ plane(X3)
| ~ line(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X3))
| ~ on(X4,X3)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X1,X2,point_1_on_line(X3)))
| ~ on(X4,plane_for_points(X1,X2,point_1_on_line(X3)))
| ~ on(X0,plane_for_points(X1,X2,point_1_on_line(X3))) ),
inference(superposition,[status(thm)],[c_109,c_24471]) ).
tcf(c_24505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_1_on_line(X1),X0)
| ( X2 = X3 )
| ( X0 = X4 )
| ( point_1_on_line(X1) = X4 )
| ( point_1_on_line(X1) = X3 )
| ( point_1_on_line(X1) = X2 )
| ( point_1_on_line(X1) = X0 )
| ( line_through_3_points(point_1_on_line(X1),X2,X3) = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(X1))
| ~ on(X4,X1)
| ~ on(X0,X1)
| ~ collinear(point_1_on_line(X1),X2,X3)
| ~ plane(line_through_3_points(point_1_on_line(X1),X2,X3))
| ~ on(X4,line_through_3_points(point_1_on_line(X1),X2,X3))
| ~ on(X0,line_through_3_points(point_1_on_line(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_24471]) ).
tcf(c_24506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_1_on_line(X2),X0)
| ( X1 = X3 )
| ( X0 = X4 )
| ( point_1_on_line(X2) = X4 )
| ( point_1_on_line(X2) = X3 )
| ( point_1_on_line(X2) = X1 )
| ( point_1_on_line(X2) = X0 )
| ( line_through_3_points(X1,point_1_on_line(X2),X3) = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X2))
| ~ on(X4,X2)
| ~ on(X0,X2)
| ~ collinear(X1,point_1_on_line(X2),X3)
| ~ plane(line_through_3_points(X1,point_1_on_line(X2),X3))
| ~ on(X4,line_through_3_points(X1,point_1_on_line(X2),X3))
| ~ on(X0,line_through_3_points(X1,point_1_on_line(X2),X3)) ),
inference(superposition,[status(thm)],[c_118,c_24471]) ).
tcf(c_24507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_1_on_line(X3),X0)
| ( X1 = X2 )
| ( X0 = X4 )
| ( point_1_on_line(X3) = X4 )
| ( point_1_on_line(X3) = X2 )
| ( point_1_on_line(X3) = X1 )
| ( point_1_on_line(X3) = X0 )
| ( line_through_3_points(X1,X2,point_1_on_line(X3)) = X3 )
| ~ plane(X3)
| ~ line(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X3))
| ~ on(X4,X3)
| ~ on(X0,X3)
| ~ collinear(X1,X2,point_1_on_line(X3))
| ~ plane(line_through_3_points(X1,X2,point_1_on_line(X3)))
| ~ on(X4,line_through_3_points(X1,X2,point_1_on_line(X3)))
| ~ on(X0,line_through_3_points(X1,X2,point_1_on_line(X3))) ),
inference(superposition,[status(thm)],[c_119,c_24471]) ).
tcf(c_24508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_1_on_line(X1),X0)
| ( X0 = X3 )
| ( point_1_on_line(X1) = X3 )
| ( point_1_on_line(X1) = X2 )
| ( point_1_on_line(X1) = X0 )
| ( line_from_to(point_1_on_line(X1),X2) = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(X1))
| ~ on(X3,X1)
| ~ on(X0,X1)
| ~ plane(line_from_to(point_1_on_line(X1),X2))
| ~ on(X3,line_from_to(point_1_on_line(X1),X2))
| ~ on(X0,line_from_to(point_1_on_line(X1),X2)) ),
inference(superposition,[status(thm)],[c_91,c_24471]) ).
tcf(c_24509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_1_on_line(X1),X0)
| collinear(point_1_on_line(X1),X2,X3)
| ( X2 = X3 )
| ( X0 = X4 )
| ( point_1_on_line(X1) = X4 )
| ( point_1_on_line(X1) = X3 )
| ( point_1_on_line(X1) = X2 )
| ( point_1_on_line(X1) = X0 )
| ( plane_for_points(point_1_on_line(X1),X2,X3) = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(X1))
| ~ on(X4,X1)
| ~ on(X0,X1)
| ~ plane(plane_for_points(point_1_on_line(X1),X2,X3))
| ~ on(X4,plane_for_points(point_1_on_line(X1),X2,X3))
| ~ on(X0,plane_for_points(point_1_on_line(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_24471]) ).
tcf(c_24510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_1_on_line(X2),X0)
| collinear(X1,point_1_on_line(X2),X3)
| ( X1 = X3 )
| ( X0 = X4 )
| ( point_1_on_line(X2) = X4 )
| ( point_1_on_line(X2) = X3 )
| ( point_1_on_line(X2) = X1 )
| ( point_1_on_line(X2) = X0 )
| ( plane_for_points(X1,point_1_on_line(X2),X3) = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(X2))
| ~ on(X4,X2)
| ~ on(X0,X2)
| ~ plane(plane_for_points(X1,point_1_on_line(X2),X3))
| ~ on(X4,plane_for_points(X1,point_1_on_line(X2),X3))
| ~ on(X0,plane_for_points(X1,point_1_on_line(X2),X3)) ),
inference(superposition,[status(thm)],[c_108,c_24471]) ).
tcf(c_24512,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point_1_on_line(X1),X0)
| ( X0 = X2 )
| ( point_1_on_line(X1) = X2 )
| ( point_1_on_line(X1) = X1 )
| ( point_1_on_line(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ plane(point_1_on_line(X1))
| ~ line(point_1_on_line(X1))
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(X2,point_1_on_line(X1))
| ~ on(X0,point_1_on_line(X1)) ),
inference(superposition,[status(thm)],[c_18002,c_24471]) ).
tcf(c_24791,plain,
! [X0: $i,X1: $i] :
( on(X1,point_2_on_line(X1))
| ( point_2_on_line(X1) = X0 )
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_2_on_line(X1))
| ~ line(point_2_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_2_on_line(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19965,c_98]) ).
tcf(c_24816,plain,
! [X0: $i] :
( on(X0,point_2_on_line(X0))
| ( point_1_on_line(point_2_on_line(X0)) = point_2_on_line(X0) )
| ~ line(X0)
| ~ plane(point_2_on_line(X0))
| ~ line(point_2_on_line(X0))
| ~ point(point_1_on_line(point_2_on_line(X0)))
| ~ on(point_1_on_line(point_2_on_line(X0)),X0) ),
inference(superposition,[status(thm)],[c_95,c_24791]) ).
tcf(c_24817,plain,
! [X0: $i] :
( on(X0,point_2_on_line(X0))
| ( point_2_on_line(point_2_on_line(X0)) = point_2_on_line(X0) )
| ~ line(X0)
| ~ plane(point_2_on_line(X0))
| ~ line(point_2_on_line(X0))
| ~ point(point_2_on_line(point_2_on_line(X0)))
| ~ on(point_2_on_line(point_2_on_line(X0)),X0) ),
inference(superposition,[status(thm)],[c_96,c_24791]) ).
tcf(c_24818,plain,
! [X0: $i] :
( on(X0,point_2_on_line(X0))
| ( point_on_plane(point_2_on_line(X0)) = point_2_on_line(X0) )
| ~ line(X0)
| ~ plane(point_2_on_line(X0))
| ~ line(point_2_on_line(X0))
| ~ point(point_on_plane(point_2_on_line(X0)))
| ~ on(point_on_plane(point_2_on_line(X0)),X0) ),
inference(superposition,[status(thm)],[c_103,c_24791]) ).
tcf(c_24819,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X0,point_2_on_line(X0))
| ( point_2_on_line(X0) = X1 )
| ( common_point_on_planes(point_2_on_line(X0),X1,X2) = point_2_on_line(X0) )
| ~ plane(X1)
| ~ line(X0)
| ~ point(X2)
| ~ plane(point_2_on_line(X0))
| ~ line(point_2_on_line(X0))
| ~ on(X2,X1)
| ~ on(X2,point_2_on_line(X0))
| ~ point(common_point_on_planes(point_2_on_line(X0),X1,X2))
| ~ on(common_point_on_planes(point_2_on_line(X0),X1,X2),X0) ),
inference(superposition,[status(thm)],[c_113,c_24791]) ).
tcf(c_24820,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,point_2_on_line(X1))
| ( point_2_on_line(X1) = X0 )
| ( common_point_on_planes(X0,point_2_on_line(X1),X2) = point_2_on_line(X1) )
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ plane(point_2_on_line(X1))
| ~ line(point_2_on_line(X1))
| ~ on(X2,X0)
| ~ on(X2,point_2_on_line(X1))
| ~ point(common_point_on_planes(X0,point_2_on_line(X1),X2))
| ~ on(common_point_on_planes(X0,point_2_on_line(X1),X2),X1) ),
inference(superposition,[status(thm)],[c_114,c_24791]) ).
tcf(c_24877,plain,
! [X0: $i] :
( on(X0,point_2_on_line(X0))
| ( point_1_on_line(point_2_on_line(X0)) = point_2_on_line(X0) )
| ~ line(X0)
| ~ plane(point_2_on_line(X0))
| ~ line(point_2_on_line(X0))
| ~ on(point_1_on_line(point_2_on_line(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24816,c_97]) ).
tcf(c_24903,plain,
! [X0: $i] :
( on(X0,point_2_on_line(X0))
| ( point_2_on_line(point_2_on_line(X0)) = point_2_on_line(X0) )
| ~ line(X0)
| ~ plane(point_2_on_line(X0))
| ~ line(point_2_on_line(X0))
| ~ on(point_2_on_line(point_2_on_line(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24817,c_98]) ).
tcf(c_24929,plain,
! [X0: $i] :
( on(X0,point_2_on_line(X0))
| ( point_on_plane(point_2_on_line(X0)) = point_2_on_line(X0) )
| ~ line(X0)
| ~ plane(point_2_on_line(X0))
| ~ line(point_2_on_line(X0))
| ~ on(point_on_plane(point_2_on_line(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24818,c_104]) ).
tcf(c_24961,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point2,point_2_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_12492]) ).
tcf(c_24962,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point2,point_2_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24961,c_125]) ).
tcf(c_24997,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point2,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_12493]) ).
tcf(c_24998,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point2,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24997,c_125]) ).
tcf(c_25033,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point2,point_2_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_12494]) ).
tcf(c_25034,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point2,point_2_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25033,c_125]) ).
tcf(c_25069,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point2,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_12495]) ).
tcf(c_25070,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point2,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25069,c_125]) ).
tcf(c_25105,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point2,point_1_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_12623]) ).
tcf(c_25106,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point2,point_1_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25105,c_125]) ).
tcf(c_25141,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point2,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_12624]) ).
tcf(c_25142,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point2,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25141,c_125]) ).
tcf(c_25153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_2_on_line(X0),X2)
| ( X2 = X3 )
| ( X0 = X1 )
| ( point_2_on_line(X0) = X3 )
| ( point_2_on_line(X0) = X2 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X3)
| ~ point(X2)
| ~ on(point_2_on_line(X0),X1)
| ~ on(X2,X0)
| ~ on(X2,X1)
| ~ on(X3,X0)
| ~ on(X3,X1) ),
inference(global_subsumption_just,[status(thm)],[c_3360,c_98,c_3360]) ).
tcf(c_25154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_2_on_line(X0),X2)
| ( X2 = X3 )
| ( X0 = X1 )
| ( point_2_on_line(X0) = X3 )
| ( point_2_on_line(X0) = X2 )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X3)
| ~ point(X2)
| ~ on(X3,X1)
| ~ on(X3,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_2_on_line(X0),X1) ),
inference(renaming,[status(thm)],[c_25153]) ).
tcf(c_25185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_2_on_line(X2),X0)
| ( X0 = X3 )
| ( point_2_on_line(X2) = X3 )
| ( point_2_on_line(X2) = X1 )
| ( point_2_on_line(X2) = X0 )
| ( line_from_to(X1,point_2_on_line(X2)) = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X2))
| ~ on(X3,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(X1,point_2_on_line(X2)))
| ~ on(X3,line_from_to(X1,point_2_on_line(X2)))
| ~ on(X0,line_from_to(X1,point_2_on_line(X2))) ),
inference(superposition,[status(thm)],[c_92,c_25154]) ).
tcf(c_25187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_2_on_line(X3),X0)
| collinear(X1,X2,point_2_on_line(X3))
| ( X1 = X2 )
| ( X0 = X4 )
| ( point_2_on_line(X3) = X4 )
| ( point_2_on_line(X3) = X2 )
| ( point_2_on_line(X3) = X1 )
| ( point_2_on_line(X3) = X0 )
| ( plane_for_points(X1,X2,point_2_on_line(X3)) = X3 )
| ~ plane(X3)
| ~ line(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X3))
| ~ on(X4,X3)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X1,X2,point_2_on_line(X3)))
| ~ on(X4,plane_for_points(X1,X2,point_2_on_line(X3)))
| ~ on(X0,plane_for_points(X1,X2,point_2_on_line(X3))) ),
inference(superposition,[status(thm)],[c_109,c_25154]) ).
tcf(c_25188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_2_on_line(X1),X0)
| ( X2 = X3 )
| ( X0 = X4 )
| ( point_2_on_line(X1) = X4 )
| ( point_2_on_line(X1) = X3 )
| ( point_2_on_line(X1) = X2 )
| ( point_2_on_line(X1) = X0 )
| ( line_through_3_points(point_2_on_line(X1),X2,X3) = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(X1))
| ~ on(X4,X1)
| ~ on(X0,X1)
| ~ collinear(point_2_on_line(X1),X2,X3)
| ~ plane(line_through_3_points(point_2_on_line(X1),X2,X3))
| ~ on(X4,line_through_3_points(point_2_on_line(X1),X2,X3))
| ~ on(X0,line_through_3_points(point_2_on_line(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_25154]) ).
tcf(c_25189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_2_on_line(X2),X0)
| ( X1 = X3 )
| ( X0 = X4 )
| ( point_2_on_line(X2) = X4 )
| ( point_2_on_line(X2) = X3 )
| ( point_2_on_line(X2) = X1 )
| ( point_2_on_line(X2) = X0 )
| ( line_through_3_points(X1,point_2_on_line(X2),X3) = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X2))
| ~ on(X4,X2)
| ~ on(X0,X2)
| ~ collinear(X1,point_2_on_line(X2),X3)
| ~ plane(line_through_3_points(X1,point_2_on_line(X2),X3))
| ~ on(X4,line_through_3_points(X1,point_2_on_line(X2),X3))
| ~ on(X0,line_through_3_points(X1,point_2_on_line(X2),X3)) ),
inference(superposition,[status(thm)],[c_118,c_25154]) ).
tcf(c_25190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_2_on_line(X3),X0)
| ( X1 = X2 )
| ( X0 = X4 )
| ( point_2_on_line(X3) = X4 )
| ( point_2_on_line(X3) = X2 )
| ( point_2_on_line(X3) = X1 )
| ( point_2_on_line(X3) = X0 )
| ( line_through_3_points(X1,X2,point_2_on_line(X3)) = X3 )
| ~ plane(X3)
| ~ line(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X3))
| ~ on(X4,X3)
| ~ on(X0,X3)
| ~ collinear(X1,X2,point_2_on_line(X3))
| ~ plane(line_through_3_points(X1,X2,point_2_on_line(X3)))
| ~ on(X4,line_through_3_points(X1,X2,point_2_on_line(X3)))
| ~ on(X0,line_through_3_points(X1,X2,point_2_on_line(X3))) ),
inference(superposition,[status(thm)],[c_119,c_25154]) ).
tcf(c_25191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_2_on_line(X1),X0)
| ( X0 = X3 )
| ( point_2_on_line(X1) = X3 )
| ( point_2_on_line(X1) = X2 )
| ( point_2_on_line(X1) = X0 )
| ( line_from_to(point_2_on_line(X1),X2) = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(X1))
| ~ on(X3,X1)
| ~ on(X0,X1)
| ~ plane(line_from_to(point_2_on_line(X1),X2))
| ~ on(X3,line_from_to(point_2_on_line(X1),X2))
| ~ on(X0,line_from_to(point_2_on_line(X1),X2)) ),
inference(superposition,[status(thm)],[c_91,c_25154]) ).
tcf(c_25192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_2_on_line(X1),X0)
| collinear(point_2_on_line(X1),X2,X3)
| ( X2 = X3 )
| ( X0 = X4 )
| ( point_2_on_line(X1) = X4 )
| ( point_2_on_line(X1) = X3 )
| ( point_2_on_line(X1) = X2 )
| ( point_2_on_line(X1) = X0 )
| ( plane_for_points(point_2_on_line(X1),X2,X3) = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(X1))
| ~ on(X4,X1)
| ~ on(X0,X1)
| ~ plane(plane_for_points(point_2_on_line(X1),X2,X3))
| ~ on(X4,plane_for_points(point_2_on_line(X1),X2,X3))
| ~ on(X0,plane_for_points(point_2_on_line(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_25154]) ).
tcf(c_25193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_2_on_line(X2),X0)
| collinear(X1,point_2_on_line(X2),X3)
| ( X1 = X3 )
| ( X0 = X4 )
| ( point_2_on_line(X2) = X4 )
| ( point_2_on_line(X2) = X3 )
| ( point_2_on_line(X2) = X1 )
| ( point_2_on_line(X2) = X0 )
| ( plane_for_points(X1,point_2_on_line(X2),X3) = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X2))
| ~ on(X4,X2)
| ~ on(X0,X2)
| ~ plane(plane_for_points(X1,point_2_on_line(X2),X3))
| ~ on(X4,plane_for_points(X1,point_2_on_line(X2),X3))
| ~ on(X0,plane_for_points(X1,point_2_on_line(X2),X3)) ),
inference(superposition,[status(thm)],[c_108,c_25154]) ).
tcf(c_25195,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point_2_on_line(X1),X0)
| ( X0 = X2 )
| ( point_2_on_line(X1) = X2 )
| ( point_2_on_line(X1) = X1 )
| ( point_2_on_line(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ plane(point_2_on_line(X1))
| ~ line(point_2_on_line(X1))
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(X2,point_2_on_line(X1))
| ~ on(X0,point_2_on_line(X1)) ),
inference(superposition,[status(thm)],[c_18002,c_25154]) ).
tcf(c_25383,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,X0)
| ( point_2_on_line(X0) = X2 )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ on(point_2_on_line(X0),X1)
| ~ on(X2,X0)
| ~ on(X2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_2914,c_98,c_2914]) ).
tcf(c_25384,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,X0)
| ( point_2_on_line(X0) = X2 )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_2_on_line(X0),X1) ),
inference(renaming,[status(thm)],[c_25383]) ).
tcf(c_25403,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_from_to(X1,point_2_on_line(X2)),X2)
| ( point_2_on_line(X2) = X1 )
| ( point_2_on_line(X2) = X0 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X2))
| ~ on(X0,X2)
| ~ line(line_from_to(X1,point_2_on_line(X2)))
| ~ on(X0,line_from_to(X1,point_2_on_line(X2))) ),
inference(superposition,[status(thm)],[c_92,c_25384]) ).
tcf(c_25404,plain,
! [X0: $i,X1: $i] :
( on(X1,X1)
| ( point_2_on_line(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X0)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_25384]) ).
tcf(c_25405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,X2,point_2_on_line(X3))
| on(plane_for_points(X1,X2,point_2_on_line(X3)),X3)
| ( X1 = X2 )
| ( point_2_on_line(X3) = X2 )
| ( point_2_on_line(X3) = X1 )
| ( point_2_on_line(X3) = X0 )
| ~ plane(X3)
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X3))
| ~ on(X0,X3)
| ~ line(plane_for_points(X1,X2,point_2_on_line(X3)))
| ~ on(X0,plane_for_points(X1,X2,point_2_on_line(X3))) ),
inference(superposition,[status(thm)],[c_109,c_25384]) ).
tcf(c_25406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(line_through_3_points(point_2_on_line(X1),X2,X3),X1)
| ( X2 = X3 )
| ( point_2_on_line(X1) = X3 )
| ( point_2_on_line(X1) = X2 )
| ( point_2_on_line(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(X1))
| ~ on(X0,X1)
| ~ collinear(point_2_on_line(X1),X2,X3)
| ~ line(line_through_3_points(point_2_on_line(X1),X2,X3))
| ~ on(X0,line_through_3_points(point_2_on_line(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_25384]) ).
tcf(c_25407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(line_through_3_points(X1,point_2_on_line(X2),X3),X2)
| ( X1 = X3 )
| ( point_2_on_line(X2) = X3 )
| ( point_2_on_line(X2) = X1 )
| ( point_2_on_line(X2) = X0 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X2))
| ~ on(X0,X2)
| ~ collinear(X1,point_2_on_line(X2),X3)
| ~ line(line_through_3_points(X1,point_2_on_line(X2),X3))
| ~ on(X0,line_through_3_points(X1,point_2_on_line(X2),X3)) ),
inference(superposition,[status(thm)],[c_118,c_25384]) ).
tcf(c_25408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(line_through_3_points(X1,X2,point_2_on_line(X3)),X3)
| ( X1 = X2 )
| ( point_2_on_line(X3) = X2 )
| ( point_2_on_line(X3) = X1 )
| ( point_2_on_line(X3) = X0 )
| ~ plane(X3)
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X3))
| ~ on(X0,X3)
| ~ collinear(X1,X2,point_2_on_line(X3))
| ~ line(line_through_3_points(X1,X2,point_2_on_line(X3)))
| ~ on(X0,line_through_3_points(X1,X2,point_2_on_line(X3))) ),
inference(superposition,[status(thm)],[c_119,c_25384]) ).
tcf(c_25409,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(line_from_to(point_2_on_line(X1),X2),X1)
| ( point_2_on_line(X1) = X2 )
| ( point_2_on_line(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(X1))
| ~ on(X0,X1)
| ~ line(line_from_to(point_2_on_line(X1),X2))
| ~ on(X0,line_from_to(point_2_on_line(X1),X2)) ),
inference(superposition,[status(thm)],[c_91,c_25384]) ).
tcf(c_25410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(point_2_on_line(X1),X2,X3)
| on(plane_for_points(point_2_on_line(X1),X2,X3),X1)
| ( X2 = X3 )
| ( point_2_on_line(X1) = X3 )
| ( point_2_on_line(X1) = X2 )
| ( point_2_on_line(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(X1))
| ~ on(X0,X1)
| ~ line(plane_for_points(point_2_on_line(X1),X2,X3))
| ~ on(X0,plane_for_points(point_2_on_line(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_25384]) ).
tcf(c_25411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,point_2_on_line(X2),X3)
| on(plane_for_points(X1,point_2_on_line(X2),X3),X2)
| ( X1 = X3 )
| ( point_2_on_line(X2) = X3 )
| ( point_2_on_line(X2) = X1 )
| ( point_2_on_line(X2) = X0 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(X2))
| ~ on(X0,X2)
| ~ line(plane_for_points(X1,point_2_on_line(X2),X3))
| ~ on(X0,plane_for_points(X1,point_2_on_line(X2),X3)) ),
inference(superposition,[status(thm)],[c_108,c_25384]) ).
tcf(c_25413,plain,
! [X0: $i,X1: $i] :
( on(point_2_on_line(X1),X1)
| ( point_2_on_line(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_2_on_line(X1))
| ~ line(point_2_on_line(X1))
| ~ on(X0,X1)
| ~ on(X0,point_2_on_line(X1)) ),
inference(superposition,[status(thm)],[c_18002,c_25384]) ).
tcf(c_25800,plain,
! [X0: $i] :
( on(line_from_to(point1,X0),a_line)
| ( X0 = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_91,c_4628]) ).
tcf(c_25803,plain,
( on(line_from_to(point2,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ on(point1,a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_4628]) ).
tcf(c_25804,plain,
( on(line_from_to(point2,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ on(point1,a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_4628]) ).
tcf(c_25806,plain,
( on(line_from_to(point1,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_4628]) ).
tcf(c_25808,plain,
( on(line_from_to(point1,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_4628]) ).
tcf(c_25809,plain,
( on(line_from_to(point_1_on_line(a_line),point2),a_line)
| ( point1 = point2 )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ on(point1,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_4628]) ).
tcf(c_25810,plain,
( on(line_from_to(point_2_on_line(a_line),point2),a_line)
| ( point1 = point2 )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ on(point1,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_4628]) ).
tcf(c_25811,plain,
! [X0: $i] :
( on(line_from_to(point1,X0),a_line)
| ( X0 = point1 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25800,c_122]) ).
tcf(c_25822,plain,
( on(line_from_to(point2,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25804,c_123,c_126,c_9364]) ).
tcf(c_25829,plain,
( on(line_from_to(point2,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25803,c_123,c_126,c_9468]) ).
tcf(c_25848,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ line(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_25811]) ).
tcf(c_25851,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = point1 )
| ( line_from_to(point1,X0) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),X1) ),
inference(superposition,[status(thm)],[c_25811,c_94]) ).
tcf(c_25852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_from_to(point1,X0),X2)
| ( X2 = X3 )
| ( X1 = a_line )
| ( X0 = point1 )
| ( line_from_to(point1,X0) = X3 )
| ( line_from_to(point1,X0) = X2 )
| ~ plane(a_line)
| ~ plane(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X1)
| ~ on(X2,X1)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),X1) ),
inference(superposition,[status(thm)],[c_25811,c_111]) ).
tcf(c_25853,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,a_line)
| ( X0 = point1 )
| ( line_from_to(point1,X0) = X2 )
| ~ plane(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),X1) ),
inference(superposition,[status(thm)],[c_25811,c_112]) ).
tcf(c_25854,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( line_from_to(point1,X1) = a_line )
| ( line_from_to(point1,X1) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point1,X1))
| ~ line(line_from_to(point1,X1))
| ~ point(line_from_to(point1,X1))
| ~ on(X0,line_from_to(point1,X1)) ),
inference(superposition,[status(thm)],[c_25811,c_18010]) ).
tcf(c_25855,plain,
! [X0: $i,X1: $i] :
( on(a_line,line_from_to(point1,X1))
| ( X1 = point1 )
| ( line_from_to(point1,X1) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point1,X1))
| ~ line(line_from_to(point1,X1))
| ~ point(line_from_to(point1,X1))
| ~ on(X0,line_from_to(point1,X1)) ),
inference(superposition,[status(thm)],[c_25811,c_18012]) ).
tcf(c_25858,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point1 )
| ( line_from_to(point1,X0) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),a_line) ),
inference(superposition,[status(thm)],[c_25811,c_2934]) ).
tcf(c_25861,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(point1,X0),X1)
| ( X1 = X2 )
| ( X0 = point1 )
| ( line_from_to(point1,X0) = X2 )
| ( line_from_to(point1,X0) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_25811,c_121]) ).
tcf(c_25862,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point1 )
| ( line_from_to(point1,X0) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),a_line) ),
inference(superposition,[status(thm)],[c_25811,c_2925]) ).
tcf(c_25863,plain,
! [X0: $i] :
( ( point1 = a_line )
| ( X0 = point1 )
| ( line_from_to(point1,X0) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),point1) ),
inference(superposition,[status(thm)],[c_25811,c_21610]) ).
tcf(c_25864,plain,
! [X0: $i] :
( ( point2 = a_line )
| ( X0 = point1 )
| ( line_from_to(point1,X0) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),point2) ),
inference(superposition,[status(thm)],[c_25811,c_21602]) ).
tcf(c_25865,plain,
! [X0: $i] :
( on(a_line,point1)
| ( X0 = point1 )
| ( line_from_to(point1,X0) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),point1) ),
inference(superposition,[status(thm)],[c_25811,c_20018]) ).
tcf(c_25866,plain,
! [X0: $i] :
( on(a_line,point2)
| ( X0 = point1 )
| ( line_from_to(point1,X0) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),point2) ),
inference(superposition,[status(thm)],[c_25811,c_20010]) ).
tcf(c_25867,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point1,X0))
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(a_line,line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_25811,c_18013]) ).
tcf(c_25868,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ( line_from_to(point1,X0) = point2 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point1,X0))
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(point2,line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_25811,c_18017]) ).
tcf(c_25869,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = point1 )
| ( line_from_to(line_from_to(point1,X0),point1) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_25811,c_12246]) ).
tcf(c_25870,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = point1 )
| ( line_from_to(point1,line_from_to(point1,X0)) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_25811,c_11471]) ).
tcf(c_25871,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = point2 )
| ( line_from_to(line_from_to(point1,X0),point2) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_25811,c_11016]) ).
tcf(c_25872,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = point2 )
| ( line_from_to(point2,line_from_to(point1,X0)) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_25811,c_9014]) ).
tcf(c_25873,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(light_normalisation,[status(thm)],[c_25848,c_11046]) ).
tcf(c_25961,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point1 )
| ( line_from_to(point1,X0) = point2 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25862,c_125,c_127]) ).
tcf(c_25971,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point1 )
| ( line_from_to(point1,X0) = point1 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25858,c_125,c_126]) ).
tcf(c_26004,plain,
! [X0: $i,X1: $i] :
( on(a_line,line_from_to(point1,X1))
| ( X1 = point1 )
| ( line_from_to(point1,X1) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point1,X1))
| ~ line(line_from_to(point1,X1))
| ~ point(line_from_to(point1,X1))
| ~ on(X0,line_from_to(point1,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25855,c_125]) ).
tcf(c_26017,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( line_from_to(point1,X1) = a_line )
| ( line_from_to(point1,X1) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point1,X1))
| ~ line(line_from_to(point1,X1))
| ~ point(line_from_to(point1,X1))
| ~ on(X0,line_from_to(point1,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25854,c_125]) ).
tcf(c_26030,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = point1 )
| ( line_from_to(point1,X0) = X2 )
| ~ plane(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0))
| ~ on(line_from_to(point1,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25851,c_125]) ).
tcf(c_26044,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(point1,X0),X1)
| ( X1 = X2 )
| ( X0 = point1 )
| ( line_from_to(point1,X0) = X2 )
| ( line_from_to(point1,X0) = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25861,c_125]) ).
tcf(c_26183,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point2,point_1_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_12625]) ).
tcf(c_26184,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point2,point_1_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26183,c_125]) ).
tcf(c_26219,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point2,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_12626]) ).
tcf(c_26220,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point2,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26219,c_125]) ).
tcf(c_26255,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point1 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point1),point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_12941]) ).
tcf(c_26256,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point1 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point1),point1) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26255,c_125]) ).
tcf(c_26277,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point1 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point1),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_12340,c_26256]) ).
tcf(c_26306,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point1 )
| ( line_from_to(point1,line_from_to(point_1_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_12942]) ).
tcf(c_26307,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point1 )
| ( line_from_to(point1,line_from_to(point_1_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26306,c_125]) ).
tcf(c_26318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_on_plane(X0),X2)
| ( X2 = X3 )
| ( X0 = X1 )
| ( point_on_plane(X0) = X3 )
| ( point_on_plane(X0) = X2 )
| ~ plane(X1)
| ~ plane(X0)
| ~ point(X3)
| ~ point(X2)
| ~ on(point_on_plane(X0),X1)
| ~ on(X2,X0)
| ~ on(X2,X1)
| ~ on(X3,X0)
| ~ on(X3,X1) ),
inference(global_subsumption_just,[status(thm)],[c_3361,c_104,c_3361]) ).
tcf(c_26319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_on_plane(X0),X2)
| ( X2 = X3 )
| ( X0 = X1 )
| ( point_on_plane(X0) = X3 )
| ( point_on_plane(X0) = X2 )
| ~ plane(X1)
| ~ plane(X0)
| ~ point(X3)
| ~ point(X2)
| ~ on(X3,X1)
| ~ on(X3,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_on_plane(X0),X1) ),
inference(renaming,[status(thm)],[c_26318]) ).
tcf(c_26348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_on_plane(X2),X0)
| ( X0 = X3 )
| ( point_on_plane(X2) = X3 )
| ( point_on_plane(X2) = X1 )
| ( point_on_plane(X2) = X0 )
| ( line_from_to(X1,point_on_plane(X2)) = X2 )
| ~ plane(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X2))
| ~ on(X3,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(X1,point_on_plane(X2)))
| ~ on(X3,line_from_to(X1,point_on_plane(X2)))
| ~ on(X0,line_from_to(X1,point_on_plane(X2))) ),
inference(superposition,[status(thm)],[c_92,c_26319]) ).
tcf(c_26350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_on_plane(X3),X0)
| collinear(X1,X2,point_on_plane(X3))
| ( X1 = X2 )
| ( X0 = X4 )
| ( point_on_plane(X3) = X4 )
| ( point_on_plane(X3) = X2 )
| ( point_on_plane(X3) = X1 )
| ( point_on_plane(X3) = X0 )
| ( plane_for_points(X1,X2,point_on_plane(X3)) = X3 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X3))
| ~ on(X4,X3)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X1,X2,point_on_plane(X3)))
| ~ on(X4,plane_for_points(X1,X2,point_on_plane(X3)))
| ~ on(X0,plane_for_points(X1,X2,point_on_plane(X3))) ),
inference(superposition,[status(thm)],[c_109,c_26319]) ).
tcf(c_26351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_on_plane(X1),X0)
| ( X2 = X3 )
| ( X0 = X4 )
| ( point_on_plane(X1) = X4 )
| ( point_on_plane(X1) = X3 )
| ( point_on_plane(X1) = X2 )
| ( point_on_plane(X1) = X0 )
| ( line_through_3_points(point_on_plane(X1),X2,X3) = X1 )
| ~ plane(X1)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_on_plane(X1))
| ~ on(X4,X1)
| ~ on(X0,X1)
| ~ collinear(point_on_plane(X1),X2,X3)
| ~ plane(line_through_3_points(point_on_plane(X1),X2,X3))
| ~ on(X4,line_through_3_points(point_on_plane(X1),X2,X3))
| ~ on(X0,line_through_3_points(point_on_plane(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_26319]) ).
tcf(c_26352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_on_plane(X2),X0)
| ( X1 = X3 )
| ( X0 = X4 )
| ( point_on_plane(X2) = X4 )
| ( point_on_plane(X2) = X3 )
| ( point_on_plane(X2) = X1 )
| ( point_on_plane(X2) = X0 )
| ( line_through_3_points(X1,point_on_plane(X2),X3) = X2 )
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X2))
| ~ on(X4,X2)
| ~ on(X0,X2)
| ~ collinear(X1,point_on_plane(X2),X3)
| ~ plane(line_through_3_points(X1,point_on_plane(X2),X3))
| ~ on(X4,line_through_3_points(X1,point_on_plane(X2),X3))
| ~ on(X0,line_through_3_points(X1,point_on_plane(X2),X3)) ),
inference(superposition,[status(thm)],[c_118,c_26319]) ).
tcf(c_26353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_on_plane(X3),X0)
| ( X1 = X2 )
| ( X0 = X4 )
| ( point_on_plane(X3) = X4 )
| ( point_on_plane(X3) = X2 )
| ( point_on_plane(X3) = X1 )
| ( point_on_plane(X3) = X0 )
| ( line_through_3_points(X1,X2,point_on_plane(X3)) = X3 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X3))
| ~ on(X4,X3)
| ~ on(X0,X3)
| ~ collinear(X1,X2,point_on_plane(X3))
| ~ plane(line_through_3_points(X1,X2,point_on_plane(X3)))
| ~ on(X4,line_through_3_points(X1,X2,point_on_plane(X3)))
| ~ on(X0,line_through_3_points(X1,X2,point_on_plane(X3))) ),
inference(superposition,[status(thm)],[c_119,c_26319]) ).
tcf(c_26354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,point_on_plane(X1),X0)
| ( X0 = X3 )
| ( point_on_plane(X1) = X3 )
| ( point_on_plane(X1) = X2 )
| ( point_on_plane(X1) = X0 )
| ( line_from_to(point_on_plane(X1),X2) = X1 )
| ~ plane(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_on_plane(X1))
| ~ on(X3,X1)
| ~ on(X0,X1)
| ~ plane(line_from_to(point_on_plane(X1),X2))
| ~ on(X3,line_from_to(point_on_plane(X1),X2))
| ~ on(X0,line_from_to(point_on_plane(X1),X2)) ),
inference(superposition,[status(thm)],[c_91,c_26319]) ).
tcf(c_26355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_on_plane(X1),X0)
| collinear(point_on_plane(X1),X2,X3)
| ( X2 = X3 )
| ( X0 = X4 )
| ( point_on_plane(X1) = X4 )
| ( point_on_plane(X1) = X3 )
| ( point_on_plane(X1) = X2 )
| ( point_on_plane(X1) = X0 )
| ( plane_for_points(point_on_plane(X1),X2,X3) = X1 )
| ~ plane(X1)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_on_plane(X1))
| ~ on(X4,X1)
| ~ on(X0,X1)
| ~ plane(plane_for_points(point_on_plane(X1),X2,X3))
| ~ on(X4,plane_for_points(point_on_plane(X1),X2,X3))
| ~ on(X0,plane_for_points(point_on_plane(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_26319]) ).
tcf(c_26356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,point_on_plane(X2),X0)
| collinear(X1,point_on_plane(X2),X3)
| ( X1 = X3 )
| ( X0 = X4 )
| ( point_on_plane(X2) = X4 )
| ( point_on_plane(X2) = X3 )
| ( point_on_plane(X2) = X1 )
| ( point_on_plane(X2) = X0 )
| ( plane_for_points(X1,point_on_plane(X2),X3) = X2 )
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X2))
| ~ on(X4,X2)
| ~ on(X0,X2)
| ~ plane(plane_for_points(X1,point_on_plane(X2),X3))
| ~ on(X4,plane_for_points(X1,point_on_plane(X2),X3))
| ~ on(X0,plane_for_points(X1,point_on_plane(X2),X3)) ),
inference(superposition,[status(thm)],[c_108,c_26319]) ).
tcf(c_26357,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point_on_plane(X1),X0)
| ( X0 = X2 )
| ( point_on_plane(X1) = X2 )
| ( point_on_plane(X1) = X1 )
| ( point_on_plane(X1) = X0 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ plane(point_on_plane(X1))
| ~ line(point_on_plane(X1))
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(X2,point_on_plane(X1))
| ~ on(X0,point_on_plane(X1)) ),
inference(superposition,[status(thm)],[c_18002,c_26319]) ).
tcf(c_26542,plain,
! [X0: $i] :
( on(line_from_to(X0,point1),a_line)
| ( X0 = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_92,c_4636]) ).
tcf(c_26546,plain,
( on(line_from_to(point2,point_1_on_line(a_line)),a_line)
| ( point1 = point2 )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ on(point1,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_4636]) ).
tcf(c_26547,plain,
( on(line_from_to(point2,point_2_on_line(a_line)),a_line)
| ( point1 = point2 )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ on(point1,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_4636]) ).
tcf(c_26548,plain,
( on(line_from_to(point_2_on_line(a_line),point1),a_line)
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_4636]) ).
tcf(c_26550,plain,
( on(line_from_to(point_1_on_line(a_line),point1),a_line)
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_4636]) ).
tcf(c_26552,plain,
( on(line_from_to(point_1_on_line(a_line),point2),a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ on(point1,a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_4636]) ).
tcf(c_26553,plain,
( on(line_from_to(point_2_on_line(a_line),point2),a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point2)
| ~ on(point1,a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_4636]) ).
tcf(c_26554,plain,
! [X0: $i] :
( on(line_from_to(X0,point1),a_line)
| ( X0 = point1 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26542,c_122]) ).
tcf(c_26565,plain,
( on(line_from_to(point_2_on_line(a_line),point2),a_line)
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26553,c_123,c_126,c_9364]) ).
tcf(c_26572,plain,
( on(line_from_to(point_1_on_line(a_line),point2),a_line)
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26552,c_123,c_126,c_9468]) ).
tcf(c_26591,plain,
( on(a_line,a_line)
| ( point1 = point2 )
| ~ plane(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ line(line_from_to(point2,point1)) ),
inference(superposition,[status(thm)],[c_9035,c_26554]) ).
tcf(c_26594,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = point1 )
| ( line_from_to(X0,point1) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),X1) ),
inference(superposition,[status(thm)],[c_26554,c_94]) ).
tcf(c_26595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_from_to(X0,point1),X2)
| ( X2 = X3 )
| ( X1 = a_line )
| ( X0 = point1 )
| ( line_from_to(X0,point1) = X3 )
| ( line_from_to(X0,point1) = X2 )
| ~ plane(a_line)
| ~ plane(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X1)
| ~ on(X2,X1)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),X1) ),
inference(superposition,[status(thm)],[c_26554,c_111]) ).
tcf(c_26596,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,a_line)
| ( X0 = point1 )
| ( line_from_to(X0,point1) = X2 )
| ~ plane(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),X1) ),
inference(superposition,[status(thm)],[c_26554,c_112]) ).
tcf(c_26597,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( line_from_to(X1,point1) = a_line )
| ( line_from_to(X1,point1) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X1,point1))
| ~ line(line_from_to(X1,point1))
| ~ point(line_from_to(X1,point1))
| ~ on(X0,line_from_to(X1,point1)) ),
inference(superposition,[status(thm)],[c_26554,c_18010]) ).
tcf(c_26598,plain,
! [X0: $i,X1: $i] :
( on(a_line,line_from_to(X1,point1))
| ( X1 = point1 )
| ( line_from_to(X1,point1) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X1,point1))
| ~ line(line_from_to(X1,point1))
| ~ point(line_from_to(X1,point1))
| ~ on(X0,line_from_to(X1,point1)) ),
inference(superposition,[status(thm)],[c_26554,c_18012]) ).
tcf(c_26601,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point1 )
| ( line_from_to(X0,point1) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),a_line) ),
inference(superposition,[status(thm)],[c_26554,c_2934]) ).
tcf(c_26604,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(X0,point1),X1)
| ( X1 = X2 )
| ( X0 = point1 )
| ( line_from_to(X0,point1) = X2 )
| ( line_from_to(X0,point1) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_26554,c_121]) ).
tcf(c_26605,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point1 )
| ( line_from_to(X0,point1) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),a_line) ),
inference(superposition,[status(thm)],[c_26554,c_2925]) ).
tcf(c_26606,plain,
! [X0: $i] :
( ( point1 = a_line )
| ( X0 = point1 )
| ( line_from_to(X0,point1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),point1) ),
inference(superposition,[status(thm)],[c_26554,c_21610]) ).
tcf(c_26607,plain,
! [X0: $i] :
( ( point2 = a_line )
| ( X0 = point1 )
| ( line_from_to(X0,point1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),point2) ),
inference(superposition,[status(thm)],[c_26554,c_21602]) ).
tcf(c_26608,plain,
! [X0: $i] :
( on(a_line,point1)
| ( X0 = point1 )
| ( line_from_to(X0,point1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),point1) ),
inference(superposition,[status(thm)],[c_26554,c_20018]) ).
tcf(c_26609,plain,
! [X0: $i] :
( on(a_line,point2)
| ( X0 = point1 )
| ( line_from_to(X0,point1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),point2) ),
inference(superposition,[status(thm)],[c_26554,c_20010]) ).
tcf(c_26610,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,point1))
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(a_line,line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_26554,c_18013]) ).
tcf(c_26611,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ( line_from_to(X0,point1) = point2 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,point1))
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(point2,line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_26554,c_18017]) ).
tcf(c_26612,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = point1 )
| ( line_from_to(line_from_to(X0,point1),point1) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_26554,c_12246]) ).
tcf(c_26613,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = point1 )
| ( line_from_to(point1,line_from_to(X0,point1)) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_26554,c_11471]) ).
tcf(c_26614,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = point2 )
| ( line_from_to(line_from_to(X0,point1),point2) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_26554,c_11016]) ).
tcf(c_26615,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = point2 )
| ( line_from_to(point2,line_from_to(X0,point1)) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_26554,c_9014]) ).
tcf(c_26704,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point1 )
| ( line_from_to(X0,point1) = point2 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26605,c_125,c_127]) ).
tcf(c_26714,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = point1 )
| ( line_from_to(X0,point1) = point1 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26601,c_125,c_126]) ).
tcf(c_26747,plain,
! [X0: $i,X1: $i] :
( on(a_line,line_from_to(X1,point1))
| ( X1 = point1 )
| ( line_from_to(X1,point1) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X1,point1))
| ~ line(line_from_to(X1,point1))
| ~ point(line_from_to(X1,point1))
| ~ on(X0,line_from_to(X1,point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26598,c_125]) ).
tcf(c_26760,plain,
! [X0: $i,X1: $i] :
( ( X1 = point1 )
| ( line_from_to(X1,point1) = a_line )
| ( line_from_to(X1,point1) = X0 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X1,point1))
| ~ line(line_from_to(X1,point1))
| ~ point(line_from_to(X1,point1))
| ~ on(X0,line_from_to(X1,point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26597,c_125]) ).
tcf(c_26773,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = point1 )
| ( line_from_to(X0,point1) = X2 )
| ~ plane(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1))
| ~ on(line_from_to(X0,point1),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26594,c_125]) ).
tcf(c_26787,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(X0,point1),X1)
| ( X1 = X2 )
| ( X0 = point1 )
| ( line_from_to(X0,point1) = X2 )
| ( line_from_to(X0,point1) = X1 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26604,c_125]) ).
tcf(c_26847,plain,
! [X0: $i,X1: $i] :
( collinear(X1,point_2_on_line(a_line),X0)
| ( X0 = X1 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X1,a_line) ),
inference(global_subsumption_just,[status(thm)],[c_9412,c_125,c_4353,c_9412]) ).
tcf(c_26848,plain,
! [X0: $i,X1: $i] :
( collinear(X1,point_2_on_line(a_line),X0)
| ( X0 = X1 )
| ( point_2_on_line(a_line) = X1 )
| ( point_2_on_line(a_line) = X0 )
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line) ),
inference(renaming,[status(thm)],[c_26847]) ).
tcf(c_27102,plain,
! [X0: $i,X1: $i] :
( collinear(X1,point_1_on_line(a_line),X0)
| ( X0 = X1 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X1,a_line) ),
inference(global_subsumption_just,[status(thm)],[c_9516,c_125,c_4351,c_9516]) ).
tcf(c_27103,plain,
! [X0: $i,X1: $i] :
( collinear(X1,point_1_on_line(a_line),X0)
| ( X0 = X1 )
| ( point_1_on_line(a_line) = X1 )
| ( point_1_on_line(a_line) = X0 )
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line) ),
inference(renaming,[status(thm)],[c_27102]) ).
tcf(c_27134,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point1 )
| ( line_from_to(point1,line_from_to(point_1_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_12340,c_26307]) ).
tcf(c_27163,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point2 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point1),point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_12943]) ).
tcf(c_27164,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point2 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point1),point2) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27163,c_125]) ).
tcf(c_27185,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point2 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point1),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_12340,c_27164]) ).
tcf(c_27214,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point2 )
| ( line_from_to(point2,line_from_to(point_1_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_12944]) ).
tcf(c_27215,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point2 )
| ( line_from_to(point2,line_from_to(point_1_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27214,c_125]) ).
tcf(c_27236,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point_1_on_line(a_line),point1) = point2 )
| ( line_from_to(point2,line_from_to(point_1_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_12340,c_27215]) ).
tcf(c_27265,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point1 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point1),point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_13119]) ).
tcf(c_27266,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point1 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point1),point1) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27265,c_125]) ).
tcf(c_27287,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point1 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point1),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_12414,c_27266]) ).
tcf(c_27335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,X2)
| collinear(X4,X2,point_1_on_line(plane_for_points(X0,X1,X2)))
| ( X2 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = X4 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = X2 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X2,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_1_on_line(plane_for_points(X0,X1,X2)))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ on(point_1_on_line(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_95,c_3362]) ).
tcf(c_27336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,X2)
| collinear(X4,X2,point_2_on_line(plane_for_points(X0,X1,X2)))
| ( X2 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( point_2_on_line(plane_for_points(X0,X1,X2)) = X4 )
| ( point_2_on_line(plane_for_points(X0,X1,X2)) = X2 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X2,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_2_on_line(plane_for_points(X0,X1,X2)))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ on(point_2_on_line(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_96,c_3362]) ).
tcf(c_27337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,X2)
| collinear(X4,X2,point_on_plane(plane_for_points(X0,X1,X2)))
| ( X2 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( point_on_plane(plane_for_points(X0,X1,X2)) = X4 )
| ( point_on_plane(plane_for_points(X0,X1,X2)) = X2 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X2,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ point(point_on_plane(plane_for_points(X0,X1,X2)))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ on(point_on_plane(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_103,c_3362]) ).
tcf(c_27339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X1,X2,X3)
| collinear(X0,X3,X1)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( X0 = X1 )
| ( plane_for_points(X1,X2,X3) = X4 )
| ~ plane(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X4)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_3362]) ).
tcf(c_27340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X1,X2,X3)
| collinear(X0,X3,X2)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( X0 = X2 )
| ( plane_for_points(X1,X2,X3) = X4 )
| ~ plane(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X4)
| ~ on(X2,X4)
| ~ on(X0,X4)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_108,c_3362]) ).
tcf(c_27341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X0,X1,X2)
| collinear(X6,X2,common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4))
| ( X2 = X6 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X5 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4) = X6 )
| ( common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4) = X2 )
| ~ plane(X5)
| ~ plane(X3)
| ~ point(X6)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X6,X5)
| ~ on(X4,X3)
| ~ on(X2,X5)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ on(X6,plane_for_points(X0,X1,X2))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ point(common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4))
| ~ on(common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_113,c_3362]) ).
tcf(c_27342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X1,X2,X3)
| collinear(X6,X3,common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4))
| ( X3 = X6 )
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,X3) = X5 )
| ( plane_for_points(X1,X2,X3) = X0 )
| ( common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4) = X6 )
| ( common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4) = X3 )
| ~ plane(X5)
| ~ plane(X0)
| ~ point(X6)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X6,X5)
| ~ on(X4,X0)
| ~ on(X3,X5)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X6,plane_for_points(X1,X2,X3))
| ~ on(X4,plane_for_points(X1,X2,X3))
| ~ point(common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4))
| ~ on(common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_114,c_3362]) ).
tcf(c_27343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,X2)
| collinear(X4,X2,plane_for_points(X0,X1,X2))
| ( X2 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X4 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( plane_for_points(X0,X1,X2) = X2 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X2,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(plane_for_points(X0,X1,X2))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ on(plane_for_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_18002,c_3362]) ).
tcf(c_27544,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point1 )
| ( line_from_to(point1,line_from_to(point_2_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_13120]) ).
tcf(c_27545,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point1 )
| ( line_from_to(point1,line_from_to(point_2_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27544,c_125]) ).
tcf(c_27566,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point1 )
| ( line_from_to(point1,line_from_to(point_2_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_12414,c_27545]) ).
tcf(c_27595,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point2 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point1),point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_13121]) ).
tcf(c_27596,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point2 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point1),point2) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27595,c_125]) ).
tcf(c_27617,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point2 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point1),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_12414,c_27596]) ).
tcf(c_27646,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point2 )
| ( line_from_to(point2,line_from_to(point_2_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_13122]) ).
tcf(c_27647,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point2 )
| ( line_from_to(point2,line_from_to(point_2_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27646,c_125]) ).
tcf(c_27668,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point_2_on_line(a_line),point1) = point2 )
| ( line_from_to(point2,line_from_to(point_2_on_line(a_line),point1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_12414,c_27647]) ).
tcf(c_27730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X0,point_1_on_line(line_through_3_points(X0,X1,X2)))
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = X4 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = X0 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(point_1_on_line(line_through_3_points(X0,X1,X2)))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ on(point_1_on_line(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_95,c_3363]) ).
tcf(c_27731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X0,point_2_on_line(line_through_3_points(X0,X1,X2)))
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( point_2_on_line(line_through_3_points(X0,X1,X2)) = X4 )
| ( point_2_on_line(line_through_3_points(X0,X1,X2)) = X0 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(point_2_on_line(line_through_3_points(X0,X1,X2)))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ on(point_2_on_line(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_96,c_3363]) ).
tcf(c_27732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X0,point_on_plane(line_through_3_points(X0,X1,X2)))
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( point_on_plane(line_through_3_points(X0,X1,X2)) = X4 )
| ( point_on_plane(line_through_3_points(X0,X1,X2)) = X0 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ point(point_on_plane(line_through_3_points(X0,X1,X2)))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ on(point_on_plane(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_103,c_3363]) ).
tcf(c_27734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,X2)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X1,X2,X3) = X4 )
| ~ plane(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X4)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_118,c_3363]) ).
tcf(c_27735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( X0 = X1 )
| ( line_through_3_points(X1,X2,X3) = X4 )
| ~ plane(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X4)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_119,c_3363]) ).
tcf(c_27736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,X0,common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4))
| ( X1 = X2 )
| ( X0 = X6 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X5 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4) = X6 )
| ( common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4) = X0 )
| ~ plane(X5)
| ~ plane(X3)
| ~ point(X6)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X6,X5)
| ~ on(X4,X3)
| ~ on(X0,X5)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ on(X6,line_through_3_points(X0,X1,X2))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ point(common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4))
| ~ on(common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_113,c_3363]) ).
tcf(c_27737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,X1,common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4))
| ( X2 = X3 )
| ( X1 = X6 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,X3) = X5 )
| ( line_through_3_points(X1,X2,X3) = X0 )
| ( common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4) = X6 )
| ( common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4) = X1 )
| ~ plane(X5)
| ~ plane(X0)
| ~ point(X6)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X6,X5)
| ~ on(X4,X0)
| ~ on(X1,X5)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X6,line_through_3_points(X1,X2,X3))
| ~ on(X4,line_through_3_points(X1,X2,X3))
| ~ point(common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4))
| ~ on(common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_114,c_3363]) ).
tcf(c_27738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X0,line_through_3_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X4 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( line_through_3_points(X0,X1,X2) = X0 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(line_through_3_points(X0,X1,X2))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ on(line_through_3_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_18002,c_3363]) ).
tcf(c_27908,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ( point_on_plane(X0) = X2 )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ on(point_on_plane(X0),X1)
| ~ on(X2,X0)
| ~ on(X2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_3693,c_104,c_3693]) ).
tcf(c_27909,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ( point_on_plane(X0) = X2 )
| ~ plane(X0)
| ~ line(X1)
| ~ line(X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ on(point_on_plane(X0),X1) ),
inference(renaming,[status(thm)],[c_27908]) ).
tcf(c_27928,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( point_on_plane(X2) = X1 )
| ( point_on_plane(X2) = X0 )
| ( line_from_to(X1,point_on_plane(X2)) = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X2))
| ~ on(X0,X2)
| ~ line(line_from_to(X1,point_on_plane(X2)))
| ~ on(X0,line_from_to(X1,point_on_plane(X2))) ),
inference(superposition,[status(thm)],[c_92,c_27909]) ).
tcf(c_27930,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,X2,point_on_plane(X3))
| ( X1 = X2 )
| ( point_on_plane(X3) = X2 )
| ( point_on_plane(X3) = X1 )
| ( point_on_plane(X3) = X0 )
| ( plane_for_points(X1,X2,point_on_plane(X3)) = X3 )
| ~ plane(X3)
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X3))
| ~ on(X0,X3)
| ~ line(plane_for_points(X1,X2,point_on_plane(X3)))
| ~ on(X0,plane_for_points(X1,X2,point_on_plane(X3))) ),
inference(superposition,[status(thm)],[c_109,c_27909]) ).
tcf(c_27931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( point_on_plane(X1) = X3 )
| ( point_on_plane(X1) = X2 )
| ( point_on_plane(X1) = X0 )
| ( line_through_3_points(point_on_plane(X1),X2,X3) = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_on_plane(X1))
| ~ on(X0,X1)
| ~ collinear(point_on_plane(X1),X2,X3)
| ~ line(line_through_3_points(point_on_plane(X1),X2,X3))
| ~ on(X0,line_through_3_points(point_on_plane(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_27909]) ).
tcf(c_27932,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( point_on_plane(X2) = X3 )
| ( point_on_plane(X2) = X1 )
| ( point_on_plane(X2) = X0 )
| ( line_through_3_points(X1,point_on_plane(X2),X3) = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X2))
| ~ on(X0,X2)
| ~ collinear(X1,point_on_plane(X2),X3)
| ~ line(line_through_3_points(X1,point_on_plane(X2),X3))
| ~ on(X0,line_through_3_points(X1,point_on_plane(X2),X3)) ),
inference(superposition,[status(thm)],[c_118,c_27909]) ).
tcf(c_27933,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( point_on_plane(X3) = X2 )
| ( point_on_plane(X3) = X1 )
| ( point_on_plane(X3) = X0 )
| ( line_through_3_points(X1,X2,point_on_plane(X3)) = X3 )
| ~ plane(X3)
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X3))
| ~ on(X0,X3)
| ~ collinear(X1,X2,point_on_plane(X3))
| ~ line(line_through_3_points(X1,X2,point_on_plane(X3)))
| ~ on(X0,line_through_3_points(X1,X2,point_on_plane(X3))) ),
inference(superposition,[status(thm)],[c_119,c_27909]) ).
tcf(c_27934,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( point_on_plane(X1) = X2 )
| ( point_on_plane(X1) = X0 )
| ( line_from_to(point_on_plane(X1),X2) = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_on_plane(X1))
| ~ on(X0,X1)
| ~ line(line_from_to(point_on_plane(X1),X2))
| ~ on(X0,line_from_to(point_on_plane(X1),X2)) ),
inference(superposition,[status(thm)],[c_91,c_27909]) ).
tcf(c_27935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(point_on_plane(X1),X2,X3)
| ( X2 = X3 )
| ( point_on_plane(X1) = X3 )
| ( point_on_plane(X1) = X2 )
| ( point_on_plane(X1) = X0 )
| ( plane_for_points(point_on_plane(X1),X2,X3) = X1 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_on_plane(X1))
| ~ on(X0,X1)
| ~ line(plane_for_points(point_on_plane(X1),X2,X3))
| ~ on(X0,plane_for_points(point_on_plane(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_27909]) ).
tcf(c_27936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X1,point_on_plane(X2),X3)
| ( X1 = X3 )
| ( point_on_plane(X2) = X3 )
| ( point_on_plane(X2) = X1 )
| ( point_on_plane(X2) = X0 )
| ( plane_for_points(X1,point_on_plane(X2),X3) = X2 )
| ~ plane(X2)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_on_plane(X2))
| ~ on(X0,X2)
| ~ line(plane_for_points(X1,point_on_plane(X2),X3))
| ~ on(X0,plane_for_points(X1,point_on_plane(X2),X3)) ),
inference(superposition,[status(thm)],[c_108,c_27909]) ).
tcf(c_27937,plain,
! [X0: $i,X1: $i] :
( ( point_on_plane(X1) = X1 )
| ( point_on_plane(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_on_plane(X1))
| ~ line(point_on_plane(X1))
| ~ on(X0,X1)
| ~ on(X0,point_on_plane(X1)) ),
inference(superposition,[status(thm)],[c_18002,c_27909]) ).
tcf(c_28180,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point1 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point2),point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_18301]) ).
tcf(c_28181,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point1 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point2),point1) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28180,c_125]) ).
tcf(c_28202,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point1 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point2),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11151,c_28181]) ).
tcf(c_28231,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point1 )
| ( line_from_to(point1,line_from_to(point_2_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_18302]) ).
tcf(c_28232,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point1 )
| ( line_from_to(point1,line_from_to(point_2_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28231,c_125]) ).
tcf(c_28253,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point1 )
| ( line_from_to(point1,line_from_to(point_2_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11151,c_28232]) ).
tcf(c_28282,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point2 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point2),point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_18303]) ).
tcf(c_28283,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point2 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point2),point2) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28282,c_125]) ).
tcf(c_28304,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point2 )
| ( line_from_to(line_from_to(point_2_on_line(a_line),point2),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11151,c_28283]) ).
tcf(c_28333,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point2 )
| ( line_from_to(point2,line_from_to(point_2_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_18304]) ).
tcf(c_28334,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point2 )
| ( line_from_to(point2,line_from_to(point_2_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28333,c_125]) ).
tcf(c_28387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X1,point_1_on_line(line_through_3_points(X0,X1,X2)))
| ( X1 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = X4 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = X1 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X1,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(point_1_on_line(line_through_3_points(X0,X1,X2)))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ on(point_1_on_line(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_95,c_3364]) ).
tcf(c_28388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X1,point_2_on_line(line_through_3_points(X0,X1,X2)))
| ( X1 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( point_2_on_line(line_through_3_points(X0,X1,X2)) = X4 )
| ( point_2_on_line(line_through_3_points(X0,X1,X2)) = X1 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X1,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(point_2_on_line(line_through_3_points(X0,X1,X2)))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ on(point_2_on_line(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_96,c_3364]) ).
tcf(c_28389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X1,point_on_plane(line_through_3_points(X0,X1,X2)))
| ( X1 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( point_on_plane(line_through_3_points(X0,X1,X2)) = X4 )
| ( point_on_plane(line_through_3_points(X0,X1,X2)) = X1 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X1,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ point(point_on_plane(line_through_3_points(X0,X1,X2)))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ on(point_on_plane(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_103,c_3364]) ).
tcf(c_28390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X2,X1)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X1,X2,X3) = X4 )
| ~ plane(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X4)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_3364]) ).
tcf(c_28392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X2,X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( X0 = X2 )
| ( line_through_3_points(X1,X2,X3) = X4 )
| ~ plane(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X4)
| ~ on(X2,X4)
| ~ on(X0,X4)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_119,c_3364]) ).
tcf(c_28393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,X1,common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4))
| ( X1 = X6 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X5 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4) = X6 )
| ( common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4) = X1 )
| ~ plane(X5)
| ~ plane(X3)
| ~ point(X6)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X6,X5)
| ~ on(X4,X3)
| ~ on(X1,X5)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ on(X6,line_through_3_points(X0,X1,X2))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ point(common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4))
| ~ on(common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_113,c_3364]) ).
tcf(c_28394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,X2,common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4))
| ( X2 = X6 )
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,X3) = X5 )
| ( line_through_3_points(X1,X2,X3) = X0 )
| ( common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4) = X6 )
| ( common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4) = X2 )
| ~ plane(X5)
| ~ plane(X0)
| ~ point(X6)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X6,X5)
| ~ on(X4,X0)
| ~ on(X2,X5)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X6,line_through_3_points(X1,X2,X3))
| ~ on(X4,line_through_3_points(X1,X2,X3))
| ~ point(common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4))
| ~ on(common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_114,c_3364]) ).
tcf(c_28395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X1,line_through_3_points(X0,X1,X2))
| ( X1 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X4 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( line_through_3_points(X0,X1,X2) = X1 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X1,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(line_through_3_points(X0,X1,X2))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ on(line_through_3_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_18002,c_3364]) ).
tcf(c_28575,plain,
! [X0: $i,X1: $i] :
( on(X1,point_on_plane(X1))
| ( point_on_plane(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X0)
| ~ plane(point_on_plane(X1))
| ~ line(point_on_plane(X1))
| ~ on(X0,X1)
| ~ on(X0,point_on_plane(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19966,c_104]) ).
tcf(c_28603,plain,
! [X0: $i] :
( on(X0,point_on_plane(X0))
| ( point_1_on_line(point_on_plane(X0)) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ plane(point_on_plane(X0))
| ~ line(point_on_plane(X0))
| ~ point(point_1_on_line(point_on_plane(X0)))
| ~ on(point_1_on_line(point_on_plane(X0)),X0) ),
inference(superposition,[status(thm)],[c_95,c_28575]) ).
tcf(c_28604,plain,
! [X0: $i] :
( on(X0,point_on_plane(X0))
| ( point_2_on_line(point_on_plane(X0)) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ plane(point_on_plane(X0))
| ~ line(point_on_plane(X0))
| ~ point(point_2_on_line(point_on_plane(X0)))
| ~ on(point_2_on_line(point_on_plane(X0)),X0) ),
inference(superposition,[status(thm)],[c_96,c_28575]) ).
tcf(c_28605,plain,
! [X0: $i] :
( on(X0,point_on_plane(X0))
| ( point_on_plane(point_on_plane(X0)) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ plane(point_on_plane(X0))
| ~ line(point_on_plane(X0))
| ~ point(point_on_plane(point_on_plane(X0)))
| ~ on(point_on_plane(point_on_plane(X0)),X0) ),
inference(superposition,[status(thm)],[c_103,c_28575]) ).
tcf(c_28606,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X0,point_on_plane(X0))
| ( point_on_plane(X0) = X1 )
| ( common_point_on_planes(point_on_plane(X0),X1,X2) = point_on_plane(X0) )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X2)
| ~ plane(point_on_plane(X0))
| ~ line(point_on_plane(X0))
| ~ on(X2,X1)
| ~ on(X2,point_on_plane(X0))
| ~ point(common_point_on_planes(point_on_plane(X0),X1,X2))
| ~ on(common_point_on_planes(point_on_plane(X0),X1,X2),X0) ),
inference(superposition,[status(thm)],[c_113,c_28575]) ).
tcf(c_28607,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,point_on_plane(X1))
| ( point_on_plane(X1) = X0 )
| ( common_point_on_planes(X0,point_on_plane(X1),X2) = point_on_plane(X1) )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ plane(point_on_plane(X1))
| ~ line(point_on_plane(X1))
| ~ on(X2,X0)
| ~ on(X2,point_on_plane(X1))
| ~ point(common_point_on_planes(X0,point_on_plane(X1),X2))
| ~ on(common_point_on_planes(X0,point_on_plane(X1),X2),X1) ),
inference(superposition,[status(thm)],[c_114,c_28575]) ).
tcf(c_28718,plain,
! [X0: $i] :
( on(X0,point_on_plane(X0))
| ( point_1_on_line(point_on_plane(X0)) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ plane(point_on_plane(X0))
| ~ line(point_on_plane(X0))
| ~ on(point_1_on_line(point_on_plane(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28603,c_97]) ).
tcf(c_28748,plain,
! [X0: $i] :
( on(X0,point_on_plane(X0))
| ( point_2_on_line(point_on_plane(X0)) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ plane(point_on_plane(X0))
| ~ line(point_on_plane(X0))
| ~ on(point_2_on_line(point_on_plane(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28604,c_98]) ).
tcf(c_28778,plain,
! [X0: $i] :
( on(X0,point_on_plane(X0))
| ( point_on_plane(point_on_plane(X0)) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ plane(point_on_plane(X0))
| ~ line(point_on_plane(X0))
| ~ on(point_on_plane(point_on_plane(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28605,c_104]) ).
tcf(c_28810,plain,
( ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point_2_on_line(a_line),point2) = point2 )
| ( line_from_to(point2,line_from_to(point_2_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11151,c_28334]) ).
tcf(c_28913,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point1 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point2),point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_18441]) ).
tcf(c_28914,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point1 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point2),point1) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28913,c_125]) ).
tcf(c_28935,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point1 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point2),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11124,c_28914]) ).
tcf(c_28965,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point1 )
| ( line_from_to(point1,line_from_to(point_1_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_18442]) ).
tcf(c_28966,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point1 )
| ( line_from_to(point1,line_from_to(point_1_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28965,c_125]) ).
tcf(c_28988,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point1 )
| ( line_from_to(point1,line_from_to(point_1_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11124,c_28966]) ).
tcf(c_29019,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point2 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point2),point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_18443]) ).
tcf(c_29020,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point2 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point2),point2) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29019,c_125]) ).
tcf(c_29042,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point2 )
| ( line_from_to(line_from_to(point_1_on_line(a_line),point2),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11124,c_29020]) ).
tcf(c_29152,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point2 )
| ( line_from_to(point2,line_from_to(point_1_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_18444]) ).
tcf(c_29153,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point2 )
| ( line_from_to(point2,line_from_to(point_1_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29152,c_125]) ).
tcf(c_29206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X2,point_1_on_line(line_through_3_points(X0,X1,X2)))
| ( X2 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = X4 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = X2 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X2,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(point_1_on_line(line_through_3_points(X0,X1,X2)))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ on(point_1_on_line(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_95,c_3365]) ).
tcf(c_29207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X2,point_2_on_line(line_through_3_points(X0,X1,X2)))
| ( X2 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( point_2_on_line(line_through_3_points(X0,X1,X2)) = X4 )
| ( point_2_on_line(line_through_3_points(X0,X1,X2)) = X2 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X2,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(point_2_on_line(line_through_3_points(X0,X1,X2)))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ on(point_2_on_line(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_96,c_3365]) ).
tcf(c_29208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X2,point_on_plane(line_through_3_points(X0,X1,X2)))
| ( X2 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( point_on_plane(line_through_3_points(X0,X1,X2)) = X4 )
| ( point_on_plane(line_through_3_points(X0,X1,X2)) = X2 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X2,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ point(point_on_plane(line_through_3_points(X0,X1,X2)))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ on(point_on_plane(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_103,c_3365]) ).
tcf(c_29209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X3,X1)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( X0 = X1 )
| ( line_through_3_points(X1,X2,X3) = X4 )
| ~ plane(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X4)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_117,c_3365]) ).
tcf(c_29210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X3,X2)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( X0 = X2 )
| ( line_through_3_points(X1,X2,X3) = X4 )
| ~ plane(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X4)
| ~ on(X2,X4)
| ~ on(X0,X4)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_118,c_3365]) ).
tcf(c_29212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,X2,common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4))
| ( X2 = X6 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X5 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4) = X6 )
| ( common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4) = X2 )
| ~ plane(X5)
| ~ plane(X3)
| ~ point(X6)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X6,X5)
| ~ on(X4,X3)
| ~ on(X2,X5)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ on(X6,line_through_3_points(X0,X1,X2))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ point(common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4))
| ~ on(common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_113,c_3365]) ).
tcf(c_29213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,X3,common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4))
| ( X3 = X6 )
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,X3) = X5 )
| ( line_through_3_points(X1,X2,X3) = X0 )
| ( common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4) = X6 )
| ( common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4) = X3 )
| ~ plane(X5)
| ~ plane(X0)
| ~ point(X6)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X6,X5)
| ~ on(X4,X0)
| ~ on(X3,X5)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X6,line_through_3_points(X1,X2,X3))
| ~ on(X4,line_through_3_points(X1,X2,X3))
| ~ point(common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4))
| ~ on(common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_114,c_3365]) ).
tcf(c_29214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,X2,line_through_3_points(X0,X1,X2))
| ( X2 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X4 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( line_through_3_points(X0,X1,X2) = X2 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X2,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(line_through_3_points(X0,X1,X2))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ on(line_through_3_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_18002,c_3365]) ).
tcf(c_29394,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point_1_on_line(X1),X0)
| ( X0 = X2 )
| ( point_1_on_line(X1) = X2 )
| ( point_1_on_line(X1) = X0 )
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3942,c_97]) ).
tcf(c_29432,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point_2_on_line(X1),X0)
| ( X0 = X2 )
| ( point_2_on_line(X1) = X2 )
| ( point_2_on_line(X1) = X0 )
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3943,c_98]) ).
tcf(c_29481,plain,
! [X0: $i] :
( on(line_from_to(a_line,X0),a_line)
| ( X0 = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(a_line,X0)) ),
inference(superposition,[status(thm)],[c_91,c_5605]) ).
tcf(c_29482,plain,
( on(line_from_to(point2,point1),a_line)
| ( point1 = a_line )
| ( point1 = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ point(point1)
| ~ on(a_line,a_line)
| ~ on(point1,a_line)
| ~ line(line_from_to(point2,point1)) ),
inference(superposition,[status(thm)],[c_9035,c_5605]) ).
tcf(c_29483,plain,
( on(line_from_to(point1,point2),a_line)
| ( point2 = a_line )
| ( point1 = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ point(point1)
| ~ on(a_line,a_line)
| ~ on(point2,a_line)
| ~ line(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_5605]) ).
tcf(c_29484,plain,
( on(line_from_to(point2,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(a_line,a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line)
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_5605]) ).
tcf(c_29485,plain,
( on(line_from_to(point2,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(a_line,a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line)
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_5605]) ).
tcf(c_29486,plain,
( on(line_from_to(point_2_on_line(a_line),point1),a_line)
| ( point1 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(a_line,a_line)
| ~ on(point1,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_5605]) ).
tcf(c_29487,plain,
( on(line_from_to(point1,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(a_line,a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line)
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_5605]) ).
tcf(c_29488,plain,
( on(line_from_to(point_1_on_line(a_line),point1),a_line)
| ( point1 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(a_line,a_line)
| ~ on(point1,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_5605]) ).
tcf(c_29489,plain,
( on(line_from_to(point1,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(a_line,a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line)
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_5605]) ).
tcf(c_29490,plain,
( on(line_from_to(point_1_on_line(a_line),point2),a_line)
| ( point2 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(a_line,a_line)
| ~ on(point2,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_5605]) ).
tcf(c_29491,plain,
( on(line_from_to(point_2_on_line(a_line),point2),a_line)
| ( point2 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(a_line,a_line)
| ~ on(point2,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_5605]) ).
tcf(c_29501,plain,
( on(line_from_to(point_2_on_line(a_line),point2),a_line)
| ( point2 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29491,c_123,c_127]) ).
tcf(c_29510,plain,
( on(line_from_to(point_1_on_line(a_line),point2),a_line)
| ( point2 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29490,c_123,c_127]) ).
tcf(c_29519,plain,
( on(line_from_to(point_1_on_line(a_line),point1),a_line)
| ( point1 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29488,c_122,c_126]) ).
tcf(c_29528,plain,
( on(line_from_to(point_2_on_line(a_line),point1),a_line)
| ( point1 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29486,c_122,c_126]) ).
tcf(c_29537,plain,
( on(line_from_to(point1,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29489,c_122,c_9468]) ).
tcf(c_29546,plain,
( on(line_from_to(point1,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29487,c_122,c_9364]) ).
tcf(c_29555,plain,
( on(line_from_to(point2,point_2_on_line(a_line)),a_line)
| ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29485,c_123,c_9364]) ).
tcf(c_29564,plain,
( on(line_from_to(point2,point_1_on_line(a_line)),a_line)
| ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29484,c_123,c_9468]) ).
tcf(c_29574,plain,
! [X0: $i] :
( on(line_from_to(a_line,X0),a_line)
| ( X0 = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(global_subsumption_just,[status(thm)],[c_29481,c_8934,c_29481]) ).
tcf(c_29589,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = a_line )
| ( line_from_to(a_line,X0) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ point(line_from_to(a_line,X0))
| ~ on(line_from_to(a_line,X0),X1) ),
inference(superposition,[status(thm)],[c_29574,c_94]) ).
tcf(c_29590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_from_to(a_line,X0),X2)
| ( X2 = X3 )
| ( X1 = a_line )
| ( X0 = a_line )
| ( line_from_to(a_line,X0) = X3 )
| ( line_from_to(a_line,X0) = X2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X1)
| ~ on(X2,X1)
| ~ point(line_from_to(a_line,X0))
| ~ on(line_from_to(a_line,X0),X1) ),
inference(superposition,[status(thm)],[c_29574,c_111]) ).
tcf(c_29591,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,a_line)
| ( X0 = a_line )
| ( line_from_to(a_line,X0) = X2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ point(line_from_to(a_line,X0))
| ~ on(line_from_to(a_line,X0),X1) ),
inference(superposition,[status(thm)],[c_29574,c_112]) ).
tcf(c_29592,plain,
! [X0: $i,X1: $i] :
( ( X1 = a_line )
| ( line_from_to(a_line,X1) = a_line )
| ( line_from_to(a_line,X1) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(a_line,X1))
| ~ line(line_from_to(a_line,X1))
| ~ point(line_from_to(a_line,X1))
| ~ on(X0,line_from_to(a_line,X1)) ),
inference(superposition,[status(thm)],[c_29574,c_18010]) ).
tcf(c_29593,plain,
! [X0: $i,X1: $i] :
( on(a_line,line_from_to(a_line,X1))
| ( X1 = a_line )
| ( line_from_to(a_line,X1) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(a_line,X1))
| ~ line(line_from_to(a_line,X1))
| ~ point(line_from_to(a_line,X1))
| ~ on(X0,line_from_to(a_line,X1)) ),
inference(superposition,[status(thm)],[c_29574,c_18012]) ).
tcf(c_29596,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = a_line )
| ( line_from_to(a_line,X0) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0))
| ~ on(line_from_to(a_line,X0),a_line) ),
inference(superposition,[status(thm)],[c_29574,c_2934]) ).
tcf(c_29599,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(a_line,X0),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( line_from_to(a_line,X0) = X2 )
| ( line_from_to(a_line,X0) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0)) ),
inference(superposition,[status(thm)],[c_29574,c_121]) ).
tcf(c_29600,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = a_line )
| ( line_from_to(a_line,X0) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0))
| ~ on(line_from_to(a_line,X0),a_line) ),
inference(superposition,[status(thm)],[c_29574,c_2925]) ).
tcf(c_29601,plain,
! [X0: $i] :
( ( point1 = a_line )
| ( X0 = a_line )
| ( line_from_to(a_line,X0) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0))
| ~ on(line_from_to(a_line,X0),point1) ),
inference(superposition,[status(thm)],[c_29574,c_21610]) ).
tcf(c_29602,plain,
! [X0: $i] :
( ( point2 = a_line )
| ( X0 = a_line )
| ( line_from_to(a_line,X0) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0))
| ~ on(line_from_to(a_line,X0),point2) ),
inference(superposition,[status(thm)],[c_29574,c_21602]) ).
tcf(c_29603,plain,
! [X0: $i] :
( on(a_line,point1)
| ( X0 = a_line )
| ( line_from_to(a_line,X0) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0))
| ~ on(line_from_to(a_line,X0),point1) ),
inference(superposition,[status(thm)],[c_29574,c_20018]) ).
tcf(c_29604,plain,
! [X0: $i] :
( on(a_line,point2)
| ( X0 = a_line )
| ( line_from_to(a_line,X0) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0))
| ~ on(line_from_to(a_line,X0),point2) ),
inference(superposition,[status(thm)],[c_29574,c_20010]) ).
tcf(c_29605,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(a_line,X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(a_line,X0))
| ~ line(line_from_to(a_line,X0))
| ~ point(line_from_to(a_line,X0))
| ~ on(a_line,line_from_to(a_line,X0)) ),
inference(superposition,[status(thm)],[c_29574,c_18013]) ).
tcf(c_29606,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(a_line,X0) = a_line )
| ( line_from_to(a_line,X0) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(a_line,X0))
| ~ line(line_from_to(a_line,X0))
| ~ point(line_from_to(a_line,X0))
| ~ on(point2,line_from_to(a_line,X0)) ),
inference(superposition,[status(thm)],[c_29574,c_18017]) ).
tcf(c_29607,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(a_line,X0) = point1 )
| ( line_from_to(line_from_to(a_line,X0),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0)) ),
inference(superposition,[status(thm)],[c_29574,c_12246]) ).
tcf(c_29608,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(a_line,X0) = point1 )
| ( line_from_to(point1,line_from_to(a_line,X0)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0)) ),
inference(superposition,[status(thm)],[c_29574,c_11471]) ).
tcf(c_29609,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(a_line,X0) = point2 )
| ( line_from_to(line_from_to(a_line,X0),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0)) ),
inference(superposition,[status(thm)],[c_29574,c_11016]) ).
tcf(c_29610,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(a_line,X0) = point2 )
| ( line_from_to(point2,line_from_to(a_line,X0)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0)) ),
inference(superposition,[status(thm)],[c_29574,c_9014]) ).
tcf(c_29697,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = a_line )
| ( line_from_to(a_line,X0) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0))
| ~ on(line_from_to(a_line,X0),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29600,c_125,c_127]) ).
tcf(c_29707,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = a_line )
| ( line_from_to(a_line,X0) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0))
| ~ on(line_from_to(a_line,X0),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29596,c_125,c_126]) ).
tcf(c_29741,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = a_line )
| ( line_from_to(a_line,X0) = X2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ point(line_from_to(a_line,X0))
| ~ on(line_from_to(a_line,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29589,c_125]) ).
tcf(c_29755,plain,
! [X0: $i,X1: $i] :
( on(a_line,line_from_to(a_line,X1))
| ( X1 = a_line )
| ( line_from_to(a_line,X1) = X0 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(a_line,X1))
| ~ line(line_from_to(a_line,X1))
| ~ point(line_from_to(a_line,X1))
| ~ on(X0,line_from_to(a_line,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29593,c_125]) ).
tcf(c_29769,plain,
! [X0: $i,X1: $i] :
( ( X1 = a_line )
| ( line_from_to(a_line,X1) = a_line )
| ( line_from_to(a_line,X1) = X0 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(a_line,X1))
| ~ line(line_from_to(a_line,X1))
| ~ point(line_from_to(a_line,X1))
| ~ on(X0,line_from_to(a_line,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29592,c_125]) ).
tcf(c_29783,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(a_line,X0),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( line_from_to(a_line,X0) = X2 )
| ( line_from_to(a_line,X0) = X1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29599,c_125]) ).
tcf(c_29840,plain,
( ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point_1_on_line(a_line),point2) = point2 )
| ( line_from_to(point2,line_from_to(point_1_on_line(a_line),point2)) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11124,c_29153]) ).
tcf(c_29877,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point1,point_1_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_18631]) ).
tcf(c_29878,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point1,point_1_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29877,c_125]) ).
tcf(c_29899,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point1,point_1_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11755,c_29878]) ).
tcf(c_29928,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point1,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_18632]) ).
tcf(c_29929,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point1,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29928,c_125]) ).
tcf(c_29950,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point1,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11755,c_29929]) ).
tcf(c_30000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_from_to(X1,X2) = X3 )
| ~ plane(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X1,X3)
| ~ on(X0,X3)
| ~ plane(line_from_to(X1,X2))
| ~ on(X0,line_from_to(X1,X2)) ),
inference(superposition,[status(thm)],[c_92,c_3366]) ).
tcf(c_30001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,X0,point_1_on_line(line_from_to(X0,X1)))
| ( X0 = X3 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = X2 )
| ( point_1_on_line(line_from_to(X0,X1)) = X3 )
| ( point_1_on_line(line_from_to(X0,X1)) = X0 )
| ~ plane(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(point_1_on_line(line_from_to(X0,X1)))
| ~ on(X3,line_from_to(X0,X1))
| ~ on(point_1_on_line(line_from_to(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_95,c_3366]) ).
tcf(c_30002,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,X0,point_2_on_line(line_from_to(X0,X1)))
| ( X0 = X3 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = X2 )
| ( point_2_on_line(line_from_to(X0,X1)) = X3 )
| ( point_2_on_line(line_from_to(X0,X1)) = X0 )
| ~ plane(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(point_2_on_line(line_from_to(X0,X1)))
| ~ on(X3,line_from_to(X0,X1))
| ~ on(point_2_on_line(line_from_to(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_96,c_3366]) ).
tcf(c_30003,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,X0,point_on_plane(line_from_to(X0,X1)))
| ( X0 = X3 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = X2 )
| ( point_on_plane(line_from_to(X0,X1)) = X3 )
| ( point_on_plane(line_from_to(X0,X1)) = X0 )
| ~ plane(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(X0,X1))
| ~ point(point_on_plane(line_from_to(X0,X1)))
| ~ on(X3,line_from_to(X0,X1))
| ~ on(point_on_plane(line_from_to(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_103,c_3366]) ).
tcf(c_30005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X5,X0,common_point_on_planes(line_from_to(X0,X1),X2,X3))
| ( X0 = X5 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = X4 )
| ( line_from_to(X0,X1) = X2 )
| ( common_point_on_planes(line_from_to(X0,X1),X2,X3) = X5 )
| ( common_point_on_planes(line_from_to(X0,X1),X2,X3) = X0 )
| ~ plane(X4)
| ~ plane(X2)
| ~ point(X5)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X5,X4)
| ~ on(X3,X2)
| ~ on(X0,X4)
| ~ plane(line_from_to(X0,X1))
| ~ on(X5,line_from_to(X0,X1))
| ~ on(X3,line_from_to(X0,X1))
| ~ point(common_point_on_planes(line_from_to(X0,X1),X2,X3))
| ~ on(common_point_on_planes(line_from_to(X0,X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_113,c_3366]) ).
tcf(c_30006,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X5,X1,common_point_on_planes(X0,line_from_to(X1,X2),X3))
| ( X1 = X5 )
| ( X1 = X2 )
| ( line_from_to(X1,X2) = X4 )
| ( line_from_to(X1,X2) = X0 )
| ( common_point_on_planes(X0,line_from_to(X1,X2),X3) = X5 )
| ( common_point_on_planes(X0,line_from_to(X1,X2),X3) = X1 )
| ~ plane(X4)
| ~ plane(X0)
| ~ point(X5)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X5,X4)
| ~ on(X3,X0)
| ~ on(X1,X4)
| ~ plane(line_from_to(X1,X2))
| ~ on(X5,line_from_to(X1,X2))
| ~ on(X3,line_from_to(X1,X2))
| ~ point(common_point_on_planes(X0,line_from_to(X1,X2),X3))
| ~ on(common_point_on_planes(X0,line_from_to(X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_114,c_3366]) ).
tcf(c_30007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,X0,line_from_to(X0,X1))
| ( X0 = X3 )
| ( X0 = X1 )
| ( line_from_to(X0,X1) = X3 )
| ( line_from_to(X0,X1) = X2 )
| ( line_from_to(X0,X1) = X0 )
| ~ plane(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(X0,X1))
| ~ line(line_from_to(X0,X1))
| ~ point(line_from_to(X0,X1))
| ~ on(X3,line_from_to(X0,X1))
| ~ on(line_from_to(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_18002,c_3366]) ).
tcf(c_30008,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point2,X1)
| ( point1 = point2 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_from_to(point2,point1) = X2 )
| ~ point(point2)
| ~ point(point1)
| ~ plane(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(point2,X2)
| ~ on(X1,a_line)
| ~ on(X1,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(point2,point1))
| ~ on(X0,line_from_to(point2,point1)) ),
inference(superposition,[status(thm)],[c_9035,c_3366]) ).
tcf(c_30009,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point1,X1)
| ( point1 = point2 )
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( line_from_to(point1,point2) = X2 )
| ~ point(point2)
| ~ point(point1)
| ~ plane(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(point1,X2)
| ~ on(X1,a_line)
| ~ on(X1,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(point1,point2))
| ~ on(X0,line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_3366]) ).
tcf(c_30010,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X2 )
| ~ point(point2)
| ~ plane(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(point2,X2)
| ~ on(X1,a_line)
| ~ on(X1,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(X0,line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_3366]) ).
tcf(c_30011,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X2 )
| ~ point(point2)
| ~ plane(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(point2,X2)
| ~ on(X1,a_line)
| ~ on(X1,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(X0,line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_3366]) ).
tcf(c_30012,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_2_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_2_on_line(a_line) = point1 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X0 )
| ( line_from_to(point_2_on_line(a_line),point1) = X1 )
| ~ point(point1)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_2_on_line(a_line),X1)
| ~ plane(line_from_to(point_2_on_line(a_line),point1))
| ~ on(X0,line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_3366]) ).
tcf(c_30013,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point1,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X2 )
| ~ point(point1)
| ~ plane(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(point1,X2)
| ~ on(X1,a_line)
| ~ on(X1,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(X0,line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_3366]) ).
tcf(c_30014,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_1_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_1_on_line(a_line) = point1 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X0 )
| ( line_from_to(point_1_on_line(a_line),point1) = X1 )
| ~ point(point1)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_1_on_line(a_line),X1)
| ~ plane(line_from_to(point_1_on_line(a_line),point1))
| ~ on(X0,line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_3366]) ).
tcf(c_30015,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point1,X1)
| ( X1 = point1 )
| ( X0 = point1 )
| ( X0 = X1 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X2 )
| ~ point(point1)
| ~ plane(X2)
| ~ point(X1)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(point1,X2)
| ~ on(X1,a_line)
| ~ on(X1,X2)
| ~ on(X0,X2)
| ~ plane(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(X0,line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_3366]) ).
tcf(c_30016,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_1_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X0 )
| ( line_from_to(point_1_on_line(a_line),point2) = X1 )
| ~ point(point2)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_1_on_line(a_line),X1)
| ~ plane(line_from_to(point_1_on_line(a_line),point2))
| ~ on(X0,line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_3366]) ).
tcf(c_30017,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_2_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X0 )
| ( line_from_to(point_2_on_line(a_line),point2) = X1 )
| ~ point(point2)
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_2_on_line(a_line),X1)
| ~ plane(line_from_to(point_2_on_line(a_line),point2))
| ~ on(X0,line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_3366]) ).
tcf(c_30036,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point1,X2)
| ( X2 = point1 )
| ( X0 = point1 )
| ( X0 = X2 )
| ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(point1,X1)
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ plane(line_from_to(point1,point_1_on_line(a_line)))
| ~ on(X0,line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30015,c_122]) ).
tcf(c_30053,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point1,X2)
| ( X2 = point1 )
| ( X0 = point1 )
| ( X0 = X2 )
| ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(point1,X1)
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ plane(line_from_to(point1,point_2_on_line(a_line)))
| ~ on(X0,line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30013,c_122]) ).
tcf(c_30070,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point2,X2)
| ( X2 = point2 )
| ( X0 = point2 )
| ( X0 = X2 )
| ( point_2_on_line(a_line) = point2 )
| ( line_from_to(point2,point_2_on_line(a_line)) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(point2,X1)
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ plane(line_from_to(point2,point_2_on_line(a_line)))
| ~ on(X0,line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30011,c_123]) ).
tcf(c_30087,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point2,X2)
| ( X2 = point2 )
| ( X0 = point2 )
| ( X0 = X2 )
| ( point_1_on_line(a_line) = point2 )
| ( line_from_to(point2,point_1_on_line(a_line)) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(point2,X1)
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ plane(line_from_to(point2,point_1_on_line(a_line)))
| ~ on(X0,line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30010,c_123]) ).
tcf(c_30104,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_2_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_2_on_line(a_line) = point2 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X0 )
| ( line_from_to(point_2_on_line(a_line),point2) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_2_on_line(a_line),X1)
| ~ plane(line_from_to(point_2_on_line(a_line),point2))
| ~ on(X0,line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30017,c_123]) ).
tcf(c_30121,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_1_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_1_on_line(a_line) = point2 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X0 )
| ( line_from_to(point_1_on_line(a_line),point2) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_1_on_line(a_line),X1)
| ~ plane(line_from_to(point_1_on_line(a_line),point2))
| ~ on(X0,line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30016,c_123]) ).
tcf(c_30138,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_1_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_1_on_line(a_line) = point1 )
| ( point_1_on_line(a_line) = X2 )
| ( point_1_on_line(a_line) = X0 )
| ( line_from_to(point_1_on_line(a_line),point1) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_1_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_1_on_line(a_line),X1)
| ~ plane(line_from_to(point_1_on_line(a_line),point1))
| ~ on(X0,line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30014,c_122]) ).
tcf(c_30155,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,point_2_on_line(a_line),X2)
| ( X0 = X2 )
| ( point_2_on_line(a_line) = point1 )
| ( point_2_on_line(a_line) = X2 )
| ( point_2_on_line(a_line) = X0 )
| ( line_from_to(point_2_on_line(a_line),point1) = X1 )
| ~ plane(X1)
| ~ point(X2)
| ~ point(X0)
| ~ point(point_2_on_line(a_line))
| ~ on(X2,a_line)
| ~ on(X2,X1)
| ~ on(X0,X1)
| ~ on(point_2_on_line(a_line),X1)
| ~ plane(line_from_to(point_2_on_line(a_line),point1))
| ~ on(X0,line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30012,c_122]) ).
tcf(c_30359,plain,
! [X0: $i] :
( on(line_from_to(X0,a_line),a_line)
| ( X0 = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line)) ),
inference(superposition,[status(thm)],[c_92,c_5613]) ).
tcf(c_30361,plain,
( on(line_from_to(point2,point1),a_line)
| ( point2 = a_line )
| ( point1 = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ point(point1)
| ~ on(a_line,a_line)
| ~ on(point2,a_line)
| ~ line(line_from_to(point2,point1)) ),
inference(superposition,[status(thm)],[c_9035,c_5613]) ).
tcf(c_30362,plain,
( on(line_from_to(point1,point2),a_line)
| ( point1 = a_line )
| ( point1 = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ point(point1)
| ~ on(a_line,a_line)
| ~ on(point1,a_line)
| ~ line(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_5613]) ).
tcf(c_30363,plain,
( on(line_from_to(point2,point_1_on_line(a_line)),a_line)
| ( point2 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(a_line,a_line)
| ~ on(point2,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9438,c_5613]) ).
tcf(c_30364,plain,
( on(line_from_to(point2,point_2_on_line(a_line)),a_line)
| ( point2 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(a_line,a_line)
| ~ on(point2,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_9102,c_5613]) ).
tcf(c_30365,plain,
( on(line_from_to(point_2_on_line(a_line),point1),a_line)
| ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(a_line,a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12414,c_5613]) ).
tcf(c_30366,plain,
( on(line_from_to(point1,point_2_on_line(a_line)),a_line)
| ( point1 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(a_line,a_line)
| ~ on(point1,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_5613]) ).
tcf(c_30367,plain,
( on(line_from_to(point_1_on_line(a_line),point1),a_line)
| ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(a_line,a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(superposition,[status(thm)],[c_12340,c_5613]) ).
tcf(c_30368,plain,
( on(line_from_to(point1,point_1_on_line(a_line)),a_line)
| ( point1 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(a_line,a_line)
| ~ on(point1,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_5613]) ).
tcf(c_30369,plain,
( on(line_from_to(point_1_on_line(a_line),point2),a_line)
| ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(a_line,a_line)
| ~ point(point_1_on_line(a_line))
| ~ on(point_1_on_line(a_line),a_line)
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11124,c_5613]) ).
tcf(c_30370,plain,
( on(line_from_to(point_2_on_line(a_line),point2),a_line)
| ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(a_line,a_line)
| ~ point(point_2_on_line(a_line))
| ~ on(point_2_on_line(a_line),a_line)
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(superposition,[status(thm)],[c_11151,c_5613]) ).
tcf(c_30380,plain,
( on(line_from_to(point1,point_1_on_line(a_line)),a_line)
| ( point1 = a_line )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30368,c_122,c_126]) ).
tcf(c_30389,plain,
( on(line_from_to(point1,point_2_on_line(a_line)),a_line)
| ( point1 = a_line )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30366,c_122,c_126]) ).
tcf(c_30398,plain,
( on(line_from_to(point2,point_2_on_line(a_line)),a_line)
| ( point2 = a_line )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point2,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30364,c_123,c_127]) ).
tcf(c_30407,plain,
( on(line_from_to(point2,point_1_on_line(a_line)),a_line)
| ( point2 = a_line )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point2,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30363,c_123,c_127]) ).
tcf(c_30416,plain,
( on(line_from_to(point_2_on_line(a_line),point2),a_line)
| ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point_2_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30370,c_123,c_9364]) ).
tcf(c_30425,plain,
( on(line_from_to(point_1_on_line(a_line),point2),a_line)
| ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point_1_on_line(a_line),point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30369,c_123,c_9468]) ).
tcf(c_30434,plain,
( on(line_from_to(point_1_on_line(a_line),point1),a_line)
| ( point_1_on_line(a_line) = a_line )
| ( point_1_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_1_on_line(a_line))
| ~ line(line_from_to(point_1_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30367,c_122,c_9468]) ).
tcf(c_30443,plain,
( on(line_from_to(point_2_on_line(a_line),point1),a_line)
| ( point_2_on_line(a_line) = a_line )
| ( point_2_on_line(a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ on(a_line,a_line)
| ~ point(point_2_on_line(a_line))
| ~ line(line_from_to(point_2_on_line(a_line),point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30365,c_122,c_9364]) ).
tcf(c_30629,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = a_line )
| ( line_from_to(X0,a_line) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line))
| ~ on(line_from_to(X0,a_line),X1) ),
inference(superposition,[status(thm)],[c_30359,c_94]) ).
tcf(c_30630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X3,line_from_to(X0,a_line),X2)
| ( X2 = X3 )
| ( X1 = a_line )
| ( X0 = a_line )
| ( line_from_to(X0,a_line) = X3 )
| ( line_from_to(X0,a_line) = X2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X1)
| ~ point(X3)
| ~ point(X2)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X1)
| ~ on(X2,X1)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line))
| ~ on(line_from_to(X0,a_line),X1) ),
inference(superposition,[status(thm)],[c_30359,c_111]) ).
tcf(c_30631,plain,
! [X0: $i,X1: $i,X2: $i] :
( on(X1,a_line)
| ( X0 = a_line )
| ( line_from_to(X0,a_line) = X2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line))
| ~ on(line_from_to(X0,a_line),X1) ),
inference(superposition,[status(thm)],[c_30359,c_112]) ).
tcf(c_30632,plain,
! [X0: $i,X1: $i] :
( ( X1 = a_line )
| ( line_from_to(X1,a_line) = a_line )
| ( line_from_to(X1,a_line) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X1,a_line))
| ~ line(line_from_to(X1,a_line))
| ~ point(line_from_to(X1,a_line))
| ~ on(X0,line_from_to(X1,a_line)) ),
inference(superposition,[status(thm)],[c_30359,c_18010]) ).
tcf(c_30633,plain,
! [X0: $i,X1: $i] :
( on(a_line,line_from_to(X1,a_line))
| ( X1 = a_line )
| ( line_from_to(X1,a_line) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X1,a_line))
| ~ line(line_from_to(X1,a_line))
| ~ point(line_from_to(X1,a_line))
| ~ on(X0,line_from_to(X1,a_line)) ),
inference(superposition,[status(thm)],[c_30359,c_18012]) ).
tcf(c_30636,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = a_line )
| ( line_from_to(X0,a_line) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line))
| ~ on(line_from_to(X0,a_line),a_line) ),
inference(superposition,[status(thm)],[c_30359,c_2934]) ).
tcf(c_30639,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(X0,a_line),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( line_from_to(X0,a_line) = X2 )
| ( line_from_to(X0,a_line) = X1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line)) ),
inference(superposition,[status(thm)],[c_30359,c_121]) ).
tcf(c_30640,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = a_line )
| ( line_from_to(X0,a_line) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line))
| ~ on(line_from_to(X0,a_line),a_line) ),
inference(superposition,[status(thm)],[c_30359,c_2925]) ).
tcf(c_30641,plain,
! [X0: $i] :
( ( point1 = a_line )
| ( X0 = a_line )
| ( line_from_to(X0,a_line) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line))
| ~ on(line_from_to(X0,a_line),point1) ),
inference(superposition,[status(thm)],[c_30359,c_21610]) ).
tcf(c_30642,plain,
! [X0: $i] :
( ( point2 = a_line )
| ( X0 = a_line )
| ( line_from_to(X0,a_line) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line))
| ~ on(line_from_to(X0,a_line),point2) ),
inference(superposition,[status(thm)],[c_30359,c_21602]) ).
tcf(c_30643,plain,
! [X0: $i] :
( on(a_line,point1)
| ( X0 = a_line )
| ( line_from_to(X0,a_line) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line))
| ~ on(line_from_to(X0,a_line),point1) ),
inference(superposition,[status(thm)],[c_30359,c_20018]) ).
tcf(c_30644,plain,
! [X0: $i] :
( on(a_line,point2)
| ( X0 = a_line )
| ( line_from_to(X0,a_line) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line))
| ~ on(line_from_to(X0,a_line),point2) ),
inference(superposition,[status(thm)],[c_30359,c_20010]) ).
tcf(c_30645,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(X0,a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,a_line))
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line))
| ~ on(a_line,line_from_to(X0,a_line)) ),
inference(superposition,[status(thm)],[c_30359,c_18013]) ).
tcf(c_30646,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(X0,a_line) = a_line )
| ( line_from_to(X0,a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,a_line))
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line))
| ~ on(point2,line_from_to(X0,a_line)) ),
inference(superposition,[status(thm)],[c_30359,c_18017]) ).
tcf(c_30647,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(X0,a_line) = point1 )
| ( line_from_to(line_from_to(X0,a_line),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line)) ),
inference(superposition,[status(thm)],[c_30359,c_12246]) ).
tcf(c_30648,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(X0,a_line) = point1 )
| ( line_from_to(point1,line_from_to(X0,a_line)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line)) ),
inference(superposition,[status(thm)],[c_30359,c_11471]) ).
tcf(c_30649,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(X0,a_line) = point2 )
| ( line_from_to(line_from_to(X0,a_line),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line)) ),
inference(superposition,[status(thm)],[c_30359,c_11016]) ).
tcf(c_30650,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(X0,a_line) = point2 )
| ( line_from_to(point2,line_from_to(X0,a_line)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line)) ),
inference(superposition,[status(thm)],[c_30359,c_9014]) ).
tcf(c_30745,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = a_line )
| ( line_from_to(X0,a_line) = point2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line))
| ~ on(line_from_to(X0,a_line),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30640,c_125,c_127]) ).
tcf(c_30756,plain,
! [X0: $i] :
( on(a_line,a_line)
| ( X0 = a_line )
| ( line_from_to(X0,a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line))
| ~ on(line_from_to(X0,a_line),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30636,c_125,c_126]) ).
tcf(c_30792,plain,
! [X0: $i,X1: $i] :
( on(a_line,line_from_to(X1,a_line))
| ( X1 = a_line )
| ( line_from_to(X1,a_line) = X0 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X1,a_line))
| ~ line(line_from_to(X1,a_line))
| ~ point(line_from_to(X1,a_line))
| ~ on(X0,line_from_to(X1,a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30633,c_125]) ).
tcf(c_30806,plain,
! [X0: $i,X1: $i] :
( ( X1 = a_line )
| ( line_from_to(X1,a_line) = a_line )
| ( line_from_to(X1,a_line) = X0 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X1,a_line))
| ~ line(line_from_to(X1,a_line))
| ~ point(line_from_to(X1,a_line))
| ~ on(X0,line_from_to(X1,a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30632,c_125]) ).
tcf(c_30820,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = a_line )
| ( line_from_to(X0,a_line) = X2 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ on(X2,X1)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line))
| ~ on(line_from_to(X0,a_line),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30629,c_125]) ).
tcf(c_30835,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,line_from_to(X0,a_line),X1)
| ( X1 = X2 )
| ( X0 = a_line )
| ( line_from_to(X0,a_line) = X2 )
| ( line_from_to(X0,a_line) = X1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30639,c_125]) ).
tcf(c_31047,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point1,point_1_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_18633]) ).
tcf(c_31048,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point1,point_1_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31047,c_125]) ).
tcf(c_31069,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point1,point_1_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11755,c_31048]) ).
tcf(c_31098,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point1,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11755,c_18634]) ).
tcf(c_31099,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point1,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point1,point_1_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31098,c_125]) ).
tcf(c_31120,plain,
( ( point_1_on_line(a_line) = point1 )
| ( line_from_to(point1,point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point1,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11755,c_31099]) ).
tcf(c_31149,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point1,point_2_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_18803]) ).
tcf(c_31150,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point1,point_2_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31149,c_125]) ).
tcf(c_31171,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ( line_from_to(line_from_to(point1,point_2_on_line(a_line)),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11783,c_31150]) ).
tcf(c_31219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,X2)
| collinear(X4,X0,point_1_on_line(plane_for_points(X0,X1,X2)))
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = X4 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = X0 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_1_on_line(plane_for_points(X0,X1,X2)))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ on(point_1_on_line(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_95,c_3367]) ).
tcf(c_31220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,X2)
| collinear(X4,X0,point_2_on_line(plane_for_points(X0,X1,X2)))
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( point_2_on_line(plane_for_points(X0,X1,X2)) = X4 )
| ( point_2_on_line(plane_for_points(X0,X1,X2)) = X0 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_2_on_line(plane_for_points(X0,X1,X2)))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ on(point_2_on_line(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_96,c_3367]) ).
tcf(c_31221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,X2)
| collinear(X4,X0,point_on_plane(plane_for_points(X0,X1,X2)))
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( point_on_plane(plane_for_points(X0,X1,X2)) = X4 )
| ( point_on_plane(plane_for_points(X0,X1,X2)) = X0 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ point(point_on_plane(plane_for_points(X0,X1,X2)))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ on(point_on_plane(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_103,c_3367]) ).
tcf(c_31222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X1,X2,X3)
| collinear(X0,X1,X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( X0 = X1 )
| ( plane_for_points(X1,X2,X3) = X4 )
| ~ plane(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X4)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_109,c_3367]) ).
tcf(c_31224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X1,X2,X3)
| collinear(X0,X1,X2)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X1,X2,X3) = X4 )
| ~ plane(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X4)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_108,c_3367]) ).
tcf(c_31225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X0,X1,X2)
| collinear(X6,X0,common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4))
| ( X1 = X2 )
| ( X0 = X6 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X5 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4) = X6 )
| ( common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4) = X0 )
| ~ plane(X5)
| ~ plane(X3)
| ~ point(X6)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X6,X5)
| ~ on(X4,X3)
| ~ on(X0,X5)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ on(X6,plane_for_points(X0,X1,X2))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ point(common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4))
| ~ on(common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_113,c_3367]) ).
tcf(c_31226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X1,X2,X3)
| collinear(X6,X1,common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4))
| ( X2 = X3 )
| ( X1 = X6 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,X3) = X5 )
| ( plane_for_points(X1,X2,X3) = X0 )
| ( common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4) = X6 )
| ( common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4) = X1 )
| ~ plane(X5)
| ~ plane(X0)
| ~ point(X6)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X6,X5)
| ~ on(X4,X0)
| ~ on(X1,X5)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X6,plane_for_points(X1,X2,X3))
| ~ on(X4,plane_for_points(X1,X2,X3))
| ~ point(common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4))
| ~ on(common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_114,c_3367]) ).
tcf(c_31227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,X2)
| collinear(X4,X0,plane_for_points(X0,X1,X2))
| ( X1 = X2 )
| ( X0 = X4 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X4 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( plane_for_points(X0,X1,X2) = X0 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X0,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(plane_for_points(X0,X1,X2))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ on(plane_for_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_18002,c_3367]) ).
tcf(c_31437,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ( line_from_to(point1,X0) = point1 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point1,X0))
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_25811,c_18929]) ).
tcf(c_31441,plain,
( ( point1 = a_line )
| ( line_from_to(point1,a_line) = a_line )
| ( line_from_to(point1,a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ plane(line_from_to(point1,a_line))
| ~ line(line_from_to(point1,a_line))
| ~ point(line_from_to(point1,a_line)) ),
inference(superposition,[status(thm)],[c_30359,c_18929]) ).
tcf(c_31454,plain,
( ( point1 = a_line )
| ( line_from_to(point1,a_line) = a_line )
| ( line_from_to(point1,a_line) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(line_from_to(point1,a_line))
| ~ line(line_from_to(point1,a_line))
| ~ point(line_from_to(point1,a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31441,c_122,c_126]) ).
tcf(c_31479,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ( line_from_to(X0,point1) = point1 )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,point1))
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_26554,c_18938]) ).
tcf(c_31484,plain,
( ( point1 = a_line )
| ( line_from_to(a_line,point1) = a_line )
| ( line_from_to(a_line,point1) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ plane(line_from_to(a_line,point1))
| ~ line(line_from_to(a_line,point1))
| ~ point(line_from_to(a_line,point1)) ),
inference(superposition,[status(thm)],[c_29574,c_18938]) ).
tcf(c_31497,plain,
( ( point1 = a_line )
| ( line_from_to(a_line,point1) = a_line )
| ( line_from_to(a_line,point1) = point1 )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(line_from_to(a_line,point1))
| ~ line(line_from_to(a_line,point1))
| ~ point(line_from_to(a_line,point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31484,c_122,c_126]) ).
tcf(c_31529,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(a_line,X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(a_line,X0)) ),
inference(superposition,[status(thm)],[c_91,c_5845]) ).
tcf(c_31558,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(a_line,X0) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(global_subsumption_just,[status(thm)],[c_31529,c_8934,c_31529]) ).
tcf(c_31574,plain,
( ( point_1_on_line(a_line) = a_line )
| ( line_from_to(a_line,point_1_on_line(a_line)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_95,c_31558]) ).
tcf(c_31575,plain,
( ( point_2_on_line(a_line) = a_line )
| ( line_from_to(a_line,point_2_on_line(a_line)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_96,c_31558]) ).
tcf(c_31576,plain,
( ( point_on_plane(a_line) = a_line )
| ( line_from_to(a_line,point_on_plane(a_line)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_on_plane(a_line)) ),
inference(superposition,[status(thm)],[c_103,c_31558]) ).
tcf(c_31577,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = a_line )
| ( line_from_to(a_line,common_point_on_planes(a_line,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_31558]) ).
tcf(c_31578,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = a_line )
| ( line_from_to(a_line,common_point_on_planes(X0,a_line,X1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_31558]) ).
tcf(c_31580,plain,
( ( point_1_on_line(a_line) = a_line )
| ( line_from_to(a_line,point_1_on_line(a_line)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9468,c_31558]) ).
tcf(c_31581,plain,
( ( point_2_on_line(a_line) = a_line )
| ( line_from_to(a_line,point_2_on_line(a_line)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9364,c_31558]) ).
tcf(c_31583,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ( line_from_to(a_line,line_from_to(X0,point1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_26554,c_31558]) ).
tcf(c_31584,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ( line_from_to(a_line,line_from_to(point1,X0)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_25811,c_31558]) ).
tcf(c_31589,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = a_line )
| ( line_from_to(a_line,line_from_to(X0,point2)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_31558]) ).
tcf(c_31590,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = a_line )
| ( line_from_to(a_line,line_from_to(point2,X0)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_31558]) ).
tcf(c_31595,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( line_from_to(a_line,line_through_3_points(point2,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_31558]) ).
tcf(c_31596,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( line_from_to(a_line,line_through_3_points(point2,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_31558]) ).
tcf(c_31597,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( line_from_to(a_line,line_through_3_points(X0,point2,X1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_31558]) ).
tcf(c_31598,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( line_from_to(a_line,line_through_3_points(X0,point2,X1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_31558]) ).
tcf(c_31599,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( line_from_to(a_line,line_through_3_points(X0,X1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_31558]) ).
tcf(c_31600,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( line_from_to(a_line,line_through_3_points(X0,X1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_31558]) ).
tcf(c_31601,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(X0,a_line) = a_line )
| ( line_from_to(a_line,line_from_to(X0,a_line)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line)) ),
inference(superposition,[status(thm)],[c_30359,c_31558]) ).
tcf(c_31602,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(a_line,X0) = a_line )
| ( line_from_to(a_line,line_from_to(a_line,X0)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0)) ),
inference(superposition,[status(thm)],[c_29574,c_31558]) ).
tcf(c_31996,plain,
( ( point_on_plane(a_line) = a_line )
| ( line_from_to(a_line,point_on_plane(a_line)) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31576,c_104]) ).
tcf(c_32009,plain,
( ( point_1_on_line(a_line) = a_line )
| ( line_from_to(a_line,point_1_on_line(a_line)) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(global_subsumption_just,[status(thm)],[c_31580,c_125,c_4351,c_31580]) ).
tcf(c_32019,plain,
( ( point_2_on_line(a_line) = a_line )
| ( line_from_to(a_line,point_2_on_line(a_line)) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(global_subsumption_just,[status(thm)],[c_31581,c_125,c_4353,c_31581]) ).
tcf(c_32042,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point1,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_18804]) ).
tcf(c_32043,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point1,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32042,c_125]) ).
tcf(c_32064,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point1 )
| ( line_from_to(point1,line_from_to(point1,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11783,c_32043]) ).
tcf(c_32093,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point1,point_2_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_18805]) ).
tcf(c_32094,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point1,point_2_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32093,c_125]) ).
tcf(c_32115,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ( line_from_to(line_from_to(point1,point_2_on_line(a_line)),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11783,c_32094]) ).
tcf(c_32144,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point1,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(superposition,[status(thm)],[c_11783,c_18806]) ).
tcf(c_32145,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point1,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(line_from_to(point1,point_2_on_line(a_line))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32144,c_125]) ).
tcf(c_32198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,X2)
| collinear(X4,X1,point_1_on_line(plane_for_points(X0,X1,X2)))
| ( X1 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = X4 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = X1 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X1,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_1_on_line(plane_for_points(X0,X1,X2)))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ on(point_1_on_line(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_95,c_3368]) ).
tcf(c_32199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,X2)
| collinear(X4,X1,point_2_on_line(plane_for_points(X0,X1,X2)))
| ( X1 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( point_2_on_line(plane_for_points(X0,X1,X2)) = X4 )
| ( point_2_on_line(plane_for_points(X0,X1,X2)) = X1 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X1,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_2_on_line(plane_for_points(X0,X1,X2)))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ on(point_2_on_line(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_96,c_3368]) ).
tcf(c_32200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,X2)
| collinear(X4,X1,point_on_plane(plane_for_points(X0,X1,X2)))
| ( X1 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( point_on_plane(plane_for_points(X0,X1,X2)) = X4 )
| ( point_on_plane(plane_for_points(X0,X1,X2)) = X1 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X1,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ point(point_on_plane(plane_for_points(X0,X1,X2)))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ on(point_on_plane(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_103,c_3368]) ).
tcf(c_32201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X1,X2,X3)
| collinear(X0,X2,X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X3 )
| ( X0 = X2 )
| ( plane_for_points(X1,X2,X3) = X4 )
| ~ plane(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,X4)
| ~ on(X2,X4)
| ~ on(X0,X4)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_109,c_3368]) ).
tcf(c_32202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X1,X2,X3)
| collinear(X0,X2,X1)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X1,X2,X3) = X4 )
| ~ plane(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X4)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X0,plane_for_points(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_107,c_3368]) ).
tcf(c_32204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X0,X1,X2)
| collinear(X6,X1,common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4))
| ( X1 = X6 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X5 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4) = X6 )
| ( common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4) = X1 )
| ~ plane(X5)
| ~ plane(X3)
| ~ point(X6)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X6,X5)
| ~ on(X4,X3)
| ~ on(X1,X5)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ on(X6,plane_for_points(X0,X1,X2))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ point(common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4))
| ~ on(common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_113,c_3368]) ).
tcf(c_32205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X1,X2,X3)
| collinear(X6,X2,common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4))
| ( X2 = X6 )
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,X3) = X5 )
| ( plane_for_points(X1,X2,X3) = X0 )
| ( common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4) = X6 )
| ( common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4) = X2 )
| ~ plane(X5)
| ~ plane(X0)
| ~ point(X6)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X6,X5)
| ~ on(X4,X0)
| ~ on(X2,X5)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ on(X6,plane_for_points(X1,X2,X3))
| ~ on(X4,plane_for_points(X1,X2,X3))
| ~ point(common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4))
| ~ on(common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_114,c_3368]) ).
tcf(c_32206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,X2)
| collinear(X4,X1,plane_for_points(X0,X1,X2))
| ( X1 = X4 )
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X4 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( plane_for_points(X0,X1,X2) = X1 )
| ~ plane(X3)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X1,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(plane_for_points(X0,X1,X2))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ on(plane_for_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_18002,c_3368]) ).
tcf(c_32396,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(X0,a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line)) ),
inference(superposition,[status(thm)],[c_92,c_5853]) ).
tcf(c_32429,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(X0,a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_93,c_32396]) ).
tcf(c_32456,plain,
( ( point_1_on_line(a_line) = a_line )
| ( line_from_to(point_1_on_line(a_line),a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_95,c_32429]) ).
tcf(c_32457,plain,
( ( point_2_on_line(a_line) = a_line )
| ( line_from_to(point_2_on_line(a_line),a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_96,c_32429]) ).
tcf(c_32458,plain,
( ( point_on_plane(a_line) = a_line )
| ( line_from_to(point_on_plane(a_line),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_on_plane(a_line)) ),
inference(superposition,[status(thm)],[c_103,c_32429]) ).
tcf(c_32459,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = a_line )
| ( line_from_to(common_point_on_planes(a_line,X0,X1),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_32429]) ).
tcf(c_32460,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = a_line )
| ( line_from_to(common_point_on_planes(X0,a_line,X1),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ point(common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_32429]) ).
tcf(c_32462,plain,
( ( point_1_on_line(a_line) = a_line )
| ( line_from_to(point_1_on_line(a_line),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9468,c_32429]) ).
tcf(c_32463,plain,
( ( point_2_on_line(a_line) = a_line )
| ( line_from_to(point_2_on_line(a_line),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9364,c_32429]) ).
tcf(c_32465,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ( line_from_to(line_from_to(X0,point1),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_26554,c_32429]) ).
tcf(c_32466,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ( line_from_to(line_from_to(point1,X0),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_25811,c_32429]) ).
tcf(c_32471,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = a_line )
| ( line_from_to(line_from_to(X0,point2),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_32429]) ).
tcf(c_32472,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = a_line )
| ( line_from_to(line_from_to(point2,X0),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_32429]) ).
tcf(c_32477,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( line_from_to(line_through_3_points(point2,X0,X1),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_32429]) ).
tcf(c_32478,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( line_from_to(line_through_3_points(point2,X0,X1),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_32429]) ).
tcf(c_32479,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( line_from_to(line_through_3_points(X0,point2,X1),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_32429]) ).
tcf(c_32480,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( line_from_to(line_through_3_points(X0,point2,X1),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_32429]) ).
tcf(c_32481,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( line_from_to(line_through_3_points(X0,X1,point2),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_32429]) ).
tcf(c_32482,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( line_from_to(line_through_3_points(X0,X1,point2),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_32429]) ).
tcf(c_32483,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(X0,a_line) = a_line )
| ( line_from_to(line_from_to(X0,a_line),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line)) ),
inference(superposition,[status(thm)],[c_30359,c_32429]) ).
tcf(c_32484,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(a_line,X0) = a_line )
| ( line_from_to(line_from_to(a_line,X0),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(a_line,X0)) ),
inference(superposition,[status(thm)],[c_29574,c_32429]) ).
tcf(c_33009,plain,
( ( point_on_plane(a_line) = a_line )
| ( line_from_to(point_on_plane(a_line),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32458,c_104]) ).
tcf(c_33022,plain,
( ( point_1_on_line(a_line) = a_line )
| ( line_from_to(point_1_on_line(a_line),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(global_subsumption_just,[status(thm)],[c_32462,c_125,c_4351,c_32462]) ).
tcf(c_33032,plain,
( ( point_2_on_line(a_line) = a_line )
| ( line_from_to(point_2_on_line(a_line),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(global_subsumption_just,[status(thm)],[c_32463,c_125,c_4353,c_32463]) ).
tcf(c_33054,plain,
( ( point_2_on_line(a_line) = point1 )
| ( line_from_to(point1,point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,line_from_to(point1,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line) ),
inference(superposition,[status(thm)],[c_11783,c_32145]) ).
tcf(c_33090,plain,
! [X0: $i] :
( ( point_on_plane(X0) = X0 )
| ( point_1_on_line(point_on_plane(X0)) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ plane(point_on_plane(X0))
| ~ line(point_on_plane(X0))
| ~ point(point_1_on_line(point_on_plane(X0)))
| ~ on(point_1_on_line(point_on_plane(X0)),X0) ),
inference(superposition,[status(thm)],[c_95,c_27937]) ).
tcf(c_33091,plain,
! [X0: $i] :
( ( point_on_plane(X0) = X0 )
| ( point_2_on_line(point_on_plane(X0)) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ plane(point_on_plane(X0))
| ~ line(point_on_plane(X0))
| ~ point(point_2_on_line(point_on_plane(X0)))
| ~ on(point_2_on_line(point_on_plane(X0)),X0) ),
inference(superposition,[status(thm)],[c_96,c_27937]) ).
tcf(c_33092,plain,
! [X0: $i] :
( ( point_on_plane(X0) = X0 )
| ( point_on_plane(point_on_plane(X0)) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ plane(point_on_plane(X0))
| ~ line(point_on_plane(X0))
| ~ point(point_on_plane(point_on_plane(X0)))
| ~ on(point_on_plane(point_on_plane(X0)),X0) ),
inference(superposition,[status(thm)],[c_103,c_27937]) ).
tcf(c_33093,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( point_on_plane(X0) = X1 )
| ( point_on_plane(X0) = X0 )
| ( common_point_on_planes(point_on_plane(X0),X1,X2) = point_on_plane(X0) )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X2)
| ~ plane(point_on_plane(X0))
| ~ line(point_on_plane(X0))
| ~ on(X2,X1)
| ~ on(X2,point_on_plane(X0))
| ~ point(common_point_on_planes(point_on_plane(X0),X1,X2))
| ~ on(common_point_on_planes(point_on_plane(X0),X1,X2),X0) ),
inference(superposition,[status(thm)],[c_113,c_27937]) ).
tcf(c_33094,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( point_on_plane(X1) = X1 )
| ( point_on_plane(X1) = X0 )
| ( common_point_on_planes(X0,point_on_plane(X1),X2) = point_on_plane(X1) )
| ~ plane(X1)
| ~ plane(X0)
| ~ line(X1)
| ~ point(X2)
| ~ plane(point_on_plane(X1))
| ~ line(point_on_plane(X1))
| ~ on(X2,X0)
| ~ on(X2,point_on_plane(X1))
| ~ point(common_point_on_planes(X0,point_on_plane(X1),X2))
| ~ on(common_point_on_planes(X0,point_on_plane(X1),X2),X1) ),
inference(superposition,[status(thm)],[c_114,c_27937]) ).
tcf(c_33292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X5,common_point_on_planes(X2,X3,X4),X0)
| ( X2 = X3 )
| ( X0 = X5 )
| ( common_point_on_planes(X2,X3,X4) = X5 )
| ( common_point_on_planes(X2,X3,X4) = X1 )
| ( common_point_on_planes(X2,X3,X4) = X0 )
| ( line_from_to(X1,common_point_on_planes(X2,X3,X4)) = X2 )
| ~ plane(X3)
| ~ plane(X2)
| ~ point(X5)
| ~ point(X4)
| ~ point(X1)
| ~ point(X0)
| ~ on(X5,X2)
| ~ on(X4,X3)
| ~ on(X4,X2)
| ~ on(X0,X2)
| ~ point(common_point_on_planes(X2,X3,X4))
| ~ plane(line_from_to(X1,common_point_on_planes(X2,X3,X4)))
| ~ on(X5,line_from_to(X1,common_point_on_planes(X2,X3,X4)))
| ~ on(X0,line_from_to(X1,common_point_on_planes(X2,X3,X4))) ),
inference(superposition,[status(thm)],[c_92,c_3369]) ).
tcf(c_33293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,common_point_on_planes(X3,X4,X5),X0)
| collinear(X1,X2,common_point_on_planes(X3,X4,X5))
| ( X3 = X4 )
| ( X1 = X2 )
| ( X0 = X6 )
| ( common_point_on_planes(X3,X4,X5) = X6 )
| ( common_point_on_planes(X3,X4,X5) = X2 )
| ( common_point_on_planes(X3,X4,X5) = X1 )
| ( common_point_on_planes(X3,X4,X5) = X0 )
| ( plane_for_points(X1,X2,common_point_on_planes(X3,X4,X5)) = X3 )
| ~ plane(X4)
| ~ plane(X3)
| ~ point(X6)
| ~ point(X5)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X6,X3)
| ~ on(X5,X4)
| ~ on(X5,X3)
| ~ on(X0,X3)
| ~ point(common_point_on_planes(X3,X4,X5))
| ~ plane(plane_for_points(X1,X2,common_point_on_planes(X3,X4,X5)))
| ~ on(X6,plane_for_points(X1,X2,common_point_on_planes(X3,X4,X5)))
| ~ on(X0,plane_for_points(X1,X2,common_point_on_planes(X3,X4,X5))) ),
inference(superposition,[status(thm)],[c_109,c_3369]) ).
tcf(c_33294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,common_point_on_planes(X1,X2,X3),X0)
| ( X4 = X5 )
| ( X1 = X2 )
| ( X0 = X6 )
| ( common_point_on_planes(X1,X2,X3) = X6 )
| ( common_point_on_planes(X1,X2,X3) = X5 )
| ( common_point_on_planes(X1,X2,X3) = X4 )
| ( common_point_on_planes(X1,X2,X3) = X0 )
| ( line_through_3_points(common_point_on_planes(X1,X2,X3),X4,X5) = X1 )
| ~ plane(X2)
| ~ plane(X1)
| ~ point(X6)
| ~ point(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X0)
| ~ on(X6,X1)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X1)
| ~ point(common_point_on_planes(X1,X2,X3))
| ~ collinear(common_point_on_planes(X1,X2,X3),X4,X5)
| ~ plane(line_through_3_points(common_point_on_planes(X1,X2,X3),X4,X5))
| ~ on(X6,line_through_3_points(common_point_on_planes(X1,X2,X3),X4,X5))
| ~ on(X0,line_through_3_points(common_point_on_planes(X1,X2,X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_117,c_3369]) ).
tcf(c_33295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,common_point_on_planes(X2,X3,X4),X0)
| ( X2 = X3 )
| ( X1 = X5 )
| ( X0 = X6 )
| ( common_point_on_planes(X2,X3,X4) = X6 )
| ( common_point_on_planes(X2,X3,X4) = X5 )
| ( common_point_on_planes(X2,X3,X4) = X1 )
| ( common_point_on_planes(X2,X3,X4) = X0 )
| ( line_through_3_points(X1,common_point_on_planes(X2,X3,X4),X5) = X2 )
| ~ plane(X3)
| ~ plane(X2)
| ~ point(X6)
| ~ point(X5)
| ~ point(X4)
| ~ point(X1)
| ~ point(X0)
| ~ on(X6,X2)
| ~ on(X4,X3)
| ~ on(X4,X2)
| ~ on(X0,X2)
| ~ point(common_point_on_planes(X2,X3,X4))
| ~ collinear(X1,common_point_on_planes(X2,X3,X4),X5)
| ~ plane(line_through_3_points(X1,common_point_on_planes(X2,X3,X4),X5))
| ~ on(X6,line_through_3_points(X1,common_point_on_planes(X2,X3,X4),X5))
| ~ on(X0,line_through_3_points(X1,common_point_on_planes(X2,X3,X4),X5)) ),
inference(superposition,[status(thm)],[c_118,c_3369]) ).
tcf(c_33296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,common_point_on_planes(X3,X4,X5),X0)
| ( X3 = X4 )
| ( X1 = X2 )
| ( X0 = X6 )
| ( common_point_on_planes(X3,X4,X5) = X6 )
| ( common_point_on_planes(X3,X4,X5) = X2 )
| ( common_point_on_planes(X3,X4,X5) = X1 )
| ( common_point_on_planes(X3,X4,X5) = X0 )
| ( line_through_3_points(X1,X2,common_point_on_planes(X3,X4,X5)) = X3 )
| ~ plane(X4)
| ~ plane(X3)
| ~ point(X6)
| ~ point(X5)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X6,X3)
| ~ on(X5,X4)
| ~ on(X5,X3)
| ~ on(X0,X3)
| ~ point(common_point_on_planes(X3,X4,X5))
| ~ collinear(X1,X2,common_point_on_planes(X3,X4,X5))
| ~ plane(line_through_3_points(X1,X2,common_point_on_planes(X3,X4,X5)))
| ~ on(X6,line_through_3_points(X1,X2,common_point_on_planes(X3,X4,X5)))
| ~ on(X0,line_through_3_points(X1,X2,common_point_on_planes(X3,X4,X5))) ),
inference(superposition,[status(thm)],[c_119,c_3369]) ).
tcf(c_33297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X5,common_point_on_planes(X1,X2,X3),X0)
| ( X1 = X2 )
| ( X0 = X5 )
| ( common_point_on_planes(X1,X2,X3) = X5 )
| ( common_point_on_planes(X1,X2,X3) = X4 )
| ( common_point_on_planes(X1,X2,X3) = X0 )
| ( line_from_to(common_point_on_planes(X1,X2,X3),X4) = X1 )
| ~ plane(X2)
| ~ plane(X1)
| ~ point(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X0)
| ~ on(X5,X1)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X1)
| ~ point(common_point_on_planes(X1,X2,X3))
| ~ plane(line_from_to(common_point_on_planes(X1,X2,X3),X4))
| ~ on(X5,line_from_to(common_point_on_planes(X1,X2,X3),X4))
| ~ on(X0,line_from_to(common_point_on_planes(X1,X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_91,c_3369]) ).
tcf(c_33298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,common_point_on_planes(X1,X2,X3),X0)
| collinear(common_point_on_planes(X1,X2,X3),X4,X5)
| ( X4 = X5 )
| ( X1 = X2 )
| ( X0 = X6 )
| ( common_point_on_planes(X1,X2,X3) = X6 )
| ( common_point_on_planes(X1,X2,X3) = X5 )
| ( common_point_on_planes(X1,X2,X3) = X4 )
| ( common_point_on_planes(X1,X2,X3) = X0 )
| ( plane_for_points(common_point_on_planes(X1,X2,X3),X4,X5) = X1 )
| ~ plane(X2)
| ~ plane(X1)
| ~ point(X6)
| ~ point(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X0)
| ~ on(X6,X1)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X1)
| ~ point(common_point_on_planes(X1,X2,X3))
| ~ plane(plane_for_points(common_point_on_planes(X1,X2,X3),X4,X5))
| ~ on(X6,plane_for_points(common_point_on_planes(X1,X2,X3),X4,X5))
| ~ on(X0,plane_for_points(common_point_on_planes(X1,X2,X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_107,c_3369]) ).
tcf(c_33299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,common_point_on_planes(X2,X3,X4),X0)
| collinear(X1,common_point_on_planes(X2,X3,X4),X5)
| ( X2 = X3 )
| ( X1 = X5 )
| ( X0 = X6 )
| ( common_point_on_planes(X2,X3,X4) = X6 )
| ( common_point_on_planes(X2,X3,X4) = X5 )
| ( common_point_on_planes(X2,X3,X4) = X1 )
| ( common_point_on_planes(X2,X3,X4) = X0 )
| ( plane_for_points(X1,common_point_on_planes(X2,X3,X4),X5) = X2 )
| ~ plane(X3)
| ~ plane(X2)
| ~ point(X6)
| ~ point(X5)
| ~ point(X4)
| ~ point(X1)
| ~ point(X0)
| ~ on(X6,X2)
| ~ on(X4,X3)
| ~ on(X4,X2)
| ~ on(X0,X2)
| ~ point(common_point_on_planes(X2,X3,X4))
| ~ plane(plane_for_points(X1,common_point_on_planes(X2,X3,X4),X5))
| ~ on(X6,plane_for_points(X1,common_point_on_planes(X2,X3,X4),X5))
| ~ on(X0,plane_for_points(X1,common_point_on_planes(X2,X3,X4),X5)) ),
inference(superposition,[status(thm)],[c_108,c_3369]) ).
tcf(c_33301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,common_point_on_planes(X0,X1,X2),X3)
| ( X3 = X4 )
| ( X0 = X1 )
| ( common_point_on_planes(X0,X1,X2) = X4 )
| ( common_point_on_planes(X0,X1,X2) = X3 )
| ~ plane(X1)
| ~ plane(X0)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ on(X4,X1)
| ~ on(X4,X0)
| ~ on(X3,X1)
| ~ on(X3,X0)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_114,c_3369]) ).
tcf(c_33302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,common_point_on_planes(X1,X2,X3),X0)
| ( X1 = X2 )
| ( X0 = X4 )
| ( common_point_on_planes(X1,X2,X3) = X4 )
| ( common_point_on_planes(X1,X2,X3) = X1 )
| ( common_point_on_planes(X1,X2,X3) = X0 )
| ~ plane(X2)
| ~ plane(X1)
| ~ point(X4)
| ~ point(X3)
| ~ point(X0)
| ~ on(X4,X1)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X1)
| ~ plane(common_point_on_planes(X1,X2,X3))
| ~ line(common_point_on_planes(X1,X2,X3))
| ~ point(common_point_on_planes(X1,X2,X3))
| ~ on(X4,common_point_on_planes(X1,X2,X3))
| ~ on(X0,common_point_on_planes(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_18002,c_3369]) ).
tcf(c_33544,plain,
! [X0: $i,X1: $i] :
( ( a_line = X0 )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ( common_point_on_planes(a_line,X0,X1) != X1 ) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_33559,plain,
( ( a_line = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ on(point1,point1)
| ( common_point_on_planes(a_line,point1,point1) != point1 ) ),
inference(instantiation,[status(thm)],[c_33544]) ).
tcf(c_33594,plain,
! [X0: $i] :
( ( point_on_plane(X0) = X0 )
| ( point_1_on_line(point_on_plane(X0)) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ plane(point_on_plane(X0))
| ~ line(point_on_plane(X0))
| ~ on(point_1_on_line(point_on_plane(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33090,c_97]) ).
tcf(c_33624,plain,
! [X0: $i] :
( ( point_on_plane(X0) = X0 )
| ( point_2_on_line(point_on_plane(X0)) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ plane(point_on_plane(X0))
| ~ line(point_on_plane(X0))
| ~ on(point_2_on_line(point_on_plane(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33091,c_98]) ).
tcf(c_33654,plain,
! [X0: $i] :
( ( point_on_plane(X0) = X0 )
| ( point_on_plane(point_on_plane(X0)) = point_on_plane(X0) )
| ~ plane(X0)
| ~ line(X0)
| ~ plane(point_on_plane(X0))
| ~ line(point_on_plane(X0))
| ~ on(point_on_plane(point_on_plane(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33092,c_104]) ).
tcf(c_33756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X5,common_point_on_planes(X2,X3,X4),X0)
| ( X2 = X3 )
| ( X0 = X5 )
| ( common_point_on_planes(X2,X3,X4) = X5 )
| ( common_point_on_planes(X2,X3,X4) = X1 )
| ( common_point_on_planes(X2,X3,X4) = X0 )
| ( line_from_to(X1,common_point_on_planes(X2,X3,X4)) = X3 )
| ~ plane(X3)
| ~ plane(X2)
| ~ point(X5)
| ~ point(X4)
| ~ point(X1)
| ~ point(X0)
| ~ on(X5,X3)
| ~ on(X4,X3)
| ~ on(X4,X2)
| ~ on(X0,X3)
| ~ point(common_point_on_planes(X2,X3,X4))
| ~ plane(line_from_to(X1,common_point_on_planes(X2,X3,X4)))
| ~ on(X5,line_from_to(X1,common_point_on_planes(X2,X3,X4)))
| ~ on(X0,line_from_to(X1,common_point_on_planes(X2,X3,X4))) ),
inference(superposition,[status(thm)],[c_92,c_3370]) ).
tcf(c_33757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,common_point_on_planes(X3,X4,X5),X0)
| collinear(X1,X2,common_point_on_planes(X3,X4,X5))
| ( X3 = X4 )
| ( X1 = X2 )
| ( X0 = X6 )
| ( common_point_on_planes(X3,X4,X5) = X6 )
| ( common_point_on_planes(X3,X4,X5) = X2 )
| ( common_point_on_planes(X3,X4,X5) = X1 )
| ( common_point_on_planes(X3,X4,X5) = X0 )
| ( plane_for_points(X1,X2,common_point_on_planes(X3,X4,X5)) = X4 )
| ~ plane(X4)
| ~ plane(X3)
| ~ point(X6)
| ~ point(X5)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X6,X4)
| ~ on(X5,X4)
| ~ on(X5,X3)
| ~ on(X0,X4)
| ~ point(common_point_on_planes(X3,X4,X5))
| ~ plane(plane_for_points(X1,X2,common_point_on_planes(X3,X4,X5)))
| ~ on(X6,plane_for_points(X1,X2,common_point_on_planes(X3,X4,X5)))
| ~ on(X0,plane_for_points(X1,X2,common_point_on_planes(X3,X4,X5))) ),
inference(superposition,[status(thm)],[c_109,c_3370]) ).
tcf(c_33758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,common_point_on_planes(X1,X2,X3),X0)
| ( X4 = X5 )
| ( X1 = X2 )
| ( X0 = X6 )
| ( common_point_on_planes(X1,X2,X3) = X6 )
| ( common_point_on_planes(X1,X2,X3) = X5 )
| ( common_point_on_planes(X1,X2,X3) = X4 )
| ( common_point_on_planes(X1,X2,X3) = X0 )
| ( line_through_3_points(common_point_on_planes(X1,X2,X3),X4,X5) = X2 )
| ~ plane(X2)
| ~ plane(X1)
| ~ point(X6)
| ~ point(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X0)
| ~ on(X6,X2)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X2)
| ~ point(common_point_on_planes(X1,X2,X3))
| ~ collinear(common_point_on_planes(X1,X2,X3),X4,X5)
| ~ plane(line_through_3_points(common_point_on_planes(X1,X2,X3),X4,X5))
| ~ on(X6,line_through_3_points(common_point_on_planes(X1,X2,X3),X4,X5))
| ~ on(X0,line_through_3_points(common_point_on_planes(X1,X2,X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_117,c_3370]) ).
tcf(c_33759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,common_point_on_planes(X2,X3,X4),X0)
| ( X2 = X3 )
| ( X1 = X5 )
| ( X0 = X6 )
| ( common_point_on_planes(X2,X3,X4) = X6 )
| ( common_point_on_planes(X2,X3,X4) = X5 )
| ( common_point_on_planes(X2,X3,X4) = X1 )
| ( common_point_on_planes(X2,X3,X4) = X0 )
| ( line_through_3_points(X1,common_point_on_planes(X2,X3,X4),X5) = X3 )
| ~ plane(X3)
| ~ plane(X2)
| ~ point(X6)
| ~ point(X5)
| ~ point(X4)
| ~ point(X1)
| ~ point(X0)
| ~ on(X6,X3)
| ~ on(X4,X3)
| ~ on(X4,X2)
| ~ on(X0,X3)
| ~ point(common_point_on_planes(X2,X3,X4))
| ~ collinear(X1,common_point_on_planes(X2,X3,X4),X5)
| ~ plane(line_through_3_points(X1,common_point_on_planes(X2,X3,X4),X5))
| ~ on(X6,line_through_3_points(X1,common_point_on_planes(X2,X3,X4),X5))
| ~ on(X0,line_through_3_points(X1,common_point_on_planes(X2,X3,X4),X5)) ),
inference(superposition,[status(thm)],[c_118,c_3370]) ).
tcf(c_33760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,common_point_on_planes(X3,X4,X5),X0)
| ( X3 = X4 )
| ( X1 = X2 )
| ( X0 = X6 )
| ( common_point_on_planes(X3,X4,X5) = X6 )
| ( common_point_on_planes(X3,X4,X5) = X2 )
| ( common_point_on_planes(X3,X4,X5) = X1 )
| ( common_point_on_planes(X3,X4,X5) = X0 )
| ( line_through_3_points(X1,X2,common_point_on_planes(X3,X4,X5)) = X4 )
| ~ plane(X4)
| ~ plane(X3)
| ~ point(X6)
| ~ point(X5)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X6,X4)
| ~ on(X5,X4)
| ~ on(X5,X3)
| ~ on(X0,X4)
| ~ point(common_point_on_planes(X3,X4,X5))
| ~ collinear(X1,X2,common_point_on_planes(X3,X4,X5))
| ~ plane(line_through_3_points(X1,X2,common_point_on_planes(X3,X4,X5)))
| ~ on(X6,line_through_3_points(X1,X2,common_point_on_planes(X3,X4,X5)))
| ~ on(X0,line_through_3_points(X1,X2,common_point_on_planes(X3,X4,X5))) ),
inference(superposition,[status(thm)],[c_119,c_3370]) ).
tcf(c_33761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X5,common_point_on_planes(X1,X2,X3),X0)
| ( X1 = X2 )
| ( X0 = X5 )
| ( common_point_on_planes(X1,X2,X3) = X5 )
| ( common_point_on_planes(X1,X2,X3) = X4 )
| ( common_point_on_planes(X1,X2,X3) = X0 )
| ( line_from_to(common_point_on_planes(X1,X2,X3),X4) = X2 )
| ~ plane(X2)
| ~ plane(X1)
| ~ point(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X0)
| ~ on(X5,X2)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X2)
| ~ point(common_point_on_planes(X1,X2,X3))
| ~ plane(line_from_to(common_point_on_planes(X1,X2,X3),X4))
| ~ on(X5,line_from_to(common_point_on_planes(X1,X2,X3),X4))
| ~ on(X0,line_from_to(common_point_on_planes(X1,X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_91,c_3370]) ).
tcf(c_33762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,common_point_on_planes(X1,X2,X3),X0)
| collinear(common_point_on_planes(X1,X2,X3),X4,X5)
| ( X4 = X5 )
| ( X1 = X2 )
| ( X0 = X6 )
| ( common_point_on_planes(X1,X2,X3) = X6 )
| ( common_point_on_planes(X1,X2,X3) = X5 )
| ( common_point_on_planes(X1,X2,X3) = X4 )
| ( common_point_on_planes(X1,X2,X3) = X0 )
| ( plane_for_points(common_point_on_planes(X1,X2,X3),X4,X5) = X2 )
| ~ plane(X2)
| ~ plane(X1)
| ~ point(X6)
| ~ point(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X0)
| ~ on(X6,X2)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X2)
| ~ point(common_point_on_planes(X1,X2,X3))
| ~ plane(plane_for_points(common_point_on_planes(X1,X2,X3),X4,X5))
| ~ on(X6,plane_for_points(common_point_on_planes(X1,X2,X3),X4,X5))
| ~ on(X0,plane_for_points(common_point_on_planes(X1,X2,X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_107,c_3370]) ).
tcf(c_33763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( collinear(X6,common_point_on_planes(X2,X3,X4),X0)
| collinear(X1,common_point_on_planes(X2,X3,X4),X5)
| ( X2 = X3 )
| ( X1 = X5 )
| ( X0 = X6 )
| ( common_point_on_planes(X2,X3,X4) = X6 )
| ( common_point_on_planes(X2,X3,X4) = X5 )
| ( common_point_on_planes(X2,X3,X4) = X1 )
| ( common_point_on_planes(X2,X3,X4) = X0 )
| ( plane_for_points(X1,common_point_on_planes(X2,X3,X4),X5) = X3 )
| ~ plane(X3)
| ~ plane(X2)
| ~ point(X6)
| ~ point(X5)
| ~ point(X4)
| ~ point(X1)
| ~ point(X0)
| ~ on(X6,X3)
| ~ on(X4,X3)
| ~ on(X4,X2)
| ~ on(X0,X3)
| ~ point(common_point_on_planes(X2,X3,X4))
| ~ plane(plane_for_points(X1,common_point_on_planes(X2,X3,X4),X5))
| ~ on(X6,plane_for_points(X1,common_point_on_planes(X2,X3,X4),X5))
| ~ on(X0,plane_for_points(X1,common_point_on_planes(X2,X3,X4),X5)) ),
inference(superposition,[status(thm)],[c_108,c_3370]) ).
tcf(c_33766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X4,common_point_on_planes(X1,X2,X3),X0)
| ( X1 = X2 )
| ( X0 = X4 )
| ( common_point_on_planes(X1,X2,X3) = X4 )
| ( common_point_on_planes(X1,X2,X3) = X2 )
| ( common_point_on_planes(X1,X2,X3) = X0 )
| ~ plane(X2)
| ~ plane(X1)
| ~ point(X4)
| ~ point(X3)
| ~ point(X0)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ on(X3,X1)
| ~ on(X0,X2)
| ~ plane(common_point_on_planes(X1,X2,X3))
| ~ line(common_point_on_planes(X1,X2,X3))
| ~ point(common_point_on_planes(X1,X2,X3))
| ~ on(X4,common_point_on_planes(X1,X2,X3))
| ~ on(X0,common_point_on_planes(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_18002,c_3370]) ).
tcf(c_34003,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,point2,X1)
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),X2) ),
inference(superposition,[status(thm)],[c_13259,c_94]) ).
tcf(c_34004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,point2,X1)
| collinear(X4,plane_for_points(X0,point2,X1),X3)
| ( X3 = X4 )
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = X4 )
| ( plane_for_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,a_line)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),X2) ),
inference(superposition,[status(thm)],[c_13259,c_111]) ).
tcf(c_34005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,a_line)
| collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),X2) ),
inference(superposition,[status(thm)],[c_13259,c_112]) ).
tcf(c_34006,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,point2,X2)
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,point2,X2) = a_line )
| ( plane_for_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,point2,X2))
| ~ line(plane_for_points(X1,point2,X2))
| ~ point(plane_for_points(X1,point2,X2))
| ~ on(X0,plane_for_points(X1,point2,X2)) ),
inference(superposition,[status(thm)],[c_13259,c_18010]) ).
tcf(c_34007,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,point2,X2)
| on(a_line,plane_for_points(X1,point2,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,point2,X2))
| ~ line(plane_for_points(X1,point2,X2))
| ~ point(plane_for_points(X1,point2,X2))
| ~ on(X0,plane_for_points(X1,point2,X2)) ),
inference(superposition,[status(thm)],[c_13259,c_18012]) ).
tcf(c_34010,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),a_line) ),
inference(superposition,[status(thm)],[c_13259,c_2934]) ).
tcf(c_34013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,point2,X1)
| collinear(X3,plane_for_points(X0,point2,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = X3 )
| ( plane_for_points(X0,point2,X1) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13259,c_121]) ).
tcf(c_34014,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),a_line) ),
inference(superposition,[status(thm)],[c_13259,c_2925]) ).
tcf(c_34015,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = a_line )
| ( line_from_to(plane_for_points(X0,point2,X1),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13259,c_32429]) ).
tcf(c_34016,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = a_line )
| ( line_from_to(a_line,plane_for_points(X0,point2,X1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13259,c_31558]) ).
tcf(c_34017,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( point1 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),point1) ),
inference(superposition,[status(thm)],[c_13259,c_21610]) ).
tcf(c_34018,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( point2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),point2) ),
inference(superposition,[status(thm)],[c_13259,c_21602]) ).
tcf(c_34019,plain,
! [X0: $i,X1: $i] :
( on(a_line,point1)
| collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),point1) ),
inference(superposition,[status(thm)],[c_13259,c_20018]) ).
tcf(c_34020,plain,
! [X0: $i,X1: $i] :
( on(a_line,point2)
| collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),point2) ),
inference(superposition,[status(thm)],[c_13259,c_20010]) ).
tcf(c_34021,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(X0,point2,X1))
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(a_line,plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13259,c_18013]) ).
tcf(c_34022,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = a_line )
| ( plane_for_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(X0,point2,X1))
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(point2,plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13259,c_18017]) ).
tcf(c_34023,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point1 )
| ( line_from_to(plane_for_points(X0,point2,X1),point1) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13259,c_12246]) ).
tcf(c_34024,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point1 )
| ( line_from_to(point1,plane_for_points(X0,point2,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13259,c_11471]) ).
tcf(c_34025,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point2 )
| ( line_from_to(plane_for_points(X0,point2,X1),point2) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13259,c_11016]) ).
tcf(c_34026,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point2 )
| ( line_from_to(point2,plane_for_points(X0,point2,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13259,c_9014]) ).
tcf(c_34175,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34014,c_125,c_127]) ).
tcf(c_34189,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34010,c_125,c_126]) ).
tcf(c_34234,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,point2,X1)
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34003,c_125]) ).
tcf(c_34252,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,point2,X2)
| on(a_line,plane_for_points(X1,point2,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,point2,X2))
| ~ line(plane_for_points(X1,point2,X2))
| ~ point(plane_for_points(X1,point2,X2))
| ~ on(X0,plane_for_points(X1,point2,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34007,c_125]) ).
tcf(c_34269,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,point2,X2)
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,point2,X2) = a_line )
| ( plane_for_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,point2,X2))
| ~ line(plane_for_points(X1,point2,X2))
| ~ point(plane_for_points(X1,point2,X2))
| ~ on(X0,plane_for_points(X1,point2,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34006,c_125]) ).
tcf(c_34286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,point2,X1)
| collinear(X3,plane_for_points(X0,point2,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = X3 )
| ( plane_for_points(X0,point2,X1) = X2 )
| ~ plane(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34013,c_125]) ).
tcf(c_34398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(point2,X0,X1)
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_13270,c_94]) ).
tcf(c_34399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(point2,X0,X1)
| collinear(X4,plane_for_points(point2,X0,X1),X3)
| ( X3 = X4 )
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = X4 )
| ( plane_for_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,a_line)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_13270,c_111]) ).
tcf(c_34400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,a_line)
| collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_13270,c_112]) ).
tcf(c_34401,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(point2,X1,X2)
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(point2,X1,X2) = a_line )
| ( plane_for_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(point2,X1,X2))
| ~ line(plane_for_points(point2,X1,X2))
| ~ point(plane_for_points(point2,X1,X2))
| ~ on(X0,plane_for_points(point2,X1,X2)) ),
inference(superposition,[status(thm)],[c_13270,c_18010]) ).
tcf(c_34402,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(point2,X1,X2)
| on(a_line,plane_for_points(point2,X1,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(point2,X1,X2))
| ~ line(plane_for_points(point2,X1,X2))
| ~ point(plane_for_points(point2,X1,X2))
| ~ on(X0,plane_for_points(point2,X1,X2)) ),
inference(superposition,[status(thm)],[c_13270,c_18012]) ).
tcf(c_34405,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_13270,c_2934]) ).
tcf(c_34408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(point2,X0,X1)
| collinear(X3,plane_for_points(point2,X0,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = X3 )
| ( plane_for_points(point2,X0,X1) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_13270,c_121]) ).
tcf(c_34409,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_13270,c_2925]) ).
tcf(c_34410,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = a_line )
| ( line_from_to(plane_for_points(point2,X0,X1),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_13270,c_32429]) ).
tcf(c_34411,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = a_line )
| ( line_from_to(a_line,plane_for_points(point2,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_13270,c_31558]) ).
tcf(c_34412,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( point1 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),point1) ),
inference(superposition,[status(thm)],[c_13270,c_21610]) ).
tcf(c_34413,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( point2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),point2) ),
inference(superposition,[status(thm)],[c_13270,c_21602]) ).
tcf(c_34414,plain,
! [X0: $i,X1: $i] :
( on(a_line,point1)
| collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),point1) ),
inference(superposition,[status(thm)],[c_13270,c_20018]) ).
tcf(c_34415,plain,
! [X0: $i,X1: $i] :
( on(a_line,point2)
| collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),point2) ),
inference(superposition,[status(thm)],[c_13270,c_20010]) ).
tcf(c_34416,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(point2,X0,X1))
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(a_line,plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_13270,c_18013]) ).
tcf(c_34417,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = a_line )
| ( plane_for_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(point2,X0,X1))
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(point2,plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_13270,c_18017]) ).
tcf(c_34418,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point1 )
| ( line_from_to(plane_for_points(point2,X0,X1),point1) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_13270,c_12246]) ).
tcf(c_34419,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point1 )
| ( line_from_to(point1,plane_for_points(point2,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_13270,c_11471]) ).
tcf(c_34420,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point2 )
| ( line_from_to(plane_for_points(point2,X0,X1),point2) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_13270,c_11016]) ).
tcf(c_34421,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point2 )
| ( line_from_to(point2,plane_for_points(point2,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_13270,c_9014]) ).
tcf(c_34570,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34409,c_125,c_127]) ).
tcf(c_34584,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34405,c_125,c_126]) ).
tcf(c_34629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(point2,X0,X1)
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34398,c_125]) ).
tcf(c_34647,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(point2,X1,X2)
| on(a_line,plane_for_points(point2,X1,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(point2,X1,X2))
| ~ line(plane_for_points(point2,X1,X2))
| ~ point(plane_for_points(point2,X1,X2))
| ~ on(X0,plane_for_points(point2,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34402,c_125]) ).
tcf(c_34664,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(point2,X1,X2)
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(point2,X1,X2) = a_line )
| ( plane_for_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(point2,X1,X2))
| ~ line(plane_for_points(point2,X1,X2))
| ~ point(plane_for_points(point2,X1,X2))
| ~ on(X0,plane_for_points(point2,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34401,c_125]) ).
tcf(c_34681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(point2,X0,X1)
| collinear(X3,plane_for_points(point2,X0,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = X3 )
| ( plane_for_points(point2,X0,X1) = X2 )
| ~ plane(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34408,c_125]) ).
tcf(c_34836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,point2,X1)
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),X2) ),
inference(superposition,[status(thm)],[c_19388,c_94]) ).
tcf(c_34837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,point2,X1)
| collinear(X4,plane_for_points(X0,point2,X1),X3)
| ( X3 = X4 )
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = X4 )
| ( plane_for_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,a_line)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),X2) ),
inference(superposition,[status(thm)],[c_19388,c_111]) ).
tcf(c_34838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,a_line)
| collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),X2) ),
inference(superposition,[status(thm)],[c_19388,c_112]) ).
tcf(c_34839,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,point2,X2)
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,point2,X2) = a_line )
| ( plane_for_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,point2,X2))
| ~ line(plane_for_points(X1,point2,X2))
| ~ point(plane_for_points(X1,point2,X2))
| ~ on(X0,plane_for_points(X1,point2,X2)) ),
inference(superposition,[status(thm)],[c_19388,c_18010]) ).
tcf(c_34840,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,point2,X2)
| on(a_line,plane_for_points(X1,point2,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,point2,X2))
| ~ line(plane_for_points(X1,point2,X2))
| ~ point(plane_for_points(X1,point2,X2))
| ~ on(X0,plane_for_points(X1,point2,X2)) ),
inference(superposition,[status(thm)],[c_19388,c_18012]) ).
tcf(c_34843,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),a_line) ),
inference(superposition,[status(thm)],[c_19388,c_2934]) ).
tcf(c_34846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,point2,X1)
| collinear(X3,plane_for_points(X0,point2,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = X3 )
| ( plane_for_points(X0,point2,X1) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_19388,c_121]) ).
tcf(c_34847,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),a_line) ),
inference(superposition,[status(thm)],[c_19388,c_2925]) ).
tcf(c_34848,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = a_line )
| ( line_from_to(plane_for_points(X0,point2,X1),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_19388,c_32429]) ).
tcf(c_34849,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = a_line )
| ( line_from_to(a_line,plane_for_points(X0,point2,X1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_19388,c_31558]) ).
tcf(c_34850,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( point1 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),point1) ),
inference(superposition,[status(thm)],[c_19388,c_21610]) ).
tcf(c_34851,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( point2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),point2) ),
inference(superposition,[status(thm)],[c_19388,c_21602]) ).
tcf(c_34852,plain,
! [X0: $i,X1: $i] :
( on(a_line,point1)
| collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),point1) ),
inference(superposition,[status(thm)],[c_19388,c_20018]) ).
tcf(c_34853,plain,
! [X0: $i,X1: $i] :
( on(a_line,point2)
| collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),point2) ),
inference(superposition,[status(thm)],[c_19388,c_20010]) ).
tcf(c_34854,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X0,point2,X1))
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(a_line,plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_19388,c_18013]) ).
tcf(c_34855,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = a_line )
| ( plane_for_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X0,point2,X1))
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(point2,plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_19388,c_18017]) ).
tcf(c_34856,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point1 )
| ( line_from_to(plane_for_points(X0,point2,X1),point1) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_19388,c_12246]) ).
tcf(c_34857,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point1 )
| ( line_from_to(point1,plane_for_points(X0,point2,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_19388,c_11471]) ).
tcf(c_34858,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point2 )
| ( line_from_to(plane_for_points(X0,point2,X1),point2) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_19388,c_11016]) ).
tcf(c_34859,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point2 )
| ( line_from_to(point2,plane_for_points(X0,point2,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_19388,c_9014]) ).
tcf(c_35008,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34847,c_125,c_127]) ).
tcf(c_35022,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = point1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34843,c_125,c_126]) ).
tcf(c_35067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,point2,X1)
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1))
| ~ on(plane_for_points(X0,point2,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34836,c_125]) ).
tcf(c_35085,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,point2,X2)
| on(a_line,plane_for_points(X1,point2,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,point2,X2))
| ~ line(plane_for_points(X1,point2,X2))
| ~ point(plane_for_points(X1,point2,X2))
| ~ on(X0,plane_for_points(X1,point2,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34840,c_125]) ).
tcf(c_35102,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,point2,X2)
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,point2,X2) = a_line )
| ( plane_for_points(X1,point2,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,point2,X2))
| ~ line(plane_for_points(X1,point2,X2))
| ~ point(plane_for_points(X1,point2,X2))
| ~ on(X0,plane_for_points(X1,point2,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34839,c_125]) ).
tcf(c_35119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,point2,X1)
| collinear(X3,plane_for_points(X0,point2,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = X3 )
| ( plane_for_points(X0,point2,X1) = X2 )
| ~ plane(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34846,c_125]) ).
tcf(c_35258,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = point1 )
| ( line_from_to(line_from_to(X0,point2),point1) = a_line )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_93,c_16727]) ).
tcf(c_35259,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point1 )
| ( line_from_to(line_from_to(point1,point2),point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ point(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_16727]) ).
tcf(c_35262,plain,
( ( point1 = a_line )
| ( point1 = point2 )
| ( line_from_to(a_line,point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(light_normalisation,[status(thm)],[c_35259,c_11046]) ).
tcf(c_35264,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = point1 )
| ( line_from_to(line_from_to(X0,point2),point1) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35258,c_123]) ).
tcf(c_35294,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point1 )
| ( line_from_to(line_from_to(point1,point2),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(superposition,[status(thm)],[c_11046,c_35264]) ).
tcf(c_35315,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = point1 )
| ( line_from_to(point1,line_from_to(X0,point2)) = a_line )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_93,c_16728]) ).
tcf(c_35316,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point1 )
| ( line_from_to(point1,line_from_to(point1,point2)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ point(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_16728]) ).
tcf(c_35319,plain,
( ( point1 = a_line )
| ( point1 = point2 )
| ( line_from_to(point1,a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(light_normalisation,[status(thm)],[c_35316,c_11046]) ).
tcf(c_35321,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = point1 )
| ( line_from_to(point1,line_from_to(X0,point2)) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35315,c_123]) ).
tcf(c_35351,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point1 )
| ( line_from_to(point1,line_from_to(point1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(superposition,[status(thm)],[c_11046,c_35321]) ).
tcf(c_35376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,point2)
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),X2) ),
inference(superposition,[status(thm)],[c_19399,c_94]) ).
tcf(c_35377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,point2)
| collinear(X4,plane_for_points(X0,X1,point2),X3)
| ( X3 = X4 )
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = X4 )
| ( plane_for_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,a_line)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),X2) ),
inference(superposition,[status(thm)],[c_19399,c_111]) ).
tcf(c_35378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,a_line)
| collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),X2) ),
inference(superposition,[status(thm)],[c_19399,c_112]) ).
tcf(c_35379,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,X2,point2)
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,point2) = a_line )
| ( plane_for_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,X2,point2))
| ~ line(plane_for_points(X1,X2,point2))
| ~ point(plane_for_points(X1,X2,point2))
| ~ on(X0,plane_for_points(X1,X2,point2)) ),
inference(superposition,[status(thm)],[c_19399,c_18010]) ).
tcf(c_35380,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,X2,point2)
| on(a_line,plane_for_points(X1,X2,point2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,X2,point2))
| ~ line(plane_for_points(X1,X2,point2))
| ~ point(plane_for_points(X1,X2,point2))
| ~ on(X0,plane_for_points(X1,X2,point2)) ),
inference(superposition,[status(thm)],[c_19399,c_18012]) ).
tcf(c_35383,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),a_line) ),
inference(superposition,[status(thm)],[c_19399,c_2934]) ).
tcf(c_35386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,point2)
| collinear(X3,plane_for_points(X0,X1,point2),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = X3 )
| ( plane_for_points(X0,X1,point2) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19399,c_121]) ).
tcf(c_35387,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),a_line) ),
inference(superposition,[status(thm)],[c_19399,c_2925]) ).
tcf(c_35388,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = a_line )
| ( line_from_to(plane_for_points(X0,X1,point2),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19399,c_32429]) ).
tcf(c_35389,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = a_line )
| ( line_from_to(a_line,plane_for_points(X0,X1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19399,c_31558]) ).
tcf(c_35390,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( point1 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),point1) ),
inference(superposition,[status(thm)],[c_19399,c_21610]) ).
tcf(c_35391,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( point2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),point2) ),
inference(superposition,[status(thm)],[c_19399,c_21602]) ).
tcf(c_35392,plain,
! [X0: $i,X1: $i] :
( on(a_line,point1)
| collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),point1) ),
inference(superposition,[status(thm)],[c_19399,c_20018]) ).
tcf(c_35393,plain,
! [X0: $i,X1: $i] :
( on(a_line,point2)
| collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),point2) ),
inference(superposition,[status(thm)],[c_19399,c_20010]) ).
tcf(c_35394,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X0,X1,point2))
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(a_line,plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19399,c_18013]) ).
tcf(c_35395,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = a_line )
| ( plane_for_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X0,X1,point2))
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(point2,plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19399,c_18017]) ).
tcf(c_35396,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point1 )
| ( line_from_to(plane_for_points(X0,X1,point2),point1) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19399,c_12246]) ).
tcf(c_35397,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point1 )
| ( line_from_to(point1,plane_for_points(X0,X1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19399,c_11471]) ).
tcf(c_35398,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point2 )
| ( line_from_to(plane_for_points(X0,X1,point2),point2) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19399,c_11016]) ).
tcf(c_35399,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point2 )
| ( line_from_to(point2,plane_for_points(X0,X1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19399,c_9014]) ).
tcf(c_35548,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35387,c_125,c_127]) ).
tcf(c_35562,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35383,c_125,c_126]) ).
tcf(c_35607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,point2)
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35376,c_125]) ).
tcf(c_35625,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,X2,point2)
| on(a_line,plane_for_points(X1,X2,point2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,X2,point2))
| ~ line(plane_for_points(X1,X2,point2))
| ~ point(plane_for_points(X1,X2,point2))
| ~ on(X0,plane_for_points(X1,X2,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35380,c_125]) ).
tcf(c_35642,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,X2,point2)
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,point2) = a_line )
| ( plane_for_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,X2,point2))
| ~ line(plane_for_points(X1,X2,point2))
| ~ point(plane_for_points(X1,X2,point2))
| ~ on(X0,plane_for_points(X1,X2,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35379,c_125]) ).
tcf(c_35659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,point2)
| collinear(X3,plane_for_points(X0,X1,point2),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = X3 )
| ( plane_for_points(X0,X1,point2) = X2 )
| ~ plane(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35386,c_125]) ).
tcf(c_35798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(point2,X0,X1)
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19853,c_94]) ).
tcf(c_35799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(point2,X0,X1)
| collinear(X4,plane_for_points(point2,X0,X1),X3)
| ( X3 = X4 )
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = X4 )
| ( plane_for_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,a_line)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19853,c_111]) ).
tcf(c_35800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,a_line)
| collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19853,c_112]) ).
tcf(c_35801,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(point2,X1,X2)
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(point2,X1,X2) = a_line )
| ( plane_for_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(point2,X1,X2))
| ~ line(plane_for_points(point2,X1,X2))
| ~ point(plane_for_points(point2,X1,X2))
| ~ on(X0,plane_for_points(point2,X1,X2)) ),
inference(superposition,[status(thm)],[c_19853,c_18010]) ).
tcf(c_35802,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(point2,X1,X2)
| on(a_line,plane_for_points(point2,X1,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(point2,X1,X2))
| ~ line(plane_for_points(point2,X1,X2))
| ~ point(plane_for_points(point2,X1,X2))
| ~ on(X0,plane_for_points(point2,X1,X2)) ),
inference(superposition,[status(thm)],[c_19853,c_18012]) ).
tcf(c_35805,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_19853,c_2934]) ).
tcf(c_35808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(point2,X0,X1)
| collinear(X3,plane_for_points(point2,X0,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = X3 )
| ( plane_for_points(point2,X0,X1) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_19853,c_121]) ).
tcf(c_35809,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),a_line) ),
inference(superposition,[status(thm)],[c_19853,c_2925]) ).
tcf(c_35810,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = a_line )
| ( line_from_to(plane_for_points(point2,X0,X1),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_19853,c_32429]) ).
tcf(c_35811,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = a_line )
| ( line_from_to(a_line,plane_for_points(point2,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_19853,c_31558]) ).
tcf(c_35812,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( point1 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),point1) ),
inference(superposition,[status(thm)],[c_19853,c_21610]) ).
tcf(c_35813,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( point2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),point2) ),
inference(superposition,[status(thm)],[c_19853,c_21602]) ).
tcf(c_35814,plain,
! [X0: $i,X1: $i] :
( on(a_line,point1)
| collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),point1) ),
inference(superposition,[status(thm)],[c_19853,c_20018]) ).
tcf(c_35815,plain,
! [X0: $i,X1: $i] :
( on(a_line,point2)
| collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),point2) ),
inference(superposition,[status(thm)],[c_19853,c_20010]) ).
tcf(c_35816,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(point2,X0,X1))
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(a_line,plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_19853,c_18013]) ).
tcf(c_35817,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = a_line )
| ( plane_for_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(point2,X0,X1))
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(point2,plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_19853,c_18017]) ).
tcf(c_35818,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point1 )
| ( line_from_to(plane_for_points(point2,X0,X1),point1) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_19853,c_12246]) ).
tcf(c_35819,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point1 )
| ( line_from_to(point1,plane_for_points(point2,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_19853,c_11471]) ).
tcf(c_35820,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point2 )
| ( line_from_to(plane_for_points(point2,X0,X1),point2) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_19853,c_11016]) ).
tcf(c_35821,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point2 )
| ( line_from_to(point2,plane_for_points(point2,X0,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_19853,c_9014]) ).
tcf(c_35970,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35809,c_125,c_127]) ).
tcf(c_35984,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = point1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35805,c_125,c_126]) ).
tcf(c_36029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(point2,X0,X1)
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X0,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1))
| ~ on(plane_for_points(point2,X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35798,c_125]) ).
tcf(c_36047,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(point2,X1,X2)
| on(a_line,plane_for_points(point2,X1,X2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(point2,X1,X2))
| ~ line(plane_for_points(point2,X1,X2))
| ~ point(plane_for_points(point2,X1,X2))
| ~ on(X0,plane_for_points(point2,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35802,c_125]) ).
tcf(c_36064,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(point2,X1,X2)
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(point2,X1,X2) = a_line )
| ( plane_for_points(point2,X1,X2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(point2,X1,X2))
| ~ line(plane_for_points(point2,X1,X2))
| ~ point(plane_for_points(point2,X1,X2))
| ~ on(X0,plane_for_points(point2,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35801,c_125]) ).
tcf(c_36081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(point2,X0,X1)
| collinear(X3,plane_for_points(point2,X0,X1),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = X3 )
| ( plane_for_points(point2,X0,X1) = X2 )
| ~ plane(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35808,c_125]) ).
tcf(c_36287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,point2)
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),X2) ),
inference(superposition,[status(thm)],[c_19864,c_94]) ).
tcf(c_36288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( collinear(X0,X1,point2)
| collinear(X4,plane_for_points(X0,X1,point2),X3)
| ( X3 = X4 )
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = X4 )
| ( plane_for_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ plane(X2)
| ~ point(X4)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,a_line)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X4,X2)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),X2) ),
inference(superposition,[status(thm)],[c_19864,c_111]) ).
tcf(c_36289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on(X2,a_line)
| collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),X2) ),
inference(superposition,[status(thm)],[c_19864,c_112]) ).
tcf(c_36290,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,X2,point2)
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,point2) = a_line )
| ( plane_for_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,X2,point2))
| ~ line(plane_for_points(X1,X2,point2))
| ~ point(plane_for_points(X1,X2,point2))
| ~ on(X0,plane_for_points(X1,X2,point2)) ),
inference(superposition,[status(thm)],[c_19864,c_18010]) ).
tcf(c_36291,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,X2,point2)
| on(a_line,plane_for_points(X1,X2,point2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,X2,point2))
| ~ line(plane_for_points(X1,X2,point2))
| ~ point(plane_for_points(X1,X2,point2))
| ~ on(X0,plane_for_points(X1,X2,point2)) ),
inference(superposition,[status(thm)],[c_19864,c_18012]) ).
tcf(c_36294,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point1,a_line)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),a_line) ),
inference(superposition,[status(thm)],[c_19864,c_2934]) ).
tcf(c_36297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,point2)
| collinear(X3,plane_for_points(X0,X1,point2),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = X3 )
| ( plane_for_points(X0,X1,point2) = X2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19864,c_121]) ).
tcf(c_36298,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(point2,a_line)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),a_line) ),
inference(superposition,[status(thm)],[c_19864,c_2925]) ).
tcf(c_36299,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = a_line )
| ( line_from_to(plane_for_points(X0,X1,point2),a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19864,c_32429]) ).
tcf(c_36300,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = a_line )
| ( line_from_to(a_line,plane_for_points(X0,X1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19864,c_31558]) ).
tcf(c_36301,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( point1 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),point1) ),
inference(superposition,[status(thm)],[c_19864,c_21610]) ).
tcf(c_36302,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( point2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),point2) ),
inference(superposition,[status(thm)],[c_19864,c_21602]) ).
tcf(c_36303,plain,
! [X0: $i,X1: $i] :
( on(a_line,point1)
| collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),point1) ),
inference(superposition,[status(thm)],[c_19864,c_20018]) ).
tcf(c_36304,plain,
! [X0: $i,X1: $i] :
( on(a_line,point2)
| collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),point2) ),
inference(superposition,[status(thm)],[c_19864,c_20010]) ).
tcf(c_36305,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(X0,X1,point2))
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(a_line,plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19864,c_18013]) ).
tcf(c_36306,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = a_line )
| ( plane_for_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(X0,X1,point2))
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(point2,plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19864,c_18017]) ).
tcf(c_36307,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point1 )
| ( line_from_to(plane_for_points(X0,X1,point2),point1) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19864,c_12246]) ).
tcf(c_36308,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point1 )
| ( line_from_to(point1,plane_for_points(X0,X1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19864,c_11471]) ).
tcf(c_36309,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point2 )
| ( line_from_to(plane_for_points(X0,X1,point2),point2) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19864,c_11016]) ).
tcf(c_36310,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point2 )
| ( line_from_to(point2,plane_for_points(X0,X1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19864,c_9014]) ).
tcf(c_36459,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point2 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36298,c_125,c_127]) ).
tcf(c_36473,plain,
! [X0: $i,X1: $i] :
( on(a_line,a_line)
| collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = point1 )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),a_line) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36294,c_125,c_126]) ).
tcf(c_36518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,point2)
| ( X2 = a_line )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = X3 )
| ~ plane(a_line)
| ~ line(X2)
| ~ point(X3)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X1,a_line)
| ~ on(X3,X2)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2))
| ~ on(plane_for_points(X0,X1,point2),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36287,c_125]) ).
tcf(c_36536,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,X2,point2)
| on(a_line,plane_for_points(X1,X2,point2))
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,X2,point2))
| ~ line(plane_for_points(X1,X2,point2))
| ~ point(plane_for_points(X1,X2,point2))
| ~ on(X0,plane_for_points(X1,X2,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36291,c_125]) ).
tcf(c_36553,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X1,X2,point2)
| ( X2 = point2 )
| ( X1 = point2 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,point2) = a_line )
| ( plane_for_points(X1,X2,point2) = X0 )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X1,X2,point2))
| ~ line(plane_for_points(X1,X2,point2))
| ~ point(plane_for_points(X1,X2,point2))
| ~ on(X0,plane_for_points(X1,X2,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36290,c_125]) ).
tcf(c_36570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,point2)
| collinear(X3,plane_for_points(X0,X1,point2),X2)
| ( X2 = X3 )
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = X3 )
| ( plane_for_points(X0,X1,point2) = X2 )
| ~ plane(a_line)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X3,a_line)
| ~ on(X2,a_line)
| ~ on(X1,a_line)
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36297,c_125]) ).
tcf(c_36707,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = point2 )
| ( line_from_to(line_from_to(X0,point2),point2) = a_line )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_93,c_16729]) ).
tcf(c_36708,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point2 )
| ( line_from_to(line_from_to(point1,point2),point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ point(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_16729]) ).
tcf(c_36711,plain,
( ( point2 = a_line )
| ( point1 = point2 )
| ( line_from_to(a_line,point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(light_normalisation,[status(thm)],[c_36708,c_11046]) ).
tcf(c_36713,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = point2 )
| ( line_from_to(line_from_to(X0,point2),point2) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36707,c_123]) ).
tcf(c_36743,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point2 )
| ( line_from_to(line_from_to(point1,point2),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(superposition,[status(thm)],[c_11046,c_36713]) ).
tcf(c_36764,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = point2 )
| ( line_from_to(point2,line_from_to(X0,point2)) = a_line )
| ~ plane(a_line)
| ~ point(point2)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_93,c_16730]) ).
tcf(c_36765,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point2 )
| ( line_from_to(point2,line_from_to(point1,point2)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point1)
| ~ on(point1,a_line)
| ~ point(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_16730]) ).
tcf(c_36768,plain,
( ( point2 = a_line )
| ( point1 = point2 )
| ( line_from_to(point2,a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(light_normalisation,[status(thm)],[c_36765,c_11046]) ).
tcf(c_36770,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = point2 )
| ( line_from_to(point2,line_from_to(X0,point2)) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36764,c_123]) ).
tcf(c_36800,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point2 )
| ( line_from_to(point2,line_from_to(point1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point1)
| ~ on(point1,a_line) ),
inference(superposition,[status(thm)],[c_11046,c_36770]) ).
tcf(c_36821,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = point1 )
| ( line_from_to(line_from_to(point1,X0),point1) = a_line )
| ~ plane(a_line)
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_93,c_25869]) ).
tcf(c_36822,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point1 )
| ( line_from_to(line_from_to(point1,point2),point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ point(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_25869]) ).
tcf(c_36825,plain,
( ( point1 = a_line )
| ( point1 = point2 )
| ( line_from_to(a_line,point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(light_normalisation,[status(thm)],[c_36822,c_11046]) ).
tcf(c_36827,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = point1 )
| ( line_from_to(line_from_to(point1,X0),point1) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36821,c_122]) ).
tcf(c_36856,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point1 )
| ( line_from_to(line_from_to(point1,point2),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(superposition,[status(thm)],[c_11046,c_36827]) ).
tcf(c_36859,plain,
( ( point1 = a_line )
| ( point1 = point2 )
| ( line_from_to(a_line,point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(light_normalisation,[status(thm)],[c_36856,c_11046]) ).
tcf(c_36877,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = point1 )
| ( line_from_to(point1,line_from_to(point1,X0)) = a_line )
| ~ plane(a_line)
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_93,c_25870]) ).
tcf(c_36878,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point1 )
| ( line_from_to(point1,line_from_to(point1,point2)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ point(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_25870]) ).
tcf(c_36881,plain,
( ( point1 = a_line )
| ( point1 = point2 )
| ( line_from_to(point1,a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(light_normalisation,[status(thm)],[c_36878,c_11046]) ).
tcf(c_36883,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = point1 )
| ( line_from_to(point1,line_from_to(point1,X0)) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36877,c_122]) ).
tcf(c_36912,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point1 )
| ( line_from_to(point1,line_from_to(point1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(superposition,[status(thm)],[c_11046,c_36883]) ).
tcf(c_36915,plain,
( ( point1 = a_line )
| ( point1 = point2 )
| ( line_from_to(point1,a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(light_normalisation,[status(thm)],[c_36912,c_11046]) ).
tcf(c_36933,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = point2 )
| ( line_from_to(line_from_to(point1,X0),point2) = a_line )
| ~ plane(a_line)
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_93,c_25871]) ).
tcf(c_36934,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point2 )
| ( line_from_to(line_from_to(point1,point2),point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ point(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_25871]) ).
tcf(c_36937,plain,
( ( point2 = a_line )
| ( point1 = point2 )
| ( line_from_to(a_line,point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(light_normalisation,[status(thm)],[c_36934,c_11046]) ).
tcf(c_36939,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = point2 )
| ( line_from_to(line_from_to(point1,X0),point2) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36933,c_122]) ).
tcf(c_36968,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point2 )
| ( line_from_to(line_from_to(point1,point2),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(superposition,[status(thm)],[c_11046,c_36939]) ).
tcf(c_36971,plain,
( ( point2 = a_line )
| ( point1 = point2 )
| ( line_from_to(a_line,point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(light_normalisation,[status(thm)],[c_36968,c_11046]) ).
tcf(c_36989,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = point2 )
| ( line_from_to(point2,line_from_to(point1,X0)) = a_line )
| ~ plane(a_line)
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_93,c_25872]) ).
tcf(c_36990,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point2 )
| ( line_from_to(point2,line_from_to(point1,point2)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ point(line_from_to(point1,point2)) ),
inference(superposition,[status(thm)],[c_11046,c_25872]) ).
tcf(c_36993,plain,
( ( point2 = a_line )
| ( point1 = point2 )
| ( line_from_to(point2,a_line) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(light_normalisation,[status(thm)],[c_36990,c_11046]) ).
tcf(c_36995,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = point2 )
| ( line_from_to(point2,line_from_to(point1,X0)) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(point1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36989,c_122]) ).
tcf(c_37024,plain,
( ( point1 = point2 )
| ( line_from_to(point1,point2) = point2 )
| ( line_from_to(point2,line_from_to(point1,point2)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(superposition,[status(thm)],[c_11046,c_36995]) ).
tcf(c_37027,plain,
( ( point2 = a_line )
| ( point1 = point2 )
| ( line_from_to(point2,a_line) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(light_normalisation,[status(thm)],[c_37024,c_11046]) ).
tcf(c_37040,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X2,point_on_plane(X1),X0)
| ( X0 = X2 )
| ( point_on_plane(X1) = X2 )
| ( point_on_plane(X1) = X0 )
| ~ plane(X1)
| ~ line(X1)
| ~ point(X2)
| ~ point(X0)
| ~ on(X2,X1)
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3944,c_104]) ).
tcf(c_37080,plain,
! [X0: $i,X1: $i] :
( ( X1 = a_line )
| ( common_point_on_planes(a_line,X1,X0) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,X1,X0)) = a_line )
| ~ plane(a_line)
| ~ plane(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9030,c_115]) ).
tcf(c_37107,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ( common_point_on_planes(a_line,line_from_to(X0,X1),X1) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_from_to(X0,X1),X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_92,c_37080]) ).
tcf(c_37108,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,point_1_on_line(X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,X0,point_1_on_line(X0))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ point(point_1_on_line(X0))
| ~ on(point_1_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_95,c_37080]) ).
tcf(c_37109,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,point_2_on_line(X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,X0,point_2_on_line(X0))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ point(point_2_on_line(X0))
| ~ on(point_2_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_96,c_37080]) ).
tcf(c_37110,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,point_on_plane(X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,X0,point_on_plane(X0))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(point_on_plane(X0))
| ~ on(point_on_plane(X0),a_line) ),
inference(superposition,[status(thm)],[c_103,c_37080]) ).
tcf(c_37111,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(a_line,plane_for_points(X0,X1,X2),X2) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,plane_for_points(X0,X1,X2),X2)) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ plane(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_109,c_37080]) ).
tcf(c_37112,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(a_line,line_through_3_points(X0,X1,X2),X0) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_through_3_points(X0,X1,X2),X0)) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_37080]) ).
tcf(c_37113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(a_line,line_through_3_points(X0,X1,X2),X1) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_through_3_points(X0,X1,X2),X1)) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_118,c_37080]) ).
tcf(c_37114,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(a_line,line_through_3_points(X0,X1,X2),X2) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_through_3_points(X0,X1,X2),X2)) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_119,c_37080]) ).
tcf(c_37115,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ( common_point_on_planes(a_line,line_from_to(X0,X1),X0) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_from_to(X0,X1),X0)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_91,c_37080]) ).
tcf(c_37116,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(a_line,plane_for_points(X0,X1,X2),X0) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,plane_for_points(X0,X1,X2),X0)) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_37080]) ).
tcf(c_37117,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(a_line,plane_for_points(X0,X1,X2),X1) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,plane_for_points(X0,X1,X2),X1)) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_108,c_37080]) ).
tcf(c_37118,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = a_line )
| ( X0 = X1 )
| ( common_point_on_planes(a_line,X0,common_point_on_planes(X0,X1,X2)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,X0,common_point_on_planes(X0,X1,X2))) = a_line )
| ~ plane(a_line)
| ~ plane(X1)
| ~ plane(X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_113,c_37080]) ).
tcf(c_37119,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = X1 )
| ( common_point_on_planes(a_line,X1,common_point_on_planes(X0,X1,X2)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,X1,common_point_on_planes(X0,X1,X2))) = a_line )
| ~ plane(a_line)
| ~ plane(X1)
| ~ plane(X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_114,c_37080]) ).
tcf(c_37123,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X0) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,X0,X0)) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_18002,c_37080]) ).
tcf(c_37531,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,point_on_plane(X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,X0,point_on_plane(X0))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ on(point_on_plane(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_37110,c_104,c_37110]) ).
tcf(c_37547,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,point_1_on_line(X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,X0,point_1_on_line(X0))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ on(point_1_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_37108,c_97,c_37108]) ).
tcf(c_37582,plain,
( ( point1 = a_line )
| ( common_point_on_planes(a_line,point1,point1) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,point1,point1)) = a_line )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(point1) ),
inference(superposition,[status(thm)],[c_126,c_37123]) ).
tcf(c_37583,plain,
( ( point2 = a_line )
| ( common_point_on_planes(a_line,point2,point2) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,point2,point2)) = a_line )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(point2) ),
inference(superposition,[status(thm)],[c_127,c_37123]) ).
tcf(c_37584,plain,
( ( point_1_on_line(a_line) = a_line )
| ( common_point_on_planes(a_line,point_1_on_line(a_line),point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,point_1_on_line(a_line),point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_95,c_37123]) ).
tcf(c_37585,plain,
( ( point_2_on_line(a_line) = a_line )
| ( common_point_on_planes(a_line,point_2_on_line(a_line),point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,point_2_on_line(a_line),point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_96,c_37123]) ).
tcf(c_37586,plain,
( ( point_on_plane(a_line) = a_line )
| ( common_point_on_planes(a_line,point_on_plane(a_line),point_on_plane(a_line)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,point_on_plane(a_line),point_on_plane(a_line))) = a_line )
| ~ plane(a_line)
| ~ plane(point_on_plane(a_line))
| ~ line(point_on_plane(a_line))
| ~ point(point_on_plane(a_line)) ),
inference(superposition,[status(thm)],[c_103,c_37123]) ).
tcf(c_37587,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = a_line )
| ( common_point_on_planes(a_line,common_point_on_planes(a_line,X0,X1),common_point_on_planes(a_line,X0,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,common_point_on_planes(a_line,X0,X1),common_point_on_planes(a_line,X0,X1))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(a_line,X0,X1))
| ~ line(common_point_on_planes(a_line,X0,X1))
| ~ point(common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_37123]) ).
tcf(c_37588,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = a_line )
| ( common_point_on_planes(a_line,common_point_on_planes(X0,a_line,X1),common_point_on_planes(X0,a_line,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,common_point_on_planes(X0,a_line,X1),common_point_on_planes(X0,a_line,X1))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(X0,a_line,X1))
| ~ line(common_point_on_planes(X0,a_line,X1))
| ~ point(common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_37123]) ).
tcf(c_37590,plain,
( ( point_1_on_line(a_line) = a_line )
| ( common_point_on_planes(a_line,point_1_on_line(a_line),point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,point_1_on_line(a_line),point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9468,c_37123]) ).
tcf(c_37591,plain,
( ( point_2_on_line(a_line) = a_line )
| ( common_point_on_planes(a_line,point_2_on_line(a_line),point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,point_2_on_line(a_line),point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9364,c_37123]) ).
tcf(c_37593,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ( common_point_on_planes(a_line,line_from_to(X0,point1),line_from_to(X0,point1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_from_to(X0,point1),line_from_to(X0,point1))) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,point1))
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_26554,c_37123]) ).
tcf(c_37594,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ( common_point_on_planes(a_line,line_from_to(point1,X0),line_from_to(point1,X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_from_to(point1,X0),line_from_to(point1,X0))) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point1,X0))
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_25811,c_37123]) ).
tcf(c_37599,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = a_line )
| ( common_point_on_planes(a_line,line_from_to(X0,point2),line_from_to(X0,point2)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_from_to(X0,point2),line_from_to(X0,point2))) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,point2))
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_37123]) ).
tcf(c_37600,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = a_line )
| ( common_point_on_planes(a_line,line_from_to(point2,X0),line_from_to(point2,X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_from_to(point2,X0),line_from_to(point2,X0))) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,X0))
| ~ line(line_from_to(point2,X0))
| ~ point(line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_37123]) ).
tcf(c_37605,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = a_line )
| ( common_point_on_planes(a_line,plane_for_points(X0,X1,point2),plane_for_points(X0,X1,point2)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,plane_for_points(X0,X1,point2),plane_for_points(X0,X1,point2))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(X0,X1,point2))
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19864,c_37123]) ).
tcf(c_37606,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = a_line )
| ( common_point_on_planes(a_line,plane_for_points(X0,X1,point2),plane_for_points(X0,X1,point2)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,plane_for_points(X0,X1,point2),plane_for_points(X0,X1,point2))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X0,X1,point2))
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19399,c_37123]) ).
tcf(c_37607,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = a_line )
| ( common_point_on_planes(a_line,plane_for_points(point2,X0,X1),plane_for_points(point2,X0,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,plane_for_points(point2,X0,X1),plane_for_points(point2,X0,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(point2,X0,X1))
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_19853,c_37123]) ).
tcf(c_37608,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = a_line )
| ( common_point_on_planes(a_line,plane_for_points(point2,X0,X1),plane_for_points(point2,X0,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,plane_for_points(point2,X0,X1),plane_for_points(point2,X0,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(point2,X0,X1))
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_13270,c_37123]) ).
tcf(c_37609,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = a_line )
| ( common_point_on_planes(a_line,plane_for_points(X0,point2,X1),plane_for_points(X0,point2,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,plane_for_points(X0,point2,X1),plane_for_points(X0,point2,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X0,point2,X1))
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_19388,c_37123]) ).
tcf(c_37610,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = a_line )
| ( common_point_on_planes(a_line,plane_for_points(X0,point2,X1),plane_for_points(X0,point2,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,plane_for_points(X0,point2,X1),plane_for_points(X0,point2,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(X0,point2,X1))
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13259,c_37123]) ).
tcf(c_37611,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( common_point_on_planes(a_line,line_through_3_points(point2,X0,X1),line_through_3_points(point2,X0,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_through_3_points(point2,X0,X1),line_through_3_points(point2,X0,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_37123]) ).
tcf(c_37612,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( common_point_on_planes(a_line,line_through_3_points(point2,X0,X1),line_through_3_points(point2,X0,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_through_3_points(point2,X0,X1),line_through_3_points(point2,X0,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_37123]) ).
tcf(c_37613,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( common_point_on_planes(a_line,line_through_3_points(X0,point2,X1),line_through_3_points(X0,point2,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_through_3_points(X0,point2,X1),line_through_3_points(X0,point2,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_37123]) ).
tcf(c_37614,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( common_point_on_planes(a_line,line_through_3_points(X0,point2,X1),line_through_3_points(X0,point2,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_through_3_points(X0,point2,X1),line_through_3_points(X0,point2,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_37123]) ).
tcf(c_37615,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( common_point_on_planes(a_line,line_through_3_points(X0,X1,point2),line_through_3_points(X0,X1,point2)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_through_3_points(X0,X1,point2),line_through_3_points(X0,X1,point2))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_37123]) ).
tcf(c_37616,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( common_point_on_planes(a_line,line_through_3_points(X0,X1,point2),line_through_3_points(X0,X1,point2)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_through_3_points(X0,X1,point2),line_through_3_points(X0,X1,point2))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_37123]) ).
tcf(c_37617,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(X0,a_line) = a_line )
| ( common_point_on_planes(a_line,line_from_to(X0,a_line),line_from_to(X0,a_line)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_from_to(X0,a_line),line_from_to(X0,a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,a_line))
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line)) ),
inference(superposition,[status(thm)],[c_30359,c_37123]) ).
tcf(c_37618,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(a_line,X0) = a_line )
| ( common_point_on_planes(a_line,line_from_to(a_line,X0),line_from_to(a_line,X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,line_from_to(a_line,X0),line_from_to(a_line,X0))) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(a_line,X0))
| ~ line(line_from_to(a_line,X0))
| ~ point(line_from_to(a_line,X0)) ),
inference(superposition,[status(thm)],[c_29574,c_37123]) ).
tcf(c_37619,plain,
( ( point2 = a_line )
| ( common_point_on_planes(a_line,point2,point2) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,point2,point2)) = a_line )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37583,c_123]) ).
tcf(c_37626,plain,
( ( point1 = a_line )
| ( common_point_on_planes(a_line,point1,point1) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,point1,point1)) = a_line )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37582,c_122]) ).
tcf(c_38147,plain,
( ( point1 = a_line )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1) ),
inference(global_subsumption_just,[status(thm)],[c_37626,c_122,c_126,c_136,c_143,c_1808,c_8953,c_8955,c_8960,c_17750,c_22760,c_33559]) ).
tcf(c_38173,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = point1 )
| ( line_from_to(line_from_to(X0,point1),point1) = a_line )
| ~ plane(a_line)
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_93,c_26612]) ).
tcf(c_38174,plain,
( ( point1 = point2 )
| ( line_from_to(point2,point1) = point1 )
| ( line_from_to(line_from_to(point2,point1),point1) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ point(line_from_to(point2,point1)) ),
inference(superposition,[status(thm)],[c_9035,c_26612]) ).
tcf(c_38179,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = point1 )
| ( line_from_to(line_from_to(X0,point1),point1) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38173,c_122]) ).
tcf(c_38208,plain,
( ( point1 = point2 )
| ( line_from_to(point2,point1) = point1 )
| ( line_from_to(line_from_to(point2,point1),point1) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(superposition,[status(thm)],[c_9035,c_38179]) ).
tcf(c_38229,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = point1 )
| ( line_from_to(point1,line_from_to(X0,point1)) = a_line )
| ~ plane(a_line)
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_93,c_26613]) ).
tcf(c_38230,plain,
( ( point1 = point2 )
| ( line_from_to(point2,point1) = point1 )
| ( line_from_to(point1,line_from_to(point2,point1)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ point(line_from_to(point2,point1)) ),
inference(superposition,[status(thm)],[c_9035,c_26613]) ).
tcf(c_38235,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = point1 )
| ( line_from_to(point1,line_from_to(X0,point1)) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38229,c_122]) ).
tcf(c_38264,plain,
( ( point1 = point2 )
| ( line_from_to(point2,point1) = point1 )
| ( line_from_to(point1,line_from_to(point2,point1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(superposition,[status(thm)],[c_9035,c_38235]) ).
tcf(c_38285,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = point2 )
| ( line_from_to(line_from_to(X0,point1),point2) = a_line )
| ~ plane(a_line)
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_93,c_26614]) ).
tcf(c_38286,plain,
( ( point1 = point2 )
| ( line_from_to(point2,point1) = point2 )
| ( line_from_to(line_from_to(point2,point1),point2) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ point(line_from_to(point2,point1)) ),
inference(superposition,[status(thm)],[c_9035,c_26614]) ).
tcf(c_38291,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = point2 )
| ( line_from_to(line_from_to(X0,point1),point2) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38285,c_122]) ).
tcf(c_38320,plain,
( ( point1 = point2 )
| ( line_from_to(point2,point1) = point2 )
| ( line_from_to(line_from_to(point2,point1),point2) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(superposition,[status(thm)],[c_9035,c_38291]) ).
tcf(c_38341,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = point2 )
| ( line_from_to(point2,line_from_to(X0,point1)) = a_line )
| ~ plane(a_line)
| ~ point(point1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_93,c_26615]) ).
tcf(c_38342,plain,
( ( point1 = point2 )
| ( line_from_to(point2,point1) = point2 )
| ( line_from_to(point2,line_from_to(point2,point1)) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ point(point2)
| ~ on(point2,a_line)
| ~ point(line_from_to(point2,point1)) ),
inference(superposition,[status(thm)],[c_9035,c_26615]) ).
tcf(c_38347,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = point2 )
| ( line_from_to(point2,line_from_to(X0,point1)) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ point(line_from_to(X0,point1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38341,c_122]) ).
tcf(c_38376,plain,
( ( point1 = point2 )
| ( line_from_to(point2,point1) = point2 )
| ( line_from_to(point2,line_from_to(point2,point1)) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(point2)
| ~ on(point2,a_line) ),
inference(superposition,[status(thm)],[c_9035,c_38347]) ).
tcf(c_38413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( point_1_on_line(plane_for_points(X0,X1,X2)) = X2 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_1_on_line(plane_for_points(X0,X1,X2)))
| ~ on(point_1_on_line(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_95,c_3694]) ).
tcf(c_38414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( point_2_on_line(plane_for_points(X0,X1,X2)) = X2 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_2_on_line(plane_for_points(X0,X1,X2)))
| ~ on(point_2_on_line(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_96,c_3694]) ).
tcf(c_38415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( point_on_plane(plane_for_points(X0,X1,X2)) = X2 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(point_on_plane(plane_for_points(X0,X1,X2)))
| ~ on(point_on_plane(plane_for_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_103,c_3694]) ).
tcf(c_38417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X0,X3)
| ~ line(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_3694]) ).
tcf(c_38418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X1,X3)
| ~ line(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_108,c_3694]) ).
tcf(c_38419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X5 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4) = X2 )
| ~ plane(X3)
| ~ line(X5)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X2,X5)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ on(X4,plane_for_points(X0,X1,X2))
| ~ point(common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4))
| ~ on(common_point_on_planes(plane_for_points(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_113,c_3694]) ).
tcf(c_38420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( collinear(X1,X2,X3)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( plane_for_points(X1,X2,X3) = X5 )
| ( plane_for_points(X1,X2,X3) = X0 )
| ( common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4) = X3 )
| ~ plane(X0)
| ~ line(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X4,X0)
| ~ on(X3,X5)
| ~ plane(plane_for_points(X1,X2,X3))
| ~ line(plane_for_points(X1,X2,X3))
| ~ on(X4,plane_for_points(X1,X2,X3))
| ~ point(common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4))
| ~ on(common_point_on_planes(X0,plane_for_points(X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_114,c_3694]) ).
tcf(c_38421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = X3 )
| ( plane_for_points(X0,X1,X2) = X2 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ plane(plane_for_points(X0,X1,X2))
| ~ line(plane_for_points(X0,X1,X2))
| ~ point(plane_for_points(X0,X1,X2))
| ~ on(plane_for_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_18002,c_3694]) ).
tcf(c_38544,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,point_2_on_line(X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,X0,point_2_on_line(X0))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ on(point_2_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_37109,c_98,c_37109]) ).
tcf(c_38570,plain,
( ( point_on_plane(a_line) = a_line )
| ( common_point_on_planes(a_line,point_on_plane(a_line),point_on_plane(a_line)) = point2 )
| ( line_from_to(point2,common_point_on_planes(a_line,point_on_plane(a_line),point_on_plane(a_line))) = a_line )
| ~ plane(a_line)
| ~ plane(point_on_plane(a_line))
| ~ line(point_on_plane(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37586,c_104]) ).
tcf(c_38607,plain,
! [X0: $i,X1: $i] :
( ( X1 = a_line )
| ( common_point_on_planes(X1,a_line,X0) = point2 )
| ( line_from_to(point2,common_point_on_planes(X1,a_line,X0)) = a_line )
| ~ plane(a_line)
| ~ plane(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(superposition,[status(thm)],[c_115,c_9031]) ).
tcf(c_38643,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ( common_point_on_planes(line_from_to(X0,X1),a_line,X1) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_from_to(X0,X1),a_line,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_92,c_38607]) ).
tcf(c_38644,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,point_1_on_line(X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(X0,a_line,point_1_on_line(X0))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ point(point_1_on_line(X0))
| ~ on(point_1_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_95,c_38607]) ).
tcf(c_38645,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,point_2_on_line(X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(X0,a_line,point_2_on_line(X0))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ point(point_2_on_line(X0))
| ~ on(point_2_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_96,c_38607]) ).
tcf(c_38646,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,point_on_plane(X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(X0,a_line,point_on_plane(X0))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(point_on_plane(X0))
| ~ on(point_on_plane(X0),a_line) ),
inference(superposition,[status(thm)],[c_103,c_38607]) ).
tcf(c_38647,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(plane_for_points(X0,X1,X2),a_line,X2) = point2 )
| ( line_from_to(point2,common_point_on_planes(plane_for_points(X0,X1,X2),a_line,X2)) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ plane(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_109,c_38607]) ).
tcf(c_38648,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(line_through_3_points(X0,X1,X2),a_line,X0) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_through_3_points(X0,X1,X2),a_line,X0)) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_38607]) ).
tcf(c_38649,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(line_through_3_points(X0,X1,X2),a_line,X1) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_through_3_points(X0,X1,X2),a_line,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_118,c_38607]) ).
tcf(c_38650,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(line_through_3_points(X0,X1,X2),a_line,X2) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_through_3_points(X0,X1,X2),a_line,X2)) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_119,c_38607]) ).
tcf(c_38651,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ( common_point_on_planes(line_from_to(X0,X1),a_line,X0) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_from_to(X0,X1),a_line,X0)) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_91,c_38607]) ).
tcf(c_38652,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(plane_for_points(X0,X1,X2),a_line,X0) = point2 )
| ( line_from_to(point2,common_point_on_planes(plane_for_points(X0,X1,X2),a_line,X0)) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_38607]) ).
tcf(c_38653,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(plane_for_points(X0,X1,X2),a_line,X1) = point2 )
| ( line_from_to(point2,common_point_on_planes(plane_for_points(X0,X1,X2),a_line,X1)) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_108,c_38607]) ).
tcf(c_38654,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = a_line )
| ( X0 = X1 )
| ( common_point_on_planes(X0,a_line,common_point_on_planes(X0,X1,X2)) = point2 )
| ( line_from_to(point2,common_point_on_planes(X0,a_line,common_point_on_planes(X0,X1,X2))) = a_line )
| ~ plane(a_line)
| ~ plane(X1)
| ~ plane(X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_113,c_38607]) ).
tcf(c_38655,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = X1 )
| ( common_point_on_planes(X1,a_line,common_point_on_planes(X0,X1,X2)) = point2 )
| ( line_from_to(point2,common_point_on_planes(X1,a_line,common_point_on_planes(X0,X1,X2))) = a_line )
| ~ plane(a_line)
| ~ plane(X1)
| ~ plane(X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_114,c_38607]) ).
tcf(c_38659,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X0) = point2 )
| ( line_from_to(point2,common_point_on_planes(X0,a_line,X0)) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_18002,c_38607]) ).
tcf(c_38890,plain,
( ( point1 = a_line )
| ( common_point_on_planes(point1,a_line,point1) = point2 )
| ( line_from_to(point2,common_point_on_planes(point1,a_line,point1)) = a_line )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1)
| ~ point(point1) ),
inference(superposition,[status(thm)],[c_126,c_38659]) ).
tcf(c_38891,plain,
( ( point2 = a_line )
| ( common_point_on_planes(point2,a_line,point2) = point2 )
| ( line_from_to(point2,common_point_on_planes(point2,a_line,point2)) = a_line )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2)
| ~ point(point2) ),
inference(superposition,[status(thm)],[c_127,c_38659]) ).
tcf(c_38892,plain,
( ( point_1_on_line(a_line) = a_line )
| ( common_point_on_planes(point_1_on_line(a_line),a_line,point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,common_point_on_planes(point_1_on_line(a_line),a_line,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_95,c_38659]) ).
tcf(c_38893,plain,
( ( point_2_on_line(a_line) = a_line )
| ( common_point_on_planes(point_2_on_line(a_line),a_line,point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,common_point_on_planes(point_2_on_line(a_line),a_line,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ line(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_96,c_38659]) ).
tcf(c_38894,plain,
( ( point_on_plane(a_line) = a_line )
| ( common_point_on_planes(point_on_plane(a_line),a_line,point_on_plane(a_line)) = point2 )
| ( line_from_to(point2,common_point_on_planes(point_on_plane(a_line),a_line,point_on_plane(a_line))) = a_line )
| ~ plane(a_line)
| ~ plane(point_on_plane(a_line))
| ~ line(point_on_plane(a_line))
| ~ point(point_on_plane(a_line)) ),
inference(superposition,[status(thm)],[c_103,c_38659]) ).
tcf(c_38895,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X1) = a_line )
| ( common_point_on_planes(common_point_on_planes(a_line,X0,X1),a_line,common_point_on_planes(a_line,X0,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(common_point_on_planes(a_line,X0,X1),a_line,common_point_on_planes(a_line,X0,X1))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(a_line,X0,X1))
| ~ line(common_point_on_planes(a_line,X0,X1))
| ~ point(common_point_on_planes(a_line,X0,X1)) ),
inference(superposition,[status(thm)],[c_113,c_38659]) ).
tcf(c_38896,plain,
! [X0: $i,X1: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,X1) = a_line )
| ( common_point_on_planes(common_point_on_planes(X0,a_line,X1),a_line,common_point_on_planes(X0,a_line,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(common_point_on_planes(X0,a_line,X1),a_line,common_point_on_planes(X0,a_line,X1))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(X1)
| ~ on(X1,a_line)
| ~ on(X1,X0)
| ~ plane(common_point_on_planes(X0,a_line,X1))
| ~ line(common_point_on_planes(X0,a_line,X1))
| ~ point(common_point_on_planes(X0,a_line,X1)) ),
inference(superposition,[status(thm)],[c_114,c_38659]) ).
tcf(c_38898,plain,
( ( point_1_on_line(a_line) = a_line )
| ( common_point_on_planes(point_1_on_line(a_line),a_line,point_1_on_line(a_line)) = point2 )
| ( line_from_to(point2,common_point_on_planes(point_1_on_line(a_line),a_line,point_1_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ plane(point_1_on_line(a_line))
| ~ line(point_1_on_line(a_line))
| ~ point(point_1_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9468,c_38659]) ).
tcf(c_38899,plain,
( ( point_2_on_line(a_line) = a_line )
| ( common_point_on_planes(point_2_on_line(a_line),a_line,point_2_on_line(a_line)) = point2 )
| ( line_from_to(point2,common_point_on_planes(point_2_on_line(a_line),a_line,point_2_on_line(a_line))) = a_line )
| ~ plane(a_line)
| ~ plane(point_2_on_line(a_line))
| ~ line(point_2_on_line(a_line))
| ~ point(point_2_on_line(a_line)) ),
inference(superposition,[status(thm)],[c_9364,c_38659]) ).
tcf(c_38901,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(X0,point1) = a_line )
| ( common_point_on_planes(line_from_to(X0,point1),a_line,line_from_to(X0,point1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_from_to(X0,point1),a_line,line_from_to(X0,point1))) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,point1))
| ~ line(line_from_to(X0,point1))
| ~ point(line_from_to(X0,point1)) ),
inference(superposition,[status(thm)],[c_26554,c_38659]) ).
tcf(c_38902,plain,
! [X0: $i] :
( ( X0 = point1 )
| ( line_from_to(point1,X0) = a_line )
| ( common_point_on_planes(line_from_to(point1,X0),a_line,line_from_to(point1,X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_from_to(point1,X0),a_line,line_from_to(point1,X0))) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point1,X0))
| ~ line(line_from_to(point1,X0))
| ~ point(line_from_to(point1,X0)) ),
inference(superposition,[status(thm)],[c_25811,c_38659]) ).
tcf(c_38907,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(X0,point2) = a_line )
| ( common_point_on_planes(line_from_to(X0,point2),a_line,line_from_to(X0,point2)) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_from_to(X0,point2),a_line,line_from_to(X0,point2))) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,point2))
| ~ line(line_from_to(X0,point2))
| ~ point(line_from_to(X0,point2)) ),
inference(superposition,[status(thm)],[c_16653,c_38659]) ).
tcf(c_38908,plain,
! [X0: $i] :
( ( X0 = point2 )
| ( line_from_to(point2,X0) = a_line )
| ( common_point_on_planes(line_from_to(point2,X0),a_line,line_from_to(point2,X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_from_to(point2,X0),a_line,line_from_to(point2,X0))) = a_line )
| ~ plane(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(point2,X0))
| ~ line(line_from_to(point2,X0))
| ~ point(line_from_to(point2,X0)) ),
inference(superposition,[status(thm)],[c_12003,c_38659]) ).
tcf(c_38913,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = a_line )
| ( common_point_on_planes(plane_for_points(X0,X1,point2),a_line,plane_for_points(X0,X1,point2)) = point2 )
| ( line_from_to(point2,common_point_on_planes(plane_for_points(X0,X1,point2),a_line,plane_for_points(X0,X1,point2))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(X0,X1,point2))
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19864,c_38659]) ).
tcf(c_38914,plain,
! [X0: $i,X1: $i] :
( collinear(X0,X1,point2)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,point2) = a_line )
| ( common_point_on_planes(plane_for_points(X0,X1,point2),a_line,plane_for_points(X0,X1,point2)) = point2 )
| ( line_from_to(point2,common_point_on_planes(plane_for_points(X0,X1,point2),a_line,plane_for_points(X0,X1,point2))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X0,X1,point2))
| ~ line(plane_for_points(X0,X1,point2))
| ~ point(plane_for_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_19399,c_38659]) ).
tcf(c_38915,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = a_line )
| ( common_point_on_planes(plane_for_points(point2,X0,X1),a_line,plane_for_points(point2,X0,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(plane_for_points(point2,X0,X1),a_line,plane_for_points(point2,X0,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(point2,X0,X1))
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_19853,c_38659]) ).
tcf(c_38916,plain,
! [X0: $i,X1: $i] :
( collinear(point2,X0,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(point2,X0,X1) = a_line )
| ( common_point_on_planes(plane_for_points(point2,X0,X1),a_line,plane_for_points(point2,X0,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(plane_for_points(point2,X0,X1),a_line,plane_for_points(point2,X0,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(point2,X0,X1))
| ~ line(plane_for_points(point2,X0,X1))
| ~ point(plane_for_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_13270,c_38659]) ).
tcf(c_38917,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = a_line )
| ( common_point_on_planes(plane_for_points(X0,point2,X1),a_line,plane_for_points(X0,point2,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(plane_for_points(X0,point2,X1),a_line,plane_for_points(X0,point2,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X0,point2,X1))
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_19388,c_38659]) ).
tcf(c_38918,plain,
! [X0: $i,X1: $i] :
( collinear(X0,point2,X1)
| ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( plane_for_points(X0,point2,X1) = a_line )
| ( common_point_on_planes(plane_for_points(X0,point2,X1),a_line,plane_for_points(X0,point2,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(plane_for_points(X0,point2,X1),a_line,plane_for_points(X0,point2,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(X0,point2,X1))
| ~ line(plane_for_points(X0,point2,X1))
| ~ point(plane_for_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13259,c_38659]) ).
tcf(c_38919,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( common_point_on_planes(line_through_3_points(point2,X0,X1),a_line,line_through_3_points(point2,X0,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_through_3_points(point2,X0,X1),a_line,line_through_3_points(point2,X0,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14815,c_38659]) ).
tcf(c_38920,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(point2,X0,X1) = a_line )
| ( common_point_on_planes(line_through_3_points(point2,X0,X1),a_line,line_through_3_points(point2,X0,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_through_3_points(point2,X0,X1),a_line,line_through_3_points(point2,X0,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(point2,X0,X1)
| ~ plane(line_through_3_points(point2,X0,X1))
| ~ line(line_through_3_points(point2,X0,X1))
| ~ point(line_through_3_points(point2,X0,X1)) ),
inference(superposition,[status(thm)],[c_14093,c_38659]) ).
tcf(c_38921,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( common_point_on_planes(line_through_3_points(X0,point2,X1),a_line,line_through_3_points(X0,point2,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_through_3_points(X0,point2,X1),a_line,line_through_3_points(X0,point2,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_14805,c_38659]) ).
tcf(c_38922,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,point2,X1) = a_line )
| ( common_point_on_planes(line_through_3_points(X0,point2,X1),a_line,line_through_3_points(X0,point2,X1)) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_through_3_points(X0,point2,X1),a_line,line_through_3_points(X0,point2,X1))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,point2,X1)
| ~ plane(line_through_3_points(X0,point2,X1))
| ~ line(line_through_3_points(X0,point2,X1))
| ~ point(line_through_3_points(X0,point2,X1)) ),
inference(superposition,[status(thm)],[c_13784,c_38659]) ).
tcf(c_38923,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( common_point_on_planes(line_through_3_points(X0,X1,point2),a_line,line_through_3_points(X0,X1,point2)) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_through_3_points(X0,X1,point2),a_line,line_through_3_points(X0,X1,point2))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_14083,c_38659]) ).
tcf(c_38924,plain,
! [X0: $i,X1: $i] :
( ( X1 = point2 )
| ( X0 = point2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,point2) = a_line )
| ( common_point_on_planes(line_through_3_points(X0,X1,point2),a_line,line_through_3_points(X0,X1,point2)) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_through_3_points(X0,X1,point2),a_line,line_through_3_points(X0,X1,point2))) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,point2)
| ~ plane(line_through_3_points(X0,X1,point2))
| ~ line(line_through_3_points(X0,X1,point2))
| ~ point(line_through_3_points(X0,X1,point2)) ),
inference(superposition,[status(thm)],[c_13774,c_38659]) ).
tcf(c_38925,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(X0,a_line) = a_line )
| ( common_point_on_planes(line_from_to(X0,a_line),a_line,line_from_to(X0,a_line)) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_from_to(X0,a_line),a_line,line_from_to(X0,a_line))) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,a_line))
| ~ line(line_from_to(X0,a_line))
| ~ point(line_from_to(X0,a_line)) ),
inference(superposition,[status(thm)],[c_30359,c_38659]) ).
tcf(c_38926,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( line_from_to(a_line,X0) = a_line )
| ( common_point_on_planes(line_from_to(a_line,X0),a_line,line_from_to(a_line,X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(line_from_to(a_line,X0),a_line,line_from_to(a_line,X0))) = a_line )
| ~ plane(a_line)
| ~ point(a_line)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(a_line,X0))
| ~ line(line_from_to(a_line,X0))
| ~ point(line_from_to(a_line,X0)) ),
inference(superposition,[status(thm)],[c_29574,c_38659]) ).
tcf(c_38927,plain,
( ( point2 = a_line )
| ( common_point_on_planes(point2,a_line,point2) = point2 )
| ( line_from_to(point2,common_point_on_planes(point2,a_line,point2)) = a_line )
| ~ plane(a_line)
| ~ plane(point2)
| ~ line(point2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38891,c_123]) ).
tcf(c_38934,plain,
( ( point1 = a_line )
| ( common_point_on_planes(point1,a_line,point1) = point2 )
| ( line_from_to(point2,common_point_on_planes(point1,a_line,point1)) = a_line )
| ~ plane(a_line)
| ~ plane(point1)
| ~ line(point1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38890,c_122]) ).
tcf(c_39689,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,point_on_plane(X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(X0,a_line,point_on_plane(X0))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ on(point_on_plane(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_38646,c_104,c_38646]) ).
tcf(c_39757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X1,X2,X3) = X4 )
| ~ line(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X4)
| ~ on(X0,X4)
| ~ collinear(X1,X2,X3)
| ~ on(X0,line_through_3_points(X1,X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3695,c_120]) ).
tcf(c_39800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( point_1_on_line(line_through_3_points(X0,X1,X2)) = X0 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(point_1_on_line(line_through_3_points(X0,X1,X2)))
| ~ on(point_1_on_line(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_95,c_39757]) ).
tcf(c_39801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( point_2_on_line(line_through_3_points(X0,X1,X2)) = X0 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(point_2_on_line(line_through_3_points(X0,X1,X2)))
| ~ on(point_2_on_line(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_96,c_39757]) ).
tcf(c_39802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( point_on_plane(line_through_3_points(X0,X1,X2)) = X0 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ point(point_on_plane(line_through_3_points(X0,X1,X2)))
| ~ on(point_on_plane(line_through_3_points(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_103,c_39757]) ).
tcf(c_39804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,X3)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_118,c_39757]) ).
tcf(c_39805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,X3)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_119,c_39757]) ).
tcf(c_39806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X5 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4) = X0 )
| ~ plane(X3)
| ~ line(X5)
| ~ point(X4)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X4,X3)
| ~ on(X0,X5)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ on(X4,line_through_3_points(X0,X1,X2))
| ~ point(common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4))
| ~ on(common_point_on_planes(line_through_3_points(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_113,c_39757]) ).
tcf(c_39807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ( line_through_3_points(X1,X2,X3) = X5 )
| ( line_through_3_points(X1,X2,X3) = X0 )
| ( common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4) = X1 )
| ~ plane(X0)
| ~ line(X5)
| ~ point(X4)
| ~ point(X3)
| ~ point(X2)
| ~ point(X1)
| ~ on(X4,X0)
| ~ on(X1,X5)
| ~ collinear(X1,X2,X3)
| ~ plane(line_through_3_points(X1,X2,X3))
| ~ on(X4,line_through_3_points(X1,X2,X3))
| ~ point(common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4))
| ~ on(common_point_on_planes(X0,line_through_3_points(X1,X2,X3),X4),X5) ),
inference(superposition,[status(thm)],[c_114,c_39757]) ).
tcf(c_39808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = X3 )
| ( line_through_3_points(X0,X1,X2) = X0 )
| ~ line(X3)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,X3)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2))
| ~ line(line_through_3_points(X0,X1,X2))
| ~ point(line_through_3_points(X0,X1,X2))
| ~ on(line_through_3_points(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_18002,c_39757]) ).
tcf(c_39926,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,point_1_on_line(X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(X0,a_line,point_1_on_line(X0))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ on(point_1_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_38644,c_97,c_38644]) ).
tcf(c_39945,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(X0,a_line,point_2_on_line(X0)) = point2 )
| ( line_from_to(point2,common_point_on_planes(X0,a_line,point_2_on_line(X0))) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ on(point_2_on_line(X0),a_line) ),
inference(global_subsumption_just,[status(thm)],[c_38645,c_98,c_38645]) ).
tcf(c_39971,plain,
( ( point_on_plane(a_line) = a_line )
| ( common_point_on_planes(point_on_plane(a_line),a_line,point_on_plane(a_line)) = point2 )
| ( line_from_to(point2,common_point_on_planes(point_on_plane(a_line),a_line,point_on_plane(a_line))) = a_line )
| ~ plane(a_line)
| ~ plane(point_on_plane(a_line))
| ~ line(point_on_plane(a_line)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38894,c_104]) ).
tcf(c_39999,plain,
! [X0: $i,X1: $i] :
( ( X1 = a_line )
| ( common_point_on_planes(a_line,X1,X0) = point2 )
| ( line_from_to(common_point_on_planes(a_line,X1,X0),point2) = a_line )
| ~ plane(a_line)
| ~ plane(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ on(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11039,c_115]) ).
tcf(c_40026,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ( common_point_on_planes(a_line,line_from_to(X0,X1),X1) = point2 )
| ( line_from_to(common_point_on_planes(a_line,line_from_to(X0,X1),X1),point2) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_92,c_39999]) ).
tcf(c_40027,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,point_1_on_line(X0)) = point2 )
| ( line_from_to(common_point_on_planes(a_line,X0,point_1_on_line(X0)),point2) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ point(point_1_on_line(X0))
| ~ on(point_1_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_95,c_39999]) ).
tcf(c_40028,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,point_2_on_line(X0)) = point2 )
| ( line_from_to(common_point_on_planes(a_line,X0,point_2_on_line(X0)),point2) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ point(point_2_on_line(X0))
| ~ on(point_2_on_line(X0),a_line) ),
inference(superposition,[status(thm)],[c_96,c_39999]) ).
tcf(c_40029,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,point_on_plane(X0)) = point2 )
| ( line_from_to(common_point_on_planes(a_line,X0,point_on_plane(X0)),point2) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ point(point_on_plane(X0))
| ~ on(point_on_plane(X0),a_line) ),
inference(superposition,[status(thm)],[c_103,c_39999]) ).
tcf(c_40030,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(a_line,plane_for_points(X0,X1,X2),X2) = point2 )
| ( line_from_to(common_point_on_planes(a_line,plane_for_points(X0,X1,X2),X2),point2) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ plane(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_109,c_39999]) ).
tcf(c_40031,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(a_line,line_through_3_points(X0,X1,X2),X0) = point2 )
| ( line_from_to(common_point_on_planes(a_line,line_through_3_points(X0,X1,X2),X0),point2) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_117,c_39999]) ).
tcf(c_40032,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(a_line,line_through_3_points(X0,X1,X2),X1) = point2 )
| ( line_from_to(common_point_on_planes(a_line,line_through_3_points(X0,X1,X2),X1),point2) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_118,c_39999]) ).
tcf(c_40033,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( line_through_3_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(a_line,line_through_3_points(X0,X1,X2),X2) = point2 )
| ( line_from_to(common_point_on_planes(a_line,line_through_3_points(X0,X1,X2),X2),point2) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X2,a_line)
| ~ collinear(X0,X1,X2)
| ~ plane(line_through_3_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_119,c_39999]) ).
tcf(c_40034,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( line_from_to(X0,X1) = a_line )
| ( common_point_on_planes(a_line,line_from_to(X0,X1),X0) = point2 )
| ( line_from_to(common_point_on_planes(a_line,line_from_to(X0,X1),X0),point2) = a_line )
| ~ plane(a_line)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(line_from_to(X0,X1)) ),
inference(superposition,[status(thm)],[c_91,c_39999]) ).
tcf(c_40035,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(a_line,plane_for_points(X0,X1,X2),X0) = point2 )
| ( line_from_to(common_point_on_planes(a_line,plane_for_points(X0,X1,X2),X0),point2) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X0,a_line)
| ~ plane(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_107,c_39999]) ).
tcf(c_40036,plain,
! [X0: $i,X1: $i,X2: $i] :
( collinear(X0,X1,X2)
| ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ( plane_for_points(X0,X1,X2) = a_line )
| ( common_point_on_planes(a_line,plane_for_points(X0,X1,X2),X1) = point2 )
| ( line_from_to(common_point_on_planes(a_line,plane_for_points(X0,X1,X2),X1),point2) = a_line )
| ~ plane(a_line)
| ~ point(X2)
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| ~ plane(plane_for_points(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_108,c_39999]) ).
tcf(c_40037,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = a_line )
| ( X0 = X1 )
| ( common_point_on_planes(a_line,X0,common_point_on_planes(X0,X1,X2)) = point2 )
| ( line_from_to(common_point_on_planes(a_line,X0,common_point_on_planes(X0,X1,X2)),point2) = a_line )
| ~ plane(a_line)
| ~ plane(X1)
| ~ plane(X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_113,c_39999]) ).
tcf(c_40038,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = a_line )
| ( X0 = X1 )
| ( common_point_on_planes(a_line,X1,common_point_on_planes(X0,X1,X2)) = point2 )
| ( line_from_to(common_point_on_planes(a_line,X1,common_point_on_planes(X0,X1,X2)),point2) = a_line )
| ~ plane(a_line)
| ~ plane(X1)
| ~ plane(X0)
| ~ point(X2)
| ~ on(X2,X1)
| ~ on(X2,X0)
| ~ point(common_point_on_planes(X0,X1,X2))
| ~ on(common_point_on_planes(X0,X1,X2),a_line) ),
inference(superposition,[status(thm)],[c_114,c_39999]) ).
tcf(c_40042,plain,
! [X0: $i] :
( ( X0 = a_line )
| ( common_point_on_planes(a_line,X0,X0) = point2 )
| ( line_from_to(common_point_on_planes(a_line,X0,X0),point2) = a_line )
| ~ plane(a_line)
| ~ plane(X0)
| ~ line(X0)
| ~ point(X0)
| ~ on(X0,a_line) ),
inference(superposition,[status(thm)],[c_18002,c_39999]) ).
tcf(c_40354,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_40042,c_40038,c_40037,c_40036,c_40035,c_40034,c_40033,c_40032,c_40031,c_40030,c_40029,c_40028,c_40027,c_40026,c_39999,c_39971,c_39945,c_39926,c_39808,c_39807,c_39806,c_39805,c_39804,c_39802,c_39801,c_39800,c_39757,c_39689,c_38934,c_38927,c_38926,c_38925,c_38924,c_38923,c_38922,c_38921,c_38920,c_38919,c_38918,c_38917,c_38916,c_38915,c_38914,c_38913,c_38908,c_38907,c_38902,c_38901,c_38899,c_38898,c_38896,c_38895,c_38894,c_38893,c_38892,c_38891,c_38890,c_38659,c_38655,c_38654,c_38653,c_38652,c_38651,c_38650,c_38649,c_38648,c_38647,c_38646,c_38645,c_38644,c_38643,c_38607,c_38570,c_38544,c_38421,c_38420,c_38419,c_38418,c_38417,c_38415,c_38414,c_38413,c_38376,c_38347,c_38342,c_38341,c_38320,c_38291,c_38286,c_38285,c_38264,c_38235,c_38230,c_38229,c_38208,c_38179,c_38174,c_38173,c_38147,c_37626,c_37619,c_37618,c_37617,c_37616,c_37615,c_37614,c_37613,c_37612,c_37611,c_37610,c_37609,c_37608,c_37607,c_37606,c_37605,c_37600,c_37599,c_37594,c_37593,c_37591,c_37590,c_37588,c_37587,c_37586,c_37585,c_37584,c_37583,c_37582,c_37547,c_37531,c_37123,c_37119,c_37118,c_37117,c_37116,c_37115,c_37114,c_37113,c_37112,c_37111,c_37110,c_37109,c_37108,c_37107,c_37080,c_37040,c_37027,c_37024,c_36995,c_36993,c_36990,c_36989,c_36971,c_36968,c_36939,c_36937,c_36934,c_36933,c_36915,c_36912,c_36883,c_36881,c_36878,c_36877,c_36859,c_36856,c_36827,c_36825,c_36822,c_36821,c_36800,c_36770,c_36768,c_36765,c_36764,c_36743,c_36713,c_36711,c_36708,c_36707,c_36570,c_36553,c_36536,c_36518,c_36473,c_36459,c_36310,c_36309,c_36308,c_36307,c_36306,c_36305,c_36304,c_36303,c_36302,c_36301,c_36300,c_36299,c_36298,c_36297,c_36294,c_36291,c_36290,c_36289,c_36288,c_36287,c_36081,c_36064,c_36047,c_36029,c_35984,c_35970,c_35821,c_35820,c_35819,c_35818,c_35817,c_35816,c_35815,c_35814,c_35813,c_35812,c_35811,c_35810,c_35809,c_35808,c_35805,c_35802,c_35801,c_35800,c_35799,c_35798,c_35659,c_35642,c_35625,c_35607,c_35562,c_35548,c_35399,c_35398,c_35397,c_35396,c_35395,c_35394,c_35393,c_35392,c_35391,c_35390,c_35389,c_35388,c_35387,c_35386,c_35383,c_35380,c_35379,c_35378,c_35377,c_35376,c_35351,c_35321,c_35319,c_35316,c_35315,c_35294,c_35264,c_35262,c_35259,c_35258,c_35119,c_35102,c_35085,c_35067,c_35022,c_35008,c_34859,c_34858,c_34857,c_34856,c_34855,c_34854,c_34853,c_34852,c_34851,c_34850,c_34849,c_34848,c_34847,c_34846,c_34843,c_34840,c_34839,c_34838,c_34837,c_34836,c_34681,c_34664,c_34647,c_34629,c_34584,c_34570,c_34421,c_34420,c_34419,c_34418,c_34417,c_34416,c_34415,c_34414,c_34413,c_34412,c_34411,c_34410,c_34409,c_34408,c_34405,c_34402,c_34401,c_34400,c_34399,c_34398,c_34286,c_34269,c_34252,c_34234,c_34189,c_34175,c_34026,c_34025,c_34024,c_34023,c_34022,c_34021,c_34020,c_34019,c_34018,c_34017,c_34016,c_34015,c_34014,c_34013,c_34010,c_34007,c_34006,c_34005,c_34004,c_34003,c_33766,c_33763,c_33762,c_33761,c_33760,c_33759,c_33758,c_33757,c_33756,c_33654,c_33624,c_33594,c_33302,c_33301,c_33299,c_33298,c_33297,c_33296,c_33295,c_33294,c_33293,c_33292,c_33094,c_33093,c_33092,c_33091,c_33090,c_33054,c_33032,c_33022,c_33009,c_32484,c_32483,c_32482,c_32481,c_32480,c_32479,c_32478,c_32477,c_32472,c_32471,c_32466,c_32465,c_32463,c_32462,c_32460,c_32459,c_32458,c_32457,c_32456,c_32429,c_32396,c_32206,c_32205,c_32204,c_32202,c_32201,c_32200,c_32199,c_32198,c_32145,c_32144,c_32115,c_32094,c_32093,c_32064,c_32043,c_32042,c_32019,c_32009,c_31996,c_31602,c_31601,c_31600,c_31599,c_31598,c_31597,c_31596,c_31595,c_31590,c_31589,c_31584,c_31583,c_31581,c_31580,c_31578,c_31577,c_31576,c_31575,c_31574,c_31558,c_31529,c_31497,c_31484,c_31479,c_31454,c_31441,c_31437,c_31227,c_31226,c_31225,c_31224,c_31222,c_31221,c_31220,c_31219,c_31171,c_31150,c_31149,c_31120,c_31099,c_31098,c_31069,c_31048,c_31047,c_30835,c_30820,c_30806,c_30792,c_30756,c_30745,c_30650,c_30649,c_30648,c_30647,c_30646,c_30645,c_30644,c_30643,c_30642,c_30641,c_30640,c_30639,c_30636,c_30633,c_30632,c_30631,c_30630,c_30629,c_30443,c_30434,c_30425,c_30416,c_30407,c_30398,c_30389,c_30380,c_30370,c_30369,c_30368,c_30367,c_30366,c_30365,c_30364,c_30363,c_30362,c_30361,c_30359,c_30155,c_30138,c_30121,c_30104,c_30087,c_30070,c_30053,c_30036,c_30017,c_30016,c_30015,c_30014,c_30013,c_30012,c_30011,c_30010,c_30009,c_30008,c_30007,c_30006,c_30005,c_30003,c_30002,c_30001,c_30000,c_29950,c_29929,c_29928,c_29899,c_29878,c_29877,c_29840,c_29783,c_29769,c_29755,c_29741,c_29707,c_29697,c_29610,c_29609,c_29608,c_29607,c_29606,c_29605,c_29604,c_29603,c_29602,c_29601,c_29600,c_29599,c_29596,c_29593,c_29592,c_29591,c_29590,c_29589,c_29574,c_29564,c_29555,c_29546,c_29537,c_29528,c_29519,c_29510,c_29501,c_29491,c_29490,c_29489,c_29488,c_29487,c_29486,c_29485,c_29484,c_29483,c_29482,c_29481,c_29432,c_29394,c_29214,c_29213,c_29212,c_29210,c_29209,c_29208,c_29207,c_29206,c_29153,c_29152,c_29042,c_29020,c_29019,c_28988,c_28966,c_28965,c_28935,c_28914,c_28913,c_28810,c_28778,c_28748,c_28718,c_28607,c_28606,c_28605,c_28604,c_28603,c_28575,c_28395,c_28394,c_28393,c_28392,c_28390,c_28389,c_28388,c_28387,c_28334,c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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO077-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 10:43:26 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 20.20/3.81 % SZS status Started for theBenchmark.p
% 20.20/3.81 % SZS status Unsatisfiable for theBenchmark.p
% 20.20/3.81
% 20.20/3.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 20.20/3.81
% 20.20/3.81 % ------ iProver source info
% 20.20/3.81
% 20.20/3.81 % git: date: 2026-07-19 20:42:38 +0200
% 20.20/3.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 20.20/3.81 % git: non_committed_changes: false
% 20.20/3.81
% 20.20/3.81 % ------ Parsing...% successful
% 20.20/3.81
% 20.20/3.81
% 20.20/3.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 20.20/3.81
% 20.20/3.81 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 20.20/3.81
% 20.20/3.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 20.20/3.81
% 20.20/3.81 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 20.20/3.81 % ------ Proving...
% 20.20/3.81 % ------ Problem Properties
% 20.20/3.81
% 20.20/3.81 %
% 20.20/3.81 % clauses 42
% 20.20/3.81 % conjectures 1
% 20.20/3.81 % EPR 16
% 20.20/3.81 % Horn 24
% 20.20/3.81 % unary 12
% 20.20/3.81 % binary 11
% 20.20/3.81 % lits 185
% 20.20/3.81 % lits eq 46
% 20.20/3.81 % fd_pure 0
% 20.20/3.81 % fd_pseudo 0
% 20.20/3.81 % fd_cond 0
% 20.20/3.81 % fd_pseudo_cond 19
% 20.20/3.81 % AC symbols 0
% 20.20/3.81
% 20.20/3.81 % ------ Schedule dynamic 5 is on
% 20.20/3.81
% 20.20/3.81 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 20.20/3.81
% 20.20/3.81
% 20.20/3.81 % ------
% 20.20/3.81 % Current options:
% 20.20/3.81 % ------
% 20.20/3.81
% 20.20/3.81
% 20.20/3.81 %
% 20.20/3.81
% 20.20/3.81 % ------ Proving...
% 20.20/3.81 %
% 20.20/3.81
% 20.20/3.81 % SZS status Unsatisfiable for theBenchmark.p
% 20.20/3.81
% 20.20/3.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.21/3.90
% 20.21/3.90
%------------------------------------------------------------------------------