%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO188+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 01:20:12 PM UTC 2026
% Result : Theorem 3.01s 11.30s
% Output : CNFRefutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 713 ( 31 unt; 2 def)
% Number of atoms : 4702 ( 2 equ)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 3507 ( 251 ~;3225 |; 22 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 2293 ( 0 sgn2287 !; 6 ?;2198 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart2) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X1,X2)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart4) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| distinct_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart5) ).
fof(f7,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> ( distinct_points(X2,X1)
& distinct_points(X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',con1) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( ( distinct_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',cu1) ).
fof(f10,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq1) ).
fof(f11,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq2) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X1,X2)
& distinct_points(X0,X2)
& distinct_points(X0,X1) )
=> ~ apart_point_and_line(X0,line_connecting(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X1,X2)
& distinct_points(X0,X2)
& distinct_points(X0,X1) )
=> ~ apart_point_and_line(X0,line_connecting(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(flattening,[],[f17]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ( distinct_points(X2,X1)
& distinct_points(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ( distinct_points(X2,X1)
& distinct_points(X2,X0) ) ),
inference(flattening,[],[f21]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(ennf_transformation,[],[f9]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f29]) ).
fof(f32,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X1,X2)
& distinct_points(X0,X2)
& distinct_points(X0,X1)
& apart_point_and_line(X0,line_connecting(X2,X1)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X1,X2)
& distinct_points(X0,X2)
& distinct_points(X0,X1)
& apart_point_and_line(X0,line_connecting(X2,X1)) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
& distinct_points(sK1,sK2)
& distinct_points(sK0,sK2)
& distinct_points(sK0,sK1)
& apart_point_and_line(sK0,line_connecting(sK2,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f33]) ).
fof(f35,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f36,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f49,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
distinct_points(sK1,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
apart_point_and_line(sK0,line_connecting(sK2,sK1)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_49,plain,
! [X0: $i] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f35]) ).
tcf(c_50,plain,
! [X0: $i] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f36]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X0,X1)
| ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X0,line_connecting(X1,X2)) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X0,X2)
| ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X0,line_connecting(X1,X2)) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_63,negated_conjecture,
apart_point_and_line(sK0,line_connecting(sK2,sK1)),
inference(cnf_transformation,[],[f53]) ).
tcf(c_64,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f52]) ).
tcf(c_65,negated_conjecture,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f51]) ).
tcf(c_66,negated_conjecture,
distinct_points(sK1,sK2),
inference(cnf_transformation,[],[f50]) ).
tcf(c_67,negated_conjecture,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f49]) ).
tcf(c_70,plain,
~ distinct_points(sK0,sK0),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_219,definition,
iPr_def_10 = line_connecting(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_220,definition,
iPr_def_11 = line_connecting(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_221,negated_conjecture,
~ apart_point_and_line(sK2,iPr_def_10),
inference(demodulation,[status(thm)],[c_67,c_219]) ).
tcf(c_222,negated_conjecture,
distinct_points(sK1,sK2),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_223,negated_conjecture,
distinct_points(sK0,sK2),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_224,negated_conjecture,
distinct_points(sK0,sK1),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_225,negated_conjecture,
apart_point_and_line(sK0,iPr_def_11),
inference(demodulation,[status(thm)],[c_63,c_220]) ).
tcf(c_432,plain,
! [X0: $i] :
( distinct_points(sK1,X0)
| distinct_points(sK0,X0) ),
inference(superposition,[status(thm)],[c_224,c_52]) ).
tcf(c_433,plain,
! [X0: $i] :
( distinct_points(sK2,X0)
| distinct_points(sK0,X0) ),
inference(superposition,[status(thm)],[c_223,c_52]) ).
tcf(c_434,plain,
! [X0: $i] :
( distinct_points(sK1,X0)
| distinct_points(sK2,X0) ),
inference(superposition,[status(thm)],[c_222,c_52]) ).
tcf(c_456,plain,
! [X0: $i] :
( apart_point_and_line(X0,iPr_def_11)
| distinct_points(sK0,X0) ),
inference(superposition,[status(thm)],[c_225,c_60]) ).
tcf(c_465,plain,
! [X0: $i] :
( apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_225,c_61]) ).
tcf(c_474,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK1,X1)
| distinct_points(sK0,X0)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_432,c_52]) ).
tcf(c_483,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK2,X1)
| distinct_points(sK0,X0)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_433,c_52]) ).
tcf(c_491,plain,
distinct_points(sK2,sK1),
inference(superposition,[status(thm)],[c_434,c_49]) ).
tcf(c_492,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK1,X1)
| distinct_points(sK2,X0)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_434,c_52]) ).
tcf(c_501,plain,
! [X0: $i,X1: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_456,c_61]) ).
tcf(c_502,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(X1,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_456,c_60]) ).
tcf(c_514,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_465,c_53]) ).
tcf(c_524,plain,
! [X0: $i] :
( distinct_points(sK0,X0)
| distinct_points(X0,sK1) ),
inference(superposition,[status(thm)],[c_474,c_49]) ).
tcf(c_525,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,X2)
| distinct_points(sK0,X0)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_474,c_52]) ).
tcf(c_527,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,X1)
| distinct_points(sK0,X2)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_474,c_52]) ).
tcf(c_529,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,X2)
| distinct_points(sK0,X0)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_474,c_52]) ).
tcf(c_533,plain,
( distinct_points(sK1,sK0)
| distinct_points(sK0,sK0) ),
inference(equality_factoring,[status(thm)],[c_474]) ).
tcf(c_534,plain,
distinct_points(sK1,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_533,c_49]) ).
tcf(c_555,plain,
! [X0: $i] :
( distinct_points(sK0,X0)
| distinct_points(X0,sK2) ),
inference(superposition,[status(thm)],[c_483,c_49]) ).
tcf(c_556,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK2,X2)
| distinct_points(sK0,X0)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_483,c_52]) ).
tcf(c_558,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK2,X1)
| distinct_points(sK0,X2)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_483,c_52]) ).
tcf(c_560,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK2,X2)
| distinct_points(sK0,X0)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_483,c_52]) ).
tcf(c_564,plain,
( distinct_points(sK2,sK0)
| distinct_points(sK0,sK0) ),
inference(equality_factoring,[status(thm)],[c_483]) ).
tcf(c_565,plain,
distinct_points(sK2,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_564,c_49]) ).
tcf(c_589,plain,
! [X0: $i] :
( distinct_points(sK2,X0)
| distinct_points(X0,sK1) ),
inference(superposition,[status(thm)],[c_492,c_49]) ).
tcf(c_590,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,X2)
| distinct_points(sK2,X0)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_492,c_52]) ).
tcf(c_592,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,X1)
| distinct_points(sK2,X2)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_492,c_52]) ).
tcf(c_594,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,X2)
| distinct_points(sK2,X0)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_492,c_52]) ).
tcf(c_621,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_501,c_53]) ).
tcf(c_622,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X0)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_501,c_61]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_501,c_60]) ).
tcf(c_651,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_502,c_60]) ).
tcf(c_653,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X1,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_502,c_52]) ).
tcf(c_655,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_502,c_52]) ).
tcf(c_679,plain,
! [X0: $i] :
( apart_point_and_line(sK0,X0)
| distinct_lines(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_514,c_50]) ).
tcf(c_680,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_514,c_53]) ).
tcf(c_682,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK0,X2)
| distinct_lines(iPr_def_11,X0)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_514,c_53]) ).
tcf(c_701,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK0,X1)
| distinct_points(X0,sK1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_524,c_52]) ).
tcf(c_719,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X2)
| distinct_points(X2,X0)
| distinct_lines(iPr_def_11,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_501,c_55]) ).
tcf(c_720,plain,
! [X0: $i] :
( distinct_points(X0,sK2)
| ~ distinct_points(sK2,sK1)
| ~ apart_point_and_line(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_220,c_55]) ).
tcf(c_721,plain,
! [X0: $i] :
( distinct_points(X0,sK0)
| ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_219,c_55]) ).
tcf(c_722,plain,
! [X0: $i] :
( distinct_points(X0,sK0)
| ~ apart_point_and_line(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_721,c_224]) ).
tcf(c_725,plain,
! [X0: $i] :
( distinct_points(X0,sK2)
| ~ apart_point_and_line(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_720,c_491]) ).
tcf(c_732,plain,
( distinct_points(sK0,sK0)
| ~ apart_point_and_line(sK0,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_722]) ).
tcf(c_739,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X2)
| distinct_points(X2,X1)
| distinct_lines(iPr_def_11,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_501,c_56]) ).
tcf(c_740,plain,
! [X0: $i] :
( distinct_points(X0,sK1)
| ~ distinct_points(sK2,sK1)
| ~ apart_point_and_line(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_220,c_56]) ).
tcf(c_741,plain,
! [X0: $i] :
( distinct_points(X0,sK1)
| ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_219,c_56]) ).
tcf(c_742,plain,
! [X0: $i] :
( distinct_points(X0,sK1)
| ~ apart_point_and_line(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_741,c_224]) ).
tcf(c_745,plain,
! [X0: $i] :
( distinct_points(X0,sK1)
| ~ apart_point_and_line(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_740,c_491]) ).
tcf(c_766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_502,c_59]) ).
tcf(c_767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK2,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_492,c_59]) ).
tcf(c_768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK2,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_483,c_59]) ).
tcf(c_769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_474,c_59]) ).
tcf(c_770,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_224,c_59]) ).
tcf(c_771,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_223,c_59]) ).
tcf(c_773,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(X2,sK1)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_524,c_59]) ).
tcf(c_774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(X3,iPr_def_11)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_502,c_59]) ).
tcf(c_775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(sK2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_483,c_59]) ).
tcf(c_776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(sK1,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_474,c_59]) ).
tcf(c_777,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_434,c_59]) ).
tcf(c_779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(sK1,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_492,c_59]) ).
tcf(c_780,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_433,c_59]) ).
tcf(c_781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(sK2,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_492,c_59]) ).
tcf(c_782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_474,c_59]) ).
tcf(c_783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_483,c_59]) ).
tcf(c_784,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_491,c_59]) ).
tcf(c_785,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_524,c_59]) ).
tcf(c_951,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(X2,sK2)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_555,c_59]) ).
tcf(c_952,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK0,X1)
| distinct_points(X0,sK2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_555,c_52]) ).
tcf(c_988,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(X2,sK1)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_589,c_59]) ).
tcf(c_989,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK2,X1)
| distinct_points(X0,sK1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_589,c_52]) ).
tcf(c_1012,plain,
! [X0: $i] :
( distinct_lines(iPr_def_11,iPr_def_10)
| distinct_points(sK0,X0)
| distinct_points(X0,sK0) ),
inference(superposition,[status(thm)],[c_501,c_722]) ).
tcf(c_1016,plain,
( distinct_lines(iPr_def_11,iPr_def_10)
| distinct_points(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_1012]) ).
tcf(c_1052,plain,
distinct_lines(iPr_def_11,iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_1012,c_70,c_1016]) ).
tcf(c_1056,plain,
! [X0: $i] :
( distinct_lines(iPr_def_11,X0)
| distinct_lines(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_1052,c_53]) ).
tcf(c_1081,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X2)
| distinct_lines(iPr_def_11,X1)
| distinct_points(sK2,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_514,c_777]) ).
tcf(c_1083,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_514,c_777]) ).
tcf(c_1084,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK2,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_501,c_777]) ).
tcf(c_1085,plain,
! [X0: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(X0,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK2,X0) ),
inference(superposition,[status(thm)],[c_1052,c_777]) ).
tcf(c_1086,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(X0,iPr_def_11)
| distinct_points(sK2,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_679,c_777]) ).
tcf(c_1146,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X2)
| distinct_lines(iPr_def_11,X1)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_514,c_780]) ).
tcf(c_1148,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_514,c_780]) ).
tcf(c_1149,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_501,c_780]) ).
tcf(c_1150,plain,
! [X0: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,iPr_def_10)
| apart_point_and_line(X0,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK0,X0) ),
inference(superposition,[status(thm)],[c_1052,c_780]) ).
tcf(c_1152,plain,
! [X0: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(X0,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1150,c_221]) ).
tcf(c_1203,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK0,X0)
| distinct_points(X1,sK1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_525,c_49]) ).
tcf(c_1204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(sK0,X2)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| distinct_points(X3,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_525,c_59]) ).
tcf(c_1205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK0,X0)
| distinct_points(X2,X3)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_525,c_52]) ).
tcf(c_1207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(sK1,X4)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X3,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_525,c_59]) ).
tcf(c_1208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK0,X2)
| distinct_points(X1,X3)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_525,c_52]) ).
tcf(c_1210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_points(sK1,X4)
| distinct_points(sK0,X2)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_525,c_59]) ).
tcf(c_1211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK0,X0)
| distinct_points(X3,X2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_525,c_52]) ).
tcf(c_1213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_525,c_59]) ).
tcf(c_1214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X1)
| distinct_points(sK0,X3)
| distinct_points(X3,X2)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_525,c_52]) ).
tcf(c_1299,plain,
distinct_lines(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_1056,c_50]) ).
tcf(c_1300,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X0,iPr_def_11)
| distinct_lines(iPr_def_10,X1)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_1056,c_780]) ).
tcf(c_1301,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(X0,iPr_def_11)
| distinct_lines(iPr_def_10,X1)
| distinct_points(sK2,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_1056,c_777]) ).
tcf(c_1304,plain,
! [X0: $i,X1: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_lines(iPr_def_10,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1056,c_53]) ).
tcf(c_1345,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK0,X0)
| distinct_points(X1,sK2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_502,c_725]) ).
tcf(c_1363,plain,
! [X0: $i] :
( distinct_points(X0,sK1)
| distinct_points(X0,sK0) ),
inference(superposition,[status(thm)],[c_701,c_49]) ).
tcf(c_1364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(X2,sK1)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_701,c_59]) ).
tcf(c_1365,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X2)
| distinct_points(X0,sK1)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_701,c_52]) ).
tcf(c_1367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(sK0,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_701,c_59]) ).
tcf(c_1368,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,X2)
| distinct_points(sK0,X1)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_701,c_52]) ).
tcf(c_1370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK0,X3)
| distinct_points(X2,sK1)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_701,c_59]) ).
tcf(c_1371,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X2)
| distinct_points(X0,sK1)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_701,c_52]) ).
tcf(c_1480,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(X2,sK0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1363,c_59]) ).
tcf(c_1481,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK1,X1)
| distinct_points(X0,sK0)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1363,c_52]) ).
tcf(c_1497,plain,
! [X0: $i] :
( distinct_points(X0,sK2)
| distinct_points(X0,sK0) ),
inference(superposition,[status(thm)],[c_952,c_49]) ).
tcf(c_1498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(X2,sK2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_952,c_59]) ).
tcf(c_1499,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X2)
| distinct_points(X0,sK2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_952,c_52]) ).
tcf(c_1501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(sK0,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_952,c_59]) ).
tcf(c_1502,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK2,X2)
| distinct_points(sK0,X1)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_952,c_52]) ).
tcf(c_1504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK0,X3)
| distinct_points(X2,sK2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_952,c_59]) ).
tcf(c_1505,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X2)
| distinct_points(X0,sK2)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_952,c_52]) ).
tcf(c_1562,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(X2,sK0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1497,c_59]) ).
tcf(c_1563,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK2,X1)
| distinct_points(X0,sK0)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1497,c_52]) ).
tcf(c_1586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(X3,sK2)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1345,c_59]) ).
tcf(c_1587,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X2)
| distinct_points(X1,sK2)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1345,c_52]) ).
tcf(c_1628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(sK0,X4)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_527,c_59]) ).
tcf(c_1631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(sK1,X3)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| distinct_points(X2,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_527,c_59]) ).
tcf(c_1632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X1)
| distinct_points(sK0,X3)
| distinct_points(X2,X3)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_527,c_52]) ).
tcf(c_1636,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK1,X0)
| distinct_points(sK0,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_527,c_49]) ).
tcf(c_1637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_points(sK1,X4)
| distinct_points(sK0,X3)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_527,c_59]) ).
tcf(c_1638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK0,X1)
| distinct_points(X3,X2)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_527,c_52]) ).
tcf(c_1644,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK1,X0)
| distinct_points(sK0,X1)
| distinct_points(sK0,X0) ),
inference(equality_factoring,[status(thm)],[c_527]) ).
tcf(c_1648,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK1,X1)
| distinct_points(sK0,X1)
| distinct_points(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_527]) ).
tcf(c_1756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(sK0,X2)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| distinct_points(X4,X3)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_529,c_59]) ).
tcf(c_1757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK0,X0)
| distinct_points(X2,X3)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_529,c_52]) ).
tcf(c_1759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(sK1,X4)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X4,X3)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_529,c_59]) ).
tcf(c_1760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK0,X2)
| distinct_points(X3,X1)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_529,c_52]) ).
tcf(c_1765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_points(sK1,X2)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_529,c_59]) ).
tcf(c_1766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X0)
| distinct_points(sK0,X3)
| distinct_points(X3,X2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_529,c_52]) ).
tcf(c_1775,plain,
! [X0: $i] :
( distinct_points(sK0,sK0)
| distinct_points(sK1,X0)
| distinct_points(X0,sK0) ),
inference(equality_factoring,[status(thm)],[c_529]) ).
tcf(c_1777,plain,
! [X0: $i] :
( distinct_points(sK1,X0)
| distinct_points(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1775,c_49]) ).
tcf(c_1851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(sK0,X2)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| distinct_points(X3,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_556,c_59]) ).
tcf(c_1852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK2,X3)
| distinct_points(sK0,X0)
| distinct_points(X2,X3)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_556,c_52]) ).
tcf(c_1854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(sK2,X4)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X3,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_556,c_59]) ).
tcf(c_1855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK2,X3)
| distinct_points(sK0,X2)
| distinct_points(X1,X3)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_556,c_52]) ).
tcf(c_1857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_points(sK2,X4)
| distinct_points(sK0,X2)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_556,c_59]) ).
tcf(c_1858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK2,X3)
| distinct_points(sK0,X0)
| distinct_points(X3,X2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_556,c_52]) ).
tcf(c_1860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_points(sK2,X3)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_556,c_59]) ).
tcf(c_1861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK2,X1)
| distinct_points(sK0,X3)
| distinct_points(X3,X2)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_556,c_52]) ).
tcf(c_1964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(sK0,X4)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_558,c_59]) ).
tcf(c_1967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(sK2,X3)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| distinct_points(X2,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_558,c_59]) ).
tcf(c_1968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK2,X1)
| distinct_points(sK0,X3)
| distinct_points(X2,X3)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_558,c_52]) ).
tcf(c_1972,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK2,X0)
| distinct_points(sK0,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_558,c_49]) ).
tcf(c_1973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_points(sK2,X4)
| distinct_points(sK0,X3)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_558,c_59]) ).
tcf(c_1974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK2,X3)
| distinct_points(sK0,X1)
| distinct_points(X3,X2)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_558,c_52]) ).
tcf(c_1980,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK2,X0)
| distinct_points(sK0,X1)
| distinct_points(sK0,X0) ),
inference(equality_factoring,[status(thm)],[c_558]) ).
tcf(c_1984,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK2,X1)
| distinct_points(sK0,X1)
| distinct_points(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_558]) ).
tcf(c_2099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(sK0,X2)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| distinct_points(X4,X3)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_560,c_59]) ).
tcf(c_2100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK2,X3)
| distinct_points(sK0,X0)
| distinct_points(X2,X3)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_560,c_52]) ).
tcf(c_2102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(sK2,X4)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X4,X3)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_560,c_59]) ).
tcf(c_2103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK2,X3)
| distinct_points(sK0,X2)
| distinct_points(X3,X1)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_560,c_52]) ).
tcf(c_2108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_points(sK2,X2)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_560,c_59]) ).
tcf(c_2109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK2,X0)
| distinct_points(sK0,X3)
| distinct_points(X3,X2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_560,c_52]) ).
tcf(c_2118,plain,
! [X0: $i] :
( distinct_points(sK0,sK0)
| distinct_points(sK2,X0)
| distinct_points(X0,sK0) ),
inference(equality_factoring,[status(thm)],[c_560]) ).
tcf(c_2120,plain,
! [X0: $i] :
( distinct_points(sK2,X0)
| distinct_points(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2118,c_49]) ).
tcf(c_2185,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK2,X0)
| distinct_points(X1,sK1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_590,c_49]) ).
tcf(c_2186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(sK2,X2)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| distinct_points(X3,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_590,c_59]) ).
tcf(c_2187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK2,X0)
| distinct_points(X2,X3)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_590,c_52]) ).
tcf(c_2189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(sK1,X4)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X3,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_590,c_59]) ).
tcf(c_2190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK2,X2)
| distinct_points(X1,X3)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_590,c_52]) ).
tcf(c_2192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_points(sK1,X4)
| distinct_points(sK2,X2)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_590,c_59]) ).
tcf(c_2193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK2,X0)
| distinct_points(X3,X2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_590,c_52]) ).
tcf(c_2195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK2,X4)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_590,c_59]) ).
tcf(c_2196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X1)
| distinct_points(sK2,X3)
| distinct_points(X3,X2)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_590,c_52]) ).
tcf(c_2301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(sK2,X4)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_592,c_59]) ).
tcf(c_2303,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK1,X1)
| distinct_points(X0,sK2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_592,c_49]) ).
tcf(c_2304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(sK1,X3)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| distinct_points(X2,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_592,c_59]) ).
tcf(c_2305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X1)
| distinct_points(sK2,X3)
| distinct_points(X2,X3)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_592,c_52]) ).
tcf(c_2309,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK1,X0)
| distinct_points(sK2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_592,c_49]) ).
tcf(c_2310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_points(sK1,X4)
| distinct_points(sK2,X3)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_592,c_59]) ).
tcf(c_2311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK2,X1)
| distinct_points(X3,X2)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_592,c_52]) ).
tcf(c_2317,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK1,X0)
| distinct_points(sK2,X1)
| distinct_points(sK2,X0) ),
inference(equality_factoring,[status(thm)],[c_592]) ).
tcf(c_2321,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK1,X1)
| distinct_points(sK2,X1)
| distinct_points(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_592]) ).
tcf(c_2392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(sK2,X2)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| distinct_points(X4,X3)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_594,c_59]) ).
tcf(c_2393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK2,X0)
| distinct_points(X2,X3)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_594,c_52]) ).
tcf(c_2395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(sK1,X4)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X4,X3)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_594,c_59]) ).
tcf(c_2396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(sK2,X2)
| distinct_points(X3,X1)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_594,c_52]) ).
tcf(c_2401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_points(sK1,X2)
| distinct_points(sK2,X4)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_594,c_59]) ).
tcf(c_2402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X0)
| distinct_points(sK2,X3)
| distinct_points(X3,X2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_594,c_52]) ).
tcf(c_2411,plain,
! [X0: $i] :
( distinct_points(sK2,sK2)
| distinct_points(sK1,X0)
| distinct_points(X0,sK2) ),
inference(equality_factoring,[status(thm)],[c_594]) ).
tcf(c_2413,plain,
! [X0: $i] :
( distinct_points(sK1,X0)
| distinct_points(X0,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2411,c_49]) ).
tcf(c_2487,plain,
! [X0: $i] :
( distinct_points(X0,sK1)
| distinct_points(X0,sK2) ),
inference(superposition,[status(thm)],[c_989,c_49]) ).
tcf(c_2488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(X2,sK1)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_989,c_59]) ).
tcf(c_2489,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK2,X2)
| distinct_points(X0,sK1)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_989,c_52]) ).
tcf(c_2491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(sK2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_989,c_59]) ).
tcf(c_2492,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,X2)
| distinct_points(sK2,X1)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_989,c_52]) ).
tcf(c_2494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK2,X3)
| distinct_points(X2,sK1)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_989,c_59]) ).
tcf(c_2495,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK2,X2)
| distinct_points(X0,sK1)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_989,c_52]) ).
tcf(c_2576,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(X2,sK2)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2487,c_59]) ).
tcf(c_2591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(X3,sK1)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1203,c_59]) ).
tcf(c_2592,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X2)
| distinct_points(X1,sK1)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1203,c_52]) ).
tcf(c_2622,plain,
! [X0: $i] :
( distinct_lines(iPr_def_10,X0)
| distinct_lines(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1304,c_50]) ).
tcf(c_2623,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_lines(iPr_def_10,X0)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1304,c_780]) ).
tcf(c_2624,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_lines(iPr_def_10,X0)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1304,c_777]) ).
tcf(c_2627,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_lines(iPr_def_10,X0)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1304,c_53]) ).
tcf(c_2630,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(X2,iPr_def_10)
| distinct_lines(iPr_def_11,X1)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1304,c_777]) ).
tcf(c_2633,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_lines(iPr_def_10,X2)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1304,c_53]) ).
tcf(c_2635,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| distinct_lines(iPr_def_11,X2)
| distinct_lines(iPr_def_10,X1)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_1304,c_780]) ).
tcf(c_2636,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK1,X1)
| distinct_lines(iPr_def_11,X2)
| distinct_lines(iPr_def_10,X1)
| distinct_points(sK2,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_1304,c_777]) ).
tcf(c_2637,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X1)
| distinct_lines(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_1304,c_771]) ).
tcf(c_2638,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X1)
| distinct_lines(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_1304,c_770]) ).
tcf(c_2639,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_lines(iPr_def_10,X0)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1304,c_53]) ).
tcf(c_2708,plain,
! [X0: $i,X1: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_lines(X0,X1)
| ~ distinct_lines(iPr_def_11,X0) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_2751,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(sK1,X2)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1777,c_59]) ).
tcf(c_2767,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2120,c_59]) ).
tcf(c_2793,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(sK1,X2)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2413,c_59]) ).
tcf(c_2806,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,iPr_def_10)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X0,iPr_def_10)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2622,c_780]) ).
tcf(c_2807,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(X0,iPr_def_10)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK2,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2622,c_777]) ).
tcf(c_2810,plain,
! [X0: $i,X1: $i] :
( distinct_lines(iPr_def_10,X1)
| distinct_lines(X0,iPr_def_11)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2622,c_53]) ).
tcf(c_2826,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(X0,iPr_def_10)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2806,c_221]) ).
tcf(c_2856,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X1)
| distinct_lines(iPr_def_10,X2)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2826,c_61]) ).
tcf(c_2857,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(X1,iPr_def_10)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2826,c_60]) ).
tcf(c_2860,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X0,sK0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2826,c_722]) ).
tcf(c_2862,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X2,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK0,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2826,c_780]) ).
tcf(c_2863,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X2,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK2,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2826,c_777]) ).
tcf(c_2867,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X2,iPr_def_10)
| distinct_points(sK0,X2)
| distinct_points(X2,X1)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2826,c_56]) ).
tcf(c_2868,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X2,iPr_def_10)
| distinct_points(sK0,X2)
| distinct_points(X2,X0)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2826,c_55]) ).
tcf(c_2869,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(X2,iPr_def_10)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2826,c_61]) ).
tcf(c_2870,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(X0,iPr_def_10)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2826,c_60]) ).
tcf(c_3025,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(sK0,X0)
| distinct_points(X0,sK0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2860,c_780]) ).
tcf(c_3026,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK2,X2)
| distinct_points(sK0,X0)
| distinct_points(X0,sK0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2860,c_777]) ).
tcf(c_3029,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X0)
| distinct_lines(iPr_def_11,X1)
| distinct_points(sK0,X2)
| distinct_points(X2,sK0)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2860,c_53]) ).
tcf(c_3030,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X2)
| distinct_points(X2,sK0)
| distinct_points(X2,X1)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2860,c_56]) ).
tcf(c_3031,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X2)
| distinct_points(X2,sK0)
| distinct_points(X2,X0)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2860,c_55]) ).
tcf(c_3032,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X0)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X2,sK0)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2860,c_61]) ).
tcf(c_3033,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X0,sK0)
| apart_point_and_line(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2860,c_60]) ).
tcf(c_3279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,iPr_def_10)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X3,iPr_def_10)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_780]) ).
tcf(c_3280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK1,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X3,iPr_def_10)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK2,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_777]) ).
tcf(c_3281,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,iPr_def_10)
| apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X2)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_771]) ).
tcf(c_3282,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(sK1,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X2)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_770]) ).
tcf(c_3283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| distinct_lines(iPr_def_10,X1)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_53]) ).
tcf(c_3284,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(X0,iPr_def_11)
| distinct_lines(iPr_def_10,X1)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_50]) ).
tcf(c_3285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X3,iPr_def_11)
| distinct_lines(iPr_def_10,X2)
| distinct_points(sK0,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_780]) ).
tcf(c_3286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X3,iPr_def_11)
| distinct_lines(iPr_def_10,X2)
| distinct_points(sK2,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_777]) ).
tcf(c_3289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X0)
| distinct_lines(iPr_def_11,X1)
| distinct_lines(iPr_def_10,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_53]) ).
tcf(c_3290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| distinct_points(X2,X1)
| distinct_lines(iPr_def_10,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_56]) ).
tcf(c_3291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| distinct_points(X2,X0)
| distinct_lines(iPr_def_10,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_55]) ).
tcf(c_3292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| distinct_lines(iPr_def_10,X0)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_61]) ).
tcf(c_3293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X2)
| distinct_lines(iPr_def_10,X3)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_60]) ).
tcf(c_3299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_10,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| distinct_points(X2,X1)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_56]) ).
tcf(c_3300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_10,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| distinct_points(X2,X0)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_55]) ).
tcf(c_3301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X0)
| distinct_lines(iPr_def_10,X3)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_61]) ).
tcf(c_3302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| distinct_lines(iPr_def_10,X2)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2856,c_60]) ).
tcf(c_3310,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| distinct_lines(iPr_def_10,X1)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_2856]) ).
tcf(c_3410,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X2)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3281,c_221]) ).
tcf(c_3439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X3,iPr_def_10)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3279,c_221]) ).
tcf(c_3467,plain,
~ distinct_lines(iPr_def_11,iPr_def_11),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_3558,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_points(sK0,X0)
| distinct_lines(X1,iPr_def_11)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X2) ),
inference(global_subsumption_just,[status(thm)],[c_3410,c_70,c_732,c_3410]) ).
tcf(c_3559,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X2)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(renaming,[status(thm)],[c_3558]) ).
tcf(c_3567,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3559,c_60]) ).
tcf(c_3624,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_3567]) ).
tcf(c_3648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(X2,iPr_def_10)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X3)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2857,c_60]) ).
tcf(c_3650,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X1,sK1)
| apart_point_and_line(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2857,c_742]) ).
tcf(c_3651,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X1,sK0)
| apart_point_and_line(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2857,c_722]) ).
tcf(c_3653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(X3,iPr_def_11)
| apart_point_and_line(X1,iPr_def_10)
| distinct_points(sK0,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2857,c_780]) ).
tcf(c_3654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X2)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(X3,iPr_def_11)
| apart_point_and_line(X1,iPr_def_10)
| distinct_points(sK2,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2857,c_777]) ).
tcf(c_3657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(X1,iPr_def_10)
| distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X2)
| distinct_lines(X2,X3)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2857,c_53]) ).
tcf(c_3658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,iPr_def_10)
| distinct_points(sK0,X2)
| distinct_points(X2,X3)
| distinct_points(X2,X1)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2857,c_56]) ).
tcf(c_3659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,iPr_def_10)
| distinct_points(sK0,X2)
| distinct_points(X2,X3)
| distinct_points(X2,X0)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2857,c_55]) ).
tcf(c_3660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(X1,iPr_def_10)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X3)
| distinct_lines(X2,X3)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2857,c_61]) ).
tcf(c_3661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(X1,iPr_def_10)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X3)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2857,c_60]) ).
tcf(c_3668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(X4,iPr_def_10)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2857,c_59]) ).
tcf(c_3669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(X2,iPr_def_10)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X3)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2857,c_52]) ).
tcf(c_3770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X3)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_651,c_61]) ).
tcf(c_3771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X2,X3)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_651,c_60]) ).
tcf(c_3772,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X0)
| distinct_points(X2,sK1)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_651,c_745]) ).
tcf(c_3773,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X0)
| distinct_points(X2,sK2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_651,c_725]) ).
tcf(c_3775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(X4,iPr_def_11)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X3,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_651,c_59]) ).
tcf(c_3776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X1,X3)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_651,c_52]) ).
tcf(c_3778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(X4,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_651,c_59]) ).
tcf(c_3779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X3,X2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_651,c_52]) ).
tcf(c_3781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_651,c_59]) ).
tcf(c_3782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X1,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(X3,X2)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_651,c_52]) ).
tcf(c_3853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(X2,sK0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1481,c_59]) ).
tcf(c_3854,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,X2)
| distinct_points(X0,sK0)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1481,c_52]) ).
tcf(c_3859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(X2,sK0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1481,c_59]) ).
tcf(c_3860,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,X2)
| distinct_points(X0,sK0)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1481,c_52]) ).
tcf(c_3916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(X2,sK0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1563,c_59]) ).
tcf(c_3917,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK2,X2)
| distinct_points(X0,sK0)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1563,c_52]) ).
tcf(c_3922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK2,X3)
| distinct_points(X2,sK0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1563,c_59]) ).
tcf(c_3923,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK2,X2)
| distinct_points(X0,sK0)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1563,c_52]) ).
tcf(c_3962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(sK1,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1636,c_59]) ).
tcf(c_3963,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,X0)
| distinct_points(sK0,X2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1636,c_52]) ).
tcf(c_3992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(sK2,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1972,c_59]) ).
tcf(c_3993,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK2,X0)
| distinct_points(sK0,X2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1972,c_52]) ).
tcf(c_4031,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X0)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X2,sK1)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2869,c_742]) ).
tcf(c_4034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(X3,iPr_def_11)
| apart_point_and_line(X2,iPr_def_10)
| distinct_points(sK0,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2869,c_780]) ).
tcf(c_4035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(X3,iPr_def_11)
| apart_point_and_line(X2,iPr_def_10)
| distinct_points(sK2,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2869,c_777]) ).
tcf(c_4038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(X3,iPr_def_10)
| distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X3)
| apart_point_and_line(X3,X1)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2869,c_53]) ).
tcf(c_4039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(X3,iPr_def_10)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(X3,X1)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2869,c_56]) ).
tcf(c_4040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(X3,iPr_def_10)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(X3,X0)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2869,c_55]) ).
tcf(c_4041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(X3,iPr_def_10)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X3)
| apart_point_and_line(X3,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2869,c_61]) ).
tcf(c_4042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(X0,iPr_def_10)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X3)
| distinct_lines(X2,X3)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2869,c_60]) ).
tcf(c_4049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X0,iPr_def_10)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2869,c_780]) ).
tcf(c_4050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK2,X3)
| apart_point_and_line(X0,iPr_def_10)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK2,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2869,c_777]) ).
tcf(c_4051,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(X0,iPr_def_10)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2869,c_771]) ).
tcf(c_4052,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(X0,iPr_def_10)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2869,c_770]) ).
tcf(c_4053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(X3,iPr_def_10)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X3)
| apart_point_and_line(X3,X0)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2869,c_53]) ).
tcf(c_4056,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(X0,iPr_def_10)
| distinct_lines(X1,iPr_def_11)
| distinct_lines(X1,iPr_def_10)
| distinct_points(sK0,X0) ),
inference(equality_factoring,[status(thm)],[c_2869]) ).
tcf(c_4057,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(X0,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0) ),
inference(equality_factoring,[status(thm)],[c_2869]) ).
tcf(c_4212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(X2,iPr_def_10)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X3)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2870,c_60]) ).
tcf(c_4216,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(X1,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK0,X0)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2870,c_50]) ).
tcf(c_4217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(X3,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK0,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2870,c_780]) ).
tcf(c_4218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X2)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(X3,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK2,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2870,c_777]) ).
tcf(c_4221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(X0,iPr_def_10)
| distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X2)
| distinct_lines(X2,X3)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2870,c_53]) ).
tcf(c_4222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X2,iPr_def_10)
| distinct_points(sK0,X2)
| distinct_points(X3,X1)
| distinct_points(X2,X3)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2870,c_56]) ).
tcf(c_4223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X2,iPr_def_10)
| distinct_points(sK0,X2)
| distinct_points(X3,X0)
| distinct_points(X2,X3)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2870,c_55]) ).
tcf(c_4225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(X0,iPr_def_10)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X3)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2870,c_60]) ).
tcf(c_4232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(X4,iPr_def_10)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2870,c_59]) ).
tcf(c_4233,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(X2,iPr_def_10)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X0,X3)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2870,c_52]) ).
tcf(c_4418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(sK0,X0)
| distinct_points(X1,sK0)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_3651,c_780]) ).
tcf(c_4419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X2)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK2,X3)
| distinct_points(sK0,X0)
| distinct_points(X1,sK0)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_3651,c_777]) ).
tcf(c_4422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X2)
| distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X0)
| distinct_points(X1,sK0)
| apart_point_and_line(X0,X2)
| distinct_lines(X2,X3)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_3651,c_53]) ).
tcf(c_4424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X4)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(X4,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_3651,c_59]) ).
tcf(c_4425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X3)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_3651,c_52]) ).
tcf(c_4426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK0,X2)
| distinct_points(X3,sK0)
| distinct_points(X2,X3)
| distinct_points(X2,X1)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_3651,c_56]) ).
tcf(c_4427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK0,X2)
| distinct_points(X3,sK0)
| distinct_points(X2,X3)
| distinct_points(X2,X0)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_3651,c_55]) ).
tcf(c_4428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X2)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X1,sK0)
| apart_point_and_line(X0,X3)
| distinct_lines(X2,X3)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_3651,c_61]) ).
tcf(c_4429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X1,sK0)
| apart_point_and_line(X2,X3)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_3651,c_60]) ).
tcf(c_4431,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| distinct_lines(iPr_def_11,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X1,sK0)
| distinct_points(X0,sK1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_3651,c_745]) ).
tcf(c_4432,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| distinct_lines(iPr_def_11,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X1,sK0)
| distinct_points(X0,sK2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_3651,c_725]) ).
tcf(c_4436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X3)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X4,sK0)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_3651,c_59]) ).
tcf(c_4437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X2,sK0)
| apart_point_and_line(X0,X3)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_3651,c_52]) ).
tcf(c_4440,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X1,sK0)
| distinct_points(X0,sK2)
| distinct_points(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4432,c_50]) ).
tcf(c_4446,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X1,sK0)
| distinct_points(X0,sK1)
| distinct_points(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4431,c_50]) ).
tcf(c_4625,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X2)
| distinct_points(X2,sK1)
| distinct_points(X2,X1)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2867,c_742]) ).
tcf(c_4627,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(X1,iPr_def_10)
| distinct_points(sK0,X1)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2867,c_49]) ).
tcf(c_4628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(X4,iPr_def_10)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X3)
| apart_point_and_line(X4,X2)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2867,c_59]) ).
tcf(c_4629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,iPr_def_10)
| distinct_points(sK0,X3)
| distinct_points(X3,X2)
| distinct_points(X1,X2)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2867,c_52]) ).
tcf(c_4630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(X3,iPr_def_10)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(sK0,X2)
| distinct_points(X3,X1)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2867,c_780]) ).
tcf(c_4631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(X3,iPr_def_10)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK2,X2)
| distinct_points(sK0,X3)
| distinct_points(X3,X1)
| apart_point_and_line(sK1,line_connecting(X0,X1))
| apart_point_and_line(sK2,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2867,c_777]) ).
tcf(c_4634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,iPr_def_10)
| distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X3)
| distinct_points(X3,X1)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),X2)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2867,c_53]) ).
tcf(c_4768,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X2)
| distinct_points(X2,sK1)
| distinct_points(X2,X0)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2868,c_742]) ).
tcf(c_4770,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK0,X0)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2868,c_49]) ).
tcf(c_4771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(X4,iPr_def_10)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X3)
| apart_point_and_line(X4,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2868,c_59]) ).
tcf(c_4772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,iPr_def_10)
| distinct_points(sK0,X3)
| distinct_points(X3,X2)
| distinct_points(X0,X2)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2868,c_52]) ).
tcf(c_4773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(X3,iPr_def_10)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(sK0,X2)
| distinct_points(X3,X0)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2868,c_780]) ).
tcf(c_4774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(X3,iPr_def_10)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK2,X2)
| distinct_points(sK0,X3)
| distinct_points(X3,X0)
| apart_point_and_line(sK1,line_connecting(X0,X1))
| apart_point_and_line(sK2,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2868,c_777]) ).
tcf(c_4777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,iPr_def_10)
| distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X3)
| distinct_points(X3,X0)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| distinct_lines(line_connecting(X0,X1),X2)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2868,c_53]) ).
tcf(c_4938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X1,X3)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_653,c_61]) ).
tcf(c_4942,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(X1,iPr_def_11)
| distinct_points(X0,sK0)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_653,c_49]) ).
tcf(c_4943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(X3,iPr_def_11)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| distinct_points(X2,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_653,c_59]) ).
tcf(c_4944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X1,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(X2,X3)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_653,c_52]) ).
tcf(c_4948,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(X0,iPr_def_11)
| distinct_points(sK0,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_653,c_49]) ).
tcf(c_4949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(X4,iPr_def_11)
| distinct_points(sK0,X3)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_653,c_59]) ).
tcf(c_4950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X1)
| distinct_points(X3,X2)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_653,c_52]) ).
tcf(c_4953,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(X0,iPr_def_11)
| distinct_points(sK0,X1)
| distinct_points(sK0,X0) ),
inference(equality_factoring,[status(thm)],[c_653]) ).
tcf(c_4956,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(X1,iPr_def_11)
| distinct_points(sK0,X1)
| distinct_points(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_653]) ).
tcf(c_5041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(X3,sK1)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2185,c_59]) ).
tcf(c_5042,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK2,X2)
| distinct_points(X1,sK1)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2185,c_52]) ).
tcf(c_5073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(X2,sK2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2303,c_59]) ).
tcf(c_5074,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,X2)
| distinct_points(X0,sK2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2303,c_52]) ).
tcf(c_5079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X3)
| distinct_points(X2,sK2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2303,c_59]) ).
tcf(c_5080,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,X2)
| distinct_points(X0,sK2)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2303,c_52]) ).
tcf(c_5119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| distinct_points(sK1,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2309,c_59]) ).
tcf(c_5120,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,X0)
| distinct_points(sK2,X2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_2309,c_52]) ).
tcf(c_5145,plain,
! [X0: $i] :
( distinct_lines(X0,iPr_def_11)
| distinct_lines(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2810,c_50]) ).
tcf(c_5146,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,iPr_def_10)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X2,iPr_def_10)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2810,c_780]) ).
tcf(c_5147,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(X2,iPr_def_10)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2810,c_777]) ).
tcf(c_5148,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,iPr_def_10)
| apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X1)
| distinct_lines(X0,iPr_def_11)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2810,c_771]) ).
tcf(c_5149,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X1)
| distinct_lines(X0,iPr_def_11)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2810,c_770]) ).
tcf(c_5150,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_10,X2)
| distinct_lines(X0,iPr_def_11)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2810,c_53]) ).
tcf(c_5152,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(X2,iPr_def_11)
| distinct_lines(iPr_def_10,X1)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2810,c_780]) ).
tcf(c_5153,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(X2,iPr_def_11)
| distinct_lines(iPr_def_10,X1)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2810,c_777]) ).
tcf(c_5156,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_lines(iPr_def_10,X1)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2810,c_53]) ).
tcf(c_5159,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK1,X1)
| distinct_lines(iPr_def_10,X2)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK2,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2810,c_777]) ).
tcf(c_5160,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_10,X1)
| distinct_lines(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2810,c_771]) ).
tcf(c_5161,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_10,X1)
| distinct_lines(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2810,c_770]) ).
tcf(c_5162,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_10,X2)
| distinct_lines(X0,iPr_def_11)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_2810,c_53]) ).
tcf(c_5201,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X1)
| distinct_lines(X0,iPr_def_11)
| distinct_lines(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5148,c_221]) ).
tcf(c_5235,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(X2,iPr_def_10)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5146,c_221]) ).
tcf(c_5248,plain,
! [X0: $i] :
( distinct_lines(iPr_def_11,iPr_def_11)
| distinct_lines(X0,iPr_def_11)
| ~ distinct_lines(iPr_def_11,X0) ),
inference(instantiation,[status(thm)],[c_2708]) ).
tcf(c_5384,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X0,iPr_def_11)
| distinct_lines(X1,iPr_def_10)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_5145,c_780]) ).
tcf(c_5385,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(X0,iPr_def_11)
| distinct_lines(X1,iPr_def_10)
| distinct_points(sK2,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_5145,c_777]) ).
tcf(c_5388,plain,
! [X0: $i,X1: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_lines(X0,iPr_def_10)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5145,c_53]) ).
tcf(c_5486,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_points(X0,sK0)
| apart_point_and_line(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_4942,c_61]) ).
tcf(c_5487,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X2,iPr_def_11)
| distinct_points(X0,sK0)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_4942,c_60]) ).
tcf(c_5488,plain,
! [X0: $i,X1: $i] :
( distinct_points(X1,sK1)
| distinct_points(X0,sK0)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_4942,c_745]) ).
tcf(c_5489,plain,
! [X0: $i,X1: $i] :
( distinct_points(X1,sK2)
| distinct_points(X0,sK0)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_4942,c_725]) ).
tcf(c_5493,plain,
! [X0: $i] :
( apart_point_and_line(X0,iPr_def_11)
| distinct_points(X0,sK0) ),
inference(superposition,[status(thm)],[c_4942,c_49]) ).
tcf(c_5494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,iPr_def_11)
| distinct_points(X2,sK0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_4942,c_59]) ).
tcf(c_5495,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X2,iPr_def_11)
| distinct_points(X0,sK0)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_4942,c_52]) ).
tcf(c_5619,plain,
! [X0: $i,X1: $i] :
( distinct_lines(X0,X1)
| distinct_lines(X0,iPr_def_11)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_5201,c_70,c_732,c_5201]) ).
tcf(c_5620,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X1)
| distinct_lines(X0,iPr_def_11)
| distinct_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_5619]) ).
tcf(c_5631,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5620,c_780]) ).
tcf(c_5632,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5620,c_777]) ).
tcf(c_5635,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X1)
| distinct_lines(iPr_def_11,X2)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5620,c_53]) ).
tcf(c_5638,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(sK0,X2)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK2,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_5620,c_777]) ).
tcf(c_5641,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK0,X2)
| distinct_lines(X0,iPr_def_11)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5620,c_53]) ).
tcf(c_5694,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_5235,c_622,c_3467,c_5248]) ).
tcf(c_5705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5694,c_780]) ).
tcf(c_5706,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK2,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5694,c_777]) ).
tcf(c_5709,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X3)
| apart_point_and_line(X3,X1)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5694,c_53]) ).
tcf(c_5710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(X3,X1)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5694,c_56]) ).
tcf(c_5711,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(X3,X0)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5694,c_55]) ).
tcf(c_5712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X3)
| apart_point_and_line(X3,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5694,c_61]) ).
tcf(c_5713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X3)
| distinct_lines(X2,X3)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5694,c_60]) ).
tcf(c_5718,plain,
! [X0: $i,X1: $i] :
( distinct_lines(X1,iPr_def_11)
| distinct_lines(X1,iPr_def_10)
| distinct_points(sK0,X0)
| distinct_points(X0,sK0) ),
inference(superposition,[status(thm)],[c_5694,c_722]) ).
tcf(c_5719,plain,
! [X0: $i,X1: $i] :
( distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_5694,c_50]) ).
tcf(c_5720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X1)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_5694,c_780]) ).
tcf(c_5721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X1)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK2,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_5694,c_777]) ).
tcf(c_5722,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(sK0,X1)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_5694,c_771]) ).
tcf(c_5723,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(sK0,X1)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_5694,c_770]) ).
tcf(c_5724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X3)
| apart_point_and_line(X3,X0)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5694,c_53]) ).
tcf(c_5725,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(X0,iPr_def_11)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0) ),
inference(equality_factoring,[status(thm)],[c_5694]) ).
tcf(c_5825,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X2)
| distinct_points(X2,X1)
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5719,c_56]) ).
tcf(c_5826,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X2)
| distinct_points(X2,X0)
| distinct_lines(line_connecting(X0,X1),iPr_def_11)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5719,c_55]) ).
tcf(c_5828,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5719,c_60]) ).
tcf(c_5859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X3)
| apart_point_and_line(X3,X2)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5635,c_780]) ).
tcf(c_5860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK2,X3)
| apart_point_and_line(X3,X2)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5635,c_777]) ).
tcf(c_5863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X1)
| distinct_lines(iPr_def_11,X3)
| distinct_lines(X2,X3)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5635,c_53]) ).
tcf(c_5864,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X1)
| distinct_lines(iPr_def_11,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5635,c_50]) ).
tcf(c_5865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X1)
| distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5635,c_780]) ).
tcf(c_5866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X1)
| distinct_lines(iPr_def_11,X3)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5635,c_777]) ).
tcf(c_5867,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5635,c_771]) ).
tcf(c_5868,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5635,c_770]) ).
tcf(c_5869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X1)
| distinct_lines(iPr_def_11,X3)
| distinct_lines(X3,X2)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5635,c_53]) ).
tcf(c_5871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X3)
| distinct_lines(iPr_def_11,X1)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5635,c_780]) ).
tcf(c_5872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK2,X3)
| apart_point_and_line(sK0,X3)
| distinct_lines(iPr_def_11,X1)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5635,c_777]) ).
tcf(c_5875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK0,X3)
| distinct_lines(iPr_def_11,X1)
| distinct_lines(X3,X2)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5635,c_53]) ).
tcf(c_5878,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X1)
| distinct_lines(iPr_def_11,X0) ),
inference(equality_factoring,[status(thm)],[c_5635]) ).
tcf(c_5881,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X1)
| distinct_lines(iPr_def_11,X1)
| distinct_lines(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_5635]) ).
tcf(c_6005,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X0,X1)
| distinct_lines(X2,X1)
| distinct_lines(X0,iPr_def_11)
| apart_point_and_line(sK0,X2) ),
inference(global_subsumption_just,[status(thm)],[c_5641,c_682,c_3467,c_5248]) ).
tcf(c_6006,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK0,X2)
| distinct_lines(X0,iPr_def_11)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_6005]) ).
tcf(c_6016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X3)
| apart_point_and_line(X3,X0)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6006,c_780]) ).
tcf(c_6017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK2,X3)
| apart_point_and_line(X3,X0)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6006,c_777]) ).
tcf(c_6020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X3)
| distinct_lines(iPr_def_11,X2)
| distinct_lines(X3,X1)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6006,c_53]) ).
tcf(c_6021,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK0,X1)
| distinct_lines(X0,iPr_def_11)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6006,c_50]) ).
tcf(c_6022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X3)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6006,c_780]) ).
tcf(c_6023,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X3)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6006,c_777]) ).
tcf(c_6026,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X3)
| distinct_lines(X0,iPr_def_11)
| distinct_lines(X3,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6006,c_53]) ).
tcf(c_6027,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK0,X0)
| distinct_lines(X1,iPr_def_11)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6006,c_50]) ).
tcf(c_6028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6006,c_780]) ).
tcf(c_6029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6006,c_777]) ).
tcf(c_6030,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(X2,iPr_def_11)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6006,c_771]) ).
tcf(c_6031,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(X2,iPr_def_11)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6006,c_770]) ).
tcf(c_6032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X0)
| distinct_lines(X3,iPr_def_11)
| distinct_lines(X3,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6006,c_53]) ).
tcf(c_6034,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK0,X0)
| distinct_lines(X1,iPr_def_11)
| distinct_lines(X0,iPr_def_11) ),
inference(equality_factoring,[status(thm)],[c_6006]) ).
tcf(c_6037,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK0,X1)
| distinct_lines(X1,iPr_def_11)
| distinct_lines(X0,iPr_def_11) ),
inference(equality_factoring,[status(thm)],[c_6006]) ).
tcf(c_6200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(X4,iPr_def_11)
| distinct_points(sK0,X4)
| distinct_points(sK0,X3)
| apart_point_and_line(X4,X2)
| apart_point_and_line(X3,X1)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_780]) ).
tcf(c_6201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X2)
| apart_point_and_line(X4,iPr_def_11)
| distinct_points(sK2,X4)
| distinct_points(sK0,X3)
| apart_point_and_line(X4,X2)
| apart_point_and_line(X3,X1)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_777]) ).
tcf(c_6204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X1)
| distinct_lines(X2,X3)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_53]) ).
tcf(c_6205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(iPr_def_11,X4)
| distinct_points(sK0,X3)
| distinct_lines(X2,X4)
| distinct_points(X3,X1)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_56]) ).
tcf(c_6206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(iPr_def_11,X4)
| distinct_points(sK0,X3)
| distinct_lines(X2,X4)
| distinct_points(X3,X0)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_55]) ).
tcf(c_6207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X3)
| distinct_lines(X1,X3)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_61]) ).
tcf(c_6208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(iPr_def_11,X4)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X3)
| distinct_lines(X2,X4)
| distinct_lines(X2,X3)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_60]) ).
tcf(c_6210,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X2,sK1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_745]) ).
tcf(c_6211,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X2,sK2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_725]) ).
tcf(c_6212,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_lines(X0,iPr_def_10)
| distinct_points(sK0,X2)
| distinct_points(X2,sK1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_742]) ).
tcf(c_6213,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_lines(X0,iPr_def_10)
| distinct_points(sK0,X2)
| distinct_points(X2,sK0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_722]) ).
tcf(c_6215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X4)
| apart_point_and_line(sK2,X0)
| distinct_lines(iPr_def_11,X4)
| distinct_points(sK0,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X4)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_780]) ).
tcf(c_6216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X4)
| apart_point_and_line(sK1,X0)
| distinct_lines(iPr_def_11,X4)
| distinct_points(sK2,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X4)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_777]) ).
tcf(c_6217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X3)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_771]) ).
tcf(c_6218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X3)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_770]) ).
tcf(c_6219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X1)
| distinct_lines(X3,X2)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_53]) ).
tcf(c_6221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X0)
| distinct_lines(iPr_def_11,X1)
| distinct_points(sK0,X4)
| distinct_points(sK0,X2)
| apart_point_and_line(X4,X3)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X3)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_780]) ).
tcf(c_6222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X0)
| distinct_lines(iPr_def_11,X1)
| distinct_points(sK2,X4)
| distinct_points(sK0,X2)
| apart_point_and_line(X4,X3)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X3)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_777]) ).
tcf(c_6223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X3)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X1)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_771]) ).
tcf(c_6224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X3)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X1)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_770]) ).
tcf(c_6225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X3)
| distinct_lines(X3,X2)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5709,c_53]) ).
tcf(c_6231,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_5709]) ).
tcf(c_6607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X3)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_655,c_61]) ).
tcf(c_6608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X2,X3)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_655,c_60]) ).
tcf(c_6609,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X0)
| distinct_points(X2,sK1)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_655,c_745]) ).
tcf(c_6610,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK0,X0)
| distinct_points(X2,sK2)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_655,c_725]) ).
tcf(c_6612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(X4,iPr_def_11)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X4,X3)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_655,c_59]) ).
tcf(c_6613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X3,X1)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_655,c_52]) ).
tcf(c_6618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_655,c_59]) ).
tcf(c_6619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X0,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(X3,X2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_655,c_52]) ).
tcf(c_6808,plain,
! [X0: $i,X1: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_points(X0,sK0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_5493,c_61]) ).
tcf(c_6826,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X1)
| apart_point_and_line(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_4948,c_61]) ).
tcf(c_6827,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK0,X1)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_4948,c_60]) ).
tcf(c_6831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(X2,iPr_def_11)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_4948,c_59]) ).
tcf(c_6832,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X0,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_4948,c_52]) ).
tcf(c_6872,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_lines(X0,iPr_def_10)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5388,c_780]) ).
tcf(c_6873,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_lines(X0,iPr_def_10)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5388,c_777]) ).
tcf(c_6876,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_lines(X0,iPr_def_10)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5388,c_53]) ).
tcf(c_6883,plain,
! [X0: $i] :
( distinct_lines(iPr_def_11,X0)
| distinct_lines(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_5388,c_50]) ).
tcf(c_6884,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| distinct_lines(iPr_def_11,X2)
| distinct_lines(X1,iPr_def_10)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_5388,c_780]) ).
tcf(c_6885,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK1,X1)
| distinct_lines(iPr_def_11,X2)
| distinct_lines(X1,iPr_def_10)
| distinct_points(sK2,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_5388,c_777]) ).
tcf(c_6886,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X1)
| distinct_lines(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_5388,c_771]) ).
tcf(c_6887,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X1)
| distinct_lines(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_5388,c_770]) ).
tcf(c_6888,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_lines(X0,iPr_def_10)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5388,c_53]) ).
tcf(c_7014,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(X0,iPr_def_10)
| distinct_lines(iPr_def_11,X1)
| distinct_points(sK2,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_6883,c_777]) ).
tcf(c_7017,plain,
! [X0: $i,X1: $i] :
( distinct_lines(iPr_def_11,X0)
| distinct_lines(iPr_def_10,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6883,c_53]) ).
tcf(c_7066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(X3,sK1)
| distinct_points(X2,sK0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5488,c_59]) ).
tcf(c_7067,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X2,sK1)
| distinct_points(X0,sK0)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5488,c_52]) ).
tcf(c_7096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(X3,sK2)
| distinct_points(X2,sK0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5489,c_59]) ).
tcf(c_7097,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X2,sK2)
| distinct_points(X0,sK0)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5489,c_52]) ).
tcf(c_7124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(X4,iPr_def_11)
| distinct_points(sK0,X4)
| distinct_points(sK0,X3)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X3,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_780]) ).
tcf(c_7125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(X4,iPr_def_11)
| distinct_points(sK2,X4)
| distinct_points(sK0,X3)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X3,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_777]) ).
tcf(c_7129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X4,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_lines(X4,X2)
| distinct_points(X3,X1)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_56]) ).
tcf(c_7130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X4,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_lines(X4,X2)
| distinct_points(X3,X0)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_55]) ).
tcf(c_7131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X3)
| distinct_lines(X2,X3)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_61]) ).
tcf(c_7132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X4)
| distinct_lines(X3,X4)
| distinct_lines(X2,X3)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_60]) ).
tcf(c_7134,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X1,iPr_def_11)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X2,sK1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_745]) ).
tcf(c_7135,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X1,iPr_def_11)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X2,sK2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_725]) ).
tcf(c_7136,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X1,iPr_def_10)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X2,sK1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_742]) ).
tcf(c_7137,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X1,iPr_def_10)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X2,sK0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_722]) ).
tcf(c_7139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X1)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X4)
| distinct_points(sK0,X2)
| apart_point_and_line(X4,X3)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X2,X3)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_780]) ).
tcf(c_7140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X1)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK2,X4)
| distinct_points(sK0,X2)
| apart_point_and_line(X4,X3)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X2,X3)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_777]) ).
tcf(c_7141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X3)
| apart_point_and_line(sK0,X1)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_771]) ).
tcf(c_7142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X3)
| apart_point_and_line(sK0,X1)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_770]) ).
tcf(c_7143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X3)
| distinct_lines(X3,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_53]) ).
tcf(c_7145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X4)
| apart_point_and_line(sK2,X0)
| distinct_lines(X4,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X4)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_780]) ).
tcf(c_7146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X4)
| apart_point_and_line(sK1,X0)
| distinct_lines(X4,iPr_def_11)
| distinct_points(sK2,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X4)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_777]) ).
tcf(c_7147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X3)
| apart_point_and_line(sK0,X0)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_771]) ).
tcf(c_7148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X3)
| apart_point_and_line(sK0,X0)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_770]) ).
tcf(c_7149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X1)
| distinct_lines(X3,X2)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5712,c_53]) ).
tcf(c_7152,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(X1,iPr_def_11)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X1)
| distinct_lines(X0,X0) ),
inference(equality_factoring,[status(thm)],[c_5712]) ).
tcf(c_7154,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_5712]) ).
tcf(c_7155,plain,
! [X0: $i,X1: $i] :
( distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X1)
| apart_point_and_line(X1,X0)
| distinct_lines(X0,X0) ),
inference(equality_factoring,[status(thm)],[c_5712]) ).
tcf(c_7452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(X4,iPr_def_11)
| distinct_points(sK0,X4)
| distinct_points(sK0,X0)
| apart_point_and_line(X4,X2)
| apart_point_and_line(X1,X3)
| distinct_lines(X2,X3)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_780]) ).
tcf(c_7453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X2)
| apart_point_and_line(X4,iPr_def_11)
| distinct_points(sK2,X4)
| distinct_points(sK0,X0)
| apart_point_and_line(X4,X2)
| apart_point_and_line(X1,X3)
| distinct_lines(X2,X3)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_777]) ).
tcf(c_7458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(X4,iPr_def_11)
| apart_point_and_line(X3,X5)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_lines(X4,X5)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_59]) ).
tcf(c_7459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X1,X4)
| distinct_lines(X3,X4)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_52]) ).
tcf(c_7460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(X4,X1)
| distinct_points(X3,X4)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_56]) ).
tcf(c_7461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(X4,X0)
| distinct_points(X3,X4)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_55]) ).
tcf(c_7463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X4)
| distinct_lines(X3,X4)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_60]) ).
tcf(c_7468,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_lines(X2,iPr_def_10)
| distinct_points(sK0,X0)
| distinct_points(X1,sK0)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_722]) ).
tcf(c_7470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X4)
| apart_point_and_line(sK2,X2)
| distinct_lines(X4,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X3,X4)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_780]) ).
tcf(c_7471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X4)
| apart_point_and_line(sK1,X2)
| distinct_lines(X4,iPr_def_11)
| distinct_points(sK2,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X3,X4)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_777]) ).
tcf(c_7472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(sK0,X3)
| apart_point_and_line(sK0,X2)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_771]) ).
tcf(c_7473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X2)
| apart_point_and_line(sK0,X3)
| apart_point_and_line(sK0,X2)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_770]) ).
tcf(c_7474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X4,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X2)
| distinct_lines(X4,X3)
| distinct_lines(X2,X3)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_53]) ).
tcf(c_7476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X5)
| apart_point_and_line(X5,X1)
| apart_point_and_line(X5,X0)
| apart_point_and_line(X4,X3)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| distinct_lines(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_59]) ).
tcf(c_7477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X0,X4)
| distinct_lines(X3,X4)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5713,c_52]) ).
tcf(c_7480,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X1,iPr_def_11)
| distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_points(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_5713]) ).
tcf(c_7624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(X4,iPr_def_11)
| distinct_points(sK0,X4)
| distinct_points(sK0,X3)
| apart_point_and_line(X4,X2)
| apart_point_and_line(X3,X0)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5724,c_780]) ).
tcf(c_7625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X2)
| apart_point_and_line(X4,iPr_def_11)
| distinct_points(sK2,X4)
| distinct_points(sK0,X3)
| apart_point_and_line(X4,X2)
| apart_point_and_line(X3,X0)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5724,c_777]) ).
tcf(c_7628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X0)
| distinct_lines(X2,X3)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5724,c_53]) ).
tcf(c_7629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X4,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_lines(X4,X2)
| distinct_points(X3,X1)
| distinct_lines(line_connecting(X0,X1),X2)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5724,c_56]) ).
tcf(c_7630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X4,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_lines(X4,X2)
| distinct_points(X3,X0)
| distinct_lines(line_connecting(X0,X1),X2)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5724,c_55]) ).
tcf(c_7631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X2)
| distinct_lines(X3,X1)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5724,c_61]) ).
tcf(c_7636,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_10,X1)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X2,sK1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5724,c_742]) ).
tcf(c_7637,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_10,X1)
| distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X2,sK0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5724,c_722]) ).
tcf(c_7638,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5724,c_50]) ).
tcf(c_7639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X4)
| apart_point_and_line(sK2,X1)
| distinct_lines(X4,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X4)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5724,c_780]) ).
tcf(c_7640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X4)
| apart_point_and_line(sK1,X1)
| distinct_lines(X4,iPr_def_11)
| distinct_points(sK2,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X4)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5724,c_777]) ).
tcf(c_7641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X3)
| apart_point_and_line(sK0,X1)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5724,c_771]) ).
tcf(c_7642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X3)
| apart_point_and_line(sK0,X1)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5724,c_770]) ).
tcf(c_7643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X0)
| distinct_lines(X3,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_5724,c_53]) ).
tcf(c_7655,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X0,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_5724]) ).
tcf(c_7942,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK0,sK0)
| distinct_lines(X1,iPr_def_10)
| distinct_lines(X0,iPr_def_11)
| distinct_lines(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_7137]) ).
tcf(c_7946,plain,
! [X0: $i,X1: $i] :
( distinct_lines(X1,iPr_def_10)
| distinct_lines(X0,iPr_def_11)
| distinct_lines(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7942,c_49]) ).
tcf(c_7969,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(sK1,sK1)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK2,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_1084,c_745]) ).
tcf(c_7975,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| distinct_points(sK1,sK1)
| apart_point_and_line(X1,iPr_def_11)
| apart_point_and_line(X0,iPr_def_11)
| distinct_points(sK2,X1)
| distinct_points(sK0,X0) ),
inference(superposition,[status(thm)],[c_1084,c_745]) ).
tcf(c_7977,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| distinct_points(sK1,sK1)
| apart_point_and_line(X1,iPr_def_11)
| apart_point_and_line(X1,iPr_def_10)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK2,X1)
| distinct_points(sK0,X0) ),
inference(superposition,[status(thm)],[c_1084,c_742]) ).
tcf(c_7987,plain,
! [X0: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK2,iPr_def_11)
| distinct_points(sK2,sK2)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK0,X0) ),
inference(superposition,[status(thm)],[c_1084,c_221]) ).
tcf(c_8087,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK2,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7969,c_49]) ).
tcf(c_8101,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6021,c_780]) ).
tcf(c_8102,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6021,c_777]) ).
tcf(c_8105,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK0,X1)
| distinct_lines(iPr_def_11,X2)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6021,c_53]) ).
tcf(c_8108,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X2)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK2,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_6021,c_777]) ).
tcf(c_8166,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X0,sK0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_6808,c_780]) ).
tcf(c_8167,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(X2,iPr_def_11)
| distinct_points(sK2,X2)
| distinct_points(X0,sK0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_6808,c_777]) ).
tcf(c_8170,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_points(X2,sK0)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6808,c_53]) ).
tcf(c_8171,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X2,sK0)
| distinct_points(X2,X1)
| distinct_lines(iPr_def_11,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_6808,c_56]) ).
tcf(c_8172,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X2,sK0)
| distinct_points(X2,X0)
| distinct_lines(iPr_def_11,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_6808,c_55]) ).
tcf(c_8173,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X0)
| distinct_points(X2,sK0)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_6808,c_61]) ).
tcf(c_8276,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(X2,iPr_def_10)
| distinct_lines(iPr_def_11,X0)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_7017,c_777]) ).
tcf(c_8278,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X1)
| distinct_lines(iPr_def_11,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_7017,c_770]) ).
tcf(c_8279,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X0)
| distinct_lines(iPr_def_10,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_7017,c_53]) ).
tcf(c_8338,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(X2,iPr_def_11)
| distinct_lines(X1,iPr_def_10)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_7946,c_780]) ).
tcf(c_8339,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(X2,iPr_def_11)
| distinct_lines(X1,iPr_def_10)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_7946,c_777]) ).
tcf(c_8342,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_lines(X1,iPr_def_10)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_7946,c_53]) ).
tcf(c_8344,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| distinct_lines(X2,iPr_def_10)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_7946,c_780]) ).
tcf(c_8345,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK1,X1)
| distinct_lines(X2,iPr_def_10)
| distinct_lines(X1,iPr_def_11)
| distinct_points(sK2,X0)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_7946,c_777]) ).
tcf(c_8346,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(X1,iPr_def_10)
| distinct_lines(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_7946,c_771]) ).
tcf(c_8347,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(X1,iPr_def_10)
| distinct_lines(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_7946,c_770]) ).
tcf(c_8348,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X2,iPr_def_10)
| distinct_lines(X0,iPr_def_11)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_7946,c_53]) ).
tcf(c_8410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_780]) ).
tcf(c_8411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK2,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_777]) ).
tcf(c_8414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X3)
| apart_point_and_line(X3,X0)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_53]) ).
tcf(c_8415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X3)
| distinct_points(X3,X1)
| distinct_lines(line_connecting(X0,X1),X2)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_56]) ).
tcf(c_8416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X3)
| distinct_points(X3,X0)
| distinct_lines(line_connecting(X0,X1),X2)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_55]) ).
tcf(c_8417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_points(sK0,X3)
| apart_point_and_line(X3,X2)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_61]) ).
tcf(c_8418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X2)
| distinct_lines(X2,X3)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_60]) ).
tcf(c_8423,plain,
! [X0: $i,X1: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_lines(iPr_def_10,X1)
| distinct_points(sK0,X0)
| distinct_points(X0,sK0) ),
inference(superposition,[status(thm)],[c_621,c_722]) ).
tcf(c_8425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X1)
| distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_780]) ).
tcf(c_8426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X1)
| distinct_lines(iPr_def_11,X3)
| distinct_points(sK2,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_777]) ).
tcf(c_8427,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(sK0,X1)
| distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_771]) ).
tcf(c_8428,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(sK0,X1)
| distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_770]) ).
tcf(c_8429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X3)
| apart_point_and_line(X3,X0)
| distinct_lines(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_53]) ).
tcf(c_8430,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(X0,iPr_def_11)
| distinct_lines(iPr_def_11,X1)
| distinct_points(sK0,X0) ),
inference(equality_factoring,[status(thm)],[c_621]) ).
tcf(c_8643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apart_point_and_line(sK0,X3)
| apart_point_and_line(sK0,X2)
| distinct_lines(X4,iPr_def_11)
| apart_point_and_line(X5,X3)
| apart_point_and_line(X5,X2)
| distinct_points(X5,X1)
| distinct_lines(X4,line_connecting(X0,X1))
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5710,c_59]) ).
tcf(c_8644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X4)
| distinct_points(X3,X4)
| distinct_points(X3,X1)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5710,c_52]) ).
tcf(c_8645,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X1)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5710,c_49]) ).
tcf(c_8646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( distinct_lines(X4,iPr_def_11)
| distinct_points(sK0,X5)
| apart_point_and_line(X5,X3)
| apart_point_and_line(X5,X2)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| distinct_lines(X4,line_connecting(X0,X1))
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5710,c_59]) ).
tcf(c_8647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X4)
| distinct_points(X4,X3)
| distinct_points(X1,X3)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5710,c_52]) ).
tcf(c_8649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X4)
| distinct_lines(X4,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X4)
| distinct_points(X3,X1)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5710,c_780]) ).
tcf(c_8650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X4)
| distinct_lines(X4,iPr_def_11)
| distinct_points(sK2,X2)
| distinct_points(sK0,X3)
| apart_point_and_line(X2,X4)
| distinct_points(X3,X1)
| apart_point_and_line(sK1,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5710,c_777]) ).
tcf(c_8651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK0,X3)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X2,X1)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| apart_point_and_line(sK0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5710,c_771]) ).
tcf(c_8652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK0,X3)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X2,X1)
| apart_point_and_line(sK1,line_connecting(X0,X1))
| apart_point_and_line(sK0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5710,c_770]) ).
tcf(c_8654,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK0,sK0)
| distinct_lines(X1,iPr_def_11)
| distinct_lines(X1,line_connecting(X0,sK0))
| ~ distinct_points(X0,sK0) ),
inference(equality_factoring,[status(thm)],[c_5710]) ).
tcf(c_8656,plain,
! [X0: $i,X1: $i] :
( distinct_lines(X1,iPr_def_11)
| distinct_lines(X1,line_connecting(X0,sK0))
| ~ distinct_points(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8654,c_49]) ).
tcf(c_8860,plain,
! [X0: $i,X1: $i] :
( distinct_lines(X1,iPr_def_11)
| distinct_lines(X1,iPr_def_10)
| distinct_points(sK0,X0)
| distinct_points(X0,sK0)
| ~ distinct_points(sK0,sK1) ),
inference(superposition,[status(thm)],[c_219,c_5711]) ).
tcf(c_8862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apart_point_and_line(sK0,X3)
| apart_point_and_line(sK0,X2)
| distinct_lines(X4,iPr_def_11)
| apart_point_and_line(X5,X3)
| apart_point_and_line(X5,X2)
| distinct_points(X5,X0)
| distinct_lines(X4,line_connecting(X0,X1))
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5711,c_59]) ).
tcf(c_8863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X4)
| distinct_points(X3,X4)
| distinct_points(X3,X0)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5711,c_52]) ).
tcf(c_8864,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X0)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5711,c_49]) ).
tcf(c_8865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( distinct_lines(X4,iPr_def_11)
| distinct_points(sK0,X5)
| apart_point_and_line(X5,X3)
| apart_point_and_line(X5,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| distinct_lines(X4,line_connecting(X0,X1))
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5711,c_59]) ).
tcf(c_8866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(X2,iPr_def_11)
| distinct_points(sK0,X4)
| distinct_points(X4,X3)
| distinct_points(X0,X3)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5711,c_52]) ).
tcf(c_8868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK2,X4)
| distinct_lines(X4,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X4)
| distinct_points(X3,X0)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5711,c_780]) ).
tcf(c_8869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X4)
| distinct_lines(X4,iPr_def_11)
| distinct_points(sK2,X2)
| distinct_points(sK0,X3)
| apart_point_and_line(X2,X4)
| distinct_points(X3,X0)
| apart_point_and_line(sK1,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5711,c_777]) ).
tcf(c_8870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK0,X3)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X2,X0)
| apart_point_and_line(sK2,line_connecting(X0,X1))
| apart_point_and_line(sK0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5711,c_771]) ).
tcf(c_8871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK0,X3)
| distinct_lines(X3,iPr_def_11)
| distinct_points(sK0,X2)
| distinct_points(X2,X0)
| apart_point_and_line(sK1,line_connecting(X0,X1))
| apart_point_and_line(sK0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_5711,c_770]) ).
tcf(c_8873,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK0,sK0)
| distinct_lines(X1,iPr_def_11)
| distinct_lines(X1,line_connecting(sK0,X0))
| ~ distinct_points(sK0,X0) ),
inference(equality_factoring,[status(thm)],[c_5711]) ).
tcf(c_8875,plain,
! [X0: $i,X1: $i] :
( distinct_lines(X1,iPr_def_11)
| distinct_lines(X1,line_connecting(sK0,X0))
| ~ distinct_points(sK0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8873,c_49]) ).
tcf(c_9010,plain,
! [X0: $i] :
( apart_point_and_line(sK1,iPr_def_10)
| distinct_points(sK1,sK1)
| apart_point_and_line(X0,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK2,X0) ),
inference(superposition,[status(thm)],[c_1085,c_745]) ).
tcf(c_9023,plain,
! [X0: $i] :
( apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(X0,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9010,c_49]) ).
tcf(c_9042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X3)
| distinct_points(X3,X1)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_622,c_56]) ).
tcf(c_9043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X3)
| distinct_points(X3,X0)
| distinct_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_622,c_55]) ).
tcf(c_9044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X0)
| distinct_points(sK0,X3)
| apart_point_and_line(X3,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_622,c_61]) ).
tcf(c_9045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_points(sK0,X0)
| apart_point_and_line(X1,X3)
| distinct_lines(X2,X3)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_622,c_60]) ).
tcf(c_9050,plain,
! [X0: $i,X1: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_lines(X1,iPr_def_10)
| distinct_points(sK0,X0)
| distinct_points(X0,sK0) ),
inference(superposition,[status(thm)],[c_622,c_722]) ).
tcf(c_9113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_623,c_780]) ).
tcf(c_9114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X2)
| apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK2,X3)
| distinct_points(sK0,X0)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_623,c_777]) ).
tcf(c_9119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X4)
| apart_point_and_line(X3,X4)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_623,c_59]) ).
tcf(c_9121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK0,X2)
| distinct_points(X3,X1)
| distinct_points(X2,X3)
| distinct_lines(iPr_def_11,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_623,c_56]) ).
tcf(c_9122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK0,X2)
| distinct_points(X3,X0)
| distinct_points(X2,X3)
| distinct_lines(iPr_def_11,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_623,c_55]) ).
tcf(c_9131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X4)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_623,c_59]) ).
tcf(c_9132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X0,X3)
| distinct_points(X2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_623,c_52]) ).
tcf(c_9289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK0,X3)
| apart_point_and_line(X3,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_680,c_780]) ).
tcf(c_9290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| apart_point_and_line(sK1,X2)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(X3,iPr_def_11)
| distinct_points(sK2,X3)
| apart_point_and_line(X3,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_680,c_777]) ).
tcf(c_9293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X3)
| distinct_lines(X2,X3)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_680,c_53]) ).
tcf(c_9295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X3)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_680,c_780]) ).
tcf(c_9296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X3)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_680,c_777]) ).
tcf(c_9297,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_680,c_771]) ).
tcf(c_9298,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_680,c_770]) ).
tcf(c_9299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X3)
| distinct_lines(X3,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_680,c_53]) ).
tcf(c_9302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X3)
| distinct_lines(iPr_def_11,X1)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_680,c_777]) ).
tcf(c_9305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X3)
| distinct_lines(iPr_def_11,X1)
| distinct_lines(X3,X2)
| distinct_lines(X0,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_680,c_53]) ).
tcf(c_9308,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK0,X0)
| distinct_lines(iPr_def_11,X1)
| distinct_lines(X0,iPr_def_11) ),
inference(equality_factoring,[status(thm)],[c_680]) ).
tcf(c_9445,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK0,X1)
| distinct_lines(iPr_def_11,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_682,c_50]) ).
tcf(c_9446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK2,X3)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X3)
| distinct_lines(iPr_def_11,X0)
| distinct_points(sK0,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_682,c_780]) ).
tcf(c_9447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK1,X3)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X3)
| distinct_lines(iPr_def_11,X0)
| distinct_points(sK2,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_682,c_777]) ).
tcf(c_9450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X3)
| distinct_lines(iPr_def_11,X0)
| distinct_lines(X3,X2)
| distinct_lines(X1,X2)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_682,c_53]) ).
tcf(c_9519,plain,
! [X0: $i,X1: $i] :
( distinct_points(X1,sK0)
| distinct_points(X0,sK1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1365,c_49]) ).
tcf(c_9520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(X2,sK1)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| distinct_points(X3,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1365,c_59]) ).
tcf(c_9521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK0,X3)
| distinct_points(X0,sK1)
| distinct_points(X2,X3)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1365,c_52]) ).
tcf(c_9523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| distinct_points(sK0,X4)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X3,X4)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1365,c_59]) ).
tcf(c_9524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK1,X2)
| distinct_points(sK0,X3)
| distinct_points(X1,X3)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1365,c_52]) ).
tcf(c_9526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_points(sK0,X4)
| distinct_points(X2,sK1)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1365,c_59]) ).
tcf(c_9527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK0,X3)
| distinct_points(X0,sK1)
| distinct_points(X3,X2)
| distinct_points(X1,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1365,c_52]) ).
tcf(c_9529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( distinct_points(sK0,X3)
| distinct_points(X4,sK1)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X4,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1365,c_59]) ).
tcf(c_9530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(sK0,X1)
| distinct_points(X3,sK1)
| distinct_points(X3,X2)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1365,c_52]) ).
tcf(c_9541,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK1,X1)
| distinct_points(sK0,X1)
| distinct_points(X0,sK1) ),
inference(equality_factoring,[status(thm)],[c_1365]) ).
tcf(c_9649,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_9541,c_9530,c_9529,c_9527,c_9526,c_9524,c_9523,c_9521,c_9520,c_9519,c_9450,c_9447,c_9446,c_9445,c_9308,c_9305,c_9302,c_9299,c_9298,c_9297,c_9296,c_9295,c_9293,c_9290,c_9289,c_9132,c_9131,c_9122,c_9121,c_9119,c_9114,c_9113,c_9050,c_9045,c_9044,c_9043,c_9042,c_9023,c_9010,c_8875,c_8873,c_8871,c_8870,c_8869,c_8868,c_8866,c_8865,c_8863,c_8862,c_8864,c_8860,c_8656,c_8654,c_8652,c_8651,c_8650,c_8649,c_8647,c_8646,c_8644,c_8643,c_8645,c_8430,c_8429,c_8428,c_8427,c_8426,c_8425,c_8423,c_8418,c_8417,c_8416,c_8415,c_8414,c_8411,c_8410,c_8348,c_8347,c_8346,c_8345,c_8344,c_8342,c_8339,c_8338,c_8279,c_8278,c_8276,c_8173,c_8172,c_8171,c_8170,c_8167,c_8166,c_8108,c_8105,c_8102,c_8101,c_8087,c_7987,c_7977,c_7975,c_7969,c_7946,c_7942,c_7655,c_7643,c_7642,c_7641,c_7640,c_7639,c_7638,c_7637,c_7636,c_7631,c_7630,c_7629,c_7628,c_7625,c_7624,c_7480,c_7477,c_7476,c_7474,c_7473,c_7472,c_7471,c_7470,c_7468,c_7463,c_7461,c_7460,c_7459,c_7458,c_7453,c_7452,c_7155,c_7154,c_7152,c_7149,c_7148,c_7147,c_7146,c_7145,c_7143,c_7142,c_7141,c_7140,c_7139,c_7137,c_7136,c_7135,c_7134,c_7132,c_7131,c_7130,c_7129,c_7125,c_7124,c_7097,c_7096,c_7067,c_7066,c_7017,c_7014,c_6888,c_6887,c_6886,c_6885,c_6884,c_6883,c_6876,c_6873,c_6872,c_6832,c_6831,c_6827,c_6826,c_6808,c_6619,c_6618,c_6613,c_6612,c_6610,c_6609,c_6608,c_6607,c_6231,c_6225,c_6224,c_6223,c_6222,c_6221,c_6219,c_6218,c_6217,c_6216,c_6215,c_6213,c_6212,c_6211,c_6210,c_6208,c_6207,c_6206,c_6205,c_6204,c_6201,c_6200,c_6037,c_6034,c_6032,c_6031,c_6030,c_6029,c_6028,c_6027,c_6026,c_6023,c_6022,c_6021,c_6020,c_6017,c_6016,c_6006,c_5881,c_5878,c_5875,c_5872,c_5871,c_5869,c_5868,c_5867,c_5866,c_5865,c_5864,c_5863,c_5860,c_5859,c_5828,c_5826,c_5825,c_5725,c_5724,c_5723,c_5722,c_5721,c_5720,c_5719,c_5718,c_5713,c_5712,c_5711,c_5710,c_5709,c_5706,c_5705,c_5694,c_5641,c_5638,c_5635,c_5632,c_5631,c_5620,c_5495,c_5494,c_5493,c_5489,c_5488,c_5487,c_5486,c_5388,c_5385,c_5384,c_5235,c_5201,c_5162,c_5161,c_5160,c_5159,c_5156,c_5153,c_5152,c_5150,c_5149,c_5148,c_5147,c_5146,c_5145,c_5120,c_5119,c_5080,c_5079,c_5074,c_5073,c_5042,c_5041,c_4956,c_4953,c_4950,c_4949,c_4948,c_4944,c_4943,c_4942,c_4938,c_4777,c_4774,c_4773,c_4772,c_4771,c_4770,c_4768,c_4634,c_4631,c_4630,c_4629,c_4628,c_4627,c_4625,c_4446,c_4440,c_4437,c_4436,c_4432,c_4431,c_4429,c_4428,c_4427,c_4426,c_4425,c_4424,c_4422,c_4419,c_4418,c_4233,c_4232,c_4225,c_4223,c_4222,c_4221,c_4218,c_4217,c_4216,c_4212,c_4057,c_4056,c_4053,c_4052,c_4051,c_4050,c_4049,c_4042,c_4041,c_4040,c_4039,c_4038,c_4035,c_4034,c_4031,c_3993,c_3992,c_3963,c_3962,c_3923,c_3922,c_3917,c_3916,c_3860,c_3859,c_3854,c_3853,c_3782,c_3781,c_3779,c_3778,c_3776,c_3775,c_3773,c_3772,c_3771,c_3770,c_3669,c_3668,c_3661,c_3660,c_3659,c_3658,c_3657,c_3654,c_3653,c_3651,c_3650,c_3648,c_3624,c_3567,c_3559,c_3439,c_3410,c_3310,c_3302,c_3301,c_3300,c_3299,c_3293,c_3292,c_3291,c_3290,c_3289,c_3286,c_3285,c_3284,c_3283,c_3282,c_3281,c_3280,c_3279,c_3033,c_3032,c_3031,c_3030,c_3029,c_3026,c_3025,c_2870,c_2869,c_2868,c_2867,c_2863,c_2862,c_2860,c_2857,c_2856,c_2826,c_2810,c_2807,c_2806,c_2793,c_2767,c_2751,c_2639,c_2638,c_2637,c_2636,c_2635,c_2633,c_2630,c_2627,c_2624,c_2623,c_2622,c_2592,c_2591,c_2576,c_2495,c_2494,c_2492,c_2491,c_2489,c_2488,c_2487,c_2413,c_2411,c_2402,c_2401,c_2396,c_2395,c_2393,c_2392,c_2321,c_2317,c_2311,c_2310,c_2309,c_2305,c_2304,c_2303,c_2301,c_2196,c_2195,c_2193,c_2192,c_2190,c_2189,c_2187,c_2186,c_2185,c_2120,c_2118,c_2109,c_2108,c_2103,c_2102,c_2100,c_2099,c_1984,c_1980,c_1974,c_1973,c_1972,c_1968,c_1967,c_1964,c_1861,c_1860,c_1858,c_1857,c_1855,c_1854,c_1852,c_1851,c_1777,c_1775,c_1766,c_1765,c_1760,c_1759,c_1757,c_1756,c_1648,c_1644,c_1638,c_1637,c_1636,c_1632,c_1631,c_1628,c_1587,c_1586,c_1563,c_1562,c_1505,c_1504,c_1502,c_1501,c_1499,c_1498,c_1497,c_1481,c_1480,c_1371,c_1370,c_1368,c_1367,c_1365,c_1364,c_1363,c_1345,c_1304,c_1301,c_1300,c_1299,c_1214,c_1213,c_1211,c_1210,c_1208,c_1207,c_1205,c_1204,c_1203,c_1152,c_1150,c_1149,c_1148,c_1146,c_1085,c_1084,c_1083,c_1086,c_1081,c_1056,c_1052,c_1012,c_989,c_988,c_952,c_951,c_783,c_782,c_781,c_780,c_779,c_785,c_777,c_776,c_775,c_774,c_773,c_784,c_771,c_770,c_769,c_768,c_767,c_766,c_745,c_742,c_741,c_740,c_739,c_725,c_722,c_721,c_720,c_719,c_701,c_682,c_680,c_679,c_655,c_653,c_651,c_623,c_622,c_621,c_594,c_592,c_590,c_589,c_565,c_560,c_558,c_556,c_555,c_534,c_529,c_527,c_525,c_524,c_514,c_502,c_501,c_492,c_491,c_483,c_474,c_465,c_456,c_533,c_564,c_434,c_433,c_432,c_225,c_221,c_220,c_219,c_222,c_223,c_224,c_61,c_60,c_59,c_56,c_55,c_53,c_52,c_50,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO188+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/10.38 % Computer : n011.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Wed Sep 23 11:22:09 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/10.42 Running first-order theorem proving
% 0.14/10.42 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
% 0.14/10.44
% 0.14/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.44
% 0.14/10.44 % Detected problem language: tptp
% 0.14/10.45 % Proving...
% 3.01/11.30 % SZS status Started for theBenchmark.p
% 3.01/11.30 % SZS status Theorem for theBenchmark.p
% 3.01/11.30
% 3.01/11.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.01/11.30
% 3.01/11.30 % ------ iProver source info
% 3.01/11.30
% 3.01/11.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.01/11.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.01/11.30 % git: non_committed_changes: false
% 3.01/11.30
% 3.01/11.30 % ------ Parsing...
% 3.01/11.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.01/11.30
% 3.01/11.30 % ------ Preprocessing... sf_s rm: 5 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.01/11.30
% 3.01/11.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.01/11.30
% 3.01/11.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.01/11.30 % ------ Proving...
% 3.01/11.30 % ------ Problem Properties
% 3.01/11.30
% 3.01/11.30 %
% 3.01/11.30 % clauses 16
% 3.01/11.30 % conjectures 5
% 3.01/11.30 % EPR 12
% 3.01/11.30 % Horn 11
% 3.01/11.30 % unary 9
% 3.01/11.30 % binary 0
% 3.01/11.30 % lits 33
% 3.01/11.30 % lits eq 2
% 3.01/11.30 % fd_pure 0
% 3.01/11.30 % fd_pseudo 0
% 3.01/11.30 % fd_cond 0
% 3.01/11.30 % fd_pseudo_cond 0
% 3.01/11.30 % AC symbols 0
% 3.01/11.30
% 3.01/11.30 % ------ Schedule dynamic 5 is on
% 3.01/11.30
% 3.01/11.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.01/11.30
% 3.01/11.30
% 3.01/11.30 % ------
% 3.01/11.30 % Current options:
% 3.01/11.30 % ------
% 3.01/11.30
% 3.01/11.30
% 3.01/11.30 %
% 3.01/11.30
% 3.01/11.30 % ------ Proving...
% 3.01/11.30 %
% 3.01/11.30
% 3.01/11.30 % SZS status Theorem for theBenchmark.p
% 3.01/11.30
% 3.01/11.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.01/11.32
% 3.01/11.32
%------------------------------------------------------------------------------