TSTP Solution File: GEO076-4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO076-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:34:42 EDT 2022
% Result : Unsatisfiable 5.28s 3.60s
% Output : Proof 5.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GEO076-4 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.36 % Computer : n020.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 31 05:18:00 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 5.28/3.60 % SZS status Unsatisfiable
% 5.28/3.60 % SZS output start Proof
% 5.28/3.60 tff(on_type, type, (
% 5.28/3.60 on: ( $i * $i ) > $o)).
% 5.28/3.60 tff(line_from_to_type, type, (
% 5.28/3.60 line_from_to: ( $i * $i ) > $i)).
% 5.28/3.60 tff(point_2_on_line_type, type, (
% 5.28/3.60 point_2_on_line: $i > $i)).
% 5.28/3.60 tff(at_least_one_line_type, type, (
% 5.28/3.60 at_least_one_line: $i)).
% 5.28/3.60 tff(point_not_on_line_type, type, (
% 5.28/3.60 point_not_on_line: $i > $i)).
% 5.28/3.60 tff(a_point_type, type, (
% 5.28/3.60 a_point: $i)).
% 5.28/3.60 tff(point_on_plane_type, type, (
% 5.28/3.60 point_on_plane: $i > $i)).
% 5.28/3.60 tff(plane_for_points_type, type, (
% 5.28/3.60 plane_for_points: ( $i * $i * $i ) > $i)).
% 5.28/3.60 tff(point_1_on_line_type, type, (
% 5.28/3.60 point_1_on_line: $i > $i)).
% 5.28/3.60 tff(line_type, type, (
% 5.28/3.60 line: $i > $o)).
% 5.28/3.60 tff(point_type, type, (
% 5.28/3.60 point: $i > $o)).
% 5.28/3.60 tff(collinear_type, type, (
% 5.28/3.60 collinear: ( $i * $i * $i ) > $o)).
% 5.28/3.60 tff(line_through_3_points_type, type, (
% 5.28/3.60 line_through_3_points: ( $i * $i * $i ) > $i)).
% 5.28/3.60 tff(plane_type, type, (
% 5.28/3.60 plane: $i > $o)).
% 5.28/3.60 tff(1,assumption,(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line), introduced(assumption)).
% 5.28/3.60 tff(2,plain,
% 5.28/3.60 (at_least_one_line = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))),
% 5.28/3.60 inference(symmetry,[status(thm)],[1])).
% 5.28/3.60 tff(3,plain,
% 5.28/3.60 (on(point_not_on_line(at_least_one_line), at_least_one_line) <=> on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.60 inference(monotonicity,[status(thm)],[2])).
% 5.28/3.60 tff(4,plain,
% 5.28/3.60 (on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_not_on_line(at_least_one_line), at_least_one_line)),
% 5.28/3.60 inference(symmetry,[status(thm)],[3])).
% 5.28/3.60 tff(5,assumption,(point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)), introduced(assumption)).
% 5.28/3.60 tff(6,plain,
% 5.28/3.60 (on(point_not_on_line(at_least_one_line), at_least_one_line) <=> on(point_1_on_line(at_least_one_line), at_least_one_line)),
% 5.28/3.60 inference(monotonicity,[status(thm)],[5])).
% 5.28/3.60 tff(7,plain,
% 5.28/3.60 (on(point_1_on_line(at_least_one_line), at_least_one_line) <=> on(point_not_on_line(at_least_one_line), at_least_one_line)),
% 5.28/3.60 inference(symmetry,[status(thm)],[6])).
% 5.28/3.60 tff(8,plain,
% 5.28/3.60 (line(at_least_one_line) <=> line(at_least_one_line)),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(9,axiom,(line(at_least_one_line)), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G4A')).
% 5.28/3.60 tff(10,plain,
% 5.28/3.60 (line(at_least_one_line)),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[9, 8])).
% 5.28/3.60 tff(11,plain,
% 5.28/3.60 (^[Y1: $i] : refl((on(point_1_on_line(Y1), Y1) | (~line(Y1))) <=> (on(point_1_on_line(Y1), Y1) | (~line(Y1))))),
% 5.28/3.60 inference(bind,[status(th)],[])).
% 5.28/3.60 tff(12,plain,
% 5.28/3.60 (![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1))) <=> ![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))),
% 5.28/3.60 inference(quant_intro,[status(thm)],[11])).
% 5.28/3.60 tff(13,plain,
% 5.28/3.60 (![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1))) <=> ![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(14,axiom,(![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G2A')).
% 5.28/3.60 tff(15,plain,
% 5.28/3.60 (![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[14, 13])).
% 5.28/3.60 tff(16,plain,(
% 5.28/3.60 ![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))),
% 5.28/3.60 inference(skolemize,[status(sab)],[15])).
% 5.28/3.60 tff(17,plain,
% 5.28/3.60 (![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[16, 12])).
% 5.28/3.60 tff(18,plain,
% 5.28/3.60 (((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | ((~line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), at_least_one_line))) <=> ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (~line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), at_least_one_line))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(19,plain,
% 5.28/3.60 ((on(point_1_on_line(at_least_one_line), at_least_one_line) | (~line(at_least_one_line))) <=> ((~line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), at_least_one_line))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(20,plain,
% 5.28/3.60 (((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_1_on_line(at_least_one_line), at_least_one_line) | (~line(at_least_one_line)))) <=> ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | ((~line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), at_least_one_line)))),
% 5.28/3.60 inference(monotonicity,[status(thm)],[19])).
% 5.28/3.60 tff(21,plain,
% 5.28/3.60 (((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_1_on_line(at_least_one_line), at_least_one_line) | (~line(at_least_one_line)))) <=> ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (~line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), at_least_one_line))),
% 5.28/3.60 inference(transitivity,[status(thm)],[20, 18])).
% 5.28/3.60 tff(22,plain,
% 5.28/3.60 ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_1_on_line(at_least_one_line), at_least_one_line) | (~line(at_least_one_line)))),
% 5.28/3.60 inference(quant_inst,[status(thm)],[])).
% 5.28/3.60 tff(23,plain,
% 5.28/3.60 ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (~line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), at_least_one_line)),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[22, 21])).
% 5.28/3.60 tff(24,plain,
% 5.28/3.60 (on(point_1_on_line(at_least_one_line), at_least_one_line)),
% 5.28/3.60 inference(unit_resolution,[status(thm)],[23, 17, 10])).
% 5.28/3.60 tff(25,plain,
% 5.28/3.60 (on(point_not_on_line(at_least_one_line), at_least_one_line)),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[24, 7])).
% 5.28/3.60 tff(26,plain,
% 5.28/3.60 (^[Y1: $i] : refl(((~on(point_not_on_line(Y1), Y1)) | (~line(Y1))) <=> ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1))))),
% 5.28/3.60 inference(bind,[status(th)],[])).
% 5.28/3.60 tff(27,plain,
% 5.28/3.60 (![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1))) <=> ![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(quant_intro,[status(thm)],[26])).
% 5.28/3.60 tff(28,plain,
% 5.28/3.60 (![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1))) <=> ![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(29,axiom,(![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G3A')).
% 5.28/3.60 tff(30,plain,
% 5.28/3.60 (![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[29, 28])).
% 5.28/3.60 tff(31,plain,(
% 5.28/3.60 ![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(skolemize,[status(sab)],[30])).
% 5.28/3.60 tff(32,plain,
% 5.28/3.60 (![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[31, 27])).
% 5.28/3.60 tff(33,plain,
% 5.28/3.60 (((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | ((~line(at_least_one_line)) | (~on(point_not_on_line(at_least_one_line), at_least_one_line)))) <=> ((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | (~line(at_least_one_line)) | (~on(point_not_on_line(at_least_one_line), at_least_one_line)))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(34,plain,
% 5.28/3.60 (((~on(point_not_on_line(at_least_one_line), at_least_one_line)) | (~line(at_least_one_line))) <=> ((~line(at_least_one_line)) | (~on(point_not_on_line(at_least_one_line), at_least_one_line)))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(35,plain,
% 5.28/3.60 (((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | ((~on(point_not_on_line(at_least_one_line), at_least_one_line)) | (~line(at_least_one_line)))) <=> ((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | ((~line(at_least_one_line)) | (~on(point_not_on_line(at_least_one_line), at_least_one_line))))),
% 5.28/3.60 inference(monotonicity,[status(thm)],[34])).
% 5.28/3.60 tff(36,plain,
% 5.28/3.60 (((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | ((~on(point_not_on_line(at_least_one_line), at_least_one_line)) | (~line(at_least_one_line)))) <=> ((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | (~line(at_least_one_line)) | (~on(point_not_on_line(at_least_one_line), at_least_one_line)))),
% 5.28/3.60 inference(transitivity,[status(thm)],[35, 33])).
% 5.28/3.60 tff(37,plain,
% 5.28/3.60 ((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | ((~on(point_not_on_line(at_least_one_line), at_least_one_line)) | (~line(at_least_one_line)))),
% 5.28/3.60 inference(quant_inst,[status(thm)],[])).
% 5.28/3.60 tff(38,plain,
% 5.28/3.60 ((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | (~line(at_least_one_line)) | (~on(point_not_on_line(at_least_one_line), at_least_one_line))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[37, 36])).
% 5.28/3.60 tff(39,plain,
% 5.28/3.60 (~on(point_not_on_line(at_least_one_line), at_least_one_line)),
% 5.28/3.60 inference(unit_resolution,[status(thm)],[38, 32, 10])).
% 5.28/3.60 tff(40,plain,
% 5.28/3.60 ($false),
% 5.28/3.60 inference(unit_resolution,[status(thm)],[39, 25])).
% 5.28/3.60 tff(41,plain,(~(point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line))), inference(lemma,lemma(discharge,[]))).
% 5.28/3.60 tff(42,plain,
% 5.28/3.60 (^[Y1: $i] : refl((point(point_1_on_line(Y1)) | (~line(Y1))) <=> (point(point_1_on_line(Y1)) | (~line(Y1))))),
% 5.28/3.60 inference(bind,[status(th)],[])).
% 5.28/3.60 tff(43,plain,
% 5.28/3.60 (![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1))) <=> ![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(quant_intro,[status(thm)],[42])).
% 5.28/3.60 tff(44,plain,
% 5.28/3.60 (![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1))) <=> ![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(45,axiom,(![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G2C')).
% 5.28/3.60 tff(46,plain,
% 5.28/3.60 (![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[45, 44])).
% 5.28/3.60 tff(47,plain,(
% 5.28/3.60 ![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(skolemize,[status(sab)],[46])).
% 5.28/3.60 tff(48,plain,
% 5.28/3.60 (![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[47, 43])).
% 5.28/3.60 tff(49,plain,
% 5.28/3.60 (((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | ((~line(at_least_one_line)) | point(point_1_on_line(at_least_one_line)))) <=> ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (~line(at_least_one_line)) | point(point_1_on_line(at_least_one_line)))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(50,plain,
% 5.28/3.60 ((point(point_1_on_line(at_least_one_line)) | (~line(at_least_one_line))) <=> ((~line(at_least_one_line)) | point(point_1_on_line(at_least_one_line)))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(51,plain,
% 5.28/3.60 (((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (point(point_1_on_line(at_least_one_line)) | (~line(at_least_one_line)))) <=> ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | ((~line(at_least_one_line)) | point(point_1_on_line(at_least_one_line))))),
% 5.28/3.60 inference(monotonicity,[status(thm)],[50])).
% 5.28/3.60 tff(52,plain,
% 5.28/3.60 (((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (point(point_1_on_line(at_least_one_line)) | (~line(at_least_one_line)))) <=> ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (~line(at_least_one_line)) | point(point_1_on_line(at_least_one_line)))),
% 5.28/3.60 inference(transitivity,[status(thm)],[51, 49])).
% 5.28/3.60 tff(53,plain,
% 5.28/3.60 ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (point(point_1_on_line(at_least_one_line)) | (~line(at_least_one_line)))),
% 5.28/3.60 inference(quant_inst,[status(thm)],[])).
% 5.28/3.60 tff(54,plain,
% 5.28/3.60 ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (~line(at_least_one_line)) | point(point_1_on_line(at_least_one_line))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[53, 52])).
% 5.28/3.60 tff(55,plain,
% 5.28/3.60 (point(point_1_on_line(at_least_one_line))),
% 5.28/3.60 inference(unit_resolution,[status(thm)],[54, 48, 10])).
% 5.28/3.60 tff(56,plain,
% 5.28/3.60 (^[Y1: $i] : refl((point(point_not_on_line(Y1)) | (~line(Y1))) <=> (point(point_not_on_line(Y1)) | (~line(Y1))))),
% 5.28/3.60 inference(bind,[status(th)],[])).
% 5.28/3.60 tff(57,plain,
% 5.28/3.60 (![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1))) <=> ![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(quant_intro,[status(thm)],[56])).
% 5.28/3.60 tff(58,plain,
% 5.28/3.60 (![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1))) <=> ![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(59,axiom,(![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G3B')).
% 5.28/3.60 tff(60,plain,
% 5.28/3.60 (![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[59, 58])).
% 5.28/3.60 tff(61,plain,(
% 5.28/3.60 ![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(skolemize,[status(sab)],[60])).
% 5.28/3.60 tff(62,plain,
% 5.28/3.60 (![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[61, 57])).
% 5.28/3.60 tff(63,plain,
% 5.28/3.60 (((~![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))) | ((~line(at_least_one_line)) | point(point_not_on_line(at_least_one_line)))) <=> ((~![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))) | (~line(at_least_one_line)) | point(point_not_on_line(at_least_one_line)))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(64,plain,
% 5.28/3.60 ((point(point_not_on_line(at_least_one_line)) | (~line(at_least_one_line))) <=> ((~line(at_least_one_line)) | point(point_not_on_line(at_least_one_line)))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(65,plain,
% 5.28/3.60 (((~![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))) | (point(point_not_on_line(at_least_one_line)) | (~line(at_least_one_line)))) <=> ((~![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))) | ((~line(at_least_one_line)) | point(point_not_on_line(at_least_one_line))))),
% 5.28/3.60 inference(monotonicity,[status(thm)],[64])).
% 5.28/3.60 tff(66,plain,
% 5.28/3.60 (((~![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))) | (point(point_not_on_line(at_least_one_line)) | (~line(at_least_one_line)))) <=> ((~![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))) | (~line(at_least_one_line)) | point(point_not_on_line(at_least_one_line)))),
% 5.28/3.60 inference(transitivity,[status(thm)],[65, 63])).
% 5.28/3.60 tff(67,plain,
% 5.28/3.60 ((~![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))) | (point(point_not_on_line(at_least_one_line)) | (~line(at_least_one_line)))),
% 5.28/3.60 inference(quant_inst,[status(thm)],[])).
% 5.28/3.60 tff(68,plain,
% 5.28/3.60 ((~![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))) | (~line(at_least_one_line)) | point(point_not_on_line(at_least_one_line))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[67, 66])).
% 5.28/3.60 tff(69,plain,
% 5.28/3.60 (point(point_not_on_line(at_least_one_line))),
% 5.28/3.60 inference(unit_resolution,[status(thm)],[68, 62, 10])).
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% 5.28/3.60 inference(bind,[status(th)],[])).
% 5.28/3.60 tff(71,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2))) <=> ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(quant_intro,[status(thm)],[70])).
% 5.28/3.60 tff(72,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2))) <=> ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(73,plain,
% 5.28/3.60 (^[Z1: $i, Z2: $i] : trans(monotonicity(trans(monotonicity(rewrite((on(Z1, line_from_to(Z1, Z2)) | (Z1 = Z2)) <=> ((Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))), (((on(Z1, line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) <=> (((Z1 = Z2) | on(Z1, line_from_to(Z1, Z2))) | (~point(Z1))))), rewrite((((Z1 = Z2) | on(Z1, line_from_to(Z1, Z2))) | (~point(Z1))) <=> ((~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))), (((on(Z1, line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) <=> ((~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2))))), ((((on(Z1, line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2))) <=> (((~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2))) | (~point(Z2))))), rewrite((((~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2))) | (~point(Z2))) <=> ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))), ((((on(Z1, line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2))) <=> ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))))),
% 5.28/3.60 inference(bind,[status(th)],[])).
% 5.28/3.60 tff(74,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : (((on(Z1, line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2))) <=> ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(quant_intro,[status(thm)],[73])).
% 5.28/3.60 tff(75,axiom,(![Z1: $i, Z2: $i] : (((on(Z1, line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G1A')).
% 5.28/3.60 tff(76,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[75, 74])).
% 5.28/3.60 tff(77,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[76, 72])).
% 5.28/3.60 tff(78,plain,(
% 5.28/3.60 ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(skolemize,[status(sab)],[77])).
% 5.28/3.60 tff(79,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[78, 71])).
% 5.28/3.60 tff(80,plain,
% 5.28/3.60 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(81,plain,
% 5.28/3.60 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.60 inference(quant_inst,[status(thm)],[])).
% 5.28/3.60 tff(82,plain,
% 5.28/3.60 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[81, 80])).
% 5.28/3.60 tff(83,plain,
% 5.28/3.60 ((point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.60 inference(unit_resolution,[status(thm)],[82, 79, 69, 55])).
% 5.28/3.60 tff(84,plain,
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% 5.28/3.60 inference(unit_resolution,[status(thm)],[83, 41])).
% 5.28/3.60 tff(85,plain,
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% 5.28/3.60 tff(86,plain,
% 5.28/3.60 ($false),
% 5.28/3.60 inference(unit_resolution,[status(thm)],[39, 85])).
% 5.28/3.60 tff(87,plain,(~(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line)), inference(lemma,lemma(discharge,[]))).
% 5.28/3.60 tff(88,plain,
% 5.28/3.60 (^[Z1: $i, Z2: $i] : refl(((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2))) <=> ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2))))),
% 5.28/3.60 inference(bind,[status(th)],[])).
% 5.28/3.60 tff(89,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2))) <=> ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(quant_intro,[status(thm)],[88])).
% 5.28/3.60 tff(90,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2))) <=> ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(91,plain,
% 5.28/3.60 (^[Z1: $i, Z2: $i] : trans(monotonicity(rewrite(((line(line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) <=> ((~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))), ((((line(line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2))) <=> (((~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2))) | (~point(Z2))))), rewrite((((~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2))) | (~point(Z2))) <=> ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))), ((((line(line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2))) <=> ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))))),
% 5.28/3.60 inference(bind,[status(th)],[])).
% 5.28/3.60 tff(92,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : (((line(line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2))) <=> ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(quant_intro,[status(thm)],[91])).
% 5.28/3.60 tff(93,axiom,(![Z1: $i, Z2: $i] : (((line(line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G1C')).
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% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[93, 92])).
% 5.28/3.60 tff(95,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[94, 90])).
% 5.28/3.60 tff(96,plain,(
% 5.28/3.60 ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(skolemize,[status(sab)],[95])).
% 5.28/3.60 tff(97,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[96, 89])).
% 5.28/3.60 tff(98,plain,
% 5.28/3.60 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(99,plain,
% 5.28/3.60 (((~point(point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(100,plain,
% 5.28/3.60 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line)))))),
% 5.28/3.60 inference(monotonicity,[status(thm)],[99])).
% 5.28/3.60 tff(101,plain,
% 5.28/3.60 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))))),
% 5.28/3.60 inference(transitivity,[status(thm)],[100, 98])).
% 5.28/3.60 tff(102,plain,
% 5.28/3.60 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.60 inference(quant_inst,[status(thm)],[])).
% 5.28/3.60 tff(103,plain,
% 5.28/3.60 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[102, 101])).
% 5.28/3.60 tff(104,plain,
% 5.28/3.60 (line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.60 inference(unit_resolution,[status(thm)],[103, 97, 69, 55, 41])).
% 5.28/3.60 tff(105,plain,
% 5.28/3.60 (^[Line: $i] : refl(((~line(Line)) | on(a_point, Line)) <=> ((~line(Line)) | on(a_point, Line)))),
% 5.28/3.60 inference(bind,[status(th)],[])).
% 5.28/3.60 tff(106,plain,
% 5.28/3.60 (![Line: $i] : ((~line(Line)) | on(a_point, Line)) <=> ![Line: $i] : ((~line(Line)) | on(a_point, Line))),
% 5.28/3.60 inference(quant_intro,[status(thm)],[105])).
% 5.28/3.60 tff(107,plain,
% 5.28/3.60 (![Line: $i] : ((~line(Line)) | on(a_point, Line)) <=> ![Line: $i] : ((~line(Line)) | on(a_point, Line))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(108,axiom,(![Line: $i] : ((~line(Line)) | on(a_point, Line))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_point_is_not_on_every_line')).
% 5.28/3.60 tff(109,plain,
% 5.28/3.60 (![Line: $i] : ((~line(Line)) | on(a_point, Line))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[108, 107])).
% 5.28/3.60 tff(110,plain,(
% 5.28/3.60 ![Line: $i] : ((~line(Line)) | on(a_point, Line))),
% 5.28/3.60 inference(skolemize,[status(sab)],[109])).
% 5.28/3.60 tff(111,plain,
% 5.28/3.60 (![Line: $i] : ((~line(Line)) | on(a_point, Line))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[110, 106])).
% 5.28/3.60 tff(112,plain,
% 5.28/3.60 (((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(113,plain,
% 5.28/3.60 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.60 inference(quant_inst,[status(thm)],[])).
% 5.28/3.60 tff(114,plain,
% 5.28/3.60 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[113, 112])).
% 5.28/3.60 tff(115,plain,
% 5.28/3.60 (on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.60 inference(unit_resolution,[status(thm)],[114, 111, 104])).
% 5.28/3.60 tff(116,plain,
% 5.28/3.60 (^[Z1: $i, Z2: $i] : refl(((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2))) <=> ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2))))),
% 5.28/3.60 inference(bind,[status(th)],[])).
% 5.28/3.60 tff(117,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2))) <=> ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(quant_intro,[status(thm)],[116])).
% 5.28/3.60 tff(118,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2))) <=> ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(119,plain,
% 5.28/3.60 (^[Z1: $i, Z2: $i] : trans(monotonicity(trans(monotonicity(rewrite((on(Z2, line_from_to(Z1, Z2)) | (Z1 = Z2)) <=> ((Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))), (((on(Z2, line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) <=> (((Z1 = Z2) | on(Z2, line_from_to(Z1, Z2))) | (~point(Z1))))), rewrite((((Z1 = Z2) | on(Z2, line_from_to(Z1, Z2))) | (~point(Z1))) <=> ((~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))), (((on(Z2, line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) <=> ((~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2))))), ((((on(Z2, line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2))) <=> (((~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2))) | (~point(Z2))))), rewrite((((~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2))) | (~point(Z2))) <=> ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))), ((((on(Z2, line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2))) <=> ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))))),
% 5.28/3.60 inference(bind,[status(th)],[])).
% 5.28/3.60 tff(120,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : (((on(Z2, line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2))) <=> ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(quant_intro,[status(thm)],[119])).
% 5.28/3.60 tff(121,axiom,(![Z1: $i, Z2: $i] : (((on(Z2, line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G1B')).
% 5.28/3.60 tff(122,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[121, 120])).
% 5.28/3.60 tff(123,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[122, 118])).
% 5.28/3.60 tff(124,plain,(
% 5.28/3.60 ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(skolemize,[status(sab)],[123])).
% 5.28/3.60 tff(125,plain,
% 5.28/3.60 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[124, 117])).
% 5.28/3.60 tff(126,plain,
% 5.28/3.60 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(127,plain,
% 5.28/3.60 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.60 inference(quant_inst,[status(thm)],[])).
% 5.28/3.60 tff(128,plain,
% 5.28/3.60 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[127, 126])).
% 5.28/3.60 tff(129,plain,
% 5.28/3.60 (on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.60 inference(unit_resolution,[status(thm)],[128, 125, 69, 55, 41])).
% 5.28/3.60 tff(130,plain,
% 5.28/3.60 (((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(at_least_one_line)) | on(a_point, at_least_one_line))) <=> ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(at_least_one_line)) | on(a_point, at_least_one_line))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(131,plain,
% 5.28/3.60 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(at_least_one_line)) | on(a_point, at_least_one_line))),
% 5.28/3.60 inference(quant_inst,[status(thm)],[])).
% 5.28/3.60 tff(132,plain,
% 5.28/3.60 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(at_least_one_line)) | on(a_point, at_least_one_line)),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[131, 130])).
% 5.28/3.60 tff(133,plain,
% 5.28/3.60 (on(a_point, at_least_one_line)),
% 5.28/3.60 inference(unit_resolution,[status(thm)],[132, 10, 111])).
% 5.28/3.60 tff(134,plain,
% 5.28/3.60 (point(a_point) <=> point(a_point)),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(135,axiom,(point(a_point)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','there_is_a_point')).
% 5.28/3.60 tff(136,plain,
% 5.28/3.60 (point(a_point)),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[135, 134])).
% 5.28/3.60 tff(137,plain,
% 5.28/3.60 (^[Y4: $i, Z1: $i, Y3: $i, Z2: $i] : refl(((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) <=> ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))))),
% 5.28/3.60 inference(bind,[status(th)],[])).
% 5.28/3.60 tff(138,plain,
% 5.28/3.60 (![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) <=> ![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))),
% 5.28/3.60 inference(quant_intro,[status(thm)],[137])).
% 5.28/3.60 tff(139,plain,
% 5.28/3.60 (![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) <=> ![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))),
% 5.28/3.60 inference(rewrite,[status(thm)],[])).
% 5.28/3.60 tff(140,plain,
% 5.28/3.60 (^[Y4: $i, Z1: $i, Y3: $i, Z2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) <=> ((~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))), (((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) <=> (((~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) | (Y3 = Y4)))), rewrite((((~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) | (Y3 = Y4)) <=> ((Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))), (((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) <=> ((Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))))), ((((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) | (~on(Z1, Y4))) <=> (((Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) | (~on(Z1, Y4))))), rewrite((((Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) | (~on(Z1, Y4))) <=> ((~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))), ((((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) | (~on(Z1, Y4))) <=> ((~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))))), (((((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) | (~on(Z1, Y4))) | (~on(Z2, Y4))) <=> (((~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) | (~on(Z2, Y4))))), rewrite((((~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) | (~on(Z2, Y4))) <=> ((~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))), (((((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) | (~on(Z1, Y4))) | (~on(Z2, Y4))) <=> ((~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))))), ((((((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) | (~on(Z1, Y4))) | (~on(Z2, Y4))) | (~point(Z1))) <=> (((~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) | (~point(Z1))))), rewrite((((~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) | (~point(Z1))) <=> ((~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))), ((((((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) | (~on(Z1, Y4))) | (~on(Z2, Y4))) | (~point(Z1))) <=> ((~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))))), (((((((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) | (~on(Z1, Y4))) | (~on(Z2, Y4))) | (~point(Z1))) | (~point(Z2))) <=> (((~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) | (~point(Z2))))), rewrite((((~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) | (~point(Z2))) <=> ((~point(Z2)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))), (((((((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) | (~on(Z1, Y4))) | (~on(Z2, Y4))) | (~point(Z1))) | (~point(Z2))) <=> ((~point(Z2)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))))), ((((((((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) | (~on(Z1, Y4))) | (~on(Z2, Y4))) | (~point(Z1))) | (~point(Z2))) | (~line(Y3))) <=> (((~point(Z2)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) | (~line(Y3))))), rewrite((((~point(Z2)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) | (~line(Y3))) <=> ((~point(Z2)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))), ((((((((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) | (~on(Z1, Y4))) | (~on(Z2, Y4))) | (~point(Z1))) | (~point(Z2))) | (~line(Y3))) <=> ((~point(Z2)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))))), (((((((((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) | (~on(Z1, Y4))) | (~on(Z2, Y4))) | (~point(Z1))) | (~point(Z2))) | (~line(Y3))) | (~line(Y4))) <=> (((~point(Z2)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) | (~line(Y4))))), rewrite((((~point(Z2)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3))) | (~line(Y4))) <=> ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))), (((((((((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) | (~on(Z1, Y4))) | (~on(Z2, Y4))) | (~point(Z1))) | (~point(Z2))) | (~line(Y3))) | (~line(Y4))) <=> ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))))),
% 5.28/3.60 inference(bind,[status(th)],[])).
% 5.28/3.60 tff(141,plain,
% 5.28/3.60 (![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((((((((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) | (~on(Z1, Y4))) | (~on(Z2, Y4))) | (~point(Z1))) | (~point(Z2))) | (~line(Y3))) | (~line(Y4))) <=> ![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))),
% 5.28/3.60 inference(quant_intro,[status(thm)],[140])).
% 5.28/3.60 tff(142,axiom,(![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((((((((((~on(Z1, Y3)) | (Z1 = Z2)) | (~on(Z2, Y3))) | (Y3 = Y4)) | (~on(Z1, Y4))) | (~on(Z2, Y4))) | (~point(Z1))) | (~point(Z2))) | (~line(Y3))) | (~line(Y4)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G1D')).
% 5.28/3.60 tff(143,plain,
% 5.28/3.60 (![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[142, 141])).
% 5.28/3.60 tff(144,plain,
% 5.28/3.60 (![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[143, 139])).
% 5.28/3.60 tff(145,plain,(
% 5.28/3.60 ![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))),
% 5.28/3.60 inference(skolemize,[status(sab)],[144])).
% 5.28/3.60 tff(146,plain,
% 5.28/3.60 (![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))),
% 5.28/3.60 inference(modus_ponens,[status(thm)],[145, 138])).
% 5.28/3.60 tff(147,plain,
% 5.28/3.60 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~line(at_least_one_line)) | (~point(a_point)) | (~point(point_1_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (a_point = point_1_on_line(at_least_one_line)) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~line(at_least_one_line)) | (~point(a_point)) | (~point(point_1_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (a_point = point_1_on_line(at_least_one_line)) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)))),
% 5.28/3.61 inference(rewrite,[status(thm)],[])).
% 5.28/3.61 tff(148,plain,
% 5.28/3.61 (((~point(point_1_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(a_point)) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(a_point, at_least_one_line)) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (a_point = point_1_on_line(at_least_one_line)) | (~on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~line(at_least_one_line)) | (~point(a_point)) | (~point(point_1_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (a_point = point_1_on_line(at_least_one_line)) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)))),
% 5.28/3.61 inference(rewrite,[status(thm)],[])).
% 5.28/3.61 tff(149,plain,
% 5.28/3.61 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(a_point)) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(a_point, at_least_one_line)) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (a_point = point_1_on_line(at_least_one_line)) | (~on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~line(at_least_one_line)) | (~point(a_point)) | (~point(point_1_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (a_point = point_1_on_line(at_least_one_line)) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line))))),
% 5.28/3.61 inference(monotonicity,[status(thm)],[148])).
% 5.28/3.61 tff(150,plain,
% 5.28/3.61 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(a_point)) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(a_point, at_least_one_line)) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (a_point = point_1_on_line(at_least_one_line)) | (~on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~line(at_least_one_line)) | (~point(a_point)) | (~point(point_1_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (a_point = point_1_on_line(at_least_one_line)) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)))),
% 5.28/3.61 inference(transitivity,[status(thm)],[149, 147])).
% 5.28/3.61 tff(151,plain,
% 5.28/3.61 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(a_point)) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(a_point, at_least_one_line)) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (a_point = point_1_on_line(at_least_one_line)) | (~on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.28/3.61 inference(quant_inst,[status(thm)],[])).
% 5.28/3.61 tff(152,plain,
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% 5.28/3.61 inference(unit_resolution,[status(thm)],[212, 206, 10])).
% 5.28/3.61 tff(214,plain,
% 5.28/3.61 (^[X3: $i, X2: $i, X1: $i] : refl(((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3))))),
% 5.28/3.61 inference(bind,[status(th)],[])).
% 5.28/3.61 tff(215,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(quant_intro,[status(thm)],[214])).
% 5.28/3.61 tff(216,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(rewrite,[status(thm)],[])).
% 5.28/3.61 tff(217,plain,
% 5.28/3.61 (^[X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~point(X1)) | (~point(X2))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)))), (((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3))) | (X1 = X2)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2))), (((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2)))), ((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2)) | (X1 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2)) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2))), ((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2)))), (((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2)) | (X2 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2)) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2))), (((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2)))), ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X1, line_through_3_points(X1, X2, X3))) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2)) | on(X1, line_through_3_points(X1, X2, X3))))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2)) | on(X1, line_through_3_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | on(X1, line_through_3_points(X1, X2, X3)))), ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X1, line_through_3_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | on(X1, line_through_3_points(X1, X2, X3))))), (((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X1, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | on(X1, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | on(X1, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))), (((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X1, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))))),
% 5.28/3.61 inference(bind,[status(th)],[])).
% 5.28/3.61 tff(218,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X1, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(quant_intro,[status(thm)],[217])).
% 5.28/3.61 tff(219,axiom,(![X3: $i, X2: $i, X1: $i] : ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X1, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G10A')).
% 5.28/3.61 tff(220,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(modus_ponens,[status(thm)],[219, 218])).
% 5.28/3.61 tff(221,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(modus_ponens,[status(thm)],[220, 216])).
% 5.28/3.61 tff(222,plain,(
% 5.28/3.61 ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(skolemize,[status(sab)],[221])).
% 5.28/3.61 tff(223,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(modus_ponens,[status(thm)],[222, 215])).
% 5.28/3.61 tff(224,plain,
% 5.28/3.61 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.61 inference(rewrite,[status(thm)],[])).
% 5.28/3.61 tff(225,plain,
% 5.28/3.61 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.61 inference(rewrite,[status(thm)],[])).
% 5.28/3.61 tff(226,plain,
% 5.28/3.61 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.28/3.61 inference(monotonicity,[status(thm)],[225])).
% 5.28/3.61 tff(227,plain,
% 5.28/3.61 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.61 inference(transitivity,[status(thm)],[226, 224])).
% 5.28/3.61 tff(228,plain,
% 5.28/3.61 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.61 inference(quant_inst,[status(thm)],[])).
% 5.28/3.61 tff(229,plain,
% 5.28/3.61 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.61 inference(modus_ponens,[status(thm)],[228, 227])).
% 5.28/3.61 tff(230,plain,
% 5.28/3.61 (on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.61 inference(unit_resolution,[status(thm)],[229, 223, 69, 213, 55, 41, 199, 178, 160])).
% 5.28/3.61 tff(231,plain,
% 5.28/3.61 (^[X3: $i, X2: $i, X1: $i] : refl(((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3))))),
% 5.28/3.61 inference(bind,[status(th)],[])).
% 5.28/3.61 tff(232,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(quant_intro,[status(thm)],[231])).
% 5.28/3.61 tff(233,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(rewrite,[status(thm)],[])).
% 5.28/3.61 tff(234,plain,
% 5.28/3.61 (^[X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~point(X1)) | (~point(X2))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)))), (((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3))) | (X1 = X2)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2))), (((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2)))), ((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2)) | (X1 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2)) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2))), ((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2)))), (((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2)) | (X2 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2)) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2))), (((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2)))), ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X3, line_through_3_points(X1, X2, X3))) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2)) | on(X3, line_through_3_points(X1, X2, X3))))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2)) | on(X3, line_through_3_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | on(X3, line_through_3_points(X1, X2, X3)))), ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X3, line_through_3_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | on(X3, line_through_3_points(X1, X2, X3))))), (((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X3, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | on(X3, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | on(X3, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))), (((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X3, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))))),
% 5.28/3.61 inference(bind,[status(th)],[])).
% 5.28/3.61 tff(235,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X3, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(quant_intro,[status(thm)],[234])).
% 5.28/3.61 tff(236,axiom,(![X3: $i, X2: $i, X1: $i] : ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X3, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G10C')).
% 5.28/3.61 tff(237,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(modus_ponens,[status(thm)],[236, 235])).
% 5.28/3.61 tff(238,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(modus_ponens,[status(thm)],[237, 233])).
% 5.28/3.61 tff(239,plain,(
% 5.28/3.61 ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(skolemize,[status(sab)],[238])).
% 5.28/3.61 tff(240,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(modus_ponens,[status(thm)],[239, 232])).
% 5.28/3.61 tff(241,plain,
% 5.28/3.61 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.61 inference(rewrite,[status(thm)],[])).
% 5.28/3.61 tff(242,plain,
% 5.28/3.61 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.61 inference(rewrite,[status(thm)],[])).
% 5.28/3.61 tff(243,plain,
% 5.28/3.61 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.28/3.61 inference(monotonicity,[status(thm)],[242])).
% 5.28/3.61 tff(244,plain,
% 5.28/3.61 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.61 inference(transitivity,[status(thm)],[243, 241])).
% 5.28/3.61 tff(245,plain,
% 5.28/3.61 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.61 inference(quant_inst,[status(thm)],[])).
% 5.28/3.61 tff(246,plain,
% 5.28/3.61 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.61 inference(modus_ponens,[status(thm)],[245, 244])).
% 5.28/3.61 tff(247,plain,
% 5.28/3.61 (on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.61 inference(unit_resolution,[status(thm)],[246, 240, 69, 213, 55, 41, 199, 178, 160])).
% 5.28/3.61 tff(248,plain,
% 5.28/3.61 (^[X3: $i, X2: $i, X1: $i] : refl(((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3))))),
% 5.28/3.61 inference(bind,[status(th)],[])).
% 5.28/3.61 tff(249,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(quant_intro,[status(thm)],[248])).
% 5.28/3.61 tff(250,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(rewrite,[status(thm)],[])).
% 5.28/3.61 tff(251,plain,
% 5.28/3.61 (^[X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~point(X1)) | (~point(X2))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)))), (((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3))) | (X1 = X2)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2))), (((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2)))), ((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2)) | (X1 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2)) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2))), ((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2)))), (((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2)) | (X2 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2)) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2))), (((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2)))), ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | line(line_through_3_points(X1, X2, X3))) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2)) | line(line_through_3_points(X1, X2, X3))))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2)) | line(line_through_3_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | line(line_through_3_points(X1, X2, X3)))), ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | line(line_through_3_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | line(line_through_3_points(X1, X2, X3))))), (((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | line(line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | line(line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | line(line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))), (((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | line(line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))))),
% 5.28/3.61 inference(bind,[status(th)],[])).
% 5.28/3.61 tff(252,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | line(line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(quant_intro,[status(thm)],[251])).
% 5.28/3.61 tff(253,axiom,(![X3: $i, X2: $i, X1: $i] : ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | line(line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G10D')).
% 5.28/3.61 tff(254,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))),
% 5.28/3.61 inference(modus_ponens,[status(thm)],[253, 252])).
% 5.28/3.61 tff(255,plain,
% 5.28/3.61 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))),
% 5.28/3.62 inference(modus_ponens,[status(thm)],[254, 250])).
% 5.28/3.62 tff(256,plain,(
% 5.28/3.62 ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))),
% 5.28/3.62 inference(skolemize,[status(sab)],[255])).
% 5.28/3.62 tff(257,plain,
% 5.28/3.62 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))),
% 5.28/3.62 inference(modus_ponens,[status(thm)],[256, 249])).
% 5.28/3.62 tff(258,plain,
% 5.28/3.62 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.62 inference(rewrite,[status(thm)],[])).
% 5.28/3.62 tff(259,plain,
% 5.28/3.62 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.62 inference(rewrite,[status(thm)],[])).
% 5.28/3.62 tff(260,plain,
% 5.28/3.62 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.28/3.62 inference(monotonicity,[status(thm)],[259])).
% 5.28/3.62 tff(261,plain,
% 5.28/3.62 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.62 inference(transitivity,[status(thm)],[260, 258])).
% 5.28/3.62 tff(262,plain,
% 5.28/3.62 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.62 inference(quant_inst,[status(thm)],[])).
% 5.28/3.62 tff(263,plain,
% 5.28/3.62 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.62 inference(modus_ponens,[status(thm)],[262, 261])).
% 5.28/3.62 tff(264,plain,
% 5.28/3.62 (line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.62 inference(unit_resolution,[status(thm)],[263, 257, 69, 213, 55, 41, 199, 178, 160])).
% 5.28/3.62 tff(265,plain,
% 5.28/3.62 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.28/3.62 inference(rewrite,[status(thm)],[])).
% 5.28/3.62 tff(266,plain,
% 5.28/3.62 (((~point(point_1_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_2_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.28/3.62 inference(rewrite,[status(thm)],[])).
% 5.28/3.62 tff(267,plain,
% 5.28/3.62 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_2_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.28/3.62 inference(monotonicity,[status(thm)],[266])).
% 5.28/3.62 tff(268,plain,
% 5.28/3.62 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_2_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.28/3.62 inference(transitivity,[status(thm)],[267, 265])).
% 5.28/3.62 tff(269,plain,
% 5.28/3.62 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_2_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.28/3.62 inference(quant_inst,[status(thm)],[])).
% 5.28/3.62 tff(270,plain,
% 5.28/3.62 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.62 inference(modus_ponens,[status(thm)],[269, 268])).
% 5.28/3.62 tff(271,plain,
% 5.28/3.62 (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line),
% 5.28/3.62 inference(unit_resolution,[status(thm)],[270, 146, 10, 213, 55, 24, 197, 178, 264, 247, 230])).
% 5.28/3.62 tff(272,plain,
% 5.28/3.62 (^[X3: $i, X2: $i, X1: $i] : refl(((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3))))),
% 5.28/3.62 inference(bind,[status(th)],[])).
% 5.28/3.62 tff(273,plain,
% 5.28/3.62 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))),
% 5.28/3.62 inference(quant_intro,[status(thm)],[272])).
% 5.28/3.62 tff(274,plain,
% 5.28/3.62 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))),
% 5.28/3.62 inference(rewrite,[status(thm)],[])).
% 5.28/3.62 tff(275,plain,
% 5.28/3.62 (^[X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~point(X1)) | (~point(X2))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)))), (((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3))) | (X1 = X2)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2))), (((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2)))), ((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2)) | (X1 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2)) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2))), ((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2)))), (((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2)) | (X2 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2)) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2))), (((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2)))), ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X2, line_through_3_points(X1, X2, X3))) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2)) | on(X2, line_through_3_points(X1, X2, X3))))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2)) | on(X2, line_through_3_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | on(X2, line_through_3_points(X1, X2, X3)))), ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X2, line_through_3_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | on(X2, line_through_3_points(X1, X2, X3))))), (((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X2, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | on(X2, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | on(X2, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))), (((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X2, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))))),
% 5.28/3.62 inference(bind,[status(th)],[])).
% 5.28/3.62 tff(276,plain,
% 5.28/3.62 (![X3: $i, X2: $i, X1: $i] : ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X2, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))),
% 5.28/3.62 inference(quant_intro,[status(thm)],[275])).
% 5.28/3.62 tff(277,axiom,(![X3: $i, X2: $i, X1: $i] : ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | on(X2, line_through_3_points(X1, X2, X3))) | (~collinear(X1, X2, X3)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G10B')).
% 5.28/3.62 tff(278,plain,
% 5.28/3.62 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))),
% 5.28/3.62 inference(modus_ponens,[status(thm)],[277, 276])).
% 5.28/3.62 tff(279,plain,
% 5.28/3.62 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))),
% 5.28/3.62 inference(modus_ponens,[status(thm)],[278, 274])).
% 5.28/3.62 tff(280,plain,(
% 5.28/3.62 ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))),
% 5.28/3.62 inference(skolemize,[status(sab)],[279])).
% 5.28/3.62 tff(281,plain,
% 5.28/3.62 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))),
% 5.28/3.62 inference(modus_ponens,[status(thm)],[280, 273])).
% 5.28/3.62 tff(282,plain,
% 5.28/3.62 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.62 inference(rewrite,[status(thm)],[])).
% 5.28/3.62 tff(283,plain,
% 5.28/3.62 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.62 inference(rewrite,[status(thm)],[])).
% 5.28/3.62 tff(284,plain,
% 5.28/3.62 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.28/3.62 inference(monotonicity,[status(thm)],[283])).
% 5.28/3.62 tff(285,plain,
% 5.28/3.62 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.62 inference(transitivity,[status(thm)],[284, 282])).
% 5.28/3.62 tff(286,plain,
% 5.28/3.62 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.62 inference(quant_inst,[status(thm)],[])).
% 5.28/3.62 tff(287,plain,
% 5.28/3.62 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.62 inference(modus_ponens,[status(thm)],[286, 285])).
% 5.28/3.62 tff(288,plain,
% 5.28/3.62 (on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.62 inference(unit_resolution,[status(thm)],[287, 281, 69, 213, 55, 41, 199, 178, 160])).
% 5.28/3.62 tff(289,plain,
% 5.28/3.62 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.62 inference(rewrite,[status(thm)],[])).
% 5.28/3.62 tff(290,plain,
% 5.28/3.62 (((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.62 inference(rewrite,[status(thm)],[])).
% 5.28/3.62 tff(291,plain,
% 5.28/3.62 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.28/3.62 inference(monotonicity,[status(thm)],[290])).
% 5.28/3.62 tff(292,plain,
% 5.28/3.62 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.62 inference(transitivity,[status(thm)],[291, 289])).
% 5.28/3.62 tff(293,plain,
% 5.28/3.62 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.28/3.63 inference(quant_inst,[status(thm)],[])).
% 5.28/3.63 tff(294,plain,
% 5.28/3.63 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[293, 292])).
% 5.28/3.63 tff(295,plain,
% 5.28/3.63 (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))),
% 5.28/3.63 inference(unit_resolution,[status(thm)],[294, 146, 69, 55, 41, 84, 104, 129, 264, 247, 288])).
% 5.28/3.63 tff(296,plain,
% 5.28/3.63 (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))),
% 5.28/3.63 inference(symmetry,[status(thm)],[295])).
% 5.28/3.63 tff(297,plain,
% 5.28/3.63 (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line),
% 5.28/3.63 inference(transitivity,[status(thm)],[296, 271])).
% 5.28/3.63 tff(298,plain,
% 5.28/3.63 ($false),
% 5.28/3.63 inference(unit_resolution,[status(thm)],[87, 297])).
% 5.28/3.63 tff(299,plain,(~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), inference(lemma,lemma(discharge,[]))).
% 5.28/3.63 tff(300,plain,
% 5.28/3.63 (^[X3: $i, X2: $i, X1: $i] : refl(((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3))))),
% 5.28/3.63 inference(bind,[status(th)],[])).
% 5.28/3.63 tff(301,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(quant_intro,[status(thm)],[300])).
% 5.28/3.63 tff(302,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(rewrite,[status(thm)],[])).
% 5.28/3.63 tff(303,plain,
% 5.28/3.63 (^[X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) <=> ((~point(X1)) | on(X2, plane_for_points(X1, X2, X3)))), (((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) <=> (((~point(X1)) | on(X2, plane_for_points(X1, X2, X3))) | (~point(X2))))), rewrite((((~point(X1)) | on(X2, plane_for_points(X1, X2, X3))) | (~point(X2))) <=> ((~point(X1)) | (~point(X2)) | on(X2, plane_for_points(X1, X2, X3)))), (((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) <=> ((~point(X1)) | (~point(X2)) | on(X2, plane_for_points(X1, X2, X3))))), ((((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) <=> (((~point(X1)) | (~point(X2)) | on(X2, plane_for_points(X1, X2, X3))) | (~point(X3))))), rewrite((((~point(X1)) | (~point(X2)) | on(X2, plane_for_points(X1, X2, X3))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | on(X2, plane_for_points(X1, X2, X3)))), ((((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | on(X2, plane_for_points(X1, X2, X3))))), (((((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | on(X2, plane_for_points(X1, X2, X3))) | collinear(X1, X2, X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | on(X2, plane_for_points(X1, X2, X3))) | collinear(X1, X2, X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))), (((((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3))))), ((((((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3))) | (X1 = X2)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))), ((((((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3))))), (((((((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3))) | (X1 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3))) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))), (((((((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3))))), ((((((((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3))) | (X2 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3))) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))), ((((((((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))))),
% 5.28/3.63 inference(bind,[status(th)],[])).
% 5.28/3.63 tff(304,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : (((((((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(quant_intro,[status(thm)],[303])).
% 5.28/3.63 tff(305,axiom,(![X3: $i, X2: $i, X1: $i] : (((((((on(X2, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G7B')).
% 5.28/3.63 tff(306,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[305, 304])).
% 5.28/3.63 tff(307,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[306, 302])).
% 5.28/3.63 tff(308,plain,(
% 5.28/3.63 ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(skolemize,[status(sab)],[307])).
% 5.28/3.63 tff(309,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[308, 301])).
% 5.28/3.63 tff(310,plain,
% 5.28/3.63 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.63 inference(rewrite,[status(thm)],[])).
% 5.28/3.63 tff(311,plain,
% 5.28/3.63 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.63 inference(rewrite,[status(thm)],[])).
% 5.28/3.63 tff(312,plain,
% 5.28/3.63 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.63 inference(monotonicity,[status(thm)],[311])).
% 5.28/3.63 tff(313,plain,
% 5.28/3.63 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.63 inference(transitivity,[status(thm)],[312, 310])).
% 5.28/3.63 tff(314,plain,
% 5.28/3.63 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.63 inference(quant_inst,[status(thm)],[])).
% 5.28/3.63 tff(315,plain,
% 5.28/3.63 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[314, 313])).
% 5.28/3.63 tff(316,plain,
% 5.28/3.63 (on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))),
% 5.28/3.63 inference(unit_resolution,[status(thm)],[315, 309, 69, 213, 55, 41, 199, 178])).
% 5.28/3.63 tff(317,plain,
% 5.28/3.63 (on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.63 inference(unit_resolution,[status(thm)],[316, 299])).
% 5.28/3.63 tff(318,plain,
% 5.28/3.63 (on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[317, 159])).
% 5.28/3.63 tff(319,plain,
% 5.28/3.63 (on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) <=> on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.63 inference(monotonicity,[status(thm)],[157])).
% 5.28/3.63 tff(320,plain,
% 5.28/3.63 (on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.28/3.63 inference(symmetry,[status(thm)],[319])).
% 5.28/3.63 tff(321,plain,
% 5.28/3.63 (^[X3: $i, X2: $i, X1: $i] : refl(((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3))))),
% 5.28/3.63 inference(bind,[status(th)],[])).
% 5.28/3.63 tff(322,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(quant_intro,[status(thm)],[321])).
% 5.28/3.63 tff(323,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(rewrite,[status(thm)],[])).
% 5.28/3.63 tff(324,plain,
% 5.28/3.63 (^[X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) <=> ((~point(X1)) | on(X1, plane_for_points(X1, X2, X3)))), (((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) <=> (((~point(X1)) | on(X1, plane_for_points(X1, X2, X3))) | (~point(X2))))), rewrite((((~point(X1)) | on(X1, plane_for_points(X1, X2, X3))) | (~point(X2))) <=> ((~point(X1)) | (~point(X2)) | on(X1, plane_for_points(X1, X2, X3)))), (((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) <=> ((~point(X1)) | (~point(X2)) | on(X1, plane_for_points(X1, X2, X3))))), ((((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) <=> (((~point(X1)) | (~point(X2)) | on(X1, plane_for_points(X1, X2, X3))) | (~point(X3))))), rewrite((((~point(X1)) | (~point(X2)) | on(X1, plane_for_points(X1, X2, X3))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | on(X1, plane_for_points(X1, X2, X3)))), ((((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | on(X1, plane_for_points(X1, X2, X3))))), (((((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | on(X1, plane_for_points(X1, X2, X3))) | collinear(X1, X2, X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | on(X1, plane_for_points(X1, X2, X3))) | collinear(X1, X2, X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))), (((((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3))))), ((((((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3))) | (X1 = X2)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))), ((((((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3))))), (((((((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3))) | (X1 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3))) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))), (((((((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3))))), ((((((((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3))) | (X2 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3))) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))), ((((((((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))))),
% 5.28/3.63 inference(bind,[status(th)],[])).
% 5.28/3.63 tff(325,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : (((((((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(quant_intro,[status(thm)],[324])).
% 5.28/3.63 tff(326,axiom,(![X3: $i, X2: $i, X1: $i] : (((((((on(X1, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G7A')).
% 5.28/3.63 tff(327,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[326, 325])).
% 5.28/3.63 tff(328,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[327, 323])).
% 5.28/3.63 tff(329,plain,(
% 5.28/3.63 ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(skolemize,[status(sab)],[328])).
% 5.28/3.63 tff(330,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[329, 322])).
% 5.28/3.63 tff(331,plain,
% 5.28/3.63 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.63 inference(rewrite,[status(thm)],[])).
% 5.28/3.63 tff(332,plain,
% 5.28/3.63 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.63 inference(rewrite,[status(thm)],[])).
% 5.28/3.63 tff(333,plain,
% 5.28/3.63 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.28/3.63 inference(monotonicity,[status(thm)],[332])).
% 5.28/3.63 tff(334,plain,
% 5.28/3.63 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.63 inference(transitivity,[status(thm)],[333, 331])).
% 5.28/3.63 tff(335,plain,
% 5.28/3.63 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.63 inference(quant_inst,[status(thm)],[])).
% 5.28/3.63 tff(336,plain,
% 5.28/3.63 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[335, 334])).
% 5.28/3.63 tff(337,plain,
% 5.28/3.63 (collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.63 inference(unit_resolution,[status(thm)],[336, 330, 69, 213, 55, 41, 199, 178])).
% 5.28/3.63 tff(338,plain,
% 5.28/3.63 (on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.63 inference(unit_resolution,[status(thm)],[337, 299])).
% 5.28/3.63 tff(339,plain,
% 5.28/3.63 (on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[338, 320])).
% 5.28/3.63 tff(340,plain,
% 5.28/3.63 (on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) <=> on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.63 inference(monotonicity,[status(thm)],[157])).
% 5.28/3.63 tff(341,plain,
% 5.28/3.63 (on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.28/3.63 inference(symmetry,[status(thm)],[340])).
% 5.28/3.63 tff(342,plain,
% 5.28/3.63 (^[X3: $i, X2: $i, X1: $i] : refl(((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3))))),
% 5.28/3.63 inference(bind,[status(th)],[])).
% 5.28/3.63 tff(343,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(quant_intro,[status(thm)],[342])).
% 5.28/3.63 tff(344,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(rewrite,[status(thm)],[])).
% 5.28/3.63 tff(345,plain,
% 5.28/3.63 (^[X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) <=> ((~point(X1)) | on(X3, plane_for_points(X1, X2, X3)))), (((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) <=> (((~point(X1)) | on(X3, plane_for_points(X1, X2, X3))) | (~point(X2))))), rewrite((((~point(X1)) | on(X3, plane_for_points(X1, X2, X3))) | (~point(X2))) <=> ((~point(X1)) | (~point(X2)) | on(X3, plane_for_points(X1, X2, X3)))), (((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) <=> ((~point(X1)) | (~point(X2)) | on(X3, plane_for_points(X1, X2, X3))))), ((((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) <=> (((~point(X1)) | (~point(X2)) | on(X3, plane_for_points(X1, X2, X3))) | (~point(X3))))), rewrite((((~point(X1)) | (~point(X2)) | on(X3, plane_for_points(X1, X2, X3))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | on(X3, plane_for_points(X1, X2, X3)))), ((((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | on(X3, plane_for_points(X1, X2, X3))))), (((((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | on(X3, plane_for_points(X1, X2, X3))) | collinear(X1, X2, X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | on(X3, plane_for_points(X1, X2, X3))) | collinear(X1, X2, X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))), (((((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3))))), ((((((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3))) | (X1 = X2)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))), ((((((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3))))), (((((((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3))) | (X1 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3))) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))), (((((((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3))))), ((((((((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3))) | (X2 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3))) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))), ((((((((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))))),
% 5.28/3.63 inference(bind,[status(th)],[])).
% 5.28/3.63 tff(346,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : (((((((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(quant_intro,[status(thm)],[345])).
% 5.28/3.63 tff(347,axiom,(![X3: $i, X2: $i, X1: $i] : (((((((on(X3, plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G7C')).
% 5.28/3.63 tff(348,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[347, 346])).
% 5.28/3.63 tff(349,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[348, 344])).
% 5.28/3.63 tff(350,plain,(
% 5.28/3.63 ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(skolemize,[status(sab)],[349])).
% 5.28/3.63 tff(351,plain,
% 5.28/3.63 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[350, 343])).
% 5.28/3.63 tff(352,plain,
% 5.28/3.63 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.63 inference(rewrite,[status(thm)],[])).
% 5.28/3.63 tff(353,plain,
% 5.28/3.63 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.63 inference(rewrite,[status(thm)],[])).
% 5.28/3.63 tff(354,plain,
% 5.28/3.63 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.28/3.63 inference(monotonicity,[status(thm)],[353])).
% 5.28/3.63 tff(355,plain,
% 5.28/3.63 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.63 inference(transitivity,[status(thm)],[354, 352])).
% 5.28/3.63 tff(356,plain,
% 5.28/3.63 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.28/3.63 inference(quant_inst,[status(thm)],[])).
% 5.28/3.63 tff(357,plain,
% 5.28/3.63 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[356, 355])).
% 5.28/3.63 tff(358,plain,
% 5.28/3.63 (collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.63 inference(unit_resolution,[status(thm)],[357, 351, 69, 213, 55, 41, 199, 178])).
% 5.28/3.63 tff(359,plain,
% 5.28/3.63 (on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.28/3.63 inference(unit_resolution,[status(thm)],[358, 299])).
% 5.28/3.63 tff(360,plain,
% 5.28/3.63 (on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.28/3.63 inference(modus_ponens,[status(thm)],[359, 341])).
% 5.28/3.63 tff(361,plain,
% 5.28/3.63 (plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))),
% 5.28/3.64 inference(monotonicity,[status(thm)],[155])).
% 5.28/3.64 tff(362,plain,
% 5.28/3.64 (on(point_2_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) <=> on(point_2_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.28/3.64 inference(monotonicity,[status(thm)],[361])).
% 5.28/3.64 tff(363,assumption,(collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), introduced(assumption)).
% 5.28/3.64 tff(364,assumption,(~(point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line))), introduced(assumption)).
% 5.28/3.64 tff(365,plain,
% 5.28/3.64 ((point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) <=> (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line))),
% 5.28/3.64 inference(commutativity,[status(thm)],[])).
% 5.28/3.64 tff(366,plain,
% 5.28/3.64 ((point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) <=> (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line))),
% 5.28/3.64 inference(symmetry,[status(thm)],[365])).
% 5.28/3.64 tff(367,plain,
% 5.28/3.64 ((~(point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line))) <=> (~(point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)))),
% 5.28/3.64 inference(monotonicity,[status(thm)],[366])).
% 5.28/3.64 tff(368,plain,
% 5.28/3.64 (~(point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line))),
% 5.28/3.64 inference(modus_ponens,[status(thm)],[41, 367])).
% 5.28/3.64 tff(369,plain,
% 5.28/3.64 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.64 inference(rewrite,[status(thm)],[])).
% 5.28/3.64 tff(370,plain,
% 5.28/3.64 (((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.64 inference(rewrite,[status(thm)],[])).
% 5.28/3.64 tff(371,plain,
% 5.28/3.64 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.28/3.64 inference(monotonicity,[status(thm)],[370])).
% 5.28/3.64 tff(372,plain,
% 5.28/3.64 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.64 inference(transitivity,[status(thm)],[371, 369])).
% 5.28/3.64 tff(373,plain,
% 5.28/3.64 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.64 inference(quant_inst,[status(thm)],[])).
% 5.28/3.64 tff(374,plain,
% 5.28/3.64 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.28/3.64 inference(modus_ponens,[status(thm)],[373, 372])).
% 5.28/3.64 tff(375,plain,
% 5.28/3.64 ((~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.28/3.64 inference(unit_resolution,[status(thm)],[374, 223, 69, 177, 213, 55, 368, 364])).
% 5.28/3.64 tff(376,plain,
% 5.28/3.64 (on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.28/3.64 inference(unit_resolution,[status(thm)],[375, 363])).
% 5.28/3.64 tff(377,plain,
% 5.28/3.64 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.64 inference(rewrite,[status(thm)],[])).
% 5.28/3.64 tff(378,plain,
% 5.28/3.64 (((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.64 inference(rewrite,[status(thm)],[])).
% 5.28/3.64 tff(379,plain,
% 5.28/3.64 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.28/3.64 inference(monotonicity,[status(thm)],[378])).
% 5.28/3.64 tff(380,plain,
% 5.28/3.64 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.64 inference(transitivity,[status(thm)],[379, 377])).
% 5.28/3.64 tff(381,plain,
% 5.28/3.64 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.64 inference(quant_inst,[status(thm)],[])).
% 5.28/3.64 tff(382,plain,
% 5.28/3.64 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.28/3.64 inference(modus_ponens,[status(thm)],[381, 380])).
% 5.28/3.64 tff(383,plain,
% 5.28/3.64 ((~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.28/3.64 inference(unit_resolution,[status(thm)],[382, 281, 69, 177, 213, 55, 368, 364])).
% 5.28/3.64 tff(384,plain,
% 5.28/3.64 (on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.28/3.64 inference(unit_resolution,[status(thm)],[383, 363])).
% 5.28/3.64 tff(385,plain,
% 5.28/3.64 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.64 inference(rewrite,[status(thm)],[])).
% 5.28/3.64 tff(386,plain,
% 5.28/3.64 (((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.64 inference(rewrite,[status(thm)],[])).
% 5.28/3.64 tff(387,plain,
% 5.28/3.64 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.28/3.64 inference(monotonicity,[status(thm)],[386])).
% 5.28/3.64 tff(388,plain,
% 5.28/3.64 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.64 inference(transitivity,[status(thm)],[387, 385])).
% 5.28/3.64 tff(389,plain,
% 5.28/3.64 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.64 inference(quant_inst,[status(thm)],[])).
% 5.28/3.64 tff(390,plain,
% 5.28/3.64 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.28/3.64 inference(modus_ponens,[status(thm)],[389, 388])).
% 5.28/3.64 tff(391,plain,
% 5.28/3.64 ((~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.28/3.64 inference(unit_resolution,[status(thm)],[390, 257, 69, 177, 213, 55, 368, 364])).
% 5.28/3.64 tff(392,plain,
% 5.28/3.64 (line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.28/3.64 inference(unit_resolution,[status(thm)],[391, 363])).
% 5.28/3.64 tff(393,plain,
% 5.28/3.64 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line))),
% 5.28/3.64 inference(rewrite,[status(thm)],[])).
% 5.28/3.64 tff(394,plain,
% 5.28/3.64 (((~point(point_2_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line))),
% 5.28/3.64 inference(rewrite,[status(thm)],[])).
% 5.28/3.64 tff(395,plain,
% 5.28/3.64 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line)))),
% 5.28/3.64 inference(monotonicity,[status(thm)],[394])).
% 5.28/3.64 tff(396,plain,
% 5.28/3.64 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line))),
% 5.28/3.64 inference(transitivity,[status(thm)],[395, 393])).
% 5.28/3.64 tff(397,plain,
% 5.28/3.64 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.28/3.64 inference(quant_inst,[status(thm)],[])).
% 5.28/3.64 tff(398,plain,
% 5.28/3.64 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line)),
% 5.28/3.64 inference(modus_ponens,[status(thm)],[397, 396])).
% 5.28/3.64 tff(399,plain,
% 5.28/3.64 (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line),
% 5.28/3.64 inference(unit_resolution,[status(thm)],[398, 146, 10, 177, 213, 55, 24, 197, 392, 384, 376])).
% 5.28/3.64 tff(400,plain,
% 5.28/3.64 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.64 inference(rewrite,[status(thm)],[])).
% 5.28/3.64 tff(401,plain,
% 5.28/3.64 (((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.64 inference(rewrite,[status(thm)],[])).
% 5.28/3.64 tff(402,plain,
% 5.28/3.64 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.28/3.64 inference(monotonicity,[status(thm)],[401])).
% 5.28/3.64 tff(403,plain,
% 5.28/3.64 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.65 inference(transitivity,[status(thm)],[402, 400])).
% 5.28/3.65 tff(404,plain,
% 5.28/3.65 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.28/3.65 inference(quant_inst,[status(thm)],[])).
% 5.28/3.65 tff(405,plain,
% 5.28/3.65 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.28/3.65 inference(modus_ponens,[status(thm)],[404, 403])).
% 5.28/3.65 tff(406,plain,
% 5.28/3.65 ((~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.28/3.65 inference(unit_resolution,[status(thm)],[405, 240, 69, 177, 213, 55, 368, 364])).
% 5.28/3.65 tff(407,plain,
% 5.28/3.65 (on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.28/3.65 inference(unit_resolution,[status(thm)],[406, 363])).
% 5.28/3.65 tff(408,plain,
% 5.28/3.65 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.28/3.65 inference(rewrite,[status(thm)],[])).
% 5.28/3.65 tff(409,plain,
% 5.28/3.65 (((~point(point_not_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.36/3.65 inference(rewrite,[status(thm)],[])).
% 5.36/3.65 tff(410,plain,
% 5.36/3.65 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 5.36/3.65 inference(monotonicity,[status(thm)],[409])).
% 5.36/3.65 tff(411,plain,
% 5.36/3.65 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.36/3.65 inference(transitivity,[status(thm)],[410, 408])).
% 5.36/3.65 tff(412,plain,
% 5.36/3.65 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.36/3.65 inference(quant_inst,[status(thm)],[])).
% 5.36/3.65 tff(413,plain,
% 5.36/3.65 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.36/3.65 inference(modus_ponens,[status(thm)],[412, 411])).
% 5.36/3.65 tff(414,plain,
% 5.36/3.65 (line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))),
% 5.36/3.65 inference(unit_resolution,[status(thm)],[413, 146, 69, 55, 84, 368, 104, 129, 392, 407, 376])).
% 5.36/3.65 tff(415,plain,
% 5.36/3.65 (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_through_3_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))),
% 5.36/3.65 inference(symmetry,[status(thm)],[414])).
% 5.36/3.65 tff(416,plain,
% 5.36/3.65 (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = at_least_one_line),
% 5.36/3.65 inference(transitivity,[status(thm)],[415, 399])).
% 5.36/3.65 tff(417,plain,
% 5.36/3.65 ($false),
% 5.36/3.65 inference(unit_resolution,[status(thm)],[87, 416])).
% 5.36/3.65 tff(418,plain,((~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line))), inference(lemma,lemma(discharge,[]))).
% 5.36/3.65 tff(419,plain,
% 5.36/3.65 (~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))),
% 5.36/3.65 inference(unit_resolution,[status(thm)],[418, 199])).
% 5.36/3.65 tff(420,plain,
% 5.36/3.65 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.65 inference(rewrite,[status(thm)],[])).
% 5.36/3.65 tff(421,plain,
% 5.36/3.65 (((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.65 inference(rewrite,[status(thm)],[])).
% 5.36/3.65 tff(422,plain,
% 5.36/3.65 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.36/3.65 inference(monotonicity,[status(thm)],[421])).
% 5.36/3.65 tff(423,plain,
% 5.36/3.65 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.65 inference(transitivity,[status(thm)],[422, 420])).
% 5.36/3.65 tff(424,plain,
% 5.36/3.65 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.36/3.65 inference(quant_inst,[status(thm)],[])).
% 5.36/3.65 tff(425,plain,
% 5.36/3.65 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X2, plane_for_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))),
% 5.36/3.65 inference(modus_ponens,[status(thm)],[424, 423])).
% 5.36/3.65 tff(426,plain,
% 5.36/3.65 (on(point_2_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.65 inference(unit_resolution,[status(thm)],[425, 309, 69, 177, 213, 55, 368, 199, 419])).
% 5.36/3.65 tff(427,plain,
% 5.36/3.65 (on(point_2_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.65 inference(modus_ponens,[status(thm)],[426, 362])).
% 5.36/3.65 tff(428,plain,
% 5.36/3.65 (on(point_1_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) <=> on(point_1_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.65 inference(monotonicity,[status(thm)],[361])).
% 5.36/3.65 tff(429,plain,
% 5.36/3.65 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.65 inference(rewrite,[status(thm)],[])).
% 5.36/3.65 tff(430,plain,
% 5.36/3.65 (((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.65 inference(rewrite,[status(thm)],[])).
% 5.36/3.65 tff(431,plain,
% 5.36/3.65 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.36/3.65 inference(monotonicity,[status(thm)],[430])).
% 5.36/3.65 tff(432,plain,
% 5.36/3.65 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.65 inference(transitivity,[status(thm)],[431, 429])).
% 5.36/3.65 tff(433,plain,
% 5.36/3.65 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.36/3.65 inference(quant_inst,[status(thm)],[])).
% 5.36/3.65 tff(434,plain,
% 5.36/3.65 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X1, plane_for_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))),
% 5.36/3.65 inference(modus_ponens,[status(thm)],[433, 432])).
% 5.36/3.65 tff(435,plain,
% 5.36/3.65 (on(point_1_on_line(at_least_one_line), plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.65 inference(unit_resolution,[status(thm)],[434, 330, 69, 177, 213, 55, 368, 199, 419])).
% 5.36/3.65 tff(436,plain,
% 5.36/3.65 (on(point_1_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.65 inference(modus_ponens,[status(thm)],[435, 428])).
% 5.36/3.65 tff(437,plain,
% 5.36/3.65 (plane(plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) <=> plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.65 inference(monotonicity,[status(thm)],[361])).
% 5.36/3.65 tff(438,plain,
% 5.36/3.65 (^[X3: $i, X2: $i, X1: $i] : refl(((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3))))),
% 5.36/3.65 inference(bind,[status(th)],[])).
% 5.36/3.65 tff(439,plain,
% 5.36/3.65 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))),
% 5.36/3.65 inference(quant_intro,[status(thm)],[438])).
% 5.36/3.65 tff(440,plain,
% 5.36/3.65 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))),
% 5.36/3.65 inference(rewrite,[status(thm)],[])).
% 5.36/3.65 tff(441,plain,
% 5.36/3.65 (^[X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) <=> ((~point(X1)) | plane(plane_for_points(X1, X2, X3)))), (((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) <=> (((~point(X1)) | plane(plane_for_points(X1, X2, X3))) | (~point(X2))))), rewrite((((~point(X1)) | plane(plane_for_points(X1, X2, X3))) | (~point(X2))) <=> ((~point(X1)) | (~point(X2)) | plane(plane_for_points(X1, X2, X3)))), (((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) <=> ((~point(X1)) | (~point(X2)) | plane(plane_for_points(X1, X2, X3))))), ((((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) <=> (((~point(X1)) | (~point(X2)) | plane(plane_for_points(X1, X2, X3))) | (~point(X3))))), rewrite((((~point(X1)) | (~point(X2)) | plane(plane_for_points(X1, X2, X3))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | plane(plane_for_points(X1, X2, X3)))), ((((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | plane(plane_for_points(X1, X2, X3))))), (((((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | plane(plane_for_points(X1, X2, X3))) | collinear(X1, X2, X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | plane(plane_for_points(X1, X2, X3))) | collinear(X1, X2, X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))), (((((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3))))), ((((((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3))) | (X1 = X2)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))), ((((((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3))))), (((((((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3))) | (X1 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3))) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))), (((((((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3))))), ((((((((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3))) | (X2 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3))) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))), ((((((((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))))),
% 5.36/3.65 inference(bind,[status(th)],[])).
% 5.36/3.65 tff(442,plain,
% 5.36/3.65 (![X3: $i, X2: $i, X1: $i] : (((((((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))),
% 5.36/3.65 inference(quant_intro,[status(thm)],[441])).
% 5.36/3.65 tff(443,axiom,(![X3: $i, X2: $i, X1: $i] : (((((((plane(plane_for_points(X1, X2, X3)) | (~point(X1))) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G7D')).
% 5.36/3.65 tff(444,plain,
% 5.36/3.65 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))),
% 5.36/3.65 inference(modus_ponens,[status(thm)],[443, 442])).
% 5.36/3.65 tff(445,plain,
% 5.36/3.65 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))),
% 5.36/3.65 inference(modus_ponens,[status(thm)],[444, 440])).
% 5.36/3.66 tff(446,plain,(
% 5.36/3.66 ![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))),
% 5.36/3.66 inference(skolemize,[status(sab)],[445])).
% 5.36/3.66 tff(447,plain,
% 5.36/3.66 (![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))),
% 5.36/3.66 inference(modus_ponens,[status(thm)],[446, 439])).
% 5.36/3.66 tff(448,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | plane(plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | plane(plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.66 inference(rewrite,[status(thm)],[])).
% 5.36/3.66 tff(449,plain,
% 5.36/3.66 (((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | plane(plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | plane(plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.66 inference(rewrite,[status(thm)],[])).
% 5.36/3.66 tff(450,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | plane(plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | plane(plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.36/3.66 inference(monotonicity,[status(thm)],[449])).
% 5.36/3.66 tff(451,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | plane(plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | plane(plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.66 inference(transitivity,[status(thm)],[450, 448])).
% 5.36/3.66 tff(452,plain,
% 5.36/3.66 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | plane(plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.36/3.66 inference(quant_inst,[status(thm)],[])).
% 5.36/3.66 tff(453,plain,
% 5.36/3.66 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | plane(plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))),
% 5.36/3.66 inference(modus_ponens,[status(thm)],[452, 451])).
% 5.36/3.66 tff(454,plain,
% 5.36/3.66 (plane(plane_for_points(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.66 inference(unit_resolution,[status(thm)],[453, 447, 69, 177, 213, 55, 368, 199, 419])).
% 5.36/3.66 tff(455,plain,
% 5.36/3.66 (plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.36/3.66 inference(modus_ponens,[status(thm)],[454, 437])).
% 5.36/3.66 tff(456,plain,
% 5.36/3.66 ((point_2_on_line(at_least_one_line) = a_point) <=> (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line))),
% 5.36/3.66 inference(monotonicity,[status(thm)],[154])).
% 5.36/3.66 tff(457,plain,
% 5.36/3.66 ((point_2_on_line(at_least_one_line) = a_point) <=> (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))),
% 5.36/3.66 inference(transitivity,[status(thm)],[456, 161])).
% 5.36/3.66 tff(458,plain,
% 5.36/3.66 ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) <=> (point_2_on_line(at_least_one_line) = a_point)),
% 5.36/3.66 inference(symmetry,[status(thm)],[457])).
% 5.36/3.66 tff(459,plain,
% 5.36/3.66 ((~(point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))) <=> (~(point_2_on_line(at_least_one_line) = a_point))),
% 5.36/3.66 inference(monotonicity,[status(thm)],[458])).
% 5.36/3.66 tff(460,plain,
% 5.36/3.66 (~(point_2_on_line(at_least_one_line) = a_point)),
% 5.36/3.66 inference(modus_ponens,[status(thm)],[177, 459])).
% 5.36/3.66 tff(461,assumption,(~(point_2_on_line(at_least_one_line) = a_point)), introduced(assumption)).
% 5.36/3.66 tff(462,assumption,(~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))), introduced(assumption)).
% 5.36/3.66 tff(463,plain,
% 5.36/3.66 ((point_not_on_line(at_least_one_line) = a_point) <=> (a_point = point_not_on_line(at_least_one_line))),
% 5.36/3.66 inference(commutativity,[status(thm)],[])).
% 5.36/3.66 tff(464,plain,
% 5.36/3.66 ((a_point = point_not_on_line(at_least_one_line)) <=> (point_not_on_line(at_least_one_line) = a_point)),
% 5.36/3.66 inference(symmetry,[status(thm)],[463])).
% 5.36/3.66 tff(465,plain,
% 5.36/3.66 ((~(a_point = point_not_on_line(at_least_one_line))) <=> (~(point_not_on_line(at_least_one_line) = a_point))),
% 5.36/3.66 inference(monotonicity,[status(thm)],[464])).
% 5.36/3.66 tff(466,assumption,(a_point = point_not_on_line(at_least_one_line)), introduced(assumption)).
% 5.36/3.66 tff(467,plain,
% 5.36/3.66 (on(a_point, at_least_one_line) <=> on(point_not_on_line(at_least_one_line), at_least_one_line)),
% 5.36/3.66 inference(monotonicity,[status(thm)],[466])).
% 5.36/3.66 tff(468,plain,
% 5.36/3.66 (on(point_not_on_line(at_least_one_line), at_least_one_line) <=> on(a_point, at_least_one_line)),
% 5.36/3.66 inference(symmetry,[status(thm)],[467])).
% 5.36/3.66 tff(469,plain,
% 5.36/3.66 ((~on(point_not_on_line(at_least_one_line), at_least_one_line)) <=> (~on(a_point, at_least_one_line))),
% 5.36/3.66 inference(monotonicity,[status(thm)],[468])).
% 5.36/3.66 tff(470,plain,
% 5.36/3.66 (~on(a_point, at_least_one_line)),
% 5.36/3.66 inference(modus_ponens,[status(thm)],[39, 469])).
% 5.36/3.66 tff(471,plain,
% 5.36/3.66 ($false),
% 5.36/3.66 inference(unit_resolution,[status(thm)],[133, 470])).
% 5.36/3.66 tff(472,plain,(~(a_point = point_not_on_line(at_least_one_line))), inference(lemma,lemma(discharge,[]))).
% 5.36/3.66 tff(473,plain,
% 5.36/3.66 (~(point_not_on_line(at_least_one_line) = a_point)),
% 5.36/3.66 inference(modus_ponens,[status(thm)],[472, 465])).
% 5.36/3.66 tff(474,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))))),
% 5.36/3.66 inference(rewrite,[status(thm)],[])).
% 5.36/3.66 tff(475,plain,
% 5.36/3.66 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) | plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) <=> ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))))),
% 5.36/3.66 inference(rewrite,[status(thm)],[])).
% 5.36/3.66 tff(476,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) | plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line)))))),
% 5.36/3.66 inference(monotonicity,[status(thm)],[475])).
% 5.36/3.66 tff(477,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) | plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))))),
% 5.36/3.66 inference(transitivity,[status(thm)],[476, 474])).
% 5.36/3.66 tff(478,plain,
% 5.36/3.66 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) | plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.36/3.66 inference(quant_inst,[status(thm)],[])).
% 5.36/3.66 tff(479,plain,
% 5.36/3.66 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | plane(plane_for_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line)))),
% 5.36/3.66 inference(modus_ponens,[status(thm)],[478, 477])).
% 5.36/3.66 tff(480,plain,
% 5.36/3.66 ((point_2_on_line(at_least_one_line) = a_point) | (point_not_on_line(at_least_one_line) = a_point) | plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line))),
% 5.36/3.66 inference(unit_resolution,[status(thm)],[479, 447, 136, 69, 213])).
% 5.36/3.66 tff(481,plain,
% 5.36/3.66 ((point_2_on_line(at_least_one_line) = a_point) | plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line))),
% 5.36/3.66 inference(unit_resolution,[status(thm)],[480, 473])).
% 5.36/3.66 tff(482,plain,
% 5.36/3.66 (collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)),
% 5.36/3.66 inference(unit_resolution,[status(thm)],[481, 364, 462, 461])).
% 5.36/3.66 tff(483,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.36/3.66 inference(rewrite,[status(thm)],[])).
% 5.36/3.66 tff(484,plain,
% 5.36/3.66 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) <=> ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.36/3.66 inference(rewrite,[status(thm)],[])).
% 5.36/3.66 tff(485,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))),
% 5.36/3.66 inference(monotonicity,[status(thm)],[484])).
% 5.36/3.66 tff(486,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.36/3.66 inference(transitivity,[status(thm)],[485, 483])).
% 5.36/3.66 tff(487,plain,
% 5.36/3.66 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.36/3.66 inference(quant_inst,[status(thm)],[])).
% 5.36/3.66 tff(488,plain,
% 5.36/3.66 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.36/3.66 inference(modus_ponens,[status(thm)],[487, 486])).
% 5.36/3.66 tff(489,plain,
% 5.36/3.66 (on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.36/3.66 inference(unit_resolution,[status(thm)],[488, 223, 136, 69, 213, 461, 473, 364, 482])).
% 5.36/3.66 tff(490,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.36/3.66 inference(rewrite,[status(thm)],[])).
% 5.36/3.66 tff(491,plain,
% 5.36/3.66 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) <=> ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.36/3.66 inference(rewrite,[status(thm)],[])).
% 5.36/3.66 tff(492,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))),
% 5.36/3.66 inference(monotonicity,[status(thm)],[491])).
% 5.36/3.66 tff(493,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.36/3.66 inference(transitivity,[status(thm)],[492, 490])).
% 5.36/3.66 tff(494,plain,
% 5.36/3.66 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.36/3.66 inference(quant_inst,[status(thm)],[])).
% 5.36/3.66 tff(495,plain,
% 5.36/3.66 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.36/3.66 inference(modus_ponens,[status(thm)],[494, 493])).
% 5.36/3.66 tff(496,plain,
% 5.36/3.66 (on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.36/3.66 inference(unit_resolution,[status(thm)],[495, 240, 136, 69, 213, 461, 473, 364, 482])).
% 5.36/3.66 tff(497,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.36/3.66 inference(rewrite,[status(thm)],[])).
% 5.36/3.66 tff(498,plain,
% 5.36/3.66 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) <=> ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.36/3.66 inference(rewrite,[status(thm)],[])).
% 5.36/3.66 tff(499,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))),
% 5.36/3.66 inference(monotonicity,[status(thm)],[498])).
% 5.36/3.66 tff(500,plain,
% 5.36/3.66 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.36/3.66 inference(transitivity,[status(thm)],[499, 497])).
% 5.36/3.66 tff(501,plain,
% 5.36/3.66 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.36/3.66 inference(quant_inst,[status(thm)],[])).
% 5.36/3.66 tff(502,plain,
% 5.36/3.66 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.36/3.67 inference(modus_ponens,[status(thm)],[501, 500])).
% 5.36/3.67 tff(503,plain,
% 5.36/3.67 (line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.36/3.67 inference(unit_resolution,[status(thm)],[502, 257, 136, 69, 213, 461, 473, 364, 482])).
% 5.36/3.67 tff(504,plain,
% 5.36/3.67 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~line(at_least_one_line)) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = at_least_one_line) | (~on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~line(at_least_one_line)) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = at_least_one_line) | (~on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))),
% 5.36/3.67 inference(rewrite,[status(thm)],[])).
% 5.36/3.67 tff(505,plain,
% 5.36/3.67 (((~point(a_point)) | (~line(at_least_one_line)) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~point(point_2_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = at_least_one_line) | (~on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (point_2_on_line(at_least_one_line) = a_point) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~line(at_least_one_line)) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = at_least_one_line) | (~on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))),
% 5.36/3.67 inference(rewrite,[status(thm)],[])).
% 5.36/3.67 tff(506,plain,
% 5.36/3.67 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(a_point)) | (~line(at_least_one_line)) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~point(point_2_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = at_least_one_line) | (~on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (point_2_on_line(at_least_one_line) = a_point) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~line(at_least_one_line)) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = at_least_one_line) | (~on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))))),
% 5.36/3.67 inference(monotonicity,[status(thm)],[505])).
% 5.36/3.67 tff(507,plain,
% 5.36/3.67 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(a_point)) | (~line(at_least_one_line)) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~point(point_2_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = at_least_one_line) | (~on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (point_2_on_line(at_least_one_line) = a_point) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~line(at_least_one_line)) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = at_least_one_line) | (~on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))),
% 5.38/3.67 inference(transitivity,[status(thm)],[506, 504])).
% 5.38/3.67 tff(508,plain,
% 5.38/3.67 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(a_point)) | (~line(at_least_one_line)) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~point(point_2_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = at_least_one_line) | (~on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (point_2_on_line(at_least_one_line) = a_point) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))),
% 5.38/3.67 inference(quant_inst,[status(thm)],[])).
% 5.38/3.67 tff(509,plain,
% 5.38/3.67 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~line(at_least_one_line)) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (~on(a_point, at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~line(line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = at_least_one_line) | (~on(a_point, line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.38/3.67 inference(modus_ponens,[status(thm)],[508, 507])).
% 5.38/3.67 tff(510,plain,
% 5.38/3.67 (line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = at_least_one_line),
% 5.38/3.67 inference(unit_resolution,[status(thm)],[509, 146, 10, 136, 133, 213, 197, 461, 503, 496, 489])).
% 5.38/3.67 tff(511,plain,
% 5.38/3.67 (on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) <=> on(point_not_on_line(at_least_one_line), at_least_one_line)),
% 5.38/3.67 inference(monotonicity,[status(thm)],[510])).
% 5.38/3.67 tff(512,plain,
% 5.38/3.67 (on(point_not_on_line(at_least_one_line), at_least_one_line) <=> on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.38/3.67 inference(symmetry,[status(thm)],[511])).
% 5.38/3.67 tff(513,plain,
% 5.38/3.67 ((~on(point_not_on_line(at_least_one_line), at_least_one_line)) <=> (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.38/3.67 inference(monotonicity,[status(thm)],[512])).
% 5.38/3.67 tff(514,plain,
% 5.38/3.67 (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.38/3.67 inference(modus_ponens,[status(thm)],[39, 513])).
% 5.38/3.67 tff(515,plain,
% 5.38/3.67 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.38/3.67 inference(rewrite,[status(thm)],[])).
% 5.38/3.67 tff(516,plain,
% 5.38/3.67 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) <=> ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.38/3.67 inference(rewrite,[status(thm)],[])).
% 5.38/3.67 tff(517,plain,
% 5.38/3.67 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))),
% 5.38/3.67 inference(monotonicity,[status(thm)],[516])).
% 5.38/3.67 tff(518,plain,
% 5.38/3.67 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.38/3.67 inference(transitivity,[status(thm)],[517, 515])).
% 5.38/3.67 tff(519,plain,
% 5.38/3.67 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(a_point)) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.38/3.67 inference(quant_inst,[status(thm)],[])).
% 5.38/3.67 tff(520,plain,
% 5.38/3.67 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | (~point(a_point)) | (point_2_on_line(at_least_one_line) = a_point) | (~point(point_2_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = a_point) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.38/3.67 inference(modus_ponens,[status(thm)],[519, 518])).
% 5.38/3.67 tff(521,plain,
% 5.38/3.67 (on(point_not_on_line(at_least_one_line), line_through_3_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.38/3.67 inference(unit_resolution,[status(thm)],[520, 281, 136, 69, 213, 461, 473, 364, 482])).
% 5.38/3.67 tff(522,plain,
% 5.38/3.67 ($false),
% 5.38/3.67 inference(unit_resolution,[status(thm)],[521, 514])).
% 5.38/3.67 tff(523,plain,((point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = a_point) | plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))), inference(lemma,lemma(discharge,[]))).
% 5.38/3.67 tff(524,plain,
% 5.38/3.67 ((point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.38/3.67 inference(unit_resolution,[status(thm)],[523, 460])).
% 5.38/3.67 tff(525,plain,
% 5.38/3.67 (plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.38/3.67 inference(unit_resolution,[status(thm)],[524, 199])).
% 5.38/3.67 tff(526,plain,
% 5.38/3.67 (collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) <=> collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))),
% 5.38/3.67 inference(monotonicity,[status(thm)],[155])).
% 5.38/3.67 tff(527,plain,
% 5.38/3.67 (collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) <=> collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))),
% 5.38/3.67 inference(symmetry,[status(thm)],[526])).
% 5.38/3.67 tff(528,assumption,(collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), introduced(assumption)).
% 5.38/3.67 tff(529,plain,
% 5.38/3.67 (collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))),
% 5.38/3.67 inference(modus_ponens,[status(thm)],[528, 527])).
% 5.38/3.67 tff(530,assumption,(~collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), introduced(assumption)).
% 5.38/3.67 tff(531,plain,
% 5.38/3.67 ($false),
% 5.38/3.67 inference(unit_resolution,[status(thm)],[530, 529])).
% 5.38/3.67 tff(532,plain,((~collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | collinear(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), inference(lemma,lemma(discharge,[]))).
% 5.38/3.67 tff(533,plain,
% 5.38/3.67 (~collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))),
% 5.38/3.67 inference(unit_resolution,[status(thm)],[532, 419])).
% 5.38/3.67 tff(534,plain,
% 5.38/3.67 ((a_point = point_2_on_line(at_least_one_line)) <=> (point_2_on_line(at_least_one_line) = a_point)),
% 5.38/3.67 inference(commutativity,[status(thm)],[])).
% 5.38/3.67 tff(535,plain,
% 5.38/3.67 ((point_2_on_line(at_least_one_line) = a_point) <=> (a_point = point_2_on_line(at_least_one_line))),
% 5.38/3.67 inference(symmetry,[status(thm)],[534])).
% 5.38/3.67 tff(536,plain,
% 5.38/3.67 ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) <=> (a_point = point_2_on_line(at_least_one_line))),
% 5.38/3.67 inference(transitivity,[status(thm)],[458, 535])).
% 5.38/3.67 tff(537,plain,
% 5.38/3.67 ((~(point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))) <=> (~(a_point = point_2_on_line(at_least_one_line)))),
% 5.38/3.67 inference(monotonicity,[status(thm)],[536])).
% 5.38/3.67 tff(538,plain,
% 5.38/3.67 (~(a_point = point_2_on_line(at_least_one_line))),
% 5.38/3.67 inference(modus_ponens,[status(thm)],[177, 537])).
% 5.38/3.67 tff(539,plain,
% 5.38/3.67 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | ((~point(a_point)) | (~point(point_2_on_line(at_least_one_line))) | (a_point = point_not_on_line(at_least_one_line)) | collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (a_point = point_2_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | (~point(a_point)) | (~point(point_2_on_line(at_least_one_line))) | (a_point = point_not_on_line(at_least_one_line)) | collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (a_point = point_2_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))))),
% 5.38/3.67 inference(rewrite,[status(thm)],[])).
% 5.38/3.67 tff(540,plain,
% 5.38/3.67 (((~point(a_point)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (a_point = point_not_on_line(at_least_one_line)) | (a_point = point_2_on_line(at_least_one_line)) | collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> ((~point(a_point)) | (~point(point_2_on_line(at_least_one_line))) | (a_point = point_not_on_line(at_least_one_line)) | collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (a_point = point_2_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))))),
% 5.38/3.67 inference(rewrite,[status(thm)],[])).
% 5.38/3.67 tff(541,plain,
% 5.38/3.67 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | ((~point(a_point)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (a_point = point_not_on_line(at_least_one_line)) | (a_point = point_2_on_line(at_least_one_line)) | collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | ((~point(a_point)) | (~point(point_2_on_line(at_least_one_line))) | (a_point = point_not_on_line(at_least_one_line)) | collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (a_point = point_2_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line)))))),
% 5.38/3.67 inference(monotonicity,[status(thm)],[540])).
% 5.38/3.67 tff(542,plain,
% 5.38/3.67 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | ((~point(a_point)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (a_point = point_not_on_line(at_least_one_line)) | (a_point = point_2_on_line(at_least_one_line)) | collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | (~point(a_point)) | (~point(point_2_on_line(at_least_one_line))) | (a_point = point_not_on_line(at_least_one_line)) | collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (a_point = point_2_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))))),
% 5.38/3.67 inference(transitivity,[status(thm)],[541, 539])).
% 5.38/3.67 tff(543,plain,
% 5.38/3.67 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | ((~point(a_point)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (a_point = point_not_on_line(at_least_one_line)) | (a_point = point_2_on_line(at_least_one_line)) | collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.38/3.67 inference(quant_inst,[status(thm)],[])).
% 5.38/3.67 tff(544,plain,
% 5.38/3.67 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | on(X3, plane_for_points(X1, X2, X3)))) | (~point(a_point)) | (~point(point_2_on_line(at_least_one_line))) | (a_point = point_not_on_line(at_least_one_line)) | collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (a_point = point_2_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line)))),
% 5.38/3.67 inference(modus_ponens,[status(thm)],[543, 542])).
% 5.38/3.67 tff(545,plain,
% 5.38/3.67 ((a_point = point_not_on_line(at_least_one_line)) | collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (a_point = point_2_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.38/3.67 inference(unit_resolution,[status(thm)],[544, 351, 136, 69, 213])).
% 5.38/3.67 tff(546,plain,
% 5.38/3.67 (collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (a_point = point_2_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.38/3.67 inference(unit_resolution,[status(thm)],[545, 472])).
% 5.38/3.67 tff(547,plain,
% 5.38/3.67 (collinear(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.38/3.67 inference(unit_resolution,[status(thm)],[546, 538])).
% 5.38/3.67 tff(548,plain,
% 5.38/3.67 (on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.38/3.67 inference(unit_resolution,[status(thm)],[547, 533, 199])).
% 5.38/3.67 tff(549,plain,
% 5.38/3.67 (^[Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : refl(((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))))),
% 5.38/3.67 inference(bind,[status(th)],[])).
% 5.38/3.67 tff(550,plain,
% 5.38/3.67 (![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) <=> ![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))),
% 5.38/3.67 inference(quant_intro,[status(thm)],[549])).
% 5.38/3.67 tff(551,plain,
% 5.38/3.67 (![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) <=> ![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))),
% 5.38/3.67 inference(rewrite,[status(thm)],[])).
% 5.38/3.67 tff(552,plain,
% 5.38/3.67 (^[Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~point(X1)) | (~point(X2))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)))), (((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3))) | collinear(X1, X2, X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3))) | collinear(X1, X2, X3)) <=> ((~point(X1)) | (~point(X2)) | collinear(X1, X2, X3) | (~point(X3)))), (((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) <=> ((~point(X1)) | (~point(X2)) | collinear(X1, X2, X3) | (~point(X3))))), ((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) <=> (((~point(X1)) | (~point(X2)) | collinear(X1, X2, X3) | (~point(X3))) | (X1 = X2)))), rewrite((((~point(X1)) | (~point(X2)) | collinear(X1, X2, X3) | (~point(X3))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (X1 = X2) | collinear(X1, X2, X3) | (~point(X3)))), ((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (X1 = X2) | collinear(X1, X2, X3) | (~point(X3))))), (((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) <=> (((~point(X1)) | (~point(X2)) | (X1 = X2) | collinear(X1, X2, X3) | (~point(X3))) | (X1 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (X1 = X2) | collinear(X1, X2, X3) | (~point(X3))) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (X1 = X2) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))), (((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (X1 = X2) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))))), ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> (((~point(X1)) | (~point(X2)) | (X1 = X2) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (X2 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (X1 = X2) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (X1 = X2) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))), ((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (X1 = X2) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))))), (((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) <=> (((~point(X1)) | (~point(X2)) | (X1 = X2) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~on(X1, Z1))))), rewrite((((~point(X1)) | (~point(X2)) | (X1 = X2) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~on(X1, Z1))) <=> ((~point(X1)) | (~point(X2)) | (X1 = X2) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))), (((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) <=> ((~point(X1)) | (~point(X2)) | (X1 = X2) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))))), ((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) <=> (((~point(X1)) | (~point(X2)) | (X1 = X2) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~on(X2, Z1))))), rewrite((((~point(X1)) | (~point(X2)) | (X1 = X2) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~on(X2, Z1))) <=> ((~point(X1)) | (~point(X2)) | (X1 = X2) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))), ((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) <=> ((~point(X1)) | (~point(X2)) | (X1 = X2) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))))), (((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) <=> (((~point(X1)) | (~point(X2)) | (X1 = X2) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~on(X3, Z1))))), rewrite((((~point(X1)) | (~point(X2)) | (X1 = X2) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~on(X3, Z1))) <=> ((~point(X1)) | (~point(X2)) | (X1 = X2) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))), (((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) <=> ((~point(X1)) | (~point(X2)) | (X1 = X2) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))))), ((((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) | (~plane(Z1))) <=> (((~point(X1)) | (~point(X2)) | (X1 = X2) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~plane(Z1))))), rewrite((((~point(X1)) | (~point(X2)) | (X1 = X2) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~plane(Z1))) <=> ((~point(X1)) | (~point(X2)) | (X1 = X2) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))), ((((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) | (~plane(Z1))) <=> ((~point(X1)) | (~point(X2)) | (X1 = X2) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))))), (((((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) | (~plane(Z1))) | (~on(X1, Z2))) <=> (((~point(X1)) | (~point(X2)) | (X1 = X2) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~on(X1, Z2))))), rewrite((((~point(X1)) | (~point(X2)) | (X1 = X2) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~on(X1, Z2))) <=> ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (X1 = X2) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))), (((((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) | (~plane(Z1))) | (~on(X1, Z2))) <=> ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (X1 = X2) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))))), ((((((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) | (~plane(Z1))) | (~on(X1, Z2))) | (~on(X2, Z2))) <=> (((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (X1 = X2) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~on(X2, Z2))))), rewrite((((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (X1 = X2) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~on(X2, Z2))) <=> ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))), ((((((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) | (~plane(Z1))) | (~on(X1, Z2))) | (~on(X2, Z2))) <=> ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))))), (((((((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) | (~plane(Z1))) | (~on(X1, Z2))) | (~on(X2, Z2))) | (~on(X3, Z2))) <=> (((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~on(X3, Z2))))), rewrite((((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~on(X3, Z2))) <=> ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))), (((((((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) | (~plane(Z1))) | (~on(X1, Z2))) | (~on(X2, Z2))) | (~on(X3, Z2))) <=> ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))))), ((((((((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) | (~plane(Z1))) | (~on(X1, Z2))) | (~on(X2, Z2))) | (~on(X3, Z2))) | (~plane(Z2))) <=> (((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~plane(Z2))))), rewrite((((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (~plane(Z2))) <=> ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))), ((((((((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) | (~plane(Z1))) | (~on(X1, Z2))) | (~on(X2, Z2))) | (~on(X3, Z2))) | (~plane(Z2))) <=> ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))))), (((((((((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) | (~plane(Z1))) | (~on(X1, Z2))) | (~on(X2, Z2))) | (~on(X3, Z2))) | (~plane(Z2))) | (Z1 = Z2)) <=> (((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (Z1 = Z2)))), rewrite((((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3))) | (Z1 = Z2)) <=> ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))), (((((((((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) | (~plane(Z1))) | (~on(X1, Z2))) | (~on(X2, Z2))) | (~on(X3, Z2))) | (~plane(Z2))) | (Z1 = Z2)) <=> ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))))),
% 5.38/3.67 inference(bind,[status(th)],[])).
% 5.38/3.67 tff(553,plain,
% 5.38/3.67 (![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((((((((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) | (~plane(Z1))) | (~on(X1, Z2))) | (~on(X2, Z2))) | (~on(X3, Z2))) | (~plane(Z2))) | (Z1 = Z2)) <=> ![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))),
% 5.38/3.67 inference(quant_intro,[status(thm)],[552])).
% 5.38/3.67 tff(554,axiom,(![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((((((((((((((((~point(X1)) | (~point(X2))) | (~point(X3))) | collinear(X1, X2, X3)) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~on(X1, Z1))) | (~on(X2, Z1))) | (~on(X3, Z1))) | (~plane(Z1))) | (~on(X1, Z2))) | (~on(X2, Z2))) | (~on(X3, Z2))) | (~plane(Z2))) | (Z1 = Z2))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G7E')).
% 5.38/3.67 tff(555,plain,
% 5.38/3.67 (![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))),
% 5.38/3.67 inference(modus_ponens,[status(thm)],[554, 553])).
% 5.38/3.67 tff(556,plain,
% 5.38/3.67 (![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))),
% 5.38/3.67 inference(modus_ponens,[status(thm)],[555, 551])).
% 5.38/3.67 tff(557,plain,(
% 5.38/3.67 ![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))),
% 5.38/3.67 inference(skolemize,[status(sab)],[556])).
% 5.38/3.67 tff(558,plain,
% 5.38/3.67 (![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))),
% 5.38/3.67 inference(modus_ponens,[status(thm)],[557, 550])).
% 5.38/3.67 tff(559,plain,
% 5.38/3.67 (((~![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.38/3.68 inference(rewrite,[status(thm)],[])).
% 5.38/3.68 tff(560,plain,
% 5.38/3.68 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line)))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.38/3.68 inference(rewrite,[status(thm)],[])).
% 5.38/3.68 tff(561,plain,
% 5.38/3.68 (((~![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))))) <=> ((~![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(monotonicity,[status(thm)],[560])).
% 5.38/3.68 tff(562,plain,
% 5.38/3.68 (((~![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))))) <=> ((~![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.38/3.68 inference(transitivity,[status(thm)],[561, 559])).
% 5.38/3.68 tff(563,plain,
% 5.38/3.68 ((~![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))))),
% 5.38/3.68 inference(quant_inst,[status(thm)],[])).
% 5.38/3.68 tff(564,plain,
% 5.38/3.68 ((~![Z1: $i, X3: $i, X2: $i, Z2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~on(X1, Z2)) | (~on(X2, Z2)) | (X1 = X2) | (Z1 = Z2) | (~plane(Z2)) | (~on(X3, Z2)) | (~plane(Z1)) | (~on(X3, Z1)) | (~on(X2, Z1)) | (~on(X1, Z1)) | (X2 = X3) | (X1 = X3) | collinear(X1, X2, X3) | (~point(X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_1_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (~on(point_2_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.38/3.68 inference(modus_ponens,[status(thm)],[563, 562])).
% 5.38/3.68 tff(565,plain,
% 5.38/3.68 ((~on(point_not_on_line(at_least_one_line), plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | (plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.38/3.68 inference(unit_resolution,[status(thm)],[564, 558, 69, 213, 55, 41, 199, 548, 525, 178, 455, 436, 427, 299, 360, 339])).
% 5.38/3.68 tff(566,plain,
% 5.38/3.68 (plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))),
% 5.38/3.68 inference(unit_resolution,[status(thm)],[565, 318])).
% 5.38/3.68 tff(567,plain,
% 5.38/3.68 (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.38/3.68 inference(monotonicity,[status(thm)],[566])).
% 5.38/3.68 tff(568,plain,
% 5.38/3.68 (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.38/3.68 inference(symmetry,[status(thm)],[567])).
% 5.38/3.68 tff(569,plain,
% 5.38/3.68 (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.68 inference(monotonicity,[status(thm)],[568])).
% 5.38/3.68 tff(570,plain,
% 5.38/3.68 (line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(monotonicity,[status(thm)],[569])).
% 5.38/3.68 tff(571,plain,
% 5.38/3.68 (on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> on(a_point, line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(monotonicity,[status(thm)],[155])).
% 5.38/3.68 tff(572,plain,
% 5.38/3.68 (on(a_point, line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(symmetry,[status(thm)],[571])).
% 5.38/3.68 tff(573,assumption,(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))), introduced(assumption)).
% 5.38/3.68 tff(574,plain,
% 5.38/3.68 (point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.38/3.68 inference(symmetry,[status(thm)],[573])).
% 5.38/3.68 tff(575,plain,
% 5.38/3.68 ((point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.68 inference(monotonicity,[status(thm)],[574])).
% 5.38/3.68 tff(576,plain,
% 5.38/3.68 ((~(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> (~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(monotonicity,[status(thm)],[575])).
% 5.38/3.68 tff(577,assumption,(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))), introduced(assumption)).
% 5.38/3.68 tff(578,plain,
% 5.38/3.68 (on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.68 inference(monotonicity,[status(thm)],[577])).
% 5.38/3.68 tff(579,plain,
% 5.38/3.68 (on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.68 inference(symmetry,[status(thm)],[578])).
% 5.38/3.68 tff(580,plain,
% 5.38/3.68 (((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(rewrite,[status(thm)],[])).
% 5.38/3.68 tff(581,plain,
% 5.38/3.68 ((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(quant_inst,[status(thm)],[])).
% 5.38/3.68 tff(582,plain,
% 5.38/3.68 ((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.68 inference(modus_ponens,[status(thm)],[581, 580])).
% 5.38/3.68 tff(583,plain,
% 5.38/3.68 (on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.68 inference(unit_resolution,[status(thm)],[582, 190, 104])).
% 5.38/3.68 tff(584,plain,
% 5.38/3.68 (on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.68 inference(modus_ponens,[status(thm)],[583, 579])).
% 5.38/3.68 tff(585,plain,
% 5.38/3.68 (((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | ((~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(rewrite,[status(thm)],[])).
% 5.38/3.68 tff(586,plain,
% 5.38/3.68 (((~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(rewrite,[status(thm)],[])).
% 5.38/3.68 tff(587,plain,
% 5.38/3.68 (((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | ((~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | ((~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.68 inference(monotonicity,[status(thm)],[586])).
% 5.38/3.68 tff(588,plain,
% 5.38/3.68 (((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | ((~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(transitivity,[status(thm)],[587, 585])).
% 5.38/3.68 tff(589,plain,
% 5.38/3.68 ((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | ((~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(quant_inst,[status(thm)],[])).
% 5.38/3.68 tff(590,plain,
% 5.38/3.68 ((~![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.68 inference(modus_ponens,[status(thm)],[589, 588])).
% 5.38/3.68 tff(591,plain,
% 5.38/3.68 (~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.68 inference(unit_resolution,[status(thm)],[590, 32, 104])).
% 5.38/3.68 tff(592,plain,
% 5.38/3.68 ($false),
% 5.38/3.68 inference(unit_resolution,[status(thm)],[591, 584])).
% 5.38/3.68 tff(593,plain,(~(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))), inference(lemma,lemma(discharge,[]))).
% 5.38/3.68 tff(594,plain,
% 5.38/3.68 (~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.68 inference(modus_ponens,[status(thm)],[593, 576])).
% 5.38/3.68 tff(595,plain,
% 5.38/3.68 (^[Z1: $i] : refl(((~plane(Z1)) | point(point_on_plane(Z1))) <=> ((~plane(Z1)) | point(point_on_plane(Z1))))),
% 5.38/3.68 inference(bind,[status(th)],[])).
% 5.38/3.68 tff(596,plain,
% 5.38/3.68 (![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1))) <=> ![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1)))),
% 5.38/3.68 inference(quant_intro,[status(thm)],[595])).
% 5.38/3.68 tff(597,plain,
% 5.38/3.68 (![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1))) <=> ![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1)))),
% 5.38/3.68 inference(rewrite,[status(thm)],[])).
% 5.38/3.68 tff(598,axiom,(![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G5B')).
% 5.38/3.68 tff(599,plain,
% 5.38/3.68 (![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1)))),
% 5.38/3.68 inference(modus_ponens,[status(thm)],[598, 597])).
% 5.38/3.68 tff(600,plain,(
% 5.38/3.68 ![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1)))),
% 5.38/3.68 inference(skolemize,[status(sab)],[599])).
% 5.38/3.68 tff(601,plain,
% 5.38/3.68 (![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1)))),
% 5.38/3.68 inference(modus_ponens,[status(thm)],[600, 596])).
% 5.38/3.68 tff(602,plain,
% 5.38/3.68 (((~![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1)))) | ((~plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1)))) | (~plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(rewrite,[status(thm)],[])).
% 5.38/3.68 tff(603,plain,
% 5.38/3.68 ((~![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1)))) | ((~plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(quant_inst,[status(thm)],[])).
% 5.38/3.68 tff(604,plain,
% 5.38/3.68 ((~![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1)))) | (~plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.38/3.68 inference(modus_ponens,[status(thm)],[603, 602])).
% 5.38/3.68 tff(605,plain,
% 5.38/3.68 (point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.38/3.68 inference(unit_resolution,[status(thm)],[604, 601, 455])).
% 5.38/3.68 tff(606,plain,
% 5.38/3.68 (((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(rewrite,[status(thm)],[])).
% 5.38/3.68 tff(607,plain,
% 5.38/3.68 ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(quant_inst,[status(thm)],[])).
% 5.38/3.68 tff(608,plain,
% 5.38/3.68 ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.68 inference(modus_ponens,[status(thm)],[607, 606])).
% 5.38/3.68 tff(609,plain,
% 5.38/3.68 (point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.68 inference(unit_resolution,[status(thm)],[608, 206, 104])).
% 5.38/3.68 tff(610,plain,
% 5.38/3.68 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.68 inference(rewrite,[status(thm)],[])).
% 5.38/3.68 tff(611,plain,
% 5.38/3.68 (((~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.68 inference(rewrite,[status(thm)],[])).
% 5.38/3.68 tff(612,plain,
% 5.38/3.68 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))),
% 5.38/3.68 inference(monotonicity,[status(thm)],[611])).
% 5.38/3.68 tff(613,plain,
% 5.38/3.68 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.68 inference(transitivity,[status(thm)],[612, 610])).
% 5.38/3.68 tff(614,plain,
% 5.38/3.68 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.68 inference(quant_inst,[status(thm)],[])).
% 5.38/3.68 tff(615,plain,
% 5.38/3.68 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(modus_ponens,[status(thm)],[614, 613])).
% 5.38/3.68 tff(616,plain,
% 5.38/3.68 (line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.68 inference(unit_resolution,[status(thm)],[615, 97, 609, 605, 594])).
% 5.38/3.68 tff(617,plain,
% 5.38/3.68 (((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.68 inference(rewrite,[status(thm)],[])).
% 5.38/3.68 tff(618,plain,
% 5.38/3.68 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.68 inference(quant_inst,[status(thm)],[])).
% 5.38/3.68 tff(619,plain,
% 5.38/3.68 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(modus_ponens,[status(thm)],[618, 617])).
% 5.38/3.69 tff(620,plain,
% 5.38/3.69 (on(a_point, line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(unit_resolution,[status(thm)],[619, 111, 616])).
% 5.38/3.69 tff(621,plain,
% 5.38/3.69 (on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(modus_ponens,[status(thm)],[620, 572])).
% 5.38/3.69 tff(622,plain,
% 5.38/3.69 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.69 inference(rewrite,[status(thm)],[])).
% 5.38/3.69 tff(623,plain,
% 5.38/3.69 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.69 inference(quant_inst,[status(thm)],[])).
% 5.38/3.69 tff(624,plain,
% 5.38/3.69 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(modus_ponens,[status(thm)],[623, 622])).
% 5.38/3.69 tff(625,plain,
% 5.38/3.69 (on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(unit_resolution,[status(thm)],[624, 125, 609, 605, 594])).
% 5.38/3.69 tff(626,plain,
% 5.38/3.69 ((point_1_on_line(at_least_one_line) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line))),
% 5.38/3.69 inference(commutativity,[status(thm)],[])).
% 5.38/3.69 tff(627,plain,
% 5.38/3.69 (on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.69 inference(monotonicity,[status(thm)],[567])).
% 5.38/3.69 tff(628,plain,
% 5.38/3.69 (on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.69 inference(symmetry,[status(thm)],[627])).
% 5.38/3.69 tff(629,plain,
% 5.38/3.69 (on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.69 inference(monotonicity,[status(thm)],[574])).
% 5.38/3.69 tff(630,plain,
% 5.38/3.69 (on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.69 inference(transitivity,[status(thm)],[629, 628])).
% 5.38/3.69 tff(631,plain,
% 5.38/3.69 ((~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (~on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.69 inference(monotonicity,[status(thm)],[630])).
% 5.38/3.69 tff(632,plain,
% 5.38/3.69 (~on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.69 inference(modus_ponens,[status(thm)],[591, 631])).
% 5.38/3.69 tff(633,plain,
% 5.38/3.69 (((~![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1)))) | ((~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))) <=> ((~![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1)))) | (~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))),
% 5.38/3.69 inference(rewrite,[status(thm)],[])).
% 5.38/3.69 tff(634,plain,
% 5.38/3.69 ((~![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1)))) | ((~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))),
% 5.38/3.69 inference(quant_inst,[status(thm)],[])).
% 5.38/3.69 tff(635,plain,
% 5.38/3.69 ((~![Z1: $i] : ((~plane(Z1)) | point(point_on_plane(Z1)))) | (~plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))) | point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.38/3.69 inference(modus_ponens,[status(thm)],[634, 633])).
% 5.38/3.69 tff(636,plain,
% 5.38/3.69 (point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.38/3.69 inference(unit_resolution,[status(thm)],[635, 601, 525])).
% 5.38/3.69 tff(637,assumption,(point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))), introduced(assumption)).
% 5.38/3.69 tff(638,assumption,(point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))), introduced(assumption)).
% 5.38/3.69 tff(639,assumption,(~(point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))), introduced(assumption)).
% 5.38/3.69 tff(640,assumption,(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), introduced(assumption)).
% 5.38/3.69 tff(641,assumption,(~on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))), introduced(assumption)).
% 5.38/3.69 tff(642,plain,
% 5.38/3.69 (on(a_point, line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(monotonicity,[status(thm)],[154])).
% 5.38/3.69 tff(643,plain,
% 5.38/3.69 (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.38/3.69 inference(monotonicity,[status(thm)],[640])).
% 5.38/3.69 tff(644,plain,
% 5.38/3.69 (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.38/3.69 inference(symmetry,[status(thm)],[643])).
% 5.38/3.69 tff(645,plain,
% 5.38/3.69 (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.69 inference(monotonicity,[status(thm)],[644])).
% 5.38/3.69 tff(646,plain,
% 5.38/3.69 (line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(monotonicity,[status(thm)],[645])).
% 5.38/3.69 tff(647,plain,
% 5.38/3.69 ((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.69 inference(monotonicity,[status(thm)],[644])).
% 5.38/3.69 tff(648,plain,
% 5.38/3.69 ((point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.69 inference(symmetry,[status(thm)],[647])).
% 5.38/3.69 tff(649,plain,
% 5.38/3.69 ((~(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> (~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(monotonicity,[status(thm)],[648])).
% 5.38/3.69 tff(650,assumption,(~(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))), introduced(assumption)).
% 5.38/3.69 tff(651,plain,
% 5.38/3.69 (~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.69 inference(modus_ponens,[status(thm)],[650, 649])).
% 5.38/3.69 tff(652,plain,
% 5.38/3.69 (((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | ((~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(rewrite,[status(thm)],[])).
% 5.38/3.69 tff(653,plain,
% 5.38/3.69 ((point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(rewrite,[status(thm)],[])).
% 5.38/3.69 tff(654,plain,
% 5.38/3.69 (((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | ((~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.69 inference(monotonicity,[status(thm)],[653])).
% 5.38/3.69 tff(655,plain,
% 5.38/3.69 (((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(transitivity,[status(thm)],[654, 652])).
% 5.38/3.69 tff(656,plain,
% 5.38/3.69 ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(quant_inst,[status(thm)],[])).
% 5.38/3.69 tff(657,plain,
% 5.38/3.69 ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.69 inference(modus_ponens,[status(thm)],[656, 655])).
% 5.38/3.69 tff(658,plain,
% 5.38/3.69 (point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.69 inference(unit_resolution,[status(thm)],[657, 48, 104])).
% 5.38/3.69 tff(659,plain,
% 5.38/3.69 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.69 inference(rewrite,[status(thm)],[])).
% 5.38/3.69 tff(660,plain,
% 5.38/3.69 (((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.69 inference(rewrite,[status(thm)],[])).
% 5.38/3.69 tff(661,plain,
% 5.38/3.69 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))),
% 5.38/3.69 inference(monotonicity,[status(thm)],[660])).
% 5.38/3.69 tff(662,plain,
% 5.38/3.69 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.69 inference(transitivity,[status(thm)],[661, 659])).
% 5.38/3.69 tff(663,plain,
% 5.38/3.69 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.69 inference(quant_inst,[status(thm)],[])).
% 5.38/3.69 tff(664,plain,
% 5.38/3.69 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(modus_ponens,[status(thm)],[663, 662])).
% 5.38/3.69 tff(665,plain,
% 5.38/3.69 ((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(unit_resolution,[status(thm)],[664, 97, 658, 638])).
% 5.38/3.69 tff(666,plain,
% 5.38/3.69 (line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(unit_resolution,[status(thm)],[665, 651])).
% 5.38/3.69 tff(667,plain,
% 5.38/3.69 (line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(modus_ponens,[status(thm)],[666, 646])).
% 5.38/3.69 tff(668,plain,
% 5.38/3.69 (((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.69 inference(rewrite,[status(thm)],[])).
% 5.38/3.69 tff(669,plain,
% 5.38/3.69 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.69 inference(quant_inst,[status(thm)],[])).
% 5.38/3.69 tff(670,plain,
% 5.38/3.69 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(modus_ponens,[status(thm)],[669, 668])).
% 5.38/3.69 tff(671,plain,
% 5.38/3.69 (on(a_point, line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(unit_resolution,[status(thm)],[670, 111, 667])).
% 5.38/3.69 tff(672,plain,
% 5.38/3.69 (on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(modus_ponens,[status(thm)],[671, 642])).
% 5.38/3.69 tff(673,plain,
% 5.38/3.69 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) | (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | (~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) | (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.69 inference(rewrite,[status(thm)],[])).
% 5.38/3.69 tff(674,plain,
% 5.38/3.69 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) | (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.69 inference(quant_inst,[status(thm)],[])).
% 5.38/3.69 tff(675,plain,
% 5.38/3.69 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | (~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) | (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(modus_ponens,[status(thm)],[674, 673])).
% 5.38/3.69 tff(676,plain,
% 5.38/3.69 ((~point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) | (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(unit_resolution,[status(thm)],[675, 125, 658])).
% 5.38/3.69 tff(677,plain,
% 5.38/3.69 (on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(unit_resolution,[status(thm)],[676, 650, 637])).
% 5.38/3.69 tff(678,plain,
% 5.38/3.69 (((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | ((~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.69 inference(rewrite,[status(thm)],[])).
% 5.38/3.69 tff(679,plain,
% 5.38/3.69 ((on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.69 inference(rewrite,[status(thm)],[])).
% 5.38/3.69 tff(680,plain,
% 5.38/3.69 (((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | ((~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(monotonicity,[status(thm)],[679])).
% 5.38/3.69 tff(681,plain,
% 5.38/3.69 (((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.69 inference(transitivity,[status(thm)],[680, 678])).
% 5.38/3.69 tff(682,plain,
% 5.38/3.69 ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.69 inference(quant_inst,[status(thm)],[])).
% 5.38/3.69 tff(683,plain,
% 5.38/3.69 ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.69 inference(modus_ponens,[status(thm)],[682, 681])).
% 5.38/3.69 tff(684,plain,
% 5.38/3.69 (on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.69 inference(unit_resolution,[status(thm)],[683, 17, 104])).
% 5.38/3.69 tff(685,plain,
% 5.38/3.69 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.69 inference(rewrite,[status(thm)],[])).
% 5.38/3.69 tff(686,plain,
% 5.38/3.69 (((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.69 inference(rewrite,[status(thm)],[])).
% 5.38/3.69 tff(687,plain,
% 5.38/3.69 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))),
% 5.38/3.70 inference(monotonicity,[status(thm)],[686])).
% 5.38/3.70 tff(688,plain,
% 5.38/3.70 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.70 inference(transitivity,[status(thm)],[687, 685])).
% 5.38/3.70 tff(689,plain,
% 5.38/3.70 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.70 inference(quant_inst,[status(thm)],[])).
% 5.38/3.70 tff(690,plain,
% 5.38/3.70 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.70 inference(modus_ponens,[status(thm)],[689, 688])).
% 5.38/3.70 tff(691,plain,
% 5.38/3.70 (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.70 inference(unit_resolution,[status(thm)],[690, 146, 55, 104, 129, 658, 684, 677, 639, 667, 672])).
% 5.38/3.70 tff(692,plain,
% 5.38/3.70 (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))),
% 5.38/3.70 inference(symmetry,[status(thm)],[691])).
% 5.38/3.70 tff(693,plain,
% 5.38/3.70 (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))),
% 5.38/3.70 inference(transitivity,[status(thm)],[645, 692])).
% 5.38/3.70 tff(694,plain,
% 5.38/3.70 (on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.70 inference(monotonicity,[status(thm)],[644, 693])).
% 5.38/3.70 tff(695,plain,
% 5.38/3.70 (on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.70 inference(symmetry,[status(thm)],[694])).
% 5.38/3.70 tff(696,plain,
% 5.38/3.70 ((~on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.70 inference(monotonicity,[status(thm)],[695])).
% 5.38/3.70 tff(697,plain,
% 5.38/3.70 (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.70 inference(modus_ponens,[status(thm)],[641, 696])).
% 5.38/3.70 tff(698,plain,
% 5.38/3.70 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.70 inference(rewrite,[status(thm)],[])).
% 5.38/3.70 tff(699,plain,
% 5.38/3.70 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.70 inference(quant_inst,[status(thm)],[])).
% 5.38/3.70 tff(700,plain,
% 5.38/3.70 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (~point(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.70 inference(modus_ponens,[status(thm)],[699, 698])).
% 5.38/3.70 tff(701,plain,
% 5.38/3.70 ((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.70 inference(unit_resolution,[status(thm)],[700, 79, 658, 638])).
% 5.38/3.70 tff(702,plain,
% 5.38/3.70 (on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.70 inference(unit_resolution,[status(thm)],[701, 651])).
% 5.38/3.70 tff(703,plain,
% 5.38/3.70 ($false),
% 5.38/3.70 inference(unit_resolution,[status(thm)],[702, 697])).
% 5.38/3.70 tff(704,plain,((point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))), inference(lemma,lemma(discharge,[]))).
% 5.38/3.70 tff(705,plain,
% 5.38/3.70 (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.70 inference(unit_resolution,[status(thm)],[704, 641, 640, 639, 638, 637])).
% 5.38/3.70 tff(706,plain,
% 5.38/3.70 (on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.70 inference(monotonicity,[status(thm)],[705])).
% 5.38/3.70 tff(707,plain,
% 5.38/3.70 (on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.70 inference(symmetry,[status(thm)],[706])).
% 5.38/3.70 tff(708,plain,
% 5.38/3.70 (on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.70 inference(modus_ponens,[status(thm)],[684, 707])).
% 5.38/3.70 tff(709,plain,
% 5.38/3.70 ($false),
% 5.38/3.70 inference(unit_resolution,[status(thm)],[641, 708])).
% 5.38/3.70 tff(710,plain,(on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))))), inference(lemma,lemma(discharge,[]))).
% 5.38/3.70 tff(711,plain,
% 5.38/3.70 (on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point) = plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.70 inference(unit_resolution,[status(thm)],[710, 636, 605])).
% 5.38/3.70 tff(712,plain,
% 5.38/3.70 (on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.70 inference(unit_resolution,[status(thm)],[711, 566])).
% 5.38/3.70 tff(713,plain,
% 5.38/3.70 (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.70 inference(unit_resolution,[status(thm)],[712, 632])).
% 5.38/3.70 tff(714,plain,
% 5.38/3.70 (point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)),
% 5.38/3.70 inference(symmetry,[status(thm)],[713])).
% 5.38/3.70 tff(715,plain,
% 5.38/3.70 ((point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (point_1_on_line(at_least_one_line) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.70 inference(monotonicity,[status(thm)],[714])).
% 5.38/3.70 tff(716,plain,
% 5.38/3.70 ((point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line))),
% 5.38/3.70 inference(transitivity,[status(thm)],[715, 626])).
% 5.38/3.70 tff(717,plain,
% 5.38/3.70 ((~(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> (~(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)))),
% 5.38/3.70 inference(monotonicity,[status(thm)],[716])).
% 5.38/3.70 tff(718,plain,
% 5.38/3.70 (((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | ((~(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | (~(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.70 inference(rewrite,[status(thm)],[])).
% 5.38/3.70 tff(719,plain,
% 5.38/3.70 ((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | ((~(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.70 inference(quant_inst,[status(thm)],[])).
% 5.38/3.70 tff(720,plain,
% 5.38/3.70 ((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | (~(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.70 inference(modus_ponens,[status(thm)],[719, 718])).
% 5.38/3.70 tff(721,plain,
% 5.38/3.70 (~(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.70 inference(unit_resolution,[status(thm)],[720, 170, 104])).
% 5.38/3.70 tff(722,plain,
% 5.38/3.70 (~(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line))),
% 5.38/3.70 inference(modus_ponens,[status(thm)],[721, 717])).
% 5.38/3.70 tff(723,plain,
% 5.38/3.70 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.70 inference(rewrite,[status(thm)],[])).
% 5.38/3.70 tff(724,plain,
% 5.38/3.70 (((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.70 inference(rewrite,[status(thm)],[])).
% 5.38/3.70 tff(725,plain,
% 5.38/3.70 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.70 inference(monotonicity,[status(thm)],[724])).
% 5.38/3.70 tff(726,plain,
% 5.38/3.70 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.70 inference(transitivity,[status(thm)],[725, 723])).
% 5.38/3.70 tff(727,plain,
% 5.38/3.70 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))),
% 5.38/3.71 inference(quant_inst,[status(thm)],[])).
% 5.38/3.71 tff(728,plain,
% 5.38/3.71 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[727, 726])).
% 5.38/3.71 tff(729,plain,
% 5.38/3.71 (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))),
% 5.38/3.71 inference(unit_resolution,[status(thm)],[728, 146, 55, 104, 129, 609, 583, 722, 616, 625, 621])).
% 5.38/3.71 tff(730,plain,
% 5.38/3.71 (on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.71 inference(monotonicity,[status(thm)],[729])).
% 5.38/3.71 tff(731,plain,
% 5.38/3.71 (on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(symmetry,[status(thm)],[730])).
% 5.38/3.71 tff(732,plain,
% 5.38/3.71 ((~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.71 inference(monotonicity,[status(thm)],[731])).
% 5.38/3.71 tff(733,plain,
% 5.38/3.71 ((~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.71 inference(monotonicity,[status(thm)],[629])).
% 5.38/3.71 tff(734,plain,
% 5.38/3.71 (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[591, 733])).
% 5.38/3.71 tff(735,plain,
% 5.38/3.71 (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[734, 732])).
% 5.38/3.71 tff(736,plain,
% 5.38/3.71 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.71 inference(rewrite,[status(thm)],[])).
% 5.38/3.71 tff(737,plain,
% 5.38/3.71 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.71 inference(quant_inst,[status(thm)],[])).
% 5.38/3.71 tff(738,plain,
% 5.38/3.71 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (~point(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[737, 736])).
% 5.38/3.71 tff(739,plain,
% 5.38/3.71 ((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(unit_resolution,[status(thm)],[738, 79, 609, 605])).
% 5.38/3.71 tff(740,plain,
% 5.38/3.71 (on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(unit_resolution,[status(thm)],[739, 594])).
% 5.38/3.71 tff(741,plain,
% 5.38/3.71 ($false),
% 5.38/3.71 inference(unit_resolution,[status(thm)],[740, 735])).
% 5.38/3.71 tff(742,plain,(~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))), inference(lemma,lemma(discharge,[]))).
% 5.38/3.71 tff(743,plain,
% 5.38/3.71 (((~![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))) | (point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))) | point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(rewrite,[status(thm)],[])).
% 5.38/3.71 tff(744,plain,
% 5.38/3.71 ((~![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))) | (point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(quant_inst,[status(thm)],[])).
% 5.38/3.71 tff(745,plain,
% 5.38/3.71 ((~![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))) | point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[744, 743])).
% 5.38/3.71 tff(746,plain,
% 5.38/3.71 (point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.71 inference(unit_resolution,[status(thm)],[745, 62, 104])).
% 5.38/3.71 tff(747,plain,
% 5.38/3.71 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (~point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.71 inference(rewrite,[status(thm)],[])).
% 5.38/3.71 tff(748,plain,
% 5.38/3.71 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.71 inference(quant_inst,[status(thm)],[])).
% 5.38/3.71 tff(749,plain,
% 5.38/3.71 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (~point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[748, 747])).
% 5.38/3.71 tff(750,plain,
% 5.38/3.71 (line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(unit_resolution,[status(thm)],[749, 97, 746, 605, 742])).
% 5.38/3.71 tff(751,plain,
% 5.38/3.71 (line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[750, 570])).
% 5.38/3.71 tff(752,plain,
% 5.38/3.71 (on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(monotonicity,[status(thm)],[568])).
% 5.38/3.71 tff(753,plain,
% 5.38/3.71 (on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(symmetry,[status(thm)],[752])).
% 5.38/3.71 tff(754,plain,
% 5.38/3.71 ((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.71 inference(monotonicity,[status(thm)],[568])).
% 5.38/3.71 tff(755,plain,
% 5.38/3.71 ((~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> (~(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(monotonicity,[status(thm)],[754])).
% 5.38/3.71 tff(756,plain,
% 5.38/3.71 (~(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[742, 755])).
% 5.38/3.71 tff(757,plain,
% 5.38/3.71 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) | (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (~point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) | (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.71 inference(rewrite,[status(thm)],[])).
% 5.38/3.71 tff(758,plain,
% 5.38/3.71 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) | (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.71 inference(quant_inst,[status(thm)],[])).
% 5.38/3.71 tff(759,plain,
% 5.38/3.71 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (~point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) | (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[758, 757])).
% 5.38/3.71 tff(760,plain,
% 5.38/3.71 ((~point(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))) | (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(unit_resolution,[status(thm)],[759, 79, 746])).
% 5.38/3.71 tff(761,plain,
% 5.38/3.71 ((point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(unit_resolution,[status(thm)],[760, 636])).
% 5.38/3.71 tff(762,plain,
% 5.38/3.71 (on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(unit_resolution,[status(thm)],[761, 756])).
% 5.38/3.71 tff(763,plain,
% 5.38/3.71 (on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[762, 753])).
% 5.38/3.71 tff(764,plain,
% 5.38/3.71 (on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(monotonicity,[status(thm)],[569])).
% 5.38/3.71 tff(765,plain,
% 5.38/3.71 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | ((~point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | (~point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.71 inference(rewrite,[status(thm)],[])).
% 5.38/3.71 tff(766,plain,
% 5.38/3.71 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | ((~point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.71 inference(quant_inst,[status(thm)],[])).
% 5.38/3.71 tff(767,plain,
% 5.38/3.71 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | (~point(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[766, 765])).
% 5.38/3.71 tff(768,plain,
% 5.38/3.71 (on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(unit_resolution,[status(thm)],[767, 125, 746, 605, 742])).
% 5.38/3.71 tff(769,plain,
% 5.38/3.71 (on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[768, 764])).
% 5.38/3.71 tff(770,assumption,(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), introduced(assumption)).
% 5.38/3.71 tff(771,plain,
% 5.38/3.71 (on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.71 inference(monotonicity,[status(thm)],[770])).
% 5.38/3.71 tff(772,plain,
% 5.38/3.71 (on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(symmetry,[status(thm)],[771])).
% 5.38/3.71 tff(773,plain,
% 5.38/3.71 ((~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.71 inference(monotonicity,[status(thm)],[772])).
% 5.38/3.71 tff(774,plain,
% 5.38/3.71 (~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[591, 773])).
% 5.38/3.71 tff(775,assumption,(on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))), introduced(assumption)).
% 5.38/3.71 tff(776,plain,
% 5.38/3.71 ($false),
% 5.38/3.71 inference(unit_resolution,[status(thm)],[775, 774])).
% 5.38/3.71 tff(777,plain,((~(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))), inference(lemma,lemma(discharge,[]))).
% 5.38/3.71 tff(778,plain,
% 5.38/3.71 (~(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.71 inference(unit_resolution,[status(thm)],[777, 769])).
% 5.38/3.71 tff(779,plain,
% 5.38/3.71 ((~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (~on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.38/3.71 inference(monotonicity,[status(thm)],[628])).
% 5.38/3.71 tff(780,assumption,(on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))), introduced(assumption)).
% 5.38/3.71 tff(781,plain,
% 5.38/3.71 ((line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.38/3.71 inference(commutativity,[status(thm)],[])).
% 5.38/3.71 tff(782,plain,
% 5.38/3.71 ((line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(symmetry,[status(thm)],[781])).
% 5.38/3.71 tff(783,plain,
% 5.38/3.71 ((~(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (~(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.71 inference(monotonicity,[status(thm)],[782])).
% 5.38/3.71 tff(784,assumption,(~(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))), introduced(assumption)).
% 5.38/3.71 tff(785,plain,
% 5.38/3.71 (~(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[784, 783])).
% 5.38/3.71 tff(786,assumption,(~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line))), introduced(assumption)).
% 5.38/3.71 tff(787,assumption,(line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))), introduced(assumption)).
% 5.38/3.71 tff(788,plain,
% 5.38/3.71 (on(a_point, line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(monotonicity,[status(thm)],[154])).
% 5.38/3.71 tff(789,plain,
% 5.38/3.71 (((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.71 inference(rewrite,[status(thm)],[])).
% 5.38/3.71 tff(790,plain,
% 5.38/3.71 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.38/3.71 inference(quant_inst,[status(thm)],[])).
% 5.38/3.71 tff(791,plain,
% 5.38/3.71 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[790, 789])).
% 5.38/3.71 tff(792,plain,
% 5.38/3.71 (on(a_point, line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(unit_resolution,[status(thm)],[791, 111, 787])).
% 5.38/3.71 tff(793,plain,
% 5.38/3.71 (on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(modus_ponens,[status(thm)],[792, 788])).
% 5.38/3.71 tff(794,plain,
% 5.38/3.71 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.71 inference(rewrite,[status(thm)],[])).
% 5.38/3.71 tff(795,plain,
% 5.38/3.71 (((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.38/3.72 inference(rewrite,[status(thm)],[])).
% 5.38/3.72 tff(796,plain,
% 5.38/3.72 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.43/3.72 inference(monotonicity,[status(thm)],[795])).
% 5.43/3.72 tff(797,plain,
% 5.43/3.72 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.72 inference(transitivity,[status(thm)],[796, 794])).
% 5.43/3.72 tff(798,plain,
% 5.43/3.72 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.72 inference(quant_inst,[status(thm)],[])).
% 5.43/3.72 tff(799,plain,
% 5.43/3.72 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.72 inference(modus_ponens,[status(thm)],[798, 797])).
% 5.43/3.72 tff(800,plain,
% 5.43/3.72 ((~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.72 inference(unit_resolution,[status(thm)],[799, 146, 55, 104, 129, 605, 793, 787])).
% 5.43/3.72 tff(801,plain,
% 5.43/3.72 (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.43/3.72 inference(unit_resolution,[status(thm)],[800, 786, 785, 780])).
% 5.43/3.72 tff(802,plain,
% 5.43/3.72 (~on(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.43/3.72 inference(modus_ponens,[status(thm)],[801, 779])).
% 5.43/3.72 tff(803,plain,
% 5.43/3.72 (point_1_on_line(at_least_one_line) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.43/3.72 inference(unit_resolution,[status(thm)],[712, 802])).
% 5.43/3.72 tff(804,plain,
% 5.43/3.72 (point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)),
% 5.43/3.72 inference(symmetry,[status(thm)],[803])).
% 5.43/3.72 tff(805,plain,
% 5.43/3.72 ((point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (point_1_on_line(at_least_one_line) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.72 inference(monotonicity,[status(thm)],[804])).
% 5.43/3.72 tff(806,plain,
% 5.43/3.72 ((point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line))),
% 5.43/3.72 inference(transitivity,[status(thm)],[805, 626])).
% 5.43/3.72 tff(807,plain,
% 5.43/3.72 ((~(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> (~(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)))),
% 5.43/3.72 inference(monotonicity,[status(thm)],[806])).
% 5.43/3.72 tff(808,plain,
% 5.43/3.72 (~(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line))),
% 5.43/3.72 inference(modus_ponens,[status(thm)],[721, 807])).
% 5.43/3.72 tff(809,plain,
% 5.43/3.72 (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.72 inference(monotonicity,[status(thm)],[568, 803])).
% 5.43/3.72 tff(810,plain,
% 5.43/3.72 (on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(at_least_one_line))) <=> on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.72 inference(monotonicity,[status(thm)],[809])).
% 5.43/3.72 tff(811,plain,
% 5.43/3.72 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(at_least_one_line))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(at_least_one_line))))),
% 5.43/3.72 inference(rewrite,[status(thm)],[])).
% 5.43/3.72 tff(812,plain,
% 5.43/3.72 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(at_least_one_line))))),
% 5.43/3.72 inference(quant_inst,[status(thm)],[])).
% 5.43/3.72 tff(813,plain,
% 5.43/3.72 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(at_least_one_line)))),
% 5.43/3.72 inference(modus_ponens,[status(thm)],[812, 811])).
% 5.43/3.72 tff(814,plain,
% 5.43/3.72 (on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(at_least_one_line)))),
% 5.43/3.72 inference(unit_resolution,[status(thm)],[813, 79, 55, 605, 786])).
% 5.43/3.72 tff(815,plain,
% 5.43/3.72 (on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.72 inference(modus_ponens,[status(thm)],[814, 810])).
% 5.43/3.72 tff(816,plain,
% 5.43/3.72 (line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(at_least_one_line))) <=> line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.72 inference(monotonicity,[status(thm)],[809])).
% 5.43/3.72 tff(817,plain,
% 5.43/3.72 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(at_least_one_line))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(at_least_one_line))))),
% 5.43/3.72 inference(rewrite,[status(thm)],[])).
% 5.43/3.72 tff(818,plain,
% 5.43/3.72 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_1_on_line(at_least_one_line))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(at_least_one_line))))),
% 5.43/3.72 inference(quant_inst,[status(thm)],[])).
% 5.43/3.72 tff(819,plain,
% 5.43/3.72 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (~point(point_1_on_line(at_least_one_line))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(at_least_one_line)))),
% 5.43/3.72 inference(modus_ponens,[status(thm)],[818, 817])).
% 5.43/3.72 tff(820,plain,
% 5.43/3.72 (line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_1_on_line(at_least_one_line)))),
% 5.43/3.72 inference(unit_resolution,[status(thm)],[819, 97, 55, 605, 786])).
% 5.43/3.72 tff(821,plain,
% 5.43/3.72 (line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.72 inference(modus_ponens,[status(thm)],[820, 816])).
% 5.43/3.72 tff(822,plain,
% 5.43/3.72 (on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.72 inference(monotonicity,[status(thm)],[803])).
% 5.43/3.72 tff(823,plain,
% 5.43/3.72 (on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.72 inference(symmetry,[status(thm)],[822])).
% 5.43/3.72 tff(824,plain,
% 5.43/3.72 ((point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line))),
% 5.43/3.72 inference(monotonicity,[status(thm)],[567, 804])).
% 5.43/3.72 tff(825,plain,
% 5.43/3.72 ((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) <=> (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.72 inference(symmetry,[status(thm)],[824])).
% 5.43/3.72 tff(826,plain,
% 5.43/3.72 ((~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line))) <=> (~(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.72 inference(monotonicity,[status(thm)],[825])).
% 5.43/3.72 tff(827,plain,
% 5.43/3.72 (~(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.72 inference(modus_ponens,[status(thm)],[786, 826])).
% 5.43/3.72 tff(828,plain,
% 5.43/3.72 ((point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.72 inference(unit_resolution,[status(thm)],[676, 636])).
% 5.43/3.72 tff(829,plain,
% 5.43/3.72 (on(point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.72 inference(unit_resolution,[status(thm)],[828, 827])).
% 5.43/3.72 tff(830,plain,
% 5.43/3.72 (on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.72 inference(modus_ponens,[status(thm)],[829, 823])).
% 5.43/3.72 tff(831,plain,
% 5.43/3.72 ((line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.72 inference(commutativity,[status(thm)],[])).
% 5.43/3.72 tff(832,plain,
% 5.43/3.72 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))),
% 5.43/3.72 inference(rewrite,[status(thm)],[])).
% 5.43/3.72 tff(833,plain,
% 5.43/3.72 (((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~point(point_1_on_line(at_least_one_line))) | (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))),
% 5.43/3.72 inference(rewrite,[status(thm)],[])).
% 5.43/3.72 tff(834,plain,
% 5.43/3.72 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))))),
% 5.43/3.73 inference(monotonicity,[status(thm)],[833])).
% 5.43/3.73 tff(835,plain,
% 5.43/3.73 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))),
% 5.43/3.73 inference(transitivity,[status(thm)],[834, 832])).
% 5.43/3.73 tff(836,plain,
% 5.43/3.73 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))),
% 5.43/3.73 inference(quant_inst,[status(thm)],[])).
% 5.43/3.73 tff(837,plain,
% 5.43/3.73 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.43/3.73 inference(modus_ponens,[status(thm)],[836, 835])).
% 5.43/3.73 tff(838,plain,
% 5.43/3.73 (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.73 inference(unit_resolution,[status(thm)],[837, 146, 55, 605, 786, 793, 787, 780, 830, 821, 815])).
% 5.43/3.73 tff(839,plain,
% 5.43/3.73 ((line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.43/3.73 inference(monotonicity,[status(thm)],[838])).
% 5.43/3.73 tff(840,plain,
% 5.43/3.73 ((line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.73 inference(transitivity,[status(thm)],[839, 831])).
% 5.43/3.73 tff(841,plain,
% 5.43/3.73 ((~(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (~(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.43/3.73 inference(monotonicity,[status(thm)],[840])).
% 5.43/3.73 tff(842,plain,
% 5.43/3.73 (~(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.73 inference(modus_ponens,[status(thm)],[784, 841])).
% 5.43/3.73 tff(843,plain,
% 5.43/3.73 (on(a_point, line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.73 inference(monotonicity,[status(thm)],[154])).
% 5.43/3.73 tff(844,assumption,(~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))), introduced(assumption)).
% 5.43/3.73 tff(845,plain,
% 5.43/3.73 (line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.73 inference(unit_resolution,[status(thm)],[615, 97, 609, 605, 844])).
% 5.43/3.73 tff(846,plain,
% 5.43/3.73 (on(a_point, line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.73 inference(unit_resolution,[status(thm)],[619, 111, 845])).
% 5.43/3.73 tff(847,plain,
% 5.43/3.73 (on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.73 inference(modus_ponens,[status(thm)],[846, 843])).
% 5.43/3.73 tff(848,assumption,(on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))), introduced(assumption)).
% 5.43/3.73 tff(849,assumption,(line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))), introduced(assumption)).
% 5.43/3.73 tff(850,assumption,(on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))), introduced(assumption)).
% 5.43/3.73 tff(851,plain,
% 5.43/3.73 (on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.73 inference(unit_resolution,[status(thm)],[739, 844])).
% 5.43/3.73 tff(852,plain,
% 5.43/3.73 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))),
% 5.43/3.73 inference(rewrite,[status(thm)],[])).
% 5.43/3.73 tff(853,plain,
% 5.43/3.73 (((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))) <=> ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))),
% 5.43/3.73 inference(rewrite,[status(thm)],[])).
% 5.43/3.73 tff(854,plain,
% 5.43/3.73 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))))),
% 5.43/3.73 inference(monotonicity,[status(thm)],[853])).
% 5.43/3.73 tff(855,plain,
% 5.43/3.73 (((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))) <=> ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))),
% 5.43/3.73 inference(transitivity,[status(thm)],[854, 852])).
% 5.43/3.73 tff(856,plain,
% 5.43/3.73 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))))),
% 5.43/3.73 inference(quant_inst,[status(thm)],[])).
% 5.43/3.73 tff(857,plain,
% 5.43/3.73 ((~![Y4: $i, Z1: $i, Y3: $i, Z2: $i] : ((~point(Z2)) | (~line(Y4)) | (~line(Y3)) | (~point(Z1)) | (~on(Z2, Y4)) | (~on(Z1, Y4)) | (Y3 = Y4) | (~on(Z2, Y3)) | (Z1 = Z2) | (~on(Z1, Y3)))) | (~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (~line(line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.43/3.74 inference(modus_ponens,[status(thm)],[856, 855])).
% 5.43/3.74 tff(858,plain,
% 5.43/3.74 (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.74 inference(unit_resolution,[status(thm)],[857, 146, 55, 605, 786, 851, 850, 849, 848, 845, 847])).
% 5.43/3.74 tff(859,plain,
% 5.43/3.74 (on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.74 inference(unit_resolution,[status(thm)],[624, 125, 609, 605, 844])).
% 5.43/3.74 tff(860,assumption,(~(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line))), introduced(assumption)).
% 5.43/3.74 tff(861,plain,
% 5.43/3.74 (line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))),
% 5.43/3.74 inference(unit_resolution,[status(thm)],[728, 146, 55, 104, 129, 609, 583, 860, 845, 847, 859])).
% 5.43/3.74 tff(862,plain,
% 5.43/3.74 (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.74 inference(symmetry,[status(thm)],[861])).
% 5.43/3.74 tff(863,plain,
% 5.43/3.74 (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.74 inference(transitivity,[status(thm)],[862, 858])).
% 5.43/3.74 tff(864,assumption,(~(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))), introduced(assumption)).
% 5.43/3.74 tff(865,plain,
% 5.43/3.74 ($false),
% 5.43/3.74 inference(unit_resolution,[status(thm)],[864, 863])).
% 5.43/3.74 tff(866,plain,((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) = line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) | (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_1_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line))), inference(lemma,lemma(discharge,[]))).
% 5.43/3.74 tff(867,plain,
% 5.43/3.74 (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.43/3.74 inference(unit_resolution,[status(thm)],[866, 842, 786, 830, 821, 815, 808])).
% 5.43/3.74 tff(868,plain,
% 5.43/3.74 (point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.43/3.74 inference(symmetry,[status(thm)],[867])).
% 5.43/3.74 tff(869,plain,
% 5.43/3.74 (on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.43/3.74 inference(monotonicity,[status(thm)],[868])).
% 5.43/3.74 tff(870,plain,
% 5.43/3.74 (on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.43/3.74 inference(symmetry,[status(thm)],[869])).
% 5.43/3.74 tff(871,plain,
% 5.43/3.74 ((~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.74 inference(monotonicity,[status(thm)],[870])).
% 5.43/3.74 tff(872,plain,
% 5.43/3.74 (~on(point_2_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.43/3.74 inference(modus_ponens,[status(thm)],[801, 871])).
% 5.43/3.74 tff(873,plain,
% 5.43/3.74 ($false),
% 5.43/3.74 inference(unit_resolution,[status(thm)],[583, 872])).
% 5.43/3.74 tff(874,plain,((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) | (line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) = line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)), point_not_on_line(line_from_to(point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))), inference(lemma,lemma(discharge,[]))).
% 5.43/3.74 tff(875,plain,
% 5.43/3.74 (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)),
% 5.43/3.74 inference(unit_resolution,[status(thm)],[874, 778, 763, 751])).
% 5.43/3.74 tff(876,plain,
% 5.43/3.74 ((point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(at_least_one_line)) <=> (point_1_on_line(at_least_one_line) = point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.43/3.74 inference(commutativity,[status(thm)],[])).
% 5.43/3.74 tff(877,plain,
% 5.43/3.74 ((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) <=> (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(at_least_one_line))),
% 5.43/3.74 inference(monotonicity,[status(thm)],[568])).
% 5.43/3.74 tff(878,plain,
% 5.43/3.74 ((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)) <=> (point_1_on_line(at_least_one_line) = point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))),
% 5.43/3.74 inference(transitivity,[status(thm)],[877, 876])).
% 5.43/3.74 tff(879,assumption,(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)), introduced(assumption)).
% 5.43/3.74 tff(880,plain,
% 5.43/3.74 (point_1_on_line(at_least_one_line) = point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.43/3.74 inference(modus_ponens,[status(thm)],[879, 878])).
% 5.43/3.74 tff(881,assumption,(~(point_1_on_line(at_least_one_line) = point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))), introduced(assumption)).
% 5.43/3.74 tff(882,plain,
% 5.43/3.74 ($false),
% 5.43/3.74 inference(unit_resolution,[status(thm)],[881, 880])).
% 5.43/3.74 tff(883,plain,((~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line))) | (point_1_on_line(at_least_one_line) = point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)))), inference(lemma,lemma(discharge,[]))).
% 5.43/3.74 tff(884,plain,
% 5.43/3.74 (point_1_on_line(at_least_one_line) = point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point))),
% 5.43/3.74 inference(unit_resolution,[status(thm)],[883, 875])).
% 5.43/3.74 tff(885,plain,
% 5.43/3.74 (a_point = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 5.43/3.74 inference(transitivity,[status(thm)],[154, 884, 567])).
% 5.43/3.74 tff(886,plain,
% 5.43/3.74 (on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))) <=> on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))),
% 5.43/3.74 inference(monotonicity,[status(thm)],[885])).
% 5.43/3.74 tff(887,plain,
% 5.43/3.74 (on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))) <=> on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))),
% 5.43/3.74 inference(symmetry,[status(thm)],[886])).
% 5.43/3.74 tff(888,plain,
% 5.43/3.74 ((~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) <=> (~on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 5.43/3.74 inference(monotonicity,[status(thm)],[887])).
% 5.43/3.74 tff(889,plain,
% 5.43/3.74 ((point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) <=> (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))),
% 5.43/3.74 inference(commutativity,[status(thm)],[])).
% 5.43/3.74 tff(890,plain,
% 5.43/3.74 ((~(point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line))) <=> (~(point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)))),
% 5.43/3.74 inference(monotonicity,[status(thm)],[889])).
% 5.43/3.74 tff(891,plain,
% 5.43/3.74 (~(point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))),
% 5.43/3.74 inference(modus_ponens,[status(thm)],[199, 890])).
% 5.43/3.74 tff(892,plain,
% 5.43/3.74 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 5.43/3.74 inference(rewrite,[status(thm)],[])).
% 5.43/3.74 tff(893,plain,
% 5.43/3.74 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 5.43/3.74 inference(quant_inst,[status(thm)],[])).
% 5.43/3.74 tff(894,plain,
% 5.43/3.74 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))),
% 5.43/3.74 inference(modus_ponens,[status(thm)],[893, 892])).
% 5.43/3.74 tff(895,plain,
% 5.43/3.74 (on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))),
% 5.43/3.74 inference(unit_resolution,[status(thm)],[894, 125, 69, 213, 891])).
% 5.43/3.74 tff(896,plain,
% 5.43/3.74 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 5.43/3.74 inference(rewrite,[status(thm)],[])).
% 5.43/3.74 tff(897,plain,
% 5.43/3.74 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) <=> ((point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 5.43/3.74 inference(rewrite,[status(thm)],[])).
% 5.43/3.74 tff(898,plain,
% 5.43/3.74 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))))),
% 5.43/3.74 inference(monotonicity,[status(thm)],[897])).
% 5.43/3.74 tff(899,plain,
% 5.43/3.74 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 5.43/3.74 inference(transitivity,[status(thm)],[898, 896])).
% 5.43/3.74 tff(900,plain,
% 5.43/3.74 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 5.43/3.74 inference(quant_inst,[status(thm)],[])).
% 5.43/3.74 tff(901,plain,
% 5.43/3.74 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))),
% 5.43/3.74 inference(modus_ponens,[status(thm)],[900, 899])).
% 5.43/3.74 tff(902,plain,
% 5.43/3.74 (line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))),
% 5.43/3.74 inference(unit_resolution,[status(thm)],[901, 97, 69, 213, 891])).
% 5.43/3.74 tff(903,plain,
% 5.43/3.74 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 5.43/3.74 inference(rewrite,[status(thm)],[])).
% 5.43/3.74 tff(904,plain,
% 5.43/3.74 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 5.43/3.74 inference(quant_inst,[status(thm)],[])).
% 5.43/3.74 tff(905,plain,
% 5.43/3.74 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))),
% 5.43/3.74 inference(modus_ponens,[status(thm)],[904, 903])).
% 5.43/3.74 tff(906,plain,
% 5.43/3.74 (on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))),
% 5.43/3.74 inference(unit_resolution,[status(thm)],[905, 79, 69, 213, 891])).
% 5.43/3.74 tff(907,plain,
% 5.43/3.74 (point_on_plane(plane_for_points(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), a_point)) = point_1_on_line(at_least_one_line)),
% 5.43/3.74 inference(symmetry,[status(thm)],[884])).
% 5.43/3.74 tff(908,plain,
% 5.43/3.74 (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = a_point),
% 5.43/3.74 inference(transitivity,[status(thm)],[568, 907, 155])).
% 5.43/3.74 tff(909,plain,
% 5.43/3.74 (collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), a_point)),
% 5.43/3.74 inference(monotonicity,[status(thm)],[908])).
% 5.43/3.74 tff(910,plain,
% 5.43/3.74 (collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), a_point) <=> collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.43/3.74 inference(symmetry,[status(thm)],[909])).
% 5.43/3.74 tff(911,plain,
% 5.43/3.74 ((~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), a_point)) <=> (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.43/3.74 inference(monotonicity,[status(thm)],[910])).
% 5.43/3.74 tff(912,plain,
% 5.43/3.74 (collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) <=> collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), a_point)),
% 5.43/3.74 inference(monotonicity,[status(thm)],[155])).
% 5.43/3.74 tff(913,plain,
% 5.43/3.74 ((~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) <=> (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), a_point))),
% 5.43/3.74 inference(monotonicity,[status(thm)],[912])).
% 5.43/3.74 tff(914,assumption,(collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), introduced(assumption)).
% 5.43/3.74 tff(915,plain,
% 5.43/3.74 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.74 inference(rewrite,[status(thm)],[])).
% 5.43/3.74 tff(916,plain,
% 5.43/3.74 (((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.74 inference(rewrite,[status(thm)],[])).
% 5.43/3.74 tff(917,plain,
% 5.43/3.74 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.74 inference(monotonicity,[status(thm)],[916])).
% 5.43/3.74 tff(918,plain,
% 5.43/3.74 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.74 inference(transitivity,[status(thm)],[917, 915])).
% 5.43/3.74 tff(919,plain,
% 5.43/3.74 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.74 inference(quant_inst,[status(thm)],[])).
% 5.43/3.74 tff(920,plain,
% 5.43/3.74 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X1, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.43/3.74 inference(modus_ponens,[status(thm)],[919, 918])).
% 5.43/3.74 tff(921,plain,
% 5.43/3.74 (on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.43/3.74 inference(unit_resolution,[status(thm)],[920, 223, 69, 213, 55, 41, 891, 178, 914])).
% 5.43/3.74 tff(922,plain,
% 5.43/3.74 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.74 inference(rewrite,[status(thm)],[])).
% 5.43/3.74 tff(923,plain,
% 5.43/3.74 (((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.74 inference(rewrite,[status(thm)],[])).
% 5.43/3.74 tff(924,plain,
% 5.43/3.74 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.43/3.74 inference(monotonicity,[status(thm)],[923])).
% 5.43/3.74 tff(925,plain,
% 5.43/3.74 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.74 inference(transitivity,[status(thm)],[924, 922])).
% 5.43/3.74 tff(926,plain,
% 5.43/3.74 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.43/3.74 inference(quant_inst,[status(thm)],[])).
% 5.43/3.74 tff(927,plain,
% 5.43/3.74 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X2, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.43/3.74 inference(modus_ponens,[status(thm)],[926, 925])).
% 5.43/3.74 tff(928,plain,
% 5.43/3.74 (on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.43/3.74 inference(unit_resolution,[status(thm)],[927, 281, 69, 213, 55, 41, 891, 178, 914])).
% 5.43/3.74 tff(929,plain,
% 5.43/3.74 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.46/3.74 inference(rewrite,[status(thm)],[])).
% 5.46/3.74 tff(930,plain,
% 5.46/3.74 (((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.46/3.74 inference(rewrite,[status(thm)],[])).
% 5.46/3.74 tff(931,plain,
% 5.46/3.74 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.46/3.74 inference(monotonicity,[status(thm)],[930])).
% 5.46/3.75 tff(932,plain,
% 5.46/3.75 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.46/3.75 inference(transitivity,[status(thm)],[931, 929])).
% 5.46/3.75 tff(933,plain,
% 5.46/3.75 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.46/3.75 inference(quant_inst,[status(thm)],[])).
% 5.46/3.75 tff(934,plain,
% 5.46/3.75 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | on(X3, line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.46/3.75 inference(modus_ponens,[status(thm)],[933, 932])).
% 5.46/3.75 tff(935,plain,
% 5.46/3.75 (on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.46/3.75 inference(unit_resolution,[status(thm)],[934, 240, 69, 213, 55, 41, 891, 178, 914])).
% 5.46/3.75 tff(936,plain,
% 5.46/3.75 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.46/3.75 inference(rewrite,[status(thm)],[])).
% 5.46/3.75 tff(937,plain,
% 5.46/3.75 (((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.46/3.75 inference(rewrite,[status(thm)],[])).
% 5.46/3.75 tff(938,plain,
% 5.46/3.75 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.46/3.75 inference(monotonicity,[status(thm)],[937])).
% 5.46/3.75 tff(939,plain,
% 5.46/3.75 (((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.46/3.75 inference(transitivity,[status(thm)],[938, 936])).
% 5.46/3.75 tff(940,plain,
% 5.46/3.75 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_1_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.46/3.75 inference(quant_inst,[status(thm)],[])).
% 5.46/3.75 tff(941,plain,
% 5.46/3.75 ((~![X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~point(X3)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | (~collinear(X1, X2, X3)) | line(line_through_3_points(X1, X2, X3)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))) | line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.46/3.75 inference(modus_ponens,[status(thm)],[940, 939])).
% 5.46/3.75 tff(942,plain,
% 5.46/3.75 (line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))),
% 5.46/3.75 inference(unit_resolution,[status(thm)],[941, 257, 69, 213, 55, 41, 891, 178, 914])).
% 5.46/3.75 tff(943,plain,
% 5.46/3.75 (^[Y: $i, X3: $i, X2: $i, X1: $i] : refl(((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y))) <=> ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y))))),
% 5.46/3.75 inference(bind,[status(th)],[])).
% 5.46/3.75 tff(944,plain,
% 5.46/3.75 (![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y))) <=> ![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))),
% 5.46/3.75 inference(quant_intro,[status(thm)],[943])).
% 5.46/3.75 tff(945,plain,
% 5.46/3.75 (![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y))) <=> ![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))),
% 5.46/3.75 inference(rewrite,[status(thm)],[])).
% 5.46/3.75 tff(946,plain,
% 5.46/3.75 (^[Y: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((collinear(X1, X2, X3) | (~on(X1, Y))) <=> ((~on(X1, Y)) | collinear(X1, X2, X3))), (((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) <=> (((~on(X1, Y)) | collinear(X1, X2, X3)) | (~on(X2, Y))))), rewrite((((~on(X1, Y)) | collinear(X1, X2, X3)) | (~on(X2, Y))) <=> ((~on(X1, Y)) | collinear(X1, X2, X3) | (~on(X2, Y)))), (((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) <=> ((~on(X1, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))))), ((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) <=> (((~on(X1, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))) | (~on(X3, Y))))), rewrite((((~on(X1, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))) | (~on(X3, Y))) <=> ((~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y)))), ((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) <=> ((~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))))), (((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) <=> (((~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))) | (~point(X1))))), rewrite((((~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))) | (~point(X1))) <=> ((~point(X1)) | (~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y)))), (((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) <=> ((~point(X1)) | (~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))))), ((((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) | (~point(X2))) <=> (((~point(X1)) | (~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))) | (~point(X2))))), rewrite((((~point(X1)) | (~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))) | (~point(X2))) <=> ((~point(X1)) | (~point(X2)) | (~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y)))), ((((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) | (~point(X2))) <=> ((~point(X1)) | (~point(X2)) | (~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))))), (((((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) | (~point(X2))) | (~point(X3))) <=> (((~point(X1)) | (~point(X2)) | (~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))) | (~point(X3))))), rewrite((((~point(X1)) | (~point(X2)) | (~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y)))), (((((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) | (~point(X2))) | (~point(X3))) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))))), ((((((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) | (~point(X2))) | (~point(X3))) | (X1 = X2)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))) | (X1 = X2)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | collinear(X1, X2, X3) | (~on(X2, Y))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))), ((((((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) | (~point(X2))) | (~point(X3))) | (X1 = X2)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y))))), (((((((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y))) | (X1 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y))) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))), (((((((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y))))), ((((((((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y))) | (X2 = X3)))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y))) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))), ((((((((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) <=> ((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y))))), (((((((((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~line(Y))) <=> (((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y))) | (~line(Y))))), rewrite((((~point(X1)) | (~point(X2)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y))) | (~line(Y))) <=> ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))), (((((((((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~line(Y))) <=> ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))))),
% 5.46/3.75 inference(bind,[status(th)],[])).
% 5.46/3.75 tff(947,plain,
% 5.46/3.75 (![Y: $i, X3: $i, X2: $i, X1: $i] : ((((((((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~line(Y))) <=> ![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))),
% 5.46/3.75 inference(quant_intro,[status(thm)],[946])).
% 5.46/3.75 tff(948,axiom,(![Y: $i, X3: $i, X2: $i, X1: $i] : ((((((((((collinear(X1, X2, X3) | (~on(X1, Y))) | (~on(X2, Y))) | (~on(X3, Y))) | (~point(X1))) | (~point(X2))) | (~point(X3))) | (X1 = X2)) | (X1 = X3)) | (X2 = X3)) | (~line(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax','axiom_G10E')).
% 5.46/3.75 tff(949,plain,
% 5.46/3.75 (![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))),
% 5.46/3.75 inference(modus_ponens,[status(thm)],[948, 947])).
% 5.46/3.75 tff(950,plain,
% 5.46/3.75 (![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))),
% 5.46/3.75 inference(modus_ponens,[status(thm)],[949, 945])).
% 5.46/3.75 tff(951,plain,(
% 5.46/3.75 ![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))),
% 5.46/3.75 inference(skolemize,[status(sab)],[950])).
% 5.46/3.75 tff(952,plain,
% 5.46/3.75 (![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))),
% 5.46/3.75 inference(modus_ponens,[status(thm)],[951, 944])).
% 5.46/3.75 tff(953,plain,
% 5.46/3.75 (((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.46/3.75 inference(rewrite,[status(thm)],[])).
% 5.46/3.75 tff(954,plain,
% 5.46/3.75 (((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))) <=> ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.46/3.75 inference(rewrite,[status(thm)],[])).
% 5.46/3.75 tff(955,plain,
% 5.46/3.75 (((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | ((~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))))),
% 5.46/3.75 inference(monotonicity,[status(thm)],[954])).
% 5.46/3.75 tff(956,plain,
% 5.46/3.75 (((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))) <=> ((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.46/3.75 inference(transitivity,[status(thm)],[955, 953])).
% 5.46/3.75 tff(957,plain,
% 5.46/3.75 ((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | ((~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))))),
% 5.46/3.75 inference(quant_inst,[status(thm)],[])).
% 5.46/3.75 tff(958,plain,
% 5.46/3.75 ((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | (~point(point_1_on_line(at_least_one_line))) | (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)) | (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) | (~point(point_not_on_line(at_least_one_line))) | collinear(point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line), point_1_on_line(at_least_one_line)) | (~line(line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_through_3_points(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))))),
% 5.46/3.75 inference(modus_ponens,[status(thm)],[957, 956])).
% 5.46/3.75 tff(959,plain,
% 5.46/3.75 ($false),
% 5.46/3.75 inference(unit_resolution,[status(thm)],[958, 952, 69, 213, 55, 41, 199, 178, 299, 942, 935, 928, 921])).
% 5.46/3.75 tff(960,plain,(~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_1_on_line(at_least_one_line))), inference(lemma,lemma(discharge,[]))).
% 5.46/3.75 tff(961,plain,
% 5.46/3.75 (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), a_point)),
% 5.46/3.75 inference(modus_ponens,[status(thm)],[960, 913])).
% 5.46/3.75 tff(962,plain,
% 5.46/3.75 (~collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.46/3.75 inference(modus_ponens,[status(thm)],[961, 911])).
% 5.46/3.75 tff(963,plain,
% 5.46/3.75 ((point_not_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(at_least_one_line))),
% 5.46/3.75 inference(commutativity,[status(thm)],[])).
% 5.46/3.75 tff(964,plain,
% 5.46/3.75 ((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(at_least_one_line)) <=> (point_not_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.46/3.75 inference(symmetry,[status(thm)],[963])).
% 5.46/3.75 tff(965,plain,
% 5.46/3.75 ((~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(at_least_one_line))) <=> (~(point_not_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.46/3.75 inference(monotonicity,[status(thm)],[964])).
% 5.46/3.75 tff(966,plain,
% 5.46/3.75 (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)),
% 5.46/3.75 inference(transitivity,[status(thm)],[568, 907])).
% 5.46/3.75 tff(967,plain,
% 5.46/3.75 ((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(at_least_one_line)) <=> (point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line))),
% 5.46/3.75 inference(monotonicity,[status(thm)],[966])).
% 5.46/3.75 tff(968,plain,
% 5.46/3.75 ((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(at_least_one_line)) <=> (point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line))),
% 5.46/3.75 inference(transitivity,[status(thm)],[967, 365])).
% 5.46/3.75 tff(969,plain,
% 5.46/3.75 ((point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)) <=> (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(at_least_one_line))),
% 5.46/3.75 inference(symmetry,[status(thm)],[968])).
% 5.46/3.75 tff(970,plain,
% 5.46/3.75 ((~(point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line))) <=> (~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(at_least_one_line)))),
% 5.46/3.75 inference(monotonicity,[status(thm)],[969])).
% 5.46/3.75 tff(971,plain,
% 5.46/3.75 (~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_not_on_line(at_least_one_line))),
% 5.46/3.75 inference(modus_ponens,[status(thm)],[41, 970])).
% 5.46/3.75 tff(972,plain,
% 5.46/3.75 (~(point_not_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.46/3.75 inference(modus_ponens,[status(thm)],[971, 965])).
% 5.46/3.75 tff(973,plain,
% 5.46/3.75 ((point_2_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(at_least_one_line))),
% 5.46/3.75 inference(commutativity,[status(thm)],[])).
% 5.46/3.75 tff(974,plain,
% 5.46/3.75 ((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(at_least_one_line)) <=> (point_2_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.46/3.75 inference(symmetry,[status(thm)],[973])).
% 5.46/3.75 tff(975,plain,
% 5.46/3.75 ((~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(at_least_one_line))) <=> (~(point_2_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 5.46/3.75 inference(monotonicity,[status(thm)],[974])).
% 5.46/3.75 tff(976,plain,
% 5.46/3.75 ((point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(at_least_one_line)) <=> (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))),
% 5.46/3.75 inference(monotonicity,[status(thm)],[966])).
% 5.46/3.75 tff(977,plain,
% 5.46/3.75 ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) <=> (point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(at_least_one_line))),
% 5.46/3.75 inference(symmetry,[status(thm)],[976])).
% 5.46/3.75 tff(978,plain,
% 5.46/3.75 ((~(point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))) <=> (~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(at_least_one_line)))),
% 5.46/3.75 inference(monotonicity,[status(thm)],[977])).
% 5.46/3.75 tff(979,plain,
% 5.46/3.75 (~(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(at_least_one_line))),
% 5.46/3.75 inference(modus_ponens,[status(thm)],[177, 978])).
% 5.46/3.75 tff(980,plain,
% 5.46/3.75 (~(point_2_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 5.46/3.75 inference(modus_ponens,[status(thm)],[979, 975])).
% 5.46/3.75 tff(981,plain,
% 5.46/3.75 (((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | ((point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))))) <=> ((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))))),
% 5.46/3.76 inference(rewrite,[status(thm)],[])).
% 5.46/3.76 tff(982,plain,
% 5.46/3.76 (((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))) <=> ((point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))))),
% 5.46/3.76 inference(rewrite,[status(thm)],[])).
% 5.46/3.76 tff(983,plain,
% 5.46/3.76 (((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))))) <=> ((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | ((point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))))),
% 5.46/3.76 inference(monotonicity,[status(thm)],[982])).
% 5.46/3.76 tff(984,plain,
% 5.46/3.76 (((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))))) <=> ((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))))),
% 5.46/3.76 inference(transitivity,[status(thm)],[983, 981])).
% 5.46/3.76 tff(985,plain,
% 5.46/3.76 ((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | ((~point(point_not_on_line(at_least_one_line))) | (~point(point_2_on_line(at_least_one_line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))))),
% 5.46/3.76 inference(quant_inst,[status(thm)],[])).
% 5.46/3.76 tff(986,plain,
% 5.46/3.76 ((~![Y: $i, X3: $i, X2: $i, X1: $i] : ((~point(X1)) | (~point(X2)) | (~line(Y)) | (~point(X3)) | (~on(X1, Y)) | (~on(X3, Y)) | (X2 = X3) | (X1 = X3) | (X1 = X2) | collinear(X1, X2, X3) | (~on(X2, Y)))) | (point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_not_on_line(at_least_one_line))) | (~point(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | collinear(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line), point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_not_on_line(at_least_one_line) = point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_not_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 5.46/3.76 inference(modus_ponens,[status(thm)],[985, 984])).
% 5.46/3.76 tff(987,plain,
% 5.46/3.76 ((~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 5.46/3.76 inference(unit_resolution,[status(thm)],[986, 952, 69, 213, 891, 605, 980, 972, 962, 906])).
% 5.46/3.76 tff(988,plain,
% 5.46/3.76 (~on(point_on_plane(plane_for_points(a_point, point_2_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))),
% 5.46/3.76 inference(unit_resolution,[status(thm)],[987, 902, 895])).
% 5.46/3.76 tff(989,plain,
% 5.46/3.76 (~on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))),
% 5.46/3.76 inference(modus_ponens,[status(thm)],[988, 888])).
% 5.46/3.76 tff(990,plain,
% 5.46/3.76 (((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))) <=> ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 5.46/3.76 inference(rewrite,[status(thm)],[])).
% 5.46/3.76 tff(991,plain,
% 5.46/3.76 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 5.46/3.76 inference(quant_inst,[status(thm)],[])).
% 5.46/3.76 tff(992,plain,
% 5.46/3.76 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))),
% 5.46/3.76 inference(modus_ponens,[status(thm)],[991, 990])).
% 5.46/3.76 tff(993,plain,
% 5.46/3.76 (on(a_point, line_from_to(point_not_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))),
% 5.46/3.76 inference(unit_resolution,[status(thm)],[992, 111, 902])).
% 5.46/3.76 tff(994,plain,
% 5.46/3.76 ($false),
% 5.46/3.76 inference(unit_resolution,[status(thm)],[993, 989])).
% 5.46/3.76 % SZS output end Proof
%------------------------------------------------------------------------------