%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO076-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 : Sat Jun 21 05:05:31 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO076-4 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:13:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(on_type, type, (
% 0.19/0.42 on: ( $i * $i ) > $o)).
% 0.19/0.42 tff(line_from_to_type, type, (
% 0.19/0.42 line_from_to: ( $i * $i ) > $i)).
% 0.19/0.42 tff(point_not_on_line_type, type, (
% 0.19/0.42 point_not_on_line: $i > $i)).
% 0.19/0.42 tff(at_least_one_line_type, type, (
% 0.19/0.42 at_least_one_line: $i)).
% 0.19/0.42 tff(point_1_on_line_type, type, (
% 0.19/0.42 point_1_on_line: $i > $i)).
% 0.19/0.42 tff(point_2_on_line_type, type, (
% 0.19/0.42 point_2_on_line: $i > $i)).
% 0.19/0.42 tff(a_point_type, type, (
% 0.19/0.42 a_point: $i)).
% 0.19/0.42 tff(line_type, type, (
% 0.19/0.42 line: $i > $o)).
% 0.19/0.42 tff(point_type, type, (
% 0.19/0.42 point: $i > $o)).
% 0.19/0.42 tff(1,assumption,(point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line)), introduced(assumption)).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 (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)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[1])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (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)),
% 0.19/0.42 inference(symmetry,[status(thm)],[2])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 ((~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))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[3])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (line(at_least_one_line) <=> line(at_least_one_line)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(6,axiom,(line(at_least_one_line)), file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax','axiom_G4A')).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (line(at_least_one_line)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 (^[Y1: $i] : refl(((~on(point_not_on_line(Y1), Y1)) | (~line(Y1))) <=> ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1))) <=> ![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1))) <=> ![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(11,axiom,(![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax','axiom_G3A')).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.42 tff(13,plain,(
% 0.19/0.42 ![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[12])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 (![Y1: $i] : ((~on(point_not_on_line(Y1), Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 (((~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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(17,plain,
% 0.19/0.42 (((~![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))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[16])).
% 0.19/0.42 tff(18,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[17, 15])).
% 0.19/0.42 tff(19,plain,
% 0.19/0.42 ((~![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)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(20,plain,
% 0.19/0.42 ((~![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))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.42 tff(21,plain,
% 0.19/0.42 (~on(point_not_on_line(at_least_one_line), at_least_one_line)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[20, 14, 7])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 (~on(point_1_on_line(at_least_one_line), at_least_one_line)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[21, 4])).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 (^[Y1: $i] : refl((on(point_1_on_line(Y1), Y1) | (~line(Y1))) <=> (on(point_1_on_line(Y1), Y1) | (~line(Y1))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 (![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1))) <=> ![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 (![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1))) <=> ![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(26,axiom,(![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax','axiom_G2A')).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 (![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.42 tff(28,plain,(
% 0.19/0.42 ![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[27])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 (((~![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))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 ((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))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (((~![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))),
% 0.19/0.42 inference(transitivity,[status(thm)],[32, 30])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 ((~![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)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (~line(at_least_one_line)) | on(point_1_on_line(at_least_one_line), at_least_one_line)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 (on(point_1_on_line(at_least_one_line), at_least_one_line)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[35, 29, 7])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[36, 22])).
% 0.19/0.42 tff(38,plain,(~(point_1_on_line(at_least_one_line) = point_not_on_line(at_least_one_line))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (^[Y1: $i] : refl((point(point_1_on_line(Y1)) | (~line(Y1))) <=> (point(point_1_on_line(Y1)) | (~line(Y1))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1))) <=> ![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1))) <=> ![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(42,axiom,(![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax','axiom_G2C')).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.42 tff(44,plain,(
% 0.19/0.42 ![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[43])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 ((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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (((~![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))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (point(point_1_on_line(at_least_one_line)) | (~line(at_least_one_line)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (~line(at_least_one_line)) | point(point_1_on_line(at_least_one_line))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (point(point_1_on_line(at_least_one_line))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[51, 45, 7])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (^[Y1: $i] : refl((point(point_not_on_line(Y1)) | (~line(Y1))) <=> (point(point_not_on_line(Y1)) | (~line(Y1))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1))) <=> ![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 (![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1))) <=> ![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(56,axiom,(![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax','axiom_G3B')).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.42 tff(58,plain,(
% 0.19/0.42 ![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[57])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 (![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 ((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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (((~![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))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (((~![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)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[62, 60])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 ((~![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))) | (point(point_not_on_line(at_least_one_line)) | (~line(at_least_one_line)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 ((~![Y1: $i] : (point(point_not_on_line(Y1)) | (~line(Y1)))) | (~line(at_least_one_line)) | point(point_not_on_line(at_least_one_line))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 (point(point_not_on_line(at_least_one_line))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[65, 59, 7])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 (^[Z1: $i, Z2: $i] : refl(((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2))) <=> ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.43 tff(72,axiom,(![Z1: $i, Z2: $i] : (((on(Z1, line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax','axiom_G1A')).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.19/0.43 tff(75,plain,(
% 0.19/0.43 ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[74])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 (((~![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))) | on(point_1_on_line(at_least_one_line), line_from_to(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(point_not_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))) | on(point_1_on_line(at_least_one_line), line_from_to(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(point_not_on_line(at_least_one_line))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(78,plain,
% 0.19/0.43 (((~point(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_1_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_1_on_line(at_least_one_line), line_from_to(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(point_not_on_line(at_least_one_line))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(79,plain,
% 0.19/0.43 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(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_1_on_line(at_least_one_line), point_not_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))) | on(point_1_on_line(at_least_one_line), line_from_to(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(point_not_on_line(at_least_one_line)))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[78])).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(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_1_on_line(at_least_one_line), point_not_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))) | on(point_1_on_line(at_least_one_line), line_from_to(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(point_not_on_line(at_least_one_line))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[79, 77])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | ((~point(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(82,plain,
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% 0.19/0.43 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[82, 76, 66, 52, 38])).
% 0.19/0.43 tff(84,plain,
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% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(85,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.43 tff(86,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(87,plain,
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% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(88,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[87])).
% 0.19/0.43 tff(89,axiom,(![Z1: $i, Z2: $i] : (((line(line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax','axiom_G1C')).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.19/0.43 tff(92,plain,(
% 0.19/0.43 ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[91])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 (((~![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))) | line(line_from_to(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(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))) | line(line_from_to(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(point_not_on_line(at_least_one_line))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 (((~point(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)) | line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> ((~point(point_1_on_line(at_least_one_line))) | line(line_from_to(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(point_not_on_line(at_least_one_line))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(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)) | line(line_from_to(point_1_on_line(at_least_one_line), 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))) | line(line_from_to(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(point_not_on_line(at_least_one_line)))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(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)) | line(line_from_to(point_1_on_line(at_least_one_line), 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))) | line(line_from_to(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(point_not_on_line(at_least_one_line))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(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)) | line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 ((~![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))) | line(line_from_to(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(point_not_on_line(at_least_one_line)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[99, 93, 66, 52, 38])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 (^[Line: $i] : refl(((~line(Line)) | on(a_point, Line)) <=> ((~line(Line)) | on(a_point, Line)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (![Line: $i] : ((~line(Line)) | on(a_point, Line)) <=> ![Line: $i] : ((~line(Line)) | on(a_point, Line))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[101])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (![Line: $i] : ((~line(Line)) | on(a_point, Line)) <=> ![Line: $i] : ((~line(Line)) | on(a_point, Line))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(104,axiom,(![Line: $i] : ((~line(Line)) | on(a_point, Line))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_point_is_not_on_every_line')).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (![Line: $i] : ((~line(Line)) | on(a_point, Line))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.43 tff(106,plain,(
% 0.19/0.43 ![Line: $i] : ((~line(Line)) | on(a_point, Line))),
% 0.19/0.43 inference(skolemize,[status(sab)],[105])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (![Line: $i] : ((~line(Line)) | on(a_point, Line))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (on(a_point, line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[110, 107, 100])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.43 tff(117,axiom,(![Z1: $i, Z2: $i] : (((on(Z2, line_from_to(Z1, Z2)) | (Z1 = Z2)) | (~point(Z1))) | (~point(Z2)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax','axiom_G1B')).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.19/0.44 tff(120,plain,(
% 0.19/0.44 ![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[119])).
% 0.19/0.44 tff(121,plain,
% 0.19/0.44 (![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.19/0.44 tff(122,plain,
% 0.19/0.44 (((~![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_1_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_not_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_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_1_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_not_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(123,plain,
% 0.19/0.44 (((~point(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_not_on_line(at_least_one_line), line_from_to(point_1_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)) | (~point(point_not_on_line(at_least_one_line))) | on(point_not_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(124,plain,
% 0.19/0.44 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | ((~point(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_not_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_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_1_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_not_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[123])).
% 0.19/0.44 tff(125,plain,
% 0.19/0.44 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | ((~point(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_not_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_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_1_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_not_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[124, 122])).
% 0.19/0.44 tff(126,plain,
% 0.19/0.44 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | ((~point(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_not_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(127,plain,
% 0.19/0.44 ((~![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_1_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_not_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.44 tff(128,plain,
% 0.19/0.44 ((point_1_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[127, 121, 66, 52])).
% 0.19/0.44 tff(129,plain,
% 0.19/0.44 (on(point_not_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[128, 38])).
% 0.19/0.44 tff(130,assumption,(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line), introduced(assumption)).
% 0.19/0.44 tff(131,plain,
% 0.19/0.44 (on(point_not_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) <=> on(point_not_on_line(at_least_one_line), at_least_one_line)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[130])).
% 0.19/0.44 tff(132,plain,
% 0.19/0.44 (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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.44 inference(symmetry,[status(thm)],[131])).
% 0.19/0.44 tff(133,plain,
% 0.19/0.44 ((~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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[132])).
% 0.19/0.44 tff(134,plain,
% 0.19/0.44 (~on(point_not_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[21, 133])).
% 0.19/0.44 tff(135,assumption,(on(point_not_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))), introduced(assumption)).
% 0.19/0.44 tff(136,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.19/0.44 tff(137,plain,((~(line_from_to(point_1_on_line(at_least_one_line), 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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(138,plain,
% 0.19/0.44 (~(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[137, 129])).
% 0.19/0.44 tff(139,plain,
% 0.19/0.44 (((~![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))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(140,plain,
% 0.19/0.44 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(at_least_one_line)) | on(a_point, at_least_one_line))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(141,plain,
% 0.19/0.44 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(at_least_one_line)) | on(a_point, at_least_one_line)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.44 tff(142,plain,
% 0.19/0.44 (on(a_point, at_least_one_line)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[141, 7, 107])).
% 0.19/0.44 tff(143,plain,
% 0.19/0.44 (point(a_point) <=> point(a_point)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(144,axiom,(point(a_point)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','there_is_a_point')).
% 0.19/0.44 tff(145,plain,
% 0.19/0.44 (point(a_point)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.19/0.44 tff(146,plain,
% 0.19/0.44 (^[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))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(147,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[146])).
% 0.19/0.44 tff(148,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(149,plain,
% 0.19/0.44 (^[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)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(150,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[149])).
% 0.19/0.44 tff(151,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/sandbox2/benchmark/Axioms/GEO003-0.ax','axiom_G1D')).
% 0.19/0.44 tff(152,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.44 tff(153,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.19/0.44 tff(154,plain,(
% 0.19/0.44 ![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)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[153])).
% 0.19/0.44 tff(155,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.19/0.44 tff(156,plain,
% 0.19/0.44 (((~![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))) | (a_point = point_1_on_line(at_least_one_line)) | (~line(line_from_to(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), at_least_one_line)) | (~point(a_point)) | (~on(a_point, at_least_one_line)) | (line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(a_point, line_from_to(point_1_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(point_1_on_line(at_least_one_line))) | (a_point = point_1_on_line(at_least_one_line)) | (~line(line_from_to(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), at_least_one_line)) | (~point(a_point)) | (~on(a_point, at_least_one_line)) | (line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(a_point, line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(157,plain,
% 0.19/0.44 (((~point(point_1_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (a_point = point_1_on_line(at_least_one_line)) | (~on(a_point, line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (a_point = point_1_on_line(at_least_one_line)) | (~line(line_from_to(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), at_least_one_line)) | (~point(a_point)) | (~on(a_point, at_least_one_line)) | (line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(a_point, line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(158,plain,
% 0.19/0.44 (((~![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_1_on_line(at_least_one_line), point_not_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (a_point = point_1_on_line(at_least_one_line)) | (~on(a_point, line_from_to(point_1_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(point_1_on_line(at_least_one_line))) | (a_point = point_1_on_line(at_least_one_line)) | (~line(line_from_to(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), at_least_one_line)) | (~point(a_point)) | (~on(a_point, at_least_one_line)) | (line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(a_point, line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[157])).
% 0.19/0.44 tff(159,plain,
% 0.19/0.44 (((~![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_1_on_line(at_least_one_line), point_not_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (a_point = point_1_on_line(at_least_one_line)) | (~on(a_point, line_from_to(point_1_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(point_1_on_line(at_least_one_line))) | (a_point = point_1_on_line(at_least_one_line)) | (~line(line_from_to(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), at_least_one_line)) | (~point(a_point)) | (~on(a_point, at_least_one_line)) | (line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(a_point, line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[158, 156])).
% 0.19/0.44 tff(160,plain,
% 0.19/0.44 ((~![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_1_on_line(at_least_one_line), point_not_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (a_point = point_1_on_line(at_least_one_line)) | (~on(a_point, line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(161,plain,
% 0.19/0.44 ((~![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))) | (a_point = point_1_on_line(at_least_one_line)) | (~line(line_from_to(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), at_least_one_line)) | (~point(a_point)) | (~on(a_point, at_least_one_line)) | (line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(a_point, line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
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% 0.19/0.45 tff(162,plain,
% 0.19/0.45 (a_point = point_1_on_line(at_least_one_line)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[161, 155, 7, 145, 142, 52, 36, 138, 100, 111, 83])).
% 0.19/0.45 tff(163,plain,
% 0.19/0.45 (point_1_on_line(at_least_one_line) = a_point),
% 0.19/0.45 inference(symmetry,[status(thm)],[162])).
% 0.19/0.45 tff(164,plain,
% 0.19/0.45 (line_from_to(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line)) = line_from_to(a_point, point_2_on_line(at_least_one_line))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[163])).
% 0.19/0.45 tff(165,plain,
% 0.19/0.45 (line(line_from_to(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line))) <=> line(line_from_to(a_point, point_2_on_line(at_least_one_line)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[164])).
% 0.19/0.45 tff(166,plain,
% 0.19/0.45 (^[Y1: $i] : refl((point(point_2_on_line(Y1)) | (~line(Y1))) <=> (point(point_2_on_line(Y1)) | (~line(Y1))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(167,plain,
% 0.19/0.45 (![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1))) <=> ![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[166])).
% 0.19/0.45 tff(168,plain,
% 0.19/0.45 (![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1))) <=> ![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(169,axiom,(![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax','axiom_G2D')).
% 0.19/0.45 tff(170,plain,
% 0.19/0.45 (![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.19/0.45 tff(171,plain,(
% 0.19/0.45 ![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[170])).
% 0.19/0.45 tff(172,plain,
% 0.19/0.45 (![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[171, 167])).
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% 0.19/0.45 (((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | ((~line(at_least_one_line)) | point(point_2_on_line(at_least_one_line)))) <=> ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (~line(at_least_one_line)) | point(point_2_on_line(at_least_one_line)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(174,plain,
% 0.19/0.45 ((point(point_2_on_line(at_least_one_line)) | (~line(at_least_one_line))) <=> ((~line(at_least_one_line)) | point(point_2_on_line(at_least_one_line)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(175,plain,
% 0.19/0.45 (((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (point(point_2_on_line(at_least_one_line)) | (~line(at_least_one_line)))) <=> ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | ((~line(at_least_one_line)) | point(point_2_on_line(at_least_one_line))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[174])).
% 0.19/0.45 tff(176,plain,
% 0.19/0.45 (((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (point(point_2_on_line(at_least_one_line)) | (~line(at_least_one_line)))) <=> ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (~line(at_least_one_line)) | point(point_2_on_line(at_least_one_line)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[175, 173])).
% 0.19/0.45 tff(177,plain,
% 0.19/0.45 ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (point(point_2_on_line(at_least_one_line)) | (~line(at_least_one_line)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(178,plain,
% 0.19/0.45 ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (~line(at_least_one_line)) | point(point_2_on_line(at_least_one_line))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.19/0.45 tff(179,plain,
% 0.19/0.45 (point(point_2_on_line(at_least_one_line))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[178, 172, 7])).
% 0.19/0.45 tff(180,plain,
% 0.19/0.45 (^[Y1: $i] : refl(((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1))) <=> ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(181,plain,
% 0.19/0.45 (![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1))) <=> ![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[180])).
% 0.19/0.45 tff(182,plain,
% 0.19/0.45 (![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1))) <=> ![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(183,axiom,(![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax','axiom_G2E')).
% 0.19/0.45 tff(184,plain,
% 0.19/0.45 (![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.19/0.45 tff(185,plain,(
% 0.19/0.45 ![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[184])).
% 0.19/0.45 tff(186,plain,
% 0.19/0.45 (![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.19/0.45 tff(187,plain,
% 0.19/0.45 (((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | ((~line(at_least_one_line)) | (~(point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))))) <=> ((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | (~line(at_least_one_line)) | (~(point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(188,plain,
% 0.19/0.45 (((~(point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))) | (~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))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(189,plain,
% 0.19/0.45 (((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | ((~(point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))) | (~line(at_least_one_line)))) <=> ((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | ((~line(at_least_one_line)) | (~(point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[188])).
% 0.19/0.45 tff(190,plain,
% 0.19/0.45 (((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | ((~(point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))) | (~line(at_least_one_line)))) <=> ((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | (~line(at_least_one_line)) | (~(point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[189, 187])).
% 0.19/0.45 tff(191,plain,
% 0.19/0.45 ((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | ((~(point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))) | (~line(at_least_one_line)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(192,plain,
% 0.19/0.45 ((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | (~line(at_least_one_line)) | (~(point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.19/0.45 tff(193,plain,
% 0.19/0.45 (~(point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))),
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% 0.19/0.45 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((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))) | line(line_from_to(point_1_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_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))) | line(line_from_to(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
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% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(205,plain,
% 0.19/0.45 (((~![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_1_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_from_to(point_1_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_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), line_from_to(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[204])).
% 0.19/0.45 tff(206,plain,
% 0.19/0.45 (((~![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_1_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_from_to(point_1_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_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), line_from_to(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[205, 203])).
% 0.19/0.45 tff(207,plain,
% 0.19/0.45 ((~![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_1_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_from_to(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(208,plain,
% 0.19/0.45 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (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), line_from_to(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.19/0.45 tff(209,plain,
% 0.19/0.45 (on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_2_on_line(at_least_one_line)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[208, 76, 193, 179, 52])).
% 0.19/0.45 tff(210,plain,
% 0.19/0.45 (on(point_1_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[209, 202])).
% 0.19/0.45 tff(211,plain,
% 0.19/0.45 ((a_point = point_2_on_line(at_least_one_line)) <=> (point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[162])).
% 0.19/0.45 tff(212,plain,
% 0.19/0.45 ((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))),
% 0.19/0.45 inference(symmetry,[status(thm)],[211])).
% 0.19/0.45 tff(213,plain,
% 0.19/0.45 ((~(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)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[212])).
% 0.19/0.45 tff(214,plain,
% 0.19/0.45 (~(a_point = point_2_on_line(at_least_one_line))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[193, 213])).
% 0.19/0.45 tff(215,plain,
% 0.19/0.45 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | (on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line))) | (~point(a_point)) | (a_point = point_2_on_line(at_least_one_line)) | (~point(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)))) | on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line))) | (~point(a_point)) | (a_point = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(216,plain,
% 0.19/0.45 (((~point(point_2_on_line(at_least_one_line))) | (~point(a_point)) | (a_point = point_2_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))) <=> (on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line))) | (~point(a_point)) | (a_point = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(217,plain,
% 0.19/0.45 (((~![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(a_point)) | (a_point = point_2_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), line_from_to(a_point, 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)))) | (on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line))) | (~point(a_point)) | (a_point = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[216])).
% 0.19/0.45 tff(218,plain,
% 0.19/0.45 (((~![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(a_point)) | (a_point = point_2_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), line_from_to(a_point, 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)))) | on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line))) | (~point(a_point)) | (a_point = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[217, 215])).
% 0.19/0.45 tff(219,plain,
% 0.19/0.45 ((~![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(a_point)) | (a_point = point_2_on_line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(220,plain,
% 0.19/0.45 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z2, line_from_to(Z1, Z2)))) | on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line))) | (~point(a_point)) | (a_point = point_2_on_line(at_least_one_line)) | (~point(point_2_on_line(at_least_one_line)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.19/0.45 tff(221,plain,
% 0.19/0.45 (on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line))) | (a_point = point_2_on_line(at_least_one_line))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[220, 121, 145, 179])).
% 0.19/0.45 tff(222,plain,
% 0.19/0.45 (on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[221, 214])).
% 0.19/0.45 tff(223,plain,
% 0.19/0.45 ((point_2_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(at_least_one_line))),
% 0.19/0.45 inference(commutativity,[status(thm)],[])).
% 0.19/0.45 tff(224,plain,
% 0.19/0.45 ((point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)) <=> (point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line))),
% 0.19/0.45 inference(symmetry,[status(thm)],[223])).
% 0.19/0.45 tff(225,plain,
% 0.19/0.45 ((~(point_1_on_line(at_least_one_line) = point_2_on_line(at_least_one_line))) <=> (~(point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[224])).
% 0.19/0.45 tff(226,plain,
% 0.19/0.45 (~(point_2_on_line(at_least_one_line) = point_1_on_line(at_least_one_line))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[193, 225])).
% 0.19/0.45 tff(227,plain,
% 0.19/0.45 (^[Y1: $i] : refl((on(point_2_on_line(Y1), Y1) | (~line(Y1))) <=> (on(point_2_on_line(Y1), Y1) | (~line(Y1))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(228,plain,
% 0.19/0.45 (![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1))) <=> ![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[227])).
% 0.19/0.45 tff(229,plain,
% 0.19/0.45 (![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1))) <=> ![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(230,axiom,(![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax','axiom_G2B')).
% 0.19/0.45 tff(231,plain,
% 0.19/0.45 (![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.19/0.45 tff(232,plain,(
% 0.19/0.45 ![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[231])).
% 0.19/0.45 tff(233,plain,
% 0.19/0.45 (![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.19/0.45 tff(234,plain,
% 0.19/0.45 (((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | ((~line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), at_least_one_line))) <=> ((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | (~line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), at_least_one_line))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(235,plain,
% 0.19/0.45 ((on(point_2_on_line(at_least_one_line), at_least_one_line) | (~line(at_least_one_line))) <=> ((~line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), at_least_one_line))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(236,plain,
% 0.19/0.45 (((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_2_on_line(at_least_one_line), at_least_one_line) | (~line(at_least_one_line)))) <=> ((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | ((~line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), at_least_one_line)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[235])).
% 0.19/0.45 tff(237,plain,
% 0.19/0.45 (((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_2_on_line(at_least_one_line), at_least_one_line) | (~line(at_least_one_line)))) <=> ((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | (~line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), at_least_one_line))),
% 0.19/0.45 inference(transitivity,[status(thm)],[236, 234])).
% 0.19/0.45 tff(238,plain,
% 0.19/0.45 ((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_2_on_line(at_least_one_line), at_least_one_line) | (~line(at_least_one_line)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(239,plain,
% 0.19/0.45 ((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | (~line(at_least_one_line)) | on(point_2_on_line(at_least_one_line), at_least_one_line)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.19/0.45 tff(240,plain,
% 0.19/0.45 (on(point_2_on_line(at_least_one_line), at_least_one_line)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[239, 233, 7])).
% 0.19/0.45 tff(241,plain,
% 0.19/0.45 (((~![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))) | (~on(point_1_on_line(at_least_one_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_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (line_from_to(a_point, point_2_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(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_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_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (line_from_to(a_point, point_2_on_line(at_least_one_line)) = at_least_one_line))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(242,plain,
% 0.19/0.45 (((~point(point_1_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_from_to(a_point, point_2_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_from_to(a_point, point_2_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(a_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_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line))))) <=> ((~line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~on(point_1_on_line(at_least_one_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_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (line_from_to(a_point, point_2_on_line(at_least_one_line)) = at_least_one_line))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(243,plain,
% 0.19/0.45 (((~![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(a_point, point_2_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_from_to(a_point, point_2_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(a_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_2_on_line(at_least_one_line), line_from_to(a_point, point_2_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))) | (~on(point_1_on_line(at_least_one_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_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (line_from_to(a_point, point_2_on_line(at_least_one_line)) = at_least_one_line)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[242])).
% 0.19/0.45 tff(244,plain,
% 0.19/0.45 (((~![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(a_point, point_2_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_from_to(a_point, point_2_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(a_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_2_on_line(at_least_one_line), line_from_to(a_point, point_2_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))) | (~on(point_1_on_line(at_least_one_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_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (line_from_to(a_point, point_2_on_line(at_least_one_line)) = at_least_one_line))),
% 0.19/0.45 inference(transitivity,[status(thm)],[243, 241])).
% 0.19/0.45 tff(245,plain,
% 0.19/0.45 ((~![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(a_point, point_2_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_from_to(a_point, point_2_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(a_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_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(246,plain,
% 0.19/0.46 ((~![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))) | (~on(point_1_on_line(at_least_one_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_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~on(point_1_on_line(at_least_one_line), line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (line_from_to(a_point, point_2_on_line(at_least_one_line)) = at_least_one_line)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.19/0.46 tff(247,plain,
% 0.19/0.46 (line_from_to(a_point, point_2_on_line(at_least_one_line)) = at_least_one_line),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[246, 155, 7, 179, 52, 36, 240, 226, 222, 210, 201])).
% 0.19/0.46 tff(248,plain,
% 0.19/0.46 (at_least_one_line = line_from_to(a_point, point_2_on_line(at_least_one_line))),
% 0.19/0.46 inference(symmetry,[status(thm)],[247])).
% 0.19/0.46 tff(249,plain,
% 0.19/0.46 (point_2_on_line(at_least_one_line) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[248])).
% 0.19/0.46 tff(250,plain,
% 0.19/0.46 (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(at_least_one_line)),
% 0.19/0.46 inference(symmetry,[status(thm)],[249])).
% 0.19/0.46 tff(251,plain,
% 0.19/0.46 (line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) = line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[250])).
% 0.19/0.46 tff(252,plain,
% 0.19/0.46 (line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)) = line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))),
% 0.19/0.46 inference(symmetry,[status(thm)],[251])).
% 0.19/0.46 tff(253,plain,
% 0.19/0.46 (on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line))) <=> on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[252])).
% 0.19/0.46 tff(254,plain,
% 0.19/0.46 (on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) <=> on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))),
% 0.19/0.46 inference(symmetry,[status(thm)],[253])).
% 0.19/0.46 tff(255,plain,
% 0.19/0.46 ((point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) <=> (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(at_least_one_line))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[250])).
% 0.19/0.46 tff(256,plain,
% 0.19/0.46 ((point_1_on_line(line_from_to(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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))),
% 0.19/0.46 inference(symmetry,[status(thm)],[255])).
% 0.19/0.46 tff(257,plain,
% 0.19/0.46 ((~(point_1_on_line(line_from_to(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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[256])).
% 0.19/0.46 tff(258,assumption,(~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(at_least_one_line))), introduced(assumption)).
% 0.19/0.46 tff(259,plain,
% 0.19/0.46 (~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.19/0.46 tff(260,plain,
% 0.19/0.46 (((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(261,plain,
% 0.19/0.46 ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(262,plain,
% 0.19/0.46 ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | (~line(line_from_to(a_point, point_2_on_line(at_least_one_line))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.19/0.46 tff(263,plain,
% 0.19/0.46 (point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[262, 172, 201])).
% 0.19/0.46 tff(264,plain,
% 0.19/0.46 (((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(265,plain,
% 0.19/0.46 ((point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(266,plain,
% 0.19/0.46 (((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[265])).
% 0.19/0.46 tff(267,plain,
% 0.19/0.46 (((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[266, 264])).
% 0.19/0.46 tff(268,plain,
% 0.19/0.46 ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(269,plain,
% 0.19/0.46 ((~![Y1: $i] : (point(point_1_on_line(Y1)) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.19/0.46 tff(270,plain,
% 0.19/0.46 (point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[269, 45, 100])).
% 0.19/0.46 tff(271,plain,
% 0.19/0.46 (((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, 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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(272,plain,
% 0.19/0.46 (((~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))) <=> ((~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(273,plain,
% 0.19/0.46 (((~![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(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, 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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[272])).
% 0.19/0.46 tff(274,plain,
% 0.19/0.46 (((~![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(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, 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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[273, 271])).
% 0.19/0.46 tff(275,plain,
% 0.19/0.46 ((~![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(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(276,plain,
% 0.19/0.46 ((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.19/0.46 tff(277,plain,
% 0.19/0.46 ((point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[276, 76, 270, 263])).
% 0.19/0.46 tff(278,plain,
% 0.19/0.46 (on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[277, 259])).
% 0.19/0.46 tff(279,plain,
% 0.19/0.46 (on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[278, 254])).
% 0.19/0.46 tff(280,plain,
% 0.19/0.46 (line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) <=> line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[251])).
% 0.19/0.46 tff(281,plain,
% 0.19/0.46 (((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, 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(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(282,plain,
% 0.19/0.46 (((~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))) <=> ((~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(283,plain,
% 0.19/0.46 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, 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(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[282])).
% 0.19/0.46 tff(284,plain,
% 0.19/0.46 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, 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(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[283, 281])).
% 0.19/0.46 tff(285,plain,
% 0.19/0.46 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | line(line_from_to(Z1, Z2)))) | ((~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(286,plain,
% 0.19/0.46 ((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.19/0.46 tff(287,plain,
% 0.19/0.46 ((point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))) | line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[286, 93, 270, 263])).
% 0.19/0.46 tff(288,plain,
% 0.19/0.46 (line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[287, 259])).
% 0.19/0.46 tff(289,plain,
% 0.19/0.46 (line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[288, 280])).
% 0.19/0.46 tff(290,plain,
% 0.19/0.46 (on(a_point, line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line))) <=> on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[162])).
% 0.19/0.46 tff(291,plain,
% 0.19/0.46 (((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), 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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(292,plain,
% 0.19/0.46 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(293,plain,
% 0.19/0.46 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | on(a_point, line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.19/0.46 tff(294,plain,
% 0.19/0.46 (on(a_point, line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[293, 107, 289])).
% 0.19/0.46 tff(295,plain,
% 0.19/0.46 (on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[294, 290])).
% 0.19/0.46 tff(296,assumption,(point_2_on_line(at_least_one_line) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))), introduced(assumption)).
% 0.19/0.46 tff(297,plain,
% 0.19/0.46 (point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(at_least_one_line)),
% 0.19/0.46 inference(symmetry,[status(thm)],[296])).
% 0.19/0.46 tff(298,plain,
% 0.19/0.46 (on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[297])).
% 0.19/0.46 tff(299,plain,
% 0.19/0.46 (on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) <=> on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.46 inference(symmetry,[status(thm)],[298])).
% 0.19/0.46 tff(300,plain,
% 0.19/0.46 ((~on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> (~on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[299])).
% 0.19/0.46 tff(301,plain,
% 0.19/0.46 (((~![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))) | (~line(line_from_to(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), 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)) | (line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_1_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(point_1_on_line(at_least_one_line))) | (~line(line_from_to(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), 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)) | (line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(302,plain,
% 0.19/0.46 (((~point(point_1_on_line(at_least_one_line))) | (~line(at_least_one_line)) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_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_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(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_1_on_line(at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~line(at_least_one_line)) | (~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(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), 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)) | (line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(303,plain,
% 0.19/0.46 (((~![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_1_on_line(at_least_one_line), point_not_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_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(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_1_on_line(at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_1_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(point_1_on_line(at_least_one_line))) | (~line(line_from_to(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), 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)) | (line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[302])).
% 0.19/0.46 tff(304,plain,
% 0.19/0.46 (((~![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_1_on_line(at_least_one_line), point_not_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_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(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_1_on_line(at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_1_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(point_1_on_line(at_least_one_line))) | (~line(line_from_to(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), 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)) | (line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[303, 301])).
% 0.19/0.46 tff(305,plain,
% 0.19/0.46 ((~![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_1_on_line(at_least_one_line), point_not_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_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(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_1_on_line(at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(306,plain,
% 0.19/0.47 ((~![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))) | (~line(line_from_to(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), 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)) | (line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = at_least_one_line) | (~on(point_1_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(at_least_one_line), at_least_one_line)) | (~on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.19/0.47 tff(307,plain,
% 0.19/0.47 (~on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[306, 155, 7, 179, 52, 36, 240, 226, 138, 100, 83])).
% 0.19/0.47 tff(308,plain,
% 0.19/0.47 (~on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[307, 300])).
% 0.19/0.47 tff(309,plain,
% 0.19/0.47 (((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(310,plain,
% 0.19/0.47 ((on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(311,plain,
% 0.19/0.47 (((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[310])).
% 0.19/0.47 tff(312,plain,
% 0.19/0.47 (((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[311, 309])).
% 0.19/0.47 tff(313,plain,
% 0.19/0.47 ((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(314,plain,
% 0.19/0.47 ((~![Y1: $i] : (on(point_2_on_line(Y1), Y1) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.19/0.47 tff(315,plain,
% 0.19/0.47 (on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[314, 233, 100])).
% 0.19/0.47 tff(316,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[315, 308])).
% 0.19/0.47 tff(317,plain,(~(point_2_on_line(at_least_one_line) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(318,plain,
% 0.19/0.47 (line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) = line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[250])).
% 0.19/0.47 tff(319,plain,
% 0.19/0.47 (line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) = line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.47 inference(symmetry,[status(thm)],[318])).
% 0.19/0.47 tff(320,plain,
% 0.19/0.47 (on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[319])).
% 0.19/0.47 tff(321,plain,
% 0.19/0.47 (on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(symmetry,[status(thm)],[320])).
% 0.19/0.47 tff(322,plain,
% 0.19/0.47 ((point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[250])).
% 0.19/0.47 tff(323,plain,
% 0.19/0.47 ((point_2_on_line(at_least_one_line) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.47 inference(symmetry,[status(thm)],[322])).
% 0.19/0.47 tff(324,plain,
% 0.19/0.47 ((~(point_2_on_line(at_least_one_line) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> (~(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[323])).
% 0.19/0.47 tff(325,assumption,(~(point_2_on_line(at_least_one_line) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))), introduced(assumption)).
% 0.19/0.47 tff(326,plain,
% 0.19/0.47 (~(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.19/0.47 tff(327,plain,
% 0.19/0.47 (((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(328,plain,
% 0.19/0.47 ((point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(329,plain,
% 0.19/0.47 (((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[328])).
% 0.19/0.47 tff(330,plain,
% 0.19/0.47 (((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[329, 327])).
% 0.19/0.47 tff(331,plain,
% 0.19/0.47 ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(332,plain,
% 0.19/0.47 ((~![Y1: $i] : (point(point_2_on_line(Y1)) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.19/0.47 tff(333,plain,
% 0.19/0.47 (point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[332, 172, 100])).
% 0.19/0.47 tff(334,plain,
% 0.19/0.47 (((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(335,plain,
% 0.19/0.47 (((~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(336,plain,
% 0.19/0.47 (((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[335])).
% 0.19/0.47 tff(337,plain,
% 0.19/0.47 (((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[336, 334])).
% 0.19/0.47 tff(338,plain,
% 0.19/0.47 ((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(339,plain,
% 0.19/0.47 ((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.19/0.47 tff(340,plain,
% 0.19/0.47 ((point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[339, 121, 333, 263])).
% 0.19/0.47 tff(341,plain,
% 0.19/0.47 (on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[340, 326])).
% 0.19/0.47 tff(342,plain,
% 0.19/0.47 (on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[341, 321])).
% 0.19/0.47 tff(343,plain,
% 0.19/0.47 (line(line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[318])).
% 0.19/0.47 tff(344,plain,
% 0.19/0.47 (((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | line(line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, 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(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | line(line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(345,plain,
% 0.19/0.47 (((~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | line(line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | line(line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(346,plain,
% 0.19/0.47 (((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | line(line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), 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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | line(line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[345])).
% 0.19/0.47 tff(347,plain,
% 0.19/0.47 (((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | line(line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), 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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | line(line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[346, 344])).
% 0.19/0.47 tff(348,plain,
% 0.19/0.47 ((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | line(line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(349,plain,
% 0.19/0.47 ((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | line(line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.19/0.47 tff(350,plain,
% 0.19/0.47 ((point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | line(line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[349, 93, 333, 263])).
% 0.19/0.47 tff(351,plain,
% 0.19/0.47 (line(line_from_to(point_2_on_line(line_from_to(a_point, point_2_on_line(at_least_one_line))), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[350, 326])).
% 0.19/0.47 tff(352,plain,
% 0.19/0.47 (line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[351, 343])).
% 0.19/0.47 tff(353,plain,
% 0.19/0.47 (on(a_point, line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[162])).
% 0.19/0.47 tff(354,plain,
% 0.19/0.47 (((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))) <=> ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(355,plain,
% 0.19/0.47 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | ((~line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(356,plain,
% 0.19/0.47 ((~![Line: $i] : ((~line(Line)) | on(a_point, Line))) | (~line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | on(a_point, line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.19/0.47 tff(357,plain,
% 0.19/0.47 (on(a_point, line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[356, 107, 352])).
% 0.19/0.47 tff(358,plain,
% 0.19/0.47 (on(point_1_on_line(at_least_one_line), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[357, 353])).
% 0.19/0.47 tff(359,assumption,(~(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line))), introduced(assumption)).
% 0.19/0.47 tff(360,plain,
% 0.19/0.47 (((~![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_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (~line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) = line_from_to(point_1_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))) | (~line(line_from_to(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (~line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) = line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(361,plain,
% 0.19/0.48 (((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (~point(point_2_on_line(line_from_to(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) = line_from_to(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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))) <=> ((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (~line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) = line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(362,plain,
% 0.19/0.48 (((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (~point(point_2_on_line(line_from_to(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) = line_from_to(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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_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))) | (~line(line_from_to(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (~line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) = line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[361])).
% 0.19/0.48 tff(363,plain,
% 0.19/0.48 (((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (~point(point_2_on_line(line_from_to(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) = line_from_to(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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_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))) | (~line(line_from_to(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (~line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) = line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[362, 360])).
% 0.19/0.48 tff(364,plain,
% 0.19/0.48 ((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (~point(point_2_on_line(line_from_to(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) = line_from_to(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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(365,plain,
% 0.19/0.48 ((~![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_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (~line(line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) | (line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) = line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.19/0.48 tff(366,plain,
% 0.19/0.48 (line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) = line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[365, 155, 52, 333, 100, 315, 83, 359, 358, 352, 342])).
% 0.19/0.48 tff(367,plain,
% 0.19/0.48 (line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.48 inference(symmetry,[status(thm)],[366])).
% 0.19/0.48 tff(368,plain,
% 0.19/0.48 (on(point_2_on_line(at_least_one_line), line_from_to(point_1_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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[367])).
% 0.19/0.48 tff(369,plain,
% 0.19/0.48 (on(point_2_on_line(at_least_one_line), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.48 inference(symmetry,[status(thm)],[368])).
% 0.19/0.48 tff(370,plain,
% 0.19/0.48 (((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (on(point_2_on_line(at_least_one_line), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | on(point_2_on_line(at_least_one_line), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(371,plain,
% 0.19/0.48 (((~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_2_on_line(line_from_to(point_1_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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(372,plain,
% 0.19/0.48 (((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_2_on_line(line_from_to(point_1_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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | (on(point_2_on_line(at_least_one_line), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[371])).
% 0.19/0.48 tff(373,plain,
% 0.19/0.48 (((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_2_on_line(line_from_to(point_1_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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))) <=> ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | on(point_2_on_line(at_least_one_line), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[372, 370])).
% 0.19/0.48 tff(374,plain,
% 0.19/0.48 ((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~point(point_2_on_line(at_least_one_line))) | (point_2_on_line(at_least_one_line) = point_2_on_line(line_from_to(point_1_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_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(375,plain,
% 0.19/0.48 ((~![Z1: $i, Z2: $i] : ((~point(Z2)) | (~point(Z1)) | (Z1 = Z2) | on(Z1, line_from_to(Z1, Z2)))) | on(point_2_on_line(at_least_one_line), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(at_least_one_line))) | (~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.19/0.48 tff(376,plain,
% 0.19/0.48 (on(point_2_on_line(at_least_one_line), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[375, 76, 179])).
% 0.19/0.48 tff(377,plain,
% 0.19/0.48 (on(point_2_on_line(at_least_one_line), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(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_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[376, 333])).
% 0.19/0.48 tff(378,plain,
% 0.19/0.48 (on(point_2_on_line(at_least_one_line), line_from_to(point_2_on_line(at_least_one_line), point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[377, 325])).
% 0.19/0.48 tff(379,plain,
% 0.19/0.48 (on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[378, 369])).
% 0.19/0.48 tff(380,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[307, 379])).
% 0.19/0.48 tff(381,plain,((point_2_on_line(at_least_one_line) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_2_on_line(line_from_to(point_1_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,[]))).
% 0.19/0.48 tff(382,plain,
% 0.19/0.48 (point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[381, 317])).
% 0.19/0.48 tff(383,plain,
% 0.19/0.48 ((point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> (point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[382])).
% 0.19/0.48 tff(384,plain,
% 0.19/0.48 ((~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> (~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[383])).
% 0.19/0.48 tff(385,plain,
% 0.19/0.48 (((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))) <=> ((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(386,plain,
% 0.19/0.48 (((~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(387,plain,
% 0.19/0.48 (((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | ((~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[386])).
% 0.19/0.48 tff(388,plain,
% 0.19/0.48 (((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | ((~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[387, 385])).
% 0.19/0.48 tff(389,plain,
% 0.19/0.48 ((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | ((~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(390,plain,
% 0.19/0.48 ((~![Y1: $i] : ((~(point_1_on_line(Y1) = point_2_on_line(Y1))) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.19/0.48 tff(391,plain,
% 0.19/0.48 (~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[390, 186, 100])).
% 0.19/0.48 tff(392,plain,
% 0.19/0.48 (~(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_1_on_line(at_least_one_line))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[391, 384])).
% 0.19/0.48 tff(393,plain,
% 0.19/0.48 (((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(394,plain,
% 0.19/0.48 ((on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) <=> ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(395,plain,
% 0.19/0.48 (((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | ((~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[394])).
% 0.19/0.48 tff(396,plain,
% 0.19/0.48 (((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))) <=> ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[395, 393])).
% 0.19/0.48 tff(397,plain,
% 0.19/0.48 ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(398,plain,
% 0.19/0.48 ((~![Y1: $i] : (on(point_1_on_line(Y1), Y1) | (~line(Y1)))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.19/0.48 tff(399,plain,
% 0.19/0.48 (on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[398, 29, 100])).
% 0.19/0.48 tff(400,plain,
% 0.19/0.48 (((~![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_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(line_from_to(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_1_on_line(line_from_to(point_1_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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | (line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)) = line_from_to(point_1_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))) | (~line(line_from_to(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(line_from_to(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_1_on_line(line_from_to(point_1_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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | (line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)) = line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(401,plain,
% 0.19/0.48 (((~point(point_1_on_line(at_least_one_line))) | (~line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_1_on_line(line_from_to(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_1_on_line(line_from_to(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)) = line_from_to(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_1_on_line(line_from_to(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_1_on_line(line_from_to(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(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(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_1_on_line(at_least_one_line))) | (~line(line_from_to(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(line_from_to(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_1_on_line(line_from_to(point_1_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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | (line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)) = line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(402,plain,
% 0.19/0.49 (((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_1_on_line(line_from_to(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_1_on_line(line_from_to(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)) = line_from_to(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_1_on_line(line_from_to(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_1_on_line(line_from_to(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(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_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_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(line_from_to(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_1_on_line(line_from_to(point_1_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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | (line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)) = line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[401])).
% 0.19/0.49 tff(403,plain,
% 0.19/0.49 (((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_1_on_line(line_from_to(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_1_on_line(line_from_to(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)) = line_from_to(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_1_on_line(line_from_to(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_1_on_line(line_from_to(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(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_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_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(line_from_to(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_1_on_line(line_from_to(point_1_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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | (line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)) = line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[402, 400])).
% 0.19/0.49 tff(404,plain,
% 0.19/0.49 ((~![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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~line(line_from_to(point_1_on_line(line_from_to(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_1_on_line(line_from_to(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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)) = line_from_to(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_1_on_line(line_from_to(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_1_on_line(line_from_to(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(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(405,plain,
% 0.19/0.49 ((~![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_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) | (point_1_on_line(line_from_to(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_1_on_line(line_from_to(point_1_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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))) | (line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)) = line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.19/0.49 tff(406,plain,
% 0.19/0.49 (line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)) = line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[405, 155, 52, 270, 100, 83, 399, 392, 295, 289, 279])).
% 0.19/0.49 tff(407,plain,
% 0.19/0.49 (line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)) = line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line))),
% 0.19/0.49 inference(symmetry,[status(thm)],[406])).
% 0.19/0.49 tff(408,plain,
% 0.19/0.49 (on(point_2_on_line(at_least_one_line), line_from_to(point_1_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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[407])).
% 0.19/0.49 tff(409,plain,
% 0.19/0.49 (on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(line_from_to(point_1_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.49 inference(symmetry,[status(thm)],[408])).
% 0.19/0.49 tff(410,plain,
% 0.19/0.49 (((~![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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), 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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(411,plain,
% 0.19/0.49 ((~![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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(412,plain,
% 0.19/0.49 ((~![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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.19/0.49 tff(413,plain,
% 0.19/0.49 ((~point(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))) | (point_1_on_line(line_from_to(point_1_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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[412, 121, 179])).
% 0.19/0.49 tff(414,plain,
% 0.19/0.49 ((point_1_on_line(line_from_to(point_1_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_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[413, 270])).
% 0.19/0.49 tff(415,plain,
% 0.19/0.49 (on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), point_2_on_line(at_least_one_line)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[414, 258])).
% 0.19/0.49 tff(416,plain,
% 0.19/0.49 (on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[415, 409])).
% 0.19/0.49 tff(417,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[307, 416])).
% 0.19/0.49 tff(418,plain,(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) = point_2_on_line(at_least_one_line)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(419,plain,
% 0.19/0.49 (on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_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_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[418])).
% 0.19/0.49 tff(420,plain,
% 0.19/0.49 (on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))) <=> on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.49 inference(symmetry,[status(thm)],[419])).
% 0.19/0.49 tff(421,plain,
% 0.19/0.49 ((~on(point_2_on_line(at_least_one_line), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))) <=> (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[420])).
% 0.19/0.49 tff(422,plain,
% 0.19/0.49 (~on(point_1_on_line(line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line))), line_from_to(point_1_on_line(at_least_one_line), point_not_on_line(at_least_one_line)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[307, 421])).
% 0.19/0.49 tff(423,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[399, 422])).
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------