%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO257+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:06:10 AM UTC 2025
% Result : Theorem 0.19s 0.57s
% Output : Proof 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO257+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 14:43:21 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.57 % SZS status Theorem
% 0.19/0.57 % SZS output start Proof
% 0.19/0.57 tff(left_apart_point_type, type, (
% 0.19/0.57 left_apart_point: ( $i * $i ) > $o)).
% 0.19/0.57 tff(tptp_fun_L_4_type, type, (
% 0.19/0.57 tptp_fun_L_4: $i)).
% 0.19/0.57 tff(tptp_fun_B_2_type, type, (
% 0.19/0.57 tptp_fun_B_2: $i)).
% 0.19/0.57 tff(reverse_line_type, type, (
% 0.19/0.57 reverse_line: $i > $i)).
% 0.19/0.57 tff(line_connecting_type, type, (
% 0.19/0.57 line_connecting: ( $i * $i ) > $i)).
% 0.19/0.57 tff(tptp_fun_C_1_type, type, (
% 0.19/0.57 tptp_fun_C_1: $i)).
% 0.19/0.57 tff(tptp_fun_A_3_type, type, (
% 0.19/0.57 tptp_fun_A_3: $i)).
% 0.19/0.57 tff(distinct_lines_type, type, (
% 0.19/0.57 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.57 tff(right_apart_point_type, type, (
% 0.19/0.57 right_apart_point: ( $i * $i ) > $o)).
% 0.19/0.57 tff(apart_point_and_line_type, type, (
% 0.19/0.57 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.57 tff(distinct_points_type, type, (
% 0.19/0.57 distinct_points: ( $i * $i ) > $o)).
% 0.19/0.57 tff(tptp_fun_D_0_type, type, (
% 0.19/0.57 tptp_fun_D_0: $i)).
% 0.19/0.57 tff(incident_point_and_line_type, type, (
% 0.19/0.57 incident_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.57 tff(before_on_line_type, type, (
% 0.19/0.57 before_on_line: ( $i * $i * $i ) > $o)).
% 0.19/0.57 tff(unequally_directed_lines_type, type, (
% 0.19/0.57 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.19/0.57 tff(equally_directed_lines_type, type, (
% 0.19/0.57 equally_directed_lines: ( $i * $i ) > $o)).
% 0.19/0.57 tff(1,plain,
% 0.19/0.57 (^[A: $i, L: $i] : refl((~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(2,plain,
% 0.19/0.57 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.57 tff(3,plain,
% 0.19/0.57 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(4,axiom,(![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax10_basics')).
% 0.19/0.57 tff(5,plain,
% 0.19/0.57 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.57 tff(6,plain,(
% 0.19/0.57 ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.19/0.57 inference(skolemize,[status(sab)],[5])).
% 0.19/0.57 tff(7,plain,
% 0.19/0.57 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.57 tff(8,plain,
% 0.19/0.57 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(B!2, L!4) | left_apart_point(B!2, reverse_line(L!4))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(9,plain,
% 0.19/0.57 (~(left_apart_point(B!2, L!4) | left_apart_point(B!2, reverse_line(L!4)))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.57 tff(10,plain,
% 0.19/0.57 ((left_apart_point(B!2, L!4) | left_apart_point(B!2, reverse_line(L!4))) | (~left_apart_point(B!2, L!4))),
% 0.19/0.57 inference(tautology,[status(thm)],[])).
% 0.19/0.57 tff(11,plain,
% 0.19/0.57 (~left_apart_point(B!2, L!4)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.19/0.57 tff(12,plain,
% 0.19/0.57 ((left_apart_point(B!2, L!4) | left_apart_point(B!2, reverse_line(L!4))) | (~left_apart_point(B!2, reverse_line(L!4)))),
% 0.19/0.57 inference(tautology,[status(thm)],[])).
% 0.19/0.57 tff(13,plain,
% 0.19/0.57 (~left_apart_point(B!2, reverse_line(L!4))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[12, 9])).
% 0.19/0.57 tff(14,assumption,(left_apart_point(B!2, line_connecting(C!1, A!3)) | left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3)))), introduced(assumption)).
% 0.19/0.57 tff(15,plain,
% 0.19/0.57 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(B!2, line_connecting(C!1, A!3)) | left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3)))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(16,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[15, 7, 14])).
% 0.19/0.57 tff(17,plain,(~(left_apart_point(B!2, line_connecting(C!1, A!3)) | left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(18,plain,
% 0.19/0.57 ((left_apart_point(B!2, line_connecting(C!1, A!3)) | left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3)))) | (~left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3))))),
% 0.19/0.57 inference(tautology,[status(thm)],[])).
% 0.19/0.57 tff(19,plain,
% 0.19/0.57 (~left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3)))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.57 tff(20,assumption,(distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))), introduced(assumption)).
% 0.19/0.57 tff(21,assumption,(left_apart_point(A!3, line_connecting(C!1, A!3)) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3)))), introduced(assumption)).
% 0.19/0.57 tff(22,plain,
% 0.19/0.57 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(A!3, line_connecting(C!1, A!3)) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3)))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(23,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[22, 7, 21])).
% 0.19/0.57 tff(24,plain,(~(left_apart_point(A!3, line_connecting(C!1, A!3)) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(25,plain,
% 0.19/0.57 ((left_apart_point(A!3, line_connecting(C!1, A!3)) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3)))) | (~left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3))))),
% 0.19/0.57 inference(tautology,[status(thm)],[])).
% 0.19/0.57 tff(26,plain,
% 0.19/0.57 (~left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3)))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.19/0.57 tff(27,plain,
% 0.19/0.57 ((left_apart_point(A!3, line_connecting(C!1, A!3)) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3)))) | (~left_apart_point(A!3, line_connecting(C!1, A!3)))),
% 0.19/0.57 inference(tautology,[status(thm)],[])).
% 0.19/0.57 tff(28,plain,
% 0.19/0.57 (~left_apart_point(A!3, line_connecting(C!1, A!3))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.19/0.57 tff(29,assumption,(left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3)))), introduced(assumption)).
% 0.19/0.57 tff(30,plain,
% 0.19/0.57 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3)))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(31,plain,
% 0.19/0.57 ($false),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[30, 7, 29])).
% 0.19/0.57 tff(32,plain,(~(left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.57 tff(33,plain,
% 0.19/0.57 ((left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3)))) | (~left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3))))),
% 0.19/0.57 inference(tautology,[status(thm)],[])).
% 0.19/0.57 tff(34,plain,
% 0.19/0.57 (~left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3)))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.57 tff(35,plain,
% 0.19/0.57 ((left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3)))) | (~left_apart_point(C!1, line_connecting(C!1, A!3)))),
% 0.19/0.57 inference(tautology,[status(thm)],[])).
% 0.19/0.57 tff(36,plain,
% 0.19/0.57 (~left_apart_point(C!1, line_connecting(C!1, A!3))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.19/0.57 tff(37,plain,
% 0.19/0.57 (^[X: $i, Y: $i] : refl((right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(38,plain,
% 0.19/0.57 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.57 tff(39,plain,
% 0.19/0.57 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(40,axiom,(![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a2_defns')).
% 0.19/0.57 tff(41,plain,
% 0.19/0.57 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.57 tff(42,plain,(
% 0.19/0.57 ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.19/0.57 inference(skolemize,[status(sab)],[41])).
% 0.19/0.57 tff(43,plain,
% 0.19/0.57 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.57 tff(44,plain,
% 0.19/0.57 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(C!1, line_connecting(A!3, C!1)) <=> left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(45,plain,
% 0.19/0.57 (right_apart_point(C!1, line_connecting(A!3, C!1)) <=> left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1)))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.57 tff(46,plain,
% 0.19/0.57 (^[A: $i, L: $i] : refl((apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))) <=> (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(47,plain,
% 0.19/0.57 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.57 tff(48,plain,
% 0.19/0.57 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(49,axiom,(![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a6_defns')).
% 0.19/0.57 tff(50,plain,
% 0.19/0.57 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.57 tff(51,plain,(
% 0.19/0.57 ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.19/0.57 inference(skolemize,[status(sab)],[50])).
% 0.19/0.57 tff(52,plain,
% 0.19/0.57 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.57 tff(53,plain,
% 0.19/0.57 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))) | (apart_point_and_line(C!1, line_connecting(A!3, C!1)) <=> (left_apart_point(C!1, line_connecting(A!3, C!1)) | right_apart_point(C!1, line_connecting(A!3, C!1))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(54,plain,
% 0.19/0.57 (apart_point_and_line(C!1, line_connecting(A!3, C!1)) <=> (left_apart_point(C!1, line_connecting(A!3, C!1)) | right_apart_point(C!1, line_connecting(A!3, C!1)))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.57 tff(55,plain,
% 0.19/0.57 ((~(before_on_line(L!4, A!3, C!1) | (~(before_on_line(L!4, A!3, B!2) & before_on_line(L!4, B!2, C!1))) | (~(distinct_points(A!3, C!1) & distinct_points(B!2, C!1) & incident_point_and_line(C!1, L!4) & left_apart_point(D!0, L!4))))) <=> (~(before_on_line(L!4, A!3, C!1) | (~(before_on_line(L!4, A!3, B!2) & before_on_line(L!4, B!2, C!1))) | (~(distinct_points(A!3, C!1) & distinct_points(B!2, C!1) & incident_point_and_line(C!1, L!4) & left_apart_point(D!0, L!4)))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(56,plain,
% 0.19/0.57 ((~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & incident_point_and_line(C, L) & left_apart_point(D, L))))) <=> (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & incident_point_and_line(C, L) & left_apart_point(D, L)))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(57,plain,
% 0.19/0.58 ((~![L: $i, A: $i, B: $i, C: $i, D: $i] : ((((distinct_points(A, C) & distinct_points(B, C)) & incident_point_and_line(C, L)) & left_apart_point(D, L)) => ((before_on_line(L, A, B) & before_on_line(L, B, C)) => before_on_line(L, A, C)))) <=> (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & incident_point_and_line(C, L) & left_apart_point(D, L)))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(58,axiom,(~![L: $i, A: $i, B: $i, C: $i, D: $i] : ((((distinct_points(A, C) & distinct_points(B, C)) & incident_point_and_line(C, L)) & left_apart_point(D, L)) => ((before_on_line(L, A, B) & before_on_line(L, B, C)) => before_on_line(L, A, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.58 tff(59,plain,
% 0.19/0.58 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & incident_point_and_line(C, L) & left_apart_point(D, L))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.58 tff(60,plain,
% 0.19/0.58 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & incident_point_and_line(C, L) & left_apart_point(D, L))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[59, 56])).
% 0.19/0.58 tff(61,plain,
% 0.19/0.58 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & incident_point_and_line(C, L) & left_apart_point(D, L))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.19/0.58 tff(62,plain,
% 0.19/0.58 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & incident_point_and_line(C, L) & left_apart_point(D, L))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[61, 56])).
% 0.19/0.58 tff(63,plain,(
% 0.19/0.58 ~(before_on_line(L!4, A!3, C!1) | (~(before_on_line(L!4, A!3, B!2) & before_on_line(L!4, B!2, C!1))) | (~(distinct_points(A!3, C!1) & distinct_points(B!2, C!1) & incident_point_and_line(C!1, L!4) & left_apart_point(D!0, L!4))))),
% 0.19/0.58 inference(skolemize,[status(sab)],[62])).
% 0.19/0.58 tff(64,plain,
% 0.19/0.58 (~(before_on_line(L!4, A!3, C!1) | (~(before_on_line(L!4, A!3, B!2) & before_on_line(L!4, B!2, C!1))) | (~(distinct_points(A!3, C!1) & distinct_points(B!2, C!1) & incident_point_and_line(C!1, L!4) & left_apart_point(D!0, L!4))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[63, 55])).
% 0.19/0.58 tff(65,plain,
% 0.19/0.58 (distinct_points(A!3, C!1) & distinct_points(B!2, C!1) & incident_point_and_line(C!1, L!4) & left_apart_point(D!0, L!4)),
% 0.19/0.58 inference(or_elim,[status(thm)],[64])).
% 0.19/0.58 tff(66,plain,
% 0.19/0.58 (distinct_points(A!3, C!1)),
% 0.19/0.58 inference(and_elim,[status(thm)],[65])).
% 0.19/0.58 tff(67,plain,
% 0.19/0.58 (^[A: $i, B: $i] : refl(((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B))))) <=> ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B))))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(68,plain,
% 0.19/0.58 (![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B))))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.58 tff(69,plain,
% 0.19/0.58 (^[A: $i, B: $i] : rewrite(((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B))))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(70,plain,
% 0.19/0.58 (![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.58 tff(71,plain,
% 0.19/0.58 (![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(72,plain,
% 0.19/0.58 (^[A: $i, B: $i] : rewrite((distinct_points(A, B) => ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(73,plain,
% 0.19/0.58 (![A: $i, B: $i] : (distinct_points(A, B) => ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.58 tff(74,axiom,(![A: $i, B: $i] : (distinct_points(A, B) => ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax5_cons_objs')).
% 0.19/0.58 tff(75,plain,
% 0.19/0.58 (![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.58 tff(76,plain,
% 0.19/0.58 (![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.19/0.58 tff(77,plain,(
% 0.19/0.58 ![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.19/0.58 inference(skolemize,[status(sab)],[76])).
% 0.19/0.58 tff(78,plain,
% 0.19/0.58 (![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.19/0.58 tff(79,plain,
% 0.19/0.58 (![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.19/0.58 tff(80,plain,
% 0.19/0.58 (((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | ((~distinct_points(A!3, C!1)) | (~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1)))))) <=> ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | (~distinct_points(A!3, C!1)) | (~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1)))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(81,plain,
% 0.19/0.58 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | ((~distinct_points(A!3, C!1)) | (~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1)))))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(82,plain,
% 0.19/0.58 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | (~distinct_points(A!3, C!1)) | (~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.58 tff(83,plain,
% 0.19/0.58 (~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1)))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[82, 79, 66])).
% 0.19/0.58 tff(84,plain,
% 0.19/0.58 ((apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1))) | (~apart_point_and_line(C!1, line_connecting(A!3, C!1)))),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(85,plain,
% 0.19/0.58 (~apart_point_and_line(C!1, line_connecting(A!3, C!1))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.58 tff(86,plain,
% 0.19/0.58 ((~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) <=> (left_apart_point(C!1, line_connecting(A!3, C!1)) | right_apart_point(C!1, line_connecting(A!3, C!1))))) | apart_point_and_line(C!1, line_connecting(A!3, C!1)) | (~(left_apart_point(C!1, line_connecting(A!3, C!1)) | right_apart_point(C!1, line_connecting(A!3, C!1))))),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(87,plain,
% 0.19/0.58 ((~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) <=> (left_apart_point(C!1, line_connecting(A!3, C!1)) | right_apart_point(C!1, line_connecting(A!3, C!1))))) | (~(left_apart_point(C!1, line_connecting(A!3, C!1)) | right_apart_point(C!1, line_connecting(A!3, C!1))))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.58 tff(88,plain,
% 0.19/0.58 (~(left_apart_point(C!1, line_connecting(A!3, C!1)) | right_apart_point(C!1, line_connecting(A!3, C!1)))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[87, 54])).
% 0.19/0.58 tff(89,plain,
% 0.19/0.58 ((left_apart_point(C!1, line_connecting(A!3, C!1)) | right_apart_point(C!1, line_connecting(A!3, C!1))) | (~right_apart_point(C!1, line_connecting(A!3, C!1)))),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(90,plain,
% 0.19/0.58 (~right_apart_point(C!1, line_connecting(A!3, C!1))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.19/0.58 tff(91,plain,
% 0.19/0.58 ((~(right_apart_point(C!1, line_connecting(A!3, C!1)) <=> left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))))) | right_apart_point(C!1, line_connecting(A!3, C!1)) | (~left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))))),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(92,plain,
% 0.19/0.58 ((~(right_apart_point(C!1, line_connecting(A!3, C!1)) <=> left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))))) | (~left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.58 tff(93,plain,
% 0.19/0.58 (~left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1)))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[92, 45])).
% 0.19/0.58 tff(94,plain,
% 0.19/0.58 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(A!3, line_connecting(A!3, C!1)) <=> left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(95,plain,
% 0.19/0.58 (right_apart_point(A!3, line_connecting(A!3, C!1)) <=> left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1)))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[94, 43])).
% 0.19/0.58 tff(96,plain,
% 0.19/0.58 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))) | (apart_point_and_line(A!3, line_connecting(A!3, C!1)) <=> (left_apart_point(A!3, line_connecting(A!3, C!1)) | right_apart_point(A!3, line_connecting(A!3, C!1))))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(97,plain,
% 0.19/0.58 (apart_point_and_line(A!3, line_connecting(A!3, C!1)) <=> (left_apart_point(A!3, line_connecting(A!3, C!1)) | right_apart_point(A!3, line_connecting(A!3, C!1)))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[96, 52])).
% 0.19/0.58 tff(98,plain,
% 0.19/0.58 ((apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1))) | (~apart_point_and_line(A!3, line_connecting(A!3, C!1)))),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(99,plain,
% 0.19/0.58 (~apart_point_and_line(A!3, line_connecting(A!3, C!1))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[98, 83])).
% 0.19/0.58 tff(100,plain,
% 0.19/0.58 ((~(apart_point_and_line(A!3, line_connecting(A!3, C!1)) <=> (left_apart_point(A!3, line_connecting(A!3, C!1)) | right_apart_point(A!3, line_connecting(A!3, C!1))))) | apart_point_and_line(A!3, line_connecting(A!3, C!1)) | (~(left_apart_point(A!3, line_connecting(A!3, C!1)) | right_apart_point(A!3, line_connecting(A!3, C!1))))),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(101,plain,
% 0.19/0.58 ((~(apart_point_and_line(A!3, line_connecting(A!3, C!1)) <=> (left_apart_point(A!3, line_connecting(A!3, C!1)) | right_apart_point(A!3, line_connecting(A!3, C!1))))) | (~(left_apart_point(A!3, line_connecting(A!3, C!1)) | right_apart_point(A!3, line_connecting(A!3, C!1))))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.19/0.58 tff(102,plain,
% 0.19/0.58 (~(left_apart_point(A!3, line_connecting(A!3, C!1)) | right_apart_point(A!3, line_connecting(A!3, C!1)))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[101, 97])).
% 0.19/0.58 tff(103,plain,
% 0.19/0.58 ((left_apart_point(A!3, line_connecting(A!3, C!1)) | right_apart_point(A!3, line_connecting(A!3, C!1))) | (~right_apart_point(A!3, line_connecting(A!3, C!1)))),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(104,plain,
% 0.19/0.58 (~right_apart_point(A!3, line_connecting(A!3, C!1))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.19/0.58 tff(105,plain,
% 0.19/0.58 ((~(right_apart_point(A!3, line_connecting(A!3, C!1)) <=> left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))))) | right_apart_point(A!3, line_connecting(A!3, C!1)) | (~left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))))),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(106,plain,
% 0.19/0.58 ((~(right_apart_point(A!3, line_connecting(A!3, C!1)) <=> left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))))) | (~left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.58 tff(107,plain,
% 0.19/0.58 (~left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1)))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[106, 95])).
% 0.19/0.58 tff(108,plain,
% 0.19/0.58 ((left_apart_point(C!1, line_connecting(A!3, C!1)) | right_apart_point(C!1, line_connecting(A!3, C!1))) | (~left_apart_point(C!1, line_connecting(A!3, C!1)))),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(109,plain,
% 0.19/0.58 (~left_apart_point(C!1, line_connecting(A!3, C!1))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[108, 88])).
% 0.19/0.58 tff(110,plain,
% 0.19/0.58 ((left_apart_point(A!3, line_connecting(A!3, C!1)) | right_apart_point(A!3, line_connecting(A!3, C!1))) | (~left_apart_point(A!3, line_connecting(A!3, C!1)))),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(111,plain,
% 0.19/0.58 (~left_apart_point(A!3, line_connecting(A!3, C!1))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[110, 102])).
% 0.19/0.58 tff(112,plain,
% 0.19/0.58 (^[A: $i, B: $i, L: $i, M: $i] : refl((left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M))) <=> (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(113,plain,
% 0.19/0.58 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M))) <=> ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.58 tff(114,plain,
% 0.19/0.58 (^[A: $i, B: $i, L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(A, B) & distinct_lines(L, M)) <=> (~((~distinct_points(A, B)) | (~distinct_lines(L, M))))), ((~(distinct_points(A, B) & distinct_lines(L, M))) <=> (~(~((~distinct_points(A, B)) | (~distinct_lines(L, M))))))), rewrite((~(~((~distinct_points(A, B)) | (~distinct_lines(L, M))))) <=> ((~distinct_points(A, B)) | (~distinct_lines(L, M)))), ((~(distinct_points(A, B) & distinct_lines(L, M))) <=> ((~distinct_points(A, B)) | (~distinct_lines(L, M))))), ((left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M)))) <=> (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | ((~distinct_points(A, B)) | (~distinct_lines(L, M)))))), rewrite((left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | ((~distinct_points(A, B)) | (~distinct_lines(L, M)))) <=> (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))), ((left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M)))) <=> (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(115,plain,
% 0.19/0.58 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M)))) <=> ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[114])).
% 0.19/0.58 tff(116,plain,
% 0.19/0.58 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M)))) <=> ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(117,plain,
% 0.19/0.58 (^[A: $i, B: $i, L: $i, M: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((left_apart_point(A, L) | left_apart_point(B, L)) <=> (left_apart_point(B, L) | left_apart_point(A, L))), (((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) <=> ((left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, M)))), rewrite(((left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, M)) <=> (left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), (((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) <=> (left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), ((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) <=> ((left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, M)))), rewrite(((left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, M)) <=> (left_apart_point(B, M) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), ((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) <=> (left_apart_point(B, M) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), (((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) <=> ((left_apart_point(B, M) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, reverse_line(L))))), rewrite(((left_apart_point(B, M) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, reverse_line(L))) <=> (left_apart_point(B, M) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), (((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) <=> (left_apart_point(B, M) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), ((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) <=> ((left_apart_point(B, M) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, reverse_line(L))))), rewrite(((left_apart_point(B, M) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, reverse_line(L))) <=> (left_apart_point(B, M) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), ((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) <=> (left_apart_point(B, M) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) <=> ((left_apart_point(B, M) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, reverse_line(M))))), rewrite(((left_apart_point(B, M) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, reverse_line(M))) <=> (left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) <=> (left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), ((((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M))) <=> ((left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, reverse_line(M))))), rewrite(((left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, reverse_line(M))) <=> (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), ((((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M))) <=> (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), (((distinct_points(A, B) & distinct_lines(L, M)) => (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M)))) <=> ((distinct_points(A, B) & distinct_lines(L, M)) => (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))))), rewrite(((distinct_points(A, B) & distinct_lines(L, M)) => (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))) <=> (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))), (((distinct_points(A, B) & distinct_lines(L, M)) => (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M)))) <=> (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(118,plain,
% 0.19/0.58 (![A: $i, B: $i, L: $i, M: $i] : ((distinct_points(A, B) & distinct_lines(L, M)) => (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M)))) <=> ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[117])).
% 0.19/0.58 tff(119,axiom,(![A: $i, B: $i, L: $i, M: $i] : ((distinct_points(A, B) & distinct_lines(L, M)) => (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax1_uniq_cons')).
% 0.19/0.58 tff(120,plain,
% 0.19/0.58 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.58 tff(121,plain,
% 0.19/0.58 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.19/0.58 tff(122,plain,(
% 0.19/0.58 ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.19/0.58 inference(skolemize,[status(sab)],[121])).
% 0.19/0.58 tff(123,plain,
% 0.19/0.58 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.19/0.58 tff(124,plain,
% 0.19/0.58 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[123, 113])).
% 0.19/0.58 tff(125,plain,
% 0.19/0.58 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | ((~distinct_points(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(A!3, line_connecting(C!1, A!3)) | (~distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_points(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(A!3, line_connecting(C!1, A!3)) | (~distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(126,plain,
% 0.19/0.58 ((left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(A!3, line_connecting(C!1, A!3)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | (~distinct_points(A!3, C!1)) | (~distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)))) <=> ((~distinct_points(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(A!3, line_connecting(C!1, A!3)) | (~distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(127,plain,
% 0.19/0.58 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(A!3, line_connecting(C!1, A!3)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | (~distinct_points(A!3, C!1)) | (~distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | ((~distinct_points(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(A!3, line_connecting(C!1, A!3)) | (~distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)))))),
% 0.19/0.59 inference(monotonicity,[status(thm)],[126])).
% 0.19/0.59 tff(128,plain,
% 0.19/0.59 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(A!3, line_connecting(C!1, A!3)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | (~distinct_points(A!3, C!1)) | (~distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_points(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(A!3, line_connecting(C!1, A!3)) | (~distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))))),
% 0.19/0.59 inference(transitivity,[status(thm)],[127, 125])).
% 0.19/0.59 tff(129,plain,
% 0.19/0.59 ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(A!3, line_connecting(C!1, A!3)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | (~distinct_points(A!3, C!1)) | (~distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(130,plain,
% 0.19/0.59 ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_points(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(C!1, line_connecting(C!1, A!3)) | left_apart_point(A!3, reverse_line(line_connecting(C!1, A!3))) | left_apart_point(A!3, line_connecting(C!1, A!3)) | (~distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.59 tff(131,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[130, 124, 66, 111, 109, 107, 93, 36, 34, 28, 26, 20])).
% 0.19/0.59 tff(132,plain,(~distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.59 tff(133,assumption,(left_apart_point(B!2, line_connecting(A!3, C!1))), introduced(assumption)).
% 0.19/0.59 tff(134,plain,
% 0.19/0.59 (^[X: $i, Y: $i] : refl((~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))))),
% 0.19/0.59 inference(bind,[status(th)],[])).
% 0.19/0.59 tff(135,plain,
% 0.19/0.59 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.59 inference(quant_intro,[status(thm)],[134])).
% 0.19/0.59 tff(136,plain,
% 0.19/0.59 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(137,plain,
% 0.19/0.59 (^[X: $i, Y: $i] : trans(rewrite((equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))), rewrite((~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))), ((equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))))),
% 0.19/0.59 inference(bind,[status(th)],[])).
% 0.19/0.59 tff(138,plain,
% 0.19/0.59 (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.59 inference(quant_intro,[status(thm)],[137])).
% 0.19/0.59 tff(139,axiom,(![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a4_defns')).
% 0.19/0.59 tff(140,plain,
% 0.19/0.59 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.19/0.59 tff(141,plain,
% 0.19/0.59 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.19/0.59 tff(142,plain,(
% 0.19/0.59 ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.59 inference(skolemize,[status(sab)],[141])).
% 0.19/0.59 tff(143,plain,
% 0.19/0.59 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.19/0.59 tff(144,plain,
% 0.19/0.59 ((~![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))) | (~(unequally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3))) <=> equally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3)))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(145,plain,
% 0.19/0.59 (~(unequally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3))) <=> equally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.19/0.59 tff(146,plain,
% 0.19/0.59 (^[A: $i, B: $i] : refl(((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))))),
% 0.19/0.59 inference(bind,[status(th)],[])).
% 0.19/0.59 tff(147,plain,
% 0.19/0.59 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.19/0.59 inference(quant_intro,[status(thm)],[146])).
% 0.19/0.59 tff(148,plain,
% 0.19/0.59 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(149,plain,
% 0.19/0.59 (^[A: $i, B: $i] : rewrite((distinct_points(A, B) => equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))))),
% 0.19/0.59 inference(bind,[status(th)],[])).
% 0.19/0.59 tff(150,plain,
% 0.19/0.59 (![A: $i, B: $i] : (distinct_points(A, B) => equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.19/0.59 inference(quant_intro,[status(thm)],[149])).
% 0.19/0.59 tff(151,axiom,(![A: $i, B: $i] : (distinct_points(A, B) => equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax9_cons_objs')).
% 0.19/0.59 tff(152,plain,
% 0.19/0.59 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.59 tff(153,plain,
% 0.19/0.59 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.19/0.59 tff(154,plain,(
% 0.19/0.59 ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.19/0.59 inference(skolemize,[status(sab)],[153])).
% 0.19/0.59 tff(155,plain,
% 0.19/0.59 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.19/0.59 tff(156,plain,
% 0.19/0.59 (((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | ((~distinct_points(A!3, C!1)) | equally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3))))) <=> ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~distinct_points(A!3, C!1)) | equally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(157,plain,
% 0.19/0.59 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | ((~distinct_points(A!3, C!1)) | equally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(158,plain,
% 0.19/0.59 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~distinct_points(A!3, C!1)) | equally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.19/0.59 tff(159,plain,
% 0.19/0.59 (equally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3)))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[158, 155, 66])).
% 0.19/0.59 tff(160,plain,
% 0.19/0.59 ((unequally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3))) <=> equally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3)))) | (~unequally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3)))) | (~equally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3))))),
% 0.19/0.59 inference(tautology,[status(thm)],[])).
% 0.19/0.59 tff(161,plain,
% 0.19/0.59 ((unequally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3))) <=> equally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3)))) | (~unequally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3))))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.19/0.59 tff(162,plain,
% 0.19/0.59 (~unequally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3)))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[161, 145])).
% 0.19/0.59 tff(163,plain,
% 0.19/0.59 (^[L: $i, M: $i] : refl((unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.59 inference(bind,[status(th)],[])).
% 0.19/0.59 tff(164,plain,
% 0.19/0.59 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.59 inference(quant_intro,[status(thm)],[163])).
% 0.19/0.59 tff(165,plain,
% 0.19/0.59 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(166,axiom,(![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax8_basics')).
% 0.19/0.59 tff(167,plain,
% 0.19/0.59 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.59 tff(168,plain,(
% 0.19/0.59 ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.59 inference(skolemize,[status(sab)],[167])).
% 0.19/0.59 tff(169,plain,
% 0.19/0.59 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.19/0.59 tff(170,plain,
% 0.19/0.59 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)) | unequally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)) | unequally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(171,plain,
% 0.19/0.59 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)) | unequally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(172,plain,
% 0.19/0.59 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)) | unequally_directed_lines(line_connecting(A!3, C!1), reverse_line(line_connecting(C!1, A!3)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.19/0.59 tff(173,plain,
% 0.19/0.59 (unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[172, 169, 162])).
% 0.19/0.59 tff(174,plain,
% 0.19/0.59 (^[A: $i, L: $i, M: $i] : refl(((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L))) <=> ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L))))),
% 0.19/0.59 inference(bind,[status(th)],[])).
% 0.19/0.59 tff(175,plain,
% 0.19/0.59 (![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L))) <=> ![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))),
% 0.19/0.59 inference(quant_intro,[status(thm)],[174])).
% 0.19/0.59 tff(176,plain,
% 0.19/0.59 (^[A: $i, L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((left_apart_point(A, L) & unequally_directed_lines(L, M)) <=> (~((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M))))), ((~(left_apart_point(A, L) & unequally_directed_lines(L, M))) <=> (~(~((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M))))))), rewrite((~(~((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M))))) <=> ((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M)))), ((~(left_apart_point(A, L) & unequally_directed_lines(L, M))) <=> ((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M))))), ((distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M)))) <=> (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | ((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M)))))), rewrite((distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | ((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M)))) <=> ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))), ((distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M)))) <=> ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))))),
% 0.19/0.59 inference(bind,[status(th)],[])).
% 0.19/0.59 tff(177,plain,
% 0.19/0.59 (![A: $i, L: $i, M: $i] : (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M)))) <=> ![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))),
% 0.19/0.59 inference(quant_intro,[status(thm)],[176])).
% 0.19/0.59 tff(178,plain,
% 0.19/0.59 (![A: $i, L: $i, M: $i] : (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M)))) <=> ![A: $i, L: $i, M: $i] : (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(179,plain,
% 0.19/0.59 (^[A: $i, L: $i, M: $i] : rewrite(((left_apart_point(A, L) & unequally_directed_lines(L, M)) => (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)))) <=> (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M)))))),
% 0.19/0.59 inference(bind,[status(th)],[])).
% 0.19/0.59 tff(180,plain,
% 0.19/0.59 (![A: $i, L: $i, M: $i] : ((left_apart_point(A, L) & unequally_directed_lines(L, M)) => (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)))) <=> ![A: $i, L: $i, M: $i] : (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.19/0.59 inference(quant_intro,[status(thm)],[179])).
% 0.19/0.59 tff(181,axiom,(![A: $i, L: $i, M: $i] : ((left_apart_point(A, L) & unequally_directed_lines(L, M)) => (distinct_lines(L, M) | left_apart_point(A, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax2_subs')).
% 0.19/0.59 tff(182,plain,
% 0.19/0.59 (![A: $i, L: $i, M: $i] : (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.19/0.59 tff(183,plain,
% 0.19/0.59 (![A: $i, L: $i, M: $i] : (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[182, 178])).
% 0.19/0.59 tff(184,plain,(
% 0.19/0.59 ![A: $i, L: $i, M: $i] : (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.19/0.59 inference(skolemize,[status(sab)],[183])).
% 0.19/0.59 tff(185,plain,
% 0.19/0.59 (![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[184, 177])).
% 0.19/0.59 tff(186,plain,
% 0.19/0.59 (![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[185, 175])).
% 0.19/0.59 tff(187,plain,
% 0.19/0.59 (((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))) | (~left_apart_point(B!2, line_connecting(A!3, C!1))) | distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)) | left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3))))) <=> ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | (~unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))) | (~left_apart_point(B!2, line_connecting(A!3, C!1))) | distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)) | left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(188,plain,
% 0.19/0.59 (((~unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))) | distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)) | left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3))) | (~left_apart_point(B!2, line_connecting(A!3, C!1)))) <=> ((~unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))) | (~left_apart_point(B!2, line_connecting(A!3, C!1))) | distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)) | left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(189,plain,
% 0.19/0.59 (((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))) | distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)) | left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3))) | (~left_apart_point(B!2, line_connecting(A!3, C!1))))) <=> ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))) | (~left_apart_point(B!2, line_connecting(A!3, C!1))) | distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)) | left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3)))))),
% 0.19/0.59 inference(monotonicity,[status(thm)],[188])).
% 0.19/0.59 tff(190,plain,
% 0.19/0.59 (((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))) | distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)) | left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3))) | (~left_apart_point(B!2, line_connecting(A!3, C!1))))) <=> ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | (~unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))) | (~left_apart_point(B!2, line_connecting(A!3, C!1))) | distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)) | left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3))))),
% 0.19/0.59 inference(transitivity,[status(thm)],[189, 187])).
% 0.19/0.59 tff(191,plain,
% 0.19/0.59 ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))) | distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)) | left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3))) | (~left_apart_point(B!2, line_connecting(A!3, C!1))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(192,plain,
% 0.19/0.59 ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | (~unequally_directed_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3))) | (~left_apart_point(B!2, line_connecting(A!3, C!1))) | distinct_lines(line_connecting(A!3, C!1), line_connecting(C!1, A!3)) | left_apart_point(B!2, reverse_line(line_connecting(C!1, A!3)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.19/0.59 tff(193,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[192, 186, 173, 133, 132, 19])).
% 0.19/0.59 tff(194,plain,(~left_apart_point(B!2, line_connecting(A!3, C!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.59 tff(195,assumption,(left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(reverse_line(line_connecting(A!3, C!1))))), introduced(assumption)).
% 0.19/0.59 tff(196,plain,
% 0.19/0.59 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(reverse_line(line_connecting(A!3, C!1))))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(197,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[196, 7, 195])).
% 0.19/0.59 tff(198,plain,(~(left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(reverse_line(line_connecting(A!3, C!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.59 tff(199,plain,
% 0.19/0.59 ((left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(reverse_line(line_connecting(A!3, C!1))))) | (~left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))))),
% 0.19/0.59 inference(tautology,[status(thm)],[])).
% 0.19/0.59 tff(200,plain,
% 0.19/0.59 (~left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1)))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.19/0.59 tff(201,assumption,(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4))), introduced(assumption)).
% 0.19/0.59 tff(202,plain,
% 0.19/0.59 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(203,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[202, 7, 201])).
% 0.19/0.59 tff(204,plain,(~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.59 tff(205,plain,
% 0.19/0.59 ((left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4))) | (~left_apart_point(C!1, reverse_line(L!4)))),
% 0.19/0.59 inference(tautology,[status(thm)],[])).
% 0.19/0.59 tff(206,plain,
% 0.19/0.59 (~left_apart_point(C!1, reverse_line(L!4))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.19/0.59 tff(207,plain,
% 0.19/0.59 ((left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4))) | (~left_apart_point(C!1, L!4))),
% 0.19/0.59 inference(tautology,[status(thm)],[])).
% 0.19/0.59 tff(208,plain,
% 0.19/0.59 (~left_apart_point(C!1, L!4)),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[207, 204])).
% 0.19/0.59 tff(209,assumption,(left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(D!0, reverse_line(reverse_line(line_connecting(A!3, C!1))))), introduced(assumption)).
% 0.19/0.59 tff(210,plain,
% 0.19/0.59 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(D!0, reverse_line(reverse_line(line_connecting(A!3, C!1))))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(211,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[210, 7, 209])).
% 0.19/0.59 tff(212,plain,(~(left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(D!0, reverse_line(reverse_line(line_connecting(A!3, C!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.59 tff(213,plain,
% 0.19/0.59 ((left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(D!0, reverse_line(reverse_line(line_connecting(A!3, C!1))))) | (~left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))))),
% 0.19/0.59 inference(tautology,[status(thm)],[])).
% 0.19/0.59 tff(214,plain,
% 0.19/0.59 (~left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.19/0.59 tff(215,plain,
% 0.19/0.59 ((~![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))) | (~(unequally_directed_lines(L!4, line_connecting(A!3, C!1)) <=> equally_directed_lines(L!4, line_connecting(A!3, C!1))))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(216,plain,
% 0.19/0.59 (~(unequally_directed_lines(L!4, line_connecting(A!3, C!1)) <=> equally_directed_lines(L!4, line_connecting(A!3, C!1)))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[215, 143])).
% 0.19/0.59 tff(217,plain,
% 0.19/0.59 (^[L: $i, A: $i, B: $i] : refl((~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B))) <=> (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B))))),
% 0.19/0.59 inference(bind,[status(th)],[])).
% 0.19/0.59 tff(218,plain,
% 0.19/0.59 (![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B))) <=> ![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))),
% 0.19/0.59 inference(quant_intro,[status(thm)],[217])).
% 0.19/0.59 tff(219,plain,
% 0.19/0.59 (^[L: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))))), ((before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))) <=> (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))))))), rewrite((before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))))) <=> (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))), ((before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))) <=> (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B))))), rewrite((~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B))) <=> (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))), ((before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))) <=> (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))))),
% 0.19/0.59 inference(bind,[status(th)],[])).
% 0.19/0.59 tff(220,plain,
% 0.19/0.59 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))) <=> ![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))),
% 0.19/0.59 inference(quant_intro,[status(thm)],[219])).
% 0.19/0.59 tff(221,plain,
% 0.19/0.59 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(222,plain,
% 0.19/0.59 (^[L: $i, A: $i, B: $i] : rewrite((before_on_line(L, A, B) <=> (((distinct_points(A, B) & incident_point_and_line(A, L)) & incident_point_and_line(B, L)) & equally_directed_lines(L, line_connecting(A, B)))) <=> (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))))),
% 0.19/0.59 inference(bind,[status(th)],[])).
% 0.19/0.59 tff(223,plain,
% 0.19/0.59 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (((distinct_points(A, B) & incident_point_and_line(A, L)) & incident_point_and_line(B, L)) & equally_directed_lines(L, line_connecting(A, B)))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.19/0.59 inference(quant_intro,[status(thm)],[222])).
% 0.19/0.59 tff(224,axiom,(![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (((distinct_points(A, B) & incident_point_and_line(A, L)) & incident_point_and_line(B, L)) & equally_directed_lines(L, line_connecting(A, B))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax4_defns')).
% 0.19/0.59 tff(225,plain,
% 0.19/0.59 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.19/0.59 tff(226,plain,
% 0.19/0.59 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[225, 221])).
% 0.19/0.59 tff(227,plain,(
% 0.19/0.59 ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.19/0.59 inference(skolemize,[status(sab)],[226])).
% 0.19/0.59 tff(228,plain,
% 0.19/0.59 (![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[227, 220])).
% 0.19/0.59 tff(229,plain,
% 0.19/0.59 (![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[228, 218])).
% 0.19/0.59 tff(230,plain,
% 0.19/0.59 ((~![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(A!3, C!1)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(C!1, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, C!1)))) <=> before_on_line(L!4, A!3, C!1)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(231,plain,
% 0.19/0.59 (~(((~distinct_points(A!3, C!1)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(C!1, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, C!1)))) <=> before_on_line(L!4, A!3, C!1))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.19/0.60 tff(232,plain,
% 0.19/0.60 (~before_on_line(L!4, A!3, C!1)),
% 0.19/0.60 inference(or_elim,[status(thm)],[64])).
% 0.19/0.60 tff(233,plain,
% 0.19/0.60 ((((~distinct_points(A!3, C!1)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(C!1, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, C!1)))) <=> before_on_line(L!4, A!3, C!1)) | ((~distinct_points(A!3, C!1)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(C!1, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, C!1)))) | before_on_line(L!4, A!3, C!1)),
% 0.19/0.60 inference(tautology,[status(thm)],[])).
% 0.19/0.60 tff(234,plain,
% 0.19/0.60 ((((~distinct_points(A!3, C!1)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(C!1, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, C!1)))) <=> before_on_line(L!4, A!3, C!1)) | ((~distinct_points(A!3, C!1)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(C!1, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, C!1))))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.19/0.60 tff(235,plain,
% 0.19/0.60 ((~distinct_points(A!3, C!1)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(C!1, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, C!1)))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[234, 231])).
% 0.19/0.60 tff(236,plain,
% 0.19/0.60 ((~![L: $i, A: $i, B: $i] : (~(((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(A!3, B!2)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(B!2, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, B!2)))) <=> before_on_line(L!4, A!3, B!2)))),
% 0.19/0.60 inference(quant_inst,[status(thm)],[])).
% 0.19/0.60 tff(237,plain,
% 0.19/0.60 (~(((~distinct_points(A!3, B!2)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(B!2, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, B!2)))) <=> before_on_line(L!4, A!3, B!2))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[236, 229])).
% 0.19/0.60 tff(238,plain,
% 0.19/0.60 (before_on_line(L!4, A!3, B!2) & before_on_line(L!4, B!2, C!1)),
% 0.19/0.60 inference(or_elim,[status(thm)],[64])).
% 0.19/0.60 tff(239,plain,
% 0.19/0.60 (before_on_line(L!4, A!3, B!2)),
% 0.19/0.60 inference(and_elim,[status(thm)],[238])).
% 0.19/0.60 tff(240,plain,
% 0.19/0.60 ((((~distinct_points(A!3, B!2)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(B!2, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, B!2)))) <=> before_on_line(L!4, A!3, B!2)) | (~((~distinct_points(A!3, B!2)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(B!2, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, B!2))))) | (~before_on_line(L!4, A!3, B!2))),
% 0.19/0.60 inference(tautology,[status(thm)],[])).
% 0.19/0.60 tff(241,plain,
% 0.19/0.60 ((((~distinct_points(A!3, B!2)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(B!2, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, B!2)))) <=> before_on_line(L!4, A!3, B!2)) | (~((~distinct_points(A!3, B!2)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(B!2, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, B!2)))))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[240, 239])).
% 0.19/0.60 tff(242,plain,
% 0.19/0.60 (~((~distinct_points(A!3, B!2)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(B!2, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, B!2))))),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[241, 237])).
% 0.19/0.60 tff(243,plain,
% 0.19/0.60 (((~distinct_points(A!3, B!2)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(B!2, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, B!2)))) | incident_point_and_line(A!3, L!4)),
% 0.19/0.60 inference(tautology,[status(thm)],[])).
% 0.19/0.60 tff(244,plain,
% 0.19/0.60 (incident_point_and_line(A!3, L!4)),
% 0.19/0.60 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.19/0.60 tff(245,plain,
% 0.19/0.60 (incident_point_and_line(C!1, L!4)),
% 0.19/0.60 inference(and_elim,[status(thm)],[65])).
% 0.19/0.60 tff(246,plain,
% 0.19/0.60 ((~((~distinct_points(A!3, C!1)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(C!1, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, C!1))))) | (~distinct_points(A!3, C!1)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(C!1, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, C!1)))),
% 0.44/0.60 inference(tautology,[status(thm)],[])).
% 0.44/0.60 tff(247,plain,
% 0.44/0.60 ((~((~distinct_points(A!3, C!1)) | (~incident_point_and_line(A!3, L!4)) | (~incident_point_and_line(C!1, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, C!1))))) | (~incident_point_and_line(A!3, L!4)) | (~equally_directed_lines(L!4, line_connecting(A!3, C!1)))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[246, 66, 245])).
% 0.44/0.60 tff(248,plain,
% 0.44/0.60 (~equally_directed_lines(L!4, line_connecting(A!3, C!1))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[247, 244, 235])).
% 0.44/0.60 tff(249,plain,
% 0.44/0.60 ((unequally_directed_lines(L!4, line_connecting(A!3, C!1)) <=> equally_directed_lines(L!4, line_connecting(A!3, C!1))) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | equally_directed_lines(L!4, line_connecting(A!3, C!1))),
% 0.44/0.60 inference(tautology,[status(thm)],[])).
% 0.44/0.60 tff(250,plain,
% 0.44/0.60 ((unequally_directed_lines(L!4, line_connecting(A!3, C!1)) <=> equally_directed_lines(L!4, line_connecting(A!3, C!1))) | unequally_directed_lines(L!4, line_connecting(A!3, C!1))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.44/0.60 tff(251,plain,
% 0.44/0.60 (unequally_directed_lines(L!4, line_connecting(A!3, C!1))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[250, 216])).
% 0.44/0.60 tff(252,plain,
% 0.44/0.60 (left_apart_point(D!0, L!4)),
% 0.44/0.60 inference(and_elim,[status(thm)],[65])).
% 0.44/0.60 tff(253,plain,
% 0.44/0.60 (((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~left_apart_point(D!0, L!4)) | (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))))) <=> ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | (~left_apart_point(D!0, L!4)) | (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(254,plain,
% 0.44/0.60 (((~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | (~left_apart_point(D!0, L!4))) <=> ((~left_apart_point(D!0, L!4)) | (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(255,plain,
% 0.44/0.60 (((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | (~left_apart_point(D!0, L!4)))) <=> ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~left_apart_point(D!0, L!4)) | (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))))),
% 0.44/0.60 inference(monotonicity,[status(thm)],[254])).
% 0.44/0.60 tff(256,plain,
% 0.44/0.60 (((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | (~left_apart_point(D!0, L!4)))) <=> ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | (~left_apart_point(D!0, L!4)) | (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))))),
% 0.44/0.60 inference(transitivity,[status(thm)],[255, 253])).
% 0.44/0.60 tff(257,plain,
% 0.44/0.60 ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | (~left_apart_point(D!0, L!4)))),
% 0.44/0.60 inference(quant_inst,[status(thm)],[])).
% 0.44/0.60 tff(258,plain,
% 0.44/0.60 ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | (~left_apart_point(D!0, L!4)) | (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.44/0.60 tff(259,plain,
% 0.44/0.60 (distinct_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[258, 186, 252, 251])).
% 0.44/0.60 tff(260,plain,
% 0.44/0.60 (distinct_lines(L!4, line_connecting(A!3, C!1))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[259, 214])).
% 0.44/0.60 tff(261,plain,
% 0.44/0.60 (distinct_points(B!2, C!1)),
% 0.44/0.60 inference(and_elim,[status(thm)],[65])).
% 0.44/0.60 tff(262,plain,
% 0.44/0.60 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | ((~distinct_points(B!2, C!1)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(C!1, L!4) | (~distinct_lines(L!4, line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_points(B!2, C!1)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(C!1, L!4) | (~distinct_lines(L!4, line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(263,plain,
% 0.44/0.60 ((left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(C!1, L!4) | left_apart_point(B!2, L!4) | (~distinct_points(B!2, C!1)) | (~distinct_lines(L!4, line_connecting(A!3, C!1)))) <=> ((~distinct_points(B!2, C!1)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(C!1, L!4) | (~distinct_lines(L!4, line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(264,plain,
% 0.44/0.60 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(C!1, L!4) | left_apart_point(B!2, L!4) | (~distinct_points(B!2, C!1)) | (~distinct_lines(L!4, line_connecting(A!3, C!1))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | ((~distinct_points(B!2, C!1)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(C!1, L!4) | (~distinct_lines(L!4, line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4)))),
% 0.44/0.60 inference(monotonicity,[status(thm)],[263])).
% 0.44/0.60 tff(265,plain,
% 0.44/0.60 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(C!1, L!4) | left_apart_point(B!2, L!4) | (~distinct_points(B!2, C!1)) | (~distinct_lines(L!4, line_connecting(A!3, C!1))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_points(B!2, C!1)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(C!1, L!4) | (~distinct_lines(L!4, line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4))),
% 0.44/0.60 inference(transitivity,[status(thm)],[264, 262])).
% 0.44/0.60 tff(266,plain,
% 0.44/0.60 ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(C!1, L!4) | left_apart_point(B!2, L!4) | (~distinct_points(B!2, C!1)) | (~distinct_lines(L!4, line_connecting(A!3, C!1))))),
% 0.44/0.60 inference(quant_inst,[status(thm)],[])).
% 0.44/0.60 tff(267,plain,
% 0.44/0.60 ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_points(B!2, C!1)) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(C!1, L!4) | (~distinct_lines(L!4, line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4)),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.44/0.60 tff(268,plain,
% 0.44/0.60 (left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(C!1, L!4) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4)),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[267, 124, 261, 109, 260, 93])).
% 0.44/0.60 tff(269,plain,
% 0.44/0.60 (left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4)),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[268, 208, 206])).
% 0.44/0.60 tff(270,plain,
% 0.44/0.60 (left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4)),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[269, 200])).
% 0.44/0.60 tff(271,plain,
% 0.44/0.60 (left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4)),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[270, 194])).
% 0.44/0.60 tff(272,plain,
% 0.44/0.60 ($false),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[271, 13, 11])).
% 0.44/0.60 % SZS output end Proof
% 0.44/0.61 % E exiting
%------------------------------------------------------------------------------