%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO256+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:06:09 AM UTC 2025
% Result : Theorem 0.38s 0.57s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO256+3 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n015.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu Jun 19 14:43:41 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.38/0.57 % SZS status Theorem
% 0.38/0.57 % SZS output start Proof
% 0.38/0.57 tff(left_apart_point_type, type, (
% 0.38/0.57 left_apart_point: ( $i * $i ) > $o)).
% 0.38/0.57 tff(line_connecting_type, type, (
% 0.38/0.57 line_connecting: ( $i * $i ) > $i)).
% 0.38/0.57 tff(tptp_fun_C_1_type, type, (
% 0.38/0.57 tptp_fun_C_1: $i)).
% 0.38/0.57 tff(tptp_fun_A_3_type, type, (
% 0.38/0.57 tptp_fun_A_3: $i)).
% 0.38/0.57 tff(tptp_fun_B_2_type, type, (
% 0.38/0.57 tptp_fun_B_2: $i)).
% 0.38/0.57 tff(reverse_line_type, type, (
% 0.38/0.57 reverse_line: $i > $i)).
% 0.38/0.57 tff(tptp_fun_L_4_type, type, (
% 0.38/0.57 tptp_fun_L_4: $i)).
% 0.38/0.57 tff(right_apart_point_type, type, (
% 0.38/0.57 right_apart_point: ( $i * $i ) > $o)).
% 0.38/0.57 tff(apart_point_and_line_type, type, (
% 0.38/0.57 apart_point_and_line: ( $i * $i ) > $o)).
% 0.38/0.57 tff(distinct_points_type, type, (
% 0.38/0.57 distinct_points: ( $i * $i ) > $o)).
% 0.38/0.57 tff(tptp_fun_D_0_type, type, (
% 0.38/0.57 tptp_fun_D_0: $i)).
% 0.38/0.57 tff(incident_point_and_line_type, type, (
% 0.38/0.57 incident_point_and_line: ( $i * $i ) > $o)).
% 0.38/0.57 tff(before_on_line_type, type, (
% 0.38/0.57 before_on_line: ( $i * $i * $i ) > $o)).
% 0.38/0.57 tff(distinct_lines_type, type, (
% 0.38/0.57 distinct_lines: ( $i * $i ) > $o)).
% 0.38/0.57 tff(unequally_directed_lines_type, type, (
% 0.38/0.57 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.38/0.57 tff(equally_directed_lines_type, type, (
% 0.38/0.57 equally_directed_lines: ( $i * $i ) > $o)).
% 0.38/0.57 tff(1,assumption,(left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1)))), introduced(assumption)).
% 0.38/0.57 tff(2,plain,
% 0.38/0.57 (^[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)))))),
% 0.38/0.57 inference(bind,[status(th)],[])).
% 0.38/0.57 tff(3,plain,
% 0.38/0.57 (![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))))),
% 0.38/0.57 inference(quant_intro,[status(thm)],[2])).
% 0.38/0.57 tff(4,plain,
% 0.38/0.57 (![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))))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(5,axiom,(![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax10_basics')).
% 0.38/0.57 tff(6,plain,
% 0.38/0.57 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.38/0.57 tff(7,plain,(
% 0.38/0.57 ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.38/0.57 inference(skolemize,[status(sab)],[6])).
% 0.38/0.57 tff(8,plain,
% 0.38/0.57 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.38/0.57 tff(9,plain,
% 0.38/0.57 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1)))))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(10,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.38/0.57 tff(11,plain,(~(left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(12,plain,
% 0.38/0.57 ((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, line_connecting(A!3, C!1)))),
% 0.38/0.57 inference(tautology,[status(thm)],[])).
% 0.38/0.57 tff(13,plain,
% 0.38/0.57 (~left_apart_point(B!2, line_connecting(A!3, C!1))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.38/0.57 tff(14,plain,
% 0.38/0.57 ((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(line_connecting(A!3, C!1))))),
% 0.38/0.57 inference(tautology,[status(thm)],[])).
% 0.38/0.57 tff(15,plain,
% 0.38/0.57 (~left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1)))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.38/0.57 tff(16,plain,
% 0.38/0.57 ((~![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))))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(17,plain,
% 0.38/0.57 (~(left_apart_point(B!2, L!4) | left_apart_point(B!2, reverse_line(L!4)))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[16, 8])).
% 0.38/0.57 tff(18,plain,
% 0.38/0.57 ((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)))),
% 0.38/0.57 inference(tautology,[status(thm)],[])).
% 0.38/0.57 tff(19,plain,
% 0.38/0.57 (~left_apart_point(B!2, reverse_line(L!4))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.38/0.57 tff(20,assumption,(left_apart_point(A!3, L!4) | left_apart_point(A!3, reverse_line(L!4))), introduced(assumption)).
% 0.38/0.57 tff(21,plain,
% 0.38/0.57 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(A!3, L!4) | left_apart_point(A!3, reverse_line(L!4))))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(22,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[21, 8, 20])).
% 0.38/0.57 tff(23,plain,(~(left_apart_point(A!3, L!4) | left_apart_point(A!3, reverse_line(L!4)))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(24,plain,
% 0.38/0.57 ((left_apart_point(A!3, L!4) | left_apart_point(A!3, reverse_line(L!4))) | (~left_apart_point(A!3, reverse_line(L!4)))),
% 0.38/0.57 inference(tautology,[status(thm)],[])).
% 0.38/0.57 tff(25,plain,
% 0.38/0.57 (~left_apart_point(A!3, reverse_line(L!4))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.38/0.57 tff(26,plain,
% 0.38/0.57 ((left_apart_point(A!3, L!4) | left_apart_point(A!3, reverse_line(L!4))) | (~left_apart_point(A!3, L!4))),
% 0.38/0.57 inference(tautology,[status(thm)],[])).
% 0.38/0.57 tff(27,plain,
% 0.38/0.57 (~left_apart_point(A!3, L!4)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[26, 23])).
% 0.38/0.57 tff(28,plain,
% 0.38/0.57 ((left_apart_point(B!2, L!4) | left_apart_point(B!2, reverse_line(L!4))) | (~left_apart_point(B!2, L!4))),
% 0.38/0.57 inference(tautology,[status(thm)],[])).
% 0.38/0.57 tff(29,plain,
% 0.38/0.57 (~left_apart_point(B!2, L!4)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[28, 17])).
% 0.38/0.57 tff(30,plain,
% 0.38/0.57 (^[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))))),
% 0.38/0.57 inference(bind,[status(th)],[])).
% 0.38/0.57 tff(31,plain,
% 0.38/0.57 (![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)))),
% 0.38/0.57 inference(quant_intro,[status(thm)],[30])).
% 0.38/0.57 tff(32,plain,
% 0.38/0.57 (![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)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(33,axiom,(![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a2_defns')).
% 0.38/0.57 tff(34,plain,
% 0.38/0.57 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.38/0.57 tff(35,plain,(
% 0.38/0.57 ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.38/0.57 inference(skolemize,[status(sab)],[34])).
% 0.38/0.57 tff(36,plain,
% 0.38/0.57 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.38/0.57 tff(37,plain,
% 0.38/0.57 ((~![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))))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(38,plain,
% 0.38/0.57 (right_apart_point(A!3, line_connecting(A!3, C!1)) <=> left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1)))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.38/0.57 tff(39,plain,
% 0.38/0.57 (^[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))))),
% 0.38/0.57 inference(bind,[status(th)],[])).
% 0.38/0.57 tff(40,plain,
% 0.38/0.57 (![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)))),
% 0.38/0.57 inference(quant_intro,[status(thm)],[39])).
% 0.38/0.57 tff(41,plain,
% 0.38/0.57 (![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)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(42,axiom,(![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a6_defns')).
% 0.38/0.57 tff(43,plain,
% 0.38/0.57 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.38/0.57 tff(44,plain,(
% 0.38/0.57 ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.38/0.57 inference(skolemize,[status(sab)],[43])).
% 0.38/0.57 tff(45,plain,
% 0.38/0.57 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.38/0.57 tff(46,plain,
% 0.38/0.57 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))) | (apart_point_and_line(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))))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(47,plain,
% 0.38/0.57 (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)))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.38/0.57 tff(48,plain,
% 0.38/0.57 ((~(before_on_line(L!4, C!1, B!2) | before_on_line(L!4, A!3, C!1) | (~before_on_line(L!4, A!3, B!2)) | (~(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, C!1, B!2) | before_on_line(L!4, A!3, C!1) | (~before_on_line(L!4, A!3, B!2)) | (~(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)))))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(49,plain,
% 0.38/0.57 ((~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, C, B) | before_on_line(L, A, C) | (~before_on_line(L, A, B)) | (~(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, C, B) | before_on_line(L, A, C) | (~before_on_line(L, A, B)) | (~(distinct_points(A, C) & distinct_points(B, C) & incident_point_and_line(C, L) & left_apart_point(D, L)))))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(50,plain,
% 0.38/0.57 ((~![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, A, C) | before_on_line(L, C, B))))) <=> (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, C, B) | before_on_line(L, A, C) | (~before_on_line(L, A, B)) | (~(distinct_points(A, C) & distinct_points(B, C) & incident_point_and_line(C, L) & left_apart_point(D, L)))))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(51,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, A, C) | before_on_line(L, C, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.38/0.57 tff(52,plain,
% 0.38/0.57 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, C, B) | before_on_line(L, A, C) | (~before_on_line(L, A, B)) | (~(distinct_points(A, C) & distinct_points(B, C) & incident_point_and_line(C, L) & left_apart_point(D, L))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.38/0.57 tff(53,plain,
% 0.38/0.57 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, C, B) | before_on_line(L, A, C) | (~before_on_line(L, A, B)) | (~(distinct_points(A, C) & distinct_points(B, C) & incident_point_and_line(C, L) & left_apart_point(D, L))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[52, 49])).
% 0.38/0.57 tff(54,plain,
% 0.38/0.57 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, C, B) | before_on_line(L, A, C) | (~before_on_line(L, A, B)) | (~(distinct_points(A, C) & distinct_points(B, C) & incident_point_and_line(C, L) & left_apart_point(D, L))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.38/0.57 tff(55,plain,
% 0.38/0.57 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, C, B) | before_on_line(L, A, C) | (~before_on_line(L, A, B)) | (~(distinct_points(A, C) & distinct_points(B, C) & incident_point_and_line(C, L) & left_apart_point(D, L))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[54, 49])).
% 0.38/0.57 tff(56,plain,(
% 0.38/0.57 ~(before_on_line(L!4, C!1, B!2) | before_on_line(L!4, A!3, C!1) | (~before_on_line(L!4, A!3, B!2)) | (~(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))))),
% 0.38/0.57 inference(skolemize,[status(sab)],[55])).
% 0.38/0.57 tff(57,plain,
% 0.38/0.57 (~(before_on_line(L!4, C!1, B!2) | before_on_line(L!4, A!3, C!1) | (~before_on_line(L!4, A!3, B!2)) | (~(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))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[56, 48])).
% 0.38/0.57 tff(58,plain,
% 0.38/0.57 (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)),
% 0.38/0.57 inference(or_elim,[status(thm)],[57])).
% 0.38/0.57 tff(59,plain,
% 0.38/0.57 (distinct_points(A!3, C!1)),
% 0.38/0.57 inference(and_elim,[status(thm)],[58])).
% 0.38/0.57 tff(60,plain,
% 0.38/0.57 (^[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))))))),
% 0.38/0.57 inference(bind,[status(th)],[])).
% 0.38/0.57 tff(61,plain,
% 0.38/0.57 (![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)))))),
% 0.38/0.57 inference(quant_intro,[status(thm)],[60])).
% 0.38/0.57 tff(62,plain,
% 0.38/0.57 (^[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))))))),
% 0.38/0.57 inference(bind,[status(th)],[])).
% 0.38/0.57 tff(63,plain,
% 0.38/0.57 (![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)))))),
% 0.38/0.57 inference(quant_intro,[status(thm)],[62])).
% 0.38/0.57 tff(64,plain,
% 0.38/0.57 (![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)))))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(65,plain,
% 0.38/0.57 (^[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))))))),
% 0.38/0.57 inference(bind,[status(th)],[])).
% 0.38/0.57 tff(66,plain,
% 0.38/0.57 (![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)))))),
% 0.38/0.57 inference(quant_intro,[status(thm)],[65])).
% 0.38/0.57 tff(67,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/sandbox/benchmark/Axioms/GEO009+0.ax','ax5_cons_objs')).
% 0.38/0.57 tff(68,plain,
% 0.38/0.57 (![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)))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.38/0.57 tff(69,plain,
% 0.38/0.57 (![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)))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.38/0.57 tff(70,plain,(
% 0.38/0.57 ![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)))))),
% 0.38/0.57 inference(skolemize,[status(sab)],[69])).
% 0.38/0.57 tff(71,plain,
% 0.38/0.57 (![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)))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.38/0.57 tff(72,plain,
% 0.38/0.57 (![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)))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.38/0.57 tff(73,plain,
% 0.38/0.57 (((~![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)))))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(74,plain,
% 0.38/0.57 ((~![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)))))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(75,plain,
% 0.38/0.57 ((~![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))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.38/0.57 tff(76,plain,
% 0.38/0.57 (~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1)))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[75, 72, 59])).
% 0.38/0.57 tff(77,plain,
% 0.38/0.57 ((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)))),
% 0.38/0.57 inference(tautology,[status(thm)],[])).
% 0.38/0.57 tff(78,plain,
% 0.38/0.57 (~apart_point_and_line(A!3, line_connecting(A!3, C!1))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.38/0.57 tff(79,plain,
% 0.38/0.57 ((~(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))))),
% 0.38/0.57 inference(tautology,[status(thm)],[])).
% 0.38/0.57 tff(80,plain,
% 0.38/0.57 ((~(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))))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.38/0.57 tff(81,plain,
% 0.38/0.57 (~(left_apart_point(A!3, line_connecting(A!3, C!1)) | right_apart_point(A!3, line_connecting(A!3, C!1)))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[80, 47])).
% 0.38/0.57 tff(82,plain,
% 0.38/0.57 ((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)))),
% 0.38/0.57 inference(tautology,[status(thm)],[])).
% 0.38/0.57 tff(83,plain,
% 0.38/0.57 (~right_apart_point(A!3, line_connecting(A!3, C!1))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.38/0.57 tff(84,plain,
% 0.38/0.57 ((~(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))))),
% 0.38/0.57 inference(tautology,[status(thm)],[])).
% 0.38/0.57 tff(85,plain,
% 0.38/0.57 ((~(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))))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.38/0.57 tff(86,plain,
% 0.38/0.57 (~left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1)))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[85, 38])).
% 0.38/0.57 tff(87,assumption,(left_apart_point(D!0, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))), introduced(assumption)).
% 0.38/0.57 tff(88,plain,
% 0.38/0.57 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(D!0, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(89,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[88, 8, 87])).
% 0.38/0.57 tff(90,plain,(~(left_apart_point(D!0, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(91,plain,
% 0.38/0.57 ((left_apart_point(D!0, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))) | (~left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))))),
% 0.38/0.57 inference(tautology,[status(thm)],[])).
% 0.38/0.57 tff(92,plain,
% 0.38/0.57 (~left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.38/0.57 tff(93,plain,
% 0.38/0.57 (^[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))))),
% 0.38/0.57 inference(bind,[status(th)],[])).
% 0.38/0.57 tff(94,plain,
% 0.38/0.57 (![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)))),
% 0.38/0.57 inference(quant_intro,[status(thm)],[93])).
% 0.38/0.57 tff(95,plain,
% 0.38/0.57 (![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)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(96,plain,
% 0.38/0.57 (^[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)))))),
% 0.38/0.57 inference(bind,[status(th)],[])).
% 0.38/0.57 tff(97,plain,
% 0.38/0.57 (![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)))),
% 0.38/0.57 inference(quant_intro,[status(thm)],[96])).
% 0.38/0.57 tff(98,axiom,(![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a4_defns')).
% 0.38/0.57 tff(99,plain,
% 0.38/0.57 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.38/0.57 tff(100,plain,
% 0.38/0.57 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.38/0.57 tff(101,plain,(
% 0.38/0.57 ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.38/0.57 inference(skolemize,[status(sab)],[100])).
% 0.38/0.57 tff(102,plain,
% 0.38/0.57 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.38/0.57 tff(103,plain,
% 0.38/0.57 ((~![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))))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(104,plain,
% 0.38/0.57 (~(unequally_directed_lines(L!4, line_connecting(A!3, C!1)) <=> equally_directed_lines(L!4, line_connecting(A!3, C!1)))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.38/0.57 tff(105,plain,
% 0.38/0.57 (^[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))))),
% 0.38/0.57 inference(bind,[status(th)],[])).
% 0.38/0.57 tff(106,plain,
% 0.38/0.57 (![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)))),
% 0.38/0.57 inference(quant_intro,[status(thm)],[105])).
% 0.38/0.57 tff(107,plain,
% 0.38/0.57 (^[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)))))),
% 0.38/0.57 inference(bind,[status(th)],[])).
% 0.38/0.57 tff(108,plain,
% 0.38/0.57 (![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)))),
% 0.38/0.57 inference(quant_intro,[status(thm)],[107])).
% 0.38/0.57 tff(109,plain,
% 0.38/0.57 (![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))))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(110,plain,
% 0.38/0.57 (^[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)))))),
% 0.38/0.57 inference(bind,[status(th)],[])).
% 0.38/0.57 tff(111,plain,
% 0.38/0.57 (![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))))),
% 0.38/0.57 inference(quant_intro,[status(thm)],[110])).
% 0.38/0.57 tff(112,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/sandbox/benchmark/Axioms/GEO009+0.ax','ax4_defns')).
% 0.38/0.57 tff(113,plain,
% 0.38/0.57 (![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))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.38/0.57 tff(114,plain,
% 0.38/0.57 (![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))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.38/0.57 tff(115,plain,(
% 0.38/0.57 ![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))))),
% 0.38/0.57 inference(skolemize,[status(sab)],[114])).
% 0.38/0.57 tff(116,plain,
% 0.38/0.57 (![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)))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.38/0.57 tff(117,plain,
% 0.38/0.57 (![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)))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[116, 106])).
% 0.38/0.57 tff(118,plain,
% 0.38/0.57 ((~![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)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(119,plain,
% 0.38/0.58 (~(((~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))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.38/0.58 tff(120,plain,
% 0.38/0.58 (~before_on_line(L!4, A!3, C!1)),
% 0.38/0.58 inference(or_elim,[status(thm)],[57])).
% 0.38/0.58 tff(121,plain,
% 0.38/0.58 ((((~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)),
% 0.38/0.58 inference(tautology,[status(thm)],[])).
% 0.38/0.58 tff(122,plain,
% 0.38/0.58 ((((~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))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.38/0.58 tff(123,plain,
% 0.38/0.58 ((~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)))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[122, 119])).
% 0.38/0.58 tff(124,plain,
% 0.38/0.58 ((~![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)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(125,plain,
% 0.38/0.58 (~(((~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))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[124, 117])).
% 0.38/0.58 tff(126,plain,
% 0.38/0.58 (before_on_line(L!4, A!3, B!2)),
% 0.38/0.58 inference(or_elim,[status(thm)],[57])).
% 0.38/0.58 tff(127,plain,
% 0.38/0.58 ((((~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))),
% 0.38/0.58 inference(tautology,[status(thm)],[])).
% 0.38/0.58 tff(128,plain,
% 0.38/0.58 ((((~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)))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.38/0.58 tff(129,plain,
% 0.38/0.58 (~((~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))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[128, 125])).
% 0.38/0.58 tff(130,plain,
% 0.38/0.58 (((~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)),
% 0.38/0.58 inference(tautology,[status(thm)],[])).
% 0.38/0.58 tff(131,plain,
% 0.38/0.58 (incident_point_and_line(A!3, L!4)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.38/0.58 tff(132,plain,
% 0.38/0.58 (incident_point_and_line(C!1, L!4)),
% 0.38/0.58 inference(and_elim,[status(thm)],[58])).
% 0.38/0.58 tff(133,plain,
% 0.38/0.58 ((~((~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)))),
% 0.38/0.58 inference(tautology,[status(thm)],[])).
% 0.38/0.58 tff(134,plain,
% 0.38/0.58 ((~((~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)))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[133, 59, 132])).
% 0.38/0.58 tff(135,plain,
% 0.38/0.58 (~equally_directed_lines(L!4, line_connecting(A!3, C!1))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[134, 131, 123])).
% 0.38/0.58 tff(136,plain,
% 0.38/0.58 ((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))),
% 0.38/0.58 inference(tautology,[status(thm)],[])).
% 0.38/0.58 tff(137,plain,
% 0.38/0.58 ((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))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.38/0.58 tff(138,plain,
% 0.38/0.58 (unequally_directed_lines(L!4, line_connecting(A!3, C!1))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[137, 104])).
% 0.38/0.58 tff(139,plain,
% 0.38/0.58 (left_apart_point(D!0, L!4)),
% 0.38/0.58 inference(and_elim,[status(thm)],[58])).
% 0.38/0.58 tff(140,plain,
% 0.38/0.58 (^[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))))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(141,plain,
% 0.38/0.58 (![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)))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[140])).
% 0.38/0.58 tff(142,plain,
% 0.38/0.58 (^[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)))))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(143,plain,
% 0.38/0.58 (![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)))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[142])).
% 0.38/0.58 tff(144,plain,
% 0.38/0.58 (![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))))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(145,plain,
% 0.38/0.58 (^[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)))))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(146,plain,
% 0.38/0.58 (![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))))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[145])).
% 0.38/0.58 tff(147,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/sandbox/benchmark/Axioms/GEO009+0.ax','ax2_subs')).
% 0.38/0.58 tff(148,plain,
% 0.38/0.58 (![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))))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.38/0.58 tff(149,plain,
% 0.38/0.58 (![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))))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.38/0.58 tff(150,plain,(
% 0.38/0.58 ![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))))),
% 0.38/0.58 inference(skolemize,[status(sab)],[149])).
% 0.38/0.58 tff(151,plain,
% 0.38/0.58 (![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)))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.38/0.58 tff(152,plain,
% 0.38/0.58 (![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)))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[151, 141])).
% 0.38/0.58 tff(153,plain,
% 0.38/0.58 (((~![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))))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(154,plain,
% 0.38/0.58 (((~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))))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(155,plain,
% 0.38/0.58 (((~![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)))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[154])).
% 0.38/0.58 tff(156,plain,
% 0.38/0.58 (((~![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))))),
% 0.38/0.58 inference(transitivity,[status(thm)],[155, 153])).
% 0.38/0.58 tff(157,plain,
% 0.38/0.58 ((~![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)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(158,plain,
% 0.38/0.58 ((~![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)))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.38/0.58 tff(159,plain,
% 0.38/0.58 (distinct_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[158, 152, 139, 138])).
% 0.38/0.58 tff(160,plain,
% 0.38/0.58 (distinct_lines(L!4, line_connecting(A!3, C!1))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[159, 92])).
% 0.38/0.58 tff(161,plain,
% 0.38/0.58 ((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)))),
% 0.38/0.58 inference(tautology,[status(thm)],[])).
% 0.38/0.58 tff(162,plain,
% 0.38/0.58 (~left_apart_point(A!3, line_connecting(A!3, C!1))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[161, 81])).
% 0.38/0.58 tff(163,plain,
% 0.38/0.58 (((~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)))) | distinct_points(A!3, B!2)),
% 0.38/0.58 inference(tautology,[status(thm)],[])).
% 0.38/0.58 tff(164,plain,
% 0.38/0.58 (distinct_points(A!3, B!2)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[163, 129])).
% 0.38/0.58 tff(165,plain,
% 0.38/0.58 (^[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))))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(166,plain,
% 0.38/0.58 (![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)))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[165])).
% 0.38/0.58 tff(167,plain,
% 0.38/0.58 (^[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)))))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(168,plain,
% 0.38/0.58 (![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)))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[167])).
% 0.38/0.58 tff(169,plain,
% 0.38/0.58 (![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))))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(170,plain,
% 0.38/0.58 (^[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))))))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(171,plain,
% 0.38/0.58 (![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))))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[170])).
% 0.38/0.58 tff(172,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/sandbox/benchmark/Axioms/GEO009+0.ax','ax1_uniq_cons')).
% 0.38/0.58 tff(173,plain,
% 0.38/0.58 (![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))))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.38/0.58 tff(174,plain,
% 0.38/0.58 (![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))))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.38/0.58 tff(175,plain,(
% 0.38/0.58 ![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))))),
% 0.38/0.58 inference(skolemize,[status(sab)],[174])).
% 0.38/0.58 tff(176,plain,
% 0.38/0.58 (![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)))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.38/0.58 tff(177,plain,
% 0.38/0.58 (![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)))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[176, 166])).
% 0.38/0.58 tff(178,plain,
% 0.38/0.58 (((~![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, B!2)) | left_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, L!4) | left_apart_point(A!3, reverse_line(L!4)) | (~distinct_lines(L!4, 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, line_connecting(A!3, C!1)) | 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(A!3, B!2)) | left_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, L!4) | left_apart_point(A!3, reverse_line(L!4)) | (~distinct_lines(L!4, 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, line_connecting(A!3, C!1)) | left_apart_point(B!2, L!4))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(179,plain,
% 0.38/0.58 ((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(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(B!2, L!4) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, B!2)) | (~distinct_lines(L!4, line_connecting(A!3, C!1)))) <=> ((~distinct_points(A!3, B!2)) | left_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, L!4) | left_apart_point(A!3, reverse_line(L!4)) | (~distinct_lines(L!4, 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, line_connecting(A!3, C!1)) | left_apart_point(B!2, L!4))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(180,plain,
% 0.38/0.58 (((~![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(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(B!2, L!4) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, B!2)) | (~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(A!3, B!2)) | left_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, L!4) | left_apart_point(A!3, reverse_line(L!4)) | (~distinct_lines(L!4, 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, line_connecting(A!3, C!1)) | left_apart_point(B!2, L!4)))),
% 0.38/0.59 inference(monotonicity,[status(thm)],[179])).
% 0.38/0.59 tff(181,plain,
% 0.38/0.59 (((~![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(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(B!2, L!4) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, B!2)) | (~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(A!3, B!2)) | left_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, L!4) | left_apart_point(A!3, reverse_line(L!4)) | (~distinct_lines(L!4, 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, line_connecting(A!3, C!1)) | left_apart_point(B!2, L!4))),
% 0.38/0.59 inference(transitivity,[status(thm)],[180, 178])).
% 0.38/0.59 tff(182,plain,
% 0.38/0.59 ((~![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(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(B!2, L!4) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, B!2)) | (~distinct_lines(L!4, line_connecting(A!3, C!1))))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(183,plain,
% 0.38/0.59 ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_points(A!3, B!2)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(A!3, L!4) | left_apart_point(A!3, reverse_line(L!4)) | (~distinct_lines(L!4, line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, L!4)),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.38/0.59 tff(184,plain,
% 0.38/0.59 (left_apart_point(A!3, L!4) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, L!4)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[183, 177, 164, 162, 160, 86])).
% 0.38/0.59 tff(185,plain,
% 0.38/0.59 (left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, line_connecting(A!3, C!1))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[184, 29, 27, 25, 19])).
% 0.38/0.59 tff(186,plain,
% 0.38/0.59 ($false),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[185, 15, 13])).
% 0.38/0.59 % SZS output end Proof
% 0.38/0.59 % E exiting
%------------------------------------------------------------------------------