%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GEO257+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 16 20:36:08 EDT 2022

% Result   : Theorem 0.20s 0.44s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO257+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Aug 31 07:08:46 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  % SZS output start Proof
% 0.20/0.44  tff(left_apart_point_type, type, (
% 0.20/0.44     left_apart_point: ( $i * $i ) > $o)).
% 0.20/0.44  tff(reverse_line_type, type, (
% 0.20/0.44     reverse_line: $i > $i)).
% 0.20/0.44  tff(line_connecting_type, type, (
% 0.20/0.44     line_connecting: ( $i * $i ) > $i)).
% 0.20/0.44  tff(tptp_fun_C_1_type, type, (
% 0.20/0.44     tptp_fun_C_1: $i)).
% 0.20/0.44  tff(tptp_fun_A_3_type, type, (
% 0.20/0.44     tptp_fun_A_3: $i)).
% 0.20/0.44  tff(tptp_fun_D_0_type, type, (
% 0.20/0.44     tptp_fun_D_0: $i)).
% 0.20/0.44  tff(distinct_lines_type, type, (
% 0.20/0.44     distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.44  tff(tptp_fun_L_4_type, type, (
% 0.20/0.44     tptp_fun_L_4: $i)).
% 0.20/0.44  tff(tptp_fun_B_2_type, type, (
% 0.20/0.44     tptp_fun_B_2: $i)).
% 0.20/0.44  tff(right_apart_point_type, type, (
% 0.20/0.44     right_apart_point: ( $i * $i ) > $o)).
% 0.20/0.44  tff(apart_point_and_line_type, type, (
% 0.20/0.44     apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.44  tff(distinct_points_type, type, (
% 0.20/0.44     distinct_points: ( $i * $i ) > $o)).
% 0.20/0.44  tff(incident_point_and_line_type, type, (
% 0.20/0.44     incident_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.44  tff(before_on_line_type, type, (
% 0.20/0.44     before_on_line: ( $i * $i * $i ) > $o)).
% 0.20/0.44  tff(equally_directed_lines_type, type, (
% 0.20/0.44     equally_directed_lines: ( $i * $i ) > $o)).
% 0.20/0.44  tff(unequally_directed_lines_type, type, (
% 0.20/0.44     unequally_directed_lines: ( $i * $i ) > $o)).
% 0.20/0.44  tff(1,assumption,(left_apart_point(A!3, L!4) | left_apart_point(A!3, reverse_line(L!4))), introduced(assumption)).
% 0.20/0.44  tff(2,plain,
% 0.20/0.44      (^[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)))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(3,plain,
% 0.20/0.44      (![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))))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[2])).
% 0.20/0.44  tff(4,plain,
% 0.20/0.44      (![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))))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  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')).
% 0.20/0.44  tff(6,plain,
% 0.20/0.44      (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.44  tff(7,plain,(
% 0.20/0.44      ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.20/0.44      inference(skolemize,[status(sab)],[6])).
% 0.20/0.44  tff(8,plain,
% 0.20/0.44      (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.44  tff(9,plain,
% 0.20/0.44      ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(A!3, L!4) | left_apart_point(A!3, reverse_line(L!4))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(10,plain,
% 0.20/0.44      ($false),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.44  tff(11,plain,(~(left_apart_point(A!3, L!4) | left_apart_point(A!3, reverse_line(L!4)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44  tff(12,plain,
% 0.20/0.44      ((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)))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(13,plain,
% 0.20/0.44      (~left_apart_point(A!3, reverse_line(L!4))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.44  tff(14,plain,
% 0.20/0.44      ((left_apart_point(A!3, L!4) | left_apart_point(A!3, reverse_line(L!4))) | (~left_apart_point(A!3, L!4))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(15,plain,
% 0.20/0.44      (~left_apart_point(A!3, L!4)),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[14, 11])).
% 0.20/0.44  tff(16,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)).
% 0.20/0.44  tff(17,plain,
% 0.20/0.44      ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1)))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(18,plain,
% 0.20/0.44      ($false),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[17, 8, 16])).
% 0.20/0.44  tff(19,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,[]))).
% 0.20/0.44  tff(20,plain,
% 0.20/0.44      ((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))))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(21,plain,
% 0.20/0.44      (~left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1)))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.44  tff(22,plain,
% 0.20/0.44      ((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)))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(23,plain,
% 0.20/0.44      (~left_apart_point(B!2, line_connecting(A!3, C!1))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[22, 19])).
% 0.20/0.44  tff(24,assumption,(left_apart_point(B!2, L!4) | left_apart_point(B!2, reverse_line(L!4))), introduced(assumption)).
% 0.20/0.44  tff(25,plain,
% 0.20/0.44      ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(B!2, L!4) | left_apart_point(B!2, reverse_line(L!4))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(26,plain,
% 0.20/0.44      ($false),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[25, 8, 24])).
% 0.20/0.44  tff(27,plain,(~(left_apart_point(B!2, L!4) | left_apart_point(B!2, reverse_line(L!4)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44  tff(28,plain,
% 0.20/0.44      ((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)))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(29,plain,
% 0.20/0.44      (~left_apart_point(B!2, reverse_line(L!4))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.44  tff(30,plain,
% 0.20/0.44      ((left_apart_point(B!2, L!4) | left_apart_point(B!2, reverse_line(L!4))) | (~left_apart_point(B!2, L!4))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(31,plain,
% 0.20/0.44      (~left_apart_point(B!2, L!4)),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[30, 27])).
% 0.20/0.44  tff(32,plain,
% 0.20/0.44      (^[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))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(33,plain,
% 0.20/0.44      (![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)))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[32])).
% 0.20/0.44  tff(34,plain,
% 0.20/0.44      (![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)))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(35,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')).
% 0.20/0.44  tff(36,plain,
% 0.20/0.44      (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.44  tff(37,plain,(
% 0.20/0.44      ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.20/0.44      inference(skolemize,[status(sab)],[36])).
% 0.20/0.44  tff(38,plain,
% 0.20/0.44      (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.44  tff(39,plain,
% 0.20/0.44      ((~![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))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(40,plain,
% 0.20/0.44      (right_apart_point(A!3, line_connecting(A!3, C!1)) <=> left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1)))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.44  tff(41,plain,
% 0.20/0.44      (^[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))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(42,plain,
% 0.20/0.44      (![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)))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[41])).
% 0.20/0.44  tff(43,plain,
% 0.20/0.44      (![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)))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(44,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')).
% 0.20/0.44  tff(45,plain,
% 0.20/0.44      (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.44  tff(46,plain,(
% 0.20/0.44      ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.20/0.44      inference(skolemize,[status(sab)],[45])).
% 0.20/0.44  tff(47,plain,
% 0.20/0.44      (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.44  tff(48,plain,
% 0.20/0.44      ((~![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))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(49,plain,
% 0.20/0.44      (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)))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.44  tff(50,plain,
% 0.20/0.44      ((~(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)))))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(51,plain,
% 0.20/0.44      ((~![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)))))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(52,plain,
% 0.20/0.44      ((~![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)))))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(53,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/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.44  tff(54,plain,
% 0.20/0.44      (~![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))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.44  tff(55,plain,
% 0.20/0.44      (~![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))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[54, 51])).
% 0.20/0.44  tff(56,plain,
% 0.20/0.44      (~![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))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.44  tff(57,plain,
% 0.20/0.44      (~![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))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[56, 51])).
% 0.20/0.44  tff(58,plain,
% 0.20/0.44      (~![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))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[57, 51])).
% 0.20/0.44  tff(59,plain,
% 0.20/0.44      (~![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))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[58, 51])).
% 0.20/0.44  tff(60,plain,
% 0.20/0.44      (~![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))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[59, 51])).
% 0.20/0.44  tff(61,plain,(
% 0.20/0.44      ~(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))))),
% 0.20/0.44      inference(skolemize,[status(sab)],[60])).
% 0.20/0.44  tff(62,plain,
% 0.20/0.44      (~(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))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[61, 50])).
% 0.20/0.44  tff(63,plain,
% 0.20/0.44      (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)),
% 0.20/0.44      inference(or_elim,[status(thm)],[62])).
% 0.20/0.44  tff(64,plain,
% 0.20/0.44      (distinct_points(A!3, C!1)),
% 0.20/0.44      inference(and_elim,[status(thm)],[63])).
% 0.20/0.44  tff(65,plain,
% 0.20/0.44      (^[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))))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(66,plain,
% 0.20/0.44      (![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)))))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[65])).
% 0.20/0.44  tff(67,plain,
% 0.20/0.44      (^[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))))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(68,plain,
% 0.20/0.44      (![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)))))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[67])).
% 0.20/0.44  tff(69,plain,
% 0.20/0.44      (![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)))))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(70,plain,
% 0.20/0.44      (^[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))))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(71,plain,
% 0.20/0.44      (![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)))))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[70])).
% 0.20/0.44  tff(72,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')).
% 0.20/0.44  tff(73,plain,
% 0.20/0.44      (![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)))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.44  tff(74,plain,
% 0.20/0.44      (![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)))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.44  tff(75,plain,(
% 0.20/0.44      ![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)))))),
% 0.20/0.44      inference(skolemize,[status(sab)],[74])).
% 0.20/0.44  tff(76,plain,
% 0.20/0.44      (![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)))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[75, 68])).
% 0.20/0.44  tff(77,plain,
% 0.20/0.44      (![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)))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[76, 66])).
% 0.20/0.44  tff(78,plain,
% 0.20/0.44      (((~![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)))))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(79,plain,
% 0.20/0.44      ((~![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)))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(80,plain,
% 0.20/0.44      ((~![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))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.44  tff(81,plain,
% 0.20/0.44      (~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1)))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[80, 77, 64])).
% 0.20/0.45  tff(82,plain,
% 0.20/0.45      ((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)))),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(83,plain,
% 0.20/0.45      (~apart_point_and_line(A!3, line_connecting(A!3, C!1))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[82, 81])).
% 0.20/0.45  tff(84,plain,
% 0.20/0.45      ((~(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))))),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(85,plain,
% 0.20/0.45      ((~(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))))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[84, 83])).
% 0.20/0.45  tff(86,plain,
% 0.20/0.45      (~(left_apart_point(A!3, line_connecting(A!3, C!1)) | right_apart_point(A!3, line_connecting(A!3, C!1)))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[85, 49])).
% 0.20/0.45  tff(87,plain,
% 0.20/0.45      ((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)))),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(88,plain,
% 0.20/0.45      (~right_apart_point(A!3, line_connecting(A!3, C!1))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[87, 86])).
% 0.20/0.45  tff(89,plain,
% 0.20/0.45      ((~(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))))),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(90,plain,
% 0.20/0.45      ((~(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))))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.45  tff(91,plain,
% 0.20/0.45      (~left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1)))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[90, 40])).
% 0.20/0.45  tff(92,assumption,(distinct_lines(L!4, line_connecting(A!3, C!1))), introduced(assumption)).
% 0.20/0.45  tff(93,plain,
% 0.20/0.45      ((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)))),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(94,plain,
% 0.20/0.45      (~left_apart_point(A!3, line_connecting(A!3, C!1))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[93, 86])).
% 0.20/0.45  tff(95,plain,
% 0.20/0.45      (^[L: $i, A: $i, B: $i] : refl((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)))))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(96,plain,
% 0.20/0.45      (![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))))))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[95])).
% 0.20/0.45  tff(97,plain,
% 0.20/0.45      (^[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)))))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(98,plain,
% 0.20/0.45      (![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))))))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[97])).
% 0.20/0.45  tff(99,plain,
% 0.20/0.45      (![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))))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(100,plain,
% 0.20/0.45      (^[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)))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(101,plain,
% 0.20/0.45      (![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))))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[100])).
% 0.20/0.45  tff(102,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')).
% 0.20/0.45  tff(103,plain,
% 0.20/0.45      (![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))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.45  tff(104,plain,
% 0.20/0.45      (![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))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[103, 99])).
% 0.20/0.45  tff(105,plain,(
% 0.20/0.45      ![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))))),
% 0.20/0.45      inference(skolemize,[status(sab)],[104])).
% 0.20/0.45  tff(106,plain,
% 0.20/0.45      (![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))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[105, 98])).
% 0.20/0.45  tff(107,plain,
% 0.20/0.45      (![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))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[106, 96])).
% 0.20/0.45  tff(108,plain,
% 0.20/0.45      ((~![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))))))) | (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))))))),
% 0.20/0.45      inference(quant_inst,[status(thm)],[])).
% 0.20/0.45  tff(109,plain,
% 0.20/0.45      (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)))))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.45  tff(110,plain,
% 0.20/0.45      (before_on_line(L!4, A!3, B!2) & before_on_line(L!4, B!2, C!1)),
% 0.20/0.45      inference(or_elim,[status(thm)],[62])).
% 0.20/0.45  tff(111,plain,
% 0.20/0.45      (before_on_line(L!4, A!3, B!2)),
% 0.20/0.45      inference(and_elim,[status(thm)],[110])).
% 0.20/0.45  tff(112,plain,
% 0.20/0.45      ((~(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)) | (~((~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)))))),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(113,plain,
% 0.20/0.45      ((~(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))))))) | (~((~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)))))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[112, 111])).
% 0.20/0.45  tff(114,plain,
% 0.20/0.45      (~((~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))))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[113, 109])).
% 0.20/0.45  tff(115,plain,
% 0.20/0.45      (((~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)),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(116,plain,
% 0.20/0.45      (distinct_points(A!3, B!2)),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[115, 114])).
% 0.20/0.45  tff(117,plain,
% 0.20/0.45      (^[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))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(118,plain,
% 0.20/0.45      (![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)))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[117])).
% 0.20/0.45  tff(119,plain,
% 0.20/0.45      (^[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)))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(120,plain,
% 0.20/0.45      (![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)))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[119])).
% 0.20/0.45  tff(121,plain,
% 0.20/0.45      (![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))))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(122,plain,
% 0.20/0.45      (^[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))))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(123,plain,
% 0.20/0.45      (![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))))),
% 0.20/0.46      inference(quant_intro,[status(thm)],[122])).
% 0.20/0.46  tff(124,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')).
% 0.20/0.46  tff(125,plain,
% 0.20/0.46      (![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))))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.46  tff(126,plain,
% 0.20/0.46      (![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))))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[125, 121])).
% 0.20/0.46  tff(127,plain,(
% 0.20/0.46      ![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))))),
% 0.20/0.46      inference(skolemize,[status(sab)],[126])).
% 0.20/0.46  tff(128,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[127, 120])).
% 0.20/0.46  tff(129,plain,
% 0.20/0.46      (![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)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[128, 118])).
% 0.20/0.46  tff(130,plain,
% 0.20/0.46      (((~![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(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(L!4)) | left_apart_point(A!3, 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(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(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(L!4)) | left_apart_point(A!3, 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))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(131,plain,
% 0.20/0.46      ((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(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(L!4)) | left_apart_point(A!3, 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))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(132,plain,
% 0.20/0.46      (((~![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(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(L!4)) | left_apart_point(A!3, 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)))),
% 0.20/0.46      inference(monotonicity,[status(thm)],[131])).
% 0.20/0.46  tff(133,plain,
% 0.20/0.46      (((~![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(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(L!4)) | left_apart_point(A!3, 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))),
% 0.20/0.46      inference(transitivity,[status(thm)],[132, 130])).
% 0.20/0.46  tff(134,plain,
% 0.20/0.46      ((~![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))))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(135,plain,
% 0.20/0.46      ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_points(A!3, B!2)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(B!2, line_connecting(A!3, C!1)) | left_apart_point(B!2, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_lines(L!4, line_connecting(A!3, C!1))) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4)),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.46  tff(136,plain,
% 0.20/0.46      ($false),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[135, 129, 116, 94, 92, 91, 31, 29, 23, 21, 15, 13])).
% 0.20/0.46  tff(137,plain,(~distinct_lines(L!4, line_connecting(A!3, C!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46  tff(138,plain,
% 0.20/0.46      (^[X: $i, Y: $i] : refl((equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))))),
% 0.20/0.46      inference(bind,[status(th)],[])).
% 0.20/0.46  tff(139,plain,
% 0.20/0.46      (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.20/0.46      inference(quant_intro,[status(thm)],[138])).
% 0.20/0.46  tff(140,plain,
% 0.20/0.46      (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(141,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')).
% 0.20/0.46  tff(142,plain,
% 0.20/0.46      (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.46  tff(143,plain,(
% 0.20/0.46      ![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.20/0.46      inference(skolemize,[status(sab)],[142])).
% 0.20/0.46  tff(144,plain,
% 0.20/0.46      (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[143, 139])).
% 0.20/0.46  tff(145,plain,
% 0.20/0.46      ((~![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))) | (equally_directed_lines(L!4, line_connecting(A!3, C!1)) <=> (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(146,plain,
% 0.20/0.46      (equally_directed_lines(L!4, line_connecting(A!3, C!1)) <=> (~unequally_directed_lines(L!4, line_connecting(A!3, C!1)))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[145, 144])).
% 0.20/0.46  tff(147,plain,
% 0.20/0.46      ((~![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))))))) | (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))))))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(148,plain,
% 0.20/0.46      (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)))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[147, 107])).
% 0.20/0.46  tff(149,plain,
% 0.20/0.46      (~before_on_line(L!4, A!3, C!1)),
% 0.20/0.46      inference(or_elim,[status(thm)],[62])).
% 0.20/0.46  tff(150,plain,
% 0.20/0.46      ((~(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) | ((~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))))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(151,plain,
% 0.20/0.46      ((~(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))))))) | ((~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))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[150, 149])).
% 0.20/0.46  tff(152,plain,
% 0.20/0.46      ((~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)))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[151, 148])).
% 0.20/0.46  tff(153,plain,
% 0.20/0.46      (((~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)),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(154,plain,
% 0.20/0.46      (incident_point_and_line(A!3, L!4)),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[153, 114])).
% 0.20/0.46  tff(155,plain,
% 0.20/0.46      (incident_point_and_line(C!1, L!4)),
% 0.20/0.46      inference(and_elim,[status(thm)],[63])).
% 0.20/0.46  tff(156,plain,
% 0.20/0.46      ((~((~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)))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(157,plain,
% 0.20/0.46      ((~((~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)))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[156, 64, 155])).
% 0.20/0.46  tff(158,plain,
% 0.20/0.46      (~equally_directed_lines(L!4, line_connecting(A!3, C!1))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[157, 154, 152])).
% 0.20/0.46  tff(159,plain,
% 0.20/0.46      ((~(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)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(160,plain,
% 0.20/0.47      ((~(equally_directed_lines(L!4, line_connecting(A!3, C!1)) <=> (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))))) | unequally_directed_lines(L!4, line_connecting(A!3, C!1))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[159, 158])).
% 0.20/0.47  tff(161,plain,
% 0.20/0.47      (unequally_directed_lines(L!4, line_connecting(A!3, C!1))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[160, 146])).
% 0.20/0.47  tff(162,plain,
% 0.20/0.47      (left_apart_point(D!0, L!4)),
% 0.20/0.47      inference(and_elim,[status(thm)],[63])).
% 0.20/0.47  tff(163,plain,
% 0.20/0.47      (^[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))))),
% 0.20/0.47      inference(bind,[status(th)],[])).
% 0.20/0.47  tff(164,plain,
% 0.20/0.47      (![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)))),
% 0.20/0.47      inference(quant_intro,[status(thm)],[163])).
% 0.20/0.47  tff(165,plain,
% 0.20/0.47      (^[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)))))),
% 0.20/0.47      inference(bind,[status(th)],[])).
% 0.20/0.47  tff(166,plain,
% 0.20/0.47      (![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)))),
% 0.20/0.47      inference(quant_intro,[status(thm)],[165])).
% 0.20/0.47  tff(167,plain,
% 0.20/0.47      (![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))))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(168,plain,
% 0.20/0.47      (^[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)))))),
% 0.20/0.47      inference(bind,[status(th)],[])).
% 0.20/0.47  tff(169,plain,
% 0.20/0.47      (![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))))),
% 0.20/0.47      inference(quant_intro,[status(thm)],[168])).
% 0.20/0.47  tff(170,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')).
% 0.20/0.47  tff(171,plain,
% 0.20/0.47      (![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))))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[170, 169])).
% 0.20/0.47  tff(172,plain,
% 0.20/0.47      (![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))))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[171, 167])).
% 0.20/0.47  tff(173,plain,(
% 0.20/0.47      ![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))))),
% 0.20/0.47      inference(skolemize,[status(sab)],[172])).
% 0.20/0.47  tff(174,plain,
% 0.20/0.47      (![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)))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[173, 166])).
% 0.20/0.47  tff(175,plain,
% 0.20/0.47      (![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)))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[174, 164])).
% 0.20/0.47  tff(176,plain,
% 0.20/0.47      (((~![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))))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(177,plain,
% 0.20/0.47      (((~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))))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(178,plain,
% 0.20/0.47      (((~![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)))))),
% 0.20/0.47      inference(monotonicity,[status(thm)],[177])).
% 0.20/0.47  tff(179,plain,
% 0.20/0.47      (((~![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))))),
% 0.20/0.47      inference(transitivity,[status(thm)],[178, 176])).
% 0.20/0.47  tff(180,plain,
% 0.20/0.47      ((~![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)))),
% 0.20/0.47      inference(quant_inst,[status(thm)],[])).
% 0.20/0.47  tff(181,plain,
% 0.20/0.47      ((~![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)))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[180, 179])).
% 0.20/0.47  tff(182,plain,
% 0.20/0.47      (distinct_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[181, 175, 162, 161])).
% 0.20/0.47  tff(183,plain,
% 0.20/0.47      (left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[182, 137])).
% 0.20/0.47  tff(184,plain,
% 0.20/0.47      ((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))))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(185,plain,
% 0.20/0.47      (left_apart_point(D!0, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[184, 183])).
% 0.20/0.47  tff(186,plain,
% 0.20/0.47      ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(D!0, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))))),
% 0.20/0.47      inference(quant_inst,[status(thm)],[])).
% 0.20/0.47  tff(187,plain,
% 0.20/0.47      ($false),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[186, 8, 185])).
% 0.20/0.47  % SZS output end Proof
%------------------------------------------------------------------------------