%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GEO245+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n027.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 20:36:02 EDT 2022

% Result   : Theorem 0.20s 0.41s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO245+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n027.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 07:25:17 EDT 2022
% 0.13/0.35  % 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.
% 0.20/0.41  % SZS status Theorem
% 0.20/0.41  % SZS output start Proof
% 0.20/0.41  tff(left_apart_point_type, type, (
% 0.20/0.41     left_apart_point: ( $i * $i ) > $o)).
% 0.20/0.41  tff(line_connecting_type, type, (
% 0.20/0.41     line_connecting: ( $i * $i ) > $i)).
% 0.20/0.41  tff(tptp_fun_A_2_type, type, (
% 0.20/0.41     tptp_fun_A_2: $i)).
% 0.20/0.41  tff(tptp_fun_B_1_type, type, (
% 0.20/0.41     tptp_fun_B_1: $i)).
% 0.20/0.41  tff(right_apart_point_type, type, (
% 0.20/0.41     right_apart_point: ( $i * $i ) > $o)).
% 0.20/0.41  tff(apart_point_and_line_type, type, (
% 0.20/0.41     apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.41  tff(distinct_points_type, type, (
% 0.20/0.41     distinct_points: ( $i * $i ) > $o)).
% 0.20/0.41  tff(tptp_fun_C_0_type, type, (
% 0.20/0.41     tptp_fun_C_0: $i)).
% 0.20/0.41  tff(reverse_line_type, type, (
% 0.20/0.41     reverse_line: $i > $i)).
% 0.20/0.41  tff(distinct_lines_type, type, (
% 0.20/0.41     distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.41  tff(unequally_directed_lines_type, type, (
% 0.20/0.41     unequally_directed_lines: ( $i * $i ) > $o)).
% 0.20/0.41  tff(equally_directed_lines_type, type, (
% 0.20/0.41     equally_directed_lines: ( $i * $i ) > $o)).
% 0.20/0.41  tff(1,plain,
% 0.20/0.41      (^[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))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(2,plain,
% 0.20/0.41      (![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)))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41  tff(3,plain,
% 0.20/0.41      (![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)))),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(4,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')).
% 0.20/0.41  tff(5,plain,
% 0.20/0.41      (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.41  tff(6,plain,(
% 0.20/0.41      ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.20/0.41      inference(skolemize,[status(sab)],[5])).
% 0.20/0.41  tff(7,plain,
% 0.20/0.41      (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.41  tff(8,plain,
% 0.20/0.41      ((~![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!2, line_connecting(B!1, A!2)) <=> (left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2))))),
% 0.20/0.41      inference(quant_inst,[status(thm)],[])).
% 0.20/0.41  tff(9,plain,
% 0.20/0.41      (apart_point_and_line(A!2, line_connecting(B!1, A!2)) <=> (left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2)))),
% 0.20/0.41      inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.41  tff(10,assumption,(distinct_points(A!2, A!2)), introduced(assumption)).
% 0.20/0.41  tff(11,plain,
% 0.20/0.41      (^[A: $i] : refl((~distinct_points(A, A)) <=> (~distinct_points(A, A)))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(12,plain,
% 0.20/0.41      (![A: $i] : (~distinct_points(A, A)) <=> ![A: $i] : (~distinct_points(A, A))),
% 0.20/0.41      inference(quant_intro,[status(thm)],[11])).
% 0.20/0.41  tff(13,plain,
% 0.20/0.41      (![A: $i] : (~distinct_points(A, A)) <=> ![A: $i] : (~distinct_points(A, A))),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(14,axiom,(![A: $i] : (~distinct_points(A, A))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax1_basics')).
% 0.20/0.41  tff(15,plain,
% 0.20/0.41      (![A: $i] : (~distinct_points(A, A))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.41  tff(16,plain,(
% 0.20/0.41      ![A: $i] : (~distinct_points(A, A))),
% 0.20/0.41      inference(skolemize,[status(sab)],[15])).
% 0.20/0.41  tff(17,plain,
% 0.20/0.41      (![A: $i] : (~distinct_points(A, A))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.41  tff(18,plain,
% 0.20/0.41      ((~![A: $i] : (~distinct_points(A, A))) | (~distinct_points(A!2, A!2))),
% 0.20/0.41      inference(quant_inst,[status(thm)],[])).
% 0.20/0.41  tff(19,plain,
% 0.20/0.41      ($false),
% 0.20/0.41      inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 0.20/0.41  tff(20,plain,(~distinct_points(A!2, A!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41  tff(21,assumption,(~distinct_points(A!2, A!2)), introduced(assumption)).
% 0.20/0.41  tff(22,assumption,(~distinct_points(B!1, A!2)), introduced(assumption)).
% 0.20/0.41  tff(23,plain,
% 0.20/0.41      ((~(right_apart_point(B!1, line_connecting(A!2, C!0)) | (~distinct_points(A!2, B!1)) | (~left_apart_point(C!0, line_connecting(A!2, B!1))))) <=> (~(right_apart_point(B!1, line_connecting(A!2, C!0)) | (~distinct_points(A!2, B!1)) | (~left_apart_point(C!0, line_connecting(A!2, B!1)))))),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(24,plain,
% 0.20/0.41      ((~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))) <=> (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B)))))),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(25,plain,
% 0.20/0.41      ((~![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (left_apart_point(C, line_connecting(A, B)) => right_apart_point(B, line_connecting(A, C))))) <=> (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B)))))),
% 0.20/0.41      inference(rewrite,[status(thm)],[])).
% 0.20/0.41  tff(26,axiom,(~![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (left_apart_point(C, line_connecting(A, B)) => right_apart_point(B, line_connecting(A, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.41  tff(27,plain,
% 0.20/0.41      (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.41  tff(28,plain,
% 0.20/0.41      (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[27, 24])).
% 0.20/0.41  tff(29,plain,
% 0.20/0.41      (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.41  tff(30,plain,
% 0.20/0.41      (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[29, 24])).
% 0.20/0.41  tff(31,plain,
% 0.20/0.41      (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[30, 24])).
% 0.20/0.41  tff(32,plain,
% 0.20/0.41      (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.41  tff(33,plain,
% 0.20/0.41      (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[32, 24])).
% 0.20/0.41  tff(34,plain,(
% 0.20/0.41      ~(right_apart_point(B!1, line_connecting(A!2, C!0)) | (~distinct_points(A!2, B!1)) | (~left_apart_point(C!0, line_connecting(A!2, B!1))))),
% 0.20/0.41      inference(skolemize,[status(sab)],[33])).
% 0.20/0.41  tff(35,plain,
% 0.20/0.41      (~(right_apart_point(B!1, line_connecting(A!2, C!0)) | (~distinct_points(A!2, B!1)) | (~left_apart_point(C!0, line_connecting(A!2, B!1))))),
% 0.20/0.41      inference(modus_ponens,[status(thm)],[34, 23])).
% 0.20/0.41  tff(36,plain,
% 0.20/0.41      (distinct_points(A!2, B!1)),
% 0.20/0.41      inference(or_elim,[status(thm)],[35])).
% 0.20/0.41  tff(37,plain,
% 0.20/0.41      (^[A: $i, B: $i, C: $i] : refl((distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))))),
% 0.20/0.41      inference(bind,[status(th)],[])).
% 0.20/0.41  tff(38,plain,
% 0.20/0.41      (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[37])).
% 0.20/0.42  tff(39,plain,
% 0.20/0.42      (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(40,plain,
% 0.20/0.42      (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((distinct_points(A, C) | distinct_points(B, C)) <=> (distinct_points(A, C) | distinct_points(B, C))), ((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))))), rewrite((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))), ((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(41,plain,
% 0.20/0.42      (![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[40])).
% 0.20/0.42  tff(42,axiom,(![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax2_basics')).
% 0.20/0.42  tff(43,plain,
% 0.20/0.42      (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.42  tff(44,plain,
% 0.20/0.42      (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.42  tff(45,plain,(
% 0.20/0.42      ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.20/0.42      inference(skolemize,[status(sab)],[44])).
% 0.20/0.42  tff(46,plain,
% 0.20/0.42      (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[45, 38])).
% 0.20/0.42  tff(47,plain,
% 0.20/0.42      (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | ((~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(48,plain,
% 0.20/0.42      ((distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1))) <=> ((~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(49,plain,
% 0.20/0.42      (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | ((~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2)))),
% 0.20/0.42      inference(monotonicity,[status(thm)],[48])).
% 0.20/0.42  tff(50,plain,
% 0.20/0.42      (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))),
% 0.20/0.42      inference(transitivity,[status(thm)],[49, 47])).
% 0.20/0.42  tff(51,plain,
% 0.20/0.42      ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1)))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(52,plain,
% 0.20/0.42      ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2)),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.42  tff(53,plain,
% 0.20/0.42      ($false),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[52, 46, 36, 22, 21])).
% 0.20/0.42  tff(54,plain,(distinct_points(A!2, A!2) | distinct_points(B!1, A!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42  tff(55,plain,
% 0.20/0.42      (distinct_points(B!1, A!2)),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[54, 20])).
% 0.20/0.42  tff(56,plain,
% 0.20/0.42      (^[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))))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(57,plain,
% 0.20/0.42      (![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)))))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[56])).
% 0.20/0.42  tff(58,plain,
% 0.20/0.42      (^[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))))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(59,plain,
% 0.20/0.42      (![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)))))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[58])).
% 0.20/0.42  tff(60,plain,
% 0.20/0.42      (![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)))))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(61,plain,
% 0.20/0.42      (^[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))))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(62,plain,
% 0.20/0.42      (![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)))))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[61])).
% 0.20/0.42  tff(63,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')).
% 0.20/0.42  tff(64,plain,
% 0.20/0.42      (![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)))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.42  tff(65,plain,
% 0.20/0.42      (![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)))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.42  tff(66,plain,(
% 0.20/0.42      ![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)))))),
% 0.20/0.42      inference(skolemize,[status(sab)],[65])).
% 0.20/0.42  tff(67,plain,
% 0.20/0.42      (![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)))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[66, 59])).
% 0.20/0.42  tff(68,plain,
% 0.20/0.42      (![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)))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[67, 57])).
% 0.20/0.42  tff(69,plain,
% 0.20/0.42      (((~![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(B!1, A!2)) | (~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2)))))) <=> ((~![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(B!1, A!2)) | (~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2)))))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(70,plain,
% 0.20/0.42      ((~![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(B!1, A!2)) | (~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2)))))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(71,plain,
% 0.20/0.42      ((~![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(B!1, A!2)) | (~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.42  tff(72,plain,
% 0.20/0.42      ((~distinct_points(B!1, A!2)) | (~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2))))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[71, 68])).
% 0.20/0.42  tff(73,plain,
% 0.20/0.42      (~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2)))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[72, 55])).
% 0.20/0.42  tff(74,plain,
% 0.20/0.42      ((apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2))) | (~apart_point_and_line(A!2, line_connecting(B!1, A!2)))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(75,plain,
% 0.20/0.42      (~apart_point_and_line(A!2, line_connecting(B!1, A!2))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[74, 73])).
% 0.20/0.42  tff(76,plain,
% 0.20/0.42      ((~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) <=> (left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2))))) | apart_point_and_line(A!2, line_connecting(B!1, A!2)) | (~(left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2))))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(77,plain,
% 0.20/0.42      ((~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) <=> (left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2))))) | (~(left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2))))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.42  tff(78,plain,
% 0.20/0.42      (~(left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2)))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[77, 9])).
% 0.20/0.42  tff(79,plain,
% 0.20/0.42      ((left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2))) | (~left_apart_point(A!2, line_connecting(B!1, A!2)))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(80,plain,
% 0.20/0.42      (~left_apart_point(A!2, line_connecting(B!1, A!2))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[79, 78])).
% 0.20/0.42  tff(81,plain,
% 0.20/0.42      ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))) | (apart_point_and_line(B!1, line_connecting(B!1, A!2)) <=> (left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2))))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(82,plain,
% 0.20/0.42      (apart_point_and_line(B!1, line_connecting(B!1, A!2)) <=> (left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2)))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[81, 7])).
% 0.20/0.42  tff(83,plain,
% 0.20/0.42      ((apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2))) | (~apart_point_and_line(B!1, line_connecting(B!1, A!2)))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(84,plain,
% 0.20/0.42      (~apart_point_and_line(B!1, line_connecting(B!1, A!2))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[83, 73])).
% 0.20/0.42  tff(85,plain,
% 0.20/0.42      ((~(apart_point_and_line(B!1, line_connecting(B!1, A!2)) <=> (left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2))))) | apart_point_and_line(B!1, line_connecting(B!1, A!2)) | (~(left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2))))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(86,plain,
% 0.20/0.42      ((~(apart_point_and_line(B!1, line_connecting(B!1, A!2)) <=> (left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2))))) | (~(left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2))))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[85, 84])).
% 0.20/0.42  tff(87,plain,
% 0.20/0.42      (~(left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2)))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[86, 82])).
% 0.20/0.42  tff(88,plain,
% 0.20/0.42      ((left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2))) | (~left_apart_point(B!1, line_connecting(B!1, A!2)))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(89,plain,
% 0.20/0.42      (~left_apart_point(B!1, line_connecting(B!1, A!2))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[88, 87])).
% 0.20/0.42  tff(90,plain,
% 0.20/0.42      (^[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))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(91,plain,
% 0.20/0.42      (![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)))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[90])).
% 0.20/0.42  tff(92,plain,
% 0.20/0.42      (![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)))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(93,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')).
% 0.20/0.42  tff(94,plain,
% 0.20/0.42      (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.42  tff(95,plain,(
% 0.20/0.42      ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.20/0.42      inference(skolemize,[status(sab)],[94])).
% 0.20/0.42  tff(96,plain,
% 0.20/0.42      (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.42  tff(97,plain,
% 0.20/0.42      ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(B!1, line_connecting(B!1, A!2)) <=> left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(98,plain,
% 0.20/0.42      (right_apart_point(B!1, line_connecting(B!1, A!2)) <=> left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2)))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[97, 96])).
% 0.20/0.42  tff(99,plain,
% 0.20/0.42      ((left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2))) | (~right_apart_point(B!1, line_connecting(B!1, A!2)))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(100,plain,
% 0.20/0.42      (~right_apart_point(B!1, line_connecting(B!1, A!2))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[99, 87])).
% 0.20/0.42  tff(101,plain,
% 0.20/0.42      ((~(right_apart_point(B!1, line_connecting(B!1, A!2)) <=> left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))))) | right_apart_point(B!1, line_connecting(B!1, A!2)) | (~left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(102,plain,
% 0.20/0.42      ((~(right_apart_point(B!1, line_connecting(B!1, A!2)) <=> left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))))) | (~left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[101, 100])).
% 0.20/0.42  tff(103,plain,
% 0.20/0.42      (~left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2)))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[102, 98])).
% 0.20/0.42  tff(104,plain,
% 0.20/0.42      ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(A!2, line_connecting(B!1, A!2)) <=> left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(105,plain,
% 0.20/0.42      (right_apart_point(A!2, line_connecting(B!1, A!2)) <=> left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2)))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[104, 96])).
% 0.20/0.42  tff(106,plain,
% 0.20/0.42      ((left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2))) | (~right_apart_point(A!2, line_connecting(B!1, A!2)))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(107,plain,
% 0.20/0.42      (~right_apart_point(A!2, line_connecting(B!1, A!2))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[106, 78])).
% 0.20/0.42  tff(108,plain,
% 0.20/0.42      ((~(right_apart_point(A!2, line_connecting(B!1, A!2)) <=> left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))))) | right_apart_point(A!2, line_connecting(B!1, A!2)) | (~left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(109,plain,
% 0.20/0.42      ((~(right_apart_point(A!2, line_connecting(B!1, A!2)) <=> left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))))) | (~left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.42  tff(110,plain,
% 0.20/0.42      (~left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2)))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[109, 105])).
% 0.20/0.42  tff(111,assumption,(left_apart_point(C!0, line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))), introduced(assumption)).
% 0.20/0.42  tff(112,plain,
% 0.20/0.42      (^[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)))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(113,plain,
% 0.20/0.42      (![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))))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[112])).
% 0.20/0.42  tff(114,plain,
% 0.20/0.42      (![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))))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(115,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')).
% 0.20/0.42  tff(116,plain,
% 0.20/0.42      (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.42  tff(117,plain,(
% 0.20/0.42      ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.20/0.42      inference(skolemize,[status(sab)],[116])).
% 0.20/0.42  tff(118,plain,
% 0.20/0.42      (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[117, 113])).
% 0.20/0.42  tff(119,plain,
% 0.20/0.42      ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(C!0, line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(120,plain,
% 0.20/0.42      ($false),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[119, 118, 111])).
% 0.20/0.43  tff(121,plain,(~(left_apart_point(C!0, line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43  tff(122,plain,
% 0.20/0.43      ((left_apart_point(C!0, line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))) | (~left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.43      inference(tautology,[status(thm)],[])).
% 0.20/0.43  tff(123,plain,
% 0.20/0.43      (~left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))),
% 0.20/0.43      inference(unit_resolution,[status(thm)],[122, 121])).
% 0.20/0.43  tff(124,plain,
% 0.20/0.43      (^[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))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(125,plain,
% 0.20/0.43      (![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)))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[124])).
% 0.20/0.43  tff(126,plain,
% 0.20/0.43      (![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)))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(127,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')).
% 0.20/0.43  tff(128,plain,
% 0.20/0.43      (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.43  tff(129,plain,(
% 0.20/0.43      ![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.20/0.43      inference(skolemize,[status(sab)],[128])).
% 0.20/0.43  tff(130,plain,
% 0.20/0.43      (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[129, 125])).
% 0.20/0.43  tff(131,plain,
% 0.20/0.43      ((~![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))) | (equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) <=> (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))))),
% 0.20/0.43      inference(quant_inst,[status(thm)],[])).
% 0.20/0.43  tff(132,plain,
% 0.20/0.43      (equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) <=> (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.43      inference(unit_resolution,[status(thm)],[131, 130])).
% 0.20/0.43  tff(133,plain,
% 0.20/0.43      (^[A: $i, B: $i] : refl(((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(134,plain,
% 0.20/0.43      (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[133])).
% 0.20/0.43  tff(135,plain,
% 0.20/0.43      (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(136,plain,
% 0.20/0.43      (^[A: $i, B: $i] : rewrite((distinct_points(A, B) => equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(137,plain,
% 0.20/0.43      (![A: $i, B: $i] : (distinct_points(A, B) => equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[136])).
% 0.20/0.43  tff(138,axiom,(![A: $i, B: $i] : (distinct_points(A, B) => equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax9_cons_objs')).
% 0.20/0.43  tff(139,plain,
% 0.20/0.43      (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.43  tff(140,plain,
% 0.20/0.43      (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[139, 135])).
% 0.20/0.43  tff(141,plain,(
% 0.20/0.43      ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.20/0.43      inference(skolemize,[status(sab)],[140])).
% 0.20/0.43  tff(142,plain,
% 0.20/0.43      (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[141, 134])).
% 0.20/0.43  tff(143,plain,
% 0.20/0.43      (((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | ((~distinct_points(A!2, B!1)) | equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))) <=> ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~distinct_points(A!2, B!1)) | equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(144,plain,
% 0.20/0.43      ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | ((~distinct_points(A!2, B!1)) | equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.43      inference(quant_inst,[status(thm)],[])).
% 0.20/0.43  tff(145,plain,
% 0.20/0.43      ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~distinct_points(A!2, B!1)) | equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.43  tff(146,plain,
% 0.20/0.43      (equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 0.20/0.43      inference(unit_resolution,[status(thm)],[145, 142, 36])).
% 0.20/0.43  tff(147,plain,
% 0.20/0.43      ((~(equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) <=> (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.43      inference(tautology,[status(thm)],[])).
% 0.20/0.43  tff(148,plain,
% 0.20/0.43      ((~(equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) <=> (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.43      inference(unit_resolution,[status(thm)],[147, 146])).
% 0.20/0.43  tff(149,plain,
% 0.20/0.43      (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 0.20/0.43      inference(unit_resolution,[status(thm)],[148, 132])).
% 0.20/0.43  tff(150,plain,
% 0.20/0.43      (^[L: $i, M: $i] : refl((unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(151,plain,
% 0.20/0.43      (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[150])).
% 0.20/0.43  tff(152,plain,
% 0.20/0.43      (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(153,axiom,(![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax8_basics')).
% 0.20/0.43  tff(154,plain,
% 0.20/0.43      (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.43  tff(155,plain,(
% 0.20/0.43      ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.43      inference(skolemize,[status(sab)],[154])).
% 0.20/0.43  tff(156,plain,
% 0.20/0.43      (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[155, 151])).
% 0.20/0.43  tff(157,plain,
% 0.20/0.43      (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(158,plain,
% 0.20/0.43      ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.43      inference(quant_inst,[status(thm)],[])).
% 0.20/0.43  tff(159,plain,
% 0.20/0.43      ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.43  tff(160,plain,
% 0.20/0.43      (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))),
% 0.20/0.43      inference(unit_resolution,[status(thm)],[159, 156, 149])).
% 0.20/0.43  tff(161,plain,
% 0.20/0.43      (left_apart_point(C!0, line_connecting(A!2, B!1))),
% 0.20/0.43      inference(or_elim,[status(thm)],[35])).
% 0.20/0.43  tff(162,plain,
% 0.20/0.43      (^[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))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(163,plain,
% 0.20/0.43      (![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)))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[162])).
% 0.20/0.43  tff(164,plain,
% 0.20/0.43      (^[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)))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(165,plain,
% 0.20/0.43      (![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)))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[164])).
% 0.20/0.43  tff(166,plain,
% 0.20/0.43      (![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))))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(167,plain,
% 0.20/0.43      (^[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)))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(168,plain,
% 0.20/0.43      (![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))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[167])).
% 0.20/0.43  tff(169,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')).
% 0.20/0.43  tff(170,plain,
% 0.20/0.43      (![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))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.43  tff(171,plain,
% 0.20/0.43      (![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))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[170, 166])).
% 0.20/0.43  tff(172,plain,(
% 0.20/0.43      ![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))))),
% 0.20/0.43      inference(skolemize,[status(sab)],[171])).
% 0.20/0.43  tff(173,plain,
% 0.20/0.43      (![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)))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[172, 165])).
% 0.20/0.43  tff(174,plain,
% 0.20/0.43      (![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)))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[173, 163])).
% 0.20/0.43  tff(175,plain,
% 0.20/0.43      (((~![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(C!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))) <=> ((~![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(C!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(176,plain,
% 0.20/0.44      (((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))) | (~left_apart_point(C!0, line_connecting(A!2, B!1)))) <=> ((~left_apart_point(C!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(177,plain,
% 0.20/0.44      (((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))) | (~left_apart_point(C!0, line_connecting(A!2, B!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(C!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))))),
% 0.20/0.44      inference(monotonicity,[status(thm)],[176])).
% 0.20/0.44  tff(178,plain,
% 0.20/0.44      (((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))) | (~left_apart_point(C!0, line_connecting(A!2, B!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(C!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))),
% 0.20/0.44      inference(transitivity,[status(thm)],[177, 175])).
% 0.20/0.44  tff(179,plain,
% 0.20/0.44      ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))) | (~left_apart_point(C!0, line_connecting(A!2, B!1))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(180,plain,
% 0.20/0.44      ((~![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(C!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[179, 178])).
% 0.20/0.44  tff(181,plain,
% 0.20/0.44      (distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[180, 174, 161, 160])).
% 0.20/0.44  tff(182,plain,
% 0.20/0.44      (distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[181, 123])).
% 0.20/0.44  tff(183,plain,
% 0.20/0.44      ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(B!1, line_connecting(A!2, B!1)) <=> left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(184,plain,
% 0.20/0.44      (right_apart_point(B!1, line_connecting(A!2, B!1)) <=> left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[183, 96])).
% 0.20/0.44  tff(185,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(B!1, line_connecting(A!2, B!1)) <=> (left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(186,plain,
% 0.20/0.44      (apart_point_and_line(B!1, line_connecting(A!2, B!1)) <=> (left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[185, 7])).
% 0.20/0.44  tff(187,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!2, B!1)) | (~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!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!2, B!1)) | (~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!1)))))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(188,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!2, B!1)) | (~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!1)))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(189,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!2, B!1)) | (~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!1))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[188, 187])).
% 0.20/0.44  tff(190,plain,
% 0.20/0.44      (~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[189, 68, 36])).
% 0.20/0.44  tff(191,plain,
% 0.20/0.44      ((apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!1))) | (~apart_point_and_line(B!1, line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(192,plain,
% 0.20/0.44      (~apart_point_and_line(B!1, line_connecting(A!2, B!1))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[191, 190])).
% 0.20/0.44  tff(193,plain,
% 0.20/0.44      ((~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) <=> (left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1))))) | apart_point_and_line(B!1, line_connecting(A!2, B!1)) | (~(left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1))))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(194,plain,
% 0.20/0.44      ((~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) <=> (left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1))))) | (~(left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1))))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[193, 192])).
% 0.20/0.44  tff(195,plain,
% 0.20/0.44      (~(left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[194, 186])).
% 0.20/0.44  tff(196,plain,
% 0.20/0.44      ((left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1))) | (~right_apart_point(B!1, line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(197,plain,
% 0.20/0.44      (~right_apart_point(B!1, line_connecting(A!2, B!1))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[196, 195])).
% 0.20/0.44  tff(198,plain,
% 0.20/0.44      ((~(right_apart_point(B!1, line_connecting(A!2, B!1)) <=> left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))))) | right_apart_point(B!1, line_connecting(A!2, B!1)) | (~left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(199,plain,
% 0.20/0.44      ((~(right_apart_point(B!1, line_connecting(A!2, B!1)) <=> left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))))) | (~left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[198, 197])).
% 0.20/0.44  tff(200,plain,
% 0.20/0.44      (~left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[199, 184])).
% 0.20/0.44  tff(201,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!2, line_connecting(A!2, B!1)) <=> left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(202,plain,
% 0.20/0.44      (right_apart_point(A!2, line_connecting(A!2, B!1)) <=> left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[201, 96])).
% 0.20/0.44  tff(203,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!2, line_connecting(A!2, B!1)) <=> (left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(204,plain,
% 0.20/0.44      (apart_point_and_line(A!2, line_connecting(A!2, B!1)) <=> (left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[203, 7])).
% 0.20/0.44  tff(205,plain,
% 0.20/0.44      ((apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!1))) | (~apart_point_and_line(A!2, line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(206,plain,
% 0.20/0.44      (~apart_point_and_line(A!2, line_connecting(A!2, B!1))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[205, 190])).
% 0.20/0.44  tff(207,plain,
% 0.20/0.44      ((~(apart_point_and_line(A!2, line_connecting(A!2, B!1)) <=> (left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1))))) | apart_point_and_line(A!2, line_connecting(A!2, B!1)) | (~(left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1))))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(208,plain,
% 0.20/0.44      ((~(apart_point_and_line(A!2, line_connecting(A!2, B!1)) <=> (left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1))))) | (~(left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1))))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[207, 206])).
% 0.20/0.44  tff(209,plain,
% 0.20/0.44      (~(left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[208, 204])).
% 0.20/0.44  tff(210,plain,
% 0.20/0.44      ((left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1))) | (~right_apart_point(A!2, line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(211,plain,
% 0.20/0.44      (~right_apart_point(A!2, line_connecting(A!2, B!1))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[210, 209])).
% 0.20/0.44  tff(212,plain,
% 0.20/0.44      ((~(right_apart_point(A!2, line_connecting(A!2, B!1)) <=> left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))))) | right_apart_point(A!2, line_connecting(A!2, B!1)) | (~left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(213,plain,
% 0.20/0.44      ((~(right_apart_point(A!2, line_connecting(A!2, B!1)) <=> left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))))) | (~left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[212, 211])).
% 0.20/0.44  tff(214,plain,
% 0.20/0.44      (~left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[213, 202])).
% 0.20/0.44  tff(215,plain,
% 0.20/0.44      ((left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1))) | (~left_apart_point(B!1, line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(216,plain,
% 0.20/0.44      (~left_apart_point(B!1, line_connecting(A!2, B!1))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[215, 195])).
% 0.20/0.44  tff(217,plain,
% 0.20/0.44      ((left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1))) | (~left_apart_point(A!2, line_connecting(A!2, B!1)))),
% 0.20/0.44      inference(tautology,[status(thm)],[])).
% 0.20/0.44  tff(218,plain,
% 0.20/0.44      (~left_apart_point(A!2, line_connecting(A!2, B!1))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[217, 209])).
% 0.20/0.44  tff(219,plain,
% 0.20/0.44      (^[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))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(220,plain,
% 0.20/0.44      (![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)))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[219])).
% 0.20/0.44  tff(221,plain,
% 0.20/0.44      (^[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(222,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)],[221])).
% 0.20/0.45  tff(223,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(224,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(225,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))))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[224])).
% 0.20/0.45  tff(226,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')).
% 0.20/0.45  tff(227,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))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[226, 225])).
% 0.20/0.45  tff(228,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))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[227, 223])).
% 0.20/0.45  tff(229,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))))),
% 0.20/0.45      inference(skolemize,[status(sab)],[228])).
% 0.20/0.45  tff(230,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)))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[229, 222])).
% 0.20/0.45  tff(231,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)))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[230, 220])).
% 0.20/0.45  tff(232,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)))) | ((~distinct_points(A!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))) <=> ((~![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!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(233,plain,
% 0.20/0.45      ((left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | (~distinct_points(A!2, B!1)) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)))) <=> ((~distinct_points(A!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(234,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!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | (~distinct_points(A!2, B!1)) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))) <=> ((~![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!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)))))),
% 0.20/0.46      inference(monotonicity,[status(thm)],[233])).
% 0.20/0.46  tff(235,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!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | (~distinct_points(A!2, B!1)) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))) <=> ((~![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!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))),
% 0.20/0.47      inference(transitivity,[status(thm)],[234, 232])).
% 0.20/0.47  tff(236,plain,
% 0.20/0.47      ((~![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!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | (~distinct_points(A!2, B!1)) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))),
% 0.20/0.47      inference(quant_inst,[status(thm)],[])).
% 0.20/0.47  tff(237,plain,
% 0.20/0.47      ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_points(A!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[236, 235])).
% 0.20/0.47  tff(238,plain,
% 0.20/0.47      (left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2)))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[237, 231, 36, 218, 216, 214, 200, 182])).
% 0.20/0.47  tff(239,plain,
% 0.20/0.47      ($false),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[238, 110, 103, 89, 80])).
% 0.20/0.47  % SZS output end Proof
%------------------------------------------------------------------------------