TSTP Solution File: GEO243+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO243+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 20:36:01 EDT 2022
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO243+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n014.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 07:10:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(left_apart_point_type, type, (
% 0.21/0.40 left_apart_point: ( $i * $i ) > $o)).
% 0.21/0.40 tff(line_connecting_type, type, (
% 0.21/0.40 line_connecting: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_A_2_type, type, (
% 0.21/0.40 tptp_fun_A_2: $i)).
% 0.21/0.40 tff(tptp_fun_B_1_type, type, (
% 0.21/0.40 tptp_fun_B_1: $i)).
% 0.21/0.40 tff(reverse_line_type, type, (
% 0.21/0.40 reverse_line: $i > $i)).
% 0.21/0.40 tff(distinct_lines_type, type, (
% 0.21/0.40 distinct_lines: ( $i * $i ) > $o)).
% 0.21/0.40 tff(unequally_directed_lines_type, type, (
% 0.21/0.40 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.21/0.40 tff(equally_directed_lines_type, type, (
% 0.21/0.40 equally_directed_lines: ( $i * $i ) > $o)).
% 0.21/0.40 tff(distinct_points_type, type, (
% 0.21/0.40 distinct_points: ( $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_C_0_type, type, (
% 0.21/0.40 tptp_fun_C_0: $i)).
% 0.21/0.40 tff(right_apart_point_type, type, (
% 0.21/0.40 right_apart_point: ( $i * $i ) > $o)).
% 0.21/0.40 tff(apart_point_and_line_type, type, (
% 0.21/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.40 tff(1,assumption,(left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2)))), introduced(assumption)).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 (^[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)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.40 tff(4,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(5,axiom,(![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax10_basics')).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.40 tff(7,plain,(
% 0.21/0.40 ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[6])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2)))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.40 tff(11,plain,(~(left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 ((left_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, line_connecting(B!1, A!2)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 (~left_apart_point(A!2, line_connecting(B!1, A!2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 ((left_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))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 (~left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.21/0.40 tff(16,assumption,(left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2)))), introduced(assumption)).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2)))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[17, 8, 16])).
% 0.21/0.41 tff(19,plain,(~(left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 ((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(B!1, line_connecting(B!1, A!2)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (~left_apart_point(B!1, line_connecting(B!1, A!2))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 ((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(B!1, reverse_line(line_connecting(B!1, A!2))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (~left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[22, 19])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(27,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')).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.41 tff(29,plain,(
% 0.21/0.41 ![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[28])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 ((~![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)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (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))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 ((~(right_apart_point(C!0, line_connecting(B!1, A!2)) | (~distinct_points(A!2, B!1)) | (~left_apart_point(C!0, line_connecting(A!2, B!1))))) <=> (~(right_apart_point(C!0, line_connecting(B!1, A!2)) | (~distinct_points(A!2, B!1)) | (~left_apart_point(C!0, line_connecting(A!2, B!1)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : (right_apart_point(C, line_connecting(B, A)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))) <=> (~![A: $i, B: $i, C: $i] : (right_apart_point(C, line_connecting(B, A)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (left_apart_point(C, line_connecting(A, B)) => right_apart_point(C, line_connecting(B, A))))) <=> (~![A: $i, B: $i, C: $i] : (right_apart_point(C, line_connecting(B, A)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(36,axiom,(~![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (left_apart_point(C, line_connecting(A, B)) => right_apart_point(C, line_connecting(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : (right_apart_point(C, line_connecting(B, A)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : (right_apart_point(C, line_connecting(B, A)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : (right_apart_point(C, line_connecting(B, A)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : (right_apart_point(C, line_connecting(B, A)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : (right_apart_point(C, line_connecting(B, A)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[40, 34])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : (right_apart_point(C, line_connecting(B, A)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : (right_apart_point(C, line_connecting(B, A)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[42, 34])).
% 0.21/0.41 tff(44,plain,(
% 0.21/0.41 ~(right_apart_point(C!0, line_connecting(B!1, A!2)) | (~distinct_points(A!2, B!1)) | (~left_apart_point(C!0, line_connecting(A!2, B!1))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[43])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (~(right_apart_point(C!0, line_connecting(B!1, A!2)) | (~distinct_points(A!2, B!1)) | (~left_apart_point(C!0, line_connecting(A!2, B!1))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[44, 33])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (distinct_points(A!2, B!1)),
% 0.21/0.41 inference(or_elim,[status(thm)],[45])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (^[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)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (^[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)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.41 tff(52,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')).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.21/0.41 tff(55,plain,(
% 0.21/0.41 ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[54])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (((~![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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 ((~![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))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 ((~![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[59, 56, 46])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 ((~(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))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 ((~(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))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[62, 32])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(67,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')).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.41 tff(69,plain,(
% 0.21/0.41 ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[68])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (((~![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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 ((~![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))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 ((~![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[73, 70, 63])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(78,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')).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.41 tff(80,plain,(
% 0.21/0.41 ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[79])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(C!0, line_connecting(B!1, A!2)) <=> left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (right_apart_point(C!0, line_connecting(B!1, A!2)) <=> left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 (~right_apart_point(C!0, line_connecting(B!1, A!2))),
% 0.21/0.41 inference(or_elim,[status(thm)],[45])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 ((~(right_apart_point(C!0, line_connecting(B!1, A!2)) <=> left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))) | right_apart_point(C!0, line_connecting(B!1, A!2)) | (~left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 ((~(right_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))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 (~left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[86, 83])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (left_apart_point(C!0, line_connecting(A!2, B!1))),
% 0.21/0.41 inference(or_elim,[status(thm)],[45])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[89])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 (^[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)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[91])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 (^[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)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(95,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[94])).
% 0.21/0.42 tff(96,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')).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.21/0.42 tff(99,plain,(
% 0.21/0.42 ![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))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[98])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[100, 90])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (((~![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))) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))) | (~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)))) <=> ((~![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))) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))) | (~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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (((~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))) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))) | (~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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (((~![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))) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))) | (~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))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[103])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (((~![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))) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))) | (~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)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[104, 102])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 ((~![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))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 ((~![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))) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))) | (~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))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[107, 101, 88, 87, 74])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(B!1, line_connecting(A!2, B!1)) <=> left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (right_apart_point(B!1, line_connecting(A!2, B!1)) <=> left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[109, 81])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(114,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')).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.42 tff(116,plain,(
% 0.21/0.42 ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[115])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 ((~![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(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))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (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)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (^[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))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (![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)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[120])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (^[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))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (![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)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 (![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)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (^[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))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 (![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)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[125])).
% 0.21/0.42 tff(127,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')).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (![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)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 (![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)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.21/0.42 tff(130,plain,(
% 0.21/0.42 ![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)))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[129])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 (![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)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 (![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)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[131, 121])).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 (((~![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(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)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(134,plain,
% 0.21/0.42 ((~![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(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)))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(135,plain,
% 0.21/0.42 ((~![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(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))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.42 tff(136,plain,
% 0.21/0.42 (~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!1)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[135, 132, 46])).
% 0.21/0.42 tff(137,plain,
% 0.21/0.42 ((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)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(138,plain,
% 0.21/0.42 (~apart_point_and_line(B!1, line_connecting(A!2, B!1))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.21/0.42 tff(139,plain,
% 0.21/0.42 ((~(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))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(140,plain,
% 0.21/0.42 ((~(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))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.21/0.42 tff(141,plain,
% 0.21/0.42 (~(left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[140, 119])).
% 0.21/0.42 tff(142,plain,
% 0.21/0.42 ((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)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(143,plain,
% 0.21/0.42 (~right_apart_point(B!1, line_connecting(A!2, B!1))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.21/0.42 tff(144,plain,
% 0.21/0.42 ((~(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))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(145,plain,
% 0.21/0.42 ((~(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))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.21/0.42 tff(146,plain,
% 0.21/0.42 (~left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[145, 110])).
% 0.21/0.42 tff(147,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(A!2, line_connecting(A!2, B!1)) <=> left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(148,plain,
% 0.21/0.42 (right_apart_point(A!2, line_connecting(A!2, B!1)) <=> left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[147, 81])).
% 0.21/0.42 tff(149,plain,
% 0.21/0.42 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))) | (apart_point_and_line(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))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(150,plain,
% 0.21/0.42 (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)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[149, 117])).
% 0.21/0.42 tff(151,plain,
% 0.21/0.42 ((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)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(152,plain,
% 0.21/0.42 (~apart_point_and_line(A!2, line_connecting(A!2, B!1))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[151, 136])).
% 0.21/0.42 tff(153,plain,
% 0.21/0.42 ((~(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))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(154,plain,
% 0.21/0.43 ((~(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))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.21/0.43 tff(155,plain,
% 0.21/0.43 (~(left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[154, 150])).
% 0.21/0.43 tff(156,plain,
% 0.21/0.43 ((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)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(157,plain,
% 0.21/0.43 (~right_apart_point(A!2, line_connecting(A!2, B!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.21/0.43 tff(158,plain,
% 0.21/0.43 ((~(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))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(159,plain,
% 0.21/0.43 ((~(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))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.21/0.43 tff(160,plain,
% 0.21/0.43 (~left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[159, 148])).
% 0.21/0.43 tff(161,plain,
% 0.21/0.43 ((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)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(162,plain,
% 0.21/0.43 (~left_apart_point(B!1, line_connecting(A!2, B!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[161, 141])).
% 0.21/0.43 tff(163,plain,
% 0.21/0.43 ((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)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(164,plain,
% 0.21/0.43 (~left_apart_point(A!2, line_connecting(A!2, B!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[163, 155])).
% 0.21/0.43 tff(165,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(166,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[165])).
% 0.21/0.43 tff(167,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(168,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[167])).
% 0.21/0.43 tff(169,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(170,plain,
% 0.21/0.43 (^[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))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(171,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[170])).
% 0.21/0.43 tff(172,axiom,(![A: $i, B: $i, L: $i, M: $i] : ((distinct_points(A, B) & distinct_lines(L, M)) => (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax1_uniq_cons')).
% 0.21/0.43 tff(173,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.21/0.43 tff(174,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.21/0.43 tff(175,plain,(
% 0.21/0.43 ![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))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[174])).
% 0.21/0.43 tff(176,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.21/0.43 tff(177,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[176, 166])).
% 0.21/0.43 tff(178,plain,
% 0.21/0.43 (((~![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(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(A!2, 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(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(A!2, line_connecting(B!1, A!2)) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(179,plain,
% 0.21/0.43 ((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(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(A!2, line_connecting(B!1, A!2)) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(180,plain,
% 0.21/0.43 (((~![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(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(A!2, line_connecting(B!1, A!2)) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[179])).
% 0.21/0.43 tff(181,plain,
% 0.21/0.43 (((~![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(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(A!2, line_connecting(B!1, A!2)) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[180, 178])).
% 0.21/0.44 tff(182,plain,
% 0.21/0.44 ((~![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)))) | (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))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(183,plain,
% 0.21/0.44 ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_points(A!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.21/0.44 tff(184,plain,
% 0.21/0.44 (left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[183, 177, 46, 164, 162, 160, 146, 108])).
% 0.21/0.44 tff(185,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[184, 23, 21, 15, 13])).
% 0.21/0.44 % SZS output end Proof
%------------------------------------------------------------------------------