TSTP Solution File: GEO255+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO255+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 20:36:07 EDT 2022
% Result : Theorem 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO255+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 07:13:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(unequally_directed_lines_type, type, (
% 0.18/0.40 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.18/0.40 tff(tptp_fun_L_2_type, type, (
% 0.18/0.40 tptp_fun_L_2: $i)).
% 0.18/0.40 tff(line_connecting_type, type, (
% 0.18/0.40 line_connecting: ( $i * $i ) > $i)).
% 0.18/0.40 tff(tptp_fun_A_1_type, type, (
% 0.18/0.40 tptp_fun_A_1: $i)).
% 0.18/0.40 tff(tptp_fun_B_0_type, type, (
% 0.18/0.40 tptp_fun_B_0: $i)).
% 0.18/0.40 tff(reverse_line_type, type, (
% 0.18/0.40 reverse_line: $i > $i)).
% 0.18/0.40 tff(equally_directed_lines_type, type, (
% 0.18/0.40 equally_directed_lines: ( $i * $i ) > $o)).
% 0.18/0.40 tff(distinct_points_type, type, (
% 0.18/0.40 distinct_points: ( $i * $i ) > $o)).
% 0.18/0.40 tff(incident_point_and_line_type, type, (
% 0.18/0.40 incident_point_and_line: ( $i * $i ) > $o)).
% 0.18/0.40 tff(before_on_line_type, type, (
% 0.18/0.40 before_on_line: ( $i * $i * $i ) > $o)).
% 0.18/0.40 tff(1,plain,
% 0.18/0.40 (^[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))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(2,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.40 tff(3,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(4,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')).
% 0.18/0.40 tff(5,plain,
% 0.18/0.40 (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.40 tff(6,plain,(
% 0.18/0.40 ![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[5])).
% 0.18/0.40 tff(7,plain,
% 0.18/0.40 (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.40 tff(8,plain,
% 0.18/0.40 ((~![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))) | (equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) <=> (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(9,plain,
% 0.18/0.40 (equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) <=> (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 (^[L: $i, A: $i, B: $i] : refl((before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))))) <=> (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(11,plain,
% 0.18/0.40 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.18/0.40 tff(12,plain,
% 0.18/0.40 (^[L: $i, A: $i, B: $i] : rewrite((before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))) <=> (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B)))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(13,plain,
% 0.18/0.41 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.41 tff(14,plain,
% 0.18/0.41 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(15,plain,
% 0.18/0.41 (^[L: $i, A: $i, B: $i] : rewrite((before_on_line(L, A, B) <=> (((distinct_points(A, B) & incident_point_and_line(A, L)) & incident_point_and_line(B, L)) & equally_directed_lines(L, line_connecting(A, B)))) <=> (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(16,plain,
% 0.18/0.41 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (((distinct_points(A, B) & incident_point_and_line(A, L)) & incident_point_and_line(B, L)) & equally_directed_lines(L, line_connecting(A, B)))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.18/0.41 tff(17,axiom,(![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (((distinct_points(A, B) & incident_point_and_line(A, L)) & incident_point_and_line(B, L)) & equally_directed_lines(L, line_connecting(A, B))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax4_defns')).
% 0.18/0.41 tff(18,plain,
% 0.18/0.41 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.18/0.41 tff(19,plain,
% 0.18/0.41 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.18/0.41 tff(20,plain,(
% 0.18/0.41 ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & incident_point_and_line(A, L) & incident_point_and_line(B, L) & equally_directed_lines(L, line_connecting(A, B))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[19])).
% 0.18/0.41 tff(21,plain,
% 0.18/0.41 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.18/0.41 tff(22,plain,
% 0.18/0.41 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.18/0.41 tff(23,plain,
% 0.18/0.41 (((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B))))))) | (before_on_line(L!2, B!0, A!1) <=> (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1))))))) <=> ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B))))))) | (before_on_line(L!2, B!0, A!1) <=> (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(24,plain,
% 0.18/0.41 ((before_on_line(L!2, B!0, A!1) <=> (~((~distinct_points(B!0, A!1)) | (~incident_point_and_line(B!0, L!2)) | (~incident_point_and_line(A!1, L!2)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))))) <=> (before_on_line(L!2, B!0, A!1) <=> (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(25,plain,
% 0.18/0.41 (((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B))))))) | (before_on_line(L!2, B!0, A!1) <=> (~((~distinct_points(B!0, A!1)) | (~incident_point_and_line(B!0, L!2)) | (~incident_point_and_line(A!1, L!2)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1))))))) <=> ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B))))))) | (before_on_line(L!2, B!0, A!1) <=> (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[24])).
% 0.18/0.41 tff(26,plain,
% 0.18/0.41 (((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B))))))) | (before_on_line(L!2, B!0, A!1) <=> (~((~distinct_points(B!0, A!1)) | (~incident_point_and_line(B!0, L!2)) | (~incident_point_and_line(A!1, L!2)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1))))))) <=> ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B))))))) | (before_on_line(L!2, B!0, A!1) <=> (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[25, 23])).
% 0.18/0.41 tff(27,plain,
% 0.18/0.41 ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B))))))) | (before_on_line(L!2, B!0, A!1) <=> (~((~distinct_points(B!0, A!1)) | (~incident_point_and_line(B!0, L!2)) | (~incident_point_and_line(A!1, L!2)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1))))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(28,plain,
% 0.18/0.41 ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B))))))) | (before_on_line(L!2, B!0, A!1) <=> (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.41 tff(29,plain,
% 0.18/0.41 (before_on_line(L!2, B!0, A!1) <=> (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[28, 22])).
% 0.18/0.41 tff(30,plain,
% 0.18/0.41 ((~(~(before_on_line(L!2, A!1, B!0) & before_on_line(L!2, B!0, A!1)))) <=> (before_on_line(L!2, A!1, B!0) & before_on_line(L!2, B!0, A!1))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(31,plain,
% 0.18/0.41 ((~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))) <=> (~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(32,axiom,(~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.18/0.41 tff(33,plain,
% 0.18/0.41 (~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.18/0.41 tff(34,plain,
% 0.18/0.41 (~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[33, 31])).
% 0.18/0.41 tff(35,plain,
% 0.18/0.41 (~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.18/0.41 tff(36,plain,
% 0.18/0.41 (~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.18/0.41 tff(37,plain,
% 0.18/0.41 (~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.18/0.41 tff(38,plain,
% 0.18/0.41 (~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[37, 31])).
% 0.18/0.41 tff(39,plain,
% 0.18/0.41 (~![L: $i, A: $i, B: $i] : (~(before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.18/0.41 tff(40,plain,(
% 0.18/0.41 ~(~(before_on_line(L!2, A!1, B!0) & before_on_line(L!2, B!0, A!1)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[39])).
% 0.18/0.41 tff(41,plain,
% 0.18/0.41 (before_on_line(L!2, A!1, B!0) & before_on_line(L!2, B!0, A!1)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.18/0.41 tff(42,plain,
% 0.18/0.41 (before_on_line(L!2, B!0, A!1)),
% 0.18/0.41 inference(and_elim,[status(thm)],[41])).
% 0.18/0.41 tff(43,plain,
% 0.18/0.41 ((~(before_on_line(L!2, B!0, A!1) <=> (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1))))))) | (~before_on_line(L!2, B!0, A!1)) | (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(44,plain,
% 0.18/0.41 ((~(before_on_line(L!2, B!0, A!1) <=> (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1))))))) | (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.18/0.41 tff(45,plain,
% 0.18/0.41 (~((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[44, 29])).
% 0.18/0.41 tff(46,plain,
% 0.18/0.41 (((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) | distinct_points(B!0, A!1)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(47,plain,
% 0.18/0.41 (distinct_points(B!0, A!1)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.18/0.41 tff(48,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(49,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.18/0.41 tff(50,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(51,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(52,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.18/0.41 tff(53,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')).
% 0.18/0.41 tff(54,plain,
% 0.18/0.41 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.18/0.41 tff(55,plain,
% 0.18/0.41 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.18/0.41 tff(56,plain,(
% 0.18/0.41 ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[55])).
% 0.18/0.41 tff(57,plain,
% 0.18/0.41 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.18/0.41 tff(58,plain,
% 0.18/0.41 (((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | ((~distinct_points(B!0, A!1)) | equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))) <=> ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~distinct_points(B!0, A!1)) | equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(59,plain,
% 0.18/0.41 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | ((~distinct_points(B!0, A!1)) | equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(60,plain,
% 0.18/0.41 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~distinct_points(B!0, A!1)) | equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.18/0.41 tff(61,plain,
% 0.18/0.41 (equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[60, 57, 47])).
% 0.18/0.41 tff(62,plain,
% 0.18/0.41 ((~(equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) <=> (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(63,plain,
% 0.18/0.41 ((~(equally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) <=> (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))))) | (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.18/0.42 tff(64,plain,
% 0.18/0.42 (~unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[63, 9])).
% 0.18/0.42 tff(65,plain,
% 0.18/0.42 (^[L: $i, M: $i, N: $i] : refl((unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(66,plain,
% 0.18/0.42 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.42 tff(67,plain,
% 0.18/0.42 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(68,plain,
% 0.18/0.42 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(L, N) | unequally_directed_lines(M, N)) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))))), rewrite((unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(69,plain,
% 0.18/0.42 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[68])).
% 0.18/0.42 tff(70,axiom,(![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax6_basics')).
% 0.18/0.42 tff(71,plain,
% 0.18/0.42 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.42 tff(72,plain,
% 0.18/0.42 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.18/0.42 tff(73,plain,(
% 0.18/0.42 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[72])).
% 0.18/0.42 tff(74,plain,
% 0.18/0.42 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.18/0.42 tff(75,plain,
% 0.18/0.42 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(76,plain,
% 0.18/0.42 ((unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)))) <=> (unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(77,plain,
% 0.18/0.42 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[76])).
% 0.18/0.42 tff(78,plain,
% 0.18/0.42 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[77, 75])).
% 0.18/0.42 tff(79,plain,
% 0.18/0.42 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(80,plain,
% 0.18/0.42 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!0, A!1), reverse_line(line_connecting(A!1, B!0))) | (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.18/0.42 tff(81,plain,
% 0.18/0.42 (~unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[80, 74, 64])).
% 0.18/0.42 tff(82,plain,
% 0.18/0.42 ((~![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))) | (equally_directed_lines(L!2, line_connecting(B!0, A!1)) <=> (~unequally_directed_lines(L!2, line_connecting(B!0, A!1))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(83,plain,
% 0.18/0.42 (equally_directed_lines(L!2, line_connecting(B!0, A!1)) <=> (~unequally_directed_lines(L!2, line_connecting(B!0, A!1)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[82, 7])).
% 0.18/0.42 tff(84,plain,
% 0.18/0.42 (((~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~distinct_points(B!0, A!1)) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1)))) | equally_directed_lines(L!2, line_connecting(B!0, A!1))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(85,plain,
% 0.18/0.42 (equally_directed_lines(L!2, line_connecting(B!0, A!1))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[84, 45])).
% 0.18/0.42 tff(86,plain,
% 0.18/0.42 ((~(equally_directed_lines(L!2, line_connecting(B!0, A!1)) <=> (~unequally_directed_lines(L!2, line_connecting(B!0, A!1))))) | (~equally_directed_lines(L!2, line_connecting(B!0, A!1))) | (~unequally_directed_lines(L!2, line_connecting(B!0, A!1)))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(87,plain,
% 0.18/0.42 ((~(equally_directed_lines(L!2, line_connecting(B!0, A!1)) <=> (~unequally_directed_lines(L!2, line_connecting(B!0, A!1))))) | (~unequally_directed_lines(L!2, line_connecting(B!0, A!1)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.18/0.42 tff(88,plain,
% 0.18/0.42 (~unequally_directed_lines(L!2, line_connecting(B!0, A!1))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[87, 83])).
% 0.18/0.42 tff(89,plain,
% 0.18/0.42 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | (~unequally_directed_lines(line_connecting(B!0, A!1), L!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | (~unequally_directed_lines(line_connecting(B!0, A!1), L!2)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(90,plain,
% 0.18/0.42 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | (~unequally_directed_lines(line_connecting(B!0, A!1), L!2)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(91,plain,
% 0.18/0.42 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(B!0, A!1), line_connecting(B!0, A!1)) | (~unequally_directed_lines(line_connecting(B!0, A!1), L!2))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.18/0.42 tff(92,plain,
% 0.18/0.42 (~unequally_directed_lines(line_connecting(B!0, A!1), L!2)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[91, 74, 88, 81])).
% 0.18/0.42 tff(93,plain,
% 0.18/0.42 ((~![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))) | (equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) <=> (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(94,plain,
% 0.18/0.42 (equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) <=> (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[93, 7])).
% 0.18/0.42 tff(95,plain,
% 0.18/0.42 ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~((~distinct_points(A, B)) | (~incident_point_and_line(A, L)) | (~incident_point_and_line(B, L)) | (~equally_directed_lines(L, line_connecting(A, B))))))) | (before_on_line(L!2, A!1, B!0) <=> (~((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0))))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(96,plain,
% 0.18/0.42 (before_on_line(L!2, A!1, B!0) <=> (~((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0)))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[95, 22])).
% 0.18/0.42 tff(97,plain,
% 0.18/0.42 (before_on_line(L!2, A!1, B!0)),
% 0.18/0.42 inference(and_elim,[status(thm)],[41])).
% 0.18/0.42 tff(98,plain,
% 0.18/0.42 ((~(before_on_line(L!2, A!1, B!0) <=> (~((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0))))))) | (~before_on_line(L!2, A!1, B!0)) | (~((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0)))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(99,plain,
% 0.18/0.42 ((~(before_on_line(L!2, A!1, B!0) <=> (~((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0))))))) | (~((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0)))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.18/0.42 tff(100,plain,
% 0.18/0.42 (~((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.18/0.42 tff(101,plain,
% 0.18/0.42 (((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0)))) | distinct_points(A!1, B!0)),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(102,plain,
% 0.18/0.42 (distinct_points(A!1, B!0)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.18/0.42 tff(103,plain,
% 0.18/0.42 (((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | ((~distinct_points(A!1, B!0)) | equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))) <=> ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~distinct_points(A!1, B!0)) | equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(104,plain,
% 0.18/0.42 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | ((~distinct_points(A!1, B!0)) | equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(105,plain,
% 0.18/0.42 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~distinct_points(A!1, B!0)) | equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.18/0.42 tff(106,plain,
% 0.18/0.42 (equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[105, 57, 102])).
% 0.18/0.42 tff(107,plain,
% 0.18/0.42 ((~(equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) <=> (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))))) | (~equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(108,plain,
% 0.18/0.42 ((~(equally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) <=> (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.18/0.42 tff(109,plain,
% 0.18/0.42 (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[108, 94])).
% 0.18/0.42 tff(110,plain,
% 0.18/0.42 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(111,plain,
% 0.18/0.43 ((unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)))) <=> (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(112,plain,
% 0.18/0.43 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[111])).
% 0.18/0.43 tff(113,plain,
% 0.18/0.43 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[112, 110])).
% 0.18/0.43 tff(114,plain,
% 0.18/0.43 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(115,plain,
% 0.18/0.43 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.18/0.43 tff(116,plain,
% 0.18/0.43 (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[115, 74, 109])).
% 0.18/0.43 tff(117,plain,
% 0.18/0.43 ((~![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))) | (equally_directed_lines(L!2, line_connecting(A!1, B!0)) <=> (~unequally_directed_lines(L!2, line_connecting(A!1, B!0))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(118,plain,
% 0.18/0.43 (equally_directed_lines(L!2, line_connecting(A!1, B!0)) <=> (~unequally_directed_lines(L!2, line_connecting(A!1, B!0)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[117, 7])).
% 0.18/0.43 tff(119,plain,
% 0.18/0.43 (((~distinct_points(A!1, B!0)) | (~incident_point_and_line(A!1, L!2)) | (~incident_point_and_line(B!0, L!2)) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0)))) | equally_directed_lines(L!2, line_connecting(A!1, B!0))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(120,plain,
% 0.18/0.43 (equally_directed_lines(L!2, line_connecting(A!1, B!0))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[119, 100])).
% 0.18/0.43 tff(121,plain,
% 0.18/0.43 ((~(equally_directed_lines(L!2, line_connecting(A!1, B!0)) <=> (~unequally_directed_lines(L!2, line_connecting(A!1, B!0))))) | (~equally_directed_lines(L!2, line_connecting(A!1, B!0))) | (~unequally_directed_lines(L!2, line_connecting(A!1, B!0)))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(122,plain,
% 0.18/0.43 ((~(equally_directed_lines(L!2, line_connecting(A!1, B!0)) <=> (~unequally_directed_lines(L!2, line_connecting(A!1, B!0))))) | (~unequally_directed_lines(L!2, line_connecting(A!1, B!0)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.18/0.43 tff(123,plain,
% 0.18/0.43 (~unequally_directed_lines(L!2, line_connecting(A!1, B!0))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[122, 118])).
% 0.18/0.43 tff(124,plain,
% 0.18/0.43 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)) | (~unequally_directed_lines(line_connecting(A!1, B!0), L!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)) | (~unequally_directed_lines(line_connecting(A!1, B!0), L!2)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(125,plain,
% 0.18/0.43 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)) | (~unequally_directed_lines(line_connecting(A!1, B!0), L!2)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(126,plain,
% 0.18/0.43 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(A!1, B!0)) | (~unequally_directed_lines(line_connecting(A!1, B!0), L!2))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.18/0.43 tff(127,plain,
% 0.18/0.43 (~unequally_directed_lines(line_connecting(A!1, B!0), L!2)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[126, 74, 123, 116])).
% 0.18/0.43 tff(128,plain,
% 0.18/0.43 (^[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))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(129,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[128])).
% 0.18/0.43 tff(130,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(131,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')).
% 0.18/0.43 tff(132,plain,
% 0.18/0.43 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.18/0.43 tff(133,plain,(
% 0.18/0.43 ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.18/0.43 inference(skolemize,[status(sab)],[132])).
% 0.18/0.43 tff(134,plain,
% 0.18/0.43 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.18/0.43 tff(135,plain,
% 0.18/0.43 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(136,plain,
% 0.18/0.43 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(137,plain,
% 0.18/0.43 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.18/0.43 tff(138,plain,
% 0.18/0.43 (unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[137, 134, 109])).
% 0.18/0.43 tff(139,plain,
% 0.18/0.43 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), L!2))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), L!2))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(140,plain,
% 0.18/0.43 ((unequally_directed_lines(line_connecting(B!0, A!1), L!2) | unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1)))) <=> (unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), L!2))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(141,plain,
% 0.18/0.43 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), L!2) | unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), L!2)))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[140])).
% 0.18/0.43 tff(142,plain,
% 0.18/0.43 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), L!2) | unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), L!2))),
% 0.18/0.43 inference(transitivity,[status(thm)],[141, 139])).
% 0.18/0.43 tff(143,plain,
% 0.18/0.43 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!0, A!1), L!2) | unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(144,plain,
% 0.18/0.43 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), L!2) | (~unequally_directed_lines(line_connecting(A!1, B!0), line_connecting(B!0, A!1))) | unequally_directed_lines(line_connecting(B!0, A!1), L!2)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.18/0.43 tff(145,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[144, 74, 138, 127, 92])).
% 0.18/0.43 % SZS output end Proof
%------------------------------------------------------------------------------