TSTP Solution File: GEO259+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO259+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:36:08 EDT 2022
% Result : Theorem 3.71s 2.66s
% Output : Proof 3.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO259+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n008.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 07:16:25 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.
% 3.71/2.66 % SZS status Theorem
% 3.71/2.66 % SZS output start Proof
% 3.71/2.66 tff(unequally_directed_lines_type, type, (
% 3.71/2.66 unequally_directed_lines: ( $i * $i ) > $o)).
% 3.71/2.66 tff(line_connecting_type, type, (
% 3.71/2.66 line_connecting: ( $i * $i ) > $i)).
% 3.71/2.66 tff(tptp_fun_B_1_type, type, (
% 3.71/2.66 tptp_fun_B_1: $i)).
% 3.71/2.66 tff(reverse_line_type, type, (
% 3.71/2.66 reverse_line: $i > $i)).
% 3.71/2.66 tff(tptp_fun_L_3_type, type, (
% 3.71/2.66 tptp_fun_L_3: $i)).
% 3.71/2.66 tff(left_convergent_lines_type, type, (
% 3.71/2.66 left_convergent_lines: ( $i * $i ) > $o)).
% 3.71/2.66 tff(line_type, type, (
% 3.71/2.66 line: $i > $o)).
% 3.71/2.66 tff(distinct_points_type, type, (
% 3.71/2.66 distinct_points: ( $i * $i ) > $o)).
% 3.71/2.66 tff(tptp_fun_A_2_type, type, (
% 3.71/2.66 tptp_fun_A_2: $i)).
% 3.71/2.66 tff(tptp_fun_C_0_type, type, (
% 3.71/2.66 tptp_fun_C_0: $i)).
% 3.71/2.66 tff(between_on_line_type, type, (
% 3.71/2.66 between_on_line: ( $i * $i * $i * $i ) > $o)).
% 3.71/2.66 tff(1,assumption,(left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))), introduced(assumption)).
% 3.71/2.66 tff(2,plain,
% 3.71/2.66 (^[L: $i, M: $i] : refl((~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))))),
% 3.71/2.66 inference(bind,[status(th)],[])).
% 3.71/2.66 tff(3,plain,
% 3.71/2.66 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 3.71/2.66 inference(quant_intro,[status(thm)],[2])).
% 3.71/2.66 tff(4,plain,
% 3.71/2.66 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 3.71/2.66 inference(rewrite,[status(thm)],[])).
% 3.71/2.66 tff(5,axiom,(![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag11')).
% 3.71/2.66 tff(6,plain,
% 3.71/2.66 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 3.71/2.66 inference(modus_ponens,[status(thm)],[5, 4])).
% 3.71/2.66 tff(7,plain,(
% 3.71/2.66 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 3.71/2.66 inference(skolemize,[status(sab)],[6])).
% 3.71/2.66 tff(8,plain,
% 3.71/2.66 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 3.71/2.66 inference(modus_ponens,[status(thm)],[7, 3])).
% 3.71/2.66 tff(9,plain,
% 3.71/2.66 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 3.71/2.66 inference(quant_inst,[status(thm)],[])).
% 3.71/2.66 tff(10,plain,
% 3.71/2.66 ($false),
% 3.71/2.66 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 3.71/2.66 tff(11,plain,(~(left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))), inference(lemma,lemma(discharge,[]))).
% 3.71/2.66 tff(12,plain,
% 3.71/2.66 ((left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))) | (~left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.66 inference(tautology,[status(thm)],[])).
% 3.71/2.66 tff(13,plain,
% 3.71/2.66 (~left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))),
% 3.71/2.66 inference(unit_resolution,[status(thm)],[12, 11])).
% 3.71/2.66 tff(14,plain,
% 3.71/2.66 ((left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))) | (~left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)))),
% 3.71/2.66 inference(tautology,[status(thm)],[])).
% 3.71/2.66 tff(15,plain,
% 3.71/2.66 (~left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))),
% 3.71/2.66 inference(unit_resolution,[status(thm)],[14, 11])).
% 3.71/2.66 tff(16,assumption,(~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))), introduced(assumption)).
% 3.71/2.66 tff(17,assumption,(unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))), introduced(assumption)).
% 3.71/2.66 tff(18,plain,
% 3.71/2.66 (^[L: $i] : refl((~unequally_directed_lines(L, L)) <=> (~unequally_directed_lines(L, L)))),
% 3.71/2.66 inference(bind,[status(th)],[])).
% 3.71/2.66 tff(19,plain,
% 3.71/2.66 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 3.71/2.66 inference(quant_intro,[status(thm)],[18])).
% 3.71/2.66 tff(20,plain,
% 3.71/2.66 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 3.71/2.66 inference(rewrite,[status(thm)],[])).
% 3.71/2.66 tff(21,axiom,(![L: $i] : (~unequally_directed_lines(L, L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag5')).
% 3.71/2.66 tff(22,plain,
% 3.71/2.66 (![L: $i] : (~unequally_directed_lines(L, L))),
% 3.71/2.66 inference(modus_ponens,[status(thm)],[21, 20])).
% 3.71/2.66 tff(23,plain,(
% 3.71/2.66 ![L: $i] : (~unequally_directed_lines(L, L))),
% 3.71/2.66 inference(skolemize,[status(sab)],[22])).
% 3.71/2.66 tff(24,plain,
% 3.71/2.66 (![L: $i] : (~unequally_directed_lines(L, L))),
% 3.71/2.66 inference(modus_ponens,[status(thm)],[23, 19])).
% 3.71/2.66 tff(25,plain,
% 3.71/2.66 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))))),
% 3.71/2.66 inference(quant_inst,[status(thm)],[])).
% 3.71/2.66 tff(26,plain,
% 3.71/2.66 ($false),
% 3.71/2.66 inference(unit_resolution,[status(thm)],[25, 24, 17])).
% 3.71/2.66 tff(27,plain,(~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))), inference(lemma,lemma(discharge,[]))).
% 3.71/2.66 tff(28,plain,
% 3.71/2.66 ((~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))) <=> (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B)))))),
% 3.71/2.66 inference(rewrite,[status(thm)],[])).
% 3.71/2.66 tff(29,plain,
% 3.71/2.66 ((~![L: $i, A: $i, B: $i, C: $i] : ((((line(L) & distinct_points(A, C)) & distinct_points(B, C)) & distinct_points(A, B)) => (~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))))) <=> (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B)))))),
% 3.71/2.66 inference(rewrite,[status(thm)],[])).
% 3.71/2.66 tff(30,axiom,(~![L: $i, A: $i, B: $i, C: $i] : ((((line(L) & distinct_points(A, C)) & distinct_points(B, C)) & distinct_points(A, B)) => (~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 3.71/2.66 tff(31,plain,
% 3.71/2.66 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 3.71/2.66 inference(modus_ponens,[status(thm)],[30, 29])).
% 3.71/2.66 tff(32,plain,
% 3.71/2.66 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 3.71/2.66 inference(modus_ponens,[status(thm)],[31, 28])).
% 3.71/2.66 tff(33,plain,
% 3.71/2.66 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 3.71/2.66 inference(modus_ponens,[status(thm)],[32, 28])).
% 3.71/2.66 tff(34,plain,
% 3.71/2.66 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 3.71/2.66 inference(modus_ponens,[status(thm)],[33, 28])).
% 3.71/2.66 tff(35,plain,
% 3.71/2.66 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[34, 28])).
% 3.71/2.67 tff(36,plain,
% 3.71/2.67 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[35, 28])).
% 3.71/2.67 tff(37,plain,
% 3.71/2.67 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[36, 28])).
% 3.71/2.67 tff(38,plain,(
% 3.71/2.67 ~((~(between_on_line(L!3, A!2, B!1, C!0) & between_on_line(L!3, B!1, A!2, C!0))) | (~(line(L!3) & distinct_points(A!2, C!0) & distinct_points(B!1, C!0) & distinct_points(A!2, B!1))))),
% 3.71/2.67 inference(skolemize,[status(sab)],[37])).
% 3.71/2.67 tff(39,plain,
% 3.71/2.67 (line(L!3) & distinct_points(A!2, C!0) & distinct_points(B!1, C!0) & distinct_points(A!2, B!1)),
% 3.71/2.67 inference(or_elim,[status(thm)],[38])).
% 3.71/2.67 tff(40,plain,
% 3.71/2.67 (line(L!3)),
% 3.71/2.67 inference(and_elim,[status(thm)],[39])).
% 3.71/2.67 tff(41,plain,
% 3.71/2.67 (^[L: $i] : refl((line(reverse_line(L)) | (~line(L))) <=> (line(reverse_line(L)) | (~line(L))))),
% 3.71/2.67 inference(bind,[status(th)],[])).
% 3.71/2.67 tff(42,plain,
% 3.71/2.67 (![L: $i] : (line(reverse_line(L)) | (~line(L))) <=> ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[41])).
% 3.71/2.67 tff(43,plain,
% 3.71/2.67 (![L: $i] : (line(reverse_line(L)) | (~line(L))) <=> ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(44,plain,
% 3.71/2.67 (^[L: $i] : rewrite((line(L) => line(reverse_line(L))) <=> (line(reverse_line(L)) | (~line(L))))),
% 3.71/2.67 inference(bind,[status(th)],[])).
% 3.71/2.67 tff(45,plain,
% 3.71/2.67 (![L: $i] : (line(L) => line(reverse_line(L))) <=> ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[44])).
% 3.71/2.67 tff(46,axiom,(![L: $i] : (line(L) => line(reverse_line(L)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oagco4')).
% 3.71/2.67 tff(47,plain,
% 3.71/2.67 (![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[46, 45])).
% 3.71/2.67 tff(48,plain,
% 3.71/2.67 (![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[47, 43])).
% 3.71/2.67 tff(49,plain,(
% 3.71/2.67 ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 3.71/2.67 inference(skolemize,[status(sab)],[48])).
% 3.71/2.67 tff(50,plain,
% 3.71/2.67 (![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[49, 42])).
% 3.71/2.67 tff(51,plain,
% 3.71/2.67 (((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | (line(reverse_line(L!3)) | (~line(L!3)))) <=> ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | line(reverse_line(L!3)) | (~line(L!3)))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(52,plain,
% 3.71/2.67 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | (line(reverse_line(L!3)) | (~line(L!3)))),
% 3.71/2.67 inference(quant_inst,[status(thm)],[])).
% 3.71/2.67 tff(53,plain,
% 3.71/2.67 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | line(reverse_line(L!3)) | (~line(L!3))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[52, 51])).
% 3.71/2.67 tff(54,plain,
% 3.71/2.67 (line(reverse_line(L!3))),
% 3.71/2.67 inference(unit_resolution,[status(thm)],[53, 50, 40])).
% 3.71/2.67 tff(55,plain,
% 3.71/2.67 (((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | (line(reverse_line(reverse_line(L!3))) | (~line(reverse_line(L!3))))) <=> ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | line(reverse_line(reverse_line(L!3))) | (~line(reverse_line(L!3))))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(56,plain,
% 3.71/2.67 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | (line(reverse_line(reverse_line(L!3))) | (~line(reverse_line(L!3))))),
% 3.71/2.67 inference(quant_inst,[status(thm)],[])).
% 3.71/2.67 tff(57,plain,
% 3.71/2.67 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | line(reverse_line(reverse_line(L!3))) | (~line(reverse_line(L!3)))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[56, 55])).
% 3.71/2.67 tff(58,plain,
% 3.71/2.67 (line(reverse_line(reverse_line(L!3)))),
% 3.71/2.67 inference(unit_resolution,[status(thm)],[57, 50, 54])).
% 3.71/2.67 tff(59,plain,
% 3.71/2.67 (^[L: $i, M: $i] : refl((unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L))))),
% 3.71/2.67 inference(bind,[status(th)],[])).
% 3.71/2.67 tff(60,plain,
% 3.71/2.67 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[59])).
% 3.71/2.67 tff(61,plain,
% 3.71/2.67 (^[L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((line(L) & line(M)) <=> (~((~line(M)) | (~line(L))))), ((~(line(L) & line(M))) <=> (~(~((~line(M)) | (~line(L))))))), rewrite((~(~((~line(M)) | (~line(L))))) <=> ((~line(M)) | (~line(L)))), ((~(line(L) & line(M))) <=> ((~line(M)) | (~line(L))))), ((unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | ((~line(M)) | (~line(L)))))), rewrite((unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | ((~line(M)) | (~line(L)))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))), ((unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))))),
% 3.71/2.67 inference(bind,[status(th)],[])).
% 3.71/2.67 tff(62,plain,
% 3.71/2.67 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[61])).
% 3.71/2.67 tff(63,plain,
% 3.71/2.67 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(64,plain,
% 3.71/2.67 (^[L: $i, M: $i] : rewrite(((line(L) & line(M)) => (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))))),
% 3.71/2.67 inference(bind,[status(th)],[])).
% 3.71/2.67 tff(65,plain,
% 3.71/2.67 (![L: $i, M: $i] : ((line(L) & line(M)) => (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[64])).
% 3.71/2.67 tff(66,axiom,(![L: $i, M: $i] : ((line(L) & line(M)) => (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag8')).
% 3.71/2.67 tff(67,plain,
% 3.71/2.67 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[66, 65])).
% 3.71/2.67 tff(68,plain,
% 3.71/2.67 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[67, 63])).
% 3.71/2.67 tff(69,plain,(
% 3.71/2.67 ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 3.71/2.67 inference(skolemize,[status(sab)],[68])).
% 3.71/2.67 tff(70,plain,
% 3.71/2.67 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[69, 62])).
% 3.71/2.67 tff(71,plain,
% 3.71/2.67 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[70, 60])).
% 3.71/2.67 tff(72,plain,
% 3.71/2.67 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(73,plain,
% 3.71/2.67 ((unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | (~line(reverse_line(reverse_line(L!3))))) <=> (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(74,plain,
% 3.71/2.67 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | (~line(reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3))))))),
% 3.71/2.67 inference(monotonicity,[status(thm)],[73])).
% 3.71/2.67 tff(75,plain,
% 3.71/2.67 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | (~line(reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 3.71/2.67 inference(transitivity,[status(thm)],[74, 72])).
% 3.71/2.67 tff(76,plain,
% 3.71/2.67 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | (~line(reverse_line(reverse_line(L!3)))))),
% 3.71/2.67 inference(quant_inst,[status(thm)],[])).
% 3.71/2.67 tff(77,plain,
% 3.71/2.67 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3))))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[76, 75])).
% 3.71/2.67 tff(78,plain,
% 3.71/2.67 (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3))))),
% 3.71/2.67 inference(unit_resolution,[status(thm)],[77, 71, 58])).
% 3.71/2.67 tff(79,plain,
% 3.71/2.67 (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3))))),
% 3.71/2.67 inference(unit_resolution,[status(thm)],[78, 27])).
% 3.71/2.67 tff(80,plain,
% 3.71/2.67 (^[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))))),
% 3.71/2.67 inference(bind,[status(th)],[])).
% 3.71/2.67 tff(81,plain,
% 3.71/2.67 (![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)))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[80])).
% 3.71/2.67 tff(82,plain,
% 3.71/2.67 (![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)))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(83,plain,
% 3.71/2.67 (^[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)))))),
% 3.71/2.67 inference(bind,[status(th)],[])).
% 3.71/2.67 tff(84,plain,
% 3.71/2.67 (![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)))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[83])).
% 3.71/2.67 tff(85,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/GEO007+0.ax','oag6')).
% 3.71/2.67 tff(86,plain,
% 3.71/2.67 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[85, 84])).
% 3.71/2.67 tff(87,plain,
% 3.71/2.67 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[86, 82])).
% 3.71/2.67 tff(88,plain,(
% 3.71/2.67 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 3.71/2.67 inference(skolemize,[status(sab)],[87])).
% 3.71/2.67 tff(89,plain,
% 3.71/2.67 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[88, 81])).
% 3.71/2.67 tff(90,plain,
% 3.71/2.67 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3))))))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(91,plain,
% 3.71/2.67 ((unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3)))))) <=> (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3))))))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(92,plain,
% 3.71/2.67 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3)))))))),
% 3.71/2.67 inference(monotonicity,[status(thm)],[91])).
% 3.71/2.67 tff(93,plain,
% 3.71/2.67 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3))))))),
% 3.71/2.67 inference(transitivity,[status(thm)],[92, 90])).
% 3.71/2.67 tff(94,plain,
% 3.71/2.67 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3))))))),
% 3.71/2.67 inference(quant_inst,[status(thm)],[])).
% 3.71/2.67 tff(95,plain,
% 3.71/2.67 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[94, 93])).
% 3.71/2.67 tff(96,plain,
% 3.71/2.67 (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 3.71/2.67 inference(unit_resolution,[status(thm)],[95, 89])).
% 3.71/2.67 tff(97,plain,
% 3.71/2.67 (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))),
% 3.71/2.67 inference(unit_resolution,[status(thm)],[96, 79, 27])).
% 3.71/2.67 tff(98,plain,
% 3.71/2.67 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!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(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(99,plain,
% 3.71/2.67 ((unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))))) <=> ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(100,plain,
% 3.71/2.67 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 3.71/2.67 inference(monotonicity,[status(thm)],[99])).
% 3.71/2.67 tff(101,plain,
% 3.71/2.67 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.67 inference(transitivity,[status(thm)],[100, 98])).
% 3.71/2.67 tff(102,plain,
% 3.71/2.67 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))),
% 3.71/2.67 inference(quant_inst,[status(thm)],[])).
% 3.71/2.67 tff(103,plain,
% 3.71/2.67 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[102, 101])).
% 3.71/2.67 tff(104,plain,
% 3.71/2.67 (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))),
% 3.71/2.67 inference(unit_resolution,[status(thm)],[103, 89, 97])).
% 3.71/2.67 tff(105,plain,
% 3.71/2.67 (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))),
% 3.71/2.67 inference(unit_resolution,[status(thm)],[104, 16])).
% 3.71/2.67 tff(106,plain,
% 3.71/2.67 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(line_connecting(B!1, B!1))))))),
% 3.71/2.67 inference(quant_inst,[status(thm)],[])).
% 3.71/2.67 tff(107,plain,
% 3.71/2.67 (~(left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(line_connecting(B!1, B!1)))))),
% 3.71/2.67 inference(unit_resolution,[status(thm)],[106, 8])).
% 3.71/2.67 tff(108,plain,
% 3.71/2.67 ((left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(line_connecting(B!1, B!1))))) | (~left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.67 inference(tautology,[status(thm)],[])).
% 3.71/2.67 tff(109,plain,
% 3.71/2.67 (~left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))),
% 3.71/2.67 inference(unit_resolution,[status(thm)],[108, 107])).
% 3.71/2.67 tff(110,plain,
% 3.71/2.67 (^[A: $i, B: $i] : refl((~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))))),
% 3.71/2.67 inference(bind,[status(th)],[])).
% 3.71/2.67 tff(111,plain,
% 3.71/2.67 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[110])).
% 3.71/2.67 tff(112,plain,
% 3.71/2.67 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(113,axiom,(![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oagco9')).
% 3.71/2.67 tff(114,plain,
% 3.71/2.67 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[113, 112])).
% 3.71/2.67 tff(115,plain,(
% 3.71/2.67 ![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 3.71/2.67 inference(skolemize,[status(sab)],[114])).
% 3.71/2.67 tff(116,plain,
% 3.71/2.67 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[115, 111])).
% 3.71/2.67 tff(117,plain,
% 3.71/2.67 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.67 inference(quant_inst,[status(thm)],[])).
% 3.71/2.67 tff(118,plain,
% 3.71/2.67 (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1)))),
% 3.71/2.67 inference(unit_resolution,[status(thm)],[117, 116])).
% 3.71/2.67 tff(119,plain,
% 3.71/2.67 (^[L: $i, M: $i, N: $i] : refl((unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M))) <=> (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M))))),
% 3.71/2.67 inference(bind,[status(th)],[])).
% 3.71/2.67 tff(120,plain,
% 3.71/2.67 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[119])).
% 3.71/2.67 tff(121,plain,
% 3.71/2.67 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(122,plain,
% 3.71/2.67 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(M, N) | left_convergent_lines(L, N)) <=> (unequally_directed_lines(M, N) | left_convergent_lines(L, N))), ((left_convergent_lines(L, M) => (unequally_directed_lines(M, N) | left_convergent_lines(L, N))) <=> (left_convergent_lines(L, M) => (unequally_directed_lines(M, N) | left_convergent_lines(L, N))))), rewrite((left_convergent_lines(L, M) => (unequally_directed_lines(M, N) | left_convergent_lines(L, N))) <=> (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))), ((left_convergent_lines(L, M) => (unequally_directed_lines(M, N) | left_convergent_lines(L, N))) <=> (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))))),
% 3.71/2.67 inference(bind,[status(th)],[])).
% 3.71/2.67 tff(123,plain,
% 3.71/2.67 (![L: $i, M: $i, N: $i] : (left_convergent_lines(L, M) => (unequally_directed_lines(M, N) | left_convergent_lines(L, N))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[122])).
% 3.71/2.67 tff(124,axiom,(![L: $i, M: $i, N: $i] : (left_convergent_lines(L, M) => (unequally_directed_lines(M, N) | left_convergent_lines(L, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oagsub3')).
% 3.71/2.67 tff(125,plain,
% 3.71/2.67 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[124, 123])).
% 3.71/2.67 tff(126,plain,
% 3.71/2.67 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[125, 121])).
% 3.71/2.67 tff(127,plain,(
% 3.71/2.67 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))),
% 3.71/2.67 inference(skolemize,[status(sab)],[126])).
% 3.71/2.67 tff(128,plain,
% 3.71/2.67 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[127, 120])).
% 3.71/2.67 tff(129,plain,
% 3.71/2.67 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(130,plain,
% 3.71/2.67 ((unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)))) <=> (unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(131,plain,
% 3.71/2.67 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))))),
% 3.71/2.67 inference(monotonicity,[status(thm)],[130])).
% 3.71/2.67 tff(132,plain,
% 3.71/2.67 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.67 inference(transitivity,[status(thm)],[131, 129])).
% 3.71/2.67 tff(133,plain,
% 3.71/2.67 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))))),
% 3.71/2.67 inference(quant_inst,[status(thm)],[])).
% 3.71/2.67 tff(134,plain,
% 3.71/2.67 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | left_convergent_lines(L, N) | (~left_convergent_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[133, 132])).
% 3.71/2.67 tff(135,plain,
% 3.71/2.67 (~left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))),
% 3.71/2.67 inference(unit_resolution,[status(thm)],[134, 128, 118, 109])).
% 3.71/2.67 tff(136,plain,
% 3.71/2.67 (^[L: $i, M: $i] : refl((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))),
% 3.71/2.67 inference(bind,[status(th)],[])).
% 3.71/2.67 tff(137,plain,
% 3.71/2.67 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[136])).
% 3.71/2.67 tff(138,plain,
% 3.71/2.67 (^[L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 3.71/2.67 inference(bind,[status(th)],[])).
% 3.71/2.67 tff(139,plain,
% 3.71/2.67 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[138])).
% 3.71/2.67 tff(140,plain,
% 3.71/2.67 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(141,plain,
% 3.71/2.67 (^[L: $i, M: $i] : rewrite(((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))))),
% 3.71/2.67 inference(bind,[status(th)],[])).
% 3.71/2.67 tff(142,plain,
% 3.71/2.67 (![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[141])).
% 3.71/2.67 tff(143,axiom,(![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag9')).
% 3.71/2.67 tff(144,plain,
% 3.71/2.67 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[143, 142])).
% 3.71/2.67 tff(145,plain,
% 3.71/2.67 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[144, 140])).
% 3.71/2.67 tff(146,plain,(
% 3.71/2.67 ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 3.71/2.67 inference(skolemize,[status(sab)],[145])).
% 3.71/2.67 tff(147,plain,
% 3.71/2.67 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[146, 139])).
% 3.71/2.67 tff(148,plain,
% 3.71/2.67 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 3.71/2.67 inference(modus_ponens,[status(thm)],[147, 137])).
% 3.71/2.67 tff(149,plain,
% 3.71/2.67 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(150,plain,
% 3.71/2.67 ((left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))))) <=> (left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(151,plain,
% 3.71/2.67 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)))))),
% 3.71/2.67 inference(monotonicity,[status(thm)],[150])).
% 3.71/2.67 tff(152,plain,
% 3.71/2.67 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))))),
% 3.71/2.67 inference(transitivity,[status(thm)],[151, 149])).
% 3.71/2.67 tff(153,plain,
% 3.71/2.67 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))))),
% 3.71/2.67 inference(quant_inst,[status(thm)],[])).
% 3.71/2.67 tff(154,plain,
% 3.71/2.67 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)))),
% 3.71/2.68 inference(modus_ponens,[status(thm)],[153, 152])).
% 3.71/2.68 tff(155,plain,
% 3.71/2.68 ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)))),
% 3.71/2.68 inference(unit_resolution,[status(thm)],[154, 148, 109, 135])).
% 3.71/2.68 tff(156,plain,
% 3.71/2.68 (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))),
% 3.71/2.68 inference(unit_resolution,[status(thm)],[155, 105])).
% 3.71/2.68 tff(157,assumption,(~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))), introduced(assumption)).
% 3.71/2.68 tff(158,assumption,(~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))), introduced(assumption)).
% 3.71/2.68 tff(159,plain,
% 3.71/2.68 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!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(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)))),
% 3.71/2.68 inference(rewrite,[status(thm)],[])).
% 3.71/2.68 tff(160,plain,
% 3.71/2.68 ((unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))))) <=> (unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)))),
% 3.71/2.68 inference(rewrite,[status(thm)],[])).
% 3.71/2.68 tff(161,plain,
% 3.71/2.68 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))))),
% 3.71/2.68 inference(monotonicity,[status(thm)],[160])).
% 3.71/2.68 tff(162,plain,
% 3.71/2.68 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)))),
% 3.71/2.68 inference(transitivity,[status(thm)],[161, 159])).
% 3.71/2.68 tff(163,plain,
% 3.71/2.68 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))),
% 3.71/2.68 inference(quant_inst,[status(thm)],[])).
% 3.71/2.68 tff(164,plain,
% 3.71/2.68 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))),
% 3.71/2.68 inference(modus_ponens,[status(thm)],[163, 162])).
% 3.71/2.68 tff(165,plain,
% 3.71/2.68 ($false),
% 3.71/2.68 inference(unit_resolution,[status(thm)],[164, 89, 97, 158, 157])).
% 3.71/2.68 tff(166,plain,(unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))), inference(lemma,lemma(discharge,[]))).
% 3.71/2.68 tff(167,plain,
% 3.71/2.68 (unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))),
% 3.71/2.68 inference(unit_resolution,[status(thm)],[166, 156])).
% 3.71/2.68 tff(168,plain,
% 3.71/2.68 (((~![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!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!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!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.68 inference(rewrite,[status(thm)],[])).
% 3.71/2.68 tff(169,plain,
% 3.71/2.68 ((unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)))) <=> (unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.68 inference(rewrite,[status(thm)],[])).
% 3.71/2.68 tff(170,plain,
% 3.71/2.68 (((~![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!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!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!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 3.71/2.68 inference(monotonicity,[status(thm)],[169])).
% 3.71/2.68 tff(171,plain,
% 3.71/2.68 (((~![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!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!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!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.68 inference(transitivity,[status(thm)],[170, 168])).
% 3.71/2.68 tff(172,plain,
% 3.71/2.68 ((~![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!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))))),
% 3.71/2.68 inference(quant_inst,[status(thm)],[])).
% 3.71/2.68 tff(173,plain,
% 3.71/2.68 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))),
% 3.71/2.68 inference(modus_ponens,[status(thm)],[172, 171])).
% 3.71/2.68 tff(174,plain,
% 3.71/2.68 ($false),
% 3.71/2.68 inference(unit_resolution,[status(thm)],[173, 89, 118, 167, 16])).
% 3.71/2.68 tff(175,plain,(unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))), inference(lemma,lemma(discharge,[]))).
% 3.71/2.68 tff(176,plain,
% 3.71/2.68 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.68 inference(rewrite,[status(thm)],[])).
% 3.71/2.68 tff(177,plain,
% 3.71/2.68 ((left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))) <=> ((~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.68 inference(rewrite,[status(thm)],[])).
% 3.71/2.68 tff(178,plain,
% 3.71/2.68 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 3.71/2.68 inference(monotonicity,[status(thm)],[177])).
% 3.71/2.68 tff(179,plain,
% 3.71/2.68 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))),
% 3.71/2.68 inference(transitivity,[status(thm)],[178, 176])).
% 3.71/2.68 tff(180,plain,
% 3.71/2.68 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 3.71/2.68 inference(quant_inst,[status(thm)],[])).
% 3.71/2.68 tff(181,plain,
% 3.71/2.68 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))),
% 3.71/2.68 inference(modus_ponens,[status(thm)],[180, 179])).
% 3.71/2.68 tff(182,plain,
% 3.71/2.68 (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))),
% 3.71/2.68 inference(unit_resolution,[status(thm)],[181, 148, 175, 15, 13])).
% 3.71/2.68 tff(183,plain,
% 3.71/2.68 (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))),
% 3.71/2.68 inference(unit_resolution,[status(thm)],[166, 182])).
% 3.71/2.68 tff(184,plain,
% 3.71/2.68 (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1)))),
% 3.71/2.68 inference(unit_resolution,[status(thm)],[155, 183])).
% 3.71/2.68 tff(185,plain,
% 3.71/2.68 (((~![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!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!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!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))))),
% 3.84/2.68 inference(rewrite,[status(thm)],[])).
% 3.84/2.68 tff(186,plain,
% 3.84/2.68 ((~![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!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1))))),
% 3.84/2.68 inference(quant_inst,[status(thm)],[])).
% 3.84/2.68 tff(187,plain,
% 3.84/2.68 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(B!1, B!1)))),
% 3.84/2.68 inference(modus_ponens,[status(thm)],[186, 185])).
% 3.84/2.68 tff(188,plain,
% 3.84/2.68 ($false),
% 3.84/2.68 inference(unit_resolution,[status(thm)],[187, 89, 118, 184, 183])).
% 3.84/2.68 % SZS output end Proof
%------------------------------------------------------------------------------