TSTP Solution File: GEO255+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO255+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 20:36:06 EDT 2022
% Result : Theorem 0.85s 0.82s
% Output : Proof 0.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO255+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.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 07:34:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.85/0.82 % SZS status Theorem
% 0.85/0.82 % SZS output start Proof
% 0.85/0.82 tff(left_convergent_lines_type, type, (
% 0.85/0.82 left_convergent_lines: ( $i * $i ) > $o)).
% 0.85/0.82 tff(line_connecting_type, type, (
% 0.85/0.82 line_connecting: ( $i * $i ) > $i)).
% 0.85/0.82 tff(tptp_fun_A_1_type, type, (
% 0.85/0.82 tptp_fun_A_1: $i)).
% 0.85/0.82 tff(tptp_fun_B_0_type, type, (
% 0.85/0.82 tptp_fun_B_0: $i)).
% 0.85/0.82 tff(reverse_line_type, type, (
% 0.85/0.82 reverse_line: $i > $i)).
% 0.85/0.82 tff(tptp_fun_L_2_type, type, (
% 0.85/0.82 tptp_fun_L_2: $i)).
% 0.85/0.82 tff(unequally_directed_lines_type, type, (
% 0.85/0.82 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.85/0.82 tff(line_type, type, (
% 0.85/0.82 line: $i > $o)).
% 0.85/0.82 tff(distinct_points_type, type, (
% 0.85/0.82 distinct_points: ( $i * $i ) > $o)).
% 0.85/0.82 tff(before_on_line_type, type, (
% 0.85/0.82 before_on_line: ( $i * $i * $i ) > $o)).
% 0.85/0.82 tff(left_apart_point_type, type, (
% 0.85/0.82 left_apart_point: ( $i * $i ) > $o)).
% 0.85/0.82 tff(1,plain,
% 0.85/0.82 (^[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)))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(2,plain,
% 0.85/0.82 (![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))))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[1])).
% 0.85/0.82 tff(3,plain,
% 0.85/0.82 (![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))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(4,axiom,(![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag11')).
% 0.85/0.82 tff(5,plain,
% 0.85/0.82 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.85/0.82 tff(6,plain,(
% 0.85/0.82 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.85/0.82 inference(skolemize,[status(sab)],[5])).
% 0.85/0.82 tff(7,plain,
% 0.85/0.82 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.85/0.82 tff(8,plain,
% 0.85/0.82 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | left_convergent_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1)))))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(9,plain,
% 0.85/0.82 (~(left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | left_convergent_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.85/0.82 tff(10,plain,
% 0.85/0.82 ((left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | left_convergent_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1)))) | (~left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)))),
% 0.85/0.82 inference(tautology,[status(thm)],[])).
% 0.85/0.82 tff(11,plain,
% 0.85/0.82 (~left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.85/0.82 tff(12,plain,
% 0.85/0.82 ((left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | left_convergent_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1)))) | (~left_convergent_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))))),
% 0.85/0.82 inference(tautology,[status(thm)],[])).
% 0.85/0.82 tff(13,plain,
% 0.85/0.82 (~left_convergent_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1)))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[12, 9])).
% 0.85/0.82 tff(14,assumption,(~unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1)))), introduced(assumption)).
% 0.85/0.82 tff(15,assumption,(unequally_directed_lines(reverse_line(L!2), reverse_line(L!2))), introduced(assumption)).
% 0.85/0.82 tff(16,plain,
% 0.85/0.82 (^[L: $i] : refl((~unequally_directed_lines(L, L)) <=> (~unequally_directed_lines(L, L)))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(17,plain,
% 0.85/0.82 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[16])).
% 0.85/0.82 tff(18,plain,
% 0.85/0.82 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(19,axiom,(![L: $i] : (~unequally_directed_lines(L, L))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag5')).
% 0.85/0.82 tff(20,plain,
% 0.85/0.82 (![L: $i] : (~unequally_directed_lines(L, L))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.85/0.82 tff(21,plain,(
% 0.85/0.82 ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.85/0.82 inference(skolemize,[status(sab)],[20])).
% 0.85/0.82 tff(22,plain,
% 0.85/0.82 (![L: $i] : (~unequally_directed_lines(L, L))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.85/0.82 tff(23,plain,
% 0.85/0.82 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(reverse_line(L!2), reverse_line(L!2)))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(24,plain,
% 0.85/0.82 ($false),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[23, 22, 15])).
% 0.85/0.82 tff(25,plain,(~unequally_directed_lines(reverse_line(L!2), reverse_line(L!2))), inference(lemma,lemma(discharge,[]))).
% 0.85/0.82 tff(26,plain,
% 0.85/0.82 ((~![L: $i, A: $i, B: $i] : ((~(line(L) & distinct_points(A, B))) | (~(before_on_line(L, A, B) & before_on_line(L, B, A))))) <=> (~![L: $i, A: $i, B: $i] : ((~(line(L) & distinct_points(A, B))) | (~(before_on_line(L, A, B) & before_on_line(L, B, A)))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(27,plain,
% 0.85/0.82 ((~![L: $i, A: $i, B: $i] : ((line(L) & distinct_points(A, B)) => (~(before_on_line(L, A, B) & before_on_line(L, B, A))))) <=> (~![L: $i, A: $i, B: $i] : ((~(line(L) & distinct_points(A, B))) | (~(before_on_line(L, A, B) & before_on_line(L, B, A)))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(28,axiom,(~![L: $i, A: $i, B: $i] : ((line(L) & distinct_points(A, B)) => (~(before_on_line(L, A, B) & before_on_line(L, B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.85/0.82 tff(29,plain,
% 0.85/0.82 (~![L: $i, A: $i, B: $i] : ((~(line(L) & distinct_points(A, B))) | (~(before_on_line(L, A, B) & before_on_line(L, B, A))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.85/0.82 tff(30,plain,
% 0.85/0.82 (~![L: $i, A: $i, B: $i] : ((~(line(L) & distinct_points(A, B))) | (~(before_on_line(L, A, B) & before_on_line(L, B, A))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.85/0.82 tff(31,plain,
% 0.85/0.82 (~![L: $i, A: $i, B: $i] : ((~(line(L) & distinct_points(A, B))) | (~(before_on_line(L, A, B) & before_on_line(L, B, A))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.85/0.82 tff(32,plain,
% 0.85/0.82 (~![L: $i, A: $i, B: $i] : ((~(line(L) & distinct_points(A, B))) | (~(before_on_line(L, A, B) & before_on_line(L, B, A))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.85/0.82 tff(33,plain,
% 0.85/0.82 (~![L: $i, A: $i, B: $i] : ((~(line(L) & distinct_points(A, B))) | (~(before_on_line(L, A, B) & before_on_line(L, B, A))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.85/0.82 tff(34,plain,
% 0.85/0.82 (~![L: $i, A: $i, B: $i] : ((~(line(L) & distinct_points(A, B))) | (~(before_on_line(L, A, B) & before_on_line(L, B, A))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.85/0.82 tff(35,plain,
% 0.85/0.82 (~![L: $i, A: $i, B: $i] : ((~(line(L) & distinct_points(A, B))) | (~(before_on_line(L, A, B) & before_on_line(L, B, A))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.85/0.82 tff(36,plain,(
% 0.85/0.82 ~((~(line(L!2) & distinct_points(A!1, B!0))) | (~(before_on_line(L!2, A!1, B!0) & before_on_line(L!2, B!0, A!1))))),
% 0.85/0.82 inference(skolemize,[status(sab)],[35])).
% 0.85/0.82 tff(37,plain,
% 0.85/0.82 (line(L!2) & distinct_points(A!1, B!0)),
% 0.85/0.82 inference(or_elim,[status(thm)],[36])).
% 0.85/0.82 tff(38,plain,
% 0.85/0.82 (line(L!2)),
% 0.85/0.82 inference(and_elim,[status(thm)],[37])).
% 0.85/0.82 tff(39,plain,
% 0.85/0.82 (^[L: $i] : refl((line(reverse_line(L)) | (~line(L))) <=> (line(reverse_line(L)) | (~line(L))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(40,plain,
% 0.85/0.82 (![L: $i] : (line(reverse_line(L)) | (~line(L))) <=> ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[39])).
% 0.85/0.82 tff(41,plain,
% 0.85/0.82 (![L: $i] : (line(reverse_line(L)) | (~line(L))) <=> ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(42,plain,
% 0.85/0.82 (^[L: $i] : rewrite((line(L) => line(reverse_line(L))) <=> (line(reverse_line(L)) | (~line(L))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(43,plain,
% 0.85/0.82 (![L: $i] : (line(L) => line(reverse_line(L))) <=> ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[42])).
% 0.85/0.82 tff(44,axiom,(![L: $i] : (line(L) => line(reverse_line(L)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oagco4')).
% 0.85/0.82 tff(45,plain,
% 0.85/0.82 (![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.85/0.82 tff(46,plain,
% 0.85/0.82 (![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.85/0.82 tff(47,plain,(
% 0.85/0.82 ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 0.85/0.82 inference(skolemize,[status(sab)],[46])).
% 0.85/0.82 tff(48,plain,
% 0.85/0.82 (![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.85/0.82 tff(49,plain,
% 0.85/0.82 (((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | (line(reverse_line(L!2)) | (~line(L!2)))) <=> ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | line(reverse_line(L!2)) | (~line(L!2)))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(50,plain,
% 0.85/0.82 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | (line(reverse_line(L!2)) | (~line(L!2)))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(51,plain,
% 0.85/0.82 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | line(reverse_line(L!2)) | (~line(L!2))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.85/0.82 tff(52,plain,
% 0.85/0.82 (line(reverse_line(L!2))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[51, 48, 38])).
% 0.85/0.82 tff(53,plain,
% 0.85/0.82 (^[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))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(54,plain,
% 0.85/0.82 (![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)))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[53])).
% 0.85/0.82 tff(55,plain,
% 0.85/0.82 (^[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)))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(56,plain,
% 0.85/0.82 (![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)))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[55])).
% 0.85/0.82 tff(57,plain,
% 0.85/0.82 (![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))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(58,plain,
% 0.85/0.82 (^[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)))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(59,plain,
% 0.85/0.82 (![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))))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[58])).
% 0.85/0.82 tff(60,axiom,(![L: $i, M: $i] : ((line(L) & line(M)) => (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag8')).
% 0.85/0.82 tff(61,plain,
% 0.85/0.82 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.85/0.82 tff(62,plain,
% 0.85/0.82 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.85/0.82 tff(63,plain,(
% 0.85/0.82 ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 0.85/0.82 inference(skolemize,[status(sab)],[62])).
% 0.85/0.82 tff(64,plain,
% 0.85/0.82 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.85/0.82 tff(65,plain,
% 0.85/0.82 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.85/0.82 tff(66,plain,
% 0.85/0.82 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | ((~line(L!2)) | unequally_directed_lines(reverse_line(L!2), reverse_line(L!2)) | (~line(reverse_line(L!2))) | unequally_directed_lines(reverse_line(L!2), L!2))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (~line(L!2)) | unequally_directed_lines(reverse_line(L!2), reverse_line(L!2)) | (~line(reverse_line(L!2))) | unequally_directed_lines(reverse_line(L!2), L!2))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(67,plain,
% 0.85/0.82 ((unequally_directed_lines(reverse_line(L!2), reverse_line(L!2)) | unequally_directed_lines(reverse_line(L!2), L!2) | (~line(L!2)) | (~line(reverse_line(L!2)))) <=> ((~line(L!2)) | unequally_directed_lines(reverse_line(L!2), reverse_line(L!2)) | (~line(reverse_line(L!2))) | unequally_directed_lines(reverse_line(L!2), L!2))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(68,plain,
% 0.85/0.82 (((~![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(L!2), reverse_line(L!2)) | unequally_directed_lines(reverse_line(L!2), L!2) | (~line(L!2)) | (~line(reverse_line(L!2))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | ((~line(L!2)) | unequally_directed_lines(reverse_line(L!2), reverse_line(L!2)) | (~line(reverse_line(L!2))) | unequally_directed_lines(reverse_line(L!2), L!2)))),
% 0.85/0.82 inference(monotonicity,[status(thm)],[67])).
% 0.85/0.82 tff(69,plain,
% 0.85/0.82 (((~![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(L!2), reverse_line(L!2)) | unequally_directed_lines(reverse_line(L!2), L!2) | (~line(L!2)) | (~line(reverse_line(L!2))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (~line(L!2)) | unequally_directed_lines(reverse_line(L!2), reverse_line(L!2)) | (~line(reverse_line(L!2))) | unequally_directed_lines(reverse_line(L!2), L!2))),
% 0.85/0.82 inference(transitivity,[status(thm)],[68, 66])).
% 0.85/0.82 tff(70,plain,
% 0.85/0.82 ((~![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(L!2), reverse_line(L!2)) | unequally_directed_lines(reverse_line(L!2), L!2) | (~line(L!2)) | (~line(reverse_line(L!2))))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(71,plain,
% 0.85/0.82 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (~line(L!2)) | unequally_directed_lines(reverse_line(L!2), reverse_line(L!2)) | (~line(reverse_line(L!2))) | unequally_directed_lines(reverse_line(L!2), L!2)),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.85/0.82 tff(72,plain,
% 0.85/0.82 (unequally_directed_lines(reverse_line(L!2), reverse_line(L!2)) | unequally_directed_lines(reverse_line(L!2), L!2)),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[71, 65, 38, 52])).
% 0.85/0.82 tff(73,plain,
% 0.85/0.82 (unequally_directed_lines(reverse_line(L!2), L!2)),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[72, 25])).
% 0.85/0.82 tff(74,plain,
% 0.85/0.82 (^[L: $i, A: $i, B: $i] : refl((before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))))) <=> (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(75,plain,
% 0.85/0.82 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[74])).
% 0.85/0.82 tff(76,plain,
% 0.85/0.82 (^[L: $i, A: $i, B: $i] : rewrite((before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(77,plain,
% 0.85/0.82 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[76])).
% 0.85/0.82 tff(78,plain,
% 0.85/0.82 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(79,plain,
% 0.85/0.82 (^[L: $i, A: $i, B: $i] : rewrite((before_on_line(L, A, B) <=> (((distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L))))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(80,plain,
% 0.85/0.82 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (((distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L))))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[79])).
% 0.85/0.82 tff(81,axiom,(![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (((distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L))))) & (~unequally_directed_lines(L, line_connecting(A, B)))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','bf_def')).
% 0.85/0.82 tff(82,plain,
% 0.85/0.82 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.85/0.82 tff(83,plain,
% 0.85/0.82 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.85/0.82 tff(84,plain,(
% 0.85/0.82 ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 0.85/0.82 inference(skolemize,[status(sab)],[83])).
% 0.85/0.82 tff(85,plain,
% 0.85/0.82 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.85/0.82 tff(86,plain,
% 0.85/0.82 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.85/0.82 tff(87,plain,
% 0.85/0.82 ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!2, A!1, B!0) <=> (~(unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(A!1, B!0)))))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(88,plain,
% 0.85/0.82 (before_on_line(L!2, A!1, B!0) <=> (~(unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(A!1, B!0))))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.85/0.82 tff(89,plain,
% 0.85/0.82 (before_on_line(L!2, A!1, B!0) & before_on_line(L!2, B!0, A!1)),
% 0.85/0.82 inference(or_elim,[status(thm)],[36])).
% 0.85/0.82 tff(90,plain,
% 0.85/0.82 (before_on_line(L!2, A!1, B!0)),
% 0.85/0.82 inference(and_elim,[status(thm)],[89])).
% 0.85/0.82 tff(91,plain,
% 0.85/0.82 ((~(before_on_line(L!2, A!1, B!0) <=> (~(unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(A!1, B!0)))))) | (~before_on_line(L!2, A!1, B!0)) | (~(unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(A!1, B!0))))),
% 0.85/0.82 inference(tautology,[status(thm)],[])).
% 0.85/0.82 tff(92,plain,
% 0.85/0.82 ((~(before_on_line(L!2, A!1, B!0) <=> (~(unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(A!1, B!0)))))) | (~(unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(A!1, B!0))))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.85/0.82 tff(93,plain,
% 0.85/0.82 (~(unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(A!1, B!0)))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[92, 88])).
% 0.85/0.82 tff(94,plain,
% 0.85/0.82 ((unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(A!1, B!0))) | (~unequally_directed_lines(L!2, line_connecting(A!1, B!0)))),
% 0.85/0.82 inference(tautology,[status(thm)],[])).
% 0.85/0.82 tff(95,plain,
% 0.85/0.82 (~unequally_directed_lines(L!2, line_connecting(A!1, B!0))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.85/0.82 tff(96,plain,
% 0.85/0.82 (^[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))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(97,plain,
% 0.85/0.82 (![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)))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[96])).
% 0.85/0.82 tff(98,plain,
% 0.85/0.82 (![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)))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(99,plain,
% 0.85/0.82 (^[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)))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(100,plain,
% 0.85/0.82 (![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)))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[99])).
% 0.85/0.82 tff(101,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/sandbox2/benchmark/Axioms/GEO007+0.ax','oag6')).
% 0.85/0.82 tff(102,plain,
% 0.85/0.82 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.85/0.82 tff(103,plain,
% 0.85/0.82 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.85/0.82 tff(104,plain,(
% 0.85/0.82 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.85/0.82 inference(skolemize,[status(sab)],[103])).
% 0.85/0.82 tff(105,plain,
% 0.85/0.82 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.85/0.82 tff(106,plain,
% 0.85/0.82 (((~![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(reverse_line(L!2), L!2)) | unequally_directed_lines(reverse_line(L!2), 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(L!2, line_connecting(A!1, B!0)) | (~unequally_directed_lines(reverse_line(L!2), L!2)) | unequally_directed_lines(reverse_line(L!2), line_connecting(A!1, B!0)))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(107,plain,
% 0.85/0.82 ((unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | unequally_directed_lines(reverse_line(L!2), line_connecting(A!1, B!0)) | (~unequally_directed_lines(reverse_line(L!2), L!2))) <=> (unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | (~unequally_directed_lines(reverse_line(L!2), L!2)) | unequally_directed_lines(reverse_line(L!2), line_connecting(A!1, B!0)))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(108,plain,
% 0.85/0.82 (((~![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(reverse_line(L!2), line_connecting(A!1, B!0)) | (~unequally_directed_lines(reverse_line(L!2), 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(reverse_line(L!2), L!2)) | unequally_directed_lines(reverse_line(L!2), line_connecting(A!1, B!0))))),
% 0.85/0.82 inference(monotonicity,[status(thm)],[107])).
% 0.85/0.82 tff(109,plain,
% 0.85/0.82 (((~![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(reverse_line(L!2), line_connecting(A!1, B!0)) | (~unequally_directed_lines(reverse_line(L!2), 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(reverse_line(L!2), L!2)) | unequally_directed_lines(reverse_line(L!2), line_connecting(A!1, B!0)))),
% 0.85/0.82 inference(transitivity,[status(thm)],[108, 106])).
% 0.85/0.82 tff(110,plain,
% 0.85/0.82 ((~![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(reverse_line(L!2), line_connecting(A!1, B!0)) | (~unequally_directed_lines(reverse_line(L!2), L!2)))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(111,plain,
% 0.85/0.82 ((~![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(reverse_line(L!2), L!2)) | unequally_directed_lines(reverse_line(L!2), line_connecting(A!1, B!0))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.85/0.82 tff(112,plain,
% 0.85/0.82 (unequally_directed_lines(reverse_line(L!2), line_connecting(A!1, B!0))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[111, 105, 95, 73])).
% 0.85/0.82 tff(113,plain,
% 0.85/0.82 (^[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)))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(114,plain,
% 0.85/0.82 (![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))))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[113])).
% 0.85/0.82 tff(115,plain,
% 0.85/0.82 (![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))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(116,axiom,(![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oagco9')).
% 0.85/0.82 tff(117,plain,
% 0.85/0.82 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.85/0.82 tff(118,plain,(
% 0.85/0.82 ![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.85/0.82 inference(skolemize,[status(sab)],[117])).
% 0.85/0.82 tff(119,plain,
% 0.85/0.82 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.85/0.82 tff(120,plain,
% 0.85/0.82 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(121,plain,
% 0.85/0.82 (~unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1)))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.85/0.82 tff(122,plain,
% 0.85/0.82 (((~![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(reverse_line(L!2), line_connecting(A!1, B!0))) | unequally_directed_lines(reverse_line(L!2), reverse_line(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), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(reverse_line(L!2), line_connecting(A!1, B!0))) | unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(123,plain,
% 0.85/0.82 ((unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(reverse_line(L!2), 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(reverse_line(L!2), line_connecting(A!1, B!0))) | unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(124,plain,
% 0.85/0.83 (((~![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(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(reverse_line(L!2), 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(reverse_line(L!2), line_connecting(A!1, B!0))) | unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1)))))),
% 0.85/0.83 inference(monotonicity,[status(thm)],[123])).
% 0.85/0.83 tff(125,plain,
% 0.85/0.83 (((~![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(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(reverse_line(L!2), 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(reverse_line(L!2), line_connecting(A!1, B!0))) | unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))))),
% 0.85/0.83 inference(transitivity,[status(thm)],[124, 122])).
% 0.85/0.83 tff(126,plain,
% 0.85/0.83 ((~![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(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(reverse_line(L!2), line_connecting(A!1, B!0))))),
% 0.85/0.83 inference(quant_inst,[status(thm)],[])).
% 0.85/0.83 tff(127,plain,
% 0.85/0.83 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!1, B!0), reverse_line(line_connecting(B!0, A!1))) | (~unequally_directed_lines(reverse_line(L!2), line_connecting(A!1, B!0))) | unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1)))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.85/0.83 tff(128,plain,
% 0.85/0.83 ($false),
% 0.85/0.83 inference(unit_resolution,[status(thm)],[127, 105, 121, 112, 14])).
% 0.85/0.83 tff(129,plain,(unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1)))), inference(lemma,lemma(discharge,[]))).
% 0.85/0.83 tff(130,plain,
% 0.85/0.83 (((~![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(L!2, 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(L!2, L!2)))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(131,plain,
% 0.85/0.83 ((unequally_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, L!2))) <=> (unequally_directed_lines(L!2, line_connecting(A!1, B!0)) | (~unequally_directed_lines(L!2, L!2)))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(132,plain,
% 0.85/0.83 (((~![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(L!2, line_connecting(A!1, B!0)) | (~unequally_directed_lines(L!2, 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(L!2, L!2))))),
% 0.85/0.83 inference(monotonicity,[status(thm)],[131])).
% 0.85/0.83 tff(133,plain,
% 0.85/0.83 (((~![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(L!2, line_connecting(A!1, B!0)) | (~unequally_directed_lines(L!2, 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(L!2, L!2)))),
% 0.85/0.83 inference(transitivity,[status(thm)],[132, 130])).
% 0.85/0.83 tff(134,plain,
% 0.85/0.83 ((~![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(L!2, line_connecting(A!1, B!0)) | (~unequally_directed_lines(L!2, L!2)))),
% 0.85/0.83 inference(quant_inst,[status(thm)],[])).
% 0.85/0.83 tff(135,plain,
% 0.85/0.83 ((~![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(L!2, L!2))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.85/0.83 tff(136,plain,
% 0.85/0.83 (~unequally_directed_lines(L!2, L!2)),
% 0.85/0.83 inference(unit_resolution,[status(thm)],[135, 105, 95])).
% 0.85/0.83 tff(137,plain,
% 0.85/0.83 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!2, L!2) | (~line(L!2)) | unequally_directed_lines(L!2, reverse_line(L!2)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | unequally_directed_lines(L!2, L!2) | (~line(L!2)) | unequally_directed_lines(L!2, reverse_line(L!2)))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(138,plain,
% 0.85/0.83 ((unequally_directed_lines(L!2, reverse_line(L!2)) | unequally_directed_lines(L!2, L!2) | (~line(L!2)) | (~line(L!2))) <=> (unequally_directed_lines(L!2, L!2) | (~line(L!2)) | unequally_directed_lines(L!2, reverse_line(L!2)))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(139,plain,
% 0.85/0.83 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!2, reverse_line(L!2)) | unequally_directed_lines(L!2, L!2) | (~line(L!2)) | (~line(L!2)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!2, L!2) | (~line(L!2)) | unequally_directed_lines(L!2, reverse_line(L!2))))),
% 0.85/0.83 inference(monotonicity,[status(thm)],[138])).
% 0.85/0.83 tff(140,plain,
% 0.85/0.83 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!2, reverse_line(L!2)) | unequally_directed_lines(L!2, L!2) | (~line(L!2)) | (~line(L!2)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | unequally_directed_lines(L!2, L!2) | (~line(L!2)) | unequally_directed_lines(L!2, reverse_line(L!2)))),
% 0.85/0.83 inference(transitivity,[status(thm)],[139, 137])).
% 0.85/0.83 tff(141,plain,
% 0.85/0.83 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!2, reverse_line(L!2)) | unequally_directed_lines(L!2, L!2) | (~line(L!2)) | (~line(L!2)))),
% 0.85/0.83 inference(quant_inst,[status(thm)],[])).
% 0.85/0.83 tff(142,plain,
% 0.85/0.83 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | unequally_directed_lines(L!2, L!2) | (~line(L!2)) | unequally_directed_lines(L!2, reverse_line(L!2))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.85/0.83 tff(143,plain,
% 0.85/0.83 (unequally_directed_lines(L!2, reverse_line(L!2))),
% 0.85/0.83 inference(unit_resolution,[status(thm)],[142, 65, 38, 136])).
% 0.85/0.83 tff(144,plain,
% 0.85/0.83 (((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!2, B!0, A!1) <=> (~(left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1)))))) <=> ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!2, B!0, A!1) <=> (~(left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1))))))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(145,plain,
% 0.85/0.83 ((before_on_line(L!2, B!0, A!1) <=> (~(unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | (~distinct_points(B!0, A!1))))) <=> (before_on_line(L!2, B!0, A!1) <=> (~(left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1)))))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(146,plain,
% 0.85/0.83 (((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!2, B!0, A!1) <=> (~(unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | (~distinct_points(B!0, A!1)))))) <=> ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!2, B!0, A!1) <=> (~(left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1))))))),
% 0.85/0.83 inference(monotonicity,[status(thm)],[145])).
% 0.85/0.83 tff(147,plain,
% 0.85/0.83 (((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!2, B!0, A!1) <=> (~(unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | (~distinct_points(B!0, A!1)))))) <=> ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!2, B!0, A!1) <=> (~(left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1))))))),
% 0.85/0.83 inference(transitivity,[status(thm)],[146, 144])).
% 0.85/0.83 tff(148,plain,
% 0.85/0.83 ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!2, B!0, A!1) <=> (~(unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | (~distinct_points(B!0, A!1)))))),
% 0.85/0.83 inference(quant_inst,[status(thm)],[])).
% 0.85/0.83 tff(149,plain,
% 0.85/0.83 ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!2, B!0, A!1) <=> (~(left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1)))))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.85/0.83 tff(150,plain,
% 0.85/0.83 (before_on_line(L!2, B!0, A!1) <=> (~(left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1))))),
% 0.85/0.83 inference(unit_resolution,[status(thm)],[149, 86])).
% 0.85/0.83 tff(151,plain,
% 0.85/0.83 (before_on_line(L!2, B!0, A!1)),
% 0.85/0.83 inference(and_elim,[status(thm)],[89])).
% 0.85/0.83 tff(152,plain,
% 0.85/0.83 ((~(before_on_line(L!2, B!0, A!1) <=> (~(left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1)))))) | (~before_on_line(L!2, B!0, A!1)) | (~(left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1))))),
% 0.85/0.83 inference(tautology,[status(thm)],[])).
% 0.85/0.83 tff(153,plain,
% 0.85/0.83 ((~(before_on_line(L!2, B!0, A!1) <=> (~(left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1)))))) | (~(left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1))))),
% 0.85/0.83 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.85/0.83 tff(154,plain,
% 0.85/0.83 (~(left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1)))),
% 0.85/0.83 inference(unit_resolution,[status(thm)],[153, 150])).
% 0.85/0.83 tff(155,plain,
% 0.85/0.83 ((left_apart_point(B!0, reverse_line(L!2)) | left_apart_point(B!0, L!2) | left_apart_point(A!1, reverse_line(L!2)) | left_apart_point(A!1, L!2) | (~distinct_points(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)))),
% 0.85/0.83 inference(tautology,[status(thm)],[])).
% 0.85/0.83 tff(156,plain,
% 0.85/0.83 (~unequally_directed_lines(L!2, line_connecting(B!0, A!1))),
% 0.85/0.83 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.85/0.83 tff(157,plain,
% 0.85/0.83 (((~![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(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(L!2, reverse_line(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(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(L!2, reverse_line(L!2))))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(158,plain,
% 0.85/0.83 ((unequally_directed_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | (~unequally_directed_lines(L!2, reverse_line(L!2)))) <=> (unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | unequally_directed_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(L!2, reverse_line(L!2))))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(159,plain,
% 0.85/0.83 (((~![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(L!2), line_connecting(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | (~unequally_directed_lines(L!2, reverse_line(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(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(L!2, reverse_line(L!2)))))),
% 0.85/0.83 inference(monotonicity,[status(thm)],[158])).
% 0.85/0.83 tff(160,plain,
% 0.85/0.83 (((~![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(L!2), line_connecting(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | (~unequally_directed_lines(L!2, reverse_line(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(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(L!2, reverse_line(L!2))))),
% 0.85/0.83 inference(transitivity,[status(thm)],[159, 157])).
% 0.85/0.83 tff(161,plain,
% 0.85/0.83 ((~![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(L!2), line_connecting(B!0, A!1)) | unequally_directed_lines(L!2, line_connecting(B!0, A!1)) | (~unequally_directed_lines(L!2, reverse_line(L!2))))),
% 0.85/0.83 inference(quant_inst,[status(thm)],[])).
% 0.85/0.83 tff(162,plain,
% 0.85/0.83 ((~![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(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(L!2, reverse_line(L!2)))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.85/0.83 tff(163,plain,
% 0.85/0.83 (unequally_directed_lines(reverse_line(L!2), line_connecting(B!0, A!1))),
% 0.85/0.83 inference(unit_resolution,[status(thm)],[162, 105, 156, 143])).
% 0.85/0.83 tff(164,plain,
% 0.85/0.83 (^[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)))))),
% 0.85/0.83 inference(bind,[status(th)],[])).
% 0.85/0.83 tff(165,plain,
% 0.85/0.83 (![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))))),
% 0.85/0.83 inference(quant_intro,[status(thm)],[164])).
% 0.85/0.83 tff(166,plain,
% 0.85/0.83 (^[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))))))),
% 0.85/0.83 inference(bind,[status(th)],[])).
% 0.85/0.83 tff(167,plain,
% 0.85/0.83 (![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))))),
% 0.85/0.83 inference(quant_intro,[status(thm)],[166])).
% 0.85/0.83 tff(168,plain,
% 0.85/0.83 (![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)))))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(169,plain,
% 0.85/0.83 (^[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))))))),
% 0.85/0.83 inference(bind,[status(th)],[])).
% 0.85/0.83 tff(170,plain,
% 0.85/0.83 (![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)))))),
% 0.85/0.83 inference(quant_intro,[status(thm)],[169])).
% 0.85/0.83 tff(171,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/sandbox2/benchmark/Axioms/GEO007+0.ax','oag9')).
% 0.85/0.83 tff(172,plain,
% 0.85/0.83 (![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)))))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.85/0.83 tff(173,plain,
% 0.85/0.83 (![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)))))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.85/0.83 tff(174,plain,(
% 0.85/0.83 ![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)))))),
% 0.85/0.83 inference(skolemize,[status(sab)],[173])).
% 0.85/0.83 tff(175,plain,
% 0.85/0.83 (![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))))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.85/0.83 tff(176,plain,
% 0.85/0.83 (![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))))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[175, 165])).
% 0.85/0.83 tff(177,plain,
% 0.85/0.83 (((~![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(L!2), line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!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(L!2), line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1)))))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(178,plain,
% 0.85/0.83 ((left_convergent_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(reverse_line(L!2), line_connecting(B!0, A!1))) | (~unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))))) <=> ((~unequally_directed_lines(reverse_line(L!2), line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1)))))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(179,plain,
% 0.85/0.83 (((~![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(L!2), reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(reverse_line(L!2), line_connecting(B!0, A!1))) | (~unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!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(L!2), line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))))))),
% 0.85/0.84 inference(monotonicity,[status(thm)],[178])).
% 0.85/0.84 tff(180,plain,
% 0.85/0.84 (((~![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(L!2), reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(reverse_line(L!2), line_connecting(B!0, A!1))) | (~unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!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(L!2), line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1)))))),
% 0.85/0.84 inference(transitivity,[status(thm)],[179, 177])).
% 0.85/0.84 tff(181,plain,
% 0.85/0.84 ((~![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(L!2), reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(reverse_line(L!2), line_connecting(B!0, A!1))) | (~unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1)))))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(182,plain,
% 0.85/0.84 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(L!2), line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1)) | (~unequally_directed_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.85/0.84 tff(183,plain,
% 0.85/0.84 (left_convergent_lines(reverse_line(L!2), reverse_line(line_connecting(B!0, A!1))) | left_convergent_lines(reverse_line(L!2), line_connecting(B!0, A!1))),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[182, 176, 163, 129])).
% 0.85/0.84 tff(184,plain,
% 0.85/0.84 ($false),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[183, 13, 11])).
% 0.85/0.84 % SZS output end Proof
%------------------------------------------------------------------------------