TSTP Solution File: GEO254+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO254+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 8.55s 5.74s
% Output : Proof 8.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO254+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 31 07:22:51 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 8.55/5.74 % SZS status Theorem
% 8.55/5.74 % SZS output start Proof
% 8.55/5.74 tff(unequally_directed_lines_type, type, (
% 8.55/5.74 unequally_directed_lines: ( $i * $i ) > $o)).
% 8.55/5.74 tff(reverse_line_type, type, (
% 8.55/5.74 reverse_line: $i > $i)).
% 8.55/5.74 tff(tptp_fun_L_0_type, type, (
% 8.55/5.74 tptp_fun_L_0: $i)).
% 8.55/5.74 tff(line_connecting_type, type, (
% 8.55/5.74 line_connecting: ( $i * $i ) > $i)).
% 8.55/5.74 tff(tptp_fun_B_1_type, type, (
% 8.55/5.74 tptp_fun_B_1: $i)).
% 8.55/5.74 tff(parallel_through_point_type, type, (
% 8.55/5.74 parallel_through_point: ( $i * $i ) > $i)).
% 8.55/5.74 tff(tptp_fun_A_2_type, type, (
% 8.55/5.74 tptp_fun_A_2: $i)).
% 8.55/5.74 tff(left_convergent_lines_type, type, (
% 8.55/5.74 left_convergent_lines: ( $i * $i ) > $o)).
% 8.55/5.74 tff(before_on_line_type, type, (
% 8.55/5.74 before_on_line: ( $i * $i * $i ) > $o)).
% 8.55/5.74 tff(distinct_points_type, type, (
% 8.55/5.74 distinct_points: ( $i * $i ) > $o)).
% 8.55/5.74 tff(left_apart_point_type, type, (
% 8.55/5.74 left_apart_point: ( $i * $i ) > $o)).
% 8.55/5.74 tff(apart_point_and_line_type, type, (
% 8.55/5.74 apart_point_and_line: ( $i * $i ) > $o)).
% 8.55/5.74 tff(1,assumption,(unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))), introduced(assumption)).
% 8.55/5.74 tff(2,assumption,(left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))), introduced(assumption)).
% 8.55/5.74 tff(3,plain,
% 8.55/5.74 (^[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)))))),
% 8.55/5.74 inference(bind,[status(th)],[])).
% 8.55/5.74 tff(4,plain,
% 8.55/5.74 (![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))))),
% 8.55/5.74 inference(quant_intro,[status(thm)],[3])).
% 8.55/5.74 tff(5,plain,
% 8.55/5.74 (![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))))),
% 8.55/5.74 inference(rewrite,[status(thm)],[])).
% 8.55/5.74 tff(6,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')).
% 8.55/5.74 tff(7,plain,
% 8.55/5.74 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[6, 5])).
% 8.55/5.74 tff(8,plain,(
% 8.55/5.74 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 8.55/5.74 inference(skolemize,[status(sab)],[7])).
% 8.55/5.74 tff(9,plain,
% 8.55/5.74 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[8, 4])).
% 8.55/5.74 tff(10,plain,
% 8.55/5.74 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))))),
% 8.55/5.74 inference(quant_inst,[status(thm)],[])).
% 8.55/5.74 tff(11,plain,
% 8.55/5.74 ($false),
% 8.55/5.74 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 8.55/5.74 tff(12,plain,(~(left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1))))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.74 tff(13,plain,
% 8.55/5.74 ((left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))) | (~left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1))))),
% 8.55/5.74 inference(tautology,[status(thm)],[])).
% 8.55/5.74 tff(14,plain,
% 8.55/5.74 (~left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))),
% 8.55/5.74 inference(unit_resolution,[status(thm)],[13, 12])).
% 8.55/5.74 tff(15,plain,
% 8.55/5.74 ((left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))) | (~left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)))),
% 8.55/5.74 inference(tautology,[status(thm)],[])).
% 8.55/5.74 tff(16,plain,
% 8.55/5.74 (~left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))),
% 8.55/5.74 inference(unit_resolution,[status(thm)],[15, 12])).
% 8.55/5.74 tff(17,assumption,(unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))), introduced(assumption)).
% 8.55/5.74 tff(18,plain,
% 8.55/5.74 (^[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)))))),
% 8.55/5.74 inference(bind,[status(th)],[])).
% 8.55/5.74 tff(19,plain,
% 8.55/5.74 (![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))))),
% 8.55/5.74 inference(quant_intro,[status(thm)],[18])).
% 8.55/5.74 tff(20,plain,
% 8.55/5.74 (^[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))))))),
% 8.55/5.74 inference(bind,[status(th)],[])).
% 8.55/5.74 tff(21,plain,
% 8.55/5.74 (![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))))),
% 8.55/5.74 inference(quant_intro,[status(thm)],[20])).
% 8.55/5.74 tff(22,plain,
% 8.55/5.74 (![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)))))),
% 8.55/5.74 inference(rewrite,[status(thm)],[])).
% 8.55/5.74 tff(23,plain,
% 8.55/5.74 (^[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))))))),
% 8.55/5.74 inference(bind,[status(th)],[])).
% 8.55/5.74 tff(24,plain,
% 8.55/5.74 (![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)))))),
% 8.55/5.74 inference(quant_intro,[status(thm)],[23])).
% 8.55/5.74 tff(25,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')).
% 8.55/5.74 tff(26,plain,
% 8.55/5.74 (![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)))))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[25, 24])).
% 8.55/5.74 tff(27,plain,
% 8.55/5.74 (![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)))))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[26, 22])).
% 8.55/5.74 tff(28,plain,(
% 8.55/5.74 ![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)))))),
% 8.55/5.74 inference(skolemize,[status(sab)],[27])).
% 8.55/5.74 tff(29,plain,
% 8.55/5.74 (![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))))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[28, 21])).
% 8.55/5.74 tff(30,plain,
% 8.55/5.74 (![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))))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[29, 19])).
% 8.55/5.74 tff(31,plain,
% 8.55/5.74 (((~![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(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), 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(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1))))),
% 8.55/5.74 inference(rewrite,[status(thm)],[])).
% 8.55/5.74 tff(32,plain,
% 8.55/5.74 ((left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1))))) <=> ((~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1))))),
% 8.55/5.74 inference(rewrite,[status(thm)],[])).
% 8.55/5.74 tff(33,plain,
% 8.55/5.74 (((~![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(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), 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(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))))),
% 8.55/5.74 inference(monotonicity,[status(thm)],[32])).
% 8.55/5.74 tff(34,plain,
% 8.55/5.74 (((~![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(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), 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(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1))))),
% 8.55/5.74 inference(transitivity,[status(thm)],[33, 31])).
% 8.55/5.74 tff(35,plain,
% 8.55/5.74 ((~![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(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))))),
% 8.55/5.74 inference(quant_inst,[status(thm)],[])).
% 8.55/5.74 tff(36,plain,
% 8.55/5.74 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))) | left_convergent_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[35, 34])).
% 8.55/5.74 tff(37,plain,
% 8.55/5.74 ($false),
% 8.55/5.74 inference(unit_resolution,[status(thm)],[36, 30, 17, 1, 16, 14])).
% 8.55/5.74 tff(38,plain,((~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.74 tff(39,plain,
% 8.55/5.74 (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1)))),
% 8.55/5.74 inference(unit_resolution,[status(thm)],[38, 1])).
% 8.55/5.74 tff(40,plain,
% 8.55/5.74 (^[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)))))),
% 8.55/5.74 inference(bind,[status(th)],[])).
% 8.55/5.74 tff(41,plain,
% 8.55/5.74 (![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))))),
% 8.55/5.74 inference(quant_intro,[status(thm)],[40])).
% 8.55/5.74 tff(42,plain,
% 8.55/5.74 (![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))))),
% 8.55/5.74 inference(rewrite,[status(thm)],[])).
% 8.55/5.74 tff(43,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')).
% 8.55/5.74 tff(44,plain,
% 8.55/5.74 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[43, 42])).
% 8.55/5.74 tff(45,plain,(
% 8.55/5.74 ![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 8.55/5.74 inference(skolemize,[status(sab)],[44])).
% 8.55/5.74 tff(46,plain,
% 8.55/5.74 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[45, 41])).
% 8.55/5.74 tff(47,plain,
% 8.55/5.74 ((~![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))))),
% 8.55/5.74 inference(quant_inst,[status(thm)],[])).
% 8.55/5.74 tff(48,plain,
% 8.55/5.74 (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1)))),
% 8.55/5.74 inference(unit_resolution,[status(thm)],[47, 46])).
% 8.55/5.74 tff(49,plain,
% 8.55/5.74 (^[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))))),
% 8.55/5.74 inference(bind,[status(th)],[])).
% 8.55/5.74 tff(50,plain,
% 8.55/5.74 (![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)))),
% 8.55/5.74 inference(quant_intro,[status(thm)],[49])).
% 8.55/5.74 tff(51,plain,
% 8.55/5.74 (![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)))),
% 8.55/5.74 inference(rewrite,[status(thm)],[])).
% 8.55/5.74 tff(52,plain,
% 8.55/5.74 (^[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)))))),
% 8.55/5.74 inference(bind,[status(th)],[])).
% 8.55/5.74 tff(53,plain,
% 8.55/5.74 (![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)))),
% 8.55/5.74 inference(quant_intro,[status(thm)],[52])).
% 8.55/5.74 tff(54,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')).
% 8.55/5.74 tff(55,plain,
% 8.55/5.74 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[54, 53])).
% 8.55/5.74 tff(56,plain,
% 8.55/5.74 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[55, 51])).
% 8.55/5.74 tff(57,plain,(
% 8.55/5.74 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 8.55/5.74 inference(skolemize,[status(sab)],[56])).
% 8.55/5.74 tff(58,plain,
% 8.55/5.74 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[57, 50])).
% 8.55/5.74 tff(59,plain,
% 8.55/5.74 (((~![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(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), 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(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))))),
% 8.55/5.74 inference(rewrite,[status(thm)],[])).
% 8.55/5.74 tff(60,plain,
% 8.55/5.74 ((~![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(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))))),
% 8.55/5.74 inference(quant_inst,[status(thm)],[])).
% 8.55/5.74 tff(61,plain,
% 8.55/5.74 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[60, 59])).
% 8.55/5.74 tff(62,plain,
% 8.55/5.74 ($false),
% 8.55/5.74 inference(unit_resolution,[status(thm)],[61, 58, 48, 39, 1])).
% 8.55/5.74 tff(63,plain,(~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.74 tff(64,assumption,(~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1))), introduced(assumption)).
% 8.55/5.74 tff(65,assumption,(unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))), introduced(assumption)).
% 8.55/5.74 tff(66,plain,
% 8.55/5.74 (((~![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), line_connecting(B!1, B!1))) | unequally_directed_lines(line_connecting(B!1, B!1), 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), line_connecting(B!1, B!1))) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))))),
% 8.55/5.74 inference(rewrite,[status(thm)],[])).
% 8.55/5.74 tff(67,plain,
% 8.55/5.74 ((unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(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(line_connecting(B!1, B!1), line_connecting(B!1, B!1)))) <=> ((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, B!1))) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))))),
% 8.55/5.74 inference(rewrite,[status(thm)],[])).
% 8.55/5.74 tff(68,plain,
% 8.55/5.74 (((~![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(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(line_connecting(B!1, B!1), 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), line_connecting(B!1, B!1))) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1)))))),
% 8.55/5.74 inference(monotonicity,[status(thm)],[67])).
% 8.55/5.74 tff(69,plain,
% 8.55/5.74 (((~![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(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(line_connecting(B!1, B!1), 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), line_connecting(B!1, B!1))) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))))),
% 8.55/5.74 inference(transitivity,[status(thm)],[68, 66])).
% 8.55/5.74 tff(70,plain,
% 8.55/5.74 ((~![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(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, B!1))))),
% 8.55/5.74 inference(quant_inst,[status(thm)],[])).
% 8.55/5.74 tff(71,plain,
% 8.55/5.74 ((~![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), line_connecting(B!1, B!1))) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1)))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[70, 69])).
% 8.55/5.74 tff(72,plain,
% 8.55/5.74 (~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, B!1))),
% 8.55/5.74 inference(unit_resolution,[status(thm)],[71, 58, 48])).
% 8.55/5.74 tff(73,plain,
% 8.55/5.74 (((~![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), line_connecting(B!1, B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.55/5.74 inference(rewrite,[status(thm)],[])).
% 8.55/5.74 tff(74,plain,
% 8.55/5.74 ((unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, B!1)) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))) <=> (unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.55/5.74 inference(rewrite,[status(thm)],[])).
% 8.55/5.74 tff(75,plain,
% 8.55/5.74 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, B!1)) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))))),
% 8.55/5.74 inference(monotonicity,[status(thm)],[74])).
% 8.55/5.74 tff(76,plain,
% 8.55/5.74 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, B!1)) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.55/5.74 inference(transitivity,[status(thm)],[75, 73])).
% 8.55/5.74 tff(77,plain,
% 8.55/5.74 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, B!1)) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.55/5.74 inference(quant_inst,[status(thm)],[])).
% 8.55/5.74 tff(78,plain,
% 8.55/5.74 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[77, 76])).
% 8.55/5.74 tff(79,plain,
% 8.55/5.74 ($false),
% 8.55/5.74 inference(unit_resolution,[status(thm)],[78, 58, 72, 65, 64])).
% 8.55/5.74 tff(80,plain,(unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.74 tff(81,plain,
% 8.55/5.74 (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))),
% 8.55/5.74 inference(unit_resolution,[status(thm)],[80, 63])).
% 8.55/5.74 tff(82,plain,
% 8.55/5.74 (^[A: $i, L: $i] : refl((~unequally_directed_lines(parallel_through_point(L, A), L)) <=> (~unequally_directed_lines(parallel_through_point(L, A), L)))),
% 8.55/5.74 inference(bind,[status(th)],[])).
% 8.55/5.74 tff(83,plain,
% 8.55/5.74 (![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))),
% 8.55/5.74 inference(quant_intro,[status(thm)],[82])).
% 8.55/5.74 tff(84,plain,
% 8.55/5.74 (![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))),
% 8.55/5.74 inference(rewrite,[status(thm)],[])).
% 8.55/5.74 tff(85,axiom,(![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oagco10')).
% 8.55/5.74 tff(86,plain,
% 8.55/5.74 (![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[85, 84])).
% 8.55/5.74 tff(87,plain,(
% 8.55/5.74 ![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))),
% 8.55/5.74 inference(skolemize,[status(sab)],[86])).
% 8.55/5.74 tff(88,plain,
% 8.55/5.74 (![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[87, 83])).
% 8.55/5.74 tff(89,plain,
% 8.55/5.74 ((~![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)))),
% 8.55/5.74 inference(quant_inst,[status(thm)],[])).
% 8.55/5.74 tff(90,plain,
% 8.55/5.74 (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1))),
% 8.55/5.74 inference(unit_resolution,[status(thm)],[89, 88])).
% 8.55/5.74 tff(91,plain,
% 8.55/5.74 ((~![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))) | (~unequally_directed_lines(parallel_through_point(reverse_line(L!0), B!1), reverse_line(L!0)))),
% 8.55/5.74 inference(quant_inst,[status(thm)],[])).
% 8.55/5.74 tff(92,plain,
% 8.55/5.74 (~unequally_directed_lines(parallel_through_point(reverse_line(L!0), B!1), reverse_line(L!0))),
% 8.55/5.74 inference(unit_resolution,[status(thm)],[91, 88])).
% 8.55/5.74 tff(93,assumption,(unequally_directed_lines(reverse_line(L!0), reverse_line(L!0))), introduced(assumption)).
% 8.55/5.74 tff(94,plain,
% 8.55/5.74 (^[L: $i] : refl((~unequally_directed_lines(L, L)) <=> (~unequally_directed_lines(L, L)))),
% 8.55/5.74 inference(bind,[status(th)],[])).
% 8.55/5.74 tff(95,plain,
% 8.55/5.74 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 8.55/5.74 inference(quant_intro,[status(thm)],[94])).
% 8.55/5.74 tff(96,plain,
% 8.55/5.74 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 8.55/5.74 inference(rewrite,[status(thm)],[])).
% 8.55/5.74 tff(97,axiom,(![L: $i] : (~unequally_directed_lines(L, L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag5')).
% 8.55/5.74 tff(98,plain,
% 8.55/5.74 (![L: $i] : (~unequally_directed_lines(L, L))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[97, 96])).
% 8.55/5.74 tff(99,plain,(
% 8.55/5.74 ![L: $i] : (~unequally_directed_lines(L, L))),
% 8.55/5.74 inference(skolemize,[status(sab)],[98])).
% 8.55/5.74 tff(100,plain,
% 8.55/5.74 (![L: $i] : (~unequally_directed_lines(L, L))),
% 8.55/5.74 inference(modus_ponens,[status(thm)],[99, 95])).
% 8.55/5.74 tff(101,plain,
% 8.55/5.74 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)))),
% 8.55/5.74 inference(quant_inst,[status(thm)],[])).
% 8.55/5.74 tff(102,plain,
% 8.55/5.74 ($false),
% 8.55/5.74 inference(unit_resolution,[status(thm)],[101, 100, 93])).
% 8.55/5.74 tff(103,plain,(~unequally_directed_lines(reverse_line(L!0), reverse_line(L!0))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.74 tff(104,plain,
% 8.55/5.74 (((~![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!0), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(reverse_line(L!0), B!1), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), 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(L!0), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(reverse_line(L!0), B!1), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1))))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(105,plain,
% 8.55/5.75 ((unequally_directed_lines(parallel_through_point(reverse_line(L!0), B!1), reverse_line(L!0)) | unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1)))) <=> (unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(reverse_line(L!0), B!1), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1))))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(106,plain,
% 8.55/5.75 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(L!0), B!1), reverse_line(L!0)) | unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), 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(L!0), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(reverse_line(L!0), B!1), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1)))))),
% 8.55/5.75 inference(monotonicity,[status(thm)],[105])).
% 8.55/5.75 tff(107,plain,
% 8.55/5.75 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(L!0), B!1), reverse_line(L!0)) | unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), 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(L!0), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(reverse_line(L!0), B!1), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1))))),
% 8.55/5.75 inference(transitivity,[status(thm)],[106, 104])).
% 8.55/5.75 tff(108,plain,
% 8.55/5.75 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(L!0), B!1), reverse_line(L!0)) | unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1))))),
% 8.55/5.75 inference(quant_inst,[status(thm)],[])).
% 8.55/5.75 tff(109,plain,
% 8.55/5.75 ((~![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!0), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(reverse_line(L!0), B!1), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1)))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[108, 107])).
% 8.55/5.75 tff(110,plain,
% 8.55/5.75 (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[109, 58, 103, 92])).
% 8.55/5.75 tff(111,plain,
% 8.55/5.75 (((~![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!0), parallel_through_point(reverse_line(L!0), B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!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(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(112,plain,
% 8.55/5.75 ((unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))) <=> (unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(113,plain,
% 8.55/5.75 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!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(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))))),
% 8.55/5.75 inference(monotonicity,[status(thm)],[112])).
% 8.55/5.75 tff(114,plain,
% 8.55/5.75 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!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(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.55/5.75 inference(transitivity,[status(thm)],[113, 111])).
% 8.55/5.75 tff(115,plain,
% 8.55/5.75 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.55/5.75 inference(quant_inst,[status(thm)],[])).
% 8.55/5.75 tff(116,plain,
% 8.55/5.75 ((~![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!0), parallel_through_point(reverse_line(L!0), B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[115, 114])).
% 8.55/5.75 tff(117,plain,
% 8.55/5.75 (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[116, 58, 110, 90])).
% 8.55/5.75 tff(118,plain,
% 8.55/5.75 (((~![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(L!0))) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(119,plain,
% 8.55/5.75 ((unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(L!0)))) <=> ((~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(120,plain,
% 8.55/5.75 (((~![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!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(L!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(B!1, B!1), reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.55/5.75 inference(monotonicity,[status(thm)],[119])).
% 8.55/5.75 tff(121,plain,
% 8.55/5.75 (((~![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!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(L!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(B!1, B!1), reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))),
% 8.55/5.75 inference(transitivity,[status(thm)],[120, 118])).
% 8.55/5.75 tff(122,plain,
% 8.55/5.75 ((~![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!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(L!0))))),
% 8.55/5.75 inference(quant_inst,[status(thm)],[])).
% 8.55/5.75 tff(123,plain,
% 8.55/5.75 ((~![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(L!0))) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[122, 121])).
% 8.55/5.75 tff(124,plain,
% 8.55/5.75 (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(L!0))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[123, 58, 117, 81])).
% 8.55/5.75 tff(125,plain,
% 8.55/5.75 ((~![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), L!0))),
% 8.55/5.75 inference(quant_inst,[status(thm)],[])).
% 8.55/5.75 tff(126,plain,
% 8.55/5.75 (~unequally_directed_lines(parallel_through_point(L!0, A!2), L!0)),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[125, 88])).
% 8.55/5.75 tff(127,assumption,(left_convergent_lines(line_connecting(A!2, B!1), L!0) | left_convergent_lines(line_connecting(A!2, B!1), reverse_line(L!0))), introduced(assumption)).
% 8.55/5.75 tff(128,plain,
% 8.55/5.75 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(line_connecting(A!2, B!1), L!0) | left_convergent_lines(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 8.55/5.75 inference(quant_inst,[status(thm)],[])).
% 8.55/5.75 tff(129,plain,
% 8.55/5.75 ($false),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[128, 9, 127])).
% 8.55/5.75 tff(130,plain,(~(left_convergent_lines(line_connecting(A!2, B!1), L!0) | left_convergent_lines(line_connecting(A!2, B!1), reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.75 tff(131,plain,
% 8.55/5.75 ((left_convergent_lines(line_connecting(A!2, B!1), L!0) | left_convergent_lines(line_connecting(A!2, B!1), reverse_line(L!0))) | (~left_convergent_lines(line_connecting(A!2, B!1), L!0))),
% 8.55/5.75 inference(tautology,[status(thm)],[])).
% 8.55/5.75 tff(132,plain,
% 8.55/5.75 (~left_convergent_lines(line_connecting(A!2, B!1), L!0)),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[131, 130])).
% 8.55/5.75 tff(133,plain,
% 8.55/5.75 ((left_convergent_lines(line_connecting(A!2, B!1), L!0) | left_convergent_lines(line_connecting(A!2, B!1), reverse_line(L!0))) | (~left_convergent_lines(line_connecting(A!2, B!1), reverse_line(L!0)))),
% 8.55/5.75 inference(tautology,[status(thm)],[])).
% 8.55/5.75 tff(134,plain,
% 8.55/5.75 (~left_convergent_lines(line_connecting(A!2, B!1), reverse_line(L!0))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[133, 130])).
% 8.55/5.75 tff(135,plain,
% 8.55/5.75 (((~![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!0), parallel_through_point(reverse_line(L!0), B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(L!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(reverse_line(L!0), parallel_through_point(reverse_line(L!0), B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(L!0))))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(136,plain,
% 8.55/5.75 ((~![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!0), parallel_through_point(reverse_line(L!0), B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(L!0))))),
% 8.55/5.75 inference(quant_inst,[status(thm)],[])).
% 8.55/5.75 tff(137,plain,
% 8.55/5.75 ((~![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!0), parallel_through_point(reverse_line(L!0), B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), parallel_through_point(reverse_line(L!0), B!1)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(L!0)))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[136, 135])).
% 8.55/5.75 tff(138,plain,
% 8.55/5.75 (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(L!0))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[137, 58, 110, 90])).
% 8.55/5.75 tff(139,assumption,(~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))), introduced(assumption)).
% 8.55/5.75 tff(140,plain,
% 8.55/5.75 (((~![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!2, B!1), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(L!0)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, 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(A!2, B!1), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(L!0)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, B!1))))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(141,plain,
% 8.55/5.75 ((~![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!2, B!1), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(L!0)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, B!1))))),
% 8.55/5.75 inference(quant_inst,[status(thm)],[])).
% 8.55/5.75 tff(142,plain,
% 8.55/5.75 ((~![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!2, B!1), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), reverse_line(L!0)) | (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, B!1)))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[141, 140])).
% 8.55/5.75 tff(143,plain,
% 8.55/5.75 (~unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, B!1))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[142, 58, 139, 138])).
% 8.55/5.75 tff(144,assumption,(~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))), introduced(assumption)).
% 8.55/5.75 tff(145,plain,
% 8.55/5.75 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 8.55/5.75 inference(quant_inst,[status(thm)],[])).
% 8.55/5.75 tff(146,plain,
% 8.55/5.75 (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[145, 46])).
% 8.55/5.75 tff(147,plain,
% 8.55/5.75 (((~![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!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, 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(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1))))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(148,plain,
% 8.55/5.75 ((unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)))) <=> (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1))))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(149,plain,
% 8.55/5.75 (((~![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!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, 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(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)))))),
% 8.55/5.75 inference(monotonicity,[status(thm)],[148])).
% 8.55/5.75 tff(150,plain,
% 8.55/5.75 (((~![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!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, 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(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1))))),
% 8.55/5.75 inference(transitivity,[status(thm)],[149, 147])).
% 8.55/5.75 tff(151,plain,
% 8.55/5.75 ((~![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!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1))))),
% 8.55/5.75 inference(quant_inst,[status(thm)],[])).
% 8.55/5.75 tff(152,plain,
% 8.55/5.75 ((~![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!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[151, 150])).
% 8.55/5.75 tff(153,plain,
% 8.55/5.75 (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[152, 58, 146])).
% 8.55/5.75 tff(154,plain,
% 8.55/5.75 (((~![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!2, B!1), line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, 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(A!2, B!1), line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(155,plain,
% 8.55/5.75 ((unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))))) <=> (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(156,plain,
% 8.55/5.75 (((~![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(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, 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(A!2, B!1), line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))))))),
% 8.55/5.75 inference(monotonicity,[status(thm)],[155])).
% 8.55/5.75 tff(157,plain,
% 8.55/5.75 (((~![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(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, 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(A!2, B!1), line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))))),
% 8.55/5.75 inference(transitivity,[status(thm)],[156, 154])).
% 8.55/5.75 tff(158,plain,
% 8.55/5.75 ((~![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(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))))),
% 8.55/5.75 inference(quant_inst,[status(thm)],[])).
% 8.55/5.75 tff(159,plain,
% 8.55/5.75 ((~![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!2, B!1), line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[158, 157])).
% 8.55/5.75 tff(160,plain,
% 8.55/5.75 (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[159, 58, 153, 144])).
% 8.55/5.75 tff(161,assumption,(~unequally_directed_lines(L!0, line_connecting(A!2, B!1))), introduced(assumption)).
% 8.55/5.75 tff(162,plain,
% 8.55/5.75 (^[A: $i, L: $i] : refl((apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))))),
% 8.55/5.75 inference(bind,[status(th)],[])).
% 8.55/5.75 tff(163,plain,
% 8.55/5.75 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 8.55/5.75 inference(quant_intro,[status(thm)],[162])).
% 8.55/5.75 tff(164,plain,
% 8.55/5.75 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(165,axiom,(![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','apt_def')).
% 8.55/5.75 tff(166,plain,
% 8.55/5.75 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[165, 164])).
% 8.55/5.75 tff(167,plain,(
% 8.55/5.75 ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 8.55/5.75 inference(skolemize,[status(sab)],[166])).
% 8.55/5.75 tff(168,plain,
% 8.55/5.75 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[167, 163])).
% 8.55/5.75 tff(169,plain,
% 8.55/5.75 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (apart_point_and_line(B!1, L!0) <=> (left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0))))),
% 8.55/5.75 inference(quant_inst,[status(thm)],[])).
% 8.55/5.75 tff(170,plain,
% 8.55/5.75 (apart_point_and_line(B!1, L!0) <=> (left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[169, 168])).
% 8.55/5.75 tff(171,plain,
% 8.55/5.75 ((~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A)))) <=> (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A))))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(172,plain,
% 8.55/5.75 ((~![A: $i, B: $i, L: $i] : (((distinct_points(A, B) & (~apart_point_and_line(A, L))) & (~apart_point_and_line(B, L))) => (before_on_line(L, A, B) & before_on_line(L, B, A)))) <=> (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A))))),
% 8.55/5.75 inference(rewrite,[status(thm)],[])).
% 8.55/5.75 tff(173,axiom,(~![A: $i, B: $i, L: $i] : (((distinct_points(A, B) & (~apart_point_and_line(A, L))) & (~apart_point_and_line(B, L))) => (before_on_line(L, A, B) & before_on_line(L, B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 8.55/5.75 tff(174,plain,
% 8.55/5.75 (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[173, 172])).
% 8.55/5.75 tff(175,plain,
% 8.55/5.75 (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[174, 171])).
% 8.55/5.75 tff(176,plain,
% 8.55/5.75 (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[175, 171])).
% 8.55/5.75 tff(177,plain,
% 8.55/5.75 (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[176, 171])).
% 8.55/5.75 tff(178,plain,
% 8.55/5.75 (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[177, 171])).
% 8.55/5.75 tff(179,plain,
% 8.55/5.75 (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[178, 171])).
% 8.55/5.75 tff(180,plain,
% 8.55/5.75 (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 8.55/5.75 inference(modus_ponens,[status(thm)],[179, 171])).
% 8.55/5.75 tff(181,plain,(
% 8.55/5.75 ~((~(distinct_points(A!2, B!1) & (~apart_point_and_line(A!2, L!0)) & (~apart_point_and_line(B!1, L!0)))) | (before_on_line(L!0, A!2, B!1) & before_on_line(L!0, B!1, A!2)))),
% 8.55/5.75 inference(skolemize,[status(sab)],[180])).
% 8.55/5.75 tff(182,plain,
% 8.55/5.75 (distinct_points(A!2, B!1) & (~apart_point_and_line(A!2, L!0)) & (~apart_point_and_line(B!1, L!0))),
% 8.55/5.75 inference(or_elim,[status(thm)],[181])).
% 8.55/5.75 tff(183,plain,
% 8.55/5.75 (~apart_point_and_line(B!1, L!0)),
% 8.55/5.75 inference(and_elim,[status(thm)],[182])).
% 8.55/5.75 tff(184,plain,
% 8.55/5.75 ((~(apart_point_and_line(B!1, L!0) <=> (left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0))))) | apart_point_and_line(B!1, L!0) | (~(left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0))))),
% 8.55/5.75 inference(tautology,[status(thm)],[])).
% 8.55/5.75 tff(185,plain,
% 8.55/5.75 ((~(apart_point_and_line(B!1, L!0) <=> (left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0))))) | (~(left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0))))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[184, 183])).
% 8.55/5.75 tff(186,plain,
% 8.55/5.75 (~(left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[185, 170])).
% 8.55/5.75 tff(187,plain,
% 8.55/5.75 ((left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0))) | (~left_apart_point(B!1, reverse_line(L!0)))),
% 8.55/5.75 inference(tautology,[status(thm)],[])).
% 8.55/5.75 tff(188,plain,
% 8.55/5.75 (~left_apart_point(B!1, reverse_line(L!0))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[187, 186])).
% 8.55/5.75 tff(189,plain,
% 8.55/5.75 ((left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0))) | (~left_apart_point(B!1, L!0))),
% 8.55/5.75 inference(tautology,[status(thm)],[])).
% 8.55/5.75 tff(190,plain,
% 8.55/5.75 (~left_apart_point(B!1, L!0)),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[189, 186])).
% 8.55/5.75 tff(191,plain,
% 8.55/5.75 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))),
% 8.55/5.75 inference(quant_inst,[status(thm)],[])).
% 8.55/5.75 tff(192,plain,
% 8.55/5.75 (apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[191, 168])).
% 8.55/5.75 tff(193,plain,
% 8.55/5.75 (~apart_point_and_line(A!2, L!0)),
% 8.55/5.75 inference(and_elim,[status(thm)],[182])).
% 8.55/5.75 tff(194,plain,
% 8.55/5.75 ((~(apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))) | apart_point_and_line(A!2, L!0) | (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))),
% 8.55/5.75 inference(tautology,[status(thm)],[])).
% 8.55/5.75 tff(195,plain,
% 8.55/5.75 ((~(apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))) | (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[194, 193])).
% 8.55/5.75 tff(196,plain,
% 8.55/5.75 (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[195, 192])).
% 8.55/5.75 tff(197,plain,
% 8.55/5.75 ((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))) | (~left_apart_point(A!2, reverse_line(L!0)))),
% 8.55/5.75 inference(tautology,[status(thm)],[])).
% 8.55/5.75 tff(198,plain,
% 8.55/5.75 (~left_apart_point(A!2, reverse_line(L!0))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[197, 196])).
% 8.55/5.75 tff(199,plain,
% 8.55/5.75 ((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))) | (~left_apart_point(A!2, L!0))),
% 8.55/5.75 inference(tautology,[status(thm)],[])).
% 8.55/5.75 tff(200,plain,
% 8.55/5.75 (~left_apart_point(A!2, L!0)),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[199, 196])).
% 8.55/5.75 tff(201,plain,
% 8.55/5.75 (distinct_points(A!2, B!1)),
% 8.55/5.75 inference(and_elim,[status(thm)],[182])).
% 8.55/5.75 tff(202,plain,
% 8.55/5.75 ((~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)))) | left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))),
% 8.55/5.75 inference(tautology,[status(thm)],[])).
% 8.55/5.75 tff(203,plain,
% 8.55/5.75 ((~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)))) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[202, 201, 200, 198, 190, 188])).
% 8.55/5.75 tff(204,plain,
% 8.55/5.75 (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)))),
% 8.55/5.75 inference(unit_resolution,[status(thm)],[203, 161])).
% 8.55/5.75 tff(205,assumption,(~(before_on_line(L!0, A!2, B!1) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)))))), introduced(assumption)).
% 8.55/5.75 tff(206,plain,
% 8.55/5.75 (^[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))))))),
% 8.55/5.75 inference(bind,[status(th)],[])).
% 8.55/5.75 tff(207,plain,
% 8.55/5.75 (![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)))))),
% 8.55/5.76 inference(quant_intro,[status(thm)],[206])).
% 8.55/5.76 tff(208,plain,
% 8.55/5.76 (^[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))))))),
% 8.55/5.76 inference(bind,[status(th)],[])).
% 8.55/5.76 tff(209,plain,
% 8.55/5.76 (![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)))))),
% 8.55/5.76 inference(quant_intro,[status(thm)],[208])).
% 8.55/5.76 tff(210,plain,
% 8.55/5.76 (![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)))))),
% 8.55/5.76 inference(rewrite,[status(thm)],[])).
% 8.55/5.76 tff(211,plain,
% 8.55/5.76 (^[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))))))),
% 8.55/5.76 inference(bind,[status(th)],[])).
% 8.55/5.76 tff(212,plain,
% 8.55/5.76 (![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)))))),
% 8.55/5.76 inference(quant_intro,[status(thm)],[211])).
% 8.55/5.76 tff(213,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/sandbox/benchmark/Axioms/GEO007+0.ax','bf_def')).
% 8.55/5.76 tff(214,plain,
% 8.55/5.76 (![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)))))),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[213, 212])).
% 8.55/5.76 tff(215,plain,
% 8.55/5.76 (![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)))))),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[214, 210])).
% 8.55/5.76 tff(216,plain,(
% 8.55/5.76 ![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)))))),
% 8.55/5.76 inference(skolemize,[status(sab)],[215])).
% 8.55/5.76 tff(217,plain,
% 8.55/5.76 (![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)))))),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[216, 209])).
% 8.55/5.76 tff(218,plain,
% 8.55/5.76 (![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)))))),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[217, 207])).
% 8.55/5.76 tff(219,plain,
% 8.55/5.76 (((~![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!0, A!2, B!1) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!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!0, A!2, B!1) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))))))),
% 8.55/5.76 inference(rewrite,[status(thm)],[])).
% 8.55/5.76 tff(220,plain,
% 8.55/5.76 ((before_on_line(L!0, A!2, B!1) <=> (~(unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | (~distinct_points(A!2, B!1))))) <=> (before_on_line(L!0, A!2, B!1) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)))))),
% 8.55/5.76 inference(rewrite,[status(thm)],[])).
% 8.55/5.76 tff(221,plain,
% 8.55/5.76 (((~![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!0, A!2, B!1) <=> (~(unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | (~distinct_points(A!2, B!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!0, A!2, B!1) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))))))),
% 8.55/5.76 inference(monotonicity,[status(thm)],[220])).
% 8.55/5.76 tff(222,plain,
% 8.55/5.76 (((~![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!0, A!2, B!1) <=> (~(unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | (~distinct_points(A!2, B!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!0, A!2, B!1) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))))))),
% 8.55/5.76 inference(transitivity,[status(thm)],[221, 219])).
% 8.55/5.76 tff(223,plain,
% 8.55/5.76 ((~![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!0, A!2, B!1) <=> (~(unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | (~distinct_points(A!2, B!1)))))),
% 8.55/5.76 inference(quant_inst,[status(thm)],[])).
% 8.55/5.76 tff(224,plain,
% 8.55/5.76 ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!0, A!2, B!1) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)))))),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[223, 222])).
% 8.55/5.76 tff(225,plain,
% 8.55/5.76 ($false),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[224, 218, 205])).
% 8.55/5.76 tff(226,plain,(before_on_line(L!0, A!2, B!1) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.76 tff(227,plain,
% 8.55/5.76 ((~(before_on_line(L!0, A!2, B!1) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)))))) | before_on_line(L!0, A!2, B!1) | (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)))),
% 8.55/5.76 inference(tautology,[status(thm)],[])).
% 8.55/5.76 tff(228,plain,
% 8.55/5.76 (before_on_line(L!0, A!2, B!1) | (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)))),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[227, 226])).
% 8.55/5.76 tff(229,plain,
% 8.55/5.76 (before_on_line(L!0, A!2, B!1)),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[228, 204])).
% 8.55/5.76 tff(230,plain,
% 8.55/5.76 ((~(~((~before_on_line(L!0, A!2, B!1)) | (~before_on_line(L!0, B!1, A!2))))) <=> ((~before_on_line(L!0, A!2, B!1)) | (~before_on_line(L!0, B!1, A!2)))),
% 8.55/5.76 inference(rewrite,[status(thm)],[])).
% 8.55/5.76 tff(231,plain,
% 8.55/5.76 ((before_on_line(L!0, A!2, B!1) & before_on_line(L!0, B!1, A!2)) <=> (~((~before_on_line(L!0, A!2, B!1)) | (~before_on_line(L!0, B!1, A!2))))),
% 8.55/5.76 inference(rewrite,[status(thm)],[])).
% 8.55/5.76 tff(232,plain,
% 8.55/5.76 ((~(before_on_line(L!0, A!2, B!1) & before_on_line(L!0, B!1, A!2))) <=> (~(~((~before_on_line(L!0, A!2, B!1)) | (~before_on_line(L!0, B!1, A!2)))))),
% 8.55/5.76 inference(monotonicity,[status(thm)],[231])).
% 8.55/5.76 tff(233,plain,
% 8.55/5.76 ((~(before_on_line(L!0, A!2, B!1) & before_on_line(L!0, B!1, A!2))) <=> ((~before_on_line(L!0, A!2, B!1)) | (~before_on_line(L!0, B!1, A!2)))),
% 8.55/5.76 inference(transitivity,[status(thm)],[232, 230])).
% 8.55/5.76 tff(234,plain,
% 8.55/5.76 (~(before_on_line(L!0, A!2, B!1) & before_on_line(L!0, B!1, A!2))),
% 8.55/5.76 inference(or_elim,[status(thm)],[181])).
% 8.55/5.76 tff(235,plain,
% 8.55/5.76 ((~before_on_line(L!0, A!2, B!1)) | (~before_on_line(L!0, B!1, A!2))),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[234, 233])).
% 8.55/5.76 tff(236,plain,
% 8.55/5.76 (~before_on_line(L!0, B!1, A!2)),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[235, 229])).
% 8.55/5.76 tff(237,plain,
% 8.55/5.76 (((~![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!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, 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(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)))),
% 8.55/5.76 inference(rewrite,[status(thm)],[])).
% 8.55/5.76 tff(238,plain,
% 8.55/5.76 ((unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))))) <=> (unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)))),
% 8.55/5.76 inference(rewrite,[status(thm)],[])).
% 8.55/5.76 tff(239,plain,
% 8.55/5.76 (((~![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(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, 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(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))),
% 8.55/5.76 inference(monotonicity,[status(thm)],[238])).
% 8.55/5.76 tff(240,plain,
% 8.55/5.76 (((~![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(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, 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(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)))),
% 8.55/5.76 inference(transitivity,[status(thm)],[239, 237])).
% 8.55/5.76 tff(241,plain,
% 8.55/5.76 ((~![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(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))),
% 8.55/5.76 inference(quant_inst,[status(thm)],[])).
% 8.55/5.76 tff(242,plain,
% 8.55/5.76 ((~![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!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[241, 240])).
% 8.55/5.76 tff(243,plain,
% 8.55/5.76 (unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[242, 58])).
% 8.55/5.76 tff(244,plain,
% 8.55/5.76 (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[243, 161, 144])).
% 8.55/5.76 tff(245,plain,
% 8.55/5.76 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.76 inference(quant_inst,[status(thm)],[])).
% 8.55/5.76 tff(246,plain,
% 8.55/5.76 (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[245, 46])).
% 8.55/5.76 tff(247,plain,
% 8.55/5.76 (((~![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, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))))),
% 8.55/5.76 inference(rewrite,[status(thm)],[])).
% 8.55/5.76 tff(248,plain,
% 8.55/5.76 ((~![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, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))))),
% 8.55/5.76 inference(quant_inst,[status(thm)],[])).
% 8.55/5.76 tff(249,plain,
% 8.55/5.76 ((~![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, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2)))),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[248, 247])).
% 8.55/5.76 tff(250,plain,
% 8.55/5.76 (unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2)))),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[249, 58, 246])).
% 8.55/5.76 tff(251,plain,
% 8.55/5.76 (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[250, 244])).
% 8.55/5.76 tff(252,assumption,(distinct_points(A!2, A!2)), introduced(assumption)).
% 8.55/5.76 tff(253,plain,
% 8.55/5.76 (^[A: $i] : refl((~distinct_points(A, A)) <=> (~distinct_points(A, A)))),
% 8.55/5.76 inference(bind,[status(th)],[])).
% 8.55/5.76 tff(254,plain,
% 8.55/5.76 (![A: $i] : (~distinct_points(A, A)) <=> ![A: $i] : (~distinct_points(A, A))),
% 8.55/5.76 inference(quant_intro,[status(thm)],[253])).
% 8.55/5.76 tff(255,plain,
% 8.55/5.76 (![A: $i] : (~distinct_points(A, A)) <=> ![A: $i] : (~distinct_points(A, A))),
% 8.55/5.76 inference(rewrite,[status(thm)],[])).
% 8.55/5.76 tff(256,axiom,(![A: $i] : (~distinct_points(A, A))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag1')).
% 8.55/5.76 tff(257,plain,
% 8.55/5.76 (![A: $i] : (~distinct_points(A, A))),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[256, 255])).
% 8.55/5.76 tff(258,plain,(
% 8.55/5.76 ![A: $i] : (~distinct_points(A, A))),
% 8.55/5.76 inference(skolemize,[status(sab)],[257])).
% 8.55/5.76 tff(259,plain,
% 8.55/5.76 (![A: $i] : (~distinct_points(A, A))),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[258, 254])).
% 8.55/5.76 tff(260,plain,
% 8.55/5.76 ((~![A: $i] : (~distinct_points(A, A))) | (~distinct_points(A!2, A!2))),
% 8.55/5.76 inference(quant_inst,[status(thm)],[])).
% 8.55/5.76 tff(261,plain,
% 8.55/5.76 ($false),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[260, 259, 252])).
% 8.55/5.76 tff(262,plain,(~distinct_points(A!2, A!2)), inference(lemma,lemma(discharge,[]))).
% 8.55/5.76 tff(263,plain,
% 8.55/5.76 (^[A: $i, B: $i, C: $i] : refl((distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))))),
% 8.55/5.76 inference(bind,[status(th)],[])).
% 8.55/5.76 tff(264,plain,
% 8.55/5.76 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 8.55/5.76 inference(quant_intro,[status(thm)],[263])).
% 8.55/5.76 tff(265,plain,
% 8.55/5.76 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 8.55/5.76 inference(rewrite,[status(thm)],[])).
% 8.55/5.76 tff(266,plain,
% 8.55/5.76 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((distinct_points(A, C) | distinct_points(B, C)) <=> (distinct_points(A, C) | distinct_points(B, C))), ((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))))), rewrite((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))), ((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))))),
% 8.55/5.76 inference(bind,[status(th)],[])).
% 8.55/5.76 tff(267,plain,
% 8.55/5.76 (![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 8.55/5.76 inference(quant_intro,[status(thm)],[266])).
% 8.55/5.76 tff(268,axiom,(![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag2')).
% 8.55/5.76 tff(269,plain,
% 8.55/5.76 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[268, 267])).
% 8.55/5.76 tff(270,plain,
% 8.55/5.76 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[269, 265])).
% 8.55/5.76 tff(271,plain,(
% 8.55/5.76 ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 8.55/5.76 inference(skolemize,[status(sab)],[270])).
% 8.55/5.76 tff(272,plain,
% 8.55/5.76 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[271, 264])).
% 8.55/5.76 tff(273,plain,
% 8.55/5.76 (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | ((~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))),
% 8.55/5.76 inference(rewrite,[status(thm)],[])).
% 8.55/5.76 tff(274,plain,
% 8.55/5.76 ((distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1))) <=> ((~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))),
% 8.55/5.76 inference(rewrite,[status(thm)],[])).
% 8.55/5.76 tff(275,plain,
% 8.55/5.76 (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | ((~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2)))),
% 8.55/5.76 inference(monotonicity,[status(thm)],[274])).
% 8.55/5.76 tff(276,plain,
% 8.55/5.76 (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))),
% 8.55/5.76 inference(transitivity,[status(thm)],[275, 273])).
% 8.55/5.76 tff(277,plain,
% 8.55/5.76 ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1)))),
% 8.55/5.76 inference(quant_inst,[status(thm)],[])).
% 8.55/5.76 tff(278,plain,
% 8.55/5.76 ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2)),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[277, 276])).
% 8.55/5.76 tff(279,plain,
% 8.55/5.76 (distinct_points(B!1, A!2) | distinct_points(A!2, A!2)),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[278, 272, 201])).
% 8.55/5.76 tff(280,plain,
% 8.55/5.76 (distinct_points(B!1, A!2)),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[279, 262])).
% 8.55/5.76 tff(281,plain,
% 8.55/5.76 ((~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)))) | left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 8.55/5.76 inference(tautology,[status(thm)],[])).
% 8.55/5.76 tff(282,plain,
% 8.55/5.76 ((~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)))) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[281, 200, 198, 190, 188, 280])).
% 8.55/5.76 tff(283,plain,
% 8.55/5.76 (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)))),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[282, 251])).
% 8.55/5.76 tff(284,assumption,(~(before_on_line(L!0, B!1, A!2) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)))))), introduced(assumption)).
% 8.55/5.76 tff(285,plain,
% 8.55/5.76 (((~![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!0, B!1, A!2) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)))))) <=> ((~![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!0, B!1, A!2) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))))))),
% 8.55/5.76 inference(rewrite,[status(thm)],[])).
% 8.55/5.76 tff(286,plain,
% 8.55/5.76 ((before_on_line(L!0, B!1, A!2) <=> (~(unequally_directed_lines(L!0, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | (~distinct_points(B!1, A!2))))) <=> (before_on_line(L!0, B!1, A!2) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)))))),
% 8.55/5.76 inference(rewrite,[status(thm)],[])).
% 8.55/5.76 tff(287,plain,
% 8.55/5.76 (((~![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!0, B!1, A!2) <=> (~(unequally_directed_lines(L!0, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | (~distinct_points(B!1, A!2)))))) <=> ((~![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!0, B!1, A!2) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))))))),
% 8.55/5.76 inference(monotonicity,[status(thm)],[286])).
% 8.55/5.76 tff(288,plain,
% 8.55/5.76 (((~![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!0, B!1, A!2) <=> (~(unequally_directed_lines(L!0, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | (~distinct_points(B!1, A!2)))))) <=> ((~![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!0, B!1, A!2) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))))))),
% 8.55/5.76 inference(transitivity,[status(thm)],[287, 285])).
% 8.55/5.76 tff(289,plain,
% 8.55/5.76 ((~![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!0, B!1, A!2) <=> (~(unequally_directed_lines(L!0, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | (~distinct_points(B!1, A!2)))))),
% 8.55/5.76 inference(quant_inst,[status(thm)],[])).
% 8.55/5.76 tff(290,plain,
% 8.55/5.76 ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!0, B!1, A!2) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)))))),
% 8.55/5.76 inference(modus_ponens,[status(thm)],[289, 288])).
% 8.55/5.76 tff(291,plain,
% 8.55/5.76 ($false),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[290, 218, 284])).
% 8.55/5.76 tff(292,plain,(before_on_line(L!0, B!1, A!2) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.76 tff(293,plain,
% 8.55/5.76 ((~(before_on_line(L!0, B!1, A!2) <=> (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)))))) | before_on_line(L!0, B!1, A!2) | (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)))),
% 8.55/5.76 inference(tautology,[status(thm)],[])).
% 8.55/5.76 tff(294,plain,
% 8.55/5.76 (before_on_line(L!0, B!1, A!2) | (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)))),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[293, 292])).
% 8.55/5.76 tff(295,plain,
% 8.55/5.76 ($false),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[294, 283, 236])).
% 8.55/5.76 tff(296,plain,(unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.76 tff(297,plain,
% 8.55/5.76 (unequally_directed_lines(L!0, line_connecting(A!2, B!1))),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[296, 144])).
% 8.55/5.76 tff(298,assumption,(left_convergent_lines(L!0, line_connecting(A!2, B!1)) | left_convergent_lines(L!0, reverse_line(line_connecting(A!2, B!1)))), introduced(assumption)).
% 8.55/5.76 tff(299,plain,
% 8.55/5.76 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(L!0, line_connecting(A!2, B!1)) | left_convergent_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))),
% 8.55/5.76 inference(quant_inst,[status(thm)],[])).
% 8.55/5.76 tff(300,plain,
% 8.55/5.76 ($false),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[299, 9, 298])).
% 8.55/5.76 tff(301,plain,(~(left_convergent_lines(L!0, line_connecting(A!2, B!1)) | left_convergent_lines(L!0, reverse_line(line_connecting(A!2, B!1))))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.76 tff(302,plain,
% 8.55/5.76 ((left_convergent_lines(L!0, line_connecting(A!2, B!1)) | left_convergent_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | (~left_convergent_lines(L!0, reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.76 inference(tautology,[status(thm)],[])).
% 8.55/5.76 tff(303,plain,
% 8.55/5.76 (~left_convergent_lines(L!0, reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[302, 301])).
% 8.55/5.76 tff(304,plain,
% 8.55/5.76 ((left_convergent_lines(L!0, line_connecting(A!2, B!1)) | left_convergent_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | (~left_convergent_lines(L!0, line_connecting(A!2, B!1)))),
% 8.55/5.76 inference(tautology,[status(thm)],[])).
% 8.55/5.76 tff(305,plain,
% 8.55/5.76 (~left_convergent_lines(L!0, line_connecting(A!2, B!1))),
% 8.55/5.76 inference(unit_resolution,[status(thm)],[304, 301])).
% 8.55/5.76 tff(306,assumption,(unequally_directed_lines(L!0, line_connecting(A!2, B!1))), introduced(assumption)).
% 8.55/5.76 tff(307,assumption,(unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))), introduced(assumption)).
% 8.55/5.77 tff(308,plain,
% 8.55/5.77 (((~![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(L!0, line_connecting(A!2, B!1))) | left_convergent_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | left_convergent_lines(L!0, line_connecting(A!2, 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(L!0, line_connecting(A!2, B!1))) | left_convergent_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | left_convergent_lines(L!0, line_connecting(A!2, B!1)))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(309,plain,
% 8.55/5.77 ((left_convergent_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))))) <=> ((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | left_convergent_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | left_convergent_lines(L!0, line_connecting(A!2, B!1)))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(310,plain,
% 8.55/5.77 (((~![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(L!0, reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, 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(L!0, line_connecting(A!2, B!1))) | left_convergent_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | left_convergent_lines(L!0, line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(monotonicity,[status(thm)],[309])).
% 8.55/5.77 tff(311,plain,
% 8.55/5.77 (((~![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(L!0, reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, 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(L!0, line_connecting(A!2, B!1))) | left_convergent_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | left_convergent_lines(L!0, line_connecting(A!2, B!1)))),
% 8.55/5.77 inference(transitivity,[status(thm)],[310, 308])).
% 8.55/5.77 tff(312,plain,
% 8.55/5.77 ((~![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(L!0, reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))),
% 8.55/5.77 inference(quant_inst,[status(thm)],[])).
% 8.55/5.77 tff(313,plain,
% 8.55/5.77 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | left_convergent_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | left_convergent_lines(L!0, line_connecting(A!2, B!1))),
% 8.55/5.77 inference(modus_ponens,[status(thm)],[312, 311])).
% 8.55/5.77 tff(314,plain,
% 8.55/5.77 ($false),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[313, 30, 307, 306, 305, 303])).
% 8.55/5.77 tff(315,plain,((~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1)))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.77 tff(316,plain,
% 8.55/5.77 (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[315, 297])).
% 8.55/5.77 tff(317,plain,
% 8.55/5.77 (((~![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!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, 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(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(318,plain,
% 8.55/5.77 ((unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1)))) <=> ((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(319,plain,
% 8.55/5.77 (((~![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!2, B!1), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, line_connecting(A!2, 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(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))))),
% 8.55/5.77 inference(monotonicity,[status(thm)],[318])).
% 8.55/5.77 tff(320,plain,
% 8.55/5.77 (((~![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!2, B!1), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, line_connecting(A!2, 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(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(transitivity,[status(thm)],[319, 317])).
% 8.55/5.77 tff(321,plain,
% 8.55/5.77 ((~![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!2, B!1), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(quant_inst,[status(thm)],[])).
% 8.55/5.77 tff(322,plain,
% 8.55/5.77 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.77 inference(modus_ponens,[status(thm)],[321, 320])).
% 8.55/5.77 tff(323,plain,
% 8.55/5.77 ((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[322, 58])).
% 8.55/5.77 tff(324,plain,
% 8.55/5.77 ($false),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[323, 316, 297, 160])).
% 8.55/5.77 tff(325,plain,(unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.77 tff(326,plain,
% 8.55/5.77 (((~![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(line_connecting(A!2, B!1)), reverse_line(L!0)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, 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(line_connecting(A!2, B!1)), reverse_line(L!0)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(327,plain,
% 8.55/5.77 ((unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)))) <=> (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(328,plain,
% 8.55/5.77 (((~![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!2, B!1), reverse_line(L!0)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, 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(line_connecting(A!2, B!1)), reverse_line(L!0)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)))))),
% 8.55/5.77 inference(monotonicity,[status(thm)],[327])).
% 8.55/5.77 tff(329,plain,
% 8.55/5.77 (((~![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!2, B!1), reverse_line(L!0)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, 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(line_connecting(A!2, B!1)), reverse_line(L!0)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(transitivity,[status(thm)],[328, 326])).
% 8.55/5.77 tff(330,plain,
% 8.55/5.77 ((~![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!2, B!1), reverse_line(L!0)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(quant_inst,[status(thm)],[])).
% 8.55/5.77 tff(331,plain,
% 8.55/5.77 ((~![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(line_connecting(A!2, B!1)), reverse_line(L!0)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)))),
% 8.55/5.77 inference(modus_ponens,[status(thm)],[330, 329])).
% 8.55/5.77 tff(332,plain,
% 8.55/5.77 (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[331, 58])).
% 8.55/5.77 tff(333,plain,
% 8.55/5.77 (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[332, 325])).
% 8.55/5.77 tff(334,plain,
% 8.55/5.77 (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[333, 139])).
% 8.55/5.77 tff(335,plain,
% 8.55/5.77 (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[315, 307])).
% 8.55/5.77 tff(336,plain,
% 8.55/5.77 (((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))))) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))),
% 8.55/5.77 inference(tautology,[status(thm)],[])).
% 8.55/5.77 tff(337,plain,
% 8.55/5.77 ((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[336, 335])).
% 8.55/5.77 tff(338,assumption,(unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))), introduced(assumption)).
% 8.55/5.77 tff(339,assumption,(unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))), introduced(assumption)).
% 8.55/5.77 tff(340,plain,
% 8.55/5.77 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(quant_inst,[status(thm)],[])).
% 8.55/5.77 tff(341,plain,
% 8.55/5.77 ($false),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[340, 100, 339])).
% 8.55/5.77 tff(342,plain,(~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.77 tff(343,plain,
% 8.55/5.77 (((~![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, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, 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, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(344,plain,
% 8.55/5.77 ((unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)))) <=> (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(345,plain,
% 8.55/5.77 (((~![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, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))))),
% 8.55/5.77 inference(monotonicity,[status(thm)],[344])).
% 8.55/5.77 tff(346,plain,
% 8.55/5.77 (((~![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, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(transitivity,[status(thm)],[345, 343])).
% 8.55/5.77 tff(347,plain,
% 8.55/5.77 ((~![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, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))))),
% 8.55/5.77 inference(quant_inst,[status(thm)],[])).
% 8.55/5.77 tff(348,plain,
% 8.55/5.77 ((~![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, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.77 inference(modus_ponens,[status(thm)],[347, 346])).
% 8.55/5.77 tff(349,plain,
% 8.55/5.77 (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[348, 58, 246, 342])).
% 8.55/5.77 tff(350,plain,
% 8.55/5.77 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))),
% 8.55/5.77 inference(tautology,[status(thm)],[])).
% 8.55/5.77 tff(351,plain,
% 8.55/5.77 ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[350, 349])).
% 8.55/5.77 tff(352,assumption,(~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))), introduced(assumption)).
% 8.55/5.77 tff(353,plain,
% 8.55/5.77 (((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))),
% 8.55/5.77 inference(tautology,[status(thm)],[])).
% 8.55/5.77 tff(354,plain,
% 8.55/5.77 ((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[353, 352])).
% 8.55/5.77 tff(355,plain,
% 8.55/5.77 (((~![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!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(356,plain,
% 8.55/5.77 ((unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1)))) <=> (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(357,plain,
% 8.55/5.77 (((~![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!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, line_connecting(A!2, 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(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))),
% 8.55/5.77 inference(monotonicity,[status(thm)],[356])).
% 8.55/5.77 tff(358,plain,
% 8.55/5.77 (((~![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!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, line_connecting(A!2, 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(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))))),
% 8.55/5.77 inference(transitivity,[status(thm)],[357, 355])).
% 8.55/5.77 tff(359,plain,
% 8.55/5.77 ((~![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!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(quant_inst,[status(thm)],[])).
% 8.55/5.77 tff(360,plain,
% 8.55/5.77 ((~![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!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))),
% 8.55/5.77 inference(modus_ponens,[status(thm)],[359, 358])).
% 8.55/5.77 tff(361,plain,
% 8.55/5.77 ((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[360, 58, 146])).
% 8.55/5.77 tff(362,plain,
% 8.55/5.77 (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[361, 352])).
% 8.55/5.77 tff(363,plain,
% 8.55/5.77 (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[203, 362])).
% 8.55/5.77 tff(364,plain,
% 8.55/5.77 (before_on_line(L!0, A!2, B!1)),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[228, 363])).
% 8.55/5.77 tff(365,plain,
% 8.55/5.77 (~before_on_line(L!0, B!1, A!2)),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[235, 364])).
% 8.55/5.77 tff(366,plain,
% 8.55/5.77 (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[294, 365])).
% 8.55/5.77 tff(367,plain,
% 8.55/5.77 (unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[282, 366])).
% 8.55/5.77 tff(368,plain,
% 8.55/5.77 (unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[250, 367])).
% 8.55/5.77 tff(369,assumption,(unequally_directed_lines(L!0, L!0)), introduced(assumption)).
% 8.55/5.77 tff(370,plain,
% 8.55/5.77 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(L!0, L!0))),
% 8.55/5.77 inference(quant_inst,[status(thm)],[])).
% 8.55/5.77 tff(371,plain,
% 8.55/5.77 ($false),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[370, 100, 369])).
% 8.55/5.77 tff(372,plain,(~unequally_directed_lines(L!0, L!0)), inference(lemma,lemma(discharge,[]))).
% 8.55/5.77 tff(373,plain,
% 8.55/5.77 (((~![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!0, L!0) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, 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(L!0, L!0) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(374,plain,
% 8.55/5.77 ((unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))))) <=> (unequally_directed_lines(L!0, L!0) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(375,plain,
% 8.55/5.77 (((~![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(line_connecting(A!2, B!1)), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, 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(L!0, L!0) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))))))),
% 8.55/5.77 inference(monotonicity,[status(thm)],[374])).
% 8.55/5.77 tff(376,plain,
% 8.55/5.77 (((~![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(line_connecting(A!2, B!1)), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, 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(L!0, L!0) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))),
% 8.55/5.77 inference(transitivity,[status(thm)],[375, 373])).
% 8.55/5.77 tff(377,plain,
% 8.55/5.77 ((~![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(line_connecting(A!2, B!1)), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))),
% 8.55/5.77 inference(quant_inst,[status(thm)],[])).
% 8.55/5.77 tff(378,plain,
% 8.55/5.77 ((~![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!0, L!0) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(modus_ponens,[status(thm)],[377, 376])).
% 8.55/5.77 tff(379,plain,
% 8.55/5.77 (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[378, 58, 372])).
% 8.55/5.77 tff(380,plain,
% 8.55/5.77 (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)),
% 8.55/5.77 inference(unit_resolution,[status(thm)],[379, 368])).
% 8.55/5.77 tff(381,plain,
% 8.55/5.77 (^[L: $i, M: $i, N: $i] : refl(((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))))),
% 8.55/5.77 inference(bind,[status(th)],[])).
% 8.55/5.77 tff(382,plain,
% 8.55/5.77 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 8.55/5.77 inference(quant_intro,[status(thm)],[381])).
% 8.55/5.77 tff(383,plain,
% 8.55/5.77 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) <=> (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N)))))), rewrite((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) <=> (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N)))))), 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)))))), (((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ((~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite(((~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))), (((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 8.55/5.77 inference(bind,[status(th)],[])).
% 8.55/5.77 tff(384,plain,
% 8.55/5.77 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 8.55/5.77 inference(quant_intro,[status(thm)],[383])).
% 8.55/5.77 tff(385,plain,
% 8.55/5.77 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(386,plain,
% 8.55/5.77 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite(((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N)))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))), (((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))))), rewrite(((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(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, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))))),
% 8.55/5.77 inference(bind,[status(th)],[])).
% 8.55/5.77 tff(387,plain,
% 8.55/5.77 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 8.55/5.77 inference(quant_intro,[status(thm)],[386])).
% 8.55/5.77 tff(388,axiom,(![L: $i, M: $i, N: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N)))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag7')).
% 8.55/5.77 tff(389,plain,
% 8.55/5.77 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 8.55/5.77 inference(modus_ponens,[status(thm)],[388, 387])).
% 8.55/5.77 tff(390,plain,
% 8.55/5.77 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 8.55/5.77 inference(modus_ponens,[status(thm)],[389, 385])).
% 8.55/5.77 tff(391,plain,(
% 8.55/5.77 ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 8.55/5.77 inference(skolemize,[status(sab)],[390])).
% 8.55/5.77 tff(392,plain,
% 8.55/5.77 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 8.55/5.77 inference(modus_ponens,[status(thm)],[391, 384])).
% 8.55/5.77 tff(393,plain,
% 8.55/5.77 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 8.55/5.77 inference(modus_ponens,[status(thm)],[392, 382])).
% 8.55/5.77 tff(394,plain,
% 8.55/5.77 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(395,plain,
% 8.55/5.77 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)))) <=> ((~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(396,plain,
% 8.55/5.77 ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) <=> (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))))),
% 8.55/5.77 inference(rewrite,[status(thm)],[])).
% 8.55/5.77 tff(397,plain,
% 8.55/5.77 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))))),
% 8.55/5.78 inference(monotonicity,[status(thm)],[396])).
% 8.55/5.78 tff(398,plain,
% 8.55/5.78 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)))) <=> ((~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))))),
% 8.55/5.78 inference(transitivity,[status(thm)],[397, 395])).
% 8.55/5.78 tff(399,plain,
% 8.55/5.78 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))))))),
% 8.55/5.78 inference(monotonicity,[status(thm)],[398])).
% 8.55/5.78 tff(400,plain,
% 8.55/5.78 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))))),
% 8.55/5.78 inference(transitivity,[status(thm)],[399, 394])).
% 8.55/5.78 tff(401,plain,
% 8.55/5.78 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))))),
% 8.55/5.78 inference(quant_inst,[status(thm)],[])).
% 8.55/5.78 tff(402,plain,
% 8.55/5.78 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))))),
% 8.55/5.78 inference(modus_ponens,[status(thm)],[401, 400])).
% 8.55/5.78 tff(403,plain,
% 8.55/5.78 ($false),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[402, 393, 380, 338, 354, 351])).
% 8.55/5.78 tff(404,plain,(unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.78 tff(405,plain,
% 8.55/5.78 (unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[404, 338])).
% 8.55/5.78 tff(406,plain,
% 8.55/5.78 (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[379, 307])).
% 8.55/5.78 tff(407,plain,
% 8.55/5.78 ((~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[402, 393, 338, 351])).
% 8.55/5.78 tff(408,plain,
% 8.55/5.78 (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[407, 406])).
% 8.55/5.78 tff(409,plain,
% 8.55/5.78 (((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))))) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 8.55/5.78 inference(tautology,[status(thm)],[])).
% 8.55/5.78 tff(410,plain,
% 8.55/5.78 (unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[409, 408])).
% 8.55/5.78 tff(411,plain,
% 8.55/5.78 (((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.78 inference(tautology,[status(thm)],[])).
% 8.55/5.78 tff(412,plain,
% 8.55/5.78 ((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[411, 246])).
% 8.55/5.78 tff(413,plain,
% 8.55/5.78 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))),
% 8.55/5.78 inference(rewrite,[status(thm)],[])).
% 8.55/5.78 tff(414,plain,
% 8.55/5.78 (((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))))) <=> ((~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))),
% 8.55/5.78 inference(rewrite,[status(thm)],[])).
% 8.55/5.78 tff(415,plain,
% 8.55/5.78 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))))))),
% 8.55/5.78 inference(monotonicity,[status(thm)],[414])).
% 8.55/5.78 tff(416,plain,
% 8.55/5.78 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))),
% 8.55/5.78 inference(transitivity,[status(thm)],[415, 413])).
% 8.55/5.78 tff(417,plain,
% 8.55/5.78 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))),
% 8.55/5.78 inference(quant_inst,[status(thm)],[])).
% 8.55/5.78 tff(418,plain,
% 8.55/5.78 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))))),
% 8.55/5.78 inference(modus_ponens,[status(thm)],[417, 416])).
% 8.55/5.78 tff(419,plain,
% 8.55/5.78 ($false),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[418, 393, 412, 410, 405, 337])).
% 8.55/5.78 tff(420,plain,((~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.78 tff(421,plain,
% 8.55/5.78 (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[420, 334])).
% 8.55/5.78 tff(422,assumption,(~unequally_directed_lines(L!0, reverse_line(L!0))), introduced(assumption)).
% 8.55/5.78 tff(423,plain,
% 8.55/5.78 (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[315, 306])).
% 8.55/5.78 tff(424,plain,
% 8.55/5.78 (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[250, 423])).
% 8.55/5.78 tff(425,plain,
% 8.55/5.78 ((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[409, 424])).
% 8.55/5.78 tff(426,plain,
% 8.55/5.78 (((~![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!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, L!0) | unequally_directed_lines(line_connecting(A!2, B!1), L!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!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, L!0) | unequally_directed_lines(line_connecting(A!2, B!1), L!0))),
% 8.55/5.78 inference(rewrite,[status(thm)],[])).
% 8.55/5.78 tff(427,plain,
% 8.55/5.78 ((unequally_directed_lines(line_connecting(A!2, B!1), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1)))) <=> ((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, L!0) | unequally_directed_lines(line_connecting(A!2, B!1), L!0))),
% 8.55/5.78 inference(rewrite,[status(thm)],[])).
% 8.55/5.78 tff(428,plain,
% 8.55/5.78 (((~![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!2, B!1), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, 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(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, L!0) | unequally_directed_lines(line_connecting(A!2, B!1), L!0)))),
% 8.55/5.78 inference(monotonicity,[status(thm)],[427])).
% 8.55/5.78 tff(429,plain,
% 8.55/5.78 (((~![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!2, B!1), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, 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(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, L!0) | unequally_directed_lines(line_connecting(A!2, B!1), L!0))),
% 8.55/5.78 inference(transitivity,[status(thm)],[428, 426])).
% 8.55/5.78 tff(430,plain,
% 8.55/5.78 ((~![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!2, B!1), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))))),
% 8.55/5.78 inference(quant_inst,[status(thm)],[])).
% 8.55/5.78 tff(431,plain,
% 8.55/5.78 ((~![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!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, L!0) | unequally_directed_lines(line_connecting(A!2, B!1), L!0)),
% 8.55/5.78 inference(modus_ponens,[status(thm)],[430, 429])).
% 8.55/5.78 tff(432,plain,
% 8.55/5.78 ((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), L!0)),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[431, 58, 372])).
% 8.55/5.78 tff(433,plain,
% 8.55/5.78 (unequally_directed_lines(line_connecting(A!2, B!1), L!0)),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[432, 306])).
% 8.55/5.78 tff(434,plain,
% 8.55/5.78 (((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 8.55/5.78 inference(tautology,[status(thm)],[])).
% 8.55/5.78 tff(435,plain,
% 8.55/5.78 ((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[434, 146])).
% 8.55/5.78 tff(436,plain,
% 8.55/5.78 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 8.55/5.78 inference(rewrite,[status(thm)],[])).
% 8.55/5.78 tff(437,plain,
% 8.55/5.78 (((~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)))) <=> ((~((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 8.55/5.78 inference(rewrite,[status(thm)],[])).
% 8.55/5.78 tff(438,plain,
% 8.55/5.78 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 8.55/5.78 inference(monotonicity,[status(thm)],[437])).
% 8.55/5.78 tff(439,plain,
% 8.55/5.78 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 8.55/5.78 inference(transitivity,[status(thm)],[438, 436])).
% 8.55/5.78 tff(440,plain,
% 8.55/5.78 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 8.55/5.78 inference(quant_inst,[status(thm)],[])).
% 8.55/5.78 tff(441,plain,
% 8.55/5.78 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)))),
% 8.55/5.78 inference(modus_ponens,[status(thm)],[440, 439])).
% 8.55/5.78 tff(442,plain,
% 8.55/5.78 (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[441, 393, 435, 433, 425])).
% 8.55/5.78 tff(443,plain,
% 8.55/5.78 (((~![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!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!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!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)))),
% 8.55/5.78 inference(rewrite,[status(thm)],[])).
% 8.55/5.78 tff(444,plain,
% 8.55/5.78 ((unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1)))) <=> ((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)))),
% 8.55/5.78 inference(rewrite,[status(thm)],[])).
% 8.55/5.78 tff(445,plain,
% 8.55/5.78 (((~![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!2, B!1), reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, line_connecting(A!2, 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(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 8.55/5.78 inference(monotonicity,[status(thm)],[444])).
% 8.55/5.78 tff(446,plain,
% 8.55/5.78 (((~![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!2, B!1), reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, line_connecting(A!2, 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(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)))),
% 8.55/5.78 inference(transitivity,[status(thm)],[445, 443])).
% 8.55/5.78 tff(447,plain,
% 8.55/5.78 ((~![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!2, B!1), reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))))),
% 8.55/5.78 inference(quant_inst,[status(thm)],[])).
% 8.55/5.78 tff(448,plain,
% 8.55/5.78 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))),
% 8.55/5.78 inference(modus_ponens,[status(thm)],[447, 446])).
% 8.55/5.78 tff(449,plain,
% 8.55/5.78 ($false),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[448, 58, 306, 422, 442])).
% 8.55/5.78 tff(450,plain,(unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1)))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.78 tff(451,plain,
% 8.55/5.78 (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[450, 422])).
% 8.55/5.78 tff(452,plain,
% 8.55/5.78 ((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[336, 451])).
% 8.55/5.78 tff(453,plain,
% 8.55/5.78 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.78 inference(tautology,[status(thm)],[])).
% 8.55/5.78 tff(454,plain,
% 8.55/5.78 ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[453, 342])).
% 8.55/5.78 tff(455,plain,
% 8.55/5.78 (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[203, 451])).
% 8.55/5.78 tff(456,plain,
% 8.55/5.78 (before_on_line(L!0, A!2, B!1)),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[228, 455])).
% 8.55/5.78 tff(457,plain,
% 8.55/5.78 (~before_on_line(L!0, B!1, A!2)),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[235, 456])).
% 8.55/5.78 tff(458,plain,
% 8.55/5.78 (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[294, 457])).
% 8.55/5.78 tff(459,plain,
% 8.55/5.78 (unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[282, 458])).
% 8.55/5.78 tff(460,plain,
% 8.55/5.78 (unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[250, 459])).
% 8.55/5.78 tff(461,plain,
% 8.55/5.78 (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)),
% 8.55/5.78 inference(unit_resolution,[status(thm)],[379, 460])).
% 8.55/5.78 tff(462,plain,
% 8.55/5.78 (((~![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!0, reverse_line(L!0)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!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!0, reverse_line(L!0)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)))),
% 8.55/5.78 inference(rewrite,[status(thm)],[])).
% 8.55/5.78 tff(463,plain,
% 8.55/5.78 ((~![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!0, reverse_line(L!0)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)))),
% 8.55/5.78 inference(quant_inst,[status(thm)],[])).
% 8.55/5.78 tff(464,plain,
% 8.55/5.78 ((~![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!0, reverse_line(L!0)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0))),
% 8.55/5.78 inference(modus_ponens,[status(thm)],[463, 462])).
% 8.55/5.79 tff(465,plain,
% 8.55/5.79 (unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0))),
% 8.55/5.79 inference(unit_resolution,[status(thm)],[464, 58])).
% 8.55/5.79 tff(466,plain,
% 8.55/5.79 (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))),
% 8.55/5.79 inference(unit_resolution,[status(thm)],[465, 461, 422])).
% 8.55/5.79 tff(467,plain,
% 8.55/5.79 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))))),
% 8.55/5.79 inference(rewrite,[status(thm)],[])).
% 8.55/5.79 tff(468,plain,
% 8.55/5.79 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))))),
% 8.55/5.79 inference(rewrite,[status(thm)],[])).
% 8.55/5.79 tff(469,plain,
% 8.55/5.79 ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))))) <=> (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)))))),
% 8.55/5.79 inference(rewrite,[status(thm)],[])).
% 8.55/5.79 tff(470,plain,
% 8.55/5.79 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))))),
% 8.55/5.79 inference(monotonicity,[status(thm)],[469])).
% 8.55/5.79 tff(471,plain,
% 8.55/5.79 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0)))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))))),
% 8.55/5.79 inference(transitivity,[status(thm)],[470, 468])).
% 8.55/5.79 tff(472,plain,
% 8.55/5.79 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)))))))),
% 8.55/5.79 inference(monotonicity,[status(thm)],[471])).
% 8.55/5.79 tff(473,plain,
% 8.55/5.79 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))))),
% 8.55/5.79 inference(transitivity,[status(thm)],[472, 467])).
% 8.55/5.79 tff(474,plain,
% 8.55/5.79 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))))),
% 8.55/5.79 inference(quant_inst,[status(thm)],[])).
% 8.55/5.79 tff(475,plain,
% 8.55/5.79 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(L!0))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), L!0)) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)))))),
% 8.55/5.79 inference(modus_ponens,[status(thm)],[474, 473])).
% 8.55/5.79 tff(476,plain,
% 8.55/5.79 ($false),
% 8.55/5.79 inference(unit_resolution,[status(thm)],[475, 393, 461, 466, 454, 452])).
% 8.55/5.79 tff(477,plain,(unequally_directed_lines(L!0, reverse_line(L!0))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.79 tff(478,assumption,(~unequally_directed_lines(reverse_line(L!0), L!0)), introduced(assumption)).
% 8.55/5.79 tff(479,assumption,(unequally_directed_lines(L!0, reverse_line(L!0))), introduced(assumption)).
% 8.55/5.79 tff(480,plain,
% 8.55/5.79 (((~![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!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), L!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!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), L!0))),
% 8.55/5.79 inference(rewrite,[status(thm)],[])).
% 8.55/5.79 tff(481,plain,
% 8.55/5.79 ((unequally_directed_lines(reverse_line(L!0), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(L!0)))) <=> (unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), L!0))),
% 8.55/5.79 inference(rewrite,[status(thm)],[])).
% 8.55/5.79 tff(482,plain,
% 8.55/5.79 (((~![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!0), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(L!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!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), L!0)))),
% 8.55/5.79 inference(monotonicity,[status(thm)],[481])).
% 8.55/5.79 tff(483,plain,
% 8.55/5.79 (((~![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!0), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(L!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!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), L!0))),
% 8.55/5.79 inference(transitivity,[status(thm)],[482, 480])).
% 8.55/5.79 tff(484,plain,
% 8.55/5.79 ((~![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!0), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(L!0))))),
% 8.55/5.79 inference(quant_inst,[status(thm)],[])).
% 8.55/5.79 tff(485,plain,
% 8.55/5.79 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), L!0)),
% 8.55/5.79 inference(modus_ponens,[status(thm)],[484, 483])).
% 8.55/5.79 tff(486,plain,
% 8.55/5.79 ($false),
% 8.55/5.79 inference(unit_resolution,[status(thm)],[485, 58, 372, 479, 478])).
% 8.55/5.79 tff(487,plain,(unequally_directed_lines(reverse_line(L!0), L!0) | (~unequally_directed_lines(L!0, reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.79 tff(488,plain,
% 8.55/5.79 (unequally_directed_lines(reverse_line(L!0), L!0)),
% 8.55/5.79 inference(unit_resolution,[status(thm)],[487, 477])).
% 8.55/5.79 tff(489,assumption,(~unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1)))), introduced(assumption)).
% 8.55/5.79 tff(490,assumption,(unequally_directed_lines(reverse_line(L!0), L!0)), introduced(assumption)).
% 8.55/5.79 tff(491,assumption,(~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))), introduced(assumption)).
% 8.55/5.79 tff(492,plain,
% 8.55/5.79 (((~![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!0, reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(L!0), L!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!0, reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(L!0), L!0)))),
% 8.55/5.79 inference(rewrite,[status(thm)],[])).
% 8.55/5.79 tff(493,plain,
% 8.55/5.79 ((~![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!0, reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(L!0), L!0)))),
% 8.55/5.79 inference(quant_inst,[status(thm)],[])).
% 8.55/5.79 tff(494,plain,
% 8.55/5.79 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(L!0), L!0))),
% 8.55/5.79 inference(modus_ponens,[status(thm)],[493, 492])).
% 8.55/5.79 tff(495,plain,
% 8.55/5.79 ($false),
% 8.55/5.79 inference(unit_resolution,[status(thm)],[494, 58, 491, 490, 489])).
% 8.55/5.79 tff(496,plain,(unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(L!0), L!0))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.79 tff(497,plain,
% 8.55/5.79 (unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.79 inference(unit_resolution,[status(thm)],[496, 488])).
% 8.55/5.79 tff(498,plain,
% 8.55/5.79 (unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1)))),
% 8.55/5.79 inference(unit_resolution,[status(thm)],[497, 421])).
% 8.55/5.79 tff(499,assumption,(~unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))), introduced(assumption)).
% 8.55/5.79 tff(500,assumption,(~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))), introduced(assumption)).
% 8.55/5.79 tff(501,plain,
% 8.55/5.79 ((~![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))))),
% 8.55/5.79 inference(quant_inst,[status(thm)],[])).
% 8.55/5.79 tff(502,plain,
% 8.55/5.79 (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))),
% 8.55/5.79 inference(unit_resolution,[status(thm)],[501, 88])).
% 8.55/5.79 tff(503,plain,
% 8.55/5.79 (((~![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!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))))),
% 8.55/5.79 inference(rewrite,[status(thm)],[])).
% 8.55/5.79 tff(504,plain,
% 8.55/5.79 ((unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) <=> (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))))),
% 8.55/5.79 inference(rewrite,[status(thm)],[])).
% 8.55/5.79 tff(505,plain,
% 8.55/5.79 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))))),
% 8.55/5.79 inference(monotonicity,[status(thm)],[504])).
% 8.55/5.79 tff(506,plain,
% 8.55/5.79 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))))),
% 8.55/5.79 inference(transitivity,[status(thm)],[505, 503])).
% 8.55/5.79 tff(507,plain,
% 8.55/5.79 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.55/5.79 inference(quant_inst,[status(thm)],[])).
% 8.55/5.79 tff(508,plain,
% 8.55/5.79 ((~![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!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))),
% 8.55/5.79 inference(modus_ponens,[status(thm)],[507, 506])).
% 8.55/5.79 tff(509,plain,
% 8.55/5.79 (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))),
% 8.55/5.79 inference(unit_resolution,[status(thm)],[508, 58, 146, 502])).
% 8.55/5.79 tff(510,plain,
% 8.55/5.79 (((~![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(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!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(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 8.55/5.79 inference(rewrite,[status(thm)],[])).
% 8.55/5.79 tff(511,plain,
% 8.55/5.79 ((unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 8.55/5.79 inference(rewrite,[status(thm)],[])).
% 8.55/5.79 tff(512,plain,
% 8.55/5.79 (((~![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!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, 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(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.55/5.79 inference(monotonicity,[status(thm)],[511])).
% 8.55/5.79 tff(513,plain,
% 8.55/5.79 (((~![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!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, 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(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 8.55/5.79 inference(transitivity,[status(thm)],[512, 510])).
% 8.55/5.79 tff(514,plain,
% 8.55/5.79 ((~![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!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))),
% 8.55/5.79 inference(quant_inst,[status(thm)],[])).
% 8.55/5.79 tff(515,plain,
% 8.55/5.79 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))),
% 8.55/5.79 inference(modus_ponens,[status(thm)],[514, 513])).
% 8.55/5.79 tff(516,plain,
% 8.55/5.79 ($false),
% 8.55/5.79 inference(unit_resolution,[status(thm)],[515, 58, 325, 509, 500])).
% 8.55/5.79 tff(517,plain,(unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.79 tff(518,plain,
% 8.55/5.79 (((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))),
% 8.55/5.79 inference(tautology,[status(thm)],[])).
% 8.55/5.79 tff(519,plain,
% 8.55/5.79 ((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2)))),
% 8.55/5.79 inference(unit_resolution,[status(thm)],[518, 502])).
% 8.55/5.79 tff(520,plain,
% 8.55/5.79 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2))))))),
% 8.55/5.79 inference(rewrite,[status(thm)],[])).
% 8.55/5.79 tff(521,plain,
% 8.55/5.79 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2))))))),
% 8.55/5.79 inference(rewrite,[status(thm)],[])).
% 8.55/5.79 tff(522,plain,
% 8.55/5.79 ((~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))))) <=> (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2)))))),
% 8.55/5.79 inference(rewrite,[status(thm)],[])).
% 8.55/5.79 tff(523,plain,
% 8.55/5.79 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))),
% 8.55/5.79 inference(monotonicity,[status(thm)],[522, 396])).
% 8.55/5.79 tff(524,plain,
% 8.55/5.79 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2))))))),
% 8.55/5.80 inference(transitivity,[status(thm)],[523, 521])).
% 8.55/5.80 tff(525,plain,
% 8.55/5.80 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2)))))))),
% 8.55/5.80 inference(monotonicity,[status(thm)],[524])).
% 8.55/5.80 tff(526,plain,
% 8.55/5.80 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2))))))),
% 8.55/5.80 inference(transitivity,[status(thm)],[525, 520])).
% 8.55/5.80 tff(527,plain,
% 8.55/5.80 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))),
% 8.55/5.80 inference(quant_inst,[status(thm)],[])).
% 8.55/5.80 tff(528,plain,
% 8.55/5.80 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~((~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(B!1, A!2)))))),
% 8.55/5.80 inference(modus_ponens,[status(thm)],[527, 526])).
% 8.55/5.80 tff(529,plain,
% 8.55/5.80 ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[528, 393, 519, 517])).
% 8.55/5.80 tff(530,plain,
% 8.55/5.80 (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[529, 351])).
% 8.55/5.80 tff(531,assumption,(unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1)))), introduced(assumption)).
% 8.55/5.80 tff(532,plain,
% 8.55/5.80 (((~![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!0), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!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(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.55/5.80 inference(rewrite,[status(thm)],[])).
% 8.55/5.80 tff(533,plain,
% 8.55/5.80 ((unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1))))) <=> ((~unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.55/5.80 inference(rewrite,[status(thm)],[])).
% 8.55/5.80 tff(534,plain,
% 8.55/5.80 (((~![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(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, 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(L!0), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))),
% 8.55/5.80 inference(monotonicity,[status(thm)],[533])).
% 8.55/5.80 tff(535,plain,
% 8.55/5.80 (((~![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(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, 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(L!0), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.55/5.80 inference(transitivity,[status(thm)],[534, 532])).
% 8.55/5.80 tff(536,plain,
% 8.55/5.80 ((~![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(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1)))))),
% 8.55/5.80 inference(quant_inst,[status(thm)],[])).
% 8.55/5.80 tff(537,plain,
% 8.55/5.80 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 8.55/5.80 inference(modus_ponens,[status(thm)],[536, 535])).
% 8.55/5.80 tff(538,plain,
% 8.55/5.80 ($false),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[537, 58, 531, 530, 499])).
% 8.55/5.80 tff(539,plain,(unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(line_connecting(A!2, B!1))))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.80 tff(540,plain,
% 8.55/5.80 (unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[539, 498])).
% 8.55/5.80 tff(541,assumption,(left_convergent_lines(reverse_line(L!0), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))), introduced(assumption)).
% 8.55/5.80 tff(542,plain,
% 8.55/5.80 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(L!0), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))),
% 8.55/5.80 inference(quant_inst,[status(thm)],[])).
% 8.55/5.80 tff(543,plain,
% 8.55/5.80 ($false),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[542, 9, 541])).
% 8.55/5.80 tff(544,plain,(~(left_convergent_lines(reverse_line(L!0), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.80 tff(545,plain,
% 8.55/5.80 ((left_convergent_lines(reverse_line(L!0), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.55/5.80 inference(tautology,[status(thm)],[])).
% 8.55/5.80 tff(546,plain,
% 8.55/5.80 (~left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[545, 544])).
% 8.55/5.80 tff(547,assumption,(left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))), introduced(assumption)).
% 8.55/5.80 tff(548,plain,
% 8.55/5.80 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))),
% 8.55/5.80 inference(quant_inst,[status(thm)],[])).
% 8.55/5.80 tff(549,plain,
% 8.55/5.80 ($false),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[548, 9, 547])).
% 8.55/5.80 tff(550,plain,(~(left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.80 tff(551,plain,
% 8.55/5.80 ((left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) | (~left_convergent_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))),
% 8.55/5.80 inference(tautology,[status(thm)],[])).
% 8.55/5.80 tff(552,plain,
% 8.55/5.80 (~left_convergent_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[551, 550])).
% 8.55/5.80 tff(553,assumption,(unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))), introduced(assumption)).
% 8.55/5.80 tff(554,assumption,(unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))), introduced(assumption)).
% 8.55/5.80 tff(555,plain,
% 8.55/5.80 (((~![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!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))) <=> ((~![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!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))),
% 8.55/5.80 inference(rewrite,[status(thm)],[])).
% 8.55/5.80 tff(556,plain,
% 8.55/5.80 ((left_convergent_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))) <=> ((~unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))),
% 8.55/5.80 inference(rewrite,[status(thm)],[])).
% 8.55/5.80 tff(557,plain,
% 8.55/5.80 (((~![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!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))) <=> ((~![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!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))))),
% 8.55/5.80 inference(monotonicity,[status(thm)],[556])).
% 8.55/5.80 tff(558,plain,
% 8.55/5.80 (((~![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!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))) <=> ((~![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!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))),
% 8.55/5.80 inference(transitivity,[status(thm)],[557, 555])).
% 8.55/5.80 tff(559,plain,
% 8.55/5.80 ((~![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!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))),
% 8.55/5.80 inference(quant_inst,[status(thm)],[])).
% 8.55/5.80 tff(560,plain,
% 8.55/5.80 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))),
% 8.55/5.80 inference(modus_ponens,[status(thm)],[559, 558])).
% 8.55/5.80 tff(561,plain,
% 8.55/5.80 ($false),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[560, 30, 554, 553, 552, 546])).
% 8.55/5.80 tff(562,plain,((~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.80 tff(563,plain,
% 8.55/5.80 (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[562, 540])).
% 8.55/5.80 tff(564,assumption,(~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0))), introduced(assumption)).
% 8.55/5.80 tff(565,assumption,(~unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2))), introduced(assumption)).
% 8.55/5.80 tff(566,plain,
% 8.55/5.80 (((~![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!0, L!0) | (~unequally_directed_lines(L!0, parallel_through_point(L!0, A!2))) | unequally_directed_lines(parallel_through_point(L!0, A!2), L!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!0, L!0) | (~unequally_directed_lines(L!0, parallel_through_point(L!0, A!2))) | unequally_directed_lines(parallel_through_point(L!0, A!2), L!0))),
% 8.55/5.80 inference(rewrite,[status(thm)],[])).
% 8.55/5.80 tff(567,plain,
% 8.55/5.80 ((unequally_directed_lines(parallel_through_point(L!0, A!2), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, parallel_through_point(L!0, A!2)))) <=> (unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, parallel_through_point(L!0, A!2))) | unequally_directed_lines(parallel_through_point(L!0, A!2), L!0))),
% 8.55/5.80 inference(rewrite,[status(thm)],[])).
% 8.55/5.80 tff(568,plain,
% 8.55/5.80 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(L!0, A!2), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, parallel_through_point(L!0, A!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!0, L!0) | (~unequally_directed_lines(L!0, parallel_through_point(L!0, A!2))) | unequally_directed_lines(parallel_through_point(L!0, A!2), L!0)))),
% 8.55/5.80 inference(monotonicity,[status(thm)],[567])).
% 8.55/5.80 tff(569,plain,
% 8.55/5.80 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(L!0, A!2), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, parallel_through_point(L!0, A!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!0, L!0) | (~unequally_directed_lines(L!0, parallel_through_point(L!0, A!2))) | unequally_directed_lines(parallel_through_point(L!0, A!2), L!0))),
% 8.55/5.80 inference(transitivity,[status(thm)],[568, 566])).
% 8.55/5.80 tff(570,plain,
% 8.55/5.80 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(L!0, A!2), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, parallel_through_point(L!0, A!2))))),
% 8.55/5.80 inference(quant_inst,[status(thm)],[])).
% 8.55/5.80 tff(571,plain,
% 8.55/5.80 ((~![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!0, L!0) | (~unequally_directed_lines(L!0, parallel_through_point(L!0, A!2))) | unequally_directed_lines(parallel_through_point(L!0, A!2), L!0)),
% 8.55/5.80 inference(modus_ponens,[status(thm)],[570, 569])).
% 8.55/5.80 tff(572,plain,
% 8.55/5.80 (~unequally_directed_lines(L!0, parallel_through_point(L!0, A!2))),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[571, 58, 372, 126])).
% 8.55/5.80 tff(573,plain,
% 8.55/5.80 (((~![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!0, parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(reverse_line(L!0), L!0)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!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!0, parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(reverse_line(L!0), L!0)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2)))),
% 8.55/5.80 inference(rewrite,[status(thm)],[])).
% 8.55/5.80 tff(574,plain,
% 8.55/5.80 ((unequally_directed_lines(L!0, parallel_through_point(L!0, A!2)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(reverse_line(L!0), L!0))) <=> (unequally_directed_lines(L!0, parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(reverse_line(L!0), L!0)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2)))),
% 8.55/5.80 inference(rewrite,[status(thm)],[])).
% 8.55/5.80 tff(575,plain,
% 8.55/5.80 (((~![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!0, parallel_through_point(L!0, A!2)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(reverse_line(L!0), L!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!0, parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(reverse_line(L!0), L!0)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2))))),
% 8.55/5.80 inference(monotonicity,[status(thm)],[574])).
% 8.55/5.80 tff(576,plain,
% 8.55/5.80 (((~![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!0, parallel_through_point(L!0, A!2)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(reverse_line(L!0), L!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!0, parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(reverse_line(L!0), L!0)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2)))),
% 8.55/5.80 inference(transitivity,[status(thm)],[575, 573])).
% 8.55/5.80 tff(577,plain,
% 8.55/5.80 ((~![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!0, parallel_through_point(L!0, A!2)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(reverse_line(L!0), L!0)))),
% 8.55/5.80 inference(quant_inst,[status(thm)],[])).
% 8.55/5.80 tff(578,plain,
% 8.55/5.80 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(reverse_line(L!0), L!0)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2))),
% 8.55/5.80 inference(modus_ponens,[status(thm)],[577, 576])).
% 8.55/5.80 tff(579,plain,
% 8.55/5.80 ($false),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[578, 58, 490, 572, 565])).
% 8.55/5.80 tff(580,plain,(unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(reverse_line(L!0), L!0))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.80 tff(581,plain,
% 8.55/5.80 (unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2))),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[580, 488])).
% 8.55/5.80 tff(582,plain,
% 8.55/5.80 (((~![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!0), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!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(reverse_line(L!0), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2))))),
% 8.55/5.80 inference(rewrite,[status(thm)],[])).
% 8.55/5.80 tff(583,plain,
% 8.55/5.80 ((unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0)) | unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2)))) <=> (unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2))))),
% 8.55/5.80 inference(rewrite,[status(thm)],[])).
% 8.55/5.80 tff(584,plain,
% 8.55/5.80 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0)) | unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!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(reverse_line(L!0), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2)))))),
% 8.55/5.80 inference(monotonicity,[status(thm)],[583])).
% 8.55/5.80 tff(585,plain,
% 8.55/5.80 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0)) | unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!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(reverse_line(L!0), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2))))),
% 8.55/5.80 inference(transitivity,[status(thm)],[584, 582])).
% 8.55/5.80 tff(586,plain,
% 8.55/5.80 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0)) | unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2))))),
% 8.55/5.80 inference(quant_inst,[status(thm)],[])).
% 8.55/5.80 tff(587,plain,
% 8.55/5.80 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), parallel_through_point(L!0, A!2)))),
% 8.55/5.80 inference(modus_ponens,[status(thm)],[586, 585])).
% 8.55/5.80 tff(588,plain,
% 8.55/5.80 ($false),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[587, 58, 103, 581, 564])).
% 8.55/5.80 tff(589,plain,(unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.80 tff(590,plain,
% 8.55/5.80 (((~![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!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!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(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0))))),
% 8.55/5.80 inference(rewrite,[status(thm)],[])).
% 8.55/5.80 tff(591,plain,
% 8.55/5.80 ((~![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!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0))))),
% 8.55/5.80 inference(quant_inst,[status(thm)],[])).
% 8.55/5.80 tff(592,plain,
% 8.55/5.80 ((~![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!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0)))),
% 8.55/5.80 inference(modus_ponens,[status(thm)],[591, 590])).
% 8.55/5.80 tff(593,plain,
% 8.55/5.80 (unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0)))),
% 8.55/5.80 inference(unit_resolution,[status(thm)],[592, 58])).
% 8.55/5.80 tff(594,plain,
% 8.55/5.80 (unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.55/5.81 inference(unit_resolution,[status(thm)],[593, 589])).
% 8.55/5.81 tff(595,plain,
% 8.55/5.81 (unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.55/5.81 inference(unit_resolution,[status(thm)],[594, 563])).
% 8.55/5.81 tff(596,assumption,(left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))), introduced(assumption)).
% 8.55/5.81 tff(597,plain,
% 8.55/5.81 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))),
% 8.55/5.81 inference(quant_inst,[status(thm)],[])).
% 8.55/5.81 tff(598,plain,
% 8.55/5.81 ($false),
% 8.55/5.81 inference(unit_resolution,[status(thm)],[597, 9, 596])).
% 8.55/5.81 tff(599,plain,(~(left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))), inference(lemma,lemma(discharge,[]))).
% 8.55/5.81 tff(600,plain,
% 8.55/5.81 ((left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) | (~left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))),
% 8.55/5.81 inference(tautology,[status(thm)],[])).
% 8.55/5.81 tff(601,plain,
% 8.55/5.81 (~left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.55/5.81 inference(unit_resolution,[status(thm)],[600, 599])).
% 8.55/5.81 tff(602,plain,
% 8.55/5.81 ((left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) | (~left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.55/5.81 inference(tautology,[status(thm)],[])).
% 8.55/5.81 tff(603,plain,
% 8.55/5.81 (~left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 8.55/5.81 inference(unit_resolution,[status(thm)],[602, 599])).
% 8.55/5.81 tff(604,assumption,(unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))), introduced(assumption)).
% 8.55/5.81 tff(605,assumption,(unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))), introduced(assumption)).
% 8.55/5.81 tff(606,plain,
% 8.55/5.81 (((~![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(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))) <=> ((~![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(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))),
% 8.55/5.81 inference(rewrite,[status(thm)],[])).
% 8.55/5.81 tff(607,plain,
% 8.55/5.81 ((left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))) <=> ((~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))),
% 8.55/5.81 inference(rewrite,[status(thm)],[])).
% 8.55/5.81 tff(608,plain,
% 8.55/5.81 (((~![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(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))) <=> ((~![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(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))))),
% 8.55/5.81 inference(monotonicity,[status(thm)],[607])).
% 8.55/5.81 tff(609,plain,
% 8.65/5.81 (((~![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(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))) <=> ((~![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(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))),
% 8.65/5.81 inference(transitivity,[status(thm)],[608, 606])).
% 8.65/5.81 tff(610,plain,
% 8.65/5.81 ((~![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(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))))),
% 8.65/5.81 inference(quant_inst,[status(thm)],[])).
% 8.65/5.81 tff(611,plain,
% 8.65/5.81 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) | left_convergent_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))),
% 8.65/5.81 inference(modus_ponens,[status(thm)],[610, 609])).
% 8.65/5.81 tff(612,plain,
% 8.65/5.81 ($false),
% 8.65/5.81 inference(unit_resolution,[status(thm)],[611, 30, 605, 604, 603, 601])).
% 8.65/5.81 tff(613,plain,((~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))), inference(lemma,lemma(discharge,[]))).
% 8.65/5.81 tff(614,plain,
% 8.65/5.81 (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 8.65/5.81 inference(unit_resolution,[status(thm)],[613, 595])).
% 8.65/5.81 tff(615,assumption,(~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))), introduced(assumption)).
% 8.65/5.81 tff(616,assumption,(unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1)))), introduced(assumption)).
% 8.65/5.81 tff(617,plain,
% 8.65/5.81 (((~![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(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!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(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.65/5.81 inference(rewrite,[status(thm)],[])).
% 8.65/5.81 tff(618,plain,
% 8.65/5.81 ((unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1))))) <=> (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.65/5.81 inference(rewrite,[status(thm)],[])).
% 8.65/5.81 tff(619,plain,
% 8.65/5.81 (((~![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(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, 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(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))),
% 8.65/5.81 inference(monotonicity,[status(thm)],[618])).
% 8.65/5.81 tff(620,plain,
% 8.65/5.81 (((~![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(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, 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(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 8.65/5.81 inference(transitivity,[status(thm)],[619, 617])).
% 8.65/5.81 tff(621,plain,
% 8.65/5.81 ((~![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(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1)))))),
% 8.65/5.81 inference(quant_inst,[status(thm)],[])).
% 8.65/5.81 tff(622,plain,
% 8.65/5.81 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 8.65/5.81 inference(modus_ponens,[status(thm)],[621, 620])).
% 8.65/5.81 tff(623,plain,
% 8.65/5.81 ($false),
% 8.65/5.81 inference(unit_resolution,[status(thm)],[622, 58, 530, 616, 615])).
% 8.65/5.81 tff(624,plain,(unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1))))), inference(lemma,lemma(discharge,[]))).
% 8.65/5.81 tff(625,plain,
% 8.65/5.81 (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1)))),
% 8.65/5.81 inference(unit_resolution,[status(thm)],[624, 614])).
% 8.65/5.81 tff(626,assumption,(unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2))), introduced(assumption)).
% 8.65/5.81 tff(627,assumption,(~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1)))), introduced(assumption)).
% 8.65/5.81 tff(628,plain,
% 8.65/5.81 (((~![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, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2))))),
% 8.65/5.81 inference(rewrite,[status(thm)],[])).
% 8.65/5.81 tff(629,plain,
% 8.65/5.81 ((unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2)))) <=> (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2))))),
% 8.65/5.81 inference(rewrite,[status(thm)],[])).
% 8.65/5.81 tff(630,plain,
% 8.65/5.81 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2)))))),
% 8.65/5.81 inference(monotonicity,[status(thm)],[629])).
% 8.65/5.81 tff(631,plain,
% 8.65/5.81 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2))))),
% 8.65/5.81 inference(transitivity,[status(thm)],[630, 628])).
% 8.65/5.81 tff(632,plain,
% 8.65/5.81 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2))))),
% 8.65/5.81 inference(quant_inst,[status(thm)],[])).
% 8.65/5.81 tff(633,plain,
% 8.65/5.81 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2)))),
% 8.65/5.81 inference(modus_ponens,[status(thm)],[632, 631])).
% 8.65/5.81 tff(634,plain,
% 8.65/5.81 ($false),
% 8.65/5.81 inference(unit_resolution,[status(thm)],[633, 58, 246, 627, 626])).
% 8.65/5.81 tff(635,plain,(unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2)))), inference(lemma,lemma(discharge,[]))).
% 8.65/5.81 tff(636,plain,
% 8.65/5.81 (~unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2))),
% 8.65/5.81 inference(unit_resolution,[status(thm)],[635, 625])).
% 8.65/5.81 tff(637,assumption,(~unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2))), introduced(assumption)).
% 8.65/5.81 tff(638,assumption,(unequally_directed_lines(line_connecting(B!1, A!2), L!0)), introduced(assumption)).
% 8.65/5.81 tff(639,plain,
% 8.65/5.81 (((~![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!0, parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!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!0, parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2)))),
% 8.65/5.81 inference(rewrite,[status(thm)],[])).
% 8.65/5.81 tff(640,plain,
% 8.65/5.81 ((unequally_directed_lines(L!0, parallel_through_point(L!0, A!2)) | unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0))) <=> (unequally_directed_lines(L!0, parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2)))),
% 8.65/5.81 inference(rewrite,[status(thm)],[])).
% 8.65/5.81 tff(641,plain,
% 8.65/5.81 (((~![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!0, parallel_through_point(L!0, A!2)) | unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!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!0, parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2))))),
% 8.65/5.81 inference(monotonicity,[status(thm)],[640])).
% 8.65/5.81 tff(642,plain,
% 8.65/5.81 (((~![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!0, parallel_through_point(L!0, A!2)) | unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!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!0, parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2)))),
% 8.65/5.81 inference(transitivity,[status(thm)],[641, 639])).
% 8.65/5.81 tff(643,plain,
% 8.65/5.81 ((~![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!0, parallel_through_point(L!0, A!2)) | unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)))),
% 8.65/5.81 inference(quant_inst,[status(thm)],[])).
% 8.65/5.81 tff(644,plain,
% 8.65/5.81 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2))),
% 8.65/5.81 inference(modus_ponens,[status(thm)],[643, 642])).
% 8.65/5.81 tff(645,plain,
% 8.65/5.81 ($false),
% 8.65/5.81 inference(unit_resolution,[status(thm)],[644, 58, 638, 572, 637])).
% 8.65/5.81 tff(646,plain,(unequally_directed_lines(line_connecting(B!1, A!2), parallel_through_point(L!0, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0))), inference(lemma,lemma(discharge,[]))).
% 8.65/5.81 tff(647,plain,
% 8.65/5.81 (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)),
% 8.65/5.81 inference(unit_resolution,[status(thm)],[646, 636])).
% 8.65/5.81 tff(648,plain,
% 8.65/5.81 (((~![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, A!2), L!0) | unequally_directed_lines(parallel_through_point(L!0, A!2), L!0) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), L!0) | unequally_directed_lines(parallel_through_point(L!0, A!2), L!0) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))))),
% 8.65/5.81 inference(rewrite,[status(thm)],[])).
% 8.65/5.81 tff(649,plain,
% 8.65/5.81 ((~![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, A!2), L!0) | unequally_directed_lines(parallel_through_point(L!0, A!2), L!0) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))))),
% 8.65/5.81 inference(quant_inst,[status(thm)],[])).
% 8.65/5.81 tff(650,plain,
% 8.65/5.81 ((~![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, A!2), L!0) | unequally_directed_lines(parallel_through_point(L!0, A!2), L!0) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2)))),
% 8.65/5.81 inference(modus_ponens,[status(thm)],[649, 648])).
% 8.65/5.81 tff(651,plain,
% 8.65/5.81 (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))),
% 8.65/5.81 inference(unit_resolution,[status(thm)],[650, 58, 647, 126])).
% 8.65/5.81 tff(652,plain,
% 8.65/5.81 (((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2))))) | unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))),
% 8.65/5.81 inference(tautology,[status(thm)],[])).
% 8.65/5.81 tff(653,plain,
% 8.65/5.81 ((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2))))),
% 8.65/5.81 inference(unit_resolution,[status(thm)],[652, 651])).
% 8.65/5.81 tff(654,assumption,(~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))), introduced(assumption)).
% 8.65/5.81 tff(655,assumption,(unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1))), introduced(assumption)).
% 8.65/5.81 tff(656,plain,
% 8.65/5.81 (((~![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!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1))) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!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(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1))) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))),
% 8.65/5.81 inference(rewrite,[status(thm)],[])).
% 8.65/5.81 tff(657,plain,
% 8.65/5.81 ((unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1)))) <=> (unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1))) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))),
% 8.65/5.81 inference(rewrite,[status(thm)],[])).
% 8.65/5.81 tff(658,plain,
% 8.65/5.81 (((~![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), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(reverse_line(L!0), 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(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1))) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.65/5.82 inference(monotonicity,[status(thm)],[657])).
% 8.65/5.82 tff(659,plain,
% 8.65/5.82 (((~![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(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(reverse_line(L!0), 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(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1))) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))),
% 8.65/5.82 inference(transitivity,[status(thm)],[658, 656])).
% 8.65/5.82 tff(660,plain,
% 8.65/5.82 ((~![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(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1))))),
% 8.65/5.82 inference(quant_inst,[status(thm)],[])).
% 8.65/5.82 tff(661,plain,
% 8.65/5.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(L!0), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1))) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))),
% 8.65/5.82 inference(modus_ponens,[status(thm)],[660, 659])).
% 8.65/5.82 tff(662,plain,
% 8.65/5.82 ($false),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[661, 58, 655, 117, 654])).
% 8.65/5.82 tff(663,plain,(unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1)))), inference(lemma,lemma(discharge,[]))).
% 8.65/5.82 tff(664,plain,
% 8.65/5.82 (~unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1))),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[663, 81])).
% 8.65/5.82 tff(665,plain,
% 8.65/5.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1)) | unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!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(reverse_line(L!0), line_connecting(B!1, B!1)) | unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0))))),
% 8.65/5.82 inference(rewrite,[status(thm)],[])).
% 8.65/5.82 tff(666,plain,
% 8.65/5.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1)) | unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0))))),
% 8.65/5.82 inference(quant_inst,[status(thm)],[])).
% 8.65/5.82 tff(667,plain,
% 8.65/5.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1)) | unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0)))),
% 8.65/5.82 inference(modus_ponens,[status(thm)],[666, 665])).
% 8.65/5.82 tff(668,plain,
% 8.65/5.82 (unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1)) | unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1)) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(L!0)))),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[667, 58])).
% 8.65/5.82 tff(669,plain,
% 8.65/5.82 (unequally_directed_lines(reverse_line(L!0), line_connecting(B!1, B!1)) | unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[668, 589])).
% 8.65/5.82 tff(670,plain,
% 8.65/5.82 (unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[669, 664])).
% 8.65/5.82 tff(671,assumption,((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2))))), introduced(assumption)).
% 8.65/5.82 tff(672,assumption,(unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))), introduced(assumption)).
% 8.65/5.82 tff(673,assumption,(~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1)))), introduced(assumption)).
% 8.65/5.82 tff(674,plain,
% 8.65/5.82 (((~![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(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), 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(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1))))),
% 8.65/5.82 inference(rewrite,[status(thm)],[])).
% 8.65/5.82 tff(675,plain,
% 8.65/5.82 ((unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), 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(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1))))),
% 8.65/5.82 inference(rewrite,[status(thm)],[])).
% 8.65/5.82 tff(676,plain,
% 8.65/5.82 (((~![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(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), 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(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1)))))),
% 8.65/5.82 inference(monotonicity,[status(thm)],[675])).
% 8.65/5.82 tff(677,plain,
% 8.65/5.82 (((~![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(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), 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(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1))))),
% 8.65/5.82 inference(transitivity,[status(thm)],[676, 674])).
% 8.65/5.82 tff(678,plain,
% 8.65/5.82 ((~![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(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))))),
% 8.65/5.82 inference(quant_inst,[status(thm)],[])).
% 8.65/5.82 tff(679,plain,
% 8.65/5.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1)))),
% 8.65/5.82 inference(modus_ponens,[status(thm)],[678, 677])).
% 8.65/5.82 tff(680,plain,
% 8.65/5.82 ($false),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[679, 58, 48, 672, 673])).
% 8.65/5.82 tff(681,plain,(unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1)))), inference(lemma,lemma(discharge,[]))).
% 8.65/5.82 tff(682,plain,
% 8.65/5.82 (unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1)))),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[681, 672])).
% 8.65/5.82 tff(683,assumption,((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2))))), introduced(assumption)).
% 8.65/5.82 tff(684,plain,
% 8.65/5.82 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1)))) | (~((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1)))) | (~((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))))),
% 8.65/5.82 inference(rewrite,[status(thm)],[])).
% 8.65/5.82 tff(685,plain,
% 8.65/5.82 (((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))) | (~((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1))))) <=> ((~((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1)))) | (~((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))))),
% 8.65/5.82 inference(rewrite,[status(thm)],[])).
% 8.65/5.82 tff(686,plain,
% 8.65/5.82 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))) | (~((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1)))) | (~((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1)))))),
% 8.65/5.82 inference(monotonicity,[status(thm)],[685])).
% 8.65/5.82 tff(687,plain,
% 8.65/5.82 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))) | (~((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1)))) | (~((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))))),
% 8.65/5.82 inference(transitivity,[status(thm)],[686, 684])).
% 8.65/5.82 tff(688,plain,
% 8.65/5.82 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))) | (~((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1)))))),
% 8.65/5.82 inference(quant_inst,[status(thm)],[])).
% 8.65/5.82 tff(689,plain,
% 8.65/5.82 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, B!1)))) | (~((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1)))),
% 8.65/5.82 inference(modus_ponens,[status(thm)],[688, 687])).
% 8.65/5.82 tff(690,plain,
% 8.65/5.82 ($false),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[689, 393, 672, 683, 682, 671])).
% 8.65/5.82 tff(691,plain,((~((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, B!1))) | (~((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2))))))), inference(lemma,lemma(discharge,[]))).
% 8.65/5.82 tff(692,plain,
% 8.65/5.82 ((~((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2))))))),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[691, 670])).
% 8.65/5.82 tff(693,plain,
% 8.65/5.82 (~((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[692, 653])).
% 8.65/5.82 tff(694,plain,
% 8.65/5.82 (((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2))))) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 8.65/5.82 inference(tautology,[status(thm)],[])).
% 8.65/5.82 tff(695,plain,
% 8.65/5.82 (unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[694, 693])).
% 8.65/5.82 tff(696,assumption,(unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))), introduced(assumption)).
% 8.65/5.82 tff(697,assumption,(~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))), introduced(assumption)).
% 8.65/5.82 tff(698,plain,
% 8.65/5.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!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(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))),
% 8.65/5.82 inference(rewrite,[status(thm)],[])).
% 8.65/5.82 tff(699,plain,
% 8.65/5.82 ((unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2))))) <=> (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))),
% 8.65/5.82 inference(rewrite,[status(thm)],[])).
% 8.65/5.82 tff(700,plain,
% 8.65/5.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!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(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.65/5.82 inference(monotonicity,[status(thm)],[699])).
% 8.65/5.82 tff(701,plain,
% 8.65/5.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!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(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))),
% 8.65/5.82 inference(transitivity,[status(thm)],[700, 698])).
% 8.65/5.82 tff(702,plain,
% 8.65/5.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))),
% 8.65/5.82 inference(quant_inst,[status(thm)],[])).
% 8.65/5.82 tff(703,plain,
% 8.65/5.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))),
% 8.65/5.82 inference(modus_ponens,[status(thm)],[702, 701])).
% 8.65/5.82 tff(704,plain,
% 8.65/5.82 ($false),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[703, 58, 654, 697, 696])).
% 8.65/5.82 tff(705,plain,(unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2))))), inference(lemma,lemma(discharge,[]))).
% 8.65/5.82 tff(706,plain,
% 8.65/5.82 (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[705, 81])).
% 8.65/5.82 tff(707,plain,
% 8.65/5.82 (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[706, 695])).
% 8.65/5.82 tff(708,assumption,(~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))), introduced(assumption)).
% 8.65/5.82 tff(709,plain,
% 8.65/5.82 (((~![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!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, 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(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))),
% 8.65/5.82 inference(rewrite,[status(thm)],[])).
% 8.65/5.82 tff(710,plain,
% 8.65/5.82 ((~![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!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1))))),
% 8.65/5.82 inference(quant_inst,[status(thm)],[])).
% 8.65/5.82 tff(711,plain,
% 8.65/5.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(A!2, B!1)))),
% 8.65/5.82 inference(modus_ponens,[status(thm)],[710, 709])).
% 8.65/5.82 tff(712,plain,
% 8.65/5.82 ($false),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[711, 58, 146, 708, 325])).
% 8.65/5.82 tff(713,plain,(unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))), inference(lemma,lemma(discharge,[]))).
% 8.65/5.82 tff(714,plain,
% 8.65/5.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, 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(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))))),
% 8.65/5.82 inference(rewrite,[status(thm)],[])).
% 8.65/5.82 tff(715,plain,
% 8.65/5.82 ((unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))))),
% 8.65/5.82 inference(rewrite,[status(thm)],[])).
% 8.65/5.82 tff(716,plain,
% 8.65/5.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!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(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1)))))),
% 8.65/5.82 inference(monotonicity,[status(thm)],[715])).
% 8.65/5.82 tff(717,plain,
% 8.65/5.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!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(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))))),
% 8.65/5.82 inference(transitivity,[status(thm)],[716, 714])).
% 8.65/5.82 tff(718,plain,
% 8.65/5.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))),
% 8.65/5.82 inference(quant_inst,[status(thm)],[])).
% 8.65/5.82 tff(719,plain,
% 8.65/5.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1)))),
% 8.65/5.82 inference(modus_ponens,[status(thm)],[718, 717])).
% 8.65/5.82 tff(720,plain,
% 8.65/5.82 ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1)))),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[719, 58])).
% 8.65/5.82 tff(721,plain,
% 8.65/5.82 (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1)))),
% 8.65/5.82 inference(unit_resolution,[status(thm)],[720, 342, 713])).
% 8.65/5.82 tff(722,plain,
% 8.65/5.82 (((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1))))) <=> ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)))))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(723,plain,
% 8.65/5.83 ((~(left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))))) <=> (~(left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1))))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(724,plain,
% 8.65/5.83 (((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1)))))) <=> ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)))))),
% 8.65/5.83 inference(monotonicity,[status(thm)],[723])).
% 8.65/5.83 tff(725,plain,
% 8.65/5.83 (((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1)))))) <=> ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)))))),
% 8.65/5.83 inference(transitivity,[status(thm)],[724, 722])).
% 8.65/5.83 tff(726,plain,
% 8.65/5.83 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1)))))),
% 8.65/5.83 inference(quant_inst,[status(thm)],[])).
% 8.65/5.83 tff(727,plain,
% 8.65/5.83 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1))))),
% 8.65/5.83 inference(modus_ponens,[status(thm)],[726, 725])).
% 8.65/5.83 tff(728,plain,
% 8.65/5.83 (~(left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[727, 9])).
% 8.65/5.83 tff(729,plain,
% 8.65/5.83 ((left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1))) | (~left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)))),
% 8.65/5.83 inference(tautology,[status(thm)],[])).
% 8.65/5.83 tff(730,plain,
% 8.65/5.83 (~left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[729, 728])).
% 8.65/5.83 tff(731,plain,
% 8.65/5.83 ((left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1))) | (~left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))))),
% 8.65/5.83 inference(tautology,[status(thm)],[])).
% 8.65/5.83 tff(732,plain,
% 8.65/5.83 (~left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1)))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[731, 728])).
% 8.65/5.83 tff(733,plain,
% 8.65/5.83 (((~![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(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, 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(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1)))))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(734,plain,
% 8.65/5.83 ((~![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(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1)))))),
% 8.65/5.83 inference(quant_inst,[status(thm)],[])).
% 8.65/5.83 tff(735,plain,
% 8.65/5.83 ((~![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(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))))),
% 8.65/5.83 inference(modus_ponens,[status(thm)],[734, 733])).
% 8.65/5.83 tff(736,plain,
% 8.65/5.83 ((~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(A!2, B!1))))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[735, 30, 732, 730])).
% 8.65/5.83 tff(737,plain,
% 8.65/5.83 (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[736, 721])).
% 8.65/5.83 tff(738,plain,
% 8.65/5.83 (((~![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(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!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(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(739,plain,
% 8.65/5.83 ((unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))) <=> (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(740,plain,
% 8.65/5.83 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!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(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))))),
% 8.65/5.83 inference(monotonicity,[status(thm)],[739])).
% 8.65/5.83 tff(741,plain,
% 8.65/5.83 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!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(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.65/5.83 inference(transitivity,[status(thm)],[740, 738])).
% 8.65/5.83 tff(742,plain,
% 8.65/5.83 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2))))),
% 8.65/5.83 inference(quant_inst,[status(thm)],[])).
% 8.65/5.83 tff(743,plain,
% 8.65/5.83 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), line_connecting(A!2, B!1)) | unequally_directed_lines(parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2), line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(parallel_through_point(reverse_line(L!0), B!1), A!2)))),
% 8.65/5.83 inference(modus_ponens,[status(thm)],[742, 741])).
% 8.65/5.83 tff(744,plain,
% 8.65/5.83 ($false),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[743, 58, 737, 707, 143])).
% 8.65/5.83 tff(745,plain,(unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))), inference(lemma,lemma(discharge,[]))).
% 8.65/5.83 tff(746,plain,
% 8.65/5.83 (((~![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(line_connecting(A!2, B!1), L!0)) | left_convergent_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))) | left_convergent_lines(line_connecting(A!2, B!1), L!0))) <=> ((~![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(line_connecting(A!2, B!1), L!0)) | left_convergent_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))) | left_convergent_lines(line_connecting(A!2, B!1), L!0))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(747,plain,
% 8.65/5.83 ((left_convergent_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | left_convergent_lines(line_connecting(A!2, B!1), L!0) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0)))) <=> ((~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | left_convergent_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))) | left_convergent_lines(line_connecting(A!2, B!1), L!0))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(748,plain,
% 8.65/5.83 (((~![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(line_connecting(A!2, B!1), reverse_line(L!0)) | left_convergent_lines(line_connecting(A!2, B!1), L!0) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))))) <=> ((~![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(line_connecting(A!2, B!1), L!0)) | left_convergent_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))) | left_convergent_lines(line_connecting(A!2, B!1), L!0)))),
% 8.65/5.83 inference(monotonicity,[status(thm)],[747])).
% 8.65/5.83 tff(749,plain,
% 8.65/5.83 (((~![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(line_connecting(A!2, B!1), reverse_line(L!0)) | left_convergent_lines(line_connecting(A!2, B!1), L!0) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))))) <=> ((~![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(line_connecting(A!2, B!1), L!0)) | left_convergent_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))) | left_convergent_lines(line_connecting(A!2, B!1), L!0))),
% 8.65/5.83 inference(transitivity,[status(thm)],[748, 746])).
% 8.65/5.83 tff(750,plain,
% 8.65/5.83 ((~![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(line_connecting(A!2, B!1), reverse_line(L!0)) | left_convergent_lines(line_connecting(A!2, B!1), L!0) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 8.65/5.83 inference(quant_inst,[status(thm)],[])).
% 8.65/5.83 tff(751,plain,
% 8.65/5.83 ((~![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(line_connecting(A!2, B!1), L!0)) | left_convergent_lines(line_connecting(A!2, B!1), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!0))) | left_convergent_lines(line_connecting(A!2, B!1), L!0)),
% 8.65/5.83 inference(modus_ponens,[status(thm)],[750, 749])).
% 8.65/5.83 tff(752,plain,
% 8.65/5.83 (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[751, 30, 745, 134, 132])).
% 8.65/5.83 tff(753,plain,
% 8.65/5.83 (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[432, 752])).
% 8.65/5.83 tff(754,assumption,(~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))), introduced(assumption)).
% 8.65/5.83 tff(755,plain,
% 8.65/5.83 ((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[336, 161])).
% 8.65/5.83 tff(756,plain,
% 8.65/5.83 (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[294, 236])).
% 8.65/5.83 tff(757,plain,
% 8.65/5.83 (unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[282, 756])).
% 8.65/5.83 tff(758,plain,
% 8.65/5.83 (((~![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!0, L!0) | unequally_directed_lines(line_connecting(B!1, A!2), L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!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!0, L!0) | unequally_directed_lines(line_connecting(B!1, A!2), L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(759,plain,
% 8.65/5.83 ((unequally_directed_lines(line_connecting(B!1, A!2), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2)))) <=> (unequally_directed_lines(L!0, L!0) | unequally_directed_lines(line_connecting(B!1, A!2), L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(760,plain,
% 8.65/5.83 (((~![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(B!1, A!2), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!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!0, L!0) | unequally_directed_lines(line_connecting(B!1, A!2), L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2)))))),
% 8.65/5.83 inference(monotonicity,[status(thm)],[759])).
% 8.65/5.83 tff(761,plain,
% 8.65/5.83 (((~![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(B!1, A!2), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!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!0, L!0) | unequally_directed_lines(line_connecting(B!1, A!2), L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))))),
% 8.65/5.83 inference(transitivity,[status(thm)],[760, 758])).
% 8.65/5.83 tff(762,plain,
% 8.65/5.83 ((~![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(B!1, A!2), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))))),
% 8.65/5.83 inference(quant_inst,[status(thm)],[])).
% 8.65/5.83 tff(763,plain,
% 8.65/5.83 ((~![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!0, L!0) | unequally_directed_lines(line_connecting(B!1, A!2), L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2)))),
% 8.65/5.83 inference(modus_ponens,[status(thm)],[762, 761])).
% 8.65/5.83 tff(764,plain,
% 8.65/5.83 (unequally_directed_lines(L!0, L!0) | unequally_directed_lines(line_connecting(B!1, A!2), L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2)))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[763, 58])).
% 8.65/5.83 tff(765,plain,
% 8.65/5.83 (unequally_directed_lines(line_connecting(B!1, A!2), L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2)))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[764, 372])).
% 8.65/5.83 tff(766,plain,
% 8.65/5.83 (unequally_directed_lines(line_connecting(B!1, A!2), L!0)),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[765, 757])).
% 8.65/5.83 tff(767,plain,
% 8.65/5.83 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(768,plain,
% 8.65/5.83 (((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0)))) <=> ((~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(769,plain,
% 8.65/5.83 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0))))),
% 8.65/5.83 inference(monotonicity,[status(thm)],[768])).
% 8.65/5.83 tff(770,plain,
% 8.65/5.83 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)))),
% 8.65/5.83 inference(transitivity,[status(thm)],[769, 767])).
% 8.65/5.83 tff(771,plain,
% 8.65/5.83 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))))),
% 8.65/5.83 inference(quant_inst,[status(thm)],[])).
% 8.65/5.83 tff(772,plain,
% 8.65/5.83 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))))) | (~((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1)))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0))),
% 8.65/5.83 inference(modus_ponens,[status(thm)],[771, 770])).
% 8.65/5.83 tff(773,plain,
% 8.65/5.83 (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[772, 393, 412, 766, 755])).
% 8.65/5.83 tff(774,plain,
% 8.65/5.83 (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[418, 393, 412, 757, 755])).
% 8.65/5.83 tff(775,plain,
% 8.65/5.83 (((~![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(B!1, A!2), L!0)) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2))))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(776,plain,
% 8.65/5.83 ((unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0))) <=> ((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2))))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(777,plain,
% 8.65/5.83 (((~![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!0, reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!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(B!1, A!2), L!0)) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))))),
% 8.65/5.83 inference(monotonicity,[status(thm)],[776])).
% 8.65/5.83 tff(778,plain,
% 8.65/5.83 (((~![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!0, reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!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(B!1, A!2), L!0)) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2))))),
% 8.65/5.83 inference(transitivity,[status(thm)],[777, 775])).
% 8.65/5.83 tff(779,plain,
% 8.65/5.83 ((~![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!0, reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)))),
% 8.65/5.83 inference(quant_inst,[status(thm)],[])).
% 8.65/5.83 tff(780,plain,
% 8.65/5.83 ((~![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(B!1, A!2), L!0)) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))),
% 8.65/5.83 inference(modus_ponens,[status(thm)],[779, 778])).
% 8.65/5.83 tff(781,plain,
% 8.65/5.83 ((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[780, 58])).
% 8.65/5.83 tff(782,plain,
% 8.65/5.83 (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[781, 774, 766])).
% 8.65/5.83 tff(783,assumption,(~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))), introduced(assumption)).
% 8.65/5.83 tff(784,assumption,(unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))), introduced(assumption)).
% 8.65/5.83 tff(785,plain,
% 8.65/5.83 (((~![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(B!1, A!2), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!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(B!1, A!2), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(786,plain,
% 8.65/5.83 ((unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2))))) <=> (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))),
% 8.65/5.83 inference(rewrite,[status(thm)],[])).
% 8.65/5.83 tff(787,plain,
% 8.65/5.83 (((~![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(line_connecting(B!1, A!2)), reverse_line(L!0)) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))))),
% 8.65/5.83 inference(monotonicity,[status(thm)],[786])).
% 8.65/5.83 tff(788,plain,
% 8.65/5.83 (((~![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(line_connecting(B!1, A!2)), reverse_line(L!0)) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))),
% 8.65/5.83 inference(transitivity,[status(thm)],[787, 785])).
% 8.65/5.83 tff(789,plain,
% 8.65/5.83 ((~![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(line_connecting(B!1, A!2)), reverse_line(L!0)) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))))),
% 8.65/5.83 inference(quant_inst,[status(thm)],[])).
% 8.65/5.83 tff(790,plain,
% 8.65/5.83 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))),
% 8.65/5.83 inference(modus_ponens,[status(thm)],[789, 788])).
% 8.65/5.83 tff(791,plain,
% 8.65/5.83 ($false),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[790, 58, 784, 754, 783])).
% 8.65/5.83 tff(792,plain,(unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))), inference(lemma,lemma(discharge,[]))).
% 8.65/5.83 tff(793,plain,
% 8.65/5.83 ($false),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[792, 782, 773, 754])).
% 8.65/5.83 tff(794,plain,(unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))), inference(lemma,lemma(discharge,[]))).
% 8.65/5.83 tff(795,plain,
% 8.65/5.83 (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[794, 753])).
% 8.65/5.83 tff(796,assumption,(left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), L!0) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))), introduced(assumption)).
% 8.65/5.83 tff(797,plain,
% 8.65/5.83 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), L!0) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))))),
% 8.65/5.83 inference(quant_inst,[status(thm)],[])).
% 8.65/5.83 tff(798,plain,
% 8.65/5.83 ($false),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[797, 9, 796])).
% 8.65/5.83 tff(799,plain,(~(left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), L!0) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 8.65/5.83 tff(800,plain,
% 8.65/5.83 ((left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), L!0) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))) | (~left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))),
% 8.65/5.83 inference(tautology,[status(thm)],[])).
% 8.65/5.83 tff(801,plain,
% 8.65/5.83 (~left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))),
% 8.65/5.83 inference(unit_resolution,[status(thm)],[800, 799])).
% 8.65/5.83 tff(802,plain,
% 8.65/5.83 ((left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), L!0) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))) | (~left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), L!0))),
% 8.65/5.83 inference(tautology,[status(thm)],[])).
% 8.65/5.84 tff(803,plain,
% 8.65/5.84 (~left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), L!0)),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[802, 799])).
% 8.65/5.84 tff(804,assumption,(~((~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))))), introduced(assumption)).
% 8.65/5.84 tff(805,plain,
% 8.65/5.84 (((~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))),
% 8.65/5.84 inference(tautology,[status(thm)],[])).
% 8.65/5.84 tff(806,plain,
% 8.65/5.84 (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[805, 804])).
% 8.65/5.84 tff(807,plain,
% 8.65/5.84 (((~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)),
% 8.65/5.84 inference(tautology,[status(thm)],[])).
% 8.65/5.84 tff(808,plain,
% 8.65/5.84 (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[807, 804])).
% 8.65/5.84 tff(809,plain,
% 8.65/5.84 (((~![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(line_connecting(B!1, A!2)), L!0) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))) <=> ((~![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(line_connecting(B!1, A!2)), L!0) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))),
% 8.65/5.84 inference(rewrite,[status(thm)],[])).
% 8.65/5.84 tff(810,plain,
% 8.65/5.84 ((left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), L!0) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))) <=> (left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), L!0) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))),
% 8.65/5.84 inference(rewrite,[status(thm)],[])).
% 8.65/5.84 tff(811,plain,
% 8.65/5.84 (((~![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(line_connecting(B!1, A!2)), reverse_line(L!0)) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), L!0) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))))) <=> ((~![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(line_connecting(B!1, A!2)), L!0) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))))),
% 8.65/5.84 inference(monotonicity,[status(thm)],[810])).
% 8.65/5.84 tff(812,plain,
% 8.65/5.84 (((~![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(line_connecting(B!1, A!2)), reverse_line(L!0)) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), L!0) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))))) <=> ((~![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(line_connecting(B!1, A!2)), L!0) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))),
% 8.65/5.84 inference(transitivity,[status(thm)],[811, 809])).
% 8.65/5.84 tff(813,plain,
% 8.65/5.84 ((~![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(line_connecting(B!1, A!2)), reverse_line(L!0)) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), L!0) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))))),
% 8.65/5.84 inference(quant_inst,[status(thm)],[])).
% 8.65/5.84 tff(814,plain,
% 8.65/5.84 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), L!0) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))) | left_convergent_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))),
% 8.65/5.84 inference(modus_ponens,[status(thm)],[813, 812])).
% 8.65/5.84 tff(815,plain,
% 8.65/5.84 ($false),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[814, 30, 808, 806, 803, 801])).
% 8.65/5.84 tff(816,plain,((~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 8.65/5.84 tff(817,plain,
% 8.65/5.84 ((~((~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))),
% 8.65/5.84 inference(tautology,[status(thm)],[])).
% 8.65/5.84 tff(818,plain,
% 8.65/5.84 ((~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(L!0)))),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[817, 816])).
% 8.65/5.84 tff(819,plain,
% 8.65/5.84 (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), L!0)),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[818, 795])).
% 8.65/5.84 tff(820,plain,
% 8.65/5.84 (((~![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(line_connecting(B!1, A!2)), L!0) | unequally_directed_lines(parallel_through_point(L!0, A!2), L!0) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!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(reverse_line(line_connecting(B!1, A!2)), L!0) | unequally_directed_lines(parallel_through_point(L!0, A!2), L!0) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2)))))),
% 8.65/5.84 inference(rewrite,[status(thm)],[])).
% 8.65/5.84 tff(821,plain,
% 8.65/5.84 ((~![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(line_connecting(B!1, A!2)), L!0) | unequally_directed_lines(parallel_through_point(L!0, A!2), L!0) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2)))))),
% 8.65/5.84 inference(quant_inst,[status(thm)],[])).
% 8.65/5.84 tff(822,plain,
% 8.65/5.84 ((~![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(line_connecting(B!1, A!2)), L!0) | unequally_directed_lines(parallel_through_point(L!0, A!2), L!0) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2))))),
% 8.65/5.84 inference(modus_ponens,[status(thm)],[821, 820])).
% 8.65/5.84 tff(823,plain,
% 8.65/5.84 (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2)))),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[822, 58, 819, 126])).
% 8.65/5.84 tff(824,plain,
% 8.65/5.84 (((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2))))) | unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2)))),
% 8.65/5.84 inference(tautology,[status(thm)],[])).
% 8.65/5.84 tff(825,plain,
% 8.65/5.84 ((~unequally_directed_lines(parallel_through_point(L!0, A!2), line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(L!0, A!2), reverse_line(line_connecting(B!1, A!2))))),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[824, 823])).
% 8.65/5.84 tff(826,plain,
% 8.65/5.84 (~((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2)))))),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[692, 825])).
% 8.65/5.84 tff(827,plain,
% 8.65/5.84 (((~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, A!2))))) | unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))),
% 8.65/5.84 inference(tautology,[status(thm)],[])).
% 8.65/5.84 tff(828,plain,
% 8.65/5.84 (unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[827, 826])).
% 8.65/5.84 tff(829,plain,
% 8.65/5.84 ((~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(A!2, B!1))))),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[336, 753])).
% 8.65/5.84 tff(830,plain,
% 8.65/5.84 (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)))),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[203, 753])).
% 8.65/5.84 tff(831,plain,
% 8.65/5.84 (before_on_line(L!0, A!2, B!1)),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[228, 830])).
% 8.65/5.84 tff(832,plain,
% 8.65/5.84 (~before_on_line(L!0, B!1, A!2)),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[235, 831])).
% 8.65/5.84 tff(833,plain,
% 8.65/5.84 (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[294, 832])).
% 8.65/5.84 tff(834,plain,
% 8.65/5.84 (unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[282, 833])).
% 8.65/5.84 tff(835,plain,
% 8.65/5.84 (unequally_directed_lines(line_connecting(B!1, A!2), L!0)),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[765, 834])).
% 8.65/5.84 tff(836,plain,
% 8.65/5.84 (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[772, 393, 412, 835, 829])).
% 8.65/5.84 tff(837,plain,
% 8.65/5.84 (((~![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, A!2), reverse_line(L!0)) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))))),
% 8.65/5.84 inference(rewrite,[status(thm)],[])).
% 8.65/5.84 tff(838,plain,
% 8.65/5.84 ((~![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, A!2), reverse_line(L!0)) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2))))),
% 8.65/5.84 inference(quant_inst,[status(thm)],[])).
% 8.65/5.84 tff(839,plain,
% 8.65/5.84 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(L!0)) | (~unequally_directed_lines(line_connecting(B!1, B!1), line_connecting(B!1, A!2)))),
% 8.65/5.84 inference(modus_ponens,[status(thm)],[838, 837])).
% 8.65/5.84 tff(840,plain,
% 8.65/5.84 ($false),
% 8.65/5.84 inference(unit_resolution,[status(thm)],[839, 58, 836, 828, 124])).
% 8.65/5.84 % SZS output end Proof
%------------------------------------------------------------------------------