TSTP Solution File: GEO260+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO260+1 : TPTP v8.1.0. Bugfixed v8.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 20:36:09 EDT 2022
% Result : Theorem 11.80s 12.04s
% Output : Proof 11.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO260+1 : TPTP v8.1.0. Bugfixed v8.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 06:37:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 11.80/12.04 % SZS status Theorem
% 11.80/12.04 % SZS output start Proof
% 11.80/12.04 tff(left_convergent_lines_type, type, (
% 11.80/12.04 left_convergent_lines: ( $i * $i ) > $o)).
% 11.80/12.04 tff(reverse_line_type, type, (
% 11.80/12.04 reverse_line: $i > $i)).
% 11.80/12.04 tff(line_connecting_type, type, (
% 11.80/12.04 line_connecting: ( $i * $i ) > $i)).
% 11.80/12.04 tff(tptp_fun_B_1_type, type, (
% 11.80/12.04 tptp_fun_B_1: $i)).
% 11.80/12.04 tff(tptp_fun_L_3_type, type, (
% 11.80/12.04 tptp_fun_L_3: $i)).
% 11.80/12.04 tff(unequally_directed_lines_type, type, (
% 11.80/12.04 unequally_directed_lines: ( $i * $i ) > $o)).
% 11.80/12.04 tff(line_type, type, (
% 11.80/12.04 line: $i > $o)).
% 11.80/12.04 tff(distinct_points_type, type, (
% 11.80/12.04 distinct_points: ( $i * $i ) > $o)).
% 11.80/12.04 tff(tptp_fun_A_2_type, type, (
% 11.80/12.04 tptp_fun_A_2: $i)).
% 11.80/12.04 tff(tptp_fun_C_0_type, type, (
% 11.80/12.04 tptp_fun_C_0: $i)).
% 11.80/12.04 tff(between_on_line_type, type, (
% 11.80/12.04 between_on_line: ( $i * $i * $i * $i ) > $o)).
% 11.80/12.04 tff(parallel_through_point_type, type, (
% 11.80/12.04 parallel_through_point: ( $i * $i ) > $i)).
% 11.80/12.04 tff(1,assumption,(left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))), introduced(assumption)).
% 11.80/12.04 tff(2,plain,
% 11.80/12.04 (^[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)))))),
% 11.80/12.04 inference(bind,[status(th)],[])).
% 11.80/12.04 tff(3,plain,
% 11.80/12.04 (![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))))),
% 11.80/12.04 inference(quant_intro,[status(thm)],[2])).
% 11.80/12.04 tff(4,plain,
% 11.80/12.04 (![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))))),
% 11.80/12.04 inference(rewrite,[status(thm)],[])).
% 11.80/12.04 tff(5,axiom,(![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag11')).
% 11.80/12.04 tff(6,plain,
% 11.80/12.04 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 11.80/12.04 inference(modus_ponens,[status(thm)],[5, 4])).
% 11.80/12.04 tff(7,plain,(
% 11.80/12.04 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 11.80/12.04 inference(skolemize,[status(sab)],[6])).
% 11.80/12.04 tff(8,plain,
% 11.80/12.04 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 11.80/12.04 inference(modus_ponens,[status(thm)],[7, 3])).
% 11.80/12.04 tff(9,plain,
% 11.80/12.04 (((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))))) <=> ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)))))),
% 11.80/12.04 inference(rewrite,[status(thm)],[])).
% 11.80/12.04 tff(10,plain,
% 11.80/12.04 ((~(left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))) <=> (~(left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))))),
% 11.80/12.04 inference(rewrite,[status(thm)],[])).
% 11.80/12.04 tff(11,plain,
% 11.80/12.04 (((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)))))),
% 11.80/12.04 inference(monotonicity,[status(thm)],[10])).
% 11.80/12.04 tff(12,plain,
% 11.80/12.04 (((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)))))),
% 11.80/12.04 inference(transitivity,[status(thm)],[11, 9])).
% 11.80/12.04 tff(13,plain,
% 11.80/12.04 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 11.80/12.04 inference(quant_inst,[status(thm)],[])).
% 11.80/12.04 tff(14,plain,
% 11.80/12.04 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))))),
% 11.80/12.04 inference(modus_ponens,[status(thm)],[13, 12])).
% 11.80/12.04 tff(15,plain,
% 11.80/12.04 ($false),
% 11.80/12.04 inference(unit_resolution,[status(thm)],[14, 8, 1])).
% 11.80/12.04 tff(16,plain,(~(left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)))), inference(lemma,lemma(discharge,[]))).
% 11.80/12.04 tff(17,plain,
% 11.80/12.04 ((left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))),
% 11.80/12.04 inference(tautology,[status(thm)],[])).
% 11.80/12.04 tff(18,plain,
% 11.80/12.04 (~left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))),
% 11.80/12.04 inference(unit_resolution,[status(thm)],[17, 16])).
% 11.80/12.04 tff(19,plain,
% 11.80/12.04 ((left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)))),
% 11.80/12.04 inference(tautology,[status(thm)],[])).
% 11.80/12.04 tff(20,plain,
% 11.80/12.04 (~left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))),
% 11.80/12.04 inference(unit_resolution,[status(thm)],[19, 16])).
% 11.80/12.04 tff(21,assumption,(left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))), introduced(assumption)).
% 11.80/12.04 tff(22,plain,
% 11.80/12.04 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))))),
% 11.80/12.04 inference(quant_inst,[status(thm)],[])).
% 11.80/12.04 tff(23,plain,
% 11.80/12.04 ($false),
% 11.80/12.04 inference(unit_resolution,[status(thm)],[22, 8, 21])).
% 11.80/12.04 tff(24,plain,(~(left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))))), inference(lemma,lemma(discharge,[]))).
% 11.80/12.04 tff(25,plain,
% 11.80/12.04 ((left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))) | (~left_convergent_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))))),
% 11.80/12.04 inference(tautology,[status(thm)],[])).
% 11.80/12.04 tff(26,plain,
% 11.80/12.04 (~left_convergent_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))),
% 11.80/12.04 inference(unit_resolution,[status(thm)],[25, 24])).
% 11.80/12.04 tff(27,plain,
% 11.80/12.04 ((left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | left_convergent_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))) | (~left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)))),
% 11.80/12.04 inference(tautology,[status(thm)],[])).
% 11.80/12.04 tff(28,plain,
% 11.80/12.04 (~left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1))),
% 11.80/12.04 inference(unit_resolution,[status(thm)],[27, 24])).
% 11.80/12.04 tff(29,assumption,(unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))), introduced(assumption)).
% 11.80/12.04 tff(30,plain,
% 11.80/12.04 (^[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)))))),
% 11.80/12.04 inference(bind,[status(th)],[])).
% 11.80/12.04 tff(31,plain,
% 11.80/12.04 (![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))))),
% 11.80/12.04 inference(quant_intro,[status(thm)],[30])).
% 11.80/12.04 tff(32,plain,
% 11.80/12.04 (^[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))))))),
% 11.80/12.04 inference(bind,[status(th)],[])).
% 11.80/12.04 tff(33,plain,
% 11.80/12.04 (![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))))),
% 11.80/12.04 inference(quant_intro,[status(thm)],[32])).
% 11.80/12.04 tff(34,plain,
% 11.80/12.04 (![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)))))),
% 11.80/12.04 inference(rewrite,[status(thm)],[])).
% 11.80/12.05 tff(35,plain,
% 11.80/12.05 (^[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))))))),
% 11.80/12.05 inference(bind,[status(th)],[])).
% 11.80/12.05 tff(36,plain,
% 11.80/12.05 (![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)))))),
% 11.80/12.05 inference(quant_intro,[status(thm)],[35])).
% 11.80/12.05 tff(37,axiom,(![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag9')).
% 11.80/12.05 tff(38,plain,
% 11.80/12.05 (![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)))))),
% 11.80/12.05 inference(modus_ponens,[status(thm)],[37, 36])).
% 11.80/12.05 tff(39,plain,
% 11.80/12.05 (![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)))))),
% 11.80/12.05 inference(modus_ponens,[status(thm)],[38, 34])).
% 11.80/12.05 tff(40,plain,(
% 11.80/12.05 ![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)))))),
% 11.80/12.05 inference(skolemize,[status(sab)],[39])).
% 11.80/12.05 tff(41,plain,
% 11.80/12.05 (![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))))),
% 11.80/12.05 inference(modus_ponens,[status(thm)],[40, 33])).
% 11.80/12.05 tff(42,plain,
% 11.80/12.05 (![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))))),
% 11.80/12.05 inference(modus_ponens,[status(thm)],[41, 31])).
% 11.80/12.05 tff(43,plain,
% 11.80/12.05 (((~![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!3), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))))),
% 11.80/12.05 inference(rewrite,[status(thm)],[])).
% 11.80/12.05 tff(44,plain,
% 11.80/12.05 ((left_convergent_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))))) <=> ((~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))))),
% 11.89/12.05 inference(rewrite,[status(thm)],[])).
% 11.89/12.05 tff(45,plain,
% 11.89/12.05 (((~![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!3), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))))),
% 11.89/12.05 inference(monotonicity,[status(thm)],[44])).
% 11.89/12.05 tff(46,plain,
% 11.89/12.05 (((~![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!3), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))))),
% 11.89/12.05 inference(transitivity,[status(thm)],[45, 43])).
% 11.89/12.05 tff(47,plain,
% 11.89/12.05 ((~![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!3), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))))),
% 11.89/12.05 inference(quant_inst,[status(thm)],[])).
% 11.89/12.05 tff(48,plain,
% 11.89/12.05 ((~![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!3), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))),
% 11.89/12.05 inference(modus_ponens,[status(thm)],[47, 46])).
% 11.89/12.05 tff(49,plain,
% 11.89/12.05 (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1))),
% 11.89/12.05 inference(unit_resolution,[status(thm)],[48, 42, 29, 28, 26])).
% 11.89/12.05 tff(50,assumption,(left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))), introduced(assumption)).
% 11.89/12.05 tff(51,plain,
% 11.89/12.05 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))))),
% 11.89/12.05 inference(quant_inst,[status(thm)],[])).
% 11.89/12.05 tff(52,plain,
% 11.89/12.05 ($false),
% 11.89/12.05 inference(unit_resolution,[status(thm)],[51, 8, 50])).
% 11.89/12.05 tff(53,plain,(~(left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))))), inference(lemma,lemma(discharge,[]))).
% 11.89/12.05 tff(54,plain,
% 11.89/12.05 ((left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))) | (~left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 11.89/12.05 inference(tautology,[status(thm)],[])).
% 11.89/12.05 tff(55,plain,
% 11.89/12.05 (~left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))),
% 11.89/12.05 inference(unit_resolution,[status(thm)],[54, 53])).
% 11.89/12.05 tff(56,plain,
% 11.89/12.05 ((left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))) | (~left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))))),
% 11.89/12.05 inference(tautology,[status(thm)],[])).
% 11.89/12.05 tff(57,plain,
% 11.89/12.05 (~left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))),
% 11.89/12.05 inference(unit_resolution,[status(thm)],[56, 53])).
% 11.89/12.05 tff(58,assumption,(~((~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))))), introduced(assumption)).
% 11.89/12.05 tff(59,plain,
% 11.89/12.05 (((~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))),
% 11.89/12.05 inference(tautology,[status(thm)],[])).
% 11.89/12.05 tff(60,plain,
% 11.89/12.05 (unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))),
% 11.89/12.05 inference(unit_resolution,[status(thm)],[59, 58])).
% 11.89/12.05 tff(61,plain,
% 11.89/12.05 (((~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))),
% 11.89/12.05 inference(tautology,[status(thm)],[])).
% 11.89/12.05 tff(62,plain,
% 11.89/12.05 (unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))),
% 11.89/12.05 inference(unit_resolution,[status(thm)],[61, 58])).
% 11.89/12.05 tff(63,plain,
% 11.89/12.05 (((~![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(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))))) <=> ((~![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(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))))),
% 11.89/12.05 inference(rewrite,[status(thm)],[])).
% 11.89/12.05 tff(64,plain,
% 11.89/12.05 ((left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))))),
% 11.89/12.05 inference(rewrite,[status(thm)],[])).
% 11.89/12.05 tff(65,plain,
% 11.89/12.05 (((~![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, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))))) <=> ((~![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(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))))),
% 11.89/12.05 inference(monotonicity,[status(thm)],[64])).
% 11.89/12.05 tff(66,plain,
% 11.89/12.05 (((~![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, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))))) <=> ((~![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(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))))),
% 11.89/12.05 inference(transitivity,[status(thm)],[65, 63])).
% 11.89/12.05 tff(67,plain,
% 11.89/12.05 ((~![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, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))))),
% 11.89/12.05 inference(quant_inst,[status(thm)],[])).
% 11.89/12.05 tff(68,plain,
% 11.89/12.05 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | left_convergent_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))),
% 11.89/12.05 inference(modus_ponens,[status(thm)],[67, 66])).
% 11.89/12.05 tff(69,plain,
% 11.89/12.05 ($false),
% 11.89/12.05 inference(unit_resolution,[status(thm)],[68, 42, 62, 60, 57, 55])).
% 11.89/12.05 tff(70,plain,((~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))))), inference(lemma,lemma(discharge,[]))).
% 11.89/12.05 tff(71,assumption,(unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))), introduced(assumption)).
% 11.89/12.05 tff(72,plain,
% 11.89/12.05 (^[L: $i] : refl((~unequally_directed_lines(L, L)) <=> (~unequally_directed_lines(L, L)))),
% 11.89/12.05 inference(bind,[status(th)],[])).
% 11.89/12.05 tff(73,plain,
% 11.89/12.05 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 11.89/12.05 inference(quant_intro,[status(thm)],[72])).
% 11.89/12.05 tff(74,plain,
% 11.89/12.05 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 11.89/12.05 inference(rewrite,[status(thm)],[])).
% 11.89/12.05 tff(75,axiom,(![L: $i] : (~unequally_directed_lines(L, L))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag5')).
% 11.89/12.05 tff(76,plain,
% 11.89/12.05 (![L: $i] : (~unequally_directed_lines(L, L))),
% 11.89/12.05 inference(modus_ponens,[status(thm)],[75, 74])).
% 11.89/12.05 tff(77,plain,(
% 11.89/12.05 ![L: $i] : (~unequally_directed_lines(L, L))),
% 11.89/12.05 inference(skolemize,[status(sab)],[76])).
% 11.89/12.05 tff(78,plain,
% 11.89/12.05 (![L: $i] : (~unequally_directed_lines(L, L))),
% 11.89/12.05 inference(modus_ponens,[status(thm)],[77, 73])).
% 11.89/12.05 tff(79,plain,
% 11.89/12.05 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))))),
% 11.89/12.05 inference(quant_inst,[status(thm)],[])).
% 11.89/12.05 tff(80,plain,
% 11.89/12.05 ($false),
% 11.89/12.05 inference(unit_resolution,[status(thm)],[79, 78, 71])).
% 11.89/12.05 tff(81,plain,(~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))), inference(lemma,lemma(discharge,[]))).
% 11.89/12.05 tff(82,assumption,(~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))), introduced(assumption)).
% 11.89/12.05 tff(83,plain,
% 11.89/12.05 ((~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, A, C, B))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))) <=> (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, A, C, B))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B)))))),
% 11.89/12.05 inference(rewrite,[status(thm)],[])).
% 11.89/12.05 tff(84,plain,
% 11.89/12.05 ((~![L: $i, A: $i, B: $i, C: $i] : ((((line(L) & distinct_points(A, C)) & distinct_points(B, C)) & distinct_points(A, B)) => (~(between_on_line(L, A, B, C) & between_on_line(L, A, C, B))))) <=> (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, A, C, B))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B)))))),
% 11.89/12.05 inference(rewrite,[status(thm)],[])).
% 11.89/12.05 tff(85,axiom,(~![L: $i, A: $i, B: $i, C: $i] : ((((line(L) & distinct_points(A, C)) & distinct_points(B, C)) & distinct_points(A, B)) => (~(between_on_line(L, A, B, C) & between_on_line(L, A, C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 11.89/12.06 tff(86,plain,
% 11.89/12.06 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, A, C, B))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[85, 84])).
% 11.89/12.06 tff(87,plain,
% 11.89/12.06 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, A, C, B))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[86, 83])).
% 11.89/12.06 tff(88,plain,
% 11.89/12.06 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, A, C, B))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[87, 83])).
% 11.89/12.06 tff(89,plain,
% 11.89/12.06 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, A, C, B))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[88, 83])).
% 11.89/12.06 tff(90,plain,
% 11.89/12.06 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, A, C, B))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[89, 83])).
% 11.89/12.06 tff(91,plain,
% 11.89/12.06 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, A, C, B))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[90, 83])).
% 11.89/12.06 tff(92,plain,
% 11.89/12.06 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, A, C, B))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[91, 83])).
% 11.89/12.06 tff(93,plain,(
% 11.89/12.06 ~((~(between_on_line(L!3, A!2, B!1, C!0) & between_on_line(L!3, A!2, C!0, B!1))) | (~(line(L!3) & distinct_points(A!2, C!0) & distinct_points(B!1, C!0) & distinct_points(A!2, B!1))))),
% 11.89/12.06 inference(skolemize,[status(sab)],[92])).
% 11.89/12.06 tff(94,plain,
% 11.89/12.06 (line(L!3) & distinct_points(A!2, C!0) & distinct_points(B!1, C!0) & distinct_points(A!2, B!1)),
% 11.89/12.06 inference(or_elim,[status(thm)],[93])).
% 11.89/12.06 tff(95,plain,
% 11.89/12.06 (line(L!3)),
% 11.89/12.06 inference(and_elim,[status(thm)],[94])).
% 11.89/12.06 tff(96,plain,
% 11.89/12.06 (^[L: $i] : refl((line(reverse_line(L)) | (~line(L))) <=> (line(reverse_line(L)) | (~line(L))))),
% 11.89/12.06 inference(bind,[status(th)],[])).
% 11.89/12.06 tff(97,plain,
% 11.89/12.06 (![L: $i] : (line(reverse_line(L)) | (~line(L))) <=> ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 11.89/12.06 inference(quant_intro,[status(thm)],[96])).
% 11.89/12.06 tff(98,plain,
% 11.89/12.06 (![L: $i] : (line(reverse_line(L)) | (~line(L))) <=> ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 11.89/12.06 inference(rewrite,[status(thm)],[])).
% 11.89/12.06 tff(99,plain,
% 11.89/12.06 (^[L: $i] : rewrite((line(L) => line(reverse_line(L))) <=> (line(reverse_line(L)) | (~line(L))))),
% 11.89/12.06 inference(bind,[status(th)],[])).
% 11.89/12.06 tff(100,plain,
% 11.89/12.06 (![L: $i] : (line(L) => line(reverse_line(L))) <=> ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 11.89/12.06 inference(quant_intro,[status(thm)],[99])).
% 11.89/12.06 tff(101,axiom,(![L: $i] : (line(L) => line(reverse_line(L)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oagco4')).
% 11.89/12.06 tff(102,plain,
% 11.89/12.06 (![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[101, 100])).
% 11.89/12.06 tff(103,plain,
% 11.89/12.06 (![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[102, 98])).
% 11.89/12.06 tff(104,plain,(
% 11.89/12.06 ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 11.89/12.06 inference(skolemize,[status(sab)],[103])).
% 11.89/12.06 tff(105,plain,
% 11.89/12.06 (![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[104, 97])).
% 11.89/12.06 tff(106,plain,
% 11.89/12.06 (((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | (line(reverse_line(L!3)) | (~line(L!3)))) <=> ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | line(reverse_line(L!3)) | (~line(L!3)))),
% 11.89/12.06 inference(rewrite,[status(thm)],[])).
% 11.89/12.06 tff(107,plain,
% 11.89/12.06 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | (line(reverse_line(L!3)) | (~line(L!3)))),
% 11.89/12.06 inference(quant_inst,[status(thm)],[])).
% 11.89/12.06 tff(108,plain,
% 11.89/12.06 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | line(reverse_line(L!3)) | (~line(L!3))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[107, 106])).
% 11.89/12.06 tff(109,plain,
% 11.89/12.06 (line(reverse_line(L!3))),
% 11.89/12.06 inference(unit_resolution,[status(thm)],[108, 105, 95])).
% 11.89/12.06 tff(110,plain,
% 11.89/12.06 (((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | (line(reverse_line(reverse_line(L!3))) | (~line(reverse_line(L!3))))) <=> ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | line(reverse_line(reverse_line(L!3))) | (~line(reverse_line(L!3))))),
% 11.89/12.06 inference(rewrite,[status(thm)],[])).
% 11.89/12.06 tff(111,plain,
% 11.89/12.06 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | (line(reverse_line(reverse_line(L!3))) | (~line(reverse_line(L!3))))),
% 11.89/12.06 inference(quant_inst,[status(thm)],[])).
% 11.89/12.06 tff(112,plain,
% 11.89/12.06 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | line(reverse_line(reverse_line(L!3))) | (~line(reverse_line(L!3)))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[111, 110])).
% 11.89/12.06 tff(113,plain,
% 11.89/12.06 (line(reverse_line(reverse_line(L!3))) | (~line(reverse_line(L!3)))),
% 11.89/12.06 inference(unit_resolution,[status(thm)],[112, 105])).
% 11.89/12.06 tff(114,plain,
% 11.89/12.06 (line(reverse_line(reverse_line(L!3)))),
% 11.89/12.06 inference(unit_resolution,[status(thm)],[113, 109])).
% 11.89/12.06 tff(115,plain,
% 11.89/12.06 (^[L: $i, M: $i] : refl((unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L))))),
% 11.89/12.06 inference(bind,[status(th)],[])).
% 11.89/12.06 tff(116,plain,
% 11.89/12.06 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 11.89/12.06 inference(quant_intro,[status(thm)],[115])).
% 11.89/12.06 tff(117,plain,
% 11.89/12.06 (^[L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((line(L) & line(M)) <=> (~((~line(M)) | (~line(L))))), ((~(line(L) & line(M))) <=> (~(~((~line(M)) | (~line(L))))))), rewrite((~(~((~line(M)) | (~line(L))))) <=> ((~line(M)) | (~line(L)))), ((~(line(L) & line(M))) <=> ((~line(M)) | (~line(L))))), ((unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | ((~line(M)) | (~line(L)))))), rewrite((unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | ((~line(M)) | (~line(L)))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))), ((unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))))),
% 11.89/12.06 inference(bind,[status(th)],[])).
% 11.89/12.06 tff(118,plain,
% 11.89/12.06 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 11.89/12.06 inference(quant_intro,[status(thm)],[117])).
% 11.89/12.06 tff(119,plain,
% 11.89/12.06 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 11.89/12.06 inference(rewrite,[status(thm)],[])).
% 11.89/12.06 tff(120,plain,
% 11.89/12.06 (^[L: $i, M: $i] : rewrite(((line(L) & line(M)) => (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))))),
% 11.89/12.06 inference(bind,[status(th)],[])).
% 11.89/12.06 tff(121,plain,
% 11.89/12.06 (![L: $i, M: $i] : ((line(L) & line(M)) => (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 11.89/12.06 inference(quant_intro,[status(thm)],[120])).
% 11.89/12.06 tff(122,axiom,(![L: $i, M: $i] : ((line(L) & line(M)) => (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag8')).
% 11.89/12.06 tff(123,plain,
% 11.89/12.06 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[122, 121])).
% 11.89/12.06 tff(124,plain,
% 11.89/12.06 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[123, 119])).
% 11.89/12.06 tff(125,plain,(
% 11.89/12.06 ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 11.89/12.06 inference(skolemize,[status(sab)],[124])).
% 11.89/12.06 tff(126,plain,
% 11.89/12.06 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[125, 118])).
% 11.89/12.06 tff(127,plain,
% 11.89/12.06 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[126, 116])).
% 11.89/12.06 tff(128,plain,
% 11.89/12.06 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | ((~line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (~line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3)))),
% 11.89/12.06 inference(rewrite,[status(thm)],[])).
% 11.89/12.06 tff(129,plain,
% 11.89/12.06 ((unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3)) | (~line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3))))) <=> ((~line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3)))),
% 11.89/12.06 inference(rewrite,[status(thm)],[])).
% 11.89/12.06 tff(130,plain,
% 11.89/12.06 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3)) | (~line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | ((~line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))))),
% 11.89/12.06 inference(monotonicity,[status(thm)],[129])).
% 11.89/12.06 tff(131,plain,
% 11.89/12.06 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3)) | (~line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (~line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3)))),
% 11.89/12.06 inference(transitivity,[status(thm)],[130, 128])).
% 11.89/12.06 tff(132,plain,
% 11.89/12.06 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3)) | (~line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))))),
% 11.89/12.06 inference(quant_inst,[status(thm)],[])).
% 11.89/12.06 tff(133,plain,
% 11.89/12.06 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (~line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[132, 131])).
% 11.89/12.06 tff(134,plain,
% 11.89/12.06 (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))),
% 11.89/12.06 inference(unit_resolution,[status(thm)],[133, 127, 109, 114])).
% 11.89/12.06 tff(135,plain,
% 11.89/12.06 (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))),
% 11.89/12.06 inference(unit_resolution,[status(thm)],[134, 82])).
% 11.89/12.06 tff(136,assumption,(~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))), introduced(assumption)).
% 11.89/12.06 tff(137,plain,
% 11.89/12.06 (^[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))))),
% 11.89/12.06 inference(bind,[status(th)],[])).
% 11.89/12.06 tff(138,plain,
% 11.89/12.06 (![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)))),
% 11.89/12.06 inference(quant_intro,[status(thm)],[137])).
% 11.89/12.06 tff(139,plain,
% 11.89/12.06 (![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)))),
% 11.89/12.06 inference(rewrite,[status(thm)],[])).
% 11.89/12.06 tff(140,plain,
% 11.89/12.06 (^[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)))))),
% 11.89/12.06 inference(bind,[status(th)],[])).
% 11.89/12.06 tff(141,plain,
% 11.89/12.06 (![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)))),
% 11.89/12.06 inference(quant_intro,[status(thm)],[140])).
% 11.89/12.06 tff(142,axiom,(![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag6')).
% 11.89/12.06 tff(143,plain,
% 11.89/12.06 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[142, 141])).
% 11.89/12.06 tff(144,plain,
% 11.89/12.06 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[143, 139])).
% 11.89/12.06 tff(145,plain,(
% 11.89/12.06 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 11.89/12.06 inference(skolemize,[status(sab)],[144])).
% 11.89/12.06 tff(146,plain,
% 11.89/12.06 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[145, 138])).
% 11.89/12.06 tff(147,plain,
% 11.89/12.06 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 11.89/12.06 inference(rewrite,[status(thm)],[])).
% 11.89/12.06 tff(148,plain,
% 11.89/12.06 ((unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))) <=> (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 11.89/12.06 inference(rewrite,[status(thm)],[])).
% 11.89/12.06 tff(149,plain,
% 11.89/12.06 (((~![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, B!1)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))))),
% 11.89/12.06 inference(monotonicity,[status(thm)],[148])).
% 11.89/12.06 tff(150,plain,
% 11.89/12.06 (((~![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, B!1)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 11.89/12.06 inference(transitivity,[status(thm)],[149, 147])).
% 11.89/12.06 tff(151,plain,
% 11.89/12.06 ((~![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, B!1)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 11.89/12.06 inference(quant_inst,[status(thm)],[])).
% 11.89/12.06 tff(152,plain,
% 11.89/12.06 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))),
% 11.89/12.06 inference(modus_ponens,[status(thm)],[151, 150])).
% 11.89/12.06 tff(153,plain,
% 11.89/12.06 (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))),
% 11.89/12.06 inference(unit_resolution,[status(thm)],[152, 146, 82, 136])).
% 11.89/12.06 tff(154,plain,
% 11.89/12.06 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))))),
% 11.89/12.06 inference(rewrite,[status(thm)],[])).
% 11.89/12.06 tff(155,plain,
% 11.89/12.06 ((unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3)))) <=> (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))))),
% 11.89/12.06 inference(rewrite,[status(thm)],[])).
% 11.89/12.06 tff(156,plain,
% 11.89/12.06 (((~![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!3), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3)))))),
% 11.89/12.06 inference(monotonicity,[status(thm)],[155])).
% 11.89/12.06 tff(157,plain,
% 11.89/12.06 (((~![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!3), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))))),
% 11.89/12.07 inference(transitivity,[status(thm)],[156, 154])).
% 11.89/12.07 tff(158,plain,
% 11.89/12.07 ((~![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!3), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))))),
% 11.89/12.07 inference(quant_inst,[status(thm)],[])).
% 11.89/12.07 tff(159,plain,
% 11.89/12.07 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3)))),
% 11.89/12.07 inference(modus_ponens,[status(thm)],[158, 157])).
% 11.89/12.07 tff(160,plain,
% 11.89/12.07 (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3)))),
% 11.89/12.07 inference(unit_resolution,[status(thm)],[159, 146])).
% 11.89/12.07 tff(161,plain,
% 11.89/12.07 (unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))),
% 11.89/12.07 inference(unit_resolution,[status(thm)],[160, 153, 135])).
% 11.89/12.07 tff(162,plain,
% 11.89/12.07 (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1))),
% 11.89/12.07 inference(unit_resolution,[status(thm)],[48, 42, 161, 28, 26])).
% 11.89/12.07 tff(163,plain,
% 11.89/12.07 (^[A: $i, L: $i] : refl((~unequally_directed_lines(parallel_through_point(L, A), L)) <=> (~unequally_directed_lines(parallel_through_point(L, A), L)))),
% 11.89/12.07 inference(bind,[status(th)],[])).
% 11.89/12.07 tff(164,plain,
% 11.89/12.07 (![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))),
% 11.89/12.07 inference(quant_intro,[status(thm)],[163])).
% 11.89/12.07 tff(165,plain,
% 11.89/12.07 (![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))),
% 11.89/12.07 inference(rewrite,[status(thm)],[])).
% 11.89/12.07 tff(166,axiom,(![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oagco10')).
% 11.89/12.07 tff(167,plain,
% 11.89/12.07 (![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))),
% 11.89/12.07 inference(modus_ponens,[status(thm)],[166, 165])).
% 11.89/12.07 tff(168,plain,(
% 11.89/12.07 ![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))),
% 11.89/12.07 inference(skolemize,[status(sab)],[167])).
% 11.89/12.07 tff(169,plain,
% 11.89/12.07 (![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))),
% 11.89/12.07 inference(modus_ponens,[status(thm)],[168, 164])).
% 11.89/12.07 tff(170,plain,
% 11.89/12.07 ((~![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))) | (~unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))))),
% 11.89/12.07 inference(quant_inst,[status(thm)],[])).
% 11.89/12.07 tff(171,plain,
% 11.89/12.07 (~unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3)))),
% 11.89/12.07 inference(unit_resolution,[status(thm)],[170, 169])).
% 11.89/12.07 tff(172,plain,
% 11.89/12.07 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!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(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0))))),
% 11.89/12.07 inference(rewrite,[status(thm)],[])).
% 11.89/12.07 tff(173,plain,
% 11.89/12.07 ((unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)))) <=> (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0))))),
% 11.89/12.07 inference(rewrite,[status(thm)],[])).
% 11.89/12.07 tff(174,plain,
% 11.89/12.07 (((~![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(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!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(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)))))),
% 11.89/12.07 inference(monotonicity,[status(thm)],[173])).
% 11.89/12.07 tff(175,plain,
% 11.89/12.07 (((~![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(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!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(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0))))),
% 11.89/12.07 inference(transitivity,[status(thm)],[174, 172])).
% 11.89/12.07 tff(176,plain,
% 11.89/12.07 ((~![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(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0))))),
% 11.89/12.07 inference(quant_inst,[status(thm)],[])).
% 11.89/12.07 tff(177,plain,
% 11.89/12.07 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)))),
% 11.89/12.07 inference(modus_ponens,[status(thm)],[176, 175])).
% 11.89/12.07 tff(178,plain,
% 11.89/12.07 (~unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0))),
% 11.89/12.07 inference(unit_resolution,[status(thm)],[177, 146, 82, 171])).
% 11.89/12.07 tff(179,plain,
% 11.89/12.07 (((~![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(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))))),
% 11.89/12.07 inference(rewrite,[status(thm)],[])).
% 11.89/12.07 tff(180,plain,
% 11.89/12.07 ((unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1))))) <=> (unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))))),
% 11.89/12.07 inference(rewrite,[status(thm)],[])).
% 11.89/12.07 tff(181,plain,
% 11.89/12.07 (((~![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, B!1)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), 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(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))))),
% 11.89/12.07 inference(monotonicity,[status(thm)],[180])).
% 11.89/12.07 tff(182,plain,
% 11.89/12.07 (((~![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, B!1)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), 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(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3))))),
% 11.89/12.07 inference(transitivity,[status(thm)],[181, 179])).
% 11.89/12.07 tff(183,plain,
% 11.89/12.07 ((~![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, B!1)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1)))))),
% 11.89/12.07 inference(quant_inst,[status(thm)],[])).
% 11.89/12.07 tff(184,plain,
% 11.89/12.07 ((~![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(reverse_line(L!3)), C!0), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))),
% 11.89/12.07 inference(modus_ponens,[status(thm)],[183, 182])).
% 11.89/12.07 tff(185,plain,
% 11.89/12.07 (~unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1)))),
% 11.89/12.07 inference(unit_resolution,[status(thm)],[184, 146, 171, 136])).
% 11.89/12.07 tff(186,plain,
% 11.89/12.07 (^[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)))))),
% 11.89/12.07 inference(bind,[status(th)],[])).
% 11.89/12.07 tff(187,plain,
% 11.89/12.07 (![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))))),
% 11.89/12.07 inference(quant_intro,[status(thm)],[186])).
% 11.89/12.07 tff(188,plain,
% 11.89/12.07 (![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))))),
% 11.89/12.07 inference(rewrite,[status(thm)],[])).
% 11.89/12.07 tff(189,axiom,(![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oagco9')).
% 11.89/12.07 tff(190,plain,
% 11.89/12.07 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 11.89/12.07 inference(modus_ponens,[status(thm)],[189, 188])).
% 11.89/12.07 tff(191,plain,(
% 11.89/12.07 ![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 11.89/12.07 inference(skolemize,[status(sab)],[190])).
% 11.89/12.07 tff(192,plain,
% 11.89/12.07 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 11.89/12.07 inference(modus_ponens,[status(thm)],[191, 187])).
% 11.89/12.07 tff(193,plain,
% 11.89/12.07 ((~![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))))),
% 11.89/12.07 inference(quant_inst,[status(thm)],[])).
% 11.89/12.07 tff(194,plain,
% 11.89/12.07 (~unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1)))),
% 11.89/12.07 inference(unit_resolution,[status(thm)],[193, 192])).
% 11.89/12.07 tff(195,plain,
% 11.89/12.07 (((~![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(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(reverse_line(reverse_line(L!3)), C!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(line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(reverse_line(reverse_line(L!3)), C!0))))),
% 11.89/12.07 inference(rewrite,[status(thm)],[])).
% 11.89/12.07 tff(196,plain,
% 11.89/12.07 ((unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), 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), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)))) <=> (unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(reverse_line(reverse_line(L!3)), C!0))))),
% 11.89/12.07 inference(rewrite,[status(thm)],[])).
% 11.89/12.07 tff(197,plain,
% 11.89/12.07 (((~![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(reverse_line(L!3)), C!0), 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), parallel_through_point(reverse_line(reverse_line(L!3)), C!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(line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)))))),
% 11.89/12.07 inference(monotonicity,[status(thm)],[196])).
% 11.89/12.07 tff(198,plain,
% 11.89/12.07 (((~![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(reverse_line(L!3)), C!0), 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), parallel_through_point(reverse_line(reverse_line(L!3)), C!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(line_connecting(B!1, B!1))) | unequally_directed_lines(parallel_through_point(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(reverse_line(reverse_line(L!3)), C!0))))),
% 11.89/12.07 inference(transitivity,[status(thm)],[197, 195])).
% 11.89/12.07 tff(199,plain,
% 11.89/12.07 ((~![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(reverse_line(L!3)), C!0), 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), parallel_through_point(reverse_line(reverse_line(L!3)), C!0))))),
% 11.89/12.08 inference(quant_inst,[status(thm)],[])).
% 11.89/12.08 tff(200,plain,
% 11.89/12.08 ((~![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(reverse_line(reverse_line(L!3)), C!0), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)))),
% 11.89/12.08 inference(modus_ponens,[status(thm)],[199, 198])).
% 11.89/12.08 tff(201,plain,
% 11.89/12.08 (~unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(reverse_line(reverse_line(L!3)), C!0))),
% 11.89/12.08 inference(unit_resolution,[status(thm)],[200, 146, 194, 185])).
% 11.89/12.08 tff(202,plain,
% 11.89/12.08 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))))),
% 11.89/12.08 inference(rewrite,[status(thm)],[])).
% 11.89/12.08 tff(203,plain,
% 11.89/12.08 ((unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)))) <=> (unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))))),
% 11.89/12.08 inference(rewrite,[status(thm)],[])).
% 11.89/12.08 tff(204,plain,
% 11.89/12.08 (((~![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(reverse_line(reverse_line(L!3)), C!0)) | unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)))))),
% 11.89/12.08 inference(monotonicity,[status(thm)],[203])).
% 11.89/12.08 tff(205,plain,
% 11.89/12.08 (((~![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(reverse_line(reverse_line(L!3)), C!0)) | unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))))),
% 11.89/12.08 inference(transitivity,[status(thm)],[204, 202])).
% 11.89/12.08 tff(206,plain,
% 11.89/12.08 ((~![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(reverse_line(reverse_line(L!3)), C!0)) | unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))))),
% 11.89/12.08 inference(quant_inst,[status(thm)],[])).
% 11.89/12.08 tff(207,plain,
% 11.89/12.08 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | unequally_directed_lines(line_connecting(B!1, B!1), parallel_through_point(reverse_line(reverse_line(L!3)), C!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)))),
% 11.89/12.08 inference(modus_ponens,[status(thm)],[206, 205])).
% 11.89/12.08 tff(208,plain,
% 11.89/12.08 (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))),
% 11.89/12.08 inference(unit_resolution,[status(thm)],[207, 146, 201, 178])).
% 11.89/12.08 tff(209,plain,
% 11.89/12.08 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)))),
% 11.89/12.08 inference(rewrite,[status(thm)],[])).
% 11.89/12.08 tff(210,plain,
% 11.89/12.08 ((unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3)))) <=> (unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)))),
% 11.89/12.08 inference(rewrite,[status(thm)],[])).
% 11.89/12.08 tff(211,plain,
% 11.89/12.08 (((~![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!3), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1))))),
% 11.89/12.08 inference(monotonicity,[status(thm)],[210])).
% 11.89/12.08 tff(212,plain,
% 11.89/12.08 (((~![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!3), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)))),
% 11.89/12.08 inference(transitivity,[status(thm)],[211, 209])).
% 11.89/12.08 tff(213,plain,
% 11.89/12.08 ((~![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!3), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))))),
% 11.89/12.08 inference(quant_inst,[status(thm)],[])).
% 11.89/12.08 tff(214,plain,
% 11.89/12.08 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1))),
% 11.89/12.08 inference(modus_ponens,[status(thm)],[213, 212])).
% 11.89/12.08 tff(215,plain,
% 11.89/12.08 ($false),
% 11.89/12.08 inference(unit_resolution,[status(thm)],[214, 146, 135, 208, 162])).
% 11.89/12.08 tff(216,plain,(unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))), inference(lemma,lemma(discharge,[]))).
% 11.89/12.08 tff(217,plain,
% 11.89/12.08 (unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))),
% 11.89/12.08 inference(unit_resolution,[status(thm)],[216, 81])).
% 11.89/12.08 tff(218,plain,
% 11.89/12.08 ((~((~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 11.89/12.08 inference(tautology,[status(thm)],[])).
% 11.89/12.08 tff(219,plain,
% 11.89/12.08 (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3))))),
% 11.89/12.08 inference(unit_resolution,[status(thm)],[218, 217, 70])).
% 11.89/12.08 tff(220,plain,
% 11.89/12.08 (((~![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, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(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(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(line_connecting(B!1, B!1)))))),
% 11.89/12.08 inference(rewrite,[status(thm)],[])).
% 11.89/12.08 tff(221,plain,
% 11.89/12.08 ((unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(line_connecting(B!1, B!1))))) <=> (unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(line_connecting(B!1, B!1)))))),
% 11.89/12.08 inference(rewrite,[status(thm)],[])).
% 11.89/12.08 tff(222,plain,
% 11.89/12.08 (((~![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, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(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(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(line_connecting(B!1, B!1))))))),
% 11.89/12.08 inference(monotonicity,[status(thm)],[221])).
% 11.89/12.08 tff(223,plain,
% 11.89/12.08 (((~![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, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(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(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(line_connecting(B!1, B!1)))))),
% 11.89/12.08 inference(transitivity,[status(thm)],[222, 220])).
% 11.89/12.08 tff(224,plain,
% 11.89/12.08 ((~![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, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(line_connecting(B!1, B!1)))))),
% 11.89/12.08 inference(quant_inst,[status(thm)],[])).
% 11.89/12.08 tff(225,plain,
% 11.89/12.08 ((~![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, B!1)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(line_connecting(B!1, B!1))))),
% 11.89/12.08 inference(modus_ponens,[status(thm)],[224, 223])).
% 11.89/12.08 tff(226,plain,
% 11.89/12.08 (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(line_connecting(B!1, B!1)))),
% 11.89/12.08 inference(unit_resolution,[status(thm)],[225, 146, 219])).
% 11.89/12.08 tff(227,plain,
% 11.89/12.08 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(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), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1))))),
% 11.93/12.08 inference(rewrite,[status(thm)],[])).
% 11.93/12.08 tff(228,plain,
% 11.93/12.08 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1))))),
% 11.93/12.08 inference(quant_inst,[status(thm)],[])).
% 11.93/12.08 tff(229,plain,
% 11.93/12.08 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, B!1), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), reverse_line(line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1)))),
% 11.93/12.09 inference(modus_ponens,[status(thm)],[228, 227])).
% 11.93/12.09 tff(230,plain,
% 11.93/12.09 (~unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1))),
% 11.93/12.09 inference(unit_resolution,[status(thm)],[229, 146, 194, 226])).
% 11.93/12.09 tff(231,plain,
% 11.93/12.09 (((~![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!3), reverse_line(line_connecting(B!1, B!1)))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(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(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1)))),
% 11.93/12.09 inference(rewrite,[status(thm)],[])).
% 11.93/12.09 tff(232,plain,
% 11.93/12.09 ((unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1))))) <=> ((~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1)))),
% 11.93/12.09 inference(rewrite,[status(thm)],[])).
% 11.93/12.09 tff(233,plain,
% 11.93/12.09 (((~![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, B!1)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1))))),
% 11.93/12.09 inference(monotonicity,[status(thm)],[232])).
% 11.93/12.09 tff(234,plain,
% 11.93/12.09 (((~![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, B!1)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1)))),
% 11.93/12.09 inference(transitivity,[status(thm)],[233, 231])).
% 11.93/12.09 tff(235,plain,
% 11.93/12.09 ((~![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, B!1)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))))),
% 11.93/12.09 inference(quant_inst,[status(thm)],[])).
% 11.93/12.09 tff(236,plain,
% 11.93/12.09 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1))),
% 11.93/12.09 inference(modus_ponens,[status(thm)],[235, 234])).
% 11.93/12.09 tff(237,plain,
% 11.93/12.09 ($false),
% 11.93/12.09 inference(unit_resolution,[status(thm)],[236, 146, 29, 230, 49])).
% 11.93/12.09 tff(238,plain,(~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))), inference(lemma,lemma(discharge,[]))).
% 11.93/12.09 tff(239,plain,
% 11.93/12.09 (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))),
% 11.93/12.09 inference(unit_resolution,[status(thm)],[134, 81])).
% 11.93/12.09 tff(240,plain,
% 11.93/12.09 (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, B!1)))),
% 11.93/12.09 inference(unit_resolution,[status(thm)],[160, 239])).
% 11.93/12.09 tff(241,plain,
% 11.93/12.09 (unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))),
% 11.93/12.09 inference(unit_resolution,[status(thm)],[240, 238])).
% 11.93/12.09 tff(242,assumption,(~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))), introduced(assumption)).
% 11.93/12.09 tff(243,assumption,(unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))), introduced(assumption)).
% 11.93/12.09 tff(244,plain,
% 11.93/12.09 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 11.93/12.09 inference(rewrite,[status(thm)],[])).
% 11.93/12.09 tff(245,plain,
% 11.93/12.09 ((unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))) <=> (unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 11.93/12.09 inference(rewrite,[status(thm)],[])).
% 11.93/12.09 tff(246,plain,
% 11.93/12.09 (((~![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, B!1)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))))),
% 11.93/12.09 inference(monotonicity,[status(thm)],[245])).
% 11.93/12.09 tff(247,plain,
% 11.93/12.09 (((~![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, B!1)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 11.93/12.09 inference(transitivity,[status(thm)],[246, 244])).
% 11.93/12.09 tff(248,plain,
% 11.93/12.09 ((~![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, B!1)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 11.93/12.09 inference(quant_inst,[status(thm)],[])).
% 11.93/12.09 tff(249,plain,
% 11.93/12.09 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | unequally_directed_lines(reverse_line(line_connecting(B!1, B!1)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))),
% 11.93/12.09 inference(modus_ponens,[status(thm)],[248, 247])).
% 11.93/12.09 tff(250,plain,
% 11.93/12.09 ($false),
% 11.93/12.09 inference(unit_resolution,[status(thm)],[249, 146, 243, 242, 230])).
% 11.93/12.09 tff(251,plain,(unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))), inference(lemma,lemma(discharge,[]))).
% 11.93/12.09 tff(252,plain,
% 11.93/12.09 (unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))),
% 11.93/12.09 inference(unit_resolution,[status(thm)],[251, 241])).
% 11.93/12.09 tff(253,plain,
% 11.93/12.09 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)))),
% 11.93/12.09 inference(rewrite,[status(thm)],[])).
% 11.93/12.09 tff(254,plain,
% 11.93/12.09 ((left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))))) <=> ((~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)))),
% 11.93/12.09 inference(rewrite,[status(thm)],[])).
% 11.93/12.09 tff(255,plain,
% 11.93/12.09 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))))),
% 11.93/12.09 inference(monotonicity,[status(thm)],[254])).
% 11.93/12.09 tff(256,plain,
% 11.93/12.09 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)))),
% 11.93/12.09 inference(transitivity,[status(thm)],[255, 253])).
% 11.93/12.09 tff(257,plain,
% 11.93/12.09 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1)) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))))),
% 11.93/12.10 inference(quant_inst,[status(thm)],[])).
% 11.93/12.10 tff(258,plain,
% 11.93/12.10 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1)))) | left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))),
% 11.93/12.10 inference(modus_ponens,[status(thm)],[257, 256])).
% 11.93/12.10 tff(259,plain,
% 11.93/12.10 (left_convergent_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(B!1, B!1))) | left_convergent_lines(reverse_line(reverse_line(L!3)), line_connecting(B!1, B!1))),
% 11.93/12.10 inference(unit_resolution,[status(thm)],[258, 42, 241, 252])).
% 11.93/12.10 tff(260,plain,
% 11.93/12.10 ($false),
% 11.93/12.10 inference(unit_resolution,[status(thm)],[259, 20, 18])).
% 11.93/12.10 % SZS output end Proof
%------------------------------------------------------------------------------