%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO259+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:10 AM UTC 2025
% Result : Theorem 11.99s 12.19s
% Output : Proof 12.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO259+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:44:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 11.99/12.19 % SZS status Theorem
% 11.99/12.19 % SZS output start Proof
% 11.99/12.19 tff(unequally_directed_lines_type, type, (
% 11.99/12.19 unequally_directed_lines: ( $i * $i ) > $o)).
% 11.99/12.19 tff(line_connecting_type, type, (
% 11.99/12.19 line_connecting: ( $i * $i ) > $i)).
% 11.99/12.19 tff(intersection_point_type, type, (
% 11.99/12.19 intersection_point: ( $i * $i ) > $i)).
% 11.99/12.19 tff(tptp_fun_L_3_type, type, (
% 11.99/12.19 tptp_fun_L_3: $i)).
% 11.99/12.19 tff(reverse_line_type, type, (
% 11.99/12.19 reverse_line: $i > $i)).
% 11.99/12.19 tff(tptp_fun_C_0_type, type, (
% 11.99/12.19 tptp_fun_C_0: $i)).
% 11.99/12.19 tff(tptp_fun_A_2_type, type, (
% 11.99/12.19 tptp_fun_A_2: $i)).
% 11.99/12.19 tff(line_type, type, (
% 11.99/12.19 line: $i > $o)).
% 11.99/12.19 tff(distinct_points_type, type, (
% 11.99/12.19 distinct_points: ( $i * $i ) > $o)).
% 11.99/12.19 tff(tptp_fun_B_1_type, type, (
% 11.99/12.19 tptp_fun_B_1: $i)).
% 11.99/12.19 tff(between_on_line_type, type, (
% 11.99/12.19 between_on_line: ( $i * $i * $i * $i ) > $o)).
% 11.99/12.19 tff(left_convergent_lines_type, type, (
% 11.99/12.19 left_convergent_lines: ( $i * $i ) > $o)).
% 11.99/12.19 tff(left_apart_point_type, type, (
% 11.99/12.19 left_apart_point: ( $i * $i ) > $o)).
% 11.99/12.19 tff(before_on_line_type, type, (
% 11.99/12.19 before_on_line: ( $i * $i * $i ) > $o)).
% 11.99/12.19 tff(1,assumption,(unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))), introduced(assumption)).
% 11.99/12.19 tff(2,assumption,(~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))), introduced(assumption)).
% 11.99/12.19 tff(3,plain,
% 11.99/12.19 (^[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)))))),
% 11.99/12.19 inference(bind,[status(th)],[])).
% 11.99/12.19 tff(4,plain,
% 11.99/12.19 (![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))))),
% 11.99/12.19 inference(quant_intro,[status(thm)],[3])).
% 11.99/12.19 tff(5,plain,
% 11.99/12.19 (![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))))),
% 11.99/12.19 inference(rewrite,[status(thm)],[])).
% 11.99/12.19 tff(6,axiom,(![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oagco9')).
% 11.99/12.19 tff(7,plain,
% 11.99/12.19 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 11.99/12.19 inference(modus_ponens,[status(thm)],[6, 5])).
% 11.99/12.19 tff(8,plain,(
% 11.99/12.19 ![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 11.99/12.19 inference(skolemize,[status(sab)],[7])).
% 11.99/12.19 tff(9,plain,
% 11.99/12.19 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 11.99/12.19 inference(modus_ponens,[status(thm)],[8, 4])).
% 11.99/12.19 tff(10,plain,
% 11.99/12.19 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 11.99/12.19 inference(quant_inst,[status(thm)],[])).
% 11.99/12.19 tff(11,plain,
% 11.99/12.19 (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 11.99/12.19 inference(unit_resolution,[status(thm)],[10, 9])).
% 11.99/12.19 tff(12,plain,
% 11.99/12.19 (^[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))))),
% 11.99/12.19 inference(bind,[status(th)],[])).
% 11.99/12.19 tff(13,plain,
% 11.99/12.19 (![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)))),
% 11.99/12.19 inference(quant_intro,[status(thm)],[12])).
% 11.99/12.19 tff(14,plain,
% 11.99/12.19 (![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)))),
% 11.99/12.19 inference(rewrite,[status(thm)],[])).
% 11.99/12.19 tff(15,plain,
% 11.99/12.19 (^[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)))))),
% 11.99/12.19 inference(bind,[status(th)],[])).
% 11.99/12.19 tff(16,plain,
% 11.99/12.19 (![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)))),
% 11.99/12.19 inference(quant_intro,[status(thm)],[15])).
% 11.99/12.19 tff(17,axiom,(![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag6')).
% 11.99/12.19 tff(18,plain,
% 11.99/12.19 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 11.99/12.19 inference(modus_ponens,[status(thm)],[17, 16])).
% 11.99/12.19 tff(19,plain,
% 11.99/12.19 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 11.99/12.19 inference(modus_ponens,[status(thm)],[18, 14])).
% 11.99/12.19 tff(20,plain,(
% 11.99/12.19 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 11.99/12.19 inference(skolemize,[status(sab)],[19])).
% 11.99/12.19 tff(21,plain,
% 11.99/12.19 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 11.99/12.19 inference(modus_ponens,[status(thm)],[20, 13])).
% 11.99/12.19 tff(22,plain,
% 11.99/12.19 (((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 11.99/12.19 inference(rewrite,[status(thm)],[])).
% 11.99/12.19 tff(23,plain,
% 11.99/12.19 ((unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) <=> (unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 11.99/12.19 inference(rewrite,[status(thm)],[])).
% 11.99/12.19 tff(24,plain,
% 11.99/12.19 (((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))),
% 11.99/12.19 inference(monotonicity,[status(thm)],[23])).
% 11.99/12.19 tff(25,plain,
% 11.99/12.19 (((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 11.99/12.20 inference(transitivity,[status(thm)],[24, 22])).
% 11.99/12.20 tff(26,plain,
% 11.99/12.20 ((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 11.99/12.20 inference(quant_inst,[status(thm)],[])).
% 11.99/12.20 tff(27,plain,
% 11.99/12.20 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[26, 25])).
% 11.99/12.20 tff(28,plain,
% 11.99/12.20 ($false),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[27, 21, 11, 1, 2])).
% 11.99/12.20 tff(29,plain,(unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.20 tff(30,plain,
% 11.99/12.20 (unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[29, 1])).
% 11.99/12.20 tff(31,assumption,(unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))), introduced(assumption)).
% 11.99/12.20 tff(32,assumption,(~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))), introduced(assumption)).
% 11.99/12.20 tff(33,assumption,(unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))), introduced(assumption)).
% 11.99/12.20 tff(34,plain,
% 11.99/12.20 (^[L: $i] : refl((~unequally_directed_lines(L, L)) <=> (~unequally_directed_lines(L, L)))),
% 11.99/12.20 inference(bind,[status(th)],[])).
% 11.99/12.20 tff(35,plain,
% 11.99/12.20 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 11.99/12.20 inference(quant_intro,[status(thm)],[34])).
% 11.99/12.20 tff(36,plain,
% 11.99/12.20 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(37,axiom,(![L: $i] : (~unequally_directed_lines(L, L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag5')).
% 11.99/12.20 tff(38,plain,
% 11.99/12.20 (![L: $i] : (~unequally_directed_lines(L, L))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[37, 36])).
% 11.99/12.20 tff(39,plain,(
% 11.99/12.20 ![L: $i] : (~unequally_directed_lines(L, L))),
% 11.99/12.20 inference(skolemize,[status(sab)],[38])).
% 11.99/12.20 tff(40,plain,
% 11.99/12.20 (![L: $i] : (~unequally_directed_lines(L, L))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[39, 35])).
% 11.99/12.20 tff(41,plain,
% 11.99/12.20 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))))),
% 11.99/12.20 inference(quant_inst,[status(thm)],[])).
% 11.99/12.20 tff(42,plain,
% 11.99/12.20 ($false),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[41, 40, 33])).
% 11.99/12.20 tff(43,plain,(~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.20 tff(44,plain,
% 11.99/12.20 (((~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))),
% 11.99/12.20 inference(tautology,[status(thm)],[])).
% 11.99/12.20 tff(45,plain,
% 11.99/12.20 ((~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[44, 43])).
% 11.99/12.20 tff(46,assumption,(unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))), introduced(assumption)).
% 11.99/12.20 tff(47,plain,
% 11.99/12.20 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)))),
% 11.99/12.20 inference(quant_inst,[status(thm)],[])).
% 11.99/12.20 tff(48,plain,
% 11.99/12.20 ($false),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[47, 40, 46])).
% 11.99/12.20 tff(49,plain,(~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.20 tff(50,plain,
% 11.99/12.20 (((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))),
% 11.99/12.20 inference(tautology,[status(thm)],[])).
% 11.99/12.20 tff(51,plain,
% 11.99/12.20 ((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3))))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[50, 49])).
% 11.99/12.20 tff(52,plain,
% 11.99/12.20 ((~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))) <=> (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B)))))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(53,plain,
% 11.99/12.20 ((~![L: $i, A: $i, B: $i, C: $i] : ((((line(L) & distinct_points(A, C)) & distinct_points(B, C)) & distinct_points(A, B)) => (~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))))) <=> (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B)))))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(54,axiom,(~![L: $i, A: $i, B: $i, C: $i] : ((((line(L) & distinct_points(A, C)) & distinct_points(B, C)) & distinct_points(A, B)) => (~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 11.99/12.20 tff(55,plain,
% 11.99/12.20 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[54, 53])).
% 11.99/12.20 tff(56,plain,
% 11.99/12.20 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[55, 52])).
% 11.99/12.20 tff(57,plain,
% 11.99/12.20 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[56, 52])).
% 11.99/12.20 tff(58,plain,
% 11.99/12.20 (~![L: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & between_on_line(L, B, A, C))) | (~(line(L) & distinct_points(A, C) & distinct_points(B, C) & distinct_points(A, B))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[57, 52])).
% 11.99/12.20 tff(59,plain,(
% 11.99/12.20 ~((~(between_on_line(L!3, A!2, B!1, C!0) & between_on_line(L!3, B!1, A!2, C!0))) | (~(line(L!3) & distinct_points(A!2, C!0) & distinct_points(B!1, C!0) & distinct_points(A!2, B!1))))),
% 11.99/12.20 inference(skolemize,[status(sab)],[58])).
% 11.99/12.20 tff(60,plain,
% 11.99/12.20 (line(L!3) & distinct_points(A!2, C!0) & distinct_points(B!1, C!0) & distinct_points(A!2, B!1)),
% 11.99/12.20 inference(or_elim,[status(thm)],[59])).
% 11.99/12.20 tff(61,plain,
% 11.99/12.20 (line(L!3)),
% 11.99/12.20 inference(and_elim,[status(thm)],[60])).
% 11.99/12.20 tff(62,plain,
% 11.99/12.20 (^[L: $i] : refl((line(reverse_line(L)) | (~line(L))) <=> (line(reverse_line(L)) | (~line(L))))),
% 11.99/12.20 inference(bind,[status(th)],[])).
% 11.99/12.20 tff(63,plain,
% 11.99/12.20 (![L: $i] : (line(reverse_line(L)) | (~line(L))) <=> ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 11.99/12.20 inference(quant_intro,[status(thm)],[62])).
% 11.99/12.20 tff(64,plain,
% 11.99/12.20 (![L: $i] : (line(reverse_line(L)) | (~line(L))) <=> ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(65,plain,
% 11.99/12.20 (^[L: $i] : rewrite((line(L) => line(reverse_line(L))) <=> (line(reverse_line(L)) | (~line(L))))),
% 11.99/12.20 inference(bind,[status(th)],[])).
% 11.99/12.20 tff(66,plain,
% 11.99/12.20 (![L: $i] : (line(L) => line(reverse_line(L))) <=> ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 11.99/12.20 inference(quant_intro,[status(thm)],[65])).
% 11.99/12.20 tff(67,axiom,(![L: $i] : (line(L) => line(reverse_line(L)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oagco4')).
% 11.99/12.20 tff(68,plain,
% 11.99/12.20 (![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[67, 66])).
% 11.99/12.20 tff(69,plain,
% 11.99/12.20 (![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[68, 64])).
% 11.99/12.20 tff(70,plain,(
% 11.99/12.20 ![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 11.99/12.20 inference(skolemize,[status(sab)],[69])).
% 11.99/12.20 tff(71,plain,
% 11.99/12.20 (![L: $i] : (line(reverse_line(L)) | (~line(L)))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[70, 63])).
% 11.99/12.20 tff(72,plain,
% 11.99/12.20 (((~![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)))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(73,plain,
% 11.99/12.20 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | (line(reverse_line(L!3)) | (~line(L!3)))),
% 11.99/12.20 inference(quant_inst,[status(thm)],[])).
% 11.99/12.20 tff(74,plain,
% 11.99/12.20 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | line(reverse_line(L!3)) | (~line(L!3))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[73, 72])).
% 11.99/12.20 tff(75,plain,
% 11.99/12.20 (line(reverse_line(L!3))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[74, 71, 61])).
% 11.99/12.20 tff(76,plain,
% 11.99/12.20 (^[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))))),
% 11.99/12.20 inference(bind,[status(th)],[])).
% 11.99/12.20 tff(77,plain,
% 11.99/12.20 (![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)))),
% 11.99/12.20 inference(quant_intro,[status(thm)],[76])).
% 11.99/12.20 tff(78,plain,
% 11.99/12.20 (^[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)))))),
% 11.99/12.20 inference(bind,[status(th)],[])).
% 11.99/12.20 tff(79,plain,
% 11.99/12.20 (![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)))),
% 11.99/12.20 inference(quant_intro,[status(thm)],[78])).
% 11.99/12.20 tff(80,plain,
% 11.99/12.20 (![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))))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(81,plain,
% 11.99/12.20 (^[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)))))),
% 11.99/12.20 inference(bind,[status(th)],[])).
% 11.99/12.20 tff(82,plain,
% 11.99/12.20 (![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))))),
% 11.99/12.20 inference(quant_intro,[status(thm)],[81])).
% 11.99/12.20 tff(83,axiom,(![L: $i, M: $i] : ((line(L) & line(M)) => (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag8')).
% 11.99/12.20 tff(84,plain,
% 11.99/12.20 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[83, 82])).
% 11.99/12.20 tff(85,plain,
% 11.99/12.20 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[84, 80])).
% 11.99/12.20 tff(86,plain,(
% 11.99/12.20 ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 11.99/12.20 inference(skolemize,[status(sab)],[85])).
% 11.99/12.20 tff(87,plain,
% 11.99/12.20 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[86, 79])).
% 11.99/12.20 tff(88,plain,
% 11.99/12.20 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[87, 77])).
% 11.99/12.20 tff(89,plain,
% 11.99/12.20 (((~![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(L!3), reverse_line(reverse_line(L!3))) | unequally_directed_lines(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(L!3), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(90,plain,
% 11.99/12.20 ((unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | (~line(reverse_line(L!3))) | (~line(reverse_line(L!3)))) <=> ((~line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(91,plain,
% 11.99/12.20 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | (~line(reverse_line(L!3))) | (~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(L!3), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))),
% 11.99/12.20 inference(monotonicity,[status(thm)],[90])).
% 11.99/12.20 tff(92,plain,
% 11.99/12.20 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | (~line(reverse_line(L!3))) | (~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(L!3), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)))),
% 11.99/12.20 inference(transitivity,[status(thm)],[91, 89])).
% 11.99/12.20 tff(93,plain,
% 11.99/12.20 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | (~line(reverse_line(L!3))) | (~line(reverse_line(L!3))))),
% 11.99/12.20 inference(quant_inst,[status(thm)],[])).
% 11.99/12.20 tff(94,plain,
% 11.99/12.20 ((~![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(L!3), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[93, 92])).
% 11.99/12.20 tff(95,plain,
% 11.99/12.20 ((~line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[94, 88])).
% 11.99/12.20 tff(96,plain,
% 11.99/12.20 (unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[95, 75, 49])).
% 11.99/12.20 tff(97,plain,
% 11.99/12.20 (^[L: $i, M: $i, N: $i] : refl(((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))))),
% 11.99/12.20 inference(bind,[status(th)],[])).
% 11.99/12.20 tff(98,plain,
% 11.99/12.20 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 11.99/12.20 inference(quant_intro,[status(thm)],[97])).
% 11.99/12.20 tff(99,plain,
% 11.99/12.20 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) <=> (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N)))))), rewrite((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) <=> (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N)))))), trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), (((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ((~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite(((~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))), (((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 11.99/12.20 inference(bind,[status(th)],[])).
% 11.99/12.20 tff(100,plain,
% 11.99/12.20 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 11.99/12.20 inference(quant_intro,[status(thm)],[99])).
% 11.99/12.20 tff(101,plain,
% 11.99/12.20 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(102,plain,
% 11.99/12.20 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite(((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N)))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))), (((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))))), rewrite(((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))), (((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))))),
% 11.99/12.20 inference(bind,[status(th)],[])).
% 11.99/12.20 tff(103,plain,
% 11.99/12.20 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 11.99/12.20 inference(quant_intro,[status(thm)],[102])).
% 11.99/12.20 tff(104,axiom,(![L: $i, M: $i, N: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N)))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag7')).
% 11.99/12.20 tff(105,plain,
% 11.99/12.20 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[104, 103])).
% 11.99/12.20 tff(106,plain,
% 11.99/12.20 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[105, 101])).
% 11.99/12.20 tff(107,plain,(
% 11.99/12.20 ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 11.99/12.20 inference(skolemize,[status(sab)],[106])).
% 11.99/12.20 tff(108,plain,
% 11.99/12.20 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[107, 100])).
% 11.99/12.20 tff(109,plain,
% 11.99/12.20 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[108, 98])).
% 11.99/12.20 tff(110,plain,
% 11.99/12.20 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(111,plain,
% 11.99/12.20 (((~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))) | (~((~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))))) <=> ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(112,plain,
% 11.99/12.20 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))) | (~((~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3))))))),
% 11.99/12.20 inference(monotonicity,[status(thm)],[111])).
% 11.99/12.20 tff(113,plain,
% 11.99/12.20 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))) | (~((~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))),
% 11.99/12.20 inference(transitivity,[status(thm)],[112, 110])).
% 11.99/12.20 tff(114,plain,
% 11.99/12.20 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))) | (~((~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3))))))),
% 11.99/12.20 inference(quant_inst,[status(thm)],[])).
% 11.99/12.20 tff(115,plain,
% 11.99/12.20 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[114, 113])).
% 11.99/12.20 tff(116,plain,
% 11.99/12.20 (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3))))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[115, 109, 96, 51, 45])).
% 11.99/12.20 tff(117,plain,
% 11.99/12.20 (((~![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(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(118,plain,
% 11.99/12.20 ((unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))))) <=> (unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(119,plain,
% 11.99/12.20 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, 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(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))),
% 11.99/12.20 inference(monotonicity,[status(thm)],[118])).
% 11.99/12.20 tff(120,plain,
% 11.99/12.20 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, 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(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 11.99/12.20 inference(transitivity,[status(thm)],[119, 117])).
% 11.99/12.20 tff(121,plain,
% 11.99/12.20 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))),
% 11.99/12.20 inference(quant_inst,[status(thm)],[])).
% 11.99/12.20 tff(122,plain,
% 11.99/12.20 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[121, 120])).
% 11.99/12.20 tff(123,plain,
% 11.99/12.20 ($false),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[122, 21, 116, 32, 31])).
% 11.99/12.20 tff(124,plain,(unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.20 tff(125,plain,
% 11.99/12.20 (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[124, 31])).
% 11.99/12.20 tff(126,plain,
% 11.99/12.20 (^[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)))))),
% 11.99/12.20 inference(bind,[status(th)],[])).
% 11.99/12.20 tff(127,plain,
% 11.99/12.20 (![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))))),
% 11.99/12.20 inference(quant_intro,[status(thm)],[126])).
% 11.99/12.20 tff(128,plain,
% 11.99/12.20 (![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))))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(129,axiom,(![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag11')).
% 11.99/12.20 tff(130,plain,
% 11.99/12.20 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[129, 128])).
% 11.99/12.20 tff(131,plain,(
% 11.99/12.20 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 11.99/12.20 inference(skolemize,[status(sab)],[130])).
% 11.99/12.20 tff(132,plain,
% 11.99/12.20 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[131, 127])).
% 11.99/12.20 tff(133,plain,
% 11.99/12.20 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))),
% 11.99/12.20 inference(quant_inst,[status(thm)],[])).
% 11.99/12.20 tff(134,plain,
% 11.99/12.20 (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[133, 132])).
% 11.99/12.20 tff(135,plain,
% 11.99/12.20 ((left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))) | (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 11.99/12.20 inference(tautology,[status(thm)],[])).
% 11.99/12.20 tff(136,plain,
% 11.99/12.20 (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[135, 134])).
% 11.99/12.20 tff(137,plain,
% 11.99/12.20 ((left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))) | (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))))),
% 11.99/12.20 inference(tautology,[status(thm)],[])).
% 11.99/12.20 tff(138,plain,
% 11.99/12.20 (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))),
% 11.99/12.20 inference(unit_resolution,[status(thm)],[137, 134])).
% 11.99/12.20 tff(139,plain,
% 11.99/12.20 (^[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)))))),
% 11.99/12.20 inference(bind,[status(th)],[])).
% 11.99/12.20 tff(140,plain,
% 11.99/12.20 (![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))))),
% 11.99/12.20 inference(quant_intro,[status(thm)],[139])).
% 11.99/12.20 tff(141,plain,
% 11.99/12.20 (^[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))))))),
% 11.99/12.20 inference(bind,[status(th)],[])).
% 11.99/12.20 tff(142,plain,
% 11.99/12.20 (![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))))),
% 11.99/12.20 inference(quant_intro,[status(thm)],[141])).
% 11.99/12.20 tff(143,plain,
% 11.99/12.20 (![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)))))),
% 11.99/12.20 inference(rewrite,[status(thm)],[])).
% 11.99/12.20 tff(144,plain,
% 11.99/12.20 (^[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))))))),
% 11.99/12.20 inference(bind,[status(th)],[])).
% 11.99/12.20 tff(145,plain,
% 11.99/12.20 (![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)))))),
% 11.99/12.20 inference(quant_intro,[status(thm)],[144])).
% 11.99/12.20 tff(146,axiom,(![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag9')).
% 11.99/12.20 tff(147,plain,
% 11.99/12.20 (![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)))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[146, 145])).
% 11.99/12.20 tff(148,plain,
% 11.99/12.20 (![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)))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[147, 143])).
% 11.99/12.20 tff(149,plain,(
% 11.99/12.20 ![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)))))),
% 11.99/12.20 inference(skolemize,[status(sab)],[148])).
% 11.99/12.20 tff(150,plain,
% 11.99/12.20 (![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))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[149, 142])).
% 11.99/12.20 tff(151,plain,
% 11.99/12.20 (![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))))),
% 11.99/12.20 inference(modus_ponens,[status(thm)],[150, 140])).
% 11.99/12.20 tff(152,plain,
% 11.99/12.20 (((~![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(A!2, C!0)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), 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))))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))),
% 11.99/12.21 inference(rewrite,[status(thm)],[])).
% 11.99/12.21 tff(153,plain,
% 11.99/12.21 ((left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))))) <=> (left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))),
% 11.99/12.21 inference(rewrite,[status(thm)],[])).
% 11.99/12.21 tff(154,plain,
% 11.99/12.21 (((~![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(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), 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))))) | (left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))))))),
% 11.99/12.21 inference(monotonicity,[status(thm)],[153])).
% 11.99/12.21 tff(155,plain,
% 11.99/12.21 (((~![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(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), 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))))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))),
% 11.99/12.21 inference(transitivity,[status(thm)],[154, 152])).
% 11.99/12.21 tff(156,plain,
% 11.99/12.21 ((~![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(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))),
% 11.99/12.21 inference(quant_inst,[status(thm)],[])).
% 11.99/12.21 tff(157,plain,
% 11.99/12.21 ((~![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(A!2, C!0)), reverse_line(reverse_line(L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[156, 155])).
% 11.99/12.21 tff(158,plain,
% 11.99/12.21 ((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[157, 151, 138, 136])).
% 11.99/12.21 tff(159,plain,
% 11.99/12.21 (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[158, 125])).
% 11.99/12.21 tff(160,plain,
% 11.99/12.21 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))),
% 11.99/12.21 inference(tautology,[status(thm)],[])).
% 11.99/12.21 tff(161,plain,
% 11.99/12.21 ((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[160, 159])).
% 11.99/12.21 tff(162,plain,
% 11.99/12.21 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 11.99/12.21 inference(rewrite,[status(thm)],[])).
% 11.99/12.21 tff(163,plain,
% 11.99/12.21 (((~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0)))))) <=> ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 11.99/12.21 inference(rewrite,[status(thm)],[])).
% 11.99/12.21 tff(164,plain,
% 11.99/12.21 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0)))))))),
% 11.99/12.21 inference(monotonicity,[status(thm)],[163])).
% 11.99/12.21 tff(165,plain,
% 11.99/12.21 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 11.99/12.21 inference(transitivity,[status(thm)],[164, 162])).
% 11.99/12.21 tff(166,plain,
% 11.99/12.21 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 11.99/12.21 inference(quant_inst,[status(thm)],[])).
% 11.99/12.21 tff(167,plain,
% 11.99/12.21 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0)))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[166, 165])).
% 11.99/12.21 tff(168,plain,
% 11.99/12.21 (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[167, 109, 51, 31, 161])).
% 11.99/12.21 tff(169,assumption,(~unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0)))), introduced(assumption)).
% 11.99/12.21 tff(170,plain,
% 11.99/12.21 (^[L: $i, A: $i, B: $i] : refl((~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B))) <=> (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B))))),
% 11.99/12.21 inference(bind,[status(th)],[])).
% 11.99/12.21 tff(171,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B))) <=> ![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))),
% 11.99/12.21 inference(quant_intro,[status(thm)],[170])).
% 11.99/12.21 tff(172,plain,
% 11.99/12.21 (^[L: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))))), ((before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))))))), rewrite((before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))))) <=> (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))), ((before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B))))), rewrite((~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B))) <=> (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))), ((before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))))),
% 11.99/12.21 inference(bind,[status(th)],[])).
% 11.99/12.21 tff(173,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> ![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))),
% 11.99/12.21 inference(quant_intro,[status(thm)],[172])).
% 11.99/12.21 tff(174,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 11.99/12.21 inference(rewrite,[status(thm)],[])).
% 11.99/12.21 tff(175,plain,
% 11.99/12.21 (^[L: $i, A: $i, B: $i] : rewrite((before_on_line(L, A, B) <=> (((distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L))))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))))),
% 11.99/12.21 inference(bind,[status(th)],[])).
% 11.99/12.21 tff(176,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (((distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L))))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 11.99/12.21 inference(quant_intro,[status(thm)],[175])).
% 11.99/12.21 tff(177,axiom,(![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (((distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L))))) & (~unequally_directed_lines(L, line_connecting(A, B)))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','bf_def')).
% 11.99/12.21 tff(178,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[177, 176])).
% 11.99/12.21 tff(179,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[178, 174])).
% 11.99/12.21 tff(180,plain,(
% 11.99/12.21 ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 11.99/12.21 inference(skolemize,[status(sab)],[179])).
% 11.99/12.21 tff(181,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[180, 173])).
% 11.99/12.21 tff(182,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[181, 171])).
% 11.99/12.21 tff(183,plain,
% 11.99/12.21 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)) <=> before_on_line(L!3, B!1, C!0)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)) <=> before_on_line(L!3, B!1, C!0))))),
% 11.99/12.21 inference(rewrite,[status(thm)],[])).
% 11.99/12.21 tff(184,plain,
% 11.99/12.21 ((~(((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)) <=> before_on_line(L!3, B!1, C!0))) <=> (~(((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)) <=> before_on_line(L!3, B!1, C!0)))),
% 11.99/12.21 inference(rewrite,[status(thm)],[])).
% 11.99/12.21 tff(185,plain,
% 11.99/12.21 (((unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | (~distinct_points(B!1, C!0))) <=> before_on_line(L!3, B!1, C!0)) <=> (((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)) <=> before_on_line(L!3, B!1, C!0))),
% 11.99/12.21 inference(rewrite,[status(thm)],[])).
% 11.99/12.21 tff(186,plain,
% 11.99/12.21 ((~((unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | (~distinct_points(B!1, C!0))) <=> before_on_line(L!3, B!1, C!0))) <=> (~(((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)) <=> before_on_line(L!3, B!1, C!0)))),
% 11.99/12.21 inference(monotonicity,[status(thm)],[185])).
% 11.99/12.21 tff(187,plain,
% 11.99/12.21 ((~((unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | (~distinct_points(B!1, C!0))) <=> before_on_line(L!3, B!1, C!0))) <=> (~(((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)) <=> before_on_line(L!3, B!1, C!0)))),
% 11.99/12.21 inference(transitivity,[status(thm)],[186, 184])).
% 11.99/12.21 tff(188,plain,
% 11.99/12.21 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | (~distinct_points(B!1, C!0))) <=> before_on_line(L!3, B!1, C!0)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)) <=> before_on_line(L!3, B!1, C!0))))),
% 11.99/12.21 inference(monotonicity,[status(thm)],[187])).
% 11.99/12.21 tff(189,plain,
% 11.99/12.21 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | (~distinct_points(B!1, C!0))) <=> before_on_line(L!3, B!1, C!0)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)) <=> before_on_line(L!3, B!1, C!0))))),
% 11.99/12.21 inference(transitivity,[status(thm)],[188, 183])).
% 11.99/12.21 tff(190,plain,
% 11.99/12.21 ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | (~distinct_points(B!1, C!0))) <=> before_on_line(L!3, B!1, C!0)))),
% 11.99/12.21 inference(quant_inst,[status(thm)],[])).
% 11.99/12.21 tff(191,plain,
% 11.99/12.21 ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)) <=> before_on_line(L!3, B!1, C!0)))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[190, 189])).
% 11.99/12.21 tff(192,plain,
% 11.99/12.21 (~(((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)) <=> before_on_line(L!3, B!1, C!0))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[191, 182])).
% 11.99/12.21 tff(193,assumption,(~before_on_line(L!3, B!1, A!2)), introduced(assumption)).
% 11.99/12.21 tff(194,plain,
% 11.99/12.21 (((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2))) | before_on_line(L!3, B!1, A!2)),
% 11.99/12.21 inference(tautology,[status(thm)],[])).
% 11.99/12.21 tff(195,plain,
% 11.99/12.21 ((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[194, 193])).
% 11.99/12.21 tff(196,plain,
% 11.99/12.21 (^[L: $i, A: $i, B: $i, C: $i] : refl((between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C)))))) <=> (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C)))))))),
% 11.99/12.21 inference(bind,[status(th)],[])).
% 11.99/12.21 tff(197,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C)))))) <=> ![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))),
% 11.99/12.21 inference(quant_intro,[status(thm)],[196])).
% 11.99/12.21 tff(198,plain,
% 11.99/12.21 (^[L: $i, A: $i, B: $i, C: $i] : rewrite((between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C)))) <=> (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C)))))))),
% 11.99/12.21 inference(bind,[status(th)],[])).
% 11.99/12.21 tff(199,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C)))) <=> ![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))),
% 11.99/12.21 inference(quant_intro,[status(thm)],[198])).
% 11.99/12.21 tff(200,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C)))) <=> ![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C))))),
% 11.99/12.21 inference(rewrite,[status(thm)],[])).
% 11.99/12.21 tff(201,plain,
% 11.99/12.21 (^[L: $i, A: $i, B: $i, C: $i] : rewrite((between_on_line(L, A, B, C) <=> ((before_on_line(L, A, B) & before_on_line(L, B, C)) | (before_on_line(L, C, B) & before_on_line(L, B, A)))) <=> (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C)))))),
% 11.99/12.21 inference(bind,[status(th)],[])).
% 11.99/12.21 tff(202,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, A, B) & before_on_line(L, B, C)) | (before_on_line(L, C, B) & before_on_line(L, B, A)))) <=> ![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C))))),
% 11.99/12.21 inference(quant_intro,[status(thm)],[201])).
% 11.99/12.21 tff(203,axiom,(![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, A, B) & before_on_line(L, B, C)) | (before_on_line(L, C, B) & before_on_line(L, B, A))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','bet_def')).
% 11.99/12.21 tff(204,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[203, 202])).
% 11.99/12.21 tff(205,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[204, 200])).
% 11.99/12.21 tff(206,plain,(
% 11.99/12.21 ![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C))))),
% 11.99/12.21 inference(skolemize,[status(sab)],[205])).
% 11.99/12.21 tff(207,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[206, 199])).
% 11.99/12.21 tff(208,plain,
% 11.99/12.21 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))),
% 11.99/12.21 inference(modus_ponens,[status(thm)],[207, 197])).
% 11.99/12.21 tff(209,plain,
% 11.99/12.21 ((~![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))) | (between_on_line(L!3, A!2, B!1, C!0) <=> ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))))))),
% 11.99/12.21 inference(quant_inst,[status(thm)],[])).
% 11.99/12.21 tff(210,plain,
% 11.99/12.21 (between_on_line(L!3, A!2, B!1, C!0) <=> ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))))),
% 11.99/12.21 inference(unit_resolution,[status(thm)],[209, 208])).
% 11.99/12.21 tff(211,plain,
% 11.99/12.21 (between_on_line(L!3, A!2, B!1, C!0) & between_on_line(L!3, B!1, A!2, C!0)),
% 11.99/12.21 inference(or_elim,[status(thm)],[59])).
% 11.99/12.22 tff(212,plain,
% 11.99/12.22 (between_on_line(L!3, A!2, B!1, C!0)),
% 11.99/12.22 inference(and_elim,[status(thm)],[211])).
% 11.99/12.22 tff(213,plain,
% 11.99/12.22 ((~(between_on_line(L!3, A!2, B!1, C!0) <=> ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))))))) | (~between_on_line(L!3, A!2, B!1, C!0)) | ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))))),
% 11.99/12.22 inference(tautology,[status(thm)],[])).
% 11.99/12.22 tff(214,plain,
% 11.99/12.22 ((~(between_on_line(L!3, A!2, B!1, C!0) <=> ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))))))) | ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[213, 212])).
% 11.99/12.22 tff(215,plain,
% 11.99/12.22 ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[214, 210])).
% 11.99/12.22 tff(216,plain,
% 11.99/12.22 ((~((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))))) | (~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))))),
% 11.99/12.22 inference(tautology,[status(thm)],[])).
% 11.99/12.22 tff(217,plain,
% 11.99/12.22 ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[216, 215])).
% 11.99/12.22 tff(218,plain,
% 11.99/12.22 (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[217, 195])).
% 11.99/12.22 tff(219,plain,
% 11.99/12.22 (((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))) | before_on_line(L!3, B!1, C!0)),
% 11.99/12.22 inference(tautology,[status(thm)],[])).
% 11.99/12.22 tff(220,plain,
% 11.99/12.22 (before_on_line(L!3, B!1, C!0)),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[219, 218])).
% 11.99/12.22 tff(221,plain,
% 11.99/12.22 ((((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)) <=> before_on_line(L!3, B!1, C!0)) | (~((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3))) | (~before_on_line(L!3, B!1, C!0))),
% 11.99/12.22 inference(tautology,[status(thm)],[])).
% 11.99/12.22 tff(222,plain,
% 11.99/12.22 ((((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)) <=> before_on_line(L!3, B!1, C!0)) | (~((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[221, 220])).
% 11.99/12.22 tff(223,plain,
% 11.99/12.22 (~((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[222, 192])).
% 11.99/12.22 tff(224,plain,
% 11.99/12.22 (((~distinct_points(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3)) | (~unequally_directed_lines(L!3, line_connecting(B!1, C!0)))),
% 11.99/12.22 inference(tautology,[status(thm)],[])).
% 11.99/12.22 tff(225,plain,
% 11.99/12.22 (~unequally_directed_lines(L!3, line_connecting(B!1, C!0))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[224, 223])).
% 11.99/12.22 tff(226,plain,
% 11.99/12.22 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(line_connecting(C!0, B!1))))),
% 11.99/12.22 inference(quant_inst,[status(thm)],[])).
% 11.99/12.22 tff(227,plain,
% 11.99/12.22 (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(line_connecting(C!0, B!1)))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[226, 9])).
% 11.99/12.22 tff(228,plain,
% 11.99/12.22 (((~![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, C!0), reverse_line(line_connecting(C!0, B!1))) | (~unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, 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, C!0), reverse_line(line_connecting(C!0, B!1))) | (~unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, C!0))))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(229,plain,
% 11.99/12.22 ((unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(line_connecting(C!0, B!1))) | unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(line_connecting(C!0, B!1))) | (~unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, C!0)))) <=> (unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(line_connecting(C!0, B!1))) | (~unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, C!0))))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(230,plain,
% 11.99/12.22 (((~![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, C!0), reverse_line(line_connecting(C!0, B!1))) | unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(line_connecting(C!0, B!1))) | (~unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, 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, C!0), reverse_line(line_connecting(C!0, B!1))) | (~unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, C!0)))))),
% 11.99/12.22 inference(monotonicity,[status(thm)],[229])).
% 11.99/12.22 tff(231,plain,
% 11.99/12.22 (((~![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, C!0), reverse_line(line_connecting(C!0, B!1))) | unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(line_connecting(C!0, B!1))) | (~unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, 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, C!0), reverse_line(line_connecting(C!0, B!1))) | (~unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, C!0))))),
% 11.99/12.22 inference(transitivity,[status(thm)],[230, 228])).
% 11.99/12.22 tff(232,plain,
% 11.99/12.22 ((~![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, C!0), reverse_line(line_connecting(C!0, B!1))) | unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(line_connecting(C!0, B!1))) | (~unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, C!0))))),
% 11.99/12.22 inference(quant_inst,[status(thm)],[])).
% 11.99/12.22 tff(233,plain,
% 11.99/12.22 ((~![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, C!0), reverse_line(line_connecting(C!0, B!1))) | (~unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, C!0)))),
% 11.99/12.22 inference(modus_ponens,[status(thm)],[232, 231])).
% 11.99/12.22 tff(234,plain,
% 11.99/12.22 (~unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, C!0))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[233, 21, 227])).
% 11.99/12.22 tff(235,plain,
% 11.99/12.22 (((~![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, C!0), line_connecting(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | (~unequally_directed_lines(line_connecting(B!1, C!0), 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(line_connecting(B!1, C!0), line_connecting(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | (~unequally_directed_lines(line_connecting(B!1, C!0), L!3)))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(236,plain,
% 11.99/12.22 ((unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, C!0)) | (~unequally_directed_lines(line_connecting(B!1, C!0), L!3))) <=> (unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | (~unequally_directed_lines(line_connecting(B!1, C!0), L!3)))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(237,plain,
% 11.99/12.22 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, C!0)) | (~unequally_directed_lines(line_connecting(B!1, C!0), 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(line_connecting(B!1, C!0), line_connecting(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | (~unequally_directed_lines(line_connecting(B!1, C!0), L!3))))),
% 11.99/12.22 inference(monotonicity,[status(thm)],[236])).
% 11.99/12.22 tff(238,plain,
% 11.99/12.22 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, C!0)) | (~unequally_directed_lines(line_connecting(B!1, C!0), 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(line_connecting(B!1, C!0), line_connecting(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | (~unequally_directed_lines(line_connecting(B!1, C!0), L!3)))),
% 11.99/12.22 inference(transitivity,[status(thm)],[237, 235])).
% 11.99/12.22 tff(239,plain,
% 11.99/12.22 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | unequally_directed_lines(line_connecting(B!1, C!0), line_connecting(B!1, C!0)) | (~unequally_directed_lines(line_connecting(B!1, C!0), L!3)))),
% 11.99/12.22 inference(quant_inst,[status(thm)],[])).
% 11.99/12.22 tff(240,plain,
% 11.99/12.22 ((~![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, C!0), line_connecting(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | (~unequally_directed_lines(line_connecting(B!1, C!0), L!3))),
% 11.99/12.22 inference(modus_ponens,[status(thm)],[239, 238])).
% 11.99/12.22 tff(241,plain,
% 11.99/12.22 (~unequally_directed_lines(line_connecting(B!1, C!0), L!3)),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[240, 21, 234, 225])).
% 11.99/12.22 tff(242,assumption,(unequally_directed_lines(L!3, L!3)), introduced(assumption)).
% 11.99/12.22 tff(243,plain,
% 11.99/12.22 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(L!3, L!3))),
% 11.99/12.22 inference(quant_inst,[status(thm)],[])).
% 11.99/12.22 tff(244,plain,
% 11.99/12.22 ($false),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[243, 40, 242])).
% 11.99/12.22 tff(245,plain,(~unequally_directed_lines(L!3, L!3)), inference(lemma,lemma(discharge,[]))).
% 11.99/12.22 tff(246,plain,
% 11.99/12.22 (((~unequally_directed_lines(L!3, L!3)) | (~unequally_directed_lines(L!3, reverse_line(L!3)))) | unequally_directed_lines(L!3, L!3)),
% 11.99/12.22 inference(tautology,[status(thm)],[])).
% 11.99/12.22 tff(247,plain,
% 11.99/12.22 ((~unequally_directed_lines(L!3, L!3)) | (~unequally_directed_lines(L!3, reverse_line(L!3)))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[246, 245])).
% 11.99/12.22 tff(248,plain,
% 11.99/12.22 (((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))),
% 11.99/12.22 inference(tautology,[status(thm)],[])).
% 11.99/12.22 tff(249,plain,
% 11.99/12.22 ((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[248, 49])).
% 11.99/12.22 tff(250,plain,
% 11.99/12.22 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!3, reverse_line(L!3)) | unequally_directed_lines(L!3, L!3) | (~line(L!3)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | unequally_directed_lines(L!3, reverse_line(L!3)) | unequally_directed_lines(L!3, L!3) | (~line(L!3)))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(251,plain,
% 11.99/12.22 ((unequally_directed_lines(L!3, reverse_line(L!3)) | unequally_directed_lines(L!3, L!3) | (~line(L!3)) | (~line(L!3))) <=> (unequally_directed_lines(L!3, reverse_line(L!3)) | unequally_directed_lines(L!3, L!3) | (~line(L!3)))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(252,plain,
% 11.99/12.22 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!3, reverse_line(L!3)) | unequally_directed_lines(L!3, L!3) | (~line(L!3)) | (~line(L!3)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!3, reverse_line(L!3)) | unequally_directed_lines(L!3, L!3) | (~line(L!3))))),
% 11.99/12.22 inference(monotonicity,[status(thm)],[251])).
% 11.99/12.22 tff(253,plain,
% 11.99/12.22 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!3, reverse_line(L!3)) | unequally_directed_lines(L!3, L!3) | (~line(L!3)) | (~line(L!3)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | unequally_directed_lines(L!3, reverse_line(L!3)) | unequally_directed_lines(L!3, L!3) | (~line(L!3)))),
% 11.99/12.22 inference(transitivity,[status(thm)],[252, 250])).
% 11.99/12.22 tff(254,plain,
% 11.99/12.22 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!3, reverse_line(L!3)) | unequally_directed_lines(L!3, L!3) | (~line(L!3)) | (~line(L!3)))),
% 11.99/12.22 inference(quant_inst,[status(thm)],[])).
% 11.99/12.22 tff(255,plain,
% 11.99/12.22 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | unequally_directed_lines(L!3, reverse_line(L!3)) | unequally_directed_lines(L!3, L!3) | (~line(L!3))),
% 11.99/12.22 inference(modus_ponens,[status(thm)],[254, 253])).
% 11.99/12.22 tff(256,plain,
% 11.99/12.22 (unequally_directed_lines(L!3, reverse_line(L!3)) | unequally_directed_lines(L!3, L!3)),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[255, 88, 61])).
% 11.99/12.22 tff(257,plain,
% 11.99/12.22 (unequally_directed_lines(L!3, reverse_line(L!3))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[256, 245])).
% 11.99/12.22 tff(258,plain,
% 11.99/12.22 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~((~unequally_directed_lines(L!3, L!3)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!3, reverse_line(L!3))) | (~((~unequally_directed_lines(L!3, L!3)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(259,plain,
% 11.99/12.22 (((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~((~unequally_directed_lines(L!3, L!3)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))))) <=> ((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~((~unequally_directed_lines(L!3, L!3)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(260,plain,
% 11.99/12.22 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~((~unequally_directed_lines(L!3, L!3)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~((~unequally_directed_lines(L!3, L!3)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))))))),
% 11.99/12.22 inference(monotonicity,[status(thm)],[259])).
% 11.99/12.22 tff(261,plain,
% 11.99/12.22 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~((~unequally_directed_lines(L!3, L!3)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!3, reverse_line(L!3))) | (~((~unequally_directed_lines(L!3, L!3)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))),
% 11.99/12.22 inference(transitivity,[status(thm)],[260, 258])).
% 11.99/12.22 tff(262,plain,
% 11.99/12.22 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~((~unequally_directed_lines(L!3, L!3)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))),
% 11.99/12.22 inference(quant_inst,[status(thm)],[])).
% 11.99/12.22 tff(263,plain,
% 11.99/12.22 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!3, reverse_line(L!3))) | (~((~unequally_directed_lines(L!3, L!3)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))))),
% 11.99/12.22 inference(modus_ponens,[status(thm)],[262, 261])).
% 11.99/12.22 tff(264,plain,
% 11.99/12.22 (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[263, 109, 257, 249, 247])).
% 11.99/12.22 tff(265,plain,
% 11.99/12.22 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), 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(L!3, reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3)))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(266,plain,
% 11.99/12.22 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3)))),
% 11.99/12.22 inference(quant_inst,[status(thm)],[])).
% 11.99/12.22 tff(267,plain,
% 11.99/12.22 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3))),
% 11.99/12.22 inference(modus_ponens,[status(thm)],[266, 265])).
% 11.99/12.22 tff(268,plain,
% 11.99/12.22 (~unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3)),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[267, 21, 264, 43])).
% 11.99/12.22 tff(269,plain,
% 11.99/12.22 (((~![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, C!0), L!3) | unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | (~unequally_directed_lines(line_connecting(B!1, C!0), 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(line_connecting(B!1, C!0), L!3) | unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(270,plain,
% 11.99/12.22 ((unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | unequally_directed_lines(line_connecting(B!1, C!0), L!3) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3))))) <=> (unequally_directed_lines(line_connecting(B!1, C!0), L!3) | unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(271,plain,
% 11.99/12.22 (((~![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)), L!3) | unequally_directed_lines(line_connecting(B!1, C!0), L!3) | (~unequally_directed_lines(line_connecting(B!1, C!0), 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(line_connecting(B!1, C!0), L!3) | unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3))))))),
% 11.99/12.22 inference(monotonicity,[status(thm)],[270])).
% 11.99/12.22 tff(272,plain,
% 11.99/12.22 (((~![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)), L!3) | unequally_directed_lines(line_connecting(B!1, C!0), L!3) | (~unequally_directed_lines(line_connecting(B!1, C!0), 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(line_connecting(B!1, C!0), L!3) | unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))))),
% 11.99/12.22 inference(transitivity,[status(thm)],[271, 269])).
% 11.99/12.22 tff(273,plain,
% 11.99/12.22 ((~![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)), L!3) | unequally_directed_lines(line_connecting(B!1, C!0), L!3) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))))),
% 11.99/12.22 inference(quant_inst,[status(thm)],[])).
% 11.99/12.22 tff(274,plain,
% 11.99/12.22 ((~![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, C!0), L!3) | unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3))))),
% 11.99/12.22 inference(modus_ponens,[status(thm)],[273, 272])).
% 11.99/12.22 tff(275,plain,
% 11.99/12.22 (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[274, 21, 268, 241])).
% 11.99/12.22 tff(276,plain,
% 11.99/12.22 (((~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3))))) | unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))),
% 11.99/12.22 inference(tautology,[status(thm)],[])).
% 11.99/12.22 tff(277,plain,
% 11.99/12.22 ((~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3))))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[276, 275])).
% 11.99/12.22 tff(278,plain,
% 11.99/12.22 (((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0))) | before_on_line(L!3, B!1, A!2)),
% 11.99/12.22 inference(tautology,[status(thm)],[])).
% 11.99/12.22 tff(279,plain,
% 11.99/12.22 ((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0))),
% 11.99/12.22 inference(unit_resolution,[status(thm)],[278, 193])).
% 11.99/12.22 tff(280,plain,
% 11.99/12.22 (((~![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))) | (between_on_line(L!3, B!1, A!2, C!0) <=> ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0))))))) <=> ((~![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))) | (between_on_line(L!3, B!1, A!2, C!0) <=> ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0)))))))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(281,plain,
% 11.99/12.22 ((between_on_line(L!3, B!1, A!2, C!0) <=> ((~((~before_on_line(L!3, C!0, A!2)) | (~before_on_line(L!3, A!2, B!1)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0)))))) <=> (between_on_line(L!3, B!1, A!2, C!0) <=> ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0))))))),
% 11.99/12.22 inference(rewrite,[status(thm)],[])).
% 11.99/12.22 tff(282,plain,
% 11.99/12.22 (((~![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))) | (between_on_line(L!3, B!1, A!2, C!0) <=> ((~((~before_on_line(L!3, C!0, A!2)) | (~before_on_line(L!3, A!2, B!1)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0))))))) <=> ((~![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))) | (between_on_line(L!3, B!1, A!2, C!0) <=> ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0)))))))),
% 11.99/12.22 inference(monotonicity,[status(thm)],[281])).
% 11.99/12.22 tff(283,plain,
% 11.99/12.22 (((~![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))) | (between_on_line(L!3, B!1, A!2, C!0) <=> ((~((~before_on_line(L!3, C!0, A!2)) | (~before_on_line(L!3, A!2, B!1)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0))))))) <=> ((~![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))) | (between_on_line(L!3, B!1, A!2, C!0) <=> ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0)))))))),
% 11.99/12.22 inference(transitivity,[status(thm)],[282, 280])).
% 11.99/12.22 tff(284,plain,
% 11.99/12.22 ((~![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))) | (between_on_line(L!3, B!1, A!2, C!0) <=> ((~((~before_on_line(L!3, C!0, A!2)) | (~before_on_line(L!3, A!2, B!1)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0))))))),
% 11.99/12.22 inference(quant_inst,[status(thm)],[])).
% 11.99/12.22 tff(285,plain,
% 11.99/12.22 ((~![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))) | (between_on_line(L!3, B!1, A!2, C!0) <=> ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0))))))),
% 11.99/12.23 inference(modus_ponens,[status(thm)],[284, 283])).
% 11.99/12.23 tff(286,plain,
% 11.99/12.23 (between_on_line(L!3, B!1, A!2, C!0) <=> ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0)))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[285, 208])).
% 11.99/12.23 tff(287,plain,
% 11.99/12.23 (between_on_line(L!3, B!1, A!2, C!0)),
% 11.99/12.23 inference(and_elim,[status(thm)],[211])).
% 11.99/12.23 tff(288,plain,
% 11.99/12.23 ((~(between_on_line(L!3, B!1, A!2, C!0) <=> ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0))))))) | (~between_on_line(L!3, B!1, A!2, C!0)) | ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0)))))),
% 11.99/12.23 inference(tautology,[status(thm)],[])).
% 11.99/12.23 tff(289,plain,
% 11.99/12.23 ((~(between_on_line(L!3, B!1, A!2, C!0) <=> ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0))))))) | ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0)))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[288, 287])).
% 11.99/12.23 tff(290,plain,
% 11.99/12.23 ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[289, 286])).
% 11.99/12.23 tff(291,plain,
% 11.99/12.23 ((~((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0)))))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0))))),
% 11.99/12.23 inference(tautology,[status(thm)],[])).
% 11.99/12.23 tff(292,plain,
% 11.99/12.23 ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))) | (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0))))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[291, 290])).
% 11.99/12.23 tff(293,plain,
% 11.99/12.23 (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2)))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[292, 279])).
% 11.99/12.23 tff(294,plain,
% 11.99/12.23 (((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2))) | before_on_line(L!3, C!0, A!2)),
% 11.99/12.23 inference(tautology,[status(thm)],[])).
% 11.99/12.23 tff(295,plain,
% 11.99/12.23 (before_on_line(L!3, C!0, A!2)),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[294, 293])).
% 11.99/12.23 tff(296,assumption,(((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2)), introduced(assumption)).
% 11.99/12.23 tff(297,plain,
% 11.99/12.23 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2))))),
% 11.99/12.23 inference(rewrite,[status(thm)],[])).
% 11.99/12.23 tff(298,plain,
% 11.99/12.23 ((~(((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2))) <=> (~(((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2)))),
% 11.99/12.23 inference(rewrite,[status(thm)],[])).
% 11.99/12.23 tff(299,plain,
% 11.99/12.23 (((unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | (~distinct_points(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2)) <=> (((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2))),
% 11.99/12.23 inference(rewrite,[status(thm)],[])).
% 11.99/12.23 tff(300,plain,
% 11.99/12.23 ((~((unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | (~distinct_points(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2))) <=> (~(((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2)))),
% 11.99/12.23 inference(monotonicity,[status(thm)],[299])).
% 11.99/12.23 tff(301,plain,
% 11.99/12.23 ((~((unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | (~distinct_points(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2))) <=> (~(((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2)))),
% 11.99/12.23 inference(transitivity,[status(thm)],[300, 298])).
% 11.99/12.23 tff(302,plain,
% 11.99/12.23 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | (~distinct_points(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2))))),
% 11.99/12.23 inference(monotonicity,[status(thm)],[301])).
% 11.99/12.23 tff(303,plain,
% 11.99/12.23 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | (~distinct_points(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2))))),
% 11.99/12.23 inference(transitivity,[status(thm)],[302, 297])).
% 11.99/12.23 tff(304,plain,
% 11.99/12.23 ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | (~distinct_points(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2)))),
% 11.99/12.23 inference(quant_inst,[status(thm)],[])).
% 11.99/12.23 tff(305,plain,
% 11.99/12.23 ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2)))),
% 11.99/12.23 inference(modus_ponens,[status(thm)],[304, 303])).
% 11.99/12.23 tff(306,plain,
% 11.99/12.23 ($false),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[305, 182, 296])).
% 11.99/12.23 tff(307,plain,(~(((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2))), inference(lemma,lemma(discharge,[]))).
% 11.99/12.23 tff(308,plain,
% 11.99/12.23 ((((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))) <=> before_on_line(L!3, C!0, A!2)) | (~((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2)))) | (~before_on_line(L!3, C!0, A!2))),
% 11.99/12.23 inference(tautology,[status(thm)],[])).
% 11.99/12.23 tff(309,plain,
% 11.99/12.23 ((~((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2)))) | (~before_on_line(L!3, C!0, A!2))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[308, 307])).
% 11.99/12.23 tff(310,plain,
% 11.99/12.23 (~((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2)))),
% 11.99/12.23 inference(unit_resolution,[status(thm)],[309, 295])).
% 11.99/12.23 tff(311,plain,
% 11.99/12.23 (((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))) | (~unequally_directed_lines(L!3, line_connecting(C!0, A!2)))),
% 12.07/12.23 inference(tautology,[status(thm)],[])).
% 12.07/12.23 tff(312,plain,
% 12.07/12.23 (~unequally_directed_lines(L!3, line_connecting(C!0, A!2))),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[311, 310])).
% 12.07/12.23 tff(313,assumption,(~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2))), introduced(assumption)).
% 12.07/12.23 tff(314,assumption,(unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3))))), introduced(assumption)).
% 12.07/12.23 tff(315,plain,
% 12.07/12.23 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))))),
% 12.07/12.23 inference(quant_inst,[status(thm)],[])).
% 12.07/12.23 tff(316,plain,
% 12.07/12.23 ($false),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[315, 40, 314])).
% 12.07/12.23 tff(317,plain,(~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3))))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.23 tff(318,plain,
% 12.07/12.23 (((~![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(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(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(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))))),
% 12.07/12.23 inference(rewrite,[status(thm)],[])).
% 12.07/12.23 tff(319,plain,
% 12.07/12.23 ((~![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(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))))),
% 12.07/12.23 inference(quant_inst,[status(thm)],[])).
% 12.07/12.23 tff(320,plain,
% 12.07/12.23 ((~![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(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3)))),
% 12.07/12.23 inference(modus_ponens,[status(thm)],[319, 318])).
% 12.07/12.23 tff(321,plain,
% 12.07/12.23 (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[320, 21, 317, 116])).
% 12.07/12.23 tff(322,plain,
% 12.07/12.23 (((~![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))))),
% 12.07/12.23 inference(rewrite,[status(thm)],[])).
% 12.07/12.23 tff(323,plain,
% 12.07/12.23 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | (line(reverse_line(reverse_line(L!3))) | (~line(reverse_line(L!3))))),
% 12.07/12.23 inference(quant_inst,[status(thm)],[])).
% 12.07/12.23 tff(324,plain,
% 12.07/12.23 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | line(reverse_line(reverse_line(L!3))) | (~line(reverse_line(L!3)))),
% 12.07/12.23 inference(modus_ponens,[status(thm)],[323, 322])).
% 12.07/12.23 tff(325,plain,
% 12.07/12.23 (line(reverse_line(reverse_line(L!3))) | (~line(reverse_line(L!3)))),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[324, 71])).
% 12.07/12.23 tff(326,plain,
% 12.07/12.23 (line(reverse_line(reverse_line(L!3)))),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[325, 75])).
% 12.07/12.23 tff(327,plain,
% 12.07/12.23 (((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | (line(reverse_line(reverse_line(reverse_line(L!3)))) | (~line(reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | line(reverse_line(reverse_line(reverse_line(L!3)))) | (~line(reverse_line(reverse_line(L!3)))))),
% 12.07/12.23 inference(rewrite,[status(thm)],[])).
% 12.07/12.23 tff(328,plain,
% 12.07/12.23 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | (line(reverse_line(reverse_line(reverse_line(L!3)))) | (~line(reverse_line(reverse_line(L!3)))))),
% 12.07/12.23 inference(quant_inst,[status(thm)],[])).
% 12.07/12.23 tff(329,plain,
% 12.07/12.23 ((~![L: $i] : (line(reverse_line(L)) | (~line(L)))) | line(reverse_line(reverse_line(reverse_line(L!3)))) | (~line(reverse_line(reverse_line(L!3))))),
% 12.07/12.23 inference(modus_ponens,[status(thm)],[328, 327])).
% 12.07/12.23 tff(330,plain,
% 12.07/12.23 (line(reverse_line(reverse_line(reverse_line(L!3)))) | (~line(reverse_line(reverse_line(L!3))))),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[329, 71])).
% 12.07/12.23 tff(331,plain,
% 12.07/12.23 (line(reverse_line(reverse_line(reverse_line(L!3))))),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[330, 326])).
% 12.07/12.23 tff(332,plain,
% 12.07/12.23 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | ((~line(L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3) | (~line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(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(L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3) | (~line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3)))),
% 12.07/12.23 inference(rewrite,[status(thm)],[])).
% 12.07/12.23 tff(333,plain,
% 12.07/12.23 ((unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3) | (~line(L!3)) | (~line(reverse_line(reverse_line(reverse_line(L!3)))))) <=> ((~line(L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3) | (~line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3)))),
% 12.07/12.23 inference(rewrite,[status(thm)],[])).
% 12.07/12.23 tff(334,plain,
% 12.07/12.23 (((~![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(reverse_line(L!3))), reverse_line(L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3) | (~line(L!3)) | (~line(reverse_line(reverse_line(reverse_line(L!3))))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | ((~line(L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3) | (~line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))))),
% 12.07/12.23 inference(monotonicity,[status(thm)],[333])).
% 12.07/12.23 tff(335,plain,
% 12.07/12.23 (((~![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(reverse_line(L!3))), reverse_line(L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3) | (~line(L!3)) | (~line(reverse_line(reverse_line(reverse_line(L!3))))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (~line(L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3) | (~line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3)))),
% 12.07/12.23 inference(transitivity,[status(thm)],[334, 332])).
% 12.07/12.23 tff(336,plain,
% 12.07/12.23 ((~![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(reverse_line(L!3))), reverse_line(L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3) | (~line(L!3)) | (~line(reverse_line(reverse_line(reverse_line(L!3))))))),
% 12.07/12.23 inference(quant_inst,[status(thm)],[])).
% 12.07/12.23 tff(337,plain,
% 12.07/12.23 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (~line(L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3) | (~line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))),
% 12.07/12.23 inference(modus_ponens,[status(thm)],[336, 335])).
% 12.07/12.23 tff(338,plain,
% 12.07/12.23 (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[337, 88, 61, 331])).
% 12.07/12.23 tff(339,plain,
% 12.07/12.23 (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3)),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[338, 321])).
% 12.07/12.23 tff(340,assumption,(~unequally_directed_lines(L!3, line_connecting(C!0, A!2))), introduced(assumption)).
% 12.07/12.23 tff(341,plain,
% 12.07/12.23 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2)))),
% 12.07/12.23 inference(rewrite,[status(thm)],[])).
% 12.07/12.23 tff(342,plain,
% 12.07/12.23 ((unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3))) <=> (unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2)))),
% 12.07/12.23 inference(rewrite,[status(thm)],[])).
% 12.07/12.23 tff(343,plain,
% 12.07/12.23 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), 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(L!3, line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2))))),
% 12.07/12.23 inference(monotonicity,[status(thm)],[342])).
% 12.07/12.23 tff(344,plain,
% 12.07/12.23 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), 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(L!3, line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2)))),
% 12.07/12.23 inference(transitivity,[status(thm)],[343, 341])).
% 12.07/12.23 tff(345,plain,
% 12.07/12.23 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3)))),
% 12.07/12.23 inference(quant_inst,[status(thm)],[])).
% 12.07/12.23 tff(346,plain,
% 12.07/12.23 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), L!3)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2))),
% 12.07/12.23 inference(modus_ponens,[status(thm)],[345, 344])).
% 12.07/12.23 tff(347,plain,
% 12.07/12.23 ($false),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[346, 21, 340, 339, 313])).
% 12.07/12.23 tff(348,plain,(unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2)) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.23 tff(349,plain,
% 12.07/12.23 (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2))),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[348, 312])).
% 12.07/12.23 tff(350,assumption,(~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0)))), introduced(assumption)).
% 12.07/12.23 tff(351,assumption,(unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2))), introduced(assumption)).
% 12.07/12.23 tff(352,plain,
% 12.07/12.23 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))))),
% 12.07/12.23 inference(quant_inst,[status(thm)],[])).
% 12.07/12.23 tff(353,plain,
% 12.07/12.23 (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0)))),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[352, 9])).
% 12.07/12.23 tff(354,plain,
% 12.07/12.23 (((~![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(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2))))),
% 12.07/12.23 inference(rewrite,[status(thm)],[])).
% 12.07/12.23 tff(355,plain,
% 12.07/12.23 ((~![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(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2))))),
% 12.07/12.23 inference(quant_inst,[status(thm)],[])).
% 12.07/12.23 tff(356,plain,
% 12.07/12.23 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2)))),
% 12.07/12.23 inference(modus_ponens,[status(thm)],[355, 354])).
% 12.07/12.23 tff(357,plain,
% 12.07/12.23 ($false),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[356, 21, 353, 351, 350])).
% 12.07/12.23 tff(358,plain,(unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2)))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.23 tff(359,plain,
% 12.07/12.23 (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0)))),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[358, 349])).
% 12.07/12.23 tff(360,assumption,(unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0)))), introduced(assumption)).
% 12.07/12.23 tff(361,plain,
% 12.07/12.23 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, 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(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0)))))),
% 12.07/12.23 inference(rewrite,[status(thm)],[])).
% 12.07/12.23 tff(362,plain,
% 12.07/12.23 ((unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))))) <=> (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0)))))),
% 12.07/12.23 inference(rewrite,[status(thm)],[])).
% 12.07/12.23 tff(363,plain,
% 12.07/12.23 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, 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(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))))))),
% 12.07/12.23 inference(monotonicity,[status(thm)],[362])).
% 12.07/12.23 tff(364,plain,
% 12.07/12.23 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, 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(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0)))))),
% 12.07/12.23 inference(transitivity,[status(thm)],[363, 361])).
% 12.07/12.23 tff(365,plain,
% 12.07/12.23 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0)))))),
% 12.07/12.23 inference(quant_inst,[status(thm)],[])).
% 12.07/12.23 tff(366,plain,
% 12.07/12.23 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))))),
% 12.07/12.23 inference(modus_ponens,[status(thm)],[365, 364])).
% 12.07/12.23 tff(367,plain,
% 12.07/12.23 ($false),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[366, 21, 317, 32, 360])).
% 12.07/12.23 tff(368,plain,(unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.23 tff(369,plain,
% 12.07/12.23 (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[368, 359])).
% 12.07/12.23 tff(370,plain,
% 12.07/12.23 (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))),
% 12.07/12.23 inference(unit_resolution,[status(thm)],[158, 369])).
% 12.07/12.23 tff(371,plain,
% 12.07/12.23 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, 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(L!3, reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))))),
% 12.07/12.23 inference(rewrite,[status(thm)],[])).
% 12.07/12.23 tff(372,plain,
% 12.07/12.23 ((unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))))) <=> (unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))))),
% 12.07/12.24 inference(rewrite,[status(thm)],[])).
% 12.07/12.24 tff(373,plain,
% 12.07/12.24 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, 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(L!3, reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))))))),
% 12.07/12.24 inference(monotonicity,[status(thm)],[372])).
% 12.07/12.24 tff(374,plain,
% 12.07/12.24 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, 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(L!3, reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))))),
% 12.07/12.24 inference(transitivity,[status(thm)],[373, 371])).
% 12.07/12.24 tff(375,plain,
% 12.07/12.24 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))))),
% 12.07/12.24 inference(quant_inst,[status(thm)],[])).
% 12.07/12.24 tff(376,plain,
% 12.07/12.24 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))))),
% 12.07/12.24 inference(modus_ponens,[status(thm)],[375, 374])).
% 12.07/12.24 tff(377,plain,
% 12.07/12.24 (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))),
% 12.07/12.24 inference(unit_resolution,[status(thm)],[376, 21, 264, 370])).
% 12.07/12.24 tff(378,assumption,(~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))), introduced(assumption)).
% 12.07/12.24 tff(379,assumption,(unequally_directed_lines(L!3, line_connecting(C!0, B!1))), introduced(assumption)).
% 12.07/12.24 tff(380,plain,
% 12.07/12.24 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(L!3, line_connecting(C!0, B!1))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, 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(L!3, line_connecting(C!0, B!1))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0))))),
% 12.07/12.24 inference(rewrite,[status(thm)],[])).
% 12.07/12.24 tff(381,plain,
% 12.07/12.24 ((unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, B!1)))) <=> ((~unequally_directed_lines(L!3, line_connecting(C!0, B!1))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0))))),
% 12.07/12.24 inference(rewrite,[status(thm)],[])).
% 12.07/12.24 tff(382,plain,
% 12.07/12.24 (((~![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(C!0, B!1), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(L!3, line_connecting(C!0, B!1))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0)))))),
% 12.07/12.24 inference(monotonicity,[status(thm)],[381])).
% 12.07/12.24 tff(383,plain,
% 12.07/12.24 (((~![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(C!0, B!1), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!3, line_connecting(C!0, B!1))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0))))),
% 12.07/12.24 inference(transitivity,[status(thm)],[382, 380])).
% 12.07/12.24 tff(384,plain,
% 12.07/12.24 ((~![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(C!0, B!1), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, B!1))))),
% 12.07/12.24 inference(quant_inst,[status(thm)],[])).
% 12.07/12.24 tff(385,plain,
% 12.07/12.24 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!3, line_connecting(C!0, B!1))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0)))),
% 12.07/12.24 inference(modus_ponens,[status(thm)],[384, 383])).
% 12.07/12.24 tff(386,plain,
% 12.07/12.24 ($false),
% 12.07/12.24 inference(unit_resolution,[status(thm)],[385, 21, 379, 378, 169])).
% 12.07/12.24 tff(387,plain,(unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, B!1))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.24 tff(388,plain,
% 12.07/12.24 (~unequally_directed_lines(L!3, line_connecting(C!0, B!1))),
% 12.07/12.24 inference(unit_resolution,[status(thm)],[387, 377, 169])).
% 12.07/12.24 tff(389,assumption,(~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1))), introduced(assumption)).
% 12.07/12.24 tff(390,plain,
% 12.07/12.24 (((~![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))) | (~line(L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | unequally_directed_lines(reverse_line(L!3), 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))) | (~line(L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | unequally_directed_lines(reverse_line(L!3), L!3))),
% 12.07/12.24 inference(rewrite,[status(thm)],[])).
% 12.07/12.24 tff(391,plain,
% 12.07/12.24 ((unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | unequally_directed_lines(reverse_line(L!3), L!3) | (~line(L!3)) | (~line(reverse_line(L!3)))) <=> ((~line(reverse_line(L!3))) | (~line(L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | unequally_directed_lines(reverse_line(L!3), L!3))),
% 12.07/12.24 inference(rewrite,[status(thm)],[])).
% 12.07/12.24 tff(392,plain,
% 12.07/12.24 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | unequally_directed_lines(reverse_line(L!3), L!3) | (~line(L!3)) | (~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))) | (~line(L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | unequally_directed_lines(reverse_line(L!3), L!3)))),
% 12.07/12.24 inference(monotonicity,[status(thm)],[391])).
% 12.07/12.24 tff(393,plain,
% 12.07/12.24 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | unequally_directed_lines(reverse_line(L!3), L!3) | (~line(L!3)) | (~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))) | (~line(L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | unequally_directed_lines(reverse_line(L!3), L!3))),
% 12.07/12.24 inference(transitivity,[status(thm)],[392, 390])).
% 12.07/12.24 tff(394,plain,
% 12.07/12.24 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | unequally_directed_lines(reverse_line(L!3), L!3) | (~line(L!3)) | (~line(reverse_line(L!3))))),
% 12.07/12.24 inference(quant_inst,[status(thm)],[])).
% 12.07/12.24 tff(395,plain,
% 12.07/12.24 ((~![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))) | (~line(L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | unequally_directed_lines(reverse_line(L!3), L!3)),
% 12.07/12.24 inference(modus_ponens,[status(thm)],[394, 393])).
% 12.07/12.24 tff(396,plain,
% 12.07/12.24 ((~line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), L!3)),
% 12.07/12.24 inference(unit_resolution,[status(thm)],[395, 88, 61, 49])).
% 12.07/12.24 tff(397,plain,
% 12.07/12.24 (unequally_directed_lines(reverse_line(L!3), L!3)),
% 12.07/12.24 inference(unit_resolution,[status(thm)],[396, 75])).
% 12.07/12.24 tff(398,assumption,(~unequally_directed_lines(L!3, line_connecting(C!0, B!1))), introduced(assumption)).
% 12.07/12.24 tff(399,plain,
% 12.07/12.24 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1)))),
% 12.07/12.24 inference(rewrite,[status(thm)],[])).
% 12.07/12.24 tff(400,plain,
% 12.07/12.24 ((unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1)) | (~unequally_directed_lines(reverse_line(L!3), L!3))) <=> (unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1)))),
% 12.07/12.24 inference(rewrite,[status(thm)],[])).
% 12.07/12.24 tff(401,plain,
% 12.07/12.24 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1)) | (~unequally_directed_lines(reverse_line(L!3), 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(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1))))),
% 12.07/12.24 inference(monotonicity,[status(thm)],[400])).
% 12.07/12.24 tff(402,plain,
% 12.07/12.24 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1)) | (~unequally_directed_lines(reverse_line(L!3), 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(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1)))),
% 12.07/12.24 inference(transitivity,[status(thm)],[401, 399])).
% 12.07/12.24 tff(403,plain,
% 12.07/12.24 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1)) | (~unequally_directed_lines(reverse_line(L!3), L!3)))),
% 12.07/12.24 inference(quant_inst,[status(thm)],[])).
% 12.07/12.24 tff(404,plain,
% 12.07/12.24 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1))),
% 12.07/12.24 inference(modus_ponens,[status(thm)],[403, 402])).
% 12.07/12.24 tff(405,plain,
% 12.07/12.24 ($false),
% 12.07/12.24 inference(unit_resolution,[status(thm)],[404, 21, 398, 397, 389])).
% 12.07/12.24 tff(406,plain,(unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1)) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.24 tff(407,plain,
% 12.07/12.24 (unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1))),
% 12.07/12.24 inference(unit_resolution,[status(thm)],[406, 388])).
% 12.07/12.24 tff(408,assumption,(~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0)))), introduced(assumption)).
% 12.07/12.24 tff(409,assumption,(unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1))), introduced(assumption)).
% 12.07/12.24 tff(410,plain,
% 12.07/12.24 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0))))),
% 12.07/12.24 inference(quant_inst,[status(thm)],[])).
% 12.07/12.24 tff(411,plain,
% 12.07/12.24 (~unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0)))),
% 12.07/12.24 inference(unit_resolution,[status(thm)],[410, 9])).
% 12.07/12.24 tff(412,plain,
% 12.07/12.24 (((~![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(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1))))),
% 12.07/12.24 inference(rewrite,[status(thm)],[])).
% 12.07/12.24 tff(413,plain,
% 12.07/12.24 ((~![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(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1))))),
% 12.07/12.24 inference(quant_inst,[status(thm)],[])).
% 12.07/12.24 tff(414,plain,
% 12.07/12.24 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1)))),
% 12.07/12.24 inference(modus_ponens,[status(thm)],[413, 412])).
% 12.07/12.24 tff(415,plain,
% 12.07/12.24 ($false),
% 12.07/12.24 inference(unit_resolution,[status(thm)],[414, 21, 411, 409, 408])).
% 12.07/12.24 tff(416,plain,(unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, B!1)))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.24 tff(417,plain,
% 12.07/12.24 (unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0)))),
% 12.07/12.24 inference(unit_resolution,[status(thm)],[416, 407])).
% 12.07/12.24 tff(418,assumption,(~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0))), introduced(assumption)).
% 12.07/12.24 tff(419,assumption,(~unequally_directed_lines(L!3, line_connecting(B!1, C!0))), introduced(assumption)).
% 12.07/12.24 tff(420,plain,
% 12.07/12.24 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, 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(L!3, line_connecting(B!1, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0)))),
% 12.07/12.24 inference(rewrite,[status(thm)],[])).
% 12.07/12.24 tff(421,plain,
% 12.07/12.24 ((unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3))) <=> (unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0)))),
% 12.07/12.24 inference(rewrite,[status(thm)],[])).
% 12.07/12.24 tff(422,plain,
% 12.07/12.24 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0)) | (~unequally_directed_lines(reverse_line(L!3), 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(L!3, line_connecting(B!1, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0))))),
% 12.07/12.24 inference(monotonicity,[status(thm)],[421])).
% 12.07/12.24 tff(423,plain,
% 12.07/12.24 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0)) | (~unequally_directed_lines(reverse_line(L!3), 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(L!3, line_connecting(B!1, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0)))),
% 12.07/12.24 inference(transitivity,[status(thm)],[422, 420])).
% 12.07/12.24 tff(424,plain,
% 12.07/12.24 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3)))),
% 12.07/12.24 inference(quant_inst,[status(thm)],[])).
% 12.07/12.24 tff(425,plain,
% 12.07/12.24 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, line_connecting(B!1, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0))),
% 12.07/12.24 inference(modus_ponens,[status(thm)],[424, 423])).
% 12.07/12.24 tff(426,plain,
% 12.07/12.24 ($false),
% 12.07/12.24 inference(unit_resolution,[status(thm)],[425, 21, 397, 419, 418])).
% 12.07/12.24 tff(427,plain,(unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0)) | unequally_directed_lines(L!3, line_connecting(B!1, C!0))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.24 tff(428,plain,
% 12.07/12.24 (unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0))),
% 12.07/12.24 inference(unit_resolution,[status(thm)],[427, 225])).
% 12.07/12.24 tff(429,plain,
% 12.07/12.24 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0))))),
% 12.07/12.24 inference(rewrite,[status(thm)],[])).
% 12.07/12.24 tff(430,plain,
% 12.07/12.24 (((~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0))) | (~((~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0))))) <=> ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0))))),
% 12.07/12.24 inference(rewrite,[status(thm)],[])).
% 12.07/12.24 tff(431,plain,
% 12.07/12.24 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0))) | (~((~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0)))))),
% 12.07/12.24 inference(monotonicity,[status(thm)],[430])).
% 12.07/12.24 tff(432,plain,
% 12.07/12.24 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0))) | (~((~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0))))),
% 12.07/12.24 inference(transitivity,[status(thm)],[431, 429])).
% 12.07/12.24 tff(433,plain,
% 12.07/12.24 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0))) | (~((~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0)))))),
% 12.07/12.24 inference(quant_inst,[status(thm)],[])).
% 12.07/12.24 tff(434,plain,
% 12.07/12.24 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(B!1, C!0), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, C!0)))),
% 12.07/12.24 inference(modus_ponens,[status(thm)],[433, 432])).
% 12.07/12.24 tff(435,plain,
% 12.07/12.24 ($false),
% 12.07/12.24 inference(unit_resolution,[status(thm)],[434, 109, 51, 428, 417, 277])).
% 12.07/12.24 tff(436,plain,(before_on_line(L!3, B!1, A!2) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0)))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.24 tff(437,plain,
% 12.07/12.24 (before_on_line(L!3, B!1, A!2)),
% 12.07/12.24 inference(unit_resolution,[status(thm)],[436, 169])).
% 12.07/12.24 tff(438,assumption,(((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2)), introduced(assumption)).
% 12.07/12.24 tff(439,plain,
% 12.07/12.24 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2))))),
% 12.07/12.24 inference(rewrite,[status(thm)],[])).
% 12.07/12.24 tff(440,plain,
% 12.07/12.24 ((~(((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2))) <=> (~(((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2)))),
% 12.07/12.24 inference(rewrite,[status(thm)],[])).
% 12.07/12.24 tff(441,plain,
% 12.07/12.24 (((unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | (~distinct_points(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2)) <=> (((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2))),
% 12.07/12.25 inference(rewrite,[status(thm)],[])).
% 12.07/12.25 tff(442,plain,
% 12.07/12.25 ((~((unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | (~distinct_points(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2))) <=> (~(((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2)))),
% 12.07/12.25 inference(monotonicity,[status(thm)],[441])).
% 12.07/12.25 tff(443,plain,
% 12.07/12.25 ((~((unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | (~distinct_points(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2))) <=> (~(((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2)))),
% 12.07/12.25 inference(transitivity,[status(thm)],[442, 440])).
% 12.07/12.25 tff(444,plain,
% 12.07/12.25 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | (~distinct_points(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2))))),
% 12.07/12.25 inference(monotonicity,[status(thm)],[443])).
% 12.07/12.25 tff(445,plain,
% 12.07/12.25 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | (~distinct_points(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2))))),
% 12.07/12.25 inference(transitivity,[status(thm)],[444, 439])).
% 12.07/12.25 tff(446,plain,
% 12.07/12.25 ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | (~distinct_points(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2)))),
% 12.07/12.25 inference(quant_inst,[status(thm)],[])).
% 12.07/12.25 tff(447,plain,
% 12.07/12.25 ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2)))),
% 12.07/12.25 inference(modus_ponens,[status(thm)],[446, 445])).
% 12.07/12.25 tff(448,plain,
% 12.07/12.25 ($false),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[447, 182, 438])).
% 12.07/12.25 tff(449,plain,(~(((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.25 tff(450,plain,
% 12.07/12.25 ((((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2))) <=> before_on_line(L!3, B!1, A!2)) | (~((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2)))) | (~before_on_line(L!3, B!1, A!2))),
% 12.07/12.25 inference(tautology,[status(thm)],[])).
% 12.07/12.25 tff(451,plain,
% 12.07/12.25 ((~((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2)))) | (~before_on_line(L!3, B!1, A!2))),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[450, 449])).
% 12.07/12.25 tff(452,plain,
% 12.07/12.25 (~((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2)))),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[451, 437])).
% 12.07/12.25 tff(453,plain,
% 12.07/12.25 (((~distinct_points(B!1, A!2)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!3, line_connecting(B!1, A!2)))),
% 12.07/12.25 inference(tautology,[status(thm)],[])).
% 12.07/12.25 tff(454,plain,
% 12.07/12.25 (~unequally_directed_lines(L!3, line_connecting(B!1, A!2))),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[453, 452])).
% 12.07/12.25 tff(455,assumption,(~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2))), introduced(assumption)).
% 12.07/12.25 tff(456,assumption,(unequally_directed_lines(L!3, reverse_line(L!3))), introduced(assumption)).
% 12.07/12.25 tff(457,assumption,(~unequally_directed_lines(L!3, line_connecting(B!1, A!2))), introduced(assumption)).
% 12.07/12.25 tff(458,plain,
% 12.07/12.25 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | (~unequally_directed_lines(L!3, reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | (~unequally_directed_lines(L!3, reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2)))),
% 12.07/12.25 inference(rewrite,[status(thm)],[])).
% 12.07/12.25 tff(459,plain,
% 12.07/12.25 ((unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2)) | unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | (~unequally_directed_lines(L!3, reverse_line(L!3)))) <=> (unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | (~unequally_directed_lines(L!3, reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2)))),
% 12.07/12.25 inference(rewrite,[status(thm)],[])).
% 12.07/12.25 tff(460,plain,
% 12.07/12.25 (((~![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, A!2)) | unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | (~unequally_directed_lines(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(L!3, line_connecting(B!1, A!2)) | (~unequally_directed_lines(L!3, reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2))))),
% 12.07/12.25 inference(monotonicity,[status(thm)],[459])).
% 12.07/12.25 tff(461,plain,
% 12.07/12.25 (((~![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, A!2)) | unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | (~unequally_directed_lines(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(L!3, line_connecting(B!1, A!2)) | (~unequally_directed_lines(L!3, reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2)))),
% 12.07/12.25 inference(transitivity,[status(thm)],[460, 458])).
% 12.07/12.25 tff(462,plain,
% 12.07/12.25 ((~![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, A!2)) | unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))),
% 12.07/12.25 inference(quant_inst,[status(thm)],[])).
% 12.07/12.25 tff(463,plain,
% 12.07/12.25 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | (~unequally_directed_lines(L!3, reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2))),
% 12.07/12.25 inference(modus_ponens,[status(thm)],[462, 461])).
% 12.07/12.25 tff(464,plain,
% 12.07/12.25 ($false),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[463, 21, 457, 456, 455])).
% 12.07/12.25 tff(465,plain,(unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | (~unequally_directed_lines(L!3, reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.25 tff(466,plain,
% 12.07/12.25 (unequally_directed_lines(L!3, line_connecting(B!1, A!2)) | unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2))),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[465, 257])).
% 12.07/12.25 tff(467,plain,
% 12.07/12.25 (unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2))),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[466, 454])).
% 12.07/12.25 tff(468,assumption,(~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1)))), introduced(assumption)).
% 12.07/12.25 tff(469,assumption,(unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2))), introduced(assumption)).
% 12.07/12.25 tff(470,plain,
% 12.07/12.25 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))))),
% 12.07/12.25 inference(quant_inst,[status(thm)],[])).
% 12.07/12.25 tff(471,plain,
% 12.07/12.25 (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[470, 9])).
% 12.07/12.25 tff(472,plain,
% 12.07/12.25 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2))))),
% 12.07/12.25 inference(rewrite,[status(thm)],[])).
% 12.07/12.25 tff(473,plain,
% 12.07/12.25 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2))))),
% 12.07/12.25 inference(quant_inst,[status(thm)],[])).
% 12.07/12.25 tff(474,plain,
% 12.07/12.25 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2)))),
% 12.07/12.25 inference(modus_ponens,[status(thm)],[473, 472])).
% 12.07/12.25 tff(475,plain,
% 12.07/12.25 ($false),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[474, 21, 471, 469, 468])).
% 12.07/12.25 tff(476,plain,(unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(B!1, A!2)))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.25 tff(477,plain,
% 12.07/12.25 (unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1)))),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[476, 467])).
% 12.07/12.25 tff(478,assumption,(~unequally_directed_lines(L!3, line_connecting(A!2, B!1))), introduced(assumption)).
% 12.07/12.25 tff(479,plain,
% 12.07/12.25 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 12.07/12.25 inference(quant_inst,[status(thm)],[])).
% 12.07/12.25 tff(480,plain,
% 12.07/12.25 (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[479, 9])).
% 12.07/12.25 tff(481,plain,
% 12.07/12.25 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1))))),
% 12.07/12.25 inference(rewrite,[status(thm)],[])).
% 12.07/12.25 tff(482,plain,
% 12.07/12.25 ((unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)))) <=> (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1))))),
% 12.07/12.25 inference(rewrite,[status(thm)],[])).
% 12.07/12.25 tff(483,plain,
% 12.07/12.25 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)))))),
% 12.07/12.25 inference(monotonicity,[status(thm)],[482])).
% 12.07/12.25 tff(484,plain,
% 12.07/12.25 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1))))),
% 12.07/12.25 inference(transitivity,[status(thm)],[483, 481])).
% 12.07/12.25 tff(485,plain,
% 12.07/12.25 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1))))),
% 12.07/12.25 inference(quant_inst,[status(thm)],[])).
% 12.07/12.25 tff(486,plain,
% 12.07/12.25 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)))),
% 12.07/12.25 inference(modus_ponens,[status(thm)],[485, 484])).
% 12.07/12.25 tff(487,plain,
% 12.07/12.25 (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1))),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[486, 21, 480])).
% 12.07/12.25 tff(488,plain,
% 12.07/12.25 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), 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(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!3)))),
% 12.07/12.25 inference(rewrite,[status(thm)],[])).
% 12.07/12.25 tff(489,plain,
% 12.07/12.25 ((unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!3))) <=> (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!3)))),
% 12.07/12.25 inference(rewrite,[status(thm)],[])).
% 12.07/12.25 tff(490,plain,
% 12.07/12.25 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), 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(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!3))))),
% 12.07/12.25 inference(monotonicity,[status(thm)],[489])).
% 12.07/12.25 tff(491,plain,
% 12.07/12.25 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), 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(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!3)))),
% 12.07/12.25 inference(transitivity,[status(thm)],[490, 488])).
% 12.07/12.25 tff(492,plain,
% 12.07/12.25 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!3)))),
% 12.07/12.25 inference(quant_inst,[status(thm)],[])).
% 12.07/12.25 tff(493,plain,
% 12.07/12.25 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(A!2, B!1)) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!3))),
% 12.07/12.25 inference(modus_ponens,[status(thm)],[492, 491])).
% 12.07/12.25 tff(494,plain,
% 12.07/12.25 (~unequally_directed_lines(line_connecting(A!2, B!1), L!3)),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[493, 21, 487, 478])).
% 12.07/12.25 tff(495,assumption,(~unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3)), introduced(assumption)).
% 12.07/12.25 tff(496,plain,
% 12.07/12.25 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), L!3) | unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | (~unequally_directed_lines(line_connecting(A!2, 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(line_connecting(A!2, B!1), L!3) | unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))))),
% 12.07/12.25 inference(rewrite,[status(thm)],[])).
% 12.07/12.25 tff(497,plain,
% 12.07/12.25 ((unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | unequally_directed_lines(line_connecting(A!2, B!1), L!3) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3))))) <=> (unequally_directed_lines(line_connecting(A!2, B!1), L!3) | unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))))),
% 12.07/12.25 inference(rewrite,[status(thm)],[])).
% 12.07/12.25 tff(498,plain,
% 12.07/12.25 (((~![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)), L!3) | unequally_directed_lines(line_connecting(A!2, B!1), L!3) | (~unequally_directed_lines(line_connecting(A!2, 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(line_connecting(A!2, B!1), L!3) | unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3))))))),
% 12.07/12.25 inference(monotonicity,[status(thm)],[497])).
% 12.07/12.25 tff(499,plain,
% 12.07/12.25 (((~![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)), L!3) | unequally_directed_lines(line_connecting(A!2, B!1), L!3) | (~unequally_directed_lines(line_connecting(A!2, 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(line_connecting(A!2, B!1), L!3) | unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))))),
% 12.07/12.25 inference(transitivity,[status(thm)],[498, 496])).
% 12.07/12.25 tff(500,plain,
% 12.07/12.25 ((~![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)), L!3) | unequally_directed_lines(line_connecting(A!2, B!1), L!3) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))))),
% 12.07/12.25 inference(quant_inst,[status(thm)],[])).
% 12.07/12.25 tff(501,plain,
% 12.07/12.25 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), L!3) | unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3))))),
% 12.07/12.25 inference(modus_ponens,[status(thm)],[500, 499])).
% 12.07/12.25 tff(502,plain,
% 12.07/12.25 (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[501, 21, 495, 494])).
% 12.07/12.25 tff(503,plain,
% 12.07/12.25 (((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3))))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))),
% 12.07/12.25 inference(tautology,[status(thm)],[])).
% 12.07/12.25 tff(504,plain,
% 12.07/12.25 ((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3))))),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[503, 502])).
% 12.07/12.25 tff(505,assumption,(unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1)))), introduced(assumption)).
% 12.07/12.25 tff(506,plain,
% 12.07/12.25 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1)) | (~unequally_directed_lines(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(L!3, line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))),
% 12.07/12.25 inference(rewrite,[status(thm)],[])).
% 12.07/12.25 tff(507,plain,
% 12.07/12.25 ((unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1)) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!3, reverse_line(L!3)))) <=> (unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))),
% 12.07/12.25 inference(rewrite,[status(thm)],[])).
% 12.07/12.25 tff(508,plain,
% 12.07/12.25 (((~![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(A!2, B!1)) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | (~unequally_directed_lines(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(L!3, line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!3, reverse_line(L!3)))))),
% 12.07/12.25 inference(monotonicity,[status(thm)],[507])).
% 12.07/12.25 tff(509,plain,
% 12.07/12.25 (((~![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(A!2, B!1)) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | (~unequally_directed_lines(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(L!3, line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))),
% 12.07/12.25 inference(transitivity,[status(thm)],[508, 506])).
% 12.07/12.25 tff(510,plain,
% 12.07/12.25 ((~![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(A!2, B!1)) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!3, reverse_line(L!3))))),
% 12.07/12.25 inference(quant_inst,[status(thm)],[])).
% 12.07/12.25 tff(511,plain,
% 12.07/12.25 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!3, reverse_line(L!3)))),
% 12.07/12.25 inference(modus_ponens,[status(thm)],[510, 509])).
% 12.07/12.25 tff(512,plain,
% 12.07/12.25 (unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!3, reverse_line(L!3)))),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[511, 21])).
% 12.07/12.25 tff(513,plain,
% 12.07/12.25 (unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1))),
% 12.07/12.25 inference(unit_resolution,[status(thm)],[512, 478, 257])).
% 12.07/12.25 tff(514,plain,
% 12.07/12.25 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1)))))),
% 12.07/12.25 inference(rewrite,[status(thm)],[])).
% 12.07/12.25 tff(515,plain,
% 12.07/12.25 (((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1))))) <=> ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1)))))),
% 12.07/12.26 inference(rewrite,[status(thm)],[])).
% 12.07/12.26 tff(516,plain,
% 12.07/12.26 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1))))))),
% 12.07/12.26 inference(monotonicity,[status(thm)],[515])).
% 12.07/12.26 tff(517,plain,
% 12.07/12.26 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1)))))),
% 12.07/12.26 inference(transitivity,[status(thm)],[516, 514])).
% 12.07/12.26 tff(518,plain,
% 12.07/12.26 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1)))))),
% 12.07/12.26 inference(quant_inst,[status(thm)],[])).
% 12.07/12.26 tff(519,plain,
% 12.07/12.26 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, B!1))) | (~((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1))))),
% 12.07/12.26 inference(modus_ponens,[status(thm)],[518, 517])).
% 12.07/12.26 tff(520,plain,
% 12.07/12.26 ($false),
% 12.07/12.26 inference(unit_resolution,[status(thm)],[519, 109, 513, 51, 505, 504])).
% 12.07/12.26 tff(521,plain,(unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3)), inference(lemma,lemma(discharge,[]))).
% 12.07/12.26 tff(522,plain,
% 12.07/12.26 (unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, B!1))))),
% 12.07/12.26 inference(unit_resolution,[status(thm)],[521, 268])).
% 12.07/12.26 tff(523,plain,
% 12.07/12.26 (unequally_directed_lines(L!3, line_connecting(A!2, B!1))),
% 12.07/12.26 inference(unit_resolution,[status(thm)],[522, 477])).
% 12.07/12.26 tff(524,plain,
% 12.07/12.26 (((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)) | (~unequally_directed_lines(L!3, line_connecting(A!2, B!1)))),
% 12.07/12.26 inference(tautology,[status(thm)],[])).
% 12.07/12.26 tff(525,plain,
% 12.07/12.26 ((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)),
% 12.07/12.26 inference(unit_resolution,[status(thm)],[524, 523])).
% 12.07/12.26 tff(526,assumption,(((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)) <=> before_on_line(L!3, A!2, B!1)), introduced(assumption)).
% 12.07/12.26 tff(527,plain,
% 12.07/12.26 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)) <=> before_on_line(L!3, A!2, B!1)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)) <=> before_on_line(L!3, A!2, B!1))))),
% 12.07/12.26 inference(rewrite,[status(thm)],[])).
% 12.07/12.26 tff(528,plain,
% 12.07/12.26 ((~(((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)) <=> before_on_line(L!3, A!2, B!1))) <=> (~(((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)) <=> before_on_line(L!3, A!2, B!1)))),
% 12.07/12.26 inference(rewrite,[status(thm)],[])).
% 12.07/12.26 tff(529,plain,
% 12.07/12.26 (((unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | (~distinct_points(A!2, B!1))) <=> before_on_line(L!3, A!2, B!1)) <=> (((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)) <=> before_on_line(L!3, A!2, B!1))),
% 12.07/12.26 inference(rewrite,[status(thm)],[])).
% 12.07/12.26 tff(530,plain,
% 12.07/12.26 ((~((unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | (~distinct_points(A!2, B!1))) <=> before_on_line(L!3, A!2, B!1))) <=> (~(((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)) <=> before_on_line(L!3, A!2, B!1)))),
% 12.07/12.26 inference(monotonicity,[status(thm)],[529])).
% 12.07/12.26 tff(531,plain,
% 12.07/12.26 ((~((unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | (~distinct_points(A!2, B!1))) <=> before_on_line(L!3, A!2, B!1))) <=> (~(((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)) <=> before_on_line(L!3, A!2, B!1)))),
% 12.07/12.26 inference(transitivity,[status(thm)],[530, 528])).
% 12.07/12.26 tff(532,plain,
% 12.07/12.26 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | (~distinct_points(A!2, B!1))) <=> before_on_line(L!3, A!2, B!1)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)) <=> before_on_line(L!3, A!2, B!1))))),
% 12.07/12.26 inference(monotonicity,[status(thm)],[531])).
% 12.07/12.26 tff(533,plain,
% 12.07/12.26 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | (~distinct_points(A!2, B!1))) <=> before_on_line(L!3, A!2, B!1)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)) <=> before_on_line(L!3, A!2, B!1))))),
% 12.07/12.26 inference(transitivity,[status(thm)],[532, 527])).
% 12.07/12.26 tff(534,plain,
% 12.07/12.26 ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | (~distinct_points(A!2, B!1))) <=> before_on_line(L!3, A!2, B!1)))),
% 12.07/12.26 inference(quant_inst,[status(thm)],[])).
% 12.07/12.26 tff(535,plain,
% 12.07/12.26 ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)) <=> before_on_line(L!3, A!2, B!1)))),
% 12.07/12.26 inference(modus_ponens,[status(thm)],[534, 533])).
% 12.07/12.26 tff(536,plain,
% 12.07/12.26 ($false),
% 12.07/12.26 inference(unit_resolution,[status(thm)],[535, 182, 526])).
% 12.07/12.26 tff(537,plain,(~(((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)) <=> before_on_line(L!3, A!2, B!1))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.26 tff(538,plain,
% 12.07/12.26 ((((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3)) <=> before_on_line(L!3, A!2, B!1)) | (~((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3))) | (~before_on_line(L!3, A!2, B!1))),
% 12.07/12.26 inference(tautology,[status(thm)],[])).
% 12.07/12.26 tff(539,plain,
% 12.07/12.26 ((~((~distinct_points(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3))) | (~before_on_line(L!3, A!2, B!1))),
% 12.07/12.26 inference(unit_resolution,[status(thm)],[538, 537])).
% 12.07/12.26 tff(540,plain,
% 12.07/12.26 (~before_on_line(L!3, A!2, B!1)),
% 12.07/12.26 inference(unit_resolution,[status(thm)],[539, 525])).
% 12.07/12.26 tff(541,plain,
% 12.07/12.26 (((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))) | before_on_line(L!3, A!2, B!1)),
% 12.07/12.26 inference(tautology,[status(thm)],[])).
% 12.07/12.26 tff(542,plain,
% 12.07/12.26 ((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))),
% 12.07/12.26 inference(unit_resolution,[status(thm)],[541, 540])).
% 12.07/12.26 tff(543,plain,
% 12.07/12.26 (~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))),
% 12.07/12.26 inference(unit_resolution,[status(thm)],[217, 542])).
% 12.07/12.26 tff(544,plain,
% 12.07/12.26 (((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2))) | before_on_line(L!3, C!0, B!1)),
% 12.07/12.26 inference(tautology,[status(thm)],[])).
% 12.07/12.26 tff(545,plain,
% 12.07/12.26 (before_on_line(L!3, C!0, B!1)),
% 12.07/12.26 inference(unit_resolution,[status(thm)],[544, 543])).
% 12.07/12.26 tff(546,assumption,(((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1)), introduced(assumption)).
% 12.07/12.26 tff(547,plain,
% 12.07/12.26 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1))))),
% 12.07/12.26 inference(rewrite,[status(thm)],[])).
% 12.07/12.26 tff(548,plain,
% 12.07/12.26 ((~(((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1))) <=> (~(((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1)))),
% 12.07/12.26 inference(rewrite,[status(thm)],[])).
% 12.07/12.26 tff(549,plain,
% 12.07/12.26 (((unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | (~distinct_points(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1)) <=> (((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1))),
% 12.07/12.26 inference(rewrite,[status(thm)],[])).
% 12.07/12.26 tff(550,plain,
% 12.07/12.26 ((~((unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | (~distinct_points(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1))) <=> (~(((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1)))),
% 12.07/12.26 inference(monotonicity,[status(thm)],[549])).
% 12.07/12.26 tff(551,plain,
% 12.07/12.26 ((~((unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | (~distinct_points(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1))) <=> (~(((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1)))),
% 12.07/12.26 inference(transitivity,[status(thm)],[550, 548])).
% 12.07/12.26 tff(552,plain,
% 12.07/12.26 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | (~distinct_points(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1))))),
% 12.07/12.26 inference(monotonicity,[status(thm)],[551])).
% 12.07/12.26 tff(553,plain,
% 12.07/12.26 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | (~distinct_points(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1))))),
% 12.07/12.26 inference(transitivity,[status(thm)],[552, 547])).
% 12.07/12.26 tff(554,plain,
% 12.07/12.26 ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | (~distinct_points(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1)))),
% 12.07/12.26 inference(quant_inst,[status(thm)],[])).
% 12.07/12.26 tff(555,plain,
% 12.07/12.26 ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1)))),
% 12.07/12.26 inference(modus_ponens,[status(thm)],[554, 553])).
% 12.07/12.26 tff(556,plain,
% 12.07/12.26 ($false),
% 12.07/12.26 inference(unit_resolution,[status(thm)],[555, 182, 546])).
% 12.07/12.26 tff(557,plain,(~(((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.26 tff(558,plain,
% 12.07/12.26 ((((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))) <=> before_on_line(L!3, C!0, B!1)) | (~((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)))) | (~before_on_line(L!3, C!0, B!1))),
% 12.07/12.26 inference(tautology,[status(thm)],[])).
% 12.07/12.26 tff(559,plain,
% 12.07/12.26 ((~((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)))) | (~before_on_line(L!3, C!0, B!1))),
% 12.07/12.26 inference(unit_resolution,[status(thm)],[558, 557])).
% 12.07/12.26 tff(560,plain,
% 12.07/12.26 (~((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)))),
% 12.07/12.26 inference(unit_resolution,[status(thm)],[559, 545])).
% 12.07/12.26 tff(561,plain,
% 12.07/12.26 (((~distinct_points(C!0, B!1)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(B!1, reverse_line(L!3)) | left_apart_point(B!1, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))) | (~unequally_directed_lines(L!3, line_connecting(C!0, B!1)))),
% 12.07/12.26 inference(tautology,[status(thm)],[])).
% 12.07/12.26 tff(562,plain,
% 12.07/12.26 (~unequally_directed_lines(L!3, line_connecting(C!0, B!1))),
% 12.07/12.26 inference(unit_resolution,[status(thm)],[561, 560])).
% 12.07/12.26 tff(563,plain,
% 12.07/12.26 (((~![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(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1))))),
% 12.07/12.26 inference(rewrite,[status(thm)],[])).
% 12.07/12.26 tff(564,plain,
% 12.07/12.26 ((unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)))) <=> (unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1))))),
% 12.07/12.26 inference(rewrite,[status(thm)],[])).
% 12.07/12.26 tff(565,plain,
% 12.07/12.26 (((~![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(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)))))),
% 12.07/12.27 inference(monotonicity,[status(thm)],[564])).
% 12.07/12.27 tff(566,plain,
% 12.07/12.27 (((~![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(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1))))),
% 12.07/12.27 inference(transitivity,[status(thm)],[565, 563])).
% 12.07/12.27 tff(567,plain,
% 12.07/12.27 ((~![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(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1))))),
% 12.07/12.27 inference(quant_inst,[status(thm)],[])).
% 12.07/12.27 tff(568,plain,
% 12.07/12.27 ((~![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(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)))),
% 12.07/12.27 inference(modus_ponens,[status(thm)],[567, 566])).
% 12.07/12.27 tff(569,plain,
% 12.07/12.27 (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1))),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[568, 21, 411])).
% 12.07/12.27 tff(570,plain,
% 12.07/12.27 (((~![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(C!0, B!1), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), L!3)) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), L!3)) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)))),
% 12.07/12.27 inference(rewrite,[status(thm)],[])).
% 12.07/12.27 tff(571,plain,
% 12.07/12.27 ((unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), L!3))) <=> (unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), L!3)) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)))),
% 12.07/12.27 inference(rewrite,[status(thm)],[])).
% 12.07/12.27 tff(572,plain,
% 12.07/12.27 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), 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(line_connecting(C!0, B!1), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), L!3)) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))))),
% 12.07/12.27 inference(monotonicity,[status(thm)],[571])).
% 12.07/12.27 tff(573,plain,
% 12.07/12.27 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), 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(line_connecting(C!0, B!1), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), L!3)) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)))),
% 12.07/12.27 inference(transitivity,[status(thm)],[572, 570])).
% 12.07/12.27 tff(574,plain,
% 12.07/12.27 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), L!3)))),
% 12.07/12.27 inference(quant_inst,[status(thm)],[])).
% 12.07/12.27 tff(575,plain,
% 12.07/12.27 ((~![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(C!0, B!1), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), L!3)) | unequally_directed_lines(L!3, line_connecting(C!0, B!1))),
% 12.07/12.27 inference(modus_ponens,[status(thm)],[574, 573])).
% 12.07/12.27 tff(576,plain,
% 12.07/12.27 (~unequally_directed_lines(line_connecting(C!0, B!1), L!3)),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[575, 21, 569, 562])).
% 12.07/12.27 tff(577,plain,
% 12.07/12.27 (((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2))) | before_on_line(L!3, A!2, B!1)),
% 12.07/12.27 inference(tautology,[status(thm)],[])).
% 12.07/12.27 tff(578,plain,
% 12.07/12.27 ((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2))),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[577, 540])).
% 12.07/12.27 tff(579,plain,
% 12.07/12.27 (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0)))),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[292, 578])).
% 12.07/12.27 tff(580,plain,
% 12.07/12.27 (((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0))) | before_on_line(L!3, A!2, C!0)),
% 12.07/12.27 inference(tautology,[status(thm)],[])).
% 12.07/12.27 tff(581,plain,
% 12.07/12.27 (before_on_line(L!3, A!2, C!0)),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[580, 579])).
% 12.07/12.27 tff(582,assumption,(((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0)), introduced(assumption)).
% 12.07/12.27 tff(583,plain,
% 12.07/12.27 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0))))),
% 12.07/12.27 inference(rewrite,[status(thm)],[])).
% 12.07/12.27 tff(584,plain,
% 12.07/12.27 ((~(((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0))) <=> (~(((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0)))),
% 12.07/12.27 inference(rewrite,[status(thm)],[])).
% 12.07/12.27 tff(585,plain,
% 12.07/12.27 (((unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | (~distinct_points(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0)) <=> (((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0))),
% 12.07/12.27 inference(rewrite,[status(thm)],[])).
% 12.07/12.27 tff(586,plain,
% 12.07/12.27 ((~((unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | (~distinct_points(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0))) <=> (~(((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0)))),
% 12.07/12.27 inference(monotonicity,[status(thm)],[585])).
% 12.07/12.27 tff(587,plain,
% 12.07/12.27 ((~((unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | (~distinct_points(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0))) <=> (~(((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0)))),
% 12.07/12.27 inference(transitivity,[status(thm)],[586, 584])).
% 12.07/12.27 tff(588,plain,
% 12.07/12.27 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | (~distinct_points(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0))))),
% 12.07/12.27 inference(monotonicity,[status(thm)],[587])).
% 12.07/12.27 tff(589,plain,
% 12.07/12.27 (((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | (~distinct_points(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0)))) <=> ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0))))),
% 12.07/12.27 inference(transitivity,[status(thm)],[588, 583])).
% 12.07/12.27 tff(590,plain,
% 12.07/12.27 ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | (~distinct_points(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0)))),
% 12.07/12.27 inference(quant_inst,[status(thm)],[])).
% 12.07/12.27 tff(591,plain,
% 12.07/12.27 ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~(((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0)))),
% 12.07/12.27 inference(modus_ponens,[status(thm)],[590, 589])).
% 12.07/12.27 tff(592,plain,
% 12.07/12.27 ($false),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[591, 182, 582])).
% 12.07/12.27 tff(593,plain,(~(((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.27 tff(594,plain,
% 12.07/12.27 ((((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))) <=> before_on_line(L!3, A!2, C!0)) | (~((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0)))) | (~before_on_line(L!3, A!2, C!0))),
% 12.07/12.27 inference(tautology,[status(thm)],[])).
% 12.07/12.27 tff(595,plain,
% 12.07/12.27 ((~((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0)))) | (~before_on_line(L!3, A!2, C!0))),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[594, 593])).
% 12.07/12.27 tff(596,plain,
% 12.07/12.27 (~((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0)))),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[595, 581])).
% 12.07/12.27 tff(597,plain,
% 12.07/12.27 (((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(A!2, C!0)))),
% 12.07/12.27 inference(tautology,[status(thm)],[])).
% 12.07/12.27 tff(598,plain,
% 12.07/12.27 (~unequally_directed_lines(L!3, line_connecting(A!2, C!0))),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[597, 596])).
% 12.07/12.27 tff(599,plain,
% 12.07/12.27 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))))),
% 12.07/12.27 inference(quant_inst,[status(thm)],[])).
% 12.07/12.27 tff(600,plain,
% 12.07/12.27 (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2)))),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[599, 9])).
% 12.07/12.27 tff(601,plain,
% 12.07/12.27 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, 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(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))))),
% 12.07/12.27 inference(rewrite,[status(thm)],[])).
% 12.07/12.27 tff(602,plain,
% 12.07/12.27 ((unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0)))) <=> (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))))),
% 12.07/12.27 inference(rewrite,[status(thm)],[])).
% 12.07/12.27 tff(603,plain,
% 12.07/12.27 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, 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(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0)))))),
% 12.07/12.27 inference(monotonicity,[status(thm)],[602])).
% 12.07/12.27 tff(604,plain,
% 12.07/12.27 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, 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(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))))),
% 12.07/12.27 inference(transitivity,[status(thm)],[603, 601])).
% 12.07/12.27 tff(605,plain,
% 12.07/12.27 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))))),
% 12.07/12.27 inference(quant_inst,[status(thm)],[])).
% 12.07/12.27 tff(606,plain,
% 12.07/12.27 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0)))),
% 12.07/12.27 inference(modus_ponens,[status(thm)],[605, 604])).
% 12.07/12.27 tff(607,plain,
% 12.07/12.27 (~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[606, 21, 600])).
% 12.07/12.27 tff(608,plain,
% 12.07/12.27 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0)) | unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | (~unequally_directed_lines(line_connecting(A!2, C!0), 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(line_connecting(A!2, C!0), line_connecting(A!2, C!0)) | unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | (~unequally_directed_lines(line_connecting(A!2, C!0), L!3)))),
% 12.07/12.27 inference(rewrite,[status(thm)],[])).
% 12.07/12.27 tff(609,plain,
% 12.07/12.27 ((unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0)) | (~unequally_directed_lines(line_connecting(A!2, C!0), L!3))) <=> (unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0)) | unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | (~unequally_directed_lines(line_connecting(A!2, C!0), L!3)))),
% 12.07/12.27 inference(rewrite,[status(thm)],[])).
% 12.07/12.27 tff(610,plain,
% 12.07/12.27 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0)) | (~unequally_directed_lines(line_connecting(A!2, C!0), 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(line_connecting(A!2, C!0), line_connecting(A!2, C!0)) | unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | (~unequally_directed_lines(line_connecting(A!2, C!0), L!3))))),
% 12.07/12.27 inference(monotonicity,[status(thm)],[609])).
% 12.07/12.27 tff(611,plain,
% 12.07/12.27 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0)) | (~unequally_directed_lines(line_connecting(A!2, C!0), 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(line_connecting(A!2, C!0), line_connecting(A!2, C!0)) | unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | (~unequally_directed_lines(line_connecting(A!2, C!0), L!3)))),
% 12.07/12.27 inference(transitivity,[status(thm)],[610, 608])).
% 12.07/12.27 tff(612,plain,
% 12.07/12.27 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0)) | (~unequally_directed_lines(line_connecting(A!2, C!0), L!3)))),
% 12.07/12.27 inference(quant_inst,[status(thm)],[])).
% 12.07/12.27 tff(613,plain,
% 12.07/12.27 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0)) | unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | (~unequally_directed_lines(line_connecting(A!2, C!0), L!3))),
% 12.07/12.27 inference(modus_ponens,[status(thm)],[612, 611])).
% 12.07/12.27 tff(614,plain,
% 12.07/12.27 (~unequally_directed_lines(line_connecting(A!2, C!0), L!3)),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[613, 21, 607, 598])).
% 12.07/12.27 tff(615,plain,
% 12.07/12.27 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), L!3) | unequally_directed_lines(line_connecting(C!0, B!1), L!3) | (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(A!2, 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(A!2, C!0), L!3) | unequally_directed_lines(line_connecting(C!0, B!1), L!3) | (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(A!2, C!0))))),
% 12.07/12.27 inference(rewrite,[status(thm)],[])).
% 12.07/12.27 tff(616,plain,
% 12.07/12.27 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), L!3) | unequally_directed_lines(line_connecting(C!0, B!1), L!3) | (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(A!2, C!0))))),
% 12.07/12.27 inference(quant_inst,[status(thm)],[])).
% 12.07/12.27 tff(617,plain,
% 12.07/12.27 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, C!0), L!3) | unequally_directed_lines(line_connecting(C!0, B!1), L!3) | (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(A!2, C!0)))),
% 12.07/12.27 inference(modus_ponens,[status(thm)],[616, 615])).
% 12.07/12.27 tff(618,plain,
% 12.07/12.27 (~unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(A!2, C!0))),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[617, 21, 614, 576])).
% 12.07/12.27 tff(619,plain,
% 12.07/12.27 (((~![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)), L!3) | unequally_directed_lines(line_connecting(A!2, C!0), L!3) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), L!3) | unequally_directed_lines(line_connecting(A!2, C!0), L!3) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))))),
% 12.07/12.27 inference(rewrite,[status(thm)],[])).
% 12.07/12.27 tff(620,plain,
% 12.07/12.27 ((~![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)), L!3) | unequally_directed_lines(line_connecting(A!2, C!0), L!3) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))))),
% 12.07/12.27 inference(quant_inst,[status(thm)],[])).
% 12.07/12.27 tff(621,plain,
% 12.07/12.27 ((~![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)), L!3) | unequally_directed_lines(line_connecting(A!2, C!0), L!3) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3))))),
% 12.07/12.27 inference(modus_ponens,[status(thm)],[620, 619])).
% 12.07/12.27 tff(622,plain,
% 12.07/12.27 (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[621, 21, 268, 614])).
% 12.07/12.27 tff(623,plain,
% 12.07/12.27 (((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3))))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))),
% 12.07/12.27 inference(tautology,[status(thm)],[])).
% 12.07/12.27 tff(624,plain,
% 12.07/12.27 ((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3))))),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[623, 622])).
% 12.07/12.27 tff(625,assumption,(~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))), introduced(assumption)).
% 12.07/12.27 tff(626,assumption,(~unequally_directed_lines(L!3, line_connecting(A!2, C!0))), introduced(assumption)).
% 12.07/12.27 tff(627,plain,
% 12.07/12.27 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, 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(L!3, line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0)))),
% 12.07/12.27 inference(rewrite,[status(thm)],[])).
% 12.07/12.27 tff(628,plain,
% 12.07/12.27 ((unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3))) <=> (unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0)))),
% 12.07/12.27 inference(rewrite,[status(thm)],[])).
% 12.07/12.27 tff(629,plain,
% 12.07/12.27 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(L!3), 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(L!3, line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))))),
% 12.07/12.27 inference(monotonicity,[status(thm)],[628])).
% 12.07/12.27 tff(630,plain,
% 12.07/12.27 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(L!3), 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(L!3, line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0)))),
% 12.07/12.27 inference(transitivity,[status(thm)],[629, 627])).
% 12.07/12.27 tff(631,plain,
% 12.07/12.27 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3)))),
% 12.07/12.27 inference(quant_inst,[status(thm)],[])).
% 12.07/12.27 tff(632,plain,
% 12.07/12.27 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))),
% 12.07/12.27 inference(modus_ponens,[status(thm)],[631, 630])).
% 12.07/12.27 tff(633,plain,
% 12.07/12.27 ($false),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[632, 21, 397, 626, 625])).
% 12.07/12.27 tff(634,plain,(unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0)) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))), inference(lemma,lemma(discharge,[]))).
% 12.07/12.27 tff(635,plain,
% 12.07/12.27 (unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))),
% 12.07/12.27 inference(unit_resolution,[status(thm)],[634, 598])).
% 12.07/12.27 tff(636,plain,
% 12.07/12.27 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))),
% 12.07/12.28 inference(rewrite,[status(thm)],[])).
% 12.07/12.28 tff(637,plain,
% 12.07/12.28 (((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))))) <=> ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))),
% 12.07/12.28 inference(rewrite,[status(thm)],[])).
% 12.07/12.28 tff(638,plain,
% 12.07/12.28 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))))))),
% 12.07/12.28 inference(monotonicity,[status(thm)],[637])).
% 12.07/12.28 tff(639,plain,
% 12.07/12.28 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))),
% 12.07/12.28 inference(transitivity,[status(thm)],[638, 636])).
% 12.07/12.28 tff(640,plain,
% 12.07/12.28 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))),
% 12.07/12.28 inference(quant_inst,[status(thm)],[])).
% 12.07/12.28 tff(641,plain,
% 12.07/12.28 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))))),
% 12.07/12.28 inference(modus_ponens,[status(thm)],[640, 639])).
% 12.07/12.28 tff(642,plain,
% 12.07/12.28 (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))),
% 12.07/12.28 inference(unit_resolution,[status(thm)],[641, 109, 51, 635, 624])).
% 12.07/12.28 tff(643,assumption,(~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))), introduced(assumption)).
% 12.07/12.28 tff(644,assumption,(unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))), introduced(assumption)).
% 12.07/12.28 tff(645,plain,
% 12.07/12.28 (((~![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(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))))),
% 12.12/12.28 inference(rewrite,[status(thm)],[])).
% 12.12/12.28 tff(646,plain,
% 12.12/12.28 ((~![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(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))))),
% 12.12/12.28 inference(quant_inst,[status(thm)],[])).
% 12.12/12.28 tff(647,plain,
% 12.12/12.28 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)))),
% 12.12/12.28 inference(modus_ponens,[status(thm)],[646, 645])).
% 12.12/12.28 tff(648,plain,
% 12.12/12.28 ($false),
% 12.12/12.28 inference(unit_resolution,[status(thm)],[647, 21, 353, 644, 643])).
% 12.12/12.28 tff(649,plain,(unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.28 tff(650,plain,
% 12.12/12.28 (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))),
% 12.12/12.28 inference(unit_resolution,[status(thm)],[649, 642])).
% 12.12/12.28 tff(651,assumption,(~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))), introduced(assumption)).
% 12.12/12.28 tff(652,plain,
% 12.12/12.28 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)))),
% 12.12/12.28 inference(rewrite,[status(thm)],[])).
% 12.12/12.28 tff(653,plain,
% 12.12/12.28 ((unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(L!3), L!3))) <=> (unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)))),
% 12.12/12.28 inference(rewrite,[status(thm)],[])).
% 12.12/12.28 tff(654,plain,
% 12.12/12.28 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(L!3), 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(L!3, line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))))),
% 12.12/12.28 inference(monotonicity,[status(thm)],[653])).
% 12.12/12.28 tff(655,plain,
% 12.12/12.28 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(L!3), 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(L!3, line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)))),
% 12.12/12.28 inference(transitivity,[status(thm)],[654, 652])).
% 12.12/12.28 tff(656,plain,
% 12.12/12.28 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(L!3), L!3)))),
% 12.12/12.28 inference(quant_inst,[status(thm)],[])).
% 12.12/12.28 tff(657,plain,
% 12.12/12.28 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))),
% 12.12/12.28 inference(modus_ponens,[status(thm)],[656, 655])).
% 12.12/12.28 tff(658,plain,
% 12.12/12.28 ($false),
% 12.12/12.28 inference(unit_resolution,[status(thm)],[657, 21, 397, 340, 651])).
% 12.12/12.28 tff(659,plain,(unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.28 tff(660,plain,
% 12.12/12.28 (unequally_directed_lines(L!3, line_connecting(C!0, A!2))),
% 12.12/12.28 inference(unit_resolution,[status(thm)],[659, 650])).
% 12.12/12.28 tff(661,assumption,(unequally_directed_lines(L!3, line_connecting(C!0, A!2))), introduced(assumption)).
% 12.12/12.28 tff(662,plain,
% 12.12/12.28 (((~![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(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, A!2))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, 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(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, A!2))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.28 inference(rewrite,[status(thm)],[])).
% 12.12/12.28 tff(663,plain,
% 12.12/12.28 ((unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, A!2)))) <=> (unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, A!2))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.28 inference(rewrite,[status(thm)],[])).
% 12.12/12.28 tff(664,plain,
% 12.12/12.28 (((~![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(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, A!2))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.28 inference(monotonicity,[status(thm)],[663])).
% 12.12/12.28 tff(665,plain,
% 12.12/12.28 (((~![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(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, A!2))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.28 inference(transitivity,[status(thm)],[664, 662])).
% 12.12/12.28 tff(666,plain,
% 12.12/12.28 ((~![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(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, A!2))))),
% 12.12/12.28 inference(quant_inst,[status(thm)],[])).
% 12.12/12.28 tff(667,plain,
% 12.12/12.28 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, A!2))) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.28 inference(modus_ponens,[status(thm)],[666, 665])).
% 12.12/12.28 tff(668,plain,
% 12.12/12.28 ($false),
% 12.12/12.28 inference(unit_resolution,[status(thm)],[667, 21, 353, 661, 378])).
% 12.12/12.28 tff(669,plain,(unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(L!3, line_connecting(C!0, A!2)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.28 tff(670,plain,
% 12.12/12.28 (unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.28 inference(unit_resolution,[status(thm)],[669, 660])).
% 12.12/12.28 tff(671,assumption,(~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))), introduced(assumption)).
% 12.12/12.28 tff(672,assumption,(unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))), introduced(assumption)).
% 12.12/12.28 tff(673,plain,
% 12.12/12.28 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)))),
% 12.12/12.28 inference(rewrite,[status(thm)],[])).
% 12.12/12.28 tff(674,plain,
% 12.12/12.28 ((unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))))) <=> (unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)))),
% 12.12/12.28 inference(rewrite,[status(thm)],[])).
% 12.12/12.28 tff(675,plain,
% 12.12/12.28 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, 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(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))))),
% 12.12/12.28 inference(monotonicity,[status(thm)],[674])).
% 12.12/12.28 tff(676,plain,
% 12.12/12.28 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, 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(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)))),
% 12.12/12.28 inference(transitivity,[status(thm)],[675, 673])).
% 12.12/12.28 tff(677,plain,
% 12.12/12.28 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.28 inference(quant_inst,[status(thm)],[])).
% 12.12/12.28 tff(678,plain,
% 12.12/12.28 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))),
% 12.12/12.28 inference(modus_ponens,[status(thm)],[677, 676])).
% 12.12/12.28 tff(679,plain,
% 12.12/12.28 ($false),
% 12.12/12.28 inference(unit_resolution,[status(thm)],[678, 21, 398, 672, 671])).
% 12.12/12.28 tff(680,plain,(unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | unequally_directed_lines(L!3, line_connecting(C!0, B!1)) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.28 tff(681,plain,
% 12.12/12.28 (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))),
% 12.12/12.28 inference(unit_resolution,[status(thm)],[680, 670, 562])).
% 12.12/12.28 tff(682,assumption,(unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))), introduced(assumption)).
% 12.12/12.28 tff(683,assumption,(~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))), introduced(assumption)).
% 12.12/12.28 tff(684,plain,
% 12.12/12.28 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, 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(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.28 inference(rewrite,[status(thm)],[])).
% 12.12/12.28 tff(685,plain,
% 12.12/12.28 ((unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)))) <=> (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.28 inference(rewrite,[status(thm)],[])).
% 12.12/12.28 tff(686,plain,
% 12.12/12.28 (((~![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(C!0, B!1), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.28 inference(monotonicity,[status(thm)],[685])).
% 12.12/12.28 tff(687,plain,
% 12.12/12.28 (((~![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(C!0, B!1), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.28 inference(transitivity,[status(thm)],[686, 684])).
% 12.12/12.28 tff(688,plain,
% 12.12/12.28 ((~![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(C!0, B!1), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))))),
% 12.12/12.28 inference(quant_inst,[status(thm)],[])).
% 12.12/12.28 tff(689,plain,
% 12.12/12.28 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.28 inference(modus_ponens,[status(thm)],[688, 687])).
% 12.12/12.28 tff(690,plain,
% 12.12/12.28 ($false),
% 12.12/12.28 inference(unit_resolution,[status(thm)],[689, 21, 683, 682, 169])).
% 12.12/12.28 tff(691,plain,(unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.28 tff(692,plain,
% 12.12/12.28 (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.28 inference(unit_resolution,[status(thm)],[691, 681, 169])).
% 12.12/12.28 tff(693,plain,
% 12.12/12.28 (((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))))) <=> ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)))))),
% 12.12/12.28 inference(rewrite,[status(thm)],[])).
% 12.12/12.28 tff(694,plain,
% 12.12/12.28 ((~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))))) <=> (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))))),
% 12.12/12.28 inference(rewrite,[status(thm)],[])).
% 12.12/12.28 tff(695,plain,
% 12.12/12.28 (((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) <=> ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)))))),
% 12.12/12.28 inference(monotonicity,[status(thm)],[694])).
% 12.12/12.28 tff(696,plain,
% 12.12/12.28 (((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) <=> ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)))))),
% 12.12/12.28 inference(transitivity,[status(thm)],[695, 693])).
% 12.12/12.28 tff(697,plain,
% 12.12/12.28 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.28 inference(quant_inst,[status(thm)],[])).
% 12.12/12.28 tff(698,plain,
% 12.12/12.28 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))))),
% 12.12/12.28 inference(modus_ponens,[status(thm)],[697, 696])).
% 12.12/12.28 tff(699,plain,
% 12.12/12.28 (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)))),
% 12.12/12.28 inference(unit_resolution,[status(thm)],[698, 132])).
% 12.12/12.28 tff(700,plain,
% 12.12/12.28 ((left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)))),
% 12.12/12.28 inference(tautology,[status(thm)],[])).
% 12.12/12.28 tff(701,plain,
% 12.12/12.28 (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))),
% 12.12/12.28 inference(unit_resolution,[status(thm)],[700, 699])).
% 12.12/12.28 tff(702,plain,
% 12.12/12.28 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 12.12/12.28 inference(quant_inst,[status(thm)],[])).
% 12.12/12.28 tff(703,plain,
% 12.12/12.28 (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.28 inference(unit_resolution,[status(thm)],[702, 132])).
% 12.12/12.29 tff(704,plain,
% 12.12/12.29 ((left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(A!2, C!0))))) | (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.29 inference(tautology,[status(thm)],[])).
% 12.12/12.29 tff(705,plain,
% 12.12/12.29 (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.29 inference(unit_resolution,[status(thm)],[704, 703])).
% 12.12/12.29 tff(706,plain,
% 12.12/12.29 (((~![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(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)))),
% 12.12/12.29 inference(rewrite,[status(thm)],[])).
% 12.12/12.29 tff(707,plain,
% 12.12/12.29 ((left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)))),
% 12.12/12.29 inference(rewrite,[status(thm)],[])).
% 12.12/12.29 tff(708,plain,
% 12.12/12.29 (((~![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(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))))),
% 12.12/12.29 inference(monotonicity,[status(thm)],[707])).
% 12.12/12.29 tff(709,plain,
% 12.12/12.29 (((~![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(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)))),
% 12.12/12.29 inference(transitivity,[status(thm)],[708, 706])).
% 12.12/12.29 tff(710,plain,
% 12.12/12.29 ((~![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(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.29 inference(quant_inst,[status(thm)],[])).
% 12.12/12.29 tff(711,plain,
% 12.12/12.29 ((~![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(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))),
% 12.12/12.29 inference(modus_ponens,[status(thm)],[710, 709])).
% 12.12/12.29 tff(712,plain,
% 12.12/12.29 ((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))),
% 12.12/12.29 inference(unit_resolution,[status(thm)],[711, 151, 705])).
% 12.12/12.29 tff(713,plain,
% 12.12/12.29 ((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.29 inference(unit_resolution,[status(thm)],[712, 701])).
% 12.12/12.29 tff(714,plain,
% 12.12/12.29 (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))),
% 12.12/12.29 inference(unit_resolution,[status(thm)],[713, 692])).
% 12.12/12.29 tff(715,plain,
% 12.12/12.29 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))))),
% 12.12/12.29 inference(rewrite,[status(thm)],[])).
% 12.12/12.29 tff(716,plain,
% 12.12/12.29 ((unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(A!2, C!0)) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)))) <=> (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))))),
% 12.12/12.29 inference(rewrite,[status(thm)],[])).
% 12.12/12.29 tff(717,plain,
% 12.12/12.29 (((~![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(C!0, B!1), line_connecting(A!2, C!0)) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)))))),
% 12.12/12.29 inference(monotonicity,[status(thm)],[716])).
% 12.12/12.29 tff(718,plain,
% 12.12/12.29 (((~![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(C!0, B!1), line_connecting(A!2, C!0)) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))))),
% 12.12/12.29 inference(transitivity,[status(thm)],[717, 715])).
% 12.12/12.29 tff(719,plain,
% 12.12/12.29 ((~![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(C!0, B!1), line_connecting(A!2, C!0)) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))))),
% 12.12/12.29 inference(quant_inst,[status(thm)],[])).
% 12.12/12.29 tff(720,plain,
% 12.12/12.29 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0)) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(A!2, C!0)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)))),
% 12.12/12.29 inference(modus_ponens,[status(thm)],[719, 718])).
% 12.12/12.29 tff(721,plain,
% 12.12/12.29 ($false),
% 12.12/12.29 inference(unit_resolution,[status(thm)],[720, 21, 714, 681, 618])).
% 12.12/12.29 tff(722,plain,(unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.29 tff(723,plain,
% 12.12/12.29 (((~![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(C!0, B!1), line_connecting(C!0, B!1)) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, 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(C!0, B!1), line_connecting(C!0, B!1)) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.29 inference(rewrite,[status(thm)],[])).
% 12.12/12.29 tff(724,plain,
% 12.12/12.29 ((unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0))))) <=> (unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.29 inference(rewrite,[status(thm)],[])).
% 12.12/12.29 tff(725,plain,
% 12.12/12.29 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, 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(C!0, B!1), line_connecting(C!0, B!1)) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0))))))),
% 12.12/12.29 inference(monotonicity,[status(thm)],[724])).
% 12.12/12.29 tff(726,plain,
% 12.12/12.29 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, 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(C!0, B!1), line_connecting(C!0, B!1)) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.29 inference(transitivity,[status(thm)],[725, 723])).
% 12.12/12.29 tff(727,plain,
% 12.12/12.29 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.29 inference(quant_inst,[status(thm)],[])).
% 12.12/12.29 tff(728,plain,
% 12.12/12.29 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, B!1), line_connecting(C!0, B!1)) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)) | (~unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.29 inference(modus_ponens,[status(thm)],[727, 726])).
% 12.12/12.29 tff(729,plain,
% 12.12/12.29 ($false),
% 12.12/12.29 inference(unit_resolution,[status(thm)],[728, 21, 569, 671, 722])).
% 12.12/12.29 tff(730,plain,(unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.29 tff(731,assumption,(~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))), introduced(assumption)).
% 12.12/12.29 tff(732,plain,
% 12.12/12.29 (((~![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(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))))),
% 12.12/12.29 inference(rewrite,[status(thm)],[])).
% 12.12/12.29 tff(733,plain,
% 12.12/12.29 ((~![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(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1))))),
% 12.12/12.29 inference(quant_inst,[status(thm)],[])).
% 12.12/12.29 tff(734,plain,
% 12.12/12.29 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, B!1), reverse_line(line_connecting(B!1, C!0))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)))),
% 12.12/12.29 inference(modus_ponens,[status(thm)],[733, 732])).
% 12.12/12.29 tff(735,plain,
% 12.12/12.29 ($false),
% 12.12/12.29 inference(unit_resolution,[status(thm)],[734, 21, 411, 731, 682])).
% 12.12/12.29 tff(736,plain,(unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(C!0, B!1)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.29 tff(737,plain,
% 12.12/12.29 (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))),
% 12.12/12.29 inference(unit_resolution,[status(thm)],[736, 730])).
% 12.12/12.29 tff(738,plain,
% 12.12/12.29 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))))),
% 12.12/12.29 inference(quant_inst,[status(thm)],[])).
% 12.12/12.29 tff(739,plain,
% 12.12/12.29 (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))))),
% 12.12/12.29 inference(unit_resolution,[status(thm)],[738, 132])).
% 12.12/12.29 tff(740,plain,
% 12.12/12.29 ((left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))) | (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))))),
% 12.12/12.29 inference(tautology,[status(thm)],[])).
% 12.12/12.29 tff(741,plain,
% 12.12/12.29 (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))),
% 12.12/12.29 inference(unit_resolution,[status(thm)],[740, 739])).
% 12.12/12.29 tff(742,plain,
% 12.12/12.29 ((left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))) | (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))))),
% 12.12/12.29 inference(tautology,[status(thm)],[])).
% 12.12/12.29 tff(743,plain,
% 12.12/12.29 (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))),
% 12.12/12.29 inference(unit_resolution,[status(thm)],[742, 739])).
% 12.12/12.29 tff(744,plain,
% 12.12/12.29 (((~![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(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))))),
% 12.12/12.29 inference(rewrite,[status(thm)],[])).
% 12.12/12.29 tff(745,plain,
% 12.12/12.29 ((left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))))) <=> (left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))))),
% 12.12/12.29 inference(rewrite,[status(thm)],[])).
% 12.12/12.29 tff(746,plain,
% 12.12/12.29 (((~![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(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))))),
% 12.12/12.29 inference(monotonicity,[status(thm)],[745])).
% 12.12/12.29 tff(747,plain,
% 12.12/12.29 (((~![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(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))))),
% 12.12/12.29 inference(transitivity,[status(thm)],[746, 744])).
% 12.12/12.29 tff(748,plain,
% 12.12/12.29 ((~![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(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))))),
% 12.12/12.29 inference(quant_inst,[status(thm)],[])).
% 12.12/12.29 tff(749,plain,
% 12.12/12.29 ((~![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(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0)))),
% 12.12/12.29 inference(modus_ponens,[status(thm)],[748, 747])).
% 12.12/12.29 tff(750,plain,
% 12.12/12.29 ((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(B!1, C!0))))),
% 12.12/12.29 inference(unit_resolution,[status(thm)],[749, 151, 743, 741])).
% 12.12/12.29 tff(751,plain,
% 12.12/12.29 (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))),
% 12.12/12.29 inference(unit_resolution,[status(thm)],[750, 737])).
% 12.12/12.29 tff(752,plain,
% 12.12/12.29 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, 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(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))))),
% 12.12/12.29 inference(rewrite,[status(thm)],[])).
% 12.12/12.29 tff(753,plain,
% 12.12/12.29 ((unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))))),
% 12.12/12.29 inference(rewrite,[status(thm)],[])).
% 12.12/12.29 tff(754,plain,
% 12.12/12.29 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, 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(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))))),
% 12.12/12.29 inference(monotonicity,[status(thm)],[753])).
% 12.12/12.29 tff(755,plain,
% 12.12/12.29 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, 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(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))))),
% 12.12/12.29 inference(transitivity,[status(thm)],[754, 752])).
% 12.12/12.29 tff(756,plain,
% 12.12/12.29 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.29 inference(quant_inst,[status(thm)],[])).
% 12.12/12.29 tff(757,plain,
% 12.12/12.29 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(line_connecting(B!1, C!0))))),
% 12.12/12.29 inference(modus_ponens,[status(thm)],[756, 755])).
% 12.12/12.29 tff(758,plain,
% 12.12/12.29 (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.29 inference(unit_resolution,[status(thm)],[757, 21, 751])).
% 12.12/12.29 tff(759,plain,
% 12.12/12.29 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.30 inference(tautology,[status(thm)],[])).
% 12.12/12.30 tff(760,plain,
% 12.12/12.30 ((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[759, 758])).
% 12.12/12.30 tff(761,plain,
% 12.12/12.30 (((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))))) | unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))),
% 12.12/12.30 inference(tautology,[status(thm)],[])).
% 12.12/12.30 tff(762,plain,
% 12.12/12.30 ((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[761, 607])).
% 12.12/12.30 tff(763,assumption,(~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))), introduced(assumption)).
% 12.12/12.30 tff(764,assumption,(~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))), introduced(assumption)).
% 12.12/12.30 tff(765,plain,
% 12.12/12.30 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, 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)), reverse_line(line_connecting(A!2, 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(line_connecting(A!2, 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)), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(766,plain,
% 12.12/12.30 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, 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)), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.30 inference(quant_inst,[status(thm)],[])).
% 12.12/12.30 tff(767,plain,
% 12.12/12.30 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, 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)), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.30 inference(modus_ponens,[status(thm)],[766, 765])).
% 12.12/12.30 tff(768,plain,
% 12.12/12.30 (~unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[767, 21, 43, 764])).
% 12.12/12.30 tff(769,plain,
% 12.12/12.30 (((~![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(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(A!2, 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(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(770,plain,
% 12.12/12.30 ((unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3))))) <=> (unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(771,plain,
% 12.12/12.30 (((~![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(A!2, C!0))) | unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(C!0, A!2), 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(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.30 inference(monotonicity,[status(thm)],[770])).
% 12.12/12.30 tff(772,plain,
% 12.12/12.30 (((~![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(A!2, C!0))) | unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(C!0, A!2), 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(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.30 inference(transitivity,[status(thm)],[771, 769])).
% 12.12/12.30 tff(773,plain,
% 12.12/12.30 ((~![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(A!2, C!0))) | unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))))),
% 12.12/12.30 inference(quant_inst,[status(thm)],[])).
% 12.12/12.30 tff(774,plain,
% 12.12/12.30 ((~![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(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(L!3)), reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.30 inference(modus_ponens,[status(thm)],[773, 772])).
% 12.12/12.30 tff(775,plain,
% 12.12/12.30 (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[774, 21, 353, 768])).
% 12.12/12.30 tff(776,plain,
% 12.12/12.30 (((~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3))))) | unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))),
% 12.12/12.30 inference(tautology,[status(thm)],[])).
% 12.12/12.30 tff(777,plain,
% 12.12/12.30 ((~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3))))),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[776, 775])).
% 12.12/12.30 tff(778,assumption,(unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))), introduced(assumption)).
% 12.12/12.30 tff(779,assumption,(left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))), introduced(assumption)).
% 12.12/12.30 tff(780,plain,
% 12.12/12.30 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))),
% 12.12/12.30 inference(quant_inst,[status(thm)],[])).
% 12.12/12.30 tff(781,plain,
% 12.12/12.30 ($false),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[780, 132, 779])).
% 12.12/12.30 tff(782,plain,(~(left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.30 tff(783,plain,
% 12.12/12.30 ((left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | (~left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))),
% 12.12/12.30 inference(tautology,[status(thm)],[])).
% 12.12/12.30 tff(784,plain,
% 12.12/12.30 (~left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[783, 782])).
% 12.12/12.30 tff(785,plain,
% 12.12/12.30 ((left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | (~left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)))),
% 12.12/12.30 inference(tautology,[status(thm)],[])).
% 12.12/12.30 tff(786,plain,
% 12.12/12.30 (~left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[785, 782])).
% 12.12/12.30 tff(787,assumption,(~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))), introduced(assumption)).
% 12.12/12.30 tff(788,assumption,(~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))), introduced(assumption)).
% 12.12/12.30 tff(789,plain,
% 12.12/12.30 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(L!3, reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!3, reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3)))))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(790,plain,
% 12.12/12.30 ((unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(L!3, reverse_line(L!3)))) <=> ((~unequally_directed_lines(L!3, reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3)))))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(791,plain,
% 12.12/12.30 (((~![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(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(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(L!3, reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))))),
% 12.12/12.30 inference(monotonicity,[status(thm)],[790])).
% 12.12/12.30 tff(792,plain,
% 12.12/12.30 (((~![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(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(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(L!3, reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3)))))),
% 12.12/12.30 inference(transitivity,[status(thm)],[791, 789])).
% 12.12/12.30 tff(793,plain,
% 12.12/12.30 ((~![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(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(L!3, reverse_line(L!3))))),
% 12.12/12.30 inference(quant_inst,[status(thm)],[])).
% 12.12/12.30 tff(794,plain,
% 12.12/12.30 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!3, reverse_line(L!3))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))),
% 12.12/12.30 inference(modus_ponens,[status(thm)],[793, 792])).
% 12.12/12.30 tff(795,plain,
% 12.12/12.30 ($false),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[794, 21, 257, 788, 116])).
% 12.12/12.30 tff(796,plain,(unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.30 tff(797,plain,
% 12.12/12.30 (((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))),
% 12.12/12.30 inference(tautology,[status(thm)],[])).
% 12.12/12.30 tff(798,plain,
% 12.12/12.30 ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3))))),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[797, 321])).
% 12.12/12.30 tff(799,plain,
% 12.12/12.30 (((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))))) | unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))),
% 12.12/12.30 inference(tautology,[status(thm)],[])).
% 12.12/12.30 tff(800,plain,
% 12.12/12.30 ((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3))))),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[799, 264])).
% 12.12/12.30 tff(801,plain,
% 12.12/12.30 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(802,plain,
% 12.12/12.30 (((~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3))))))) <=> ((~((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(803,plain,
% 12.12/12.30 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3))))))))),
% 12.12/12.30 inference(monotonicity,[status(thm)],[802])).
% 12.12/12.30 tff(804,plain,
% 12.12/12.30 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))))),
% 12.12/12.30 inference(transitivity,[status(thm)],[803, 801])).
% 12.12/12.30 tff(805,plain,
% 12.12/12.30 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))))),
% 12.12/12.30 inference(quant_inst,[status(thm)],[])).
% 12.12/12.30 tff(806,plain,
% 12.12/12.30 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(L!3, reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3))))))),
% 12.12/12.30 inference(modus_ponens,[status(thm)],[805, 804])).
% 12.12/12.30 tff(807,plain,
% 12.12/12.30 ((~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3))))))),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[806, 109, 800])).
% 12.12/12.30 tff(808,plain,
% 12.12/12.30 ((~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(L!3))))) | (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3))))))),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[807, 798])).
% 12.12/12.30 tff(809,plain,
% 12.12/12.30 (~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[808, 796])).
% 12.12/12.30 tff(810,assumption,(~unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))), introduced(assumption)).
% 12.12/12.30 tff(811,assumption,(~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))), introduced(assumption)).
% 12.12/12.30 tff(812,plain,
% 12.12/12.30 (((~![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), L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3))))))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(813,plain,
% 12.12/12.30 ((unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(L!3), L!3))) <=> ((~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3))))))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(814,plain,
% 12.12/12.30 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(L!3), 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(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))))),
% 12.12/12.30 inference(monotonicity,[status(thm)],[813])).
% 12.12/12.30 tff(815,plain,
% 12.12/12.30 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(L!3), 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(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3))))))),
% 12.12/12.30 inference(transitivity,[status(thm)],[814, 812])).
% 12.12/12.30 tff(816,plain,
% 12.12/12.30 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(L!3), L!3)))),
% 12.12/12.30 inference(quant_inst,[status(thm)],[])).
% 12.12/12.30 tff(817,plain,
% 12.12/12.30 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(L!3), L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))),
% 12.12/12.30 inference(modus_ponens,[status(thm)],[816, 815])).
% 12.12/12.30 tff(818,plain,
% 12.12/12.30 ($false),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[817, 21, 397, 811, 810])).
% 12.12/12.30 tff(819,plain,(unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(L!3, reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.30 tff(820,plain,
% 12.12/12.30 (unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[819, 809])).
% 12.12/12.30 tff(821,plain,
% 12.12/12.30 (((~![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(L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))) | unequally_directed_lines(reverse_line(reverse_line(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(L!3), reverse_line(L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(822,plain,
% 12.12/12.30 ((unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3))))))) <=> (unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(823,plain,
% 12.12/12.30 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))),
% 12.12/12.30 inference(monotonicity,[status(thm)],[822])).
% 12.12/12.30 tff(824,plain,
% 12.12/12.30 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)))),
% 12.12/12.30 inference(transitivity,[status(thm)],[823, 821])).
% 12.12/12.30 tff(825,plain,
% 12.12/12.30 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))))),
% 12.12/12.30 inference(quant_inst,[status(thm)],[])).
% 12.12/12.30 tff(826,plain,
% 12.12/12.30 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(reverse_line(L!3)))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))),
% 12.12/12.30 inference(modus_ponens,[status(thm)],[825, 824])).
% 12.12/12.30 tff(827,plain,
% 12.12/12.30 ($false),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[826, 21, 49, 820, 787])).
% 12.12/12.30 tff(828,plain,(unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.30 tff(829,plain,
% 12.12/12.30 (((~![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(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(830,plain,
% 12.12/12.30 ((left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)))) <=> ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(831,plain,
% 12.12/12.30 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))),
% 12.12/12.30 inference(monotonicity,[status(thm)],[830])).
% 12.12/12.30 tff(832,plain,
% 12.12/12.30 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))),
% 12.12/12.30 inference(transitivity,[status(thm)],[831, 829])).
% 12.12/12.30 tff(833,plain,
% 12.12/12.30 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))),
% 12.12/12.30 inference(quant_inst,[status(thm)],[])).
% 12.12/12.30 tff(834,plain,
% 12.12/12.30 ((~![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(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)),
% 12.12/12.30 inference(modus_ponens,[status(thm)],[833, 832])).
% 12.12/12.30 tff(835,plain,
% 12.12/12.30 ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[834, 151, 828])).
% 12.12/12.30 tff(836,plain,
% 12.12/12.30 (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[835, 786, 784])).
% 12.12/12.30 tff(837,plain,
% 12.12/12.30 (((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)),
% 12.12/12.30 inference(tautology,[status(thm)],[])).
% 12.12/12.30 tff(838,plain,
% 12.12/12.30 ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)))),
% 12.12/12.30 inference(unit_resolution,[status(thm)],[837, 836])).
% 12.12/12.30 tff(839,plain,
% 12.12/12.30 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(840,plain,
% 12.12/12.30 (((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3))))) <=> ((~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))))),
% 12.12/12.30 inference(rewrite,[status(thm)],[])).
% 12.12/12.30 tff(841,plain,
% 12.12/12.30 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3))))))),
% 12.12/12.31 inference(monotonicity,[status(thm)],[840])).
% 12.12/12.31 tff(842,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))))),
% 12.12/12.31 inference(transitivity,[status(thm)],[841, 839])).
% 12.12/12.31 tff(843,plain,
% 12.12/12.31 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))))),
% 12.12/12.31 inference(quant_inst,[status(thm)],[])).
% 12.12/12.31 tff(844,plain,
% 12.12/12.31 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), L!3)) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3))))),
% 12.12/12.31 inference(modus_ponens,[status(thm)],[843, 842])).
% 12.12/12.31 tff(845,plain,
% 12.12/12.31 ((~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3))))),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[844, 109, 249, 828])).
% 12.12/12.31 tff(846,plain,
% 12.12/12.31 (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[845, 838])).
% 12.12/12.31 tff(847,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, 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(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.31 inference(rewrite,[status(thm)],[])).
% 12.12/12.31 tff(848,plain,
% 12.12/12.31 ((unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0))))) <=> (unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.31 inference(rewrite,[status(thm)],[])).
% 12.12/12.31 tff(849,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, 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(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0))))))),
% 12.12/12.31 inference(monotonicity,[status(thm)],[848])).
% 12.12/12.31 tff(850,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, 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(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.31 inference(transitivity,[status(thm)],[849, 847])).
% 12.12/12.31 tff(851,plain,
% 12.12/12.31 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.31 inference(quant_inst,[status(thm)],[])).
% 12.12/12.31 tff(852,plain,
% 12.12/12.31 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.31 inference(modus_ponens,[status(thm)],[851, 850])).
% 12.12/12.31 tff(853,plain,
% 12.12/12.31 ($false),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[852, 21, 846, 764, 778])).
% 12.12/12.31 tff(854,plain,(unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0))))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.31 tff(855,plain,
% 12.12/12.31 (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[854, 764])).
% 12.12/12.31 tff(856,assumption,(~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))), introduced(assumption)).
% 12.12/12.31 tff(857,assumption,(unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2))), introduced(assumption)).
% 12.12/12.31 tff(858,plain,
% 12.12/12.31 (((~![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(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2))))),
% 12.12/12.31 inference(rewrite,[status(thm)],[])).
% 12.12/12.31 tff(859,plain,
% 12.12/12.31 ((~![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(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2))))),
% 12.12/12.31 inference(quant_inst,[status(thm)],[])).
% 12.12/12.31 tff(860,plain,
% 12.12/12.31 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2)))),
% 12.12/12.31 inference(modus_ponens,[status(thm)],[859, 858])).
% 12.12/12.31 tff(861,plain,
% 12.12/12.31 ($false),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[860, 21, 353, 857, 856])).
% 12.12/12.31 tff(862,plain,(unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.31 tff(863,plain,
% 12.12/12.31 (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2))),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[862, 855])).
% 12.12/12.31 tff(864,assumption,(~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2))), introduced(assumption)).
% 12.12/12.31 tff(865,assumption,(unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))), introduced(assumption)).
% 12.12/12.31 tff(866,plain,
% 12.12/12.31 (((~![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(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2)))),
% 12.12/12.31 inference(rewrite,[status(thm)],[])).
% 12.12/12.31 tff(867,plain,
% 12.12/12.31 ((unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)))) <=> (unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2)))),
% 12.12/12.31 inference(rewrite,[status(thm)],[])).
% 12.12/12.31 tff(868,plain,
% 12.12/12.31 (((~![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(C!0, A!2)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(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(L!3), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2))))),
% 12.12/12.31 inference(monotonicity,[status(thm)],[867])).
% 12.12/12.31 tff(869,plain,
% 12.12/12.31 (((~![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(C!0, A!2)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(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(L!3), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2)))),
% 12.12/12.31 inference(transitivity,[status(thm)],[868, 866])).
% 12.12/12.31 tff(870,plain,
% 12.12/12.31 ((~![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(C!0, A!2)) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))))),
% 12.12/12.31 inference(quant_inst,[status(thm)],[])).
% 12.12/12.31 tff(871,plain,
% 12.12/12.31 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2))),
% 12.12/12.31 inference(modus_ponens,[status(thm)],[870, 869])).
% 12.12/12.31 tff(872,plain,
% 12.12/12.31 ($false),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[871, 21, 651, 865, 864])).
% 12.12/12.31 tff(873,plain,(unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2)) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(L!3)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.31 tff(874,plain,
% 12.12/12.31 (unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2)) | unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[873, 828])).
% 12.12/12.31 tff(875,plain,
% 12.12/12.31 (unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[874, 863])).
% 12.12/12.31 tff(876,plain,
% 12.12/12.31 ($false),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[376, 21, 264, 764, 672])).
% 12.12/12.31 tff(877,plain,(unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.31 tff(878,plain,
% 12.12/12.31 (~unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[877, 764])).
% 12.12/12.31 tff(879,assumption,(unequally_directed_lines(line_connecting(A!2, C!0), L!3)), introduced(assumption)).
% 12.12/12.31 tff(880,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(line_connecting(A!2, C!0), L!3)) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, 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(A!2, C!0), L!3)) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.31 inference(rewrite,[status(thm)],[])).
% 12.12/12.31 tff(881,plain,
% 12.12/12.31 ((unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), L!3))) <=> ((~unequally_directed_lines(line_connecting(A!2, C!0), L!3)) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.31 inference(rewrite,[status(thm)],[])).
% 12.12/12.31 tff(882,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), 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(line_connecting(A!2, C!0), L!3)) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.31 inference(monotonicity,[status(thm)],[881])).
% 12.12/12.31 tff(883,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), 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(line_connecting(A!2, C!0), L!3)) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.31 inference(transitivity,[status(thm)],[882, 880])).
% 12.12/12.31 tff(884,plain,
% 12.12/12.31 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), L!3)))),
% 12.12/12.31 inference(quant_inst,[status(thm)],[])).
% 12.12/12.31 tff(885,plain,
% 12.12/12.31 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(line_connecting(A!2, C!0), L!3)) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.31 inference(modus_ponens,[status(thm)],[884, 883])).
% 12.12/12.31 tff(886,plain,
% 12.12/12.31 ($false),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[885, 21, 879, 378, 763])).
% 12.12/12.31 tff(887,plain,(unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), L!3)) | unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.31 tff(888,plain,
% 12.12/12.31 (~unequally_directed_lines(line_connecting(A!2, C!0), L!3)),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[887, 878, 763])).
% 12.12/12.31 tff(889,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!3, L!3) | unequally_directed_lines(line_connecting(A!2, C!0), L!3) | (~unequally_directed_lines(L!3, line_connecting(A!2, 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(L!3, L!3) | unequally_directed_lines(line_connecting(A!2, C!0), L!3) | (~unequally_directed_lines(L!3, line_connecting(A!2, C!0))))),
% 12.12/12.31 inference(rewrite,[status(thm)],[])).
% 12.12/12.31 tff(890,plain,
% 12.12/12.31 ((unequally_directed_lines(line_connecting(A!2, C!0), L!3) | unequally_directed_lines(L!3, L!3) | (~unequally_directed_lines(L!3, line_connecting(A!2, C!0)))) <=> (unequally_directed_lines(L!3, L!3) | unequally_directed_lines(line_connecting(A!2, C!0), L!3) | (~unequally_directed_lines(L!3, line_connecting(A!2, C!0))))),
% 12.12/12.31 inference(rewrite,[status(thm)],[])).
% 12.12/12.31 tff(891,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), L!3) | unequally_directed_lines(L!3, L!3) | (~unequally_directed_lines(L!3, line_connecting(A!2, 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(L!3, L!3) | unequally_directed_lines(line_connecting(A!2, C!0), L!3) | (~unequally_directed_lines(L!3, line_connecting(A!2, C!0)))))),
% 12.12/12.31 inference(monotonicity,[status(thm)],[890])).
% 12.12/12.31 tff(892,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), L!3) | unequally_directed_lines(L!3, L!3) | (~unequally_directed_lines(L!3, line_connecting(A!2, 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(L!3, L!3) | unequally_directed_lines(line_connecting(A!2, C!0), L!3) | (~unequally_directed_lines(L!3, line_connecting(A!2, C!0))))),
% 12.12/12.31 inference(transitivity,[status(thm)],[891, 889])).
% 12.12/12.31 tff(893,plain,
% 12.12/12.31 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), L!3) | unequally_directed_lines(L!3, L!3) | (~unequally_directed_lines(L!3, line_connecting(A!2, C!0))))),
% 12.12/12.31 inference(quant_inst,[status(thm)],[])).
% 12.12/12.31 tff(894,plain,
% 12.12/12.31 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!3, L!3) | unequally_directed_lines(line_connecting(A!2, C!0), L!3) | (~unequally_directed_lines(L!3, line_connecting(A!2, C!0)))),
% 12.12/12.31 inference(modus_ponens,[status(thm)],[893, 892])).
% 12.12/12.31 tff(895,plain,
% 12.12/12.31 (unequally_directed_lines(line_connecting(A!2, C!0), L!3) | (~unequally_directed_lines(L!3, line_connecting(A!2, C!0)))),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[894, 21, 245])).
% 12.12/12.31 tff(896,plain,
% 12.12/12.31 (~unequally_directed_lines(L!3, line_connecting(A!2, C!0))),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[895, 888])).
% 12.12/12.31 tff(897,plain,
% 12.12/12.31 (unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[634, 896])).
% 12.12/12.31 tff(898,assumption,(unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))), introduced(assumption)).
% 12.12/12.31 tff(899,assumption,(~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2)))), introduced(assumption)).
% 12.12/12.31 tff(900,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, 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(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))))),
% 12.12/12.31 inference(rewrite,[status(thm)],[])).
% 12.12/12.31 tff(901,plain,
% 12.12/12.31 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))))),
% 12.12/12.31 inference(quant_inst,[status(thm)],[])).
% 12.12/12.31 tff(902,plain,
% 12.12/12.31 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(C!0, A!2))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0)))),
% 12.12/12.31 inference(modus_ponens,[status(thm)],[901, 900])).
% 12.12/12.31 tff(903,plain,
% 12.12/12.31 ($false),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[902, 21, 600, 899, 898])).
% 12.12/12.31 tff(904,plain,(unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.31 tff(905,plain,
% 12.12/12.31 (unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2)))),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[904, 897])).
% 12.12/12.31 tff(906,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))) | (~((~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))) | (~((~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))))))),
% 12.12/12.31 inference(rewrite,[status(thm)],[])).
% 12.12/12.31 tff(907,plain,
% 12.12/12.31 (((~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))) | (~((~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2))))) <=> ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))) | (~((~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))))))),
% 12.12/12.31 inference(rewrite,[status(thm)],[])).
% 12.12/12.31 tff(908,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))) | (~((~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))) | (~((~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3))))))))),
% 12.12/12.31 inference(monotonicity,[status(thm)],[907])).
% 12.12/12.31 tff(909,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))) | (~((~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))) | (~((~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))))))),
% 12.12/12.31 inference(transitivity,[status(thm)],[908, 906])).
% 12.12/12.31 tff(910,plain,
% 12.12/12.31 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))) | (~((~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3)))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2)))))),
% 12.12/12.31 inference(quant_inst,[status(thm)],[])).
% 12.12/12.31 tff(911,plain,
% 12.12/12.31 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), reverse_line(L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(L!3)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(C!0, A!2)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))) | (~((~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(L!3))) | (~unequally_directed_lines(line_connecting(C!0, A!2), reverse_line(reverse_line(L!3))))))),
% 12.12/12.31 inference(modus_ponens,[status(thm)],[910, 909])).
% 12.12/12.31 tff(912,plain,
% 12.12/12.31 ($false),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[911, 109, 905, 51, 875, 777])).
% 12.12/12.31 tff(913,plain,(unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.31 tff(914,plain,
% 12.12/12.31 (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[913, 763])).
% 12.12/12.31 tff(915,plain,
% 12.12/12.31 (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[158, 914])).
% 12.12/12.31 tff(916,plain,
% 12.12/12.31 (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.31 inference(unit_resolution,[status(thm)],[368, 915])).
% 12.12/12.31 tff(917,assumption,(unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))), introduced(assumption)).
% 12.12/12.31 tff(918,plain,
% 12.12/12.31 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, 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(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.31 inference(rewrite,[status(thm)],[])).
% 12.12/12.31 tff(919,plain,
% 12.12/12.31 ((unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3)))))) <=> ((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.32 inference(rewrite,[status(thm)],[])).
% 12.12/12.32 tff(920,plain,
% 12.12/12.32 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.32 inference(monotonicity,[status(thm)],[919])).
% 12.12/12.32 tff(921,plain,
% 12.12/12.32 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.32 inference(transitivity,[status(thm)],[920, 918])).
% 12.12/12.32 tff(922,plain,
% 12.12/12.32 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))))),
% 12.12/12.32 inference(quant_inst,[status(thm)],[])).
% 12.12/12.32 tff(923,plain,
% 12.12/12.32 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.32 inference(modus_ponens,[status(thm)],[922, 921])).
% 12.12/12.32 tff(924,plain,
% 12.12/12.32 ($false),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[923, 21, 917, 763, 350])).
% 12.12/12.32 tff(925,plain,(unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), reverse_line(line_connecting(A!2, C!0)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.32 tff(926,plain,
% 12.12/12.32 (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[925, 916, 763])).
% 12.12/12.32 tff(927,assumption,(~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))), introduced(assumption)).
% 12.12/12.32 tff(928,plain,
% 12.12/12.32 (((~![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(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3)))))),
% 12.12/12.32 inference(rewrite,[status(thm)],[])).
% 12.12/12.32 tff(929,plain,
% 12.12/12.32 ((unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0)))) <=> (unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3)))))),
% 12.12/12.32 inference(rewrite,[status(thm)],[])).
% 12.12/12.32 tff(930,plain,
% 12.12/12.32 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, 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(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))))),
% 12.12/12.32 inference(monotonicity,[status(thm)],[929])).
% 12.12/12.32 tff(931,plain,
% 12.12/12.32 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, 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(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3)))))),
% 12.12/12.32 inference(transitivity,[status(thm)],[930, 928])).
% 12.12/12.32 tff(932,plain,
% 12.12/12.32 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))))),
% 12.12/12.32 inference(quant_inst,[status(thm)],[])).
% 12.12/12.32 tff(933,plain,
% 12.12/12.32 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3))))),
% 12.12/12.32 inference(modus_ponens,[status(thm)],[932, 931])).
% 12.12/12.32 tff(934,plain,
% 12.12/12.32 ($false),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[933, 21, 898, 927, 116])).
% 12.12/12.32 tff(935,plain,(unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.32 tff(936,plain,
% 12.12/12.32 (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[935, 926])).
% 12.12/12.32 tff(937,plain,
% 12.12/12.32 (unequally_directed_lines(L!3, line_connecting(A!2, C!0))),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[634, 936])).
% 12.12/12.32 tff(938,plain,
% 12.12/12.32 ((~distinct_points(A!2, C!0)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(A!2, C!0))),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[597, 937])).
% 12.12/12.32 tff(939,plain,
% 12.12/12.32 (~before_on_line(L!3, A!2, C!0)),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[595, 938])).
% 12.12/12.32 tff(940,plain,
% 12.12/12.32 (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(L!3))), line_connecting(C!0, A!2))),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[358, 916])).
% 12.12/12.32 tff(941,plain,
% 12.12/12.32 (unequally_directed_lines(L!3, line_connecting(C!0, A!2))),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[348, 940])).
% 12.12/12.32 tff(942,plain,
% 12.12/12.32 ((~distinct_points(C!0, A!2)) | left_apart_point(C!0, reverse_line(L!3)) | left_apart_point(C!0, L!3) | left_apart_point(A!2, reverse_line(L!3)) | left_apart_point(A!2, L!3) | unequally_directed_lines(L!3, line_connecting(C!0, A!2))),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[311, 941])).
% 12.12/12.32 tff(943,plain,
% 12.12/12.32 (~before_on_line(L!3, C!0, A!2)),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[309, 942])).
% 12.12/12.32 tff(944,plain,
% 12.12/12.32 ((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, C!0, A!2))),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[294, 943])).
% 12.12/12.32 tff(945,plain,
% 12.12/12.32 (~((~before_on_line(L!3, B!1, A!2)) | (~before_on_line(L!3, A!2, C!0)))),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[292, 944])).
% 12.12/12.32 tff(946,plain,
% 12.12/12.32 ($false),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[580, 945, 939])).
% 12.12/12.32 tff(947,plain,(unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.32 tff(948,plain,
% 12.12/12.32 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 12.12/12.32 inference(rewrite,[status(thm)],[])).
% 12.12/12.32 tff(949,plain,
% 12.12/12.32 (((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))))) <=> ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 12.12/12.32 inference(rewrite,[status(thm)],[])).
% 12.12/12.32 tff(950,plain,
% 12.12/12.32 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.32 inference(rewrite,[status(thm)],[])).
% 12.12/12.32 tff(951,plain,
% 12.12/12.32 ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) <=> (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0))))))),
% 12.12/12.32 inference(monotonicity,[status(thm)],[950])).
% 12.12/12.32 tff(952,plain,
% 12.12/12.32 (((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))))) <=> ((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 12.12/12.32 inference(monotonicity,[status(thm)],[951])).
% 12.12/12.32 tff(953,plain,
% 12.12/12.32 (((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))))) <=> ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 12.12/12.32 inference(transitivity,[status(thm)],[952, 949])).
% 12.12/12.32 tff(954,plain,
% 12.12/12.32 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))))))),
% 12.12/12.32 inference(monotonicity,[status(thm)],[953])).
% 12.12/12.32 tff(955,plain,
% 12.12/12.32 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 12.12/12.32 inference(transitivity,[status(thm)],[954, 948])).
% 12.12/12.32 tff(956,plain,
% 12.12/12.32 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 12.12/12.32 inference(quant_inst,[status(thm)],[])).
% 12.12/12.32 tff(957,plain,
% 12.12/12.32 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(line_connecting(A!2, C!0), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.32 inference(modus_ponens,[status(thm)],[956, 955])).
% 12.12/12.32 tff(958,plain,
% 12.12/12.32 (~unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[957, 109, 947, 762, 760])).
% 12.12/12.32 tff(959,assumption,(unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))), introduced(assumption)).
% 12.12/12.32 tff(960,assumption,(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))), introduced(assumption)).
% 12.12/12.32 tff(961,plain,
% 12.12/12.32 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))),
% 12.12/12.32 inference(quant_inst,[status(thm)],[])).
% 12.12/12.32 tff(962,plain,
% 12.12/12.32 ($false),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[961, 132, 960])).
% 12.12/12.32 tff(963,plain,(~(left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.32 tff(964,plain,
% 12.12/12.32 ((left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.32 inference(tautology,[status(thm)],[])).
% 12.12/12.32 tff(965,plain,
% 12.12/12.32 (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[964, 963])).
% 12.12/12.32 tff(966,plain,
% 12.12/12.32 ((left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.12/12.32 inference(tautology,[status(thm)],[])).
% 12.12/12.32 tff(967,plain,
% 12.12/12.32 (~left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))),
% 12.12/12.32 inference(unit_resolution,[status(thm)],[966, 963])).
% 12.12/12.32 tff(968,assumption,(unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))), introduced(assumption)).
% 12.12/12.32 tff(969,plain,
% 12.12/12.32 (((~![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(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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))))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.32 inference(rewrite,[status(thm)],[])).
% 12.12/12.32 tff(970,plain,
% 12.12/12.32 ((left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))) <=> (left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.32 inference(rewrite,[status(thm)],[])).
% 12.12/12.32 tff(971,plain,
% 12.12/12.32 (((~![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(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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))))) | (left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))),
% 12.12/12.32 inference(monotonicity,[status(thm)],[970])).
% 12.12/12.32 tff(972,plain,
% 12.12/12.32 (((~![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(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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))))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.33 inference(transitivity,[status(thm)],[971, 969])).
% 12.12/12.33 tff(973,plain,
% 12.12/12.33 ((~![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(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))),
% 12.12/12.33 inference(quant_inst,[status(thm)],[])).
% 12.12/12.33 tff(974,plain,
% 12.12/12.33 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | left_convergent_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.12/12.33 inference(modus_ponens,[status(thm)],[973, 972])).
% 12.12/12.33 tff(975,plain,
% 12.12/12.33 ($false),
% 12.12/12.33 inference(unit_resolution,[status(thm)],[974, 151, 959, 968, 967, 965])).
% 12.12/12.33 tff(976,plain,((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.33 tff(977,plain,
% 12.12/12.33 (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.12/12.33 inference(unit_resolution,[status(thm)],[976, 959])).
% 12.12/12.33 tff(978,plain,
% 12.12/12.33 (((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.33 inference(rewrite,[status(thm)],[])).
% 12.12/12.33 tff(979,plain,
% 12.12/12.33 ((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.33 inference(quant_inst,[status(thm)],[])).
% 12.12/12.33 tff(980,plain,
% 12.12/12.33 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.12/12.33 inference(modus_ponens,[status(thm)],[979, 978])).
% 12.12/12.33 tff(981,plain,
% 12.12/12.33 ($false),
% 12.12/12.33 inference(unit_resolution,[status(thm)],[980, 21, 11, 959, 977])).
% 12.12/12.33 tff(982,plain,(~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.33 tff(983,assumption,((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))))), introduced(assumption)).
% 12.12/12.33 tff(984,assumption,(~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))), introduced(assumption)).
% 12.12/12.33 tff(985,plain,
% 12.12/12.33 (((~![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(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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(L!3), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.12/12.33 inference(rewrite,[status(thm)],[])).
% 12.12/12.33 tff(986,plain,
% 12.12/12.33 ((unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))))) <=> ((~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.12/12.33 inference(rewrite,[status(thm)],[])).
% 12.12/12.33 tff(987,plain,
% 12.12/12.33 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, 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(L!3), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.33 inference(monotonicity,[status(thm)],[986])).
% 12.12/12.33 tff(988,plain,
% 12.12/12.33 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, 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(L!3), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.12/12.33 inference(transitivity,[status(thm)],[987, 985])).
% 12.12/12.33 tff(989,plain,
% 12.12/12.33 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.33 inference(quant_inst,[status(thm)],[])).
% 12.12/12.33 tff(990,plain,
% 12.12/12.33 ((~![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(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))),
% 12.12/12.33 inference(modus_ponens,[status(thm)],[989, 988])).
% 12.12/12.33 tff(991,plain,
% 12.12/12.33 ((~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))),
% 12.12/12.33 inference(unit_resolution,[status(thm)],[990, 21])).
% 12.12/12.33 tff(992,plain,
% 12.12/12.33 (unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))),
% 12.12/12.33 inference(unit_resolution,[status(thm)],[991, 984, 31])).
% 12.12/12.33 tff(993,plain,
% 12.12/12.33 (((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.33 inference(rewrite,[status(thm)],[])).
% 12.12/12.33 tff(994,plain,
% 12.12/12.33 ((unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) <=> ((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.33 inference(rewrite,[status(thm)],[])).
% 12.12/12.33 tff(995,plain,
% 12.12/12.33 (((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))),
% 12.12/12.33 inference(monotonicity,[status(thm)],[994])).
% 12.12/12.33 tff(996,plain,
% 12.12/12.33 (((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.33 inference(transitivity,[status(thm)],[995, 993])).
% 12.12/12.33 tff(997,plain,
% 12.12/12.33 ((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.33 inference(quant_inst,[status(thm)],[])).
% 12.12/12.33 tff(998,plain,
% 12.12/12.33 ((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.12/12.33 inference(modus_ponens,[status(thm)],[997, 996])).
% 12.12/12.33 tff(999,plain,
% 12.12/12.33 (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))),
% 12.12/12.33 inference(unit_resolution,[status(thm)],[998, 21, 11])).
% 12.12/12.33 tff(1000,plain,
% 12.12/12.33 (((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, 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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.33 inference(rewrite,[status(thm)],[])).
% 12.12/12.33 tff(1001,plain,
% 12.12/12.33 ((unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0))))) <=> (unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.33 inference(rewrite,[status(thm)],[])).
% 12.12/12.33 tff(1002,plain,
% 12.12/12.33 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, 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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0))))))),
% 12.12/12.33 inference(monotonicity,[status(thm)],[1001])).
% 12.12/12.33 tff(1003,plain,
% 12.12/12.33 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, 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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.33 inference(transitivity,[status(thm)],[1002, 1000])).
% 12.12/12.33 tff(1004,plain,
% 12.12/12.33 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.33 inference(quant_inst,[status(thm)],[])).
% 12.12/12.33 tff(1005,plain,
% 12.12/12.33 ((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0))))),
% 12.12/12.34 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 12.12/12.34 tff(1006,plain,
% 12.12/12.34 (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.34 inference(unit_resolution,[status(thm)],[1005, 21, 999, 984])).
% 12.12/12.34 tff(1007,plain,
% 12.12/12.34 (((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0)))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))),
% 12.12/12.34 inference(tautology,[status(thm)],[])).
% 12.12/12.34 tff(1008,plain,
% 12.12/12.34 ((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0)))),
% 12.12/12.34 inference(unit_resolution,[status(thm)],[1007, 1006])).
% 12.12/12.34 tff(1009,assumption,((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0)))), introduced(assumption)).
% 12.12/12.34 tff(1010,assumption,(unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))), introduced(assumption)).
% 12.12/12.34 tff(1011,assumption,(~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))), introduced(assumption)).
% 12.12/12.34 tff(1012,plain,
% 12.12/12.34 (((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), 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(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.34 inference(rewrite,[status(thm)],[])).
% 12.12/12.34 tff(1013,plain,
% 12.12/12.34 ((~![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(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.34 inference(quant_inst,[status(thm)],[])).
% 12.12/12.34 tff(1014,plain,
% 12.12/12.34 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.12/12.34 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 12.12/12.34 tff(1015,plain,
% 12.12/12.34 ($false),
% 12.12/12.34 inference(unit_resolution,[status(thm)],[1014, 21, 11, 1010, 1011])).
% 12.12/12.34 tff(1016,plain,(unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.34 tff(1017,plain,
% 12.12/12.34 (unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.12/12.34 inference(unit_resolution,[status(thm)],[1016, 1010])).
% 12.12/12.34 tff(1018,plain,
% 12.12/12.34 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.34 inference(rewrite,[status(thm)],[])).
% 12.12/12.34 tff(1019,plain,
% 12.12/12.34 (((~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))) <=> ((~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.34 inference(rewrite,[status(thm)],[])).
% 12.12/12.34 tff(1020,plain,
% 12.12/12.34 ((~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))) <=> (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0)))))),
% 12.12/12.34 inference(rewrite,[status(thm)],[])).
% 12.12/12.34 tff(1021,plain,
% 12.12/12.34 (((~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))) <=> ((~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))),
% 12.12/12.34 inference(monotonicity,[status(thm)],[1020])).
% 12.12/12.34 tff(1022,plain,
% 12.12/12.34 (((~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))) <=> ((~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.34 inference(transitivity,[status(thm)],[1021, 1019])).
% 12.12/12.34 tff(1023,plain,
% 12.12/12.34 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))),
% 12.12/12.34 inference(monotonicity,[status(thm)],[1022])).
% 12.12/12.34 tff(1024,plain,
% 12.12/12.34 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.12/12.34 inference(transitivity,[status(thm)],[1023, 1018])).
% 12.12/12.34 tff(1025,plain,
% 12.12/12.34 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))),
% 12.12/12.34 inference(quant_inst,[status(thm)],[])).
% 12.12/12.34 tff(1026,plain,
% 12.12/12.34 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.12/12.34 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 12.12/12.34 tff(1027,plain,
% 12.12/12.34 ($false),
% 12.12/12.34 inference(unit_resolution,[status(thm)],[1026, 109, 1010, 983, 1017, 1009])).
% 12.12/12.34 tff(1028,plain,((~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))))))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.34 tff(1029,plain,
% 12.12/12.34 ($false),
% 12.12/12.34 inference(unit_resolution,[status(thm)],[1028, 1008, 992, 983])).
% 12.12/12.34 tff(1030,plain,(unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))))), inference(lemma,lemma(discharge,[]))).
% 12.12/12.34 tff(1031,plain,
% 12.12/12.34 (~((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.34 inference(unit_resolution,[status(thm)],[1030, 31, 982])).
% 12.12/12.34 tff(1032,plain,
% 12.12/12.34 (((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0))))) | unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))),
% 12.12/12.34 inference(tautology,[status(thm)],[])).
% 12.12/12.34 tff(1033,plain,
% 12.12/12.34 (unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))),
% 12.12/12.34 inference(unit_resolution,[status(thm)],[1032, 1031])).
% 12.12/12.34 tff(1034,plain,
% 12.12/12.34 (((~![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(A!2, C!0))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, 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(L!3), line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))))),
% 12.12/12.34 inference(rewrite,[status(thm)],[])).
% 12.12/12.34 tff(1035,plain,
% 12.12/12.34 ((unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0)))) <=> ((~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))))),
% 12.18/12.34 inference(rewrite,[status(thm)],[])).
% 12.18/12.34 tff(1036,plain,
% 12.18/12.34 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, 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(L!3), line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 12.18/12.34 inference(monotonicity,[status(thm)],[1035])).
% 12.18/12.34 tff(1037,plain,
% 12.18/12.34 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, 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(L!3), line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))))),
% 12.18/12.34 inference(transitivity,[status(thm)],[1036, 1034])).
% 12.18/12.34 tff(1038,plain,
% 12.18/12.34 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))))),
% 12.18/12.34 inference(quant_inst,[status(thm)],[])).
% 12.18/12.34 tff(1039,plain,
% 12.18/12.34 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(L!3), line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(L!3), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0))))),
% 12.18/12.34 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 12.18/12.34 tff(1040,plain,
% 12.18/12.34 ($false),
% 12.18/12.34 inference(unit_resolution,[status(thm)],[1039, 21, 1033, 958, 168])).
% 12.18/12.34 tff(1041,plain,(~unequally_directed_lines(reverse_line(L!3), reverse_line(line_connecting(A!2, C!0)))), inference(lemma,lemma(discharge,[]))).
% 12.18/12.34 tff(1042,plain,
% 12.18/12.34 (~unequally_directed_lines(reverse_line(L!3), line_connecting(C!0, A!2))),
% 12.18/12.34 inference(unit_resolution,[status(thm)],[649, 1041])).
% 12.18/12.34 tff(1043,plain,
% 12.18/12.34 (unequally_directed_lines(L!3, line_connecting(C!0, A!2))),
% 12.18/12.34 inference(unit_resolution,[status(thm)],[659, 1042])).
% 12.18/12.34 tff(1044,plain,
% 12.18/12.34 (unequally_directed_lines(L!3, reverse_line(line_connecting(A!2, C!0)))),
% 12.18/12.34 inference(unit_resolution,[status(thm)],[669, 1043])).
% 12.18/12.35 tff(1045,plain,
% 12.18/12.35 (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))),
% 12.18/12.35 inference(unit_resolution,[status(thm)],[877, 1044])).
% 12.18/12.35 tff(1046,plain,
% 12.18/12.35 (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))),
% 12.18/12.35 inference(unit_resolution,[status(thm)],[158, 1045])).
% 12.18/12.35 tff(1047,plain,
% 12.18/12.35 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))),
% 12.18/12.35 inference(tautology,[status(thm)],[])).
% 12.18/12.35 tff(1048,plain,
% 12.18/12.35 ((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3)))))),
% 12.18/12.35 inference(unit_resolution,[status(thm)],[1047, 1046])).
% 12.18/12.35 tff(1049,plain,
% 12.18/12.35 (((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(reverse_line(L!3)))))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))),
% 12.18/12.35 inference(tautology,[status(thm)],[])).
% 12.18/12.35 tff(1050,plain,
% 12.18/12.35 ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(reverse_line(L!3)))))),
% 12.18/12.35 inference(unit_resolution,[status(thm)],[1049, 846])).
% 12.18/12.35 tff(1051,plain,
% 12.18/12.35 (unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(C!0, A!2))),
% 12.18/12.35 inference(unit_resolution,[status(thm)],[874, 1042])).
% 12.18/12.35 tff(1052,plain,
% 12.18/12.35 (unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))),
% 12.18/12.35 inference(unit_resolution,[status(thm)],[862, 1051])).
% 12.18/12.35 tff(1053,plain,
% 12.18/12.35 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 12.18/12.35 inference(rewrite,[status(thm)],[])).
% 12.18/12.35 tff(1054,plain,
% 12.18/12.35 (((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0)))))) <=> ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 12.18/12.35 inference(rewrite,[status(thm)],[])).
% 12.18/12.35 tff(1055,plain,
% 12.18/12.35 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0)))))))),
% 12.18/12.35 inference(monotonicity,[status(thm)],[1054])).
% 12.18/12.35 tff(1056,plain,
% 12.18/12.35 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 12.18/12.35 inference(transitivity,[status(thm)],[1055, 1053])).
% 12.18/12.35 tff(1057,plain,
% 12.18/12.35 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 12.18/12.35 inference(quant_inst,[status(thm)],[])).
% 12.18/12.35 tff(1058,plain,
% 12.18/12.35 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(L!3)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(reverse_line(L!3))))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0)))))),
% 12.18/12.35 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 12.18/12.35 tff(1059,plain,
% 12.18/12.35 (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0))))),
% 12.18/12.35 inference(unit_resolution,[status(thm)],[1058, 109, 1052, 1050, 1048])).
% 12.18/12.35 tff(1060,plain,
% 12.18/12.35 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, 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(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0)))))),
% 12.18/12.35 inference(rewrite,[status(thm)],[])).
% 12.18/12.35 tff(1061,plain,
% 12.18/12.35 ((unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0)))) <=> (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0)))))),
% 12.18/12.35 inference(rewrite,[status(thm)],[])).
% 12.18/12.35 tff(1062,plain,
% 12.18/12.35 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, 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(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0))))))),
% 12.18/12.35 inference(monotonicity,[status(thm)],[1061])).
% 12.18/12.35 tff(1063,plain,
% 12.18/12.35 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, 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(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0)))))),
% 12.18/12.35 inference(transitivity,[status(thm)],[1062, 1060])).
% 12.18/12.35 tff(1064,plain,
% 12.18/12.35 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))))),
% 12.18/12.35 inference(quant_inst,[status(thm)],[])).
% 12.18/12.35 tff(1065,plain,
% 12.18/12.35 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, C!0), reverse_line(reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(reverse_line(line_connecting(A!2, C!0))))),
% 12.18/12.35 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 12.18/12.35 tff(1066,plain,
% 12.18/12.35 (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))),
% 12.18/12.35 inference(unit_resolution,[status(thm)],[1065, 21, 958, 1059])).
% 12.18/12.35 tff(1067,plain,
% 12.18/12.35 (((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))),
% 12.18/12.35 inference(tautology,[status(thm)],[])).
% 12.18/12.35 tff(1068,plain,
% 12.18/12.35 ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0)))),
% 12.18/12.35 inference(unit_resolution,[status(thm)],[1067, 1066])).
% 12.18/12.35 tff(1069,plain,
% 12.18/12.35 (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))),
% 12.18/12.35 inference(unit_resolution,[status(thm)],[1005, 21, 999, 982])).
% 12.18/12.35 tff(1070,plain,
% 12.18/12.35 ((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0)))),
% 12.18/12.35 inference(unit_resolution,[status(thm)],[1007, 1069])).
% 12.18/12.35 tff(1071,plain,
% 12.18/12.35 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.18/12.35 inference(rewrite,[status(thm)],[])).
% 12.18/12.35 tff(1072,plain,
% 12.18/12.35 (((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))) <=> ((~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.18/12.35 inference(rewrite,[status(thm)],[])).
% 12.18/12.35 tff(1073,plain,
% 12.18/12.35 ((~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))))) <=> (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0)))))),
% 12.18/12.35 inference(rewrite,[status(thm)],[])).
% 12.18/12.35 tff(1074,plain,
% 12.18/12.35 (((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))) <=> ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))),
% 12.18/12.35 inference(monotonicity,[status(thm)],[1020, 1073])).
% 12.18/12.35 tff(1075,plain,
% 12.18/12.35 (((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))) <=> ((~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.18/12.35 inference(transitivity,[status(thm)],[1074, 1072])).
% 12.18/12.35 tff(1076,plain,
% 12.18/12.35 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))),
% 12.18/12.35 inference(monotonicity,[status(thm)],[1075])).
% 12.18/12.35 tff(1077,plain,
% 12.18/12.35 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.18/12.35 inference(transitivity,[status(thm)],[1076, 1071])).
% 12.18/12.35 tff(1078,plain,
% 12.18/12.35 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))))),
% 12.18/12.35 inference(quant_inst,[status(thm)],[])).
% 12.18/12.35 tff(1079,plain,
% 12.18/12.35 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), reverse_line(line_connecting(A!2, C!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)), line_connecting(A!2, C!0))))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.18/12.35 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 12.18/12.35 tff(1080,plain,
% 12.18/12.35 ($false),
% 12.18/12.35 inference(unit_resolution,[status(thm)],[1079, 109, 1, 1070, 1068, 30])).
% 12.18/12.35 tff(1081,plain,(~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))), inference(lemma,lemma(discharge,[]))).
% 12.18/12.35 tff(1082,plain,
% 12.18/12.35 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.18/12.35 inference(rewrite,[status(thm)],[])).
% 12.18/12.35 tff(1083,plain,
% 12.18/12.35 ((unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0))))) <=> ((~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.18/12.36 inference(rewrite,[status(thm)],[])).
% 12.18/12.36 tff(1084,plain,
% 12.18/12.36 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, 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(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))))),
% 12.18/12.36 inference(monotonicity,[status(thm)],[1083])).
% 12.18/12.36 tff(1085,plain,
% 12.18/12.36 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, 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(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))))),
% 12.18/12.36 inference(transitivity,[status(thm)],[1084, 1082])).
% 12.18/12.36 tff(1086,plain,
% 12.18/12.36 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))))),
% 12.18/12.36 inference(quant_inst,[status(thm)],[])).
% 12.18/12.36 tff(1087,plain,
% 12.18/12.36 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), reverse_line(line_connecting(A!2, C!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, C!0)), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), line_connecting(intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3), intersection_point(reverse_line(reverse_line(reverse_line(reverse_line(L!3)))), L!3)))),
% 12.18/12.36 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 12.18/12.36 tff(1088,plain,
% 12.18/12.36 ($false),
% 12.18/12.36 inference(unit_resolution,[status(thm)],[1087, 21, 1052, 982, 1081])).
% 12.18/12.36 % SZS output end Proof
% 12.21/12.36 % E exiting
%------------------------------------------------------------------------------