%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO254+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:06:09 AM UTC 2025
% Result : Theorem 11.58s 11.81s
% Output : Proof 11.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : GEO254+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 0.06/0.10 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n001.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Jun 19 14:47:33 EDT 2025
% 0.10/0.32 % CPUTime :
% 11.58/11.81 % SZS status Theorem
% 11.58/11.81 % SZS output start Proof
% 11.58/11.81 tff(unequally_directed_lines_type, type, (
% 11.58/11.81 unequally_directed_lines: ( $i * $i ) > $o)).
% 11.58/11.81 tff(reverse_line_type, type, (
% 11.58/11.81 reverse_line: $i > $i)).
% 11.58/11.81 tff(line_connecting_type, type, (
% 11.58/11.81 line_connecting: ( $i * $i ) > $i)).
% 11.58/11.81 tff(intersection_point_type, type, (
% 11.58/11.81 intersection_point: ( $i * $i ) > $i)).
% 11.58/11.81 tff(tptp_fun_L_0_type, type, (
% 11.58/11.81 tptp_fun_L_0: $i)).
% 11.58/11.81 tff(tptp_fun_B_1_type, type, (
% 11.58/11.81 tptp_fun_B_1: $i)).
% 11.58/11.81 tff(tptp_fun_A_2_type, type, (
% 11.58/11.81 tptp_fun_A_2: $i)).
% 11.58/11.81 tff(parallel_through_point_type, type, (
% 11.58/11.81 parallel_through_point: ( $i * $i ) > $i)).
% 11.58/11.81 tff(left_convergent_lines_type, type, (
% 11.58/11.81 left_convergent_lines: ( $i * $i ) > $o)).
% 11.58/11.81 tff(before_on_line_type, type, (
% 11.58/11.81 before_on_line: ( $i * $i * $i ) > $o)).
% 11.58/11.81 tff(distinct_points_type, type, (
% 11.58/11.81 distinct_points: ( $i * $i ) > $o)).
% 11.58/11.81 tff(left_apart_point_type, type, (
% 11.58/11.81 left_apart_point: ( $i * $i ) > $o)).
% 11.58/11.81 tff(apart_point_and_line_type, type, (
% 11.58/11.81 apart_point_and_line: ( $i * $i ) > $o)).
% 11.58/11.81 tff(1,assumption,(left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))), introduced(assumption)).
% 11.58/11.81 tff(2,plain,
% 11.58/11.81 (^[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)))))),
% 11.58/11.81 inference(bind,[status(th)],[])).
% 11.58/11.81 tff(3,plain,
% 11.58/11.81 (![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))))),
% 11.58/11.81 inference(quant_intro,[status(thm)],[2])).
% 11.58/11.81 tff(4,plain,
% 11.58/11.81 (![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))))),
% 11.58/11.81 inference(rewrite,[status(thm)],[])).
% 11.58/11.81 tff(5,axiom,(![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag11')).
% 11.58/11.81 tff(6,plain,
% 11.58/11.81 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[5, 4])).
% 11.58/11.81 tff(7,plain,(
% 11.58/11.81 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 11.58/11.81 inference(skolemize,[status(sab)],[6])).
% 11.58/11.81 tff(8,plain,
% 11.58/11.81 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[7, 3])).
% 11.58/11.81 tff(9,plain,
% 11.58/11.81 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))),
% 11.58/11.81 inference(quant_inst,[status(thm)],[])).
% 11.58/11.81 tff(10,plain,
% 11.58/11.81 ($false),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 11.58/11.81 tff(11,plain,(~(left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))), inference(lemma,lemma(discharge,[]))).
% 11.58/11.81 tff(12,plain,
% 11.58/11.81 ((left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) | (~left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.58/11.81 inference(tautology,[status(thm)],[])).
% 11.58/11.81 tff(13,plain,
% 11.58/11.81 (~left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[12, 11])).
% 11.58/11.81 tff(14,plain,
% 11.58/11.81 ((left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) | (~left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.58/11.81 inference(tautology,[status(thm)],[])).
% 11.58/11.81 tff(15,plain,
% 11.58/11.81 (~left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[14, 11])).
% 11.58/11.81 tff(16,assumption,(unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))), introduced(assumption)).
% 11.58/11.81 tff(17,assumption,(~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))), introduced(assumption)).
% 11.58/11.81 tff(18,plain,
% 11.58/11.81 (^[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)))))),
% 11.58/11.81 inference(bind,[status(th)],[])).
% 11.58/11.81 tff(19,plain,
% 11.58/11.81 (![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))))),
% 11.58/11.81 inference(quant_intro,[status(thm)],[18])).
% 11.58/11.81 tff(20,plain,
% 11.58/11.81 (![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))))),
% 11.58/11.81 inference(rewrite,[status(thm)],[])).
% 11.58/11.81 tff(21,axiom,(![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oagco9')).
% 11.58/11.81 tff(22,plain,
% 11.58/11.81 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[21, 20])).
% 11.58/11.81 tff(23,plain,(
% 11.58/11.81 ![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 11.58/11.81 inference(skolemize,[status(sab)],[22])).
% 11.58/11.81 tff(24,plain,
% 11.58/11.81 (![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[23, 19])).
% 11.58/11.81 tff(25,plain,
% 11.58/11.81 ((~![A: $i, B: $i] : (~unequally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.58/11.81 inference(quant_inst,[status(thm)],[])).
% 11.58/11.81 tff(26,plain,
% 11.58/11.81 (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.58/11.81 inference(unit_resolution,[status(thm)],[25, 24])).
% 11.58/11.81 tff(27,plain,
% 11.58/11.81 (^[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))))),
% 11.58/11.81 inference(bind,[status(th)],[])).
% 11.58/11.81 tff(28,plain,
% 11.58/11.81 (![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)))),
% 11.58/11.81 inference(quant_intro,[status(thm)],[27])).
% 11.58/11.81 tff(29,plain,
% 11.58/11.81 (![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)))),
% 11.58/11.81 inference(rewrite,[status(thm)],[])).
% 11.58/11.81 tff(30,plain,
% 11.58/11.81 (^[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)))))),
% 11.58/11.81 inference(bind,[status(th)],[])).
% 11.58/11.81 tff(31,plain,
% 11.58/11.81 (![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)))),
% 11.58/11.81 inference(quant_intro,[status(thm)],[30])).
% 11.58/11.81 tff(32,axiom,(![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag6')).
% 11.58/11.81 tff(33,plain,
% 11.58/11.81 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[32, 31])).
% 11.58/11.81 tff(34,plain,
% 11.58/11.81 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[33, 29])).
% 11.58/11.81 tff(35,plain,(
% 11.58/11.81 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 11.58/11.81 inference(skolemize,[status(sab)],[34])).
% 11.58/11.81 tff(36,plain,
% 11.58/11.81 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 11.58/11.81 inference(modus_ponens,[status(thm)],[35, 28])).
% 11.58/11.81 tff(37,plain,
% 11.58/11.81 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.58/11.81 inference(rewrite,[status(thm)],[])).
% 11.58/11.81 tff(38,plain,
% 11.58/11.81 ((unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) <=> (unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.81 inference(rewrite,[status(thm)],[])).
% 11.66/11.81 tff(39,plain,
% 11.66/11.81 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))),
% 11.66/11.81 inference(monotonicity,[status(thm)],[38])).
% 11.66/11.81 tff(40,plain,
% 11.66/11.81 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.81 inference(transitivity,[status(thm)],[39, 37])).
% 11.66/11.81 tff(41,plain,
% 11.66/11.81 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.81 inference(quant_inst,[status(thm)],[])).
% 11.66/11.81 tff(42,plain,
% 11.66/11.81 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.66/11.81 inference(modus_ponens,[status(thm)],[41, 40])).
% 11.66/11.81 tff(43,plain,
% 11.66/11.81 (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 11.66/11.81 inference(unit_resolution,[status(thm)],[42, 36, 26])).
% 11.66/11.81 tff(44,plain,
% 11.66/11.81 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.82 inference(rewrite,[status(thm)],[])).
% 11.66/11.82 tff(45,plain,
% 11.66/11.82 ((unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) <=> (unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.82 inference(rewrite,[status(thm)],[])).
% 11.66/11.82 tff(46,plain,
% 11.66/11.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))),
% 11.66/11.82 inference(monotonicity,[status(thm)],[45])).
% 11.66/11.82 tff(47,plain,
% 11.66/11.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.82 inference(transitivity,[status(thm)],[46, 44])).
% 11.66/11.82 tff(48,plain,
% 11.66/11.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.82 inference(quant_inst,[status(thm)],[])).
% 11.66/11.82 tff(49,plain,
% 11.66/11.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 11.66/11.82 inference(modus_ponens,[status(thm)],[48, 47])).
% 11.66/11.82 tff(50,plain,
% 11.66/11.82 (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))),
% 11.66/11.82 inference(unit_resolution,[status(thm)],[49, 36, 43, 17])).
% 11.66/11.82 tff(51,plain,
% 11.66/11.82 (^[A: $i, L: $i] : refl((~unequally_directed_lines(parallel_through_point(L, A), L)) <=> (~unequally_directed_lines(parallel_through_point(L, A), L)))),
% 11.66/11.82 inference(bind,[status(th)],[])).
% 11.66/11.82 tff(52,plain,
% 11.66/11.82 (![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))),
% 11.66/11.82 inference(quant_intro,[status(thm)],[51])).
% 11.66/11.82 tff(53,plain,
% 11.66/11.82 (![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))),
% 11.66/11.82 inference(rewrite,[status(thm)],[])).
% 11.66/11.82 tff(54,axiom,(![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oagco10')).
% 11.66/11.82 tff(55,plain,
% 11.66/11.82 (![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))),
% 11.66/11.82 inference(modus_ponens,[status(thm)],[54, 53])).
% 11.66/11.82 tff(56,plain,(
% 11.66/11.82 ![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))),
% 11.66/11.82 inference(skolemize,[status(sab)],[55])).
% 11.66/11.82 tff(57,plain,
% 11.66/11.82 (![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))),
% 11.66/11.82 inference(modus_ponens,[status(thm)],[56, 52])).
% 11.66/11.82 tff(58,plain,
% 11.66/11.82 ((~![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))))),
% 11.66/11.82 inference(quant_inst,[status(thm)],[])).
% 11.66/11.82 tff(59,plain,
% 11.66/11.82 (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2)))),
% 11.66/11.82 inference(unit_resolution,[status(thm)],[58, 57])).
% 11.66/11.82 tff(60,assumption,(unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(B!1, A!2)))), introduced(assumption)).
% 11.66/11.82 tff(61,plain,
% 11.66/11.82 (^[L: $i] : refl((~unequally_directed_lines(L, L)) <=> (~unequally_directed_lines(L, L)))),
% 11.66/11.82 inference(bind,[status(th)],[])).
% 11.66/11.82 tff(62,plain,
% 11.66/11.82 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 11.66/11.82 inference(quant_intro,[status(thm)],[61])).
% 11.66/11.82 tff(63,plain,
% 11.66/11.82 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 11.66/11.82 inference(rewrite,[status(thm)],[])).
% 11.66/11.82 tff(64,axiom,(![L: $i] : (~unequally_directed_lines(L, L))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag5')).
% 11.66/11.82 tff(65,plain,
% 11.66/11.82 (![L: $i] : (~unequally_directed_lines(L, L))),
% 11.66/11.82 inference(modus_ponens,[status(thm)],[64, 63])).
% 11.66/11.82 tff(66,plain,(
% 11.66/11.82 ![L: $i] : (~unequally_directed_lines(L, L))),
% 11.66/11.82 inference(skolemize,[status(sab)],[65])).
% 11.66/11.82 tff(67,plain,
% 11.66/11.82 (![L: $i] : (~unequally_directed_lines(L, L))),
% 11.66/11.82 inference(modus_ponens,[status(thm)],[66, 62])).
% 11.66/11.82 tff(68,plain,
% 11.66/11.82 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(B!1, A!2))))),
% 11.66/11.82 inference(quant_inst,[status(thm)],[])).
% 11.66/11.82 tff(69,plain,
% 11.66/11.82 ($false),
% 11.66/11.82 inference(unit_resolution,[status(thm)],[68, 67, 60])).
% 11.66/11.82 tff(70,plain,(~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(B!1, A!2)))), inference(lemma,lemma(discharge,[]))).
% 11.66/11.82 tff(71,plain,
% 11.66/11.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.82 inference(rewrite,[status(thm)],[])).
% 11.66/11.82 tff(72,plain,
% 11.66/11.82 ((unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) <=> (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.82 inference(rewrite,[status(thm)],[])).
% 11.66/11.82 tff(73,plain,
% 11.66/11.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))),
% 11.66/11.82 inference(monotonicity,[status(thm)],[72])).
% 11.66/11.82 tff(74,plain,
% 11.66/11.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.82 inference(transitivity,[status(thm)],[73, 71])).
% 11.66/11.82 tff(75,plain,
% 11.66/11.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.82 inference(quant_inst,[status(thm)],[])).
% 11.66/11.82 tff(76,plain,
% 11.66/11.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 11.66/11.82 inference(modus_ponens,[status(thm)],[75, 74])).
% 11.66/11.82 tff(77,plain,
% 11.66/11.82 (~unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))),
% 11.66/11.82 inference(unit_resolution,[status(thm)],[76, 36, 70, 59])).
% 11.66/11.82 tff(78,plain,
% 11.66/11.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 11.66/11.82 inference(rewrite,[status(thm)],[])).
% 11.66/11.82 tff(79,plain,
% 11.66/11.82 ((unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2))))) <=> (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 11.66/11.82 inference(rewrite,[status(thm)],[])).
% 11.66/11.82 tff(80,plain,
% 11.66/11.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.82 inference(monotonicity,[status(thm)],[79])).
% 11.66/11.82 tff(81,plain,
% 11.66/11.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 11.66/11.82 inference(transitivity,[status(thm)],[80, 78])).
% 11.66/11.82 tff(82,plain,
% 11.66/11.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))))),
% 11.66/11.82 inference(quant_inst,[status(thm)],[])).
% 11.66/11.82 tff(83,plain,
% 11.66/11.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(reverse_line(line_connecting(B!1, A!2)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))),
% 11.66/11.82 inference(modus_ponens,[status(thm)],[82, 81])).
% 11.66/11.82 tff(84,plain,
% 11.66/11.82 (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))),
% 11.66/11.82 inference(unit_resolution,[status(thm)],[83, 36, 77, 50])).
% 11.66/11.82 tff(85,plain,
% 11.66/11.82 (((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))),
% 11.66/11.82 inference(tautology,[status(thm)],[])).
% 11.66/11.82 tff(86,plain,
% 11.66/11.82 ((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2)))),
% 11.66/11.82 inference(unit_resolution,[status(thm)],[85, 84])).
% 11.66/11.82 tff(87,assumption,(~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))), introduced(assumption)).
% 11.66/11.82 tff(88,assumption,(~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))), introduced(assumption)).
% 11.66/11.82 tff(89,plain,
% 11.66/11.82 ((~![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))))),
% 11.66/11.82 inference(quant_inst,[status(thm)],[])).
% 11.66/11.82 tff(90,plain,
% 11.66/11.82 (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1)))),
% 11.66/11.82 inference(unit_resolution,[status(thm)],[89, 24])).
% 11.66/11.82 tff(91,plain,
% 11.66/11.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2))))),
% 11.66/11.82 inference(rewrite,[status(thm)],[])).
% 11.66/11.82 tff(92,plain,
% 11.66/11.82 ((unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2)))) <=> (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2))))),
% 11.66/11.82 inference(rewrite,[status(thm)],[])).
% 11.66/11.82 tff(93,plain,
% 11.66/11.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), 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(line_connecting(B!1, A!2), line_connecting(B!1, A!2)))))),
% 11.66/11.82 inference(monotonicity,[status(thm)],[92])).
% 11.66/11.82 tff(94,plain,
% 11.66/11.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), 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(line_connecting(B!1, A!2), line_connecting(B!1, A!2))))),
% 11.66/11.82 inference(transitivity,[status(thm)],[93, 91])).
% 11.66/11.82 tff(95,plain,
% 11.66/11.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2))))),
% 11.66/11.82 inference(quant_inst,[status(thm)],[])).
% 11.66/11.82 tff(96,plain,
% 11.66/11.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2)))),
% 11.66/11.82 inference(modus_ponens,[status(thm)],[95, 94])).
% 11.66/11.82 tff(97,plain,
% 11.66/11.82 (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2))),
% 11.66/11.82 inference(unit_resolution,[status(thm)],[96, 36, 90])).
% 11.66/11.82 tff(98,plain,
% 11.66/11.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)))),
% 11.66/11.82 inference(rewrite,[status(thm)],[])).
% 11.66/11.82 tff(99,plain,
% 11.66/11.82 ((unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1)))) <=> (unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)))),
% 11.66/11.82 inference(rewrite,[status(thm)],[])).
% 11.66/11.82 tff(100,plain,
% 11.66/11.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))),
% 11.66/11.82 inference(monotonicity,[status(thm)],[99])).
% 11.66/11.82 tff(101,plain,
% 11.66/11.82 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)))),
% 11.66/11.82 inference(transitivity,[status(thm)],[100, 98])).
% 11.66/11.82 tff(102,plain,
% 11.66/11.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))))),
% 11.66/11.82 inference(quant_inst,[status(thm)],[])).
% 11.66/11.82 tff(103,plain,
% 11.66/11.82 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(B!1, A!2)) | (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))),
% 11.66/11.82 inference(modus_ponens,[status(thm)],[102, 101])).
% 11.66/11.82 tff(104,plain,
% 11.66/11.82 (~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))),
% 11.66/11.82 inference(unit_resolution,[status(thm)],[103, 36, 97, 88])).
% 11.66/11.82 tff(105,plain,
% 11.66/11.82 (^[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))))),
% 11.66/11.82 inference(bind,[status(th)],[])).
% 11.66/11.82 tff(106,plain,
% 11.66/11.82 (![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)))),
% 11.66/11.82 inference(quant_intro,[status(thm)],[105])).
% 11.66/11.82 tff(107,plain,
% 11.66/11.82 (^[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)))))),
% 11.66/11.82 inference(bind,[status(th)],[])).
% 11.66/11.82 tff(108,plain,
% 11.66/11.82 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> ![L: $i, A: $i, B: $i] : (~((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)))),
% 11.66/11.82 inference(quant_intro,[status(thm)],[107])).
% 11.66/11.82 tff(109,plain,
% 11.66/11.82 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(110,plain,
% 11.66/11.83 (^[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))))))),
% 11.66/11.83 inference(bind,[status(th)],[])).
% 11.66/11.83 tff(111,plain,
% 11.66/11.83 (![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)))))),
% 11.66/11.83 inference(quant_intro,[status(thm)],[110])).
% 11.66/11.83 tff(112,axiom,(![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (((distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L))))) & (~unequally_directed_lines(L, line_connecting(A, B)))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','bf_def')).
% 11.66/11.83 tff(113,plain,
% 11.66/11.83 (![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)))))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[112, 111])).
% 11.66/11.83 tff(114,plain,
% 11.66/11.83 (![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)))))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[113, 109])).
% 11.66/11.83 tff(115,plain,(
% 11.66/11.83 ![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)))))),
% 11.66/11.83 inference(skolemize,[status(sab)],[114])).
% 11.66/11.83 tff(116,plain,
% 11.66/11.83 (![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)))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[115, 108])).
% 11.66/11.83 tff(117,plain,
% 11.66/11.83 (![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)))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[116, 106])).
% 11.66/11.83 tff(118,plain,
% 11.66/11.83 (((~![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)))) | (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1)))) <=> ((~![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)))) | (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1))))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(119,plain,
% 11.66/11.83 ((~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1))) <=> (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1)))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(120,plain,
% 11.66/11.83 (((unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | (~distinct_points(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1)) <=> ((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(121,plain,
% 11.66/11.83 ((~((unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | (~distinct_points(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1))) <=> (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1)))),
% 11.66/11.83 inference(monotonicity,[status(thm)],[120])).
% 11.66/11.83 tff(122,plain,
% 11.66/11.83 ((~((unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | (~distinct_points(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1))) <=> (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1)))),
% 11.66/11.83 inference(transitivity,[status(thm)],[121, 119])).
% 11.66/11.83 tff(123,plain,
% 11.66/11.83 (((~![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!0, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | (~distinct_points(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1)))) <=> ((~![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)))) | (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1))))),
% 11.66/11.83 inference(monotonicity,[status(thm)],[122])).
% 11.66/11.83 tff(124,plain,
% 11.66/11.83 (((~![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!0, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | (~distinct_points(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1)))) <=> ((~![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)))) | (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1))))),
% 11.66/11.83 inference(transitivity,[status(thm)],[123, 118])).
% 11.66/11.83 tff(125,plain,
% 11.66/11.83 ((~![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!0, line_connecting(A!2, B!1)) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | (~distinct_points(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1)))),
% 11.66/11.83 inference(quant_inst,[status(thm)],[])).
% 11.66/11.83 tff(126,plain,
% 11.66/11.83 ((~![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)))) | (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1)))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[125, 124])).
% 11.66/11.83 tff(127,plain,
% 11.66/11.83 (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1))),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[126, 117])).
% 11.66/11.83 tff(128,assumption,(~unequally_directed_lines(L!0, line_connecting(A!2, B!1))), introduced(assumption)).
% 11.66/11.83 tff(129,plain,
% 11.66/11.83 (^[A: $i, L: $i] : refl((apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))))),
% 11.66/11.83 inference(bind,[status(th)],[])).
% 11.66/11.83 tff(130,plain,
% 11.66/11.83 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 11.66/11.83 inference(quant_intro,[status(thm)],[129])).
% 11.66/11.83 tff(131,plain,
% 11.66/11.83 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(132,axiom,(![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','apt_def')).
% 11.66/11.83 tff(133,plain,
% 11.66/11.83 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[132, 131])).
% 11.66/11.83 tff(134,plain,(
% 11.66/11.83 ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 11.66/11.83 inference(skolemize,[status(sab)],[133])).
% 11.66/11.83 tff(135,plain,
% 11.66/11.83 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[134, 130])).
% 11.66/11.83 tff(136,plain,
% 11.66/11.83 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (apart_point_and_line(B!1, L!0) <=> (left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0))))),
% 11.66/11.83 inference(quant_inst,[status(thm)],[])).
% 11.66/11.83 tff(137,plain,
% 11.66/11.83 (apart_point_and_line(B!1, L!0) <=> (left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)))),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[136, 135])).
% 11.66/11.83 tff(138,plain,
% 11.66/11.83 ((~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A)))) <=> (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A))))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(139,plain,
% 11.66/11.83 ((~![A: $i, B: $i, L: $i] : (((distinct_points(A, B) & (~apart_point_and_line(A, L))) & (~apart_point_and_line(B, L))) => (before_on_line(L, A, B) & before_on_line(L, B, A)))) <=> (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A))))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(140,axiom,(~![A: $i, B: $i, L: $i] : (((distinct_points(A, B) & (~apart_point_and_line(A, L))) & (~apart_point_and_line(B, L))) => (before_on_line(L, A, B) & before_on_line(L, B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 11.66/11.83 tff(141,plain,
% 11.66/11.83 (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[140, 139])).
% 11.66/11.83 tff(142,plain,
% 11.66/11.83 (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[141, 138])).
% 11.66/11.83 tff(143,plain,
% 11.66/11.83 (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[142, 138])).
% 11.66/11.83 tff(144,plain,
% 11.66/11.83 (~![A: $i, B: $i, L: $i] : ((~(distinct_points(A, B) & (~apart_point_and_line(A, L)) & (~apart_point_and_line(B, L)))) | (before_on_line(L, A, B) & before_on_line(L, B, A)))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[143, 138])).
% 11.66/11.83 tff(145,plain,(
% 11.66/11.83 ~((~(distinct_points(A!2, B!1) & (~apart_point_and_line(A!2, L!0)) & (~apart_point_and_line(B!1, L!0)))) | (before_on_line(L!0, A!2, B!1) & before_on_line(L!0, B!1, A!2)))),
% 11.66/11.83 inference(skolemize,[status(sab)],[144])).
% 11.66/11.83 tff(146,plain,
% 11.66/11.83 (distinct_points(A!2, B!1) & (~apart_point_and_line(A!2, L!0)) & (~apart_point_and_line(B!1, L!0))),
% 11.66/11.83 inference(or_elim,[status(thm)],[145])).
% 11.66/11.83 tff(147,plain,
% 11.66/11.83 (~apart_point_and_line(B!1, L!0)),
% 11.66/11.83 inference(and_elim,[status(thm)],[146])).
% 11.66/11.83 tff(148,plain,
% 11.66/11.83 ((~(apart_point_and_line(B!1, L!0) <=> (left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0))))) | apart_point_and_line(B!1, L!0) | (~(left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0))))),
% 11.66/11.83 inference(tautology,[status(thm)],[])).
% 11.66/11.83 tff(149,plain,
% 11.66/11.83 ((~(apart_point_and_line(B!1, L!0) <=> (left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0))))) | (~(left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0))))),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[148, 147])).
% 11.66/11.83 tff(150,plain,
% 11.66/11.83 (~(left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)))),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[149, 137])).
% 11.66/11.83 tff(151,plain,
% 11.66/11.83 ((left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0))) | (~left_apart_point(B!1, reverse_line(L!0)))),
% 11.66/11.83 inference(tautology,[status(thm)],[])).
% 11.66/11.83 tff(152,plain,
% 11.66/11.83 (~left_apart_point(B!1, reverse_line(L!0))),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[151, 150])).
% 11.66/11.83 tff(153,plain,
% 11.66/11.83 ((left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0))) | (~left_apart_point(B!1, L!0))),
% 11.66/11.83 inference(tautology,[status(thm)],[])).
% 11.66/11.83 tff(154,plain,
% 11.66/11.83 (~left_apart_point(B!1, L!0)),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[153, 150])).
% 11.66/11.83 tff(155,plain,
% 11.66/11.83 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))),
% 11.66/11.83 inference(quant_inst,[status(thm)],[])).
% 11.66/11.83 tff(156,plain,
% 11.66/11.83 (apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)))),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[155, 135])).
% 11.66/11.83 tff(157,plain,
% 11.66/11.83 (~apart_point_and_line(A!2, L!0)),
% 11.66/11.83 inference(and_elim,[status(thm)],[146])).
% 11.66/11.83 tff(158,plain,
% 11.66/11.83 ((~(apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))) | apart_point_and_line(A!2, L!0) | (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))),
% 11.66/11.83 inference(tautology,[status(thm)],[])).
% 11.66/11.83 tff(159,plain,
% 11.66/11.83 ((~(apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))) | (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[158, 157])).
% 11.66/11.83 tff(160,plain,
% 11.66/11.83 (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)))),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[159, 156])).
% 11.66/11.83 tff(161,plain,
% 11.66/11.83 ((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))) | (~left_apart_point(A!2, reverse_line(L!0)))),
% 11.66/11.83 inference(tautology,[status(thm)],[])).
% 11.66/11.83 tff(162,plain,
% 11.66/11.83 (~left_apart_point(A!2, reverse_line(L!0))),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[161, 160])).
% 11.66/11.83 tff(163,plain,
% 11.66/11.83 ((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))) | (~left_apart_point(A!2, L!0))),
% 11.66/11.83 inference(tautology,[status(thm)],[])).
% 11.66/11.83 tff(164,plain,
% 11.66/11.83 (~left_apart_point(A!2, L!0)),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[163, 160])).
% 11.66/11.83 tff(165,plain,
% 11.66/11.83 (distinct_points(A!2, B!1)),
% 11.66/11.83 inference(and_elim,[status(thm)],[146])).
% 11.66/11.83 tff(166,plain,
% 11.66/11.83 ((~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)))) | left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))),
% 11.66/11.83 inference(tautology,[status(thm)],[])).
% 11.66/11.83 tff(167,plain,
% 11.66/11.83 (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)))),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[166, 165, 164, 162, 154, 152, 128])).
% 11.66/11.83 tff(168,plain,
% 11.66/11.83 (((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1)) | (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | before_on_line(L!0, A!2, B!1)),
% 11.66/11.83 inference(tautology,[status(thm)],[])).
% 11.66/11.83 tff(169,plain,
% 11.66/11.83 (((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1))) <=> before_on_line(L!0, A!2, B!1)) | before_on_line(L!0, A!2, B!1)),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[168, 167])).
% 11.66/11.83 tff(170,plain,
% 11.66/11.83 (before_on_line(L!0, A!2, B!1)),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[169, 127])).
% 11.66/11.83 tff(171,assumption,(~unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))), introduced(assumption)).
% 11.66/11.83 tff(172,plain,
% 11.66/11.83 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(173,plain,
% 11.66/11.83 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))))),
% 11.66/11.83 inference(quant_inst,[status(thm)],[])).
% 11.66/11.83 tff(174,plain,
% 11.66/11.83 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1)) | unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2)))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[173, 172])).
% 11.66/11.83 tff(175,plain,
% 11.66/11.83 (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[174, 36, 171, 128])).
% 11.66/11.83 tff(176,assumption,(distinct_points(A!2, A!2)), introduced(assumption)).
% 11.66/11.83 tff(177,plain,
% 11.66/11.83 (^[A: $i] : refl((~distinct_points(A, A)) <=> (~distinct_points(A, A)))),
% 11.66/11.83 inference(bind,[status(th)],[])).
% 11.66/11.83 tff(178,plain,
% 11.66/11.83 (![A: $i] : (~distinct_points(A, A)) <=> ![A: $i] : (~distinct_points(A, A))),
% 11.66/11.83 inference(quant_intro,[status(thm)],[177])).
% 11.66/11.83 tff(179,plain,
% 11.66/11.83 (![A: $i] : (~distinct_points(A, A)) <=> ![A: $i] : (~distinct_points(A, A))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(180,axiom,(![A: $i] : (~distinct_points(A, A))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag1')).
% 11.66/11.83 tff(181,plain,
% 11.66/11.83 (![A: $i] : (~distinct_points(A, A))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[180, 179])).
% 11.66/11.83 tff(182,plain,(
% 11.66/11.83 ![A: $i] : (~distinct_points(A, A))),
% 11.66/11.83 inference(skolemize,[status(sab)],[181])).
% 11.66/11.83 tff(183,plain,
% 11.66/11.83 (![A: $i] : (~distinct_points(A, A))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[182, 178])).
% 11.66/11.83 tff(184,plain,
% 11.66/11.83 ((~![A: $i] : (~distinct_points(A, A))) | (~distinct_points(A!2, A!2))),
% 11.66/11.83 inference(quant_inst,[status(thm)],[])).
% 11.66/11.83 tff(185,plain,
% 11.66/11.83 ($false),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[184, 183, 176])).
% 11.66/11.83 tff(186,plain,(~distinct_points(A!2, A!2)), inference(lemma,lemma(discharge,[]))).
% 11.66/11.83 tff(187,plain,
% 11.66/11.83 (^[A: $i, B: $i, C: $i] : refl((distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))))),
% 11.66/11.83 inference(bind,[status(th)],[])).
% 11.66/11.83 tff(188,plain,
% 11.66/11.83 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 11.66/11.83 inference(quant_intro,[status(thm)],[187])).
% 11.66/11.83 tff(189,plain,
% 11.66/11.83 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(190,plain,
% 11.66/11.83 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((distinct_points(A, C) | distinct_points(B, C)) <=> (distinct_points(A, C) | distinct_points(B, C))), ((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))))), rewrite((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))), ((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))))),
% 11.66/11.83 inference(bind,[status(th)],[])).
% 11.66/11.83 tff(191,plain,
% 11.66/11.83 (![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 11.66/11.83 inference(quant_intro,[status(thm)],[190])).
% 11.66/11.83 tff(192,axiom,(![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag2')).
% 11.66/11.83 tff(193,plain,
% 11.66/11.83 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[192, 191])).
% 11.66/11.83 tff(194,plain,
% 11.66/11.83 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[193, 189])).
% 11.66/11.83 tff(195,plain,(
% 11.66/11.83 ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 11.66/11.83 inference(skolemize,[status(sab)],[194])).
% 11.66/11.83 tff(196,plain,
% 11.66/11.83 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[195, 188])).
% 11.66/11.83 tff(197,plain,
% 11.66/11.83 (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | ((~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(198,plain,
% 11.66/11.83 ((distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1))) <=> ((~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(199,plain,
% 11.66/11.83 (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | ((~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2)))),
% 11.66/11.83 inference(monotonicity,[status(thm)],[198])).
% 11.66/11.83 tff(200,plain,
% 11.66/11.83 (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))),
% 11.66/11.83 inference(transitivity,[status(thm)],[199, 197])).
% 11.66/11.83 tff(201,plain,
% 11.66/11.83 ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1)))),
% 11.66/11.83 inference(quant_inst,[status(thm)],[])).
% 11.66/11.83 tff(202,plain,
% 11.66/11.83 ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2)),
% 11.66/11.83 inference(modus_ponens,[status(thm)],[201, 200])).
% 11.66/11.83 tff(203,plain,
% 11.66/11.83 (distinct_points(B!1, A!2) | distinct_points(A!2, A!2)),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[202, 196, 165])).
% 11.66/11.83 tff(204,plain,
% 11.66/11.83 (distinct_points(B!1, A!2)),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[203, 186])).
% 11.66/11.83 tff(205,plain,
% 11.66/11.83 ((~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)))) | left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 11.66/11.83 inference(tautology,[status(thm)],[])).
% 11.66/11.83 tff(206,plain,
% 11.66/11.83 ((~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)))) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[205, 164, 162, 154, 152, 204])).
% 11.66/11.83 tff(207,plain,
% 11.66/11.83 (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)))),
% 11.66/11.83 inference(unit_resolution,[status(thm)],[206, 175])).
% 11.66/11.83 tff(208,assumption,((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2)), introduced(assumption)).
% 11.66/11.83 tff(209,plain,
% 11.66/11.83 (((~![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)))) | (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2)))) <=> ((~![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)))) | (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2))))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(210,plain,
% 11.66/11.83 ((~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2))) <=> (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2)))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(211,plain,
% 11.66/11.83 (((unequally_directed_lines(L!0, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | (~distinct_points(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2)) <=> ((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2))),
% 11.66/11.83 inference(rewrite,[status(thm)],[])).
% 11.66/11.83 tff(212,plain,
% 11.66/11.83 ((~((unequally_directed_lines(L!0, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | (~distinct_points(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2))) <=> (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2)))),
% 11.66/11.83 inference(monotonicity,[status(thm)],[211])).
% 11.66/11.83 tff(213,plain,
% 11.66/11.83 ((~((unequally_directed_lines(L!0, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | (~distinct_points(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2))) <=> (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2)))),
% 11.66/11.83 inference(transitivity,[status(thm)],[212, 210])).
% 11.66/11.83 tff(214,plain,
% 11.66/11.83 (((~![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!0, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | (~distinct_points(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2)))) <=> ((~![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)))) | (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2))))),
% 11.66/11.83 inference(monotonicity,[status(thm)],[213])).
% 11.66/11.83 tff(215,plain,
% 11.66/11.83 (((~![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!0, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | (~distinct_points(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2)))) <=> ((~![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)))) | (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2))))),
% 11.66/11.83 inference(transitivity,[status(thm)],[214, 209])).
% 11.66/11.83 tff(216,plain,
% 11.66/11.83 ((~![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!0, line_connecting(B!1, A!2)) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(A!2, L!0) | left_apart_point(B!1, reverse_line(L!0)) | left_apart_point(B!1, L!0) | (~distinct_points(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2)))),
% 11.66/11.84 inference(quant_inst,[status(thm)],[])).
% 11.66/11.84 tff(217,plain,
% 11.66/11.84 ((~![L: $i, A: $i, B: $i] : (~((unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))) <=> before_on_line(L, A, B)))) | (~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2)))),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[216, 215])).
% 11.66/11.84 tff(218,plain,
% 11.66/11.84 ($false),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[217, 117, 208])).
% 11.66/11.84 tff(219,plain,(~((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2))), inference(lemma,lemma(discharge,[]))).
% 11.66/11.84 tff(220,plain,
% 11.66/11.84 (((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) <=> before_on_line(L!0, B!1, A!2)) | (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | before_on_line(L!0, B!1, A!2)),
% 11.66/11.84 inference(tautology,[status(thm)],[])).
% 11.66/11.84 tff(221,plain,
% 11.66/11.84 ((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)) | left_apart_point(B!1, L!0) | left_apart_point(B!1, reverse_line(L!0)) | (~distinct_points(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | before_on_line(L!0, B!1, A!2)),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[220, 219])).
% 11.66/11.84 tff(222,plain,
% 11.66/11.84 (before_on_line(L!0, B!1, A!2)),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[221, 207])).
% 11.66/11.84 tff(223,plain,
% 11.66/11.84 ((~(~((~before_on_line(L!0, A!2, B!1)) | (~before_on_line(L!0, B!1, A!2))))) <=> ((~before_on_line(L!0, A!2, B!1)) | (~before_on_line(L!0, B!1, A!2)))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(224,plain,
% 11.66/11.84 ((before_on_line(L!0, A!2, B!1) & before_on_line(L!0, B!1, A!2)) <=> (~((~before_on_line(L!0, A!2, B!1)) | (~before_on_line(L!0, B!1, A!2))))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(225,plain,
% 11.66/11.84 ((~(before_on_line(L!0, A!2, B!1) & before_on_line(L!0, B!1, A!2))) <=> (~(~((~before_on_line(L!0, A!2, B!1)) | (~before_on_line(L!0, B!1, A!2)))))),
% 11.66/11.84 inference(monotonicity,[status(thm)],[224])).
% 11.66/11.84 tff(226,plain,
% 11.66/11.84 ((~(before_on_line(L!0, A!2, B!1) & before_on_line(L!0, B!1, A!2))) <=> ((~before_on_line(L!0, A!2, B!1)) | (~before_on_line(L!0, B!1, A!2)))),
% 11.66/11.84 inference(transitivity,[status(thm)],[225, 223])).
% 11.66/11.84 tff(227,plain,
% 11.66/11.84 (~(before_on_line(L!0, A!2, B!1) & before_on_line(L!0, B!1, A!2))),
% 11.66/11.84 inference(or_elim,[status(thm)],[145])).
% 11.66/11.84 tff(228,plain,
% 11.66/11.84 ((~before_on_line(L!0, A!2, B!1)) | (~before_on_line(L!0, B!1, A!2))),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[227, 226])).
% 11.66/11.84 tff(229,plain,
% 11.66/11.84 ($false),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[228, 222, 170])).
% 11.66/11.84 tff(230,plain,(unequally_directed_lines(L!0, line_connecting(A!2, B!1)) | unequally_directed_lines(line_connecting(B!1, A!2), line_connecting(A!2, B!1))), inference(lemma,lemma(discharge,[]))).
% 11.66/11.84 tff(231,plain,
% 11.66/11.84 (unequally_directed_lines(L!0, line_connecting(A!2, B!1))),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[230, 104])).
% 11.66/11.84 tff(232,assumption,(unequally_directed_lines(L!0, L!0)), introduced(assumption)).
% 11.66/11.84 tff(233,plain,
% 11.66/11.84 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(L!0, L!0))),
% 11.66/11.84 inference(quant_inst,[status(thm)],[])).
% 11.66/11.84 tff(234,plain,
% 11.66/11.84 ($false),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[233, 67, 232])).
% 11.66/11.84 tff(235,plain,(~unequally_directed_lines(L!0, L!0)), inference(lemma,lemma(discharge,[]))).
% 11.66/11.84 tff(236,assumption,(unequally_directed_lines(L!0, line_connecting(B!1, A!2))), introduced(assumption)).
% 11.66/11.84 tff(237,assumption,(~unequally_directed_lines(L!0, L!0)), introduced(assumption)).
% 11.66/11.84 tff(238,assumption,(~unequally_directed_lines(line_connecting(B!1, A!2), L!0)), introduced(assumption)).
% 11.66/11.84 tff(239,plain,
% 11.66/11.84 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), L!0))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), L!0))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(240,plain,
% 11.66/11.84 ((unequally_directed_lines(line_connecting(B!1, A!2), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2)))) <=> (unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), L!0))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(241,plain,
% 11.66/11.84 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), L!0)))),
% 11.66/11.84 inference(monotonicity,[status(thm)],[240])).
% 11.66/11.84 tff(242,plain,
% 11.66/11.84 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), L!0))),
% 11.66/11.84 inference(transitivity,[status(thm)],[241, 239])).
% 11.66/11.84 tff(243,plain,
% 11.66/11.84 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))))),
% 11.66/11.84 inference(quant_inst,[status(thm)],[])).
% 11.66/11.84 tff(244,plain,
% 11.66/11.84 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(B!1, A!2), L!0)),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[243, 242])).
% 11.66/11.84 tff(245,plain,
% 11.66/11.84 ($false),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[244, 36, 237, 236, 238])).
% 11.66/11.84 tff(246,plain,(unequally_directed_lines(line_connecting(B!1, A!2), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2)))), inference(lemma,lemma(discharge,[]))).
% 11.66/11.84 tff(247,plain,
% 11.66/11.84 (unequally_directed_lines(line_connecting(B!1, A!2), L!0)),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[246, 237, 236])).
% 11.66/11.84 tff(248,assumption,(left_convergent_lines(line_connecting(B!1, A!2), L!0) | left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0))), introduced(assumption)).
% 11.66/11.84 tff(249,plain,
% 11.66/11.84 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(line_connecting(B!1, A!2), L!0) | left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0))))),
% 11.66/11.84 inference(quant_inst,[status(thm)],[])).
% 11.66/11.84 tff(250,plain,
% 11.66/11.84 ($false),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[249, 8, 248])).
% 11.66/11.84 tff(251,plain,(~(left_convergent_lines(line_connecting(B!1, A!2), L!0) | left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 11.66/11.84 tff(252,plain,
% 11.66/11.84 ((left_convergent_lines(line_connecting(B!1, A!2), L!0) | left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | (~left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0)))),
% 11.66/11.84 inference(tautology,[status(thm)],[])).
% 11.66/11.84 tff(253,plain,
% 11.66/11.84 (~left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0))),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[252, 251])).
% 11.66/11.84 tff(254,plain,
% 11.66/11.84 ((left_convergent_lines(line_connecting(B!1, A!2), L!0) | left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | (~left_convergent_lines(line_connecting(B!1, A!2), L!0))),
% 11.66/11.84 inference(tautology,[status(thm)],[])).
% 11.66/11.84 tff(255,plain,
% 11.66/11.84 (~left_convergent_lines(line_connecting(B!1, A!2), L!0)),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[254, 251])).
% 11.66/11.84 tff(256,assumption,(unequally_directed_lines(line_connecting(B!1, A!2), L!0)), introduced(assumption)).
% 11.66/11.84 tff(257,assumption,(unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))), introduced(assumption)).
% 11.66/11.84 tff(258,plain,
% 11.66/11.84 (^[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)))))),
% 11.66/11.84 inference(bind,[status(th)],[])).
% 11.66/11.84 tff(259,plain,
% 11.66/11.84 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ![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))))),
% 11.66/11.84 inference(quant_intro,[status(thm)],[258])).
% 11.66/11.84 tff(260,plain,
% 11.66/11.84 (^[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))))))),
% 11.66/11.84 inference(bind,[status(th)],[])).
% 11.66/11.84 tff(261,plain,
% 11.66/11.84 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![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))))),
% 11.66/11.84 inference(quant_intro,[status(thm)],[260])).
% 11.66/11.84 tff(262,plain,
% 11.66/11.84 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![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)))))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(263,plain,
% 11.66/11.84 (^[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))))))),
% 11.66/11.84 inference(bind,[status(th)],[])).
% 11.66/11.84 tff(264,plain,
% 11.66/11.84 (![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)))))),
% 11.66/11.84 inference(quant_intro,[status(thm)],[263])).
% 11.66/11.84 tff(265,axiom,(![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag9')).
% 11.66/11.84 tff(266,plain,
% 11.66/11.84 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[265, 264])).
% 11.66/11.84 tff(267,plain,
% 11.66/11.84 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[266, 262])).
% 11.66/11.84 tff(268,plain,(
% 11.66/11.84 ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 11.66/11.84 inference(skolemize,[status(sab)],[267])).
% 11.66/11.84 tff(269,plain,
% 11.66/11.84 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[268, 261])).
% 11.66/11.84 tff(270,plain,
% 11.66/11.84 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[269, 259])).
% 11.66/11.84 tff(271,plain,
% 11.66/11.84 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | left_convergent_lines(line_connecting(B!1, A!2), L!0))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | left_convergent_lines(line_connecting(B!1, A!2), L!0))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(272,plain,
% 11.66/11.84 ((left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | left_convergent_lines(line_connecting(B!1, A!2), L!0) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0)))) <=> ((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | left_convergent_lines(line_connecting(B!1, A!2), L!0))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(273,plain,
% 11.66/11.84 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | left_convergent_lines(line_connecting(B!1, A!2), L!0) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | left_convergent_lines(line_connecting(B!1, A!2), L!0)))),
% 11.66/11.84 inference(monotonicity,[status(thm)],[272])).
% 11.66/11.84 tff(274,plain,
% 11.66/11.84 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | left_convergent_lines(line_connecting(B!1, A!2), L!0) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | left_convergent_lines(line_connecting(B!1, A!2), L!0))),
% 11.66/11.84 inference(transitivity,[status(thm)],[273, 271])).
% 11.66/11.84 tff(275,plain,
% 11.66/11.84 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | left_convergent_lines(line_connecting(B!1, A!2), L!0) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))))),
% 11.66/11.84 inference(quant_inst,[status(thm)],[])).
% 11.66/11.84 tff(276,plain,
% 11.66/11.84 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | left_convergent_lines(line_connecting(B!1, A!2), reverse_line(L!0)) | left_convergent_lines(line_connecting(B!1, A!2), L!0)),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[275, 274])).
% 11.66/11.84 tff(277,plain,
% 11.66/11.84 ($false),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[276, 270, 257, 256, 255, 253])).
% 11.66/11.84 tff(278,plain,((~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))) | (~unequally_directed_lines(line_connecting(B!1, A!2), L!0))), inference(lemma,lemma(discharge,[]))).
% 11.66/11.84 tff(279,plain,
% 11.66/11.84 (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[278, 247])).
% 11.66/11.84 tff(280,plain,
% 11.66/11.84 (((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))),
% 11.66/11.84 inference(tautology,[status(thm)],[])).
% 11.66/11.84 tff(281,plain,
% 11.66/11.84 ((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0)))),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[280, 279])).
% 11.66/11.84 tff(282,plain,
% 11.66/11.84 (((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0)))) | unequally_directed_lines(L!0, L!0)),
% 11.66/11.84 inference(tautology,[status(thm)],[])).
% 11.66/11.84 tff(283,plain,
% 11.66/11.84 ((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0)))),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[282, 237])).
% 11.66/11.84 tff(284,assumption,(unequally_directed_lines(L!0, line_connecting(A!2, B!1))), introduced(assumption)).
% 11.66/11.84 tff(285,plain,
% 11.66/11.84 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), L!0))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), L!0))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(286,plain,
% 11.66/11.84 ((unequally_directed_lines(line_connecting(A!2, B!1), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1)))) <=> (unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), L!0))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(287,plain,
% 11.66/11.84 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), L!0)))),
% 11.66/11.84 inference(monotonicity,[status(thm)],[286])).
% 11.66/11.84 tff(288,plain,
% 11.66/11.84 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), L!0))),
% 11.66/11.84 inference(transitivity,[status(thm)],[287, 285])).
% 11.66/11.84 tff(289,plain,
% 11.66/11.84 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), L!0) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))))),
% 11.66/11.84 inference(quant_inst,[status(thm)],[])).
% 11.66/11.84 tff(290,plain,
% 11.66/11.84 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), L!0)),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[289, 288])).
% 11.66/11.84 tff(291,plain,
% 11.66/11.84 (unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), L!0)),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[290, 36])).
% 11.66/11.84 tff(292,plain,
% 11.66/11.84 (unequally_directed_lines(line_connecting(A!2, B!1), L!0)),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[291, 237, 284])).
% 11.66/11.84 tff(293,plain,
% 11.66/11.84 ((~![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))))),
% 11.66/11.84 inference(quant_inst,[status(thm)],[])).
% 11.66/11.84 tff(294,plain,
% 11.66/11.84 (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[293, 24])).
% 11.66/11.84 tff(295,plain,
% 11.66/11.84 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(296,plain,
% 11.66/11.84 ((unequally_directed_lines(L!0, 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), L!0))) <=> (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(297,plain,
% 11.66/11.84 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, 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), L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0))))),
% 11.66/11.84 inference(monotonicity,[status(thm)],[296])).
% 11.66/11.84 tff(298,plain,
% 11.66/11.84 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, 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), L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0)))),
% 11.66/11.84 inference(transitivity,[status(thm)],[297, 295])).
% 11.66/11.84 tff(299,plain,
% 11.66/11.84 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, 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), L!0)))),
% 11.66/11.84 inference(quant_inst,[status(thm)],[])).
% 11.66/11.84 tff(300,plain,
% 11.66/11.84 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0))),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[299, 298])).
% 11.66/11.84 tff(301,plain,
% 11.66/11.84 (unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), L!0))),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[300, 36, 294])).
% 11.66/11.84 tff(302,plain,
% 11.66/11.84 (unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[301, 292])).
% 11.66/11.84 tff(303,plain,
% 11.66/11.84 (^[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)))))),
% 11.66/11.84 inference(bind,[status(th)],[])).
% 11.66/11.84 tff(304,plain,
% 11.66/11.84 (![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))))),
% 11.66/11.84 inference(quant_intro,[status(thm)],[303])).
% 11.66/11.84 tff(305,plain,
% 11.66/11.84 (^[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))))))),
% 11.66/11.84 inference(bind,[status(th)],[])).
% 11.66/11.84 tff(306,plain,
% 11.66/11.84 (![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))))),
% 11.66/11.84 inference(quant_intro,[status(thm)],[305])).
% 11.66/11.84 tff(307,plain,
% 11.66/11.84 (![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)))))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(308,plain,
% 11.66/11.84 (^[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)))))))),
% 11.66/11.84 inference(bind,[status(th)],[])).
% 11.66/11.84 tff(309,plain,
% 11.66/11.84 (![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)))))),
% 11.66/11.84 inference(quant_intro,[status(thm)],[308])).
% 11.66/11.84 tff(310,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/sandbox2/benchmark/Axioms/GEO007+0.ax','oag7')).
% 11.66/11.84 tff(311,plain,
% 11.66/11.84 (![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)))))),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[310, 309])).
% 11.66/11.84 tff(312,plain,
% 11.66/11.84 (![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)))))),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[311, 307])).
% 11.66/11.84 tff(313,plain,(
% 11.66/11.84 ![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)))))),
% 11.66/11.84 inference(skolemize,[status(sab)],[312])).
% 11.66/11.84 tff(314,plain,
% 11.66/11.84 (![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))))),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[313, 306])).
% 11.66/11.84 tff(315,plain,
% 11.66/11.84 (![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))))),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[314, 304])).
% 11.66/11.84 tff(316,plain,
% 11.66/11.84 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))))) | (~((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0))))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))))) | (~((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0))))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(317,plain,
% 11.66/11.84 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))))) | (~((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0))))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2)))))),
% 11.66/11.84 inference(quant_inst,[status(thm)],[])).
% 11.66/11.84 tff(318,plain,
% 11.66/11.84 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~((~unequally_directed_lines(line_connecting(B!1, A!2), L!0)) | (~unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(L!0))))) | (~((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0))))) | (~unequally_directed_lines(L!0, reverse_line(line_connecting(B!1, A!2))))),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[317, 316])).
% 11.66/11.84 tff(319,plain,
% 11.66/11.84 ($false),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[318, 315, 236, 302, 283, 281])).
% 11.66/11.84 tff(320,plain,(unequally_directed_lines(L!0, L!0) | (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1)))), inference(lemma,lemma(discharge,[]))).
% 11.66/11.84 tff(321,plain,
% 11.66/11.84 ((~unequally_directed_lines(L!0, line_connecting(B!1, A!2))) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1)))),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[320, 235])).
% 11.66/11.84 tff(322,plain,
% 11.66/11.84 (~unequally_directed_lines(L!0, line_connecting(B!1, A!2))),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[321, 231])).
% 11.66/11.84 tff(323,plain,
% 11.66/11.84 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(324,plain,
% 11.66/11.84 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1))))),
% 11.66/11.84 inference(quant_inst,[status(thm)],[])).
% 11.66/11.84 tff(325,plain,
% 11.66/11.84 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1)))),
% 11.66/11.84 inference(modus_ponens,[status(thm)],[324, 323])).
% 11.66/11.84 tff(326,plain,
% 11.66/11.84 (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(L!0, line_connecting(B!1, A!2)) | (~unequally_directed_lines(L!0, line_connecting(A!2, B!1)))),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[325, 36])).
% 11.66/11.84 tff(327,plain,
% 11.66/11.84 ($false),
% 11.66/11.84 inference(unit_resolution,[status(thm)],[326, 322, 231, 88])).
% 11.66/11.84 tff(328,plain,(unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))), inference(lemma,lemma(discharge,[]))).
% 11.66/11.84 tff(329,plain,
% 11.66/11.84 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(330,plain,
% 11.66/11.84 ((unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)))) <=> (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))))),
% 11.66/11.84 inference(rewrite,[status(thm)],[])).
% 11.66/11.84 tff(331,plain,
% 11.66/11.84 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(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(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))))),
% 11.66/11.84 inference(monotonicity,[status(thm)],[330])).
% 11.66/11.84 tff(332,plain,
% 11.66/11.84 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(B!1, A!2), reverse_line(line_connecting(A!2, B!1))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(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(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))))),
% 11.66/11.84 inference(transitivity,[status(thm)],[331, 329])).
% 11.66/11.85 tff(333,plain,
% 11.66/11.85 ((~![L: $i, 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(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))),
% 11.66/11.85 inference(quant_inst,[status(thm)],[])).
% 11.66/11.85 tff(334,plain,
% 11.66/11.85 ((~![L: $i, 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(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))),
% 11.66/11.85 inference(modus_ponens,[status(thm)],[333, 332])).
% 11.66/11.85 tff(335,plain,
% 11.66/11.85 ((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[334, 36, 90])).
% 11.66/11.85 tff(336,plain,
% 11.66/11.85 (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[335, 328])).
% 11.66/11.85 tff(337,assumption,(~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))), introduced(assumption)).
% 11.66/11.85 tff(338,plain,
% 11.66/11.85 (((~![L: $i, 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(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.85 inference(rewrite,[status(thm)],[])).
% 11.66/11.85 tff(339,plain,
% 11.66/11.85 ((unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) <=> (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.85 inference(rewrite,[status(thm)],[])).
% 11.66/11.85 tff(340,plain,
% 11.66/11.85 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))))),
% 11.66/11.85 inference(monotonicity,[status(thm)],[339])).
% 11.66/11.85 tff(341,plain,
% 11.66/11.85 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.85 inference(transitivity,[status(thm)],[340, 338])).
% 11.66/11.85 tff(342,plain,
% 11.66/11.85 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.85 inference(quant_inst,[status(thm)],[])).
% 11.66/11.85 tff(343,plain,
% 11.66/11.85 ((~![L: $i, 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(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 11.66/11.85 inference(modus_ponens,[status(thm)],[342, 341])).
% 11.66/11.85 tff(344,plain,
% 11.66/11.85 (~unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[343, 36, 294, 59])).
% 11.66/11.85 tff(345,assumption,(unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))), introduced(assumption)).
% 11.66/11.85 tff(346,plain,
% 11.66/11.85 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 11.66/11.85 inference(rewrite,[status(thm)],[])).
% 11.66/11.85 tff(347,plain,
% 11.66/11.85 ((unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))))) <=> ((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 11.66/11.85 inference(rewrite,[status(thm)],[])).
% 11.66/11.85 tff(348,plain,
% 11.66/11.85 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.85 inference(monotonicity,[status(thm)],[347])).
% 11.66/11.85 tff(349,plain,
% 11.66/11.85 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))),
% 11.66/11.85 inference(transitivity,[status(thm)],[348, 346])).
% 11.66/11.85 tff(350,plain,
% 11.66/11.85 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))))),
% 11.66/11.85 inference(quant_inst,[status(thm)],[])).
% 11.66/11.85 tff(351,plain,
% 11.66/11.85 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(line_connecting(A!2, B!1), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))),
% 11.66/11.85 inference(modus_ponens,[status(thm)],[350, 349])).
% 11.66/11.85 tff(352,plain,
% 11.66/11.85 ($false),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[351, 36, 345, 344, 337])).
% 11.66/11.85 tff(353,plain,(unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1))))), inference(lemma,lemma(discharge,[]))).
% 11.66/11.85 tff(354,plain,
% 11.66/11.85 (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[353, 336])).
% 11.66/11.85 tff(355,plain,
% 11.66/11.85 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.66/11.85 inference(rewrite,[status(thm)],[])).
% 11.66/11.85 tff(356,plain,
% 11.66/11.85 ((unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2)))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.66/11.85 inference(rewrite,[status(thm)],[])).
% 11.66/11.85 tff(357,plain,
% 11.66/11.85 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.85 inference(monotonicity,[status(thm)],[356])).
% 11.66/11.85 tff(358,plain,
% 11.66/11.85 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.66/11.85 inference(transitivity,[status(thm)],[357, 355])).
% 11.66/11.85 tff(359,plain,
% 11.66/11.85 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))))),
% 11.66/11.85 inference(quant_inst,[status(thm)],[])).
% 11.66/11.85 tff(360,plain,
% 11.66/11.85 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 11.66/11.85 inference(modus_ponens,[status(thm)],[359, 358])).
% 11.66/11.85 tff(361,plain,
% 11.66/11.85 ($false),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[360, 36, 354, 17, 87])).
% 11.66/11.85 tff(362,plain,(unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))), inference(lemma,lemma(discharge,[]))).
% 11.66/11.85 tff(363,plain,
% 11.66/11.85 (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[362, 17])).
% 11.66/11.85 tff(364,plain,
% 11.66/11.85 (((~![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, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))))) <=> ((~![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, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)))))),
% 11.66/11.85 inference(rewrite,[status(thm)],[])).
% 11.66/11.85 tff(365,plain,
% 11.66/11.85 ((~(left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))) <=> (~(left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))))),
% 11.66/11.85 inference(rewrite,[status(thm)],[])).
% 11.66/11.85 tff(366,plain,
% 11.66/11.85 (((~![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, B!1)), line_connecting(B!1, A!2)) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) <=> ((~![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, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)))))),
% 11.66/11.85 inference(monotonicity,[status(thm)],[365])).
% 11.66/11.85 tff(367,plain,
% 11.66/11.85 (((~![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, B!1)), line_connecting(B!1, A!2)) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) <=> ((~![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, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)))))),
% 11.66/11.85 inference(transitivity,[status(thm)],[366, 364])).
% 11.66/11.85 tff(368,plain,
% 11.66/11.85 ((~![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, B!1)), line_connecting(B!1, A!2)) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))),
% 11.66/11.85 inference(quant_inst,[status(thm)],[])).
% 11.66/11.85 tff(369,plain,
% 11.66/11.85 ((~![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, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))))),
% 11.66/11.85 inference(modus_ponens,[status(thm)],[368, 367])).
% 11.66/11.85 tff(370,plain,
% 11.66/11.85 (~(left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)))),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[369, 8])).
% 11.66/11.85 tff(371,plain,
% 11.66/11.85 ((left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))),
% 11.66/11.85 inference(tautology,[status(thm)],[])).
% 11.66/11.85 tff(372,plain,
% 11.66/11.85 (~left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[371, 370])).
% 11.66/11.85 tff(373,plain,
% 11.66/11.85 ((left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)))),
% 11.66/11.85 inference(tautology,[status(thm)],[])).
% 11.66/11.85 tff(374,plain,
% 11.66/11.85 (~left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[373, 370])).
% 11.66/11.85 tff(375,plain,
% 11.66/11.85 (((~![L: $i, 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(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(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(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))),
% 11.66/11.85 inference(rewrite,[status(thm)],[])).
% 11.66/11.85 tff(376,plain,
% 11.66/11.85 ((unequally_directed_lines(reverse_line(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), reverse_line(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), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))),
% 11.66/11.85 inference(rewrite,[status(thm)],[])).
% 11.66/11.85 tff(377,plain,
% 11.66/11.85 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(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(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), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))),
% 11.66/11.85 inference(monotonicity,[status(thm)],[376])).
% 11.66/11.85 tff(378,plain,
% 11.66/11.85 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(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(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), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))),
% 11.66/11.85 inference(transitivity,[status(thm)],[377, 375])).
% 11.66/11.85 tff(379,plain,
% 11.66/11.85 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | unequally_directed_lines(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(A!2, B!1)))))),
% 11.66/11.85 inference(quant_inst,[status(thm)],[])).
% 11.66/11.85 tff(380,plain,
% 11.66/11.85 ((~![L: $i, 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(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))),
% 11.66/11.85 inference(modus_ponens,[status(thm)],[379, 378])).
% 11.66/11.85 tff(381,plain,
% 11.66/11.85 ((~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(A!2, B!1)))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[380, 36, 294])).
% 11.66/11.85 tff(382,plain,
% 11.66/11.85 (unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[381, 336])).
% 11.66/11.85 tff(383,plain,
% 11.66/11.85 (((~![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, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)))),
% 11.66/11.85 inference(rewrite,[status(thm)],[])).
% 11.66/11.85 tff(384,plain,
% 11.66/11.85 ((left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)))),
% 11.66/11.85 inference(rewrite,[status(thm)],[])).
% 11.66/11.85 tff(385,plain,
% 11.66/11.85 (((~![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, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) <=> ((~![L: $i, M: $i] : (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, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))))),
% 11.66/11.85 inference(monotonicity,[status(thm)],[384])).
% 11.66/11.85 tff(386,plain,
% 11.66/11.85 (((~![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, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) <=> ((~![L: $i, M: $i] : (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, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)))),
% 11.66/11.85 inference(transitivity,[status(thm)],[385, 383])).
% 11.66/11.85 tff(387,plain,
% 11.66/11.85 ((~![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, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2)) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))),
% 11.66/11.85 inference(quant_inst,[status(thm)],[])).
% 11.66/11.85 tff(388,plain,
% 11.66/11.85 ((~![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, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))),
% 11.66/11.85 inference(modus_ponens,[status(thm)],[387, 386])).
% 11.66/11.85 tff(389,plain,
% 11.66/11.85 ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))) | left_convergent_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[388, 270, 382])).
% 11.66/11.85 tff(390,plain,
% 11.66/11.85 (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[389, 374, 372])).
% 11.66/11.85 tff(391,plain,
% 11.66/11.85 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))),
% 11.66/11.85 inference(tautology,[status(thm)],[])).
% 11.66/11.85 tff(392,plain,
% 11.66/11.85 ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))),
% 11.66/11.85 inference(unit_resolution,[status(thm)],[391, 390])).
% 11.66/11.85 tff(393,plain,
% 11.66/11.85 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))),
% 11.66/11.85 inference(rewrite,[status(thm)],[])).
% 11.66/11.85 tff(394,plain,
% 11.66/11.85 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))),
% 11.66/11.86 inference(rewrite,[status(thm)],[])).
% 11.66/11.86 tff(395,plain,
% 11.66/11.86 ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) <=> (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2))))))),
% 11.66/11.86 inference(rewrite,[status(thm)],[])).
% 11.66/11.86 tff(396,plain,
% 11.66/11.86 ((~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))))) <=> (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2)))))),
% 11.66/11.86 inference(rewrite,[status(thm)],[])).
% 11.66/11.86 tff(397,plain,
% 11.66/11.86 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))),
% 11.66/11.86 inference(monotonicity,[status(thm)],[396, 395])).
% 11.66/11.86 tff(398,plain,
% 11.66/11.86 (((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))),
% 11.66/11.86 inference(transitivity,[status(thm)],[397, 394])).
% 11.66/11.86 tff(399,plain,
% 11.66/11.86 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))))),
% 11.66/11.86 inference(monotonicity,[status(thm)],[398])).
% 11.66/11.86 tff(400,plain,
% 11.66/11.86 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))),
% 11.66/11.86 inference(transitivity,[status(thm)],[399, 393])).
% 11.66/11.86 tff(401,plain,
% 11.66/11.86 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))),
% 11.66/11.86 inference(quant_inst,[status(thm)],[])).
% 11.66/11.86 tff(402,plain,
% 11.66/11.86 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(B!1, A!2))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(B!1, A!2)))))) | (~((~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(B!1, A!2))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.86 inference(modus_ponens,[status(thm)],[401, 400])).
% 11.66/11.86 tff(403,plain,
% 11.66/11.86 (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.66/11.86 inference(unit_resolution,[status(thm)],[402, 315, 392, 363, 86])).
% 11.66/11.86 tff(404,plain,
% 11.66/11.86 (((~![L: $i, 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(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.86 inference(rewrite,[status(thm)],[])).
% 11.66/11.86 tff(405,plain,
% 11.66/11.86 ((unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) <=> (unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.86 inference(rewrite,[status(thm)],[])).
% 11.66/11.86 tff(406,plain,
% 11.66/11.86 (((~![L: $i, 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(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))),
% 11.66/11.86 inference(monotonicity,[status(thm)],[405])).
% 11.66/11.86 tff(407,plain,
% 11.66/11.86 (((~![L: $i, 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(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.86 inference(transitivity,[status(thm)],[406, 404])).
% 11.66/11.86 tff(408,plain,
% 11.66/11.86 ((~![L: $i, 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(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.86 inference(quant_inst,[status(thm)],[])).
% 11.66/11.86 tff(409,plain,
% 11.66/11.86 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(reverse_line(line_connecting(A!2, B!1)), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.66/11.86 inference(modus_ponens,[status(thm)],[408, 407])).
% 11.66/11.86 tff(410,plain,
% 11.66/11.86 ($false),
% 11.66/11.86 inference(unit_resolution,[status(thm)],[409, 36, 26, 363, 403])).
% 11.66/11.86 tff(411,plain,(unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))), inference(lemma,lemma(discharge,[]))).
% 11.66/11.86 tff(412,assumption,(~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))), introduced(assumption)).
% 11.66/11.86 tff(413,assumption,(unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))), introduced(assumption)).
% 11.66/11.86 tff(414,plain,
% 11.66/11.86 (((~![L: $i, 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(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(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(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(A!2, B!1))))),
% 11.66/11.86 inference(rewrite,[status(thm)],[])).
% 11.66/11.86 tff(415,plain,
% 11.66/11.86 ((~![L: $i, 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(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(A!2, B!1))))),
% 11.66/11.86 inference(quant_inst,[status(thm)],[])).
% 11.66/11.86 tff(416,plain,
% 11.66/11.86 ((~![L: $i, 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(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), reverse_line(line_connecting(B!1, A!2))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(A!2, B!1)))),
% 11.66/11.86 inference(modus_ponens,[status(thm)],[415, 414])).
% 11.66/11.86 tff(417,plain,
% 11.66/11.86 (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(A!2, B!1))),
% 11.66/11.86 inference(unit_resolution,[status(thm)],[416, 36, 294, 59])).
% 11.66/11.86 tff(418,plain,
% 11.66/11.86 ((~![A: $i, L: $i] : (~unequally_directed_lines(parallel_through_point(L, A), L))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(A!2, B!1)))),
% 11.66/11.86 inference(quant_inst,[status(thm)],[])).
% 11.66/11.86 tff(419,plain,
% 11.66/11.86 (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(A!2, B!1))),
% 11.66/11.86 inference(unit_resolution,[status(thm)],[418, 57])).
% 11.66/11.86 tff(420,plain,
% 11.66/11.86 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(A!2, B!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(A!2, B!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(A!2, B!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(A!2, B!1)))),
% 11.66/11.86 inference(rewrite,[status(thm)],[])).
% 11.66/11.86 tff(421,plain,
% 11.66/11.86 ((unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(A!2, B!1)) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(A!2, B!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) <=> (unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(A!2, B!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(A!2, B!1)))),
% 11.66/11.86 inference(rewrite,[status(thm)],[])).
% 11.66/11.86 tff(422,plain,
% 11.66/11.86 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(A!2, B!1)) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(A!2, B!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(A!2, B!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(A!2, B!1))))),
% 11.66/11.86 inference(monotonicity,[status(thm)],[421])).
% 11.66/11.86 tff(423,plain,
% 11.66/11.86 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(A!2, B!1)) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(A!2, B!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(A!2, B!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(A!2, B!1)))),
% 11.66/11.86 inference(transitivity,[status(thm)],[422, 420])).
% 11.66/11.86 tff(424,plain,
% 11.66/11.86 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(A!2, B!1)) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(A!2, B!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.86 inference(quant_inst,[status(thm)],[])).
% 11.66/11.86 tff(425,plain,
% 11.66/11.86 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(A!2, B!1)) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(A!2, B!1))),
% 11.66/11.87 inference(modus_ponens,[status(thm)],[424, 423])).
% 11.66/11.87 tff(426,plain,
% 11.66/11.87 (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 11.66/11.87 inference(unit_resolution,[status(thm)],[425, 36, 419, 417])).
% 11.66/11.87 tff(427,plain,
% 11.66/11.87 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.66/11.87 inference(rewrite,[status(thm)],[])).
% 11.66/11.87 tff(428,plain,
% 11.66/11.87 ((unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) <=> (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.66/11.87 inference(rewrite,[status(thm)],[])).
% 11.66/11.87 tff(429,plain,
% 11.66/11.87 (((~![L: $i, 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(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.87 inference(monotonicity,[status(thm)],[428])).
% 11.66/11.87 tff(430,plain,
% 11.66/11.87 (((~![L: $i, 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(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.66/11.87 inference(transitivity,[status(thm)],[429, 427])).
% 11.66/11.87 tff(431,plain,
% 11.66/11.87 ((~![L: $i, 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(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.87 inference(quant_inst,[status(thm)],[])).
% 11.66/11.87 tff(432,plain,
% 11.66/11.87 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 11.66/11.87 inference(modus_ponens,[status(thm)],[431, 430])).
% 11.66/11.87 tff(433,plain,
% 11.66/11.87 ($false),
% 11.66/11.87 inference(unit_resolution,[status(thm)],[432, 36, 426, 413, 412])).
% 11.66/11.87 tff(434,plain,(unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(reverse_line(line_connecting(B!1, A!2)), A!2), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))), inference(lemma,lemma(discharge,[]))).
% 11.66/11.87 tff(435,plain,
% 11.66/11.87 (unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 11.66/11.87 inference(unit_resolution,[status(thm)],[434, 411])).
% 11.66/11.87 tff(436,assumption,(unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))), introduced(assumption)).
% 11.66/11.87 tff(437,assumption,(~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))), introduced(assumption)).
% 11.66/11.87 tff(438,plain,
% 11.66/11.87 (((~![L: $i, 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(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.87 inference(rewrite,[status(thm)],[])).
% 11.66/11.87 tff(439,plain,
% 11.66/11.87 ((unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) <=> (unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.87 inference(rewrite,[status(thm)],[])).
% 11.66/11.87 tff(440,plain,
% 11.66/11.87 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))),
% 11.66/11.87 inference(monotonicity,[status(thm)],[439])).
% 11.66/11.87 tff(441,plain,
% 11.66/11.87 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.87 inference(transitivity,[status(thm)],[440, 438])).
% 11.66/11.87 tff(442,plain,
% 11.66/11.87 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.87 inference(quant_inst,[status(thm)],[])).
% 11.66/11.87 tff(443,plain,
% 11.66/11.87 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.66/11.87 inference(modus_ponens,[status(thm)],[442, 441])).
% 11.66/11.87 tff(444,plain,
% 11.66/11.87 ($false),
% 11.66/11.87 inference(unit_resolution,[status(thm)],[443, 36, 43, 437, 436])).
% 11.66/11.87 tff(445,plain,(unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))), inference(lemma,lemma(discharge,[]))).
% 11.66/11.87 tff(446,plain,
% 11.66/11.87 (unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))),
% 11.66/11.87 inference(unit_resolution,[status(thm)],[445, 435])).
% 11.66/11.87 tff(447,plain,
% 11.66/11.87 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.87 inference(rewrite,[status(thm)],[])).
% 11.66/11.87 tff(448,plain,
% 11.66/11.87 ((left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> (left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.87 inference(rewrite,[status(thm)],[])).
% 11.66/11.87 tff(449,plain,
% 11.66/11.87 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))),
% 11.66/11.87 inference(monotonicity,[status(thm)],[448])).
% 11.66/11.87 tff(450,plain,
% 11.66/11.87 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.87 inference(transitivity,[status(thm)],[449, 447])).
% 11.66/11.87 tff(451,plain,
% 11.66/11.87 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))))),
% 11.66/11.87 inference(quant_inst,[status(thm)],[])).
% 11.66/11.87 tff(452,plain,
% 11.66/11.87 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))) | left_convergent_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.66/11.87 inference(modus_ponens,[status(thm)],[451, 450])).
% 11.66/11.87 tff(453,plain,
% 11.66/11.87 ($false),
% 11.66/11.87 inference(unit_resolution,[status(thm)],[452, 270, 446, 16, 15, 13])).
% 11.66/11.87 tff(454,plain,(~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))), inference(lemma,lemma(discharge,[]))).
% 11.66/11.87 tff(455,plain,
% 11.66/11.87 (((~![L: $i, 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(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.88 inference(rewrite,[status(thm)],[])).
% 11.66/11.88 tff(456,plain,
% 11.66/11.88 ((~![L: $i, 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(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))))),
% 11.66/11.88 inference(quant_inst,[status(thm)],[])).
% 11.66/11.88 tff(457,plain,
% 11.66/11.88 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), reverse_line(line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))))) | (~unequally_directed_lines(parallel_through_point(line_connecting(A!2, B!1), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0))), line_connecting(intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)), intersection_point(line_connecting(A!2, B!1), reverse_line(L!0)))))),
% 11.73/11.88 inference(modus_ponens,[status(thm)],[456, 455])).
% 11.73/11.88 tff(458,plain,
% 11.73/11.88 ($false),
% 11.73/11.88 inference(unit_resolution,[status(thm)],[457, 36, 26, 446, 454])).
% 11.73/11.88 % SZS output end Proof
% 11.73/11.88 % E exiting
%------------------------------------------------------------------------------