TSTP Solution File: GEO264+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO264+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 15:18:51 EDT 2022
% Result : Theorem 77.96s 22.90s
% Output : Proof 77.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO264+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : goeland -dmt -presko -proof %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 07:34:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 [DMT] DMT loaded with preskolemization
% 0.12/0.35 [EQ] equality loaded.
% 0.12/0.35 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.35 Conjecture not found
% 0.12/0.35 Start search
% 0.12/0.35 nb_step : 1 - limit : 37
% 0.12/0.35 Launch Gotab with destructive = true
% 77.96/22.89 % SZS output start Proof for theBenchmark.p
% 77.96/22.90 [0] ALPHA_AND : ((! [X9_9, Y10_10] : ((unequally_directed_opposite_lines(X9_9, Y10_10) <=> unequally_directed_lines(X9_9, reverse_line(Y10_10)))) & ! [X11_11, Y12_12] : ((right_apart_point(X11_11, Y12_12) <=> left_apart_point(X11_11, reverse_line(Y12_12)))) & ! [X13_13, Y14_14] : ((right_convergent_lines(X13_13, Y14_14) <=> left_convergent_lines(X13_13, reverse_line(Y14_14)))) & ! [X15_15, Y16_16] : ((equally_directed_lines(X15_15, Y16_16) <=> ~unequally_directed_lines(X15_15, Y16_16))) & ! [X17_17, Y18_18] : ((equally_directed_opposite_lines(X17_17, Y18_18) <=> ~unequally_directed_opposite_lines(X17_17, Y18_18))) & ! [A33_33] : (~distinct_points(A33_33, A33_33)) & ! [A34_34, B35_35, C36_36] : ((distinct_points(A34_34, B35_35) => (distinct_points(A34_34, C36_36) | distinct_points(B35_35, C36_36)))) & ! [L37_37] : (~distinct_lines(L37_37, L37_37)) & ! [L38_38, M39_39, N40_40] : ((distinct_lines(L38_38, M39_39) => (distinct_lines(L38_38, N40_40) | distinct_lines(M39_39, N40_40)))) & ! [L41_41] : (equally_directed_lines(L41_41, L41_41)) & ! [L42_42, M43_43, N44_44] : ((unequally_directed_lines(L42_42, M43_43) => (unequally_directed_lines(L42_42, N44_44) | unequally_directed_lines(M43_43, N44_44)))) & ! [L45_45, M46_46, N47_47] : (((unequally_directed_lines(L45_45, M46_46) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => ((unequally_directed_lines(L45_45, N47_47) & unequally_directed_lines(L45_45, reverse_line(N47_47))) | (unequally_directed_lines(M46_46, N47_47) & unequally_directed_lines(M46_46, reverse_line(N47_47)))))) & ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49)))) & ! [L50_50, M51_51] : (((unequally_directed_lines(L50_50, M51_51) & unequally_directed_lines(L50_50, reverse_line(M51_51))) => (left_convergent_lines(L50_50, M51_51) | left_convergent_lines(L50_50, reverse_line(M51_51))))) & ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53)))) & ! [L54_54, M55_55] : (~(left_convergent_lines(L54_54, M55_55) | left_convergent_lines(L54_54, reverse_line(M55_55)))) & ! [A56_56, B57_57] : ((((point(A56_56) & point(B57_57)) & distinct_points(A56_56, B57_57)) => line(line_connecting(A56_56, B57_57)))) & ! [L58_58, M59_59] : (((((line(L58_58) & line(M59_59)) & unequally_directed_lines(L58_58, M59_59)) & unequally_directed_lines(L58_58, reverse_line(M59_59))) => point(intersection_point(L58_58, M59_59)))) & ! [L60_60, A61_61] : (((point(A61_61) & line(L60_60)) => line(parallel_through_point(L60_60, A61_61)))) & ! [L62_62] : ((line(L62_62) => line(reverse_line(L62_62)))) & ! [A63_63, B64_64] : ((distinct_points(A63_63, B64_64) => (~apart_point_and_line(A63_63, line_connecting(A63_63, B64_64)) & ~apart_point_and_line(B64_64, line_connecting(A63_63, B64_64))))) & ! [L65_65, M66_66] : (((unequally_directed_lines(L65_65, M66_66) & unequally_directed_lines(L65_65, reverse_line(M66_66))) => (~apart_point_and_line(intersection_point(L65_65, M66_66), L65_65) & ~apart_point_and_line(intersection_point(L65_65, M66_66), M66_66)))) & ! [A67_67, L68_68] : (~apart_point_and_line(A67_67, parallel_through_point(L68_68, A67_67))) & ! [L69_69] : (~distinct_lines(L69_69, reverse_line(L69_69))) & ! [A70_70, B71_71] : ((distinct_points(A70_70, B71_71) => equally_directed_lines(line_connecting(A70_70, B71_71), reverse_line(line_connecting(B71_71, A70_70))))) & ! [A72_72, L73_73] : (equally_directed_lines(parallel_through_point(L73_73, A72_72), L73_73)) & ! [A74_74, B75_75, L76_76, M77_77] : (((distinct_points(A74_74, B75_75) & distinct_lines(L76_76, M77_77)) => (((((((left_apart_point(A74_74, L76_76) | left_apart_point(B75_75, L76_76)) | left_apart_point(A74_74, M77_77)) | left_apart_point(B75_75, M77_77)) | left_apart_point(A74_74, reverse_line(L76_76))) | left_apart_point(B75_75, reverse_line(L76_76))) | left_apart_point(A74_74, reverse_line(M77_77))) | left_apart_point(B75_75, reverse_line(M77_77))))) & ! [A78_78, B79_79, L80_80] : (((distinct_points(A78_78, B79_79) & left_apart_point(A78_78, L80_80)) => (left_apart_point(B79_79, L80_80) | left_convergent_lines(line_connecting(A78_78, B79_79), L80_80)))) & ! [A81_81, B82_82, L83_83] : ((left_apart_point(A81_81, L83_83) => (distinct_points(A81_81, B82_82) | left_apart_point(B82_82, L83_83)))) & ! [A84_84, L85_85, M86_86] : (((left_apart_point(A84_84, L85_85) & unequally_directed_lines(L85_85, M86_86)) => (distinct_lines(L85_85, M86_86) | left_apart_point(A84_84, reverse_line(M86_86))))) & ! [L87_87, M88_88, N89_89] : ((left_convergent_lines(L87_87, M88_88) => (unequally_directed_lines(M88_88, N89_89) | left_convergent_lines(L87_87, N89_89))))) & ~! [A90_90, B91_91, C92_92, D93_93] : ((left_apart_point(C92_92, line_connecting(A90_90, B91_91)) => ((right_apart_point(D93_93, line_connecting(B91_91, C92_92)) & right_apart_point(D93_93, line_connecting(C92_92, A90_90))) => left_apart_point(D93_93, line_connecting(A90_90, B91_91))))))
% 77.96/22.90 -> [1] (! [X9_9, Y10_10] : ((unequally_directed_opposite_lines(X9_9, Y10_10) <=> unequally_directed_lines(X9_9, reverse_line(Y10_10)))) & ! [X11_11, Y12_12] : ((right_apart_point(X11_11, Y12_12) <=> left_apart_point(X11_11, reverse_line(Y12_12)))) & ! [X13_13, Y14_14] : ((right_convergent_lines(X13_13, Y14_14) <=> left_convergent_lines(X13_13, reverse_line(Y14_14)))) & ! [X15_15, Y16_16] : ((equally_directed_lines(X15_15, Y16_16) <=> ~unequally_directed_lines(X15_15, Y16_16))) & ! [X17_17, Y18_18] : ((equally_directed_opposite_lines(X17_17, Y18_18) <=> ~unequally_directed_opposite_lines(X17_17, Y18_18))) & ! [A33_33] : (~distinct_points(A33_33, A33_33)) & ! [A34_34, B35_35, C36_36] : ((distinct_points(A34_34, B35_35) => (distinct_points(A34_34, C36_36) | distinct_points(B35_35, C36_36)))) & ! [L37_37] : (~distinct_lines(L37_37, L37_37)) & ! [L38_38, M39_39, N40_40] : ((distinct_lines(L38_38, M39_39) => (distinct_lines(L38_38, N40_40) | distinct_lines(M39_39, N40_40)))) & ! [L41_41] : (equally_directed_lines(L41_41, L41_41)) & ! [L42_42, M43_43, N44_44] : ((unequally_directed_lines(L42_42, M43_43) => (unequally_directed_lines(L42_42, N44_44) | unequally_directed_lines(M43_43, N44_44)))) & ! [L45_45, M46_46, N47_47] : (((unequally_directed_lines(L45_45, M46_46) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => ((unequally_directed_lines(L45_45, N47_47) & unequally_directed_lines(L45_45, reverse_line(N47_47))) | (unequally_directed_lines(M46_46, N47_47) & unequally_directed_lines(M46_46, reverse_line(N47_47)))))) & ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49)))) & ! [L50_50, M51_51] : (((unequally_directed_lines(L50_50, M51_51) & unequally_directed_lines(L50_50, reverse_line(M51_51))) => (left_convergent_lines(L50_50, M51_51) | left_convergent_lines(L50_50, reverse_line(M51_51))))) & ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53)))) & ! [L54_54, M55_55] : (~(left_convergent_lines(L54_54, M55_55) | left_convergent_lines(L54_54, reverse_line(M55_55)))) & ! [A56_56, B57_57] : ((((point(A56_56) & point(B57_57)) & distinct_points(A56_56, B57_57)) => line(line_connecting(A56_56, B57_57)))) & ! [L58_58, M59_59] : (((((line(L58_58) & line(M59_59)) & unequally_directed_lines(L58_58, M59_59)) & unequally_directed_lines(L58_58, reverse_line(M59_59))) => point(intersection_point(L58_58, M59_59)))) & ! [L60_60, A61_61] : (((point(A61_61) & line(L60_60)) => line(parallel_through_point(L60_60, A61_61)))) & ! [L62_62] : ((line(L62_62) => line(reverse_line(L62_62)))) & ! [A63_63, B64_64] : ((distinct_points(A63_63, B64_64) => (~apart_point_and_line(A63_63, line_connecting(A63_63, B64_64)) & ~apart_point_and_line(B64_64, line_connecting(A63_63, B64_64))))) & ! [L65_65, M66_66] : (((unequally_directed_lines(L65_65, M66_66) & unequally_directed_lines(L65_65, reverse_line(M66_66))) => (~apart_point_and_line(intersection_point(L65_65, M66_66), L65_65) & ~apart_point_and_line(intersection_point(L65_65, M66_66), M66_66)))) & ! [A67_67, L68_68] : (~apart_point_and_line(A67_67, parallel_through_point(L68_68, A67_67))) & ! [L69_69] : (~distinct_lines(L69_69, reverse_line(L69_69))) & ! [A70_70, B71_71] : ((distinct_points(A70_70, B71_71) => equally_directed_lines(line_connecting(A70_70, B71_71), reverse_line(line_connecting(B71_71, A70_70))))) & ! [A72_72, L73_73] : (equally_directed_lines(parallel_through_point(L73_73, A72_72), L73_73)) & ! [A74_74, B75_75, L76_76, M77_77] : (((distinct_points(A74_74, B75_75) & distinct_lines(L76_76, M77_77)) => (((((((left_apart_point(A74_74, L76_76) | left_apart_point(B75_75, L76_76)) | left_apart_point(A74_74, M77_77)) | left_apart_point(B75_75, M77_77)) | left_apart_point(A74_74, reverse_line(L76_76))) | left_apart_point(B75_75, reverse_line(L76_76))) | left_apart_point(A74_74, reverse_line(M77_77))) | left_apart_point(B75_75, reverse_line(M77_77))))) & ! [A78_78, B79_79, L80_80] : (((distinct_points(A78_78, B79_79) & left_apart_point(A78_78, L80_80)) => (left_apart_point(B79_79, L80_80) | left_convergent_lines(line_connecting(A78_78, B79_79), L80_80)))) & ! [A81_81, B82_82, L83_83] : ((left_apart_point(A81_81, L83_83) => (distinct_points(A81_81, B82_82) | left_apart_point(B82_82, L83_83)))) & ! [A84_84, L85_85, M86_86] : (((left_apart_point(A84_84, L85_85) & unequally_directed_lines(L85_85, M86_86)) => (distinct_lines(L85_85, M86_86) | left_apart_point(A84_84, reverse_line(M86_86))))) & ! [L87_87, M88_88, N89_89] : ((left_convergent_lines(L87_87, M88_88) => (unequally_directed_lines(M88_88, N89_89) | left_convergent_lines(L87_87, N89_89))))), ~! [A90_90, B91_91, C92_92, D93_93] : ((left_apart_point(C92_92, line_connecting(A90_90, B91_91)) => ((right_apart_point(D93_93, line_connecting(B91_91, C92_92)) & right_apart_point(D93_93, line_connecting(C92_92, A90_90))) => left_apart_point(D93_93, line_connecting(A90_90, B91_91)))))
% 77.96/22.90
% 77.96/22.90 [1] ALPHA_AND : (! [X9_9, Y10_10] : ((unequally_directed_opposite_lines(X9_9, Y10_10) <=> unequally_directed_lines(X9_9, reverse_line(Y10_10)))) & ! [X11_11, Y12_12] : ((right_apart_point(X11_11, Y12_12) <=> left_apart_point(X11_11, reverse_line(Y12_12)))) & ! [X13_13, Y14_14] : ((right_convergent_lines(X13_13, Y14_14) <=> left_convergent_lines(X13_13, reverse_line(Y14_14)))) & ! [X15_15, Y16_16] : ((equally_directed_lines(X15_15, Y16_16) <=> ~unequally_directed_lines(X15_15, Y16_16))) & ! [X17_17, Y18_18] : ((equally_directed_opposite_lines(X17_17, Y18_18) <=> ~unequally_directed_opposite_lines(X17_17, Y18_18))) & ! [A33_33] : (~distinct_points(A33_33, A33_33)) & ! [A34_34, B35_35, C36_36] : ((distinct_points(A34_34, B35_35) => (distinct_points(A34_34, C36_36) | distinct_points(B35_35, C36_36)))) & ! [L37_37] : (~distinct_lines(L37_37, L37_37)) & ! [L38_38, M39_39, N40_40] : ((distinct_lines(L38_38, M39_39) => (distinct_lines(L38_38, N40_40) | distinct_lines(M39_39, N40_40)))) & ! [L41_41] : (equally_directed_lines(L41_41, L41_41)) & ! [L42_42, M43_43, N44_44] : ((unequally_directed_lines(L42_42, M43_43) => (unequally_directed_lines(L42_42, N44_44) | unequally_directed_lines(M43_43, N44_44)))) & ! [L45_45, M46_46, N47_47] : (((unequally_directed_lines(L45_45, M46_46) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => ((unequally_directed_lines(L45_45, N47_47) & unequally_directed_lines(L45_45, reverse_line(N47_47))) | (unequally_directed_lines(M46_46, N47_47) & unequally_directed_lines(M46_46, reverse_line(N47_47)))))) & ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49)))) & ! [L50_50, M51_51] : (((unequally_directed_lines(L50_50, M51_51) & unequally_directed_lines(L50_50, reverse_line(M51_51))) => (left_convergent_lines(L50_50, M51_51) | left_convergent_lines(L50_50, reverse_line(M51_51))))) & ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53)))) & ! [L54_54, M55_55] : (~(left_convergent_lines(L54_54, M55_55) | left_convergent_lines(L54_54, reverse_line(M55_55)))) & ! [A56_56, B57_57] : ((((point(A56_56) & point(B57_57)) & distinct_points(A56_56, B57_57)) => line(line_connecting(A56_56, B57_57)))) & ! [L58_58, M59_59] : (((((line(L58_58) & line(M59_59)) & unequally_directed_lines(L58_58, M59_59)) & unequally_directed_lines(L58_58, reverse_line(M59_59))) => point(intersection_point(L58_58, M59_59)))) & ! [L60_60, A61_61] : (((point(A61_61) & line(L60_60)) => line(parallel_through_point(L60_60, A61_61)))) & ! [L62_62] : ((line(L62_62) => line(reverse_line(L62_62)))) & ! [A63_63, B64_64] : ((distinct_points(A63_63, B64_64) => (~apart_point_and_line(A63_63, line_connecting(A63_63, B64_64)) & ~apart_point_and_line(B64_64, line_connecting(A63_63, B64_64))))) & ! [L65_65, M66_66] : (((unequally_directed_lines(L65_65, M66_66) & unequally_directed_lines(L65_65, reverse_line(M66_66))) => (~apart_point_and_line(intersection_point(L65_65, M66_66), L65_65) & ~apart_point_and_line(intersection_point(L65_65, M66_66), M66_66)))) & ! [A67_67, L68_68] : (~apart_point_and_line(A67_67, parallel_through_point(L68_68, A67_67))) & ! [L69_69] : (~distinct_lines(L69_69, reverse_line(L69_69))) & ! [A70_70, B71_71] : ((distinct_points(A70_70, B71_71) => equally_directed_lines(line_connecting(A70_70, B71_71), reverse_line(line_connecting(B71_71, A70_70))))) & ! [A72_72, L73_73] : (equally_directed_lines(parallel_through_point(L73_73, A72_72), L73_73)) & ! [A74_74, B75_75, L76_76, M77_77] : (((distinct_points(A74_74, B75_75) & distinct_lines(L76_76, M77_77)) => (((((((left_apart_point(A74_74, L76_76) | left_apart_point(B75_75, L76_76)) | left_apart_point(A74_74, M77_77)) | left_apart_point(B75_75, M77_77)) | left_apart_point(A74_74, reverse_line(L76_76))) | left_apart_point(B75_75, reverse_line(L76_76))) | left_apart_point(A74_74, reverse_line(M77_77))) | left_apart_point(B75_75, reverse_line(M77_77))))) & ! [A78_78, B79_79, L80_80] : (((distinct_points(A78_78, B79_79) & left_apart_point(A78_78, L80_80)) => (left_apart_point(B79_79, L80_80) | left_convergent_lines(line_connecting(A78_78, B79_79), L80_80)))) & ! [A81_81, B82_82, L83_83] : ((left_apart_point(A81_81, L83_83) => (distinct_points(A81_81, B82_82) | left_apart_point(B82_82, L83_83)))) & ! [A84_84, L85_85, M86_86] : (((left_apart_point(A84_84, L85_85) & unequally_directed_lines(L85_85, M86_86)) => (distinct_lines(L85_85, M86_86) | left_apart_point(A84_84, reverse_line(M86_86))))) & ! [L87_87, M88_88, N89_89] : ((left_convergent_lines(L87_87, M88_88) => (unequally_directed_lines(M88_88, N89_89) | left_convergent_lines(L87_87, N89_89)))))
% 77.96/22.90 -> [2] ! [X9_9, Y10_10] : ((unequally_directed_opposite_lines(X9_9, Y10_10) <=> unequally_directed_lines(X9_9, reverse_line(Y10_10)))), ! [X11_11, Y12_12] : ((right_apart_point(X11_11, Y12_12) <=> left_apart_point(X11_11, reverse_line(Y12_12)))), ! [X13_13, Y14_14] : ((right_convergent_lines(X13_13, Y14_14) <=> left_convergent_lines(X13_13, reverse_line(Y14_14)))), ! [X15_15, Y16_16] : ((equally_directed_lines(X15_15, Y16_16) <=> ~unequally_directed_lines(X15_15, Y16_16))), ! [X17_17, Y18_18] : ((equally_directed_opposite_lines(X17_17, Y18_18) <=> ~unequally_directed_opposite_lines(X17_17, Y18_18))), ! [A33_33] : (~distinct_points(A33_33, A33_33)), ! [A34_34, B35_35, C36_36] : ((distinct_points(A34_34, B35_35) => (distinct_points(A34_34, C36_36) | distinct_points(B35_35, C36_36)))), ! [L37_37] : (~distinct_lines(L37_37, L37_37)), ! [L38_38, M39_39, N40_40] : ((distinct_lines(L38_38, M39_39) => (distinct_lines(L38_38, N40_40) | distinct_lines(M39_39, N40_40)))), ! [L41_41] : (equally_directed_lines(L41_41, L41_41)), ! [L42_42, M43_43, N44_44] : ((unequally_directed_lines(L42_42, M43_43) => (unequally_directed_lines(L42_42, N44_44) | unequally_directed_lines(M43_43, N44_44)))), ! [L45_45, M46_46, N47_47] : (((unequally_directed_lines(L45_45, M46_46) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => ((unequally_directed_lines(L45_45, N47_47) & unequally_directed_lines(L45_45, reverse_line(N47_47))) | (unequally_directed_lines(M46_46, N47_47) & unequally_directed_lines(M46_46, reverse_line(N47_47)))))), ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49)))), ! [L50_50, M51_51] : (((unequally_directed_lines(L50_50, M51_51) & unequally_directed_lines(L50_50, reverse_line(M51_51))) => (left_convergent_lines(L50_50, M51_51) | left_convergent_lines(L50_50, reverse_line(M51_51))))), ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53)))), ! [L54_54, M55_55] : (~(left_convergent_lines(L54_54, M55_55) | left_convergent_lines(L54_54, reverse_line(M55_55)))), ! [A56_56, B57_57] : ((((point(A56_56) & point(B57_57)) & distinct_points(A56_56, B57_57)) => line(line_connecting(A56_56, B57_57)))), ! [L58_58, M59_59] : (((((line(L58_58) & line(M59_59)) & unequally_directed_lines(L58_58, M59_59)) & unequally_directed_lines(L58_58, reverse_line(M59_59))) => point(intersection_point(L58_58, M59_59)))), ! [L60_60, A61_61] : (((point(A61_61) & line(L60_60)) => line(parallel_through_point(L60_60, A61_61)))), ! [L62_62] : ((line(L62_62) => line(reverse_line(L62_62)))), ! [A63_63, B64_64] : ((distinct_points(A63_63, B64_64) => (~apart_point_and_line(A63_63, line_connecting(A63_63, B64_64)) & ~apart_point_and_line(B64_64, line_connecting(A63_63, B64_64))))), ! [L65_65, M66_66] : (((unequally_directed_lines(L65_65, M66_66) & unequally_directed_lines(L65_65, reverse_line(M66_66))) => (~apart_point_and_line(intersection_point(L65_65, M66_66), L65_65) & ~apart_point_and_line(intersection_point(L65_65, M66_66), M66_66)))), ! [A67_67, L68_68] : (~apart_point_and_line(A67_67, parallel_through_point(L68_68, A67_67))), ! [L69_69] : (~distinct_lines(L69_69, reverse_line(L69_69))), ! [A70_70, B71_71] : ((distinct_points(A70_70, B71_71) => equally_directed_lines(line_connecting(A70_70, B71_71), reverse_line(line_connecting(B71_71, A70_70))))), ! [A72_72, L73_73] : (equally_directed_lines(parallel_through_point(L73_73, A72_72), L73_73)), ! [A74_74, B75_75, L76_76, M77_77] : (((distinct_points(A74_74, B75_75) & distinct_lines(L76_76, M77_77)) => (((((((left_apart_point(A74_74, L76_76) | left_apart_point(B75_75, L76_76)) | left_apart_point(A74_74, M77_77)) | left_apart_point(B75_75, M77_77)) | left_apart_point(A74_74, reverse_line(L76_76))) | left_apart_point(B75_75, reverse_line(L76_76))) | left_apart_point(A74_74, reverse_line(M77_77))) | left_apart_point(B75_75, reverse_line(M77_77))))), ! [A78_78, B79_79, L80_80] : (((distinct_points(A78_78, B79_79) & left_apart_point(A78_78, L80_80)) => (left_apart_point(B79_79, L80_80) | left_convergent_lines(line_connecting(A78_78, B79_79), L80_80)))), ! [A81_81, B82_82, L83_83] : ((left_apart_point(A81_81, L83_83) => (distinct_points(A81_81, B82_82) | left_apart_point(B82_82, L83_83)))), ! [A84_84, L85_85, M86_86] : (((left_apart_point(A84_84, L85_85) & unequally_directed_lines(L85_85, M86_86)) => (distinct_lines(L85_85, M86_86) | left_apart_point(A84_84, reverse_line(M86_86))))), ! [L87_87, M88_88, N89_89] : ((left_convergent_lines(L87_87, M88_88) => (unequally_directed_lines(M88_88, N89_89) | left_convergent_lines(L87_87, N89_89))))
% 77.96/22.90
% 77.96/22.90 [2] DELTA_NOT_FORALL : ~! [A90_90, B91_91, C92_92, D93_93] : ((left_apart_point(C92_92, line_connecting(A90_90, B91_91)) => ((right_apart_point(D93_93, line_connecting(B91_91, C92_92)) & right_apart_point(D93_93, line_connecting(C92_92, A90_90))) => left_apart_point(D93_93, line_connecting(A90_90, B91_91)))))
% 77.96/22.90 -> [3] ~(left_apart_point(skolem_C9292, line_connecting(skolem_A9090, skolem_B9191)) => ((right_apart_point(skolem_D9393, line_connecting(skolem_B9191, skolem_C9292)) & right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090))) => left_apart_point(skolem_D9393, line_connecting(skolem_A9090, skolem_B9191))))
% 77.96/22.90
% 77.96/22.90 [3] ALPHA_NOT_IMPLY : ~(left_apart_point(skolem_C9292, line_connecting(skolem_A9090, skolem_B9191)) => ((right_apart_point(skolem_D9393, line_connecting(skolem_B9191, skolem_C9292)) & right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090))) => left_apart_point(skolem_D9393, line_connecting(skolem_A9090, skolem_B9191))))
% 77.96/22.90 -> [4] left_apart_point(skolem_C9292, line_connecting(skolem_A9090, skolem_B9191)), ~((right_apart_point(skolem_D9393, line_connecting(skolem_B9191, skolem_C9292)) & right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090))) => left_apart_point(skolem_D9393, line_connecting(skolem_A9090, skolem_B9191)))
% 77.96/22.90
% 77.96/22.90 [4] ALPHA_NOT_IMPLY : ~((right_apart_point(skolem_D9393, line_connecting(skolem_B9191, skolem_C9292)) & right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090))) => left_apart_point(skolem_D9393, line_connecting(skolem_A9090, skolem_B9191)))
% 77.96/22.90 -> [5] (right_apart_point(skolem_D9393, line_connecting(skolem_B9191, skolem_C9292)) & right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090))), ~left_apart_point(skolem_D9393, line_connecting(skolem_A9090, skolem_B9191))
% 77.96/22.90
% 77.96/22.90 [5] ALPHA_AND : (right_apart_point(skolem_D9393, line_connecting(skolem_B9191, skolem_C9292)) & right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090)))
% 77.96/22.90 -> [6] right_apart_point(skolem_D9393, line_connecting(skolem_B9191, skolem_C9292)), right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090))
% 77.96/22.90
% 77.96/22.90 [6] GAMMA_FORALL : ! [X9_9, Y10_10] : ((unequally_directed_opposite_lines(X9_9, Y10_10) <=> unequally_directed_lines(X9_9, reverse_line(Y10_10))))
% 77.96/22.90 -> [7] (unequally_directed_opposite_lines(reverse_line(Y10_0_0), Y10_0_0) <=> unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0)))
% 77.96/22.90
% 77.96/22.90 [7] BETA_EQUIV : (unequally_directed_opposite_lines(reverse_line(Y10_0_0), Y10_0_0) <=> unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0)))
% 77.96/22.90 -> [8] ~unequally_directed_opposite_lines(reverse_line(Y10_0_0), Y10_0_0), ~unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0))
% 77.96/22.90 -> [9] unequally_directed_opposite_lines(reverse_line(Y10_0_0), Y10_0_0), unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0))
% 77.96/22.90
% 77.96/22.90 [9] GAMMA_FORALL : ! [X11_11, Y12_12] : ((right_apart_point(X11_11, Y12_12) <=> left_apart_point(X11_11, reverse_line(Y12_12))))
% 77.96/22.90 -> [11] (right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090)) <=> left_apart_point(skolem_D9393, reverse_line(line_connecting(skolem_C9292, skolem_A9090))))
% 77.96/22.90
% 77.96/22.90 [11] BETA_EQUIV : (right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090)) <=> left_apart_point(skolem_D9393, reverse_line(line_connecting(skolem_C9292, skolem_A9090))))
% 77.96/22.90 -> [14] ~right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090)), ~left_apart_point(skolem_D9393, reverse_line(line_connecting(skolem_C9292, skolem_A9090)))
% 77.96/22.90 -> [15] right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090)), left_apart_point(skolem_D9393, reverse_line(line_connecting(skolem_C9292, skolem_A9090)))
% 77.96/22.90
% 77.96/22.90 [14] CLOSURE : ~right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090))
% 77.96/22.90
% 77.96/22.90 [17] BETA_EQUIV : (right_convergent_lines(X13_1_2, Y14_1_2) <=> left_convergent_lines(X13_1_2, reverse_line(Y14_1_2)))
% 77.96/22.90 -> [223] ~right_convergent_lines(X13_1_2, Y14_1_2), ~left_convergent_lines(X13_1_2, reverse_line(Y14_1_2))
% 77.96/22.90 -> [224] right_convergent_lines(X13_1_2, Y14_1_2), left_convergent_lines(X13_1_2, reverse_line(Y14_1_2))
% 77.96/22.90
% 77.96/22.90 [223] GAMMA_FORALL : ! [X15_15, Y16_16] : ((equally_directed_lines(X15_15, Y16_16) <=> ~unequally_directed_lines(X15_15, Y16_16)))
% 77.96/22.90 -> [226] (equally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0)) <=> ~unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0)))
% 77.96/22.90
% 77.96/22.90 [226] BETA_EQUIV : (equally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0)) <=> ~unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0)))
% 77.96/22.90 -> [229] ~equally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0)), ~~unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0))
% 77.96/22.90 -> [230] equally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0)), ~unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0))
% 77.96/22.90
% 77.96/22.90 [229] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0))
% 77.96/22.90 -> [234] unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0))
% 77.96/22.90
% 77.96/22.90 [234] GAMMA_FORALL : ! [X17_17, Y18_18] : ((equally_directed_opposite_lines(X17_17, Y18_18) <=> ~unequally_directed_opposite_lines(X17_17, Y18_18)))
% 77.96/22.90 -> [238] (equally_directed_opposite_lines(X17_5_4, Y18_5_4) <=> ~unequally_directed_opposite_lines(X17_5_4, Y18_5_4))
% 77.96/22.90
% 77.96/22.90 [238] BETA_EQUIV : (equally_directed_opposite_lines(X17_5_4, Y18_5_4) <=> ~unequally_directed_opposite_lines(X17_5_4, Y18_5_4))
% 77.96/22.90 -> [239] ~equally_directed_opposite_lines(X17_5_4, Y18_5_4), ~~unequally_directed_opposite_lines(X17_5_4, Y18_5_4)
% 77.96/22.90 -> [240] equally_directed_opposite_lines(X17_5_4, Y18_5_4), ~unequally_directed_opposite_lines(X17_5_4, Y18_5_4)
% 77.96/22.90
% 77.96/22.90 [239] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(X17_5_4, Y18_5_4)
% 77.96/22.90 -> [242] unequally_directed_opposite_lines(X17_5_4, Y18_5_4)
% 77.96/22.90
% 77.96/22.90 [242] GAMMA_FORALL : ! [A33_33] : (~distinct_points(A33_33, A33_33))
% 77.96/22.90 -> [244] ~distinct_points(C36_4_6, C36_4_6)
% 77.96/22.90
% 77.96/22.90 [244] GAMMA_FORALL : ! [A34_34, B35_35, C36_36] : ((distinct_points(A34_34, B35_35) => (distinct_points(A34_34, C36_36) | distinct_points(B35_35, C36_36))))
% 77.96/22.90 -> [249] (distinct_points(C36_4_6, C36_4_6) => (distinct_points(C36_4_6, C36_4_6) | distinct_points(C36_4_6, C36_4_6)))
% 77.96/22.90
% 77.96/22.90 [249] BETA_IMPLY : (distinct_points(C36_4_6, C36_4_6) => (distinct_points(C36_4_6, C36_4_6) | distinct_points(C36_4_6, C36_4_6)))
% 77.96/22.90 -> [251] ~distinct_points(C36_4_6, C36_4_6)
% 77.96/22.90 -> [252] (distinct_points(C36_4_6, C36_4_6) | distinct_points(C36_4_6, C36_4_6))
% 77.96/22.90
% 77.96/22.90 [252] BETA_OR : (distinct_points(C36_4_6, C36_4_6) | distinct_points(C36_4_6, C36_4_6))
% 77.96/22.90 -> [267] distinct_points(C36_4_6, C36_4_6)
% 77.96/22.90 -> [268] distinct_points(C36_4_6, C36_4_6)
% 77.96/22.90
% 77.96/22.90 [268] CLOSURE : distinct_points(C36_4_6, C36_4_6)
% 77.96/22.90
% 77.96/22.90 [267] CLOSURE : distinct_points(C36_4_6, C36_4_6)
% 77.96/22.90
% 77.96/22.90 [273] BETA_IMPLY : (distinct_lines(N40_5_8, N40_5_8) => (distinct_lines(N40_5_8, N40_5_8) | distinct_lines(N40_5_8, N40_5_8)))
% 77.96/22.90 -> [313] ~distinct_lines(N40_5_8, N40_5_8)
% 77.96/22.90 -> [314] (distinct_lines(N40_5_8, N40_5_8) | distinct_lines(N40_5_8, N40_5_8))
% 77.96/22.90
% 77.96/22.90 [314] BETA_OR : (distinct_lines(N40_5_8, N40_5_8) | distinct_lines(N40_5_8, N40_5_8))
% 77.96/22.90 -> [315] distinct_lines(N40_5_8, N40_5_8)
% 77.96/22.90 -> [316] distinct_lines(N40_5_8, N40_5_8)
% 77.96/22.90
% 77.96/22.90 [316] CLOSURE : distinct_lines(N40_5_8, N40_5_8)
% 77.96/22.90
% 77.96/22.90 [315] CLOSURE : distinct_lines(N40_5_8, N40_5_8)
% 77.96/22.90
% 77.96/22.90 [317] CLOSURE : equally_directed_lines(L41_10_9, L41_10_9)
% 77.96/22.90
% 77.96/22.90 [240] CLOSURE : ~unequally_directed_opposite_lines(X17_5_4, Y18_5_4)
% 77.96/22.90
% 77.96/22.90 [230] CLOSURE : ~unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0))
% 77.96/22.90
% 77.96/22.90 [224] GAMMA_FORALL : ! [X15_15, Y16_16] : ((equally_directed_lines(X15_15, Y16_16) <=> ~unequally_directed_lines(X15_15, Y16_16)))
% 77.96/22.90 -> [225] (equally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0)) <=> ~unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0)))
% 77.96/22.90
% 77.96/22.90 [225] BETA_EQUIV : (equally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0)) <=> ~unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0)))
% 77.96/22.90 -> [227] ~equally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0)), ~~unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0))
% 77.96/22.90 -> [228] equally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0)), ~unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0))
% 77.96/22.90
% 77.96/22.90 [227] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0))
% 77.96/22.90 -> [233] unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0))
% 77.96/22.90
% 77.96/22.90 [233] GAMMA_FORALL : ! [X17_17, Y18_18] : ((equally_directed_opposite_lines(X17_17, Y18_18) <=> ~unequally_directed_opposite_lines(X17_17, Y18_18)))
% 77.96/22.90 -> [235] (equally_directed_opposite_lines(X17_4_4, Y18_4_4) <=> ~unequally_directed_opposite_lines(X17_4_4, Y18_4_4))
% 77.96/22.90
% 77.96/22.90 [235] BETA_EQUIV : (equally_directed_opposite_lines(X17_4_4, Y18_4_4) <=> ~unequally_directed_opposite_lines(X17_4_4, Y18_4_4))
% 77.96/22.90 -> [236] ~equally_directed_opposite_lines(X17_4_4, Y18_4_4), ~~unequally_directed_opposite_lines(X17_4_4, Y18_4_4)
% 77.96/22.90 -> [237] equally_directed_opposite_lines(X17_4_4, Y18_4_4), ~unequally_directed_opposite_lines(X17_4_4, Y18_4_4)
% 77.96/22.90
% 77.96/22.90 [237] CLOSURE : ~unequally_directed_opposite_lines(X17_4_4, Y18_4_4)
% 77.96/22.90
% 77.96/22.90 [264] BETA_IMPLY : (distinct_points(C36_5_6, C36_5_6) => (distinct_points(C36_5_6, C36_5_6) | distinct_points(C36_5_6, C36_5_6)))
% 77.96/22.90 -> [349] ~distinct_points(C36_5_6, C36_5_6)
% 77.96/22.90 -> [350] (distinct_points(C36_5_6, C36_5_6) | distinct_points(C36_5_6, C36_5_6))
% 77.96/22.90
% 77.96/22.90 [350] BETA_OR : (distinct_points(C36_5_6, C36_5_6) | distinct_points(C36_5_6, C36_5_6))
% 77.96/22.90 -> [351] distinct_points(C36_5_6, C36_5_6)
% 77.96/22.90 -> [352] distinct_points(C36_5_6, C36_5_6)
% 77.96/22.90
% 77.96/22.90 [352] CLOSURE : distinct_points(C36_5_6, C36_5_6)
% 77.96/22.90
% 77.96/22.90 [351] CLOSURE : distinct_points(C36_5_6, C36_5_6)
% 77.96/22.90
% 77.96/22.90 [354] BETA_IMPLY : (distinct_lines(N40_7_8, N40_7_8) => (distinct_lines(N40_7_8, N40_7_8) | distinct_lines(N40_7_8, N40_7_8)))
% 77.96/22.90 -> [372] ~distinct_lines(N40_7_8, N40_7_8)
% 77.96/22.90 -> [373] (distinct_lines(N40_7_8, N40_7_8) | distinct_lines(N40_7_8, N40_7_8))
% 77.96/22.90
% 77.96/22.90 [373] BETA_OR : (distinct_lines(N40_7_8, N40_7_8) | distinct_lines(N40_7_8, N40_7_8))
% 77.96/22.90 -> [374] distinct_lines(N40_7_8, N40_7_8)
% 77.96/22.90 -> [375] distinct_lines(N40_7_8, N40_7_8)
% 77.96/22.90
% 77.96/22.90 [374] CLOSURE : distinct_lines(N40_7_8, N40_7_8)
% 77.96/22.90
% 77.96/22.90 [375] CLOSURE : distinct_lines(N40_7_8, N40_7_8)
% 77.96/22.90
% 77.96/22.90 [376] CLOSURE : equally_directed_lines(L41_12_9, L41_12_9)
% 77.96/22.90
% 77.96/22.90 [228] CLOSURE : ~unequally_directed_lines(reverse_line(Y10_0_0), reverse_line(Y10_0_0))
% 77.96/22.90
% 77.96/22.90 [10] BETA_EQUIV : (right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090)) <=> left_apart_point(skolem_D9393, reverse_line(line_connecting(skolem_C9292, skolem_A9090))))
% 77.96/22.90 -> [3788] ~right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090)), ~left_apart_point(skolem_D9393, reverse_line(line_connecting(skolem_C9292, skolem_A9090)))
% 77.96/22.90 -> [3789] right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090)), left_apart_point(skolem_D9393, reverse_line(line_connecting(skolem_C9292, skolem_A9090)))
% 77.96/22.90
% 77.96/22.90 [3788] CLOSURE : ~right_apart_point(skolem_D9393, line_connecting(skolem_C9292, skolem_A9090))
% 77.96/22.90
% 77.96/22.90 [3789] GAMMA_FORALL : ! [X13_13, Y14_14] : ((right_convergent_lines(X13_13, Y14_14) <=> left_convergent_lines(X13_13, reverse_line(Y14_14))))
% 77.96/22.90 -> [3790] (right_convergent_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) <=> left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))))
% 77.96/22.90
% 77.96/22.90 [3790] BETA_EQUIV : (right_convergent_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) <=> left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))))
% 77.96/22.90 -> [3791] ~right_convergent_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)), ~left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))
% 77.96/22.90 -> [3792] right_convergent_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)), left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))
% 77.96/22.90
% 77.96/22.90 [3792] GAMMA_FORALL : ! [X15_15, Y16_16] : ((equally_directed_lines(X15_15, Y16_16) <=> ~unequally_directed_lines(X15_15, Y16_16)))
% 77.96/22.90 -> [3794] (equally_directed_lines(reverse_line(Y18_12_4), reverse_line(Y18_12_4)) <=> ~unequally_directed_lines(reverse_line(Y18_12_4), reverse_line(Y18_12_4)))
% 77.96/22.90
% 77.96/22.90 [3794] BETA_EQUIV : (equally_directed_lines(reverse_line(Y18_12_4), reverse_line(Y18_12_4)) <=> ~unequally_directed_lines(reverse_line(Y18_12_4), reverse_line(Y18_12_4)))
% 77.96/22.90 -> [3797] ~equally_directed_lines(reverse_line(Y18_12_4), reverse_line(Y18_12_4)), ~~unequally_directed_lines(reverse_line(Y18_12_4), reverse_line(Y18_12_4))
% 77.96/22.90 -> [3798] equally_directed_lines(reverse_line(Y18_12_4), reverse_line(Y18_12_4)), ~unequally_directed_lines(reverse_line(Y18_12_4), reverse_line(Y18_12_4))
% 77.96/22.90
% 77.96/22.90 [3797] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y18_12_4), reverse_line(Y18_12_4))
% 77.96/22.90 -> [3800] unequally_directed_lines(reverse_line(Y18_12_4), reverse_line(Y18_12_4))
% 77.96/22.90
% 77.96/22.90 [3800] CLOSURE : unequally_directed_lines(reverse_line(Y18_12_4), reverse_line(Y18_12_4))
% 77.96/22.90
% 77.96/22.90 [3802] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y18_12_4), Y18_12_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y18_12_4), Y18_12_4))
% 77.96/22.90 -> [4256] ~equally_directed_opposite_lines(reverse_line(Y18_12_4), Y18_12_4), ~~unequally_directed_opposite_lines(reverse_line(Y18_12_4), Y18_12_4)
% 77.96/22.90 -> [4257] equally_directed_opposite_lines(reverse_line(Y18_12_4), Y18_12_4), ~unequally_directed_opposite_lines(reverse_line(Y18_12_4), Y18_12_4)
% 77.96/22.90
% 77.96/22.90 [4256] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y18_12_4), Y18_12_4)
% 77.96/22.90 -> [4264] unequally_directed_opposite_lines(reverse_line(Y18_12_4), Y18_12_4)
% 77.96/22.90
% 77.96/22.90 [4264] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y18_12_4), Y18_12_4)
% 77.96/22.90
% 77.96/22.90 [4257] GAMMA_FORALL : ! [A33_33] : (~distinct_points(A33_33, A33_33))
% 77.96/22.90 -> [4267] ~distinct_points(C36_17_6, C36_17_6)
% 77.96/22.90
% 77.96/22.90 [4267] GAMMA_FORALL : ! [A34_34, B35_35, C36_36] : ((distinct_points(A34_34, B35_35) => (distinct_points(A34_34, C36_36) | distinct_points(B35_35, C36_36))))
% 77.96/22.90 -> [4268] (distinct_points(C36_17_6, C36_17_6) => (distinct_points(C36_17_6, C36_17_6) | distinct_points(C36_17_6, C36_17_6)))
% 77.96/22.90
% 77.96/22.90 [4268] BETA_IMPLY : (distinct_points(C36_17_6, C36_17_6) => (distinct_points(C36_17_6, C36_17_6) | distinct_points(C36_17_6, C36_17_6)))
% 77.96/22.90 -> [4269] ~distinct_points(C36_17_6, C36_17_6)
% 77.96/22.90 -> [4270] (distinct_points(C36_17_6, C36_17_6) | distinct_points(C36_17_6, C36_17_6))
% 77.96/22.90
% 77.96/22.90 [4270] BETA_OR : (distinct_points(C36_17_6, C36_17_6) | distinct_points(C36_17_6, C36_17_6))
% 77.96/22.90 -> [4271] distinct_points(C36_17_6, C36_17_6)
% 77.96/22.90 -> [4272] distinct_points(C36_17_6, C36_17_6)
% 77.96/22.90
% 77.96/22.90 [4271] CLOSURE : distinct_points(C36_17_6, C36_17_6)
% 77.96/22.90
% 77.96/22.90 [4272] CLOSURE : distinct_points(C36_17_6, C36_17_6)
% 77.96/22.90
% 77.96/22.90 [4269] GAMMA_FORALL : ! [L37_37] : (~distinct_lines(L37_37, L37_37))
% 77.96/22.90 -> [4273] ~distinct_lines(M39_26_8, M39_26_8)
% 77.96/22.90
% 77.96/22.90 [4273] GAMMA_FORALL : ! [L38_38, M39_39, N40_40] : ((distinct_lines(L38_38, M39_39) => (distinct_lines(L38_38, N40_40) | distinct_lines(M39_39, N40_40))))
% 77.96/22.90 -> [4277] (distinct_lines(M39_26_8, M39_26_8) => (distinct_lines(M39_26_8, M39_26_8) | distinct_lines(M39_26_8, M39_26_8)))
% 77.96/22.90
% 77.96/22.90 [4277] BETA_IMPLY : (distinct_lines(M39_26_8, M39_26_8) => (distinct_lines(M39_26_8, M39_26_8) | distinct_lines(M39_26_8, M39_26_8)))
% 77.96/22.90 -> [4278] ~distinct_lines(M39_26_8, M39_26_8)
% 77.96/22.90 -> [4279] (distinct_lines(M39_26_8, M39_26_8) | distinct_lines(M39_26_8, M39_26_8))
% 77.96/22.90
% 77.96/22.90 [4279] BETA_OR : (distinct_lines(M39_26_8, M39_26_8) | distinct_lines(M39_26_8, M39_26_8))
% 77.96/22.90 -> [4280] distinct_lines(M39_26_8, M39_26_8)
% 77.96/22.90 -> [4281] distinct_lines(M39_26_8, M39_26_8)
% 77.96/22.90
% 77.96/22.90 [4280] CLOSURE : distinct_lines(M39_26_8, M39_26_8)
% 77.96/22.90
% 77.96/22.90 [4281] CLOSURE : distinct_lines(M39_26_8, M39_26_8)
% 77.96/22.90
% 77.96/22.90 [4278] GAMMA_FORALL : ! [L41_41] : (equally_directed_lines(L41_41, L41_41))
% 77.96/22.90 -> [4282] equally_directed_lines(L41_45_9, L41_45_9)
% 77.96/22.90
% 77.96/22.90 [4282] GAMMA_FORALL : ! [L42_42, M43_43, N44_44] : ((unequally_directed_lines(L42_42, M43_43) => (unequally_directed_lines(L42_42, N44_44) | unequally_directed_lines(M43_43, N44_44))))
% 77.96/22.90 -> [4283] (unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) => (unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) | unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))))
% 77.96/22.90
% 77.96/22.90 [4283] BETA_IMPLY : (unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) => (unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) | unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))))
% 77.96/22.90 -> [4284] ~unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))
% 77.96/22.90 -> [4285] (unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) | unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)))
% 77.96/22.90
% 77.96/22.90 [4285] BETA_OR : (unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) | unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)))
% 77.96/22.90 -> [4286] unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))
% 77.96/22.90 -> [4287] unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))
% 77.96/22.90
% 77.96/22.90 [4287] CLOSURE : unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))
% 77.96/22.90
% 77.96/22.90 [4286] CLOSURE : unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))
% 77.96/22.90
% 77.96/22.90 [4288] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11))) & unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(reverse_line(N47_78_11))))) => ((unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) & unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))) | (unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(N47_78_11)) & unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(reverse_line(N47_78_11))))))
% 77.96/22.90 -> [4346] ~(unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11))) & unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(reverse_line(N47_78_11)))))
% 77.96/22.90 -> [4347] ((unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) & unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))) | (unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(N47_78_11)) & unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(reverse_line(N47_78_11)))))
% 77.96/22.90
% 77.96/22.90 [4346] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11))) & unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(reverse_line(N47_78_11)))))
% 77.96/22.90 -> [4348] ~unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))
% 77.96/22.90 -> [4349] ~unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(reverse_line(N47_78_11))))
% 77.96/22.90
% 77.96/22.90 [4348] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 77.96/22.90 -> [4357] (unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) | unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11))))
% 77.96/22.90
% 77.96/22.90 [4357] BETA_OR : (unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) | unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11))))
% 77.96/22.90 -> [4358] unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))
% 77.96/22.90 -> [4359] unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))
% 77.96/22.90
% 77.96/22.90 [4358] CLOSURE : unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))
% 77.96/22.90
% 77.96/22.90 [4359] CLOSURE : unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))
% 77.96/22.90
% 77.96/22.90 [4354] BETA_OR : (unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) | unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11))))
% 77.96/22.90 -> [4369] unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))
% 77.96/22.90 -> [4370] unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))
% 77.96/22.90
% 77.96/22.90 [4369] CLOSURE : unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))
% 77.96/22.90
% 77.96/22.90 [4370] GAMMA_FORALL : ! [L50_50, M51_51] : (((unequally_directed_lines(L50_50, M51_51) & unequally_directed_lines(L50_50, reverse_line(M51_51))) => (left_convergent_lines(L50_50, M51_51) | left_convergent_lines(L50_50, reverse_line(M51_51)))))
% 77.96/22.90 -> [4373] ((unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) & unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))) => (left_convergent_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) | left_convergent_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))))
% 77.96/22.90
% 77.96/22.90 [4373] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) & unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))) => (left_convergent_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) | left_convergent_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))))
% 77.96/22.90 -> [4374] ~(unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) & unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11))))
% 77.96/22.90 -> [4375] (left_convergent_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) | left_convergent_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11))))
% 77.96/22.90
% 77.96/22.90 [4375] BETA_OR : (left_convergent_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) | left_convergent_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11))))
% 77.96/22.90 -> [4377] left_convergent_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))
% 77.96/22.90 -> [4378] left_convergent_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))
% 77.96/22.90
% 77.96/22.90 [4377] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 77.96/22.90 -> [4384] ~(left_apart_point(A52_153_14, L53_153_14) | left_apart_point(A52_153_14, reverse_line(L53_153_14)))
% 77.96/22.90
% 77.96/22.90 [4384] ALPHA_NOT_OR : ~(left_apart_point(A52_153_14, L53_153_14) | left_apart_point(A52_153_14, reverse_line(L53_153_14)))
% 77.96/22.90 -> [4386] ~left_apart_point(A52_153_14, L53_153_14), ~left_apart_point(A52_153_14, reverse_line(L53_153_14))
% 77.96/22.90
% 77.96/22.90 [4386] CLOSURE : ~left_apart_point(A52_153_14, L53_153_14)
% 77.96/22.90
% 77.96/22.90 [4378] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 77.96/22.90 -> [4385] ~(left_apart_point(A52_154_14, L53_154_14) | left_apart_point(A52_154_14, reverse_line(L53_154_14)))
% 77.96/22.90
% 77.96/22.90 [4385] ALPHA_NOT_OR : ~(left_apart_point(A52_154_14, L53_154_14) | left_apart_point(A52_154_14, reverse_line(L53_154_14)))
% 77.96/22.90 -> [4387] ~left_apart_point(A52_154_14, L53_154_14), ~left_apart_point(A52_154_14, reverse_line(L53_154_14))
% 77.96/22.90
% 77.96/22.90 [4387] CLOSURE : ~left_apart_point(A52_154_14, L53_154_14)
% 77.96/22.90
% 77.96/22.90 [4374] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) & unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11))))
% 77.96/22.90 -> [4379] ~unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))
% 77.96/22.90 -> [4380] ~unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))
% 77.96/22.90
% 77.96/22.90 [4380] CLOSURE : ~unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))
% 77.96/22.90
% 77.96/22.90 [4379] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 77.96/22.90 -> [4388] ~(left_apart_point(A52_155_14, L53_155_14) | left_apart_point(A52_155_14, reverse_line(L53_155_14)))
% 77.96/22.90
% 77.96/22.90 [4388] ALPHA_NOT_OR : ~(left_apart_point(A52_155_14, L53_155_14) | left_apart_point(A52_155_14, reverse_line(L53_155_14)))
% 77.96/22.90 -> [4389] ~left_apart_point(A52_155_14, L53_155_14), ~left_apart_point(A52_155_14, reverse_line(L53_155_14))
% 77.96/22.90
% 77.96/22.90 [4389] CLOSURE : ~left_apart_point(A52_155_14, L53_155_14)
% 77.96/22.90
% 77.96/22.90 [4347] BETA_OR : ((unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) & unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))) | (unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(N47_78_11)) & unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(reverse_line(N47_78_11)))))
% 77.96/22.90 -> [4390] (unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) & unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11))))
% 77.96/22.90 -> [4391] (unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(N47_78_11)) & unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(reverse_line(N47_78_11))))
% 77.96/22.90
% 77.96/22.90 [4390] ALPHA_AND : (unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) & unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11))))
% 77.96/22.90 -> [4392] unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)), unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))
% 77.96/22.90
% 77.96/22.90 [4392] CLOSURE : unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))
% 77.96/22.90
% 77.96/22.90 [4391] ALPHA_AND : (unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(N47_78_11)) & unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(reverse_line(N47_78_11))))
% 77.96/22.90 -> [4393] unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(N47_78_11)), unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(reverse_line(N47_78_11)))
% 77.96/22.90
% 77.96/22.90 [4393] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 77.96/22.90 -> [4394] (unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) | unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11))))
% 77.96/22.90
% 77.96/22.90 [4394] BETA_OR : (unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11)) | unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11))))
% 77.96/22.90 -> [4395] unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))
% 77.96/22.90 -> [4396] unequally_directed_lines(reverse_line(N47_78_11), reverse_line(reverse_line(N47_78_11)))
% 77.96/22.90
% 77.96/22.90 [4395] CLOSURE : unequally_directed_lines(reverse_line(N47_78_11), reverse_line(N47_78_11))
% 77.96/22.90
% 77.96/22.90 [4396] GAMMA_FORALL : ! [L50_50, M51_51] : (((unequally_directed_lines(L50_50, M51_51) & unequally_directed_lines(L50_50, reverse_line(M51_51))) => (left_convergent_lines(L50_50, M51_51) | left_convergent_lines(L50_50, reverse_line(M51_51)))))
% 77.96/22.90 -> [4397] ((unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), M51_54_13) & unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(M51_54_13))) => (left_convergent_lines(reverse_line(reverse_line(N47_78_11)), M51_54_13) | left_convergent_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(M51_54_13))))
% 77.96/22.90
% 77.96/22.90 [4397] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), M51_54_13) & unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(M51_54_13))) => (left_convergent_lines(reverse_line(reverse_line(N47_78_11)), M51_54_13) | left_convergent_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(M51_54_13))))
% 77.96/22.90 -> [4398] ~(unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), M51_54_13) & unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(M51_54_13)))
% 77.96/22.90 -> [4399] (left_convergent_lines(reverse_line(reverse_line(N47_78_11)), M51_54_13) | left_convergent_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(M51_54_13)))
% 77.96/22.90
% 77.96/22.90 [4398] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), M51_54_13) & unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(M51_54_13)))
% 77.96/22.90 -> [4400] ~unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), M51_54_13)
% 77.96/22.90 -> [4401] ~unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(M51_54_13))
% 77.96/22.90
% 77.96/22.90 [4400] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), M51_54_13)
% 77.96/22.90
% 77.96/22.90 [4401] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(M51_54_13))
% 77.96/22.90
% 77.96/22.90 [4399] BETA_OR : (left_convergent_lines(reverse_line(reverse_line(N47_78_11)), M51_54_13) | left_convergent_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(M51_54_13)))
% 77.96/22.90 -> [4402] left_convergent_lines(reverse_line(reverse_line(N47_78_11)), M51_54_13)
% 77.96/22.90 -> [4403] left_convergent_lines(reverse_line(reverse_line(N47_78_11)), reverse_line(M51_54_13))
% 77.96/22.90
% 77.96/22.90 [4403] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 77.96/22.90 -> [4404] ~(left_apart_point(A52_156_14, L53_156_14) | left_apart_point(A52_156_14, reverse_line(L53_156_14)))
% 77.96/22.90
% 77.96/22.90 [4404] ALPHA_NOT_OR : ~(left_apart_point(A52_156_14, L53_156_14) | left_apart_point(A52_156_14, reverse_line(L53_156_14)))
% 77.96/22.90 -> [4405] ~left_apart_point(A52_156_14, L53_156_14), ~left_apart_point(A52_156_14, reverse_line(L53_156_14))
% 77.96/22.90
% 77.96/22.90 [4405] CLOSURE : ~left_apart_point(A52_156_14, L53_156_14)
% 77.96/22.90
% 77.96/22.90 [4402] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 77.96/22.90 -> [4406] ~(left_apart_point(A52_157_14, L53_157_14) | left_apart_point(A52_157_14, reverse_line(L53_157_14)))
% 77.96/22.90
% 77.96/22.90 [4406] ALPHA_NOT_OR : ~(left_apart_point(A52_157_14, L53_157_14) | left_apart_point(A52_157_14, reverse_line(L53_157_14)))
% 77.96/22.90 -> [4407] ~left_apart_point(A52_157_14, L53_157_14), ~left_apart_point(A52_157_14, reverse_line(L53_157_14))
% 77.96/22.90
% 77.96/22.90 [4407] CLOSURE : ~left_apart_point(A52_157_14, L53_157_14)
% 77.96/22.90
% 77.96/22.90 [3791] GAMMA_FORALL : ! [X15_15, Y16_16] : ((equally_directed_lines(X15_15, Y16_16) <=> ~unequally_directed_lines(X15_15, Y16_16)))
% 77.96/22.90 -> [3793] (equally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) <=> ~unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)))
% 77.96/22.90
% 77.96/22.90 [3793] BETA_EQUIV : (equally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) <=> ~unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)))
% 77.96/22.90 -> [3795] ~equally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)), ~~unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90 -> [3796] equally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)), ~unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90
% 77.96/22.90 [3795] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90 -> [3799] unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90
% 77.96/22.90 [3799] CLOSURE : unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90
% 77.96/22.90 [3801] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y18_11_4), Y18_11_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y18_11_4), Y18_11_4))
% 77.96/22.90 -> [4492] ~equally_directed_opposite_lines(reverse_line(Y18_11_4), Y18_11_4), ~~unequally_directed_opposite_lines(reverse_line(Y18_11_4), Y18_11_4)
% 77.96/22.90 -> [4493] equally_directed_opposite_lines(reverse_line(Y18_11_4), Y18_11_4), ~unequally_directed_opposite_lines(reverse_line(Y18_11_4), Y18_11_4)
% 77.96/22.90
% 77.96/22.90 [4493] GAMMA_FORALL : ! [A33_33] : (~distinct_points(A33_33, A33_33))
% 77.96/22.90 -> [4495] ~distinct_points(C36_18_6, C36_18_6)
% 77.96/22.90
% 77.96/22.90 [4495] GAMMA_FORALL : ! [A34_34, B35_35, C36_36] : ((distinct_points(A34_34, B35_35) => (distinct_points(A34_34, C36_36) | distinct_points(B35_35, C36_36))))
% 77.96/22.90 -> [4496] (distinct_points(C36_18_6, C36_18_6) => (distinct_points(C36_18_6, C36_18_6) | distinct_points(C36_18_6, C36_18_6)))
% 77.96/22.90
% 77.96/22.90 [4496] BETA_IMPLY : (distinct_points(C36_18_6, C36_18_6) => (distinct_points(C36_18_6, C36_18_6) | distinct_points(C36_18_6, C36_18_6)))
% 77.96/22.90 -> [4497] ~distinct_points(C36_18_6, C36_18_6)
% 77.96/22.90 -> [4498] (distinct_points(C36_18_6, C36_18_6) | distinct_points(C36_18_6, C36_18_6))
% 77.96/22.90
% 77.96/22.90 [4498] BETA_OR : (distinct_points(C36_18_6, C36_18_6) | distinct_points(C36_18_6, C36_18_6))
% 77.96/22.90 -> [4499] distinct_points(C36_18_6, C36_18_6)
% 77.96/22.90 -> [4500] distinct_points(C36_18_6, C36_18_6)
% 77.96/22.90
% 77.96/22.90 [4500] CLOSURE : distinct_points(C36_18_6, C36_18_6)
% 77.96/22.90
% 77.96/22.90 [4499] CLOSURE : distinct_points(C36_18_6, C36_18_6)
% 77.96/22.90
% 77.96/22.90 [4502] BETA_IMPLY : (distinct_lines(N40_28_8, N40_28_8) => (distinct_lines(N40_28_8, N40_28_8) | distinct_lines(N40_28_8, N40_28_8)))
% 77.96/22.90 -> [4671] ~distinct_lines(N40_28_8, N40_28_8)
% 77.96/22.90 -> [4672] (distinct_lines(N40_28_8, N40_28_8) | distinct_lines(N40_28_8, N40_28_8))
% 77.96/22.90
% 77.96/22.90 [4671] GAMMA_FORALL : ! [L41_41] : (equally_directed_lines(L41_41, L41_41))
% 77.96/22.90 -> [4675] equally_directed_lines(L41_48_9, L41_48_9)
% 77.96/22.90
% 77.96/22.90 [4675] GAMMA_FORALL : ! [L42_42, M43_43, N44_44] : ((unequally_directed_lines(L42_42, M43_43) => (unequally_directed_lines(L42_42, N44_44) | unequally_directed_lines(M43_43, N44_44))))
% 77.96/22.90 -> [4676] (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) => (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) | unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))))
% 77.96/22.90
% 77.96/22.90 [4676] BETA_IMPLY : (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) => (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) | unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))))
% 77.96/22.90 -> [4677] ~unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90 -> [4678] (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) | unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)))
% 77.96/22.90
% 77.96/22.90 [4678] BETA_OR : (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) | unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)))
% 77.96/22.90 -> [4679] unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90 -> [4680] unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90
% 77.96/22.90 [4679] CLOSURE : unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90
% 77.96/22.90 [4680] CLOSURE : unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90
% 77.96/22.90 [4681] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))) => ((unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))) | (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))))))
% 77.96/22.90 -> [4700] ~(unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))))
% 77.96/22.90 -> [4701] ((unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))) | (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))))
% 77.96/22.90
% 77.96/22.90 [4701] BETA_OR : ((unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))) | (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))))
% 77.96/22.90 -> [4704] (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))))
% 77.96/22.90 -> [4705] (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))))
% 77.96/22.90
% 77.96/22.90 [4704] ALPHA_AND : (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))))
% 77.96/22.90 -> [4706] unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)), unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))
% 77.96/22.90
% 77.96/22.90 [4706] CLOSURE : unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))
% 77.96/22.90
% 77.96/22.90 [4707] CLOSURE : unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90
% 77.96/22.90 [4700] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))))
% 77.96/22.90 -> [4731] ~unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90 -> [4732] ~unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))
% 77.96/22.90
% 77.96/22.90 [4732] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 77.96/22.90 -> [4734] (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) | unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))))
% 77.96/22.90
% 77.96/22.90 [4734] BETA_OR : (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) | unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))))
% 77.96/22.90 -> [4737] unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90 -> [4738] unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))
% 77.96/22.90
% 77.96/22.90 [4737] CLOSURE : unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90
% 77.96/22.90 [4738] CLOSURE : unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))
% 77.96/22.90
% 77.96/22.90 [4731] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 77.96/22.90 -> [4733] (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) | unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))))
% 77.96/22.90
% 77.96/22.90 [4733] BETA_OR : (unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4)) | unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))))
% 77.96/22.90 -> [4735] unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90 -> [4736] unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))
% 77.96/22.90
% 77.96/22.90 [4735] CLOSURE : unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(Y18_11_4))
% 77.96/22.90
% 77.96/22.90 [4736] GAMMA_FORALL : ! [L50_50, M51_51] : (((unequally_directed_lines(L50_50, M51_51) & unequally_directed_lines(L50_50, reverse_line(M51_51))) => (left_convergent_lines(L50_50, M51_51) | left_convergent_lines(L50_50, reverse_line(M51_51)))))
% 77.96/22.90 -> [4739] ((unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(reverse_line(Y18_11_4))))) => (left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))) | left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(reverse_line(Y18_11_4))))))
% 77.96/22.90
% 77.96/22.90 [4739] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(reverse_line(Y18_11_4))))) => (left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))) | left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(reverse_line(Y18_11_4))))))
% 77.96/22.90 -> [4740] ~(unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(reverse_line(Y18_11_4)))))
% 77.96/22.90 -> [4741] (left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))) | left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(reverse_line(Y18_11_4)))))
% 77.96/22.90
% 77.96/22.90 [4740] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))) & unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(reverse_line(Y18_11_4)))))
% 77.96/22.90 -> [4742] ~unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))
% 77.96/22.90 -> [4743] ~unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(reverse_line(Y18_11_4))))
% 77.96/22.90
% 77.96/22.90 [4742] CLOSURE : ~unequally_directed_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))
% 77.96/22.90
% 77.96/22.90 [4743] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 77.96/22.90 -> [4747] ~(left_apart_point(A52_174_14, L53_174_14) | left_apart_point(A52_174_14, reverse_line(L53_174_14)))
% 77.96/22.90
% 77.96/22.90 [4747] ALPHA_NOT_OR : ~(left_apart_point(A52_174_14, L53_174_14) | left_apart_point(A52_174_14, reverse_line(L53_174_14)))
% 77.96/22.90 -> [4748] ~left_apart_point(A52_174_14, L53_174_14), ~left_apart_point(A52_174_14, reverse_line(L53_174_14))
% 77.96/22.90
% 77.96/22.90 [4748] CLOSURE : ~left_apart_point(A52_174_14, L53_174_14)
% 77.96/22.90
% 77.96/22.90 [4741] BETA_OR : (left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4))) | left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(reverse_line(Y18_11_4)))))
% 77.96/22.90 -> [4750] left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))
% 77.96/22.90 -> [4751] left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(reverse_line(Y18_11_4))))
% 77.96/22.90
% 77.96/22.90 [4750] CLOSURE : left_convergent_lines(reverse_line(Y18_11_4), reverse_line(reverse_line(Y18_11_4)))
% 77.96/22.90
% 77.96/22.90 [4751] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 77.96/22.90 -> [4752] ~(left_apart_point(A52_175_14, L53_175_14) | left_apart_point(A52_175_14, reverse_line(L53_175_14)))
% 77.96/22.90
% 77.96/22.90 [4752] ALPHA_NOT_OR : ~(left_apart_point(A52_175_14, L53_175_14) | left_apart_point(A52_175_14, reverse_line(L53_175_14)))
% 77.96/22.90 -> [4753] ~left_apart_point(A52_175_14, L53_175_14), ~left_apart_point(A52_175_14, reverse_line(L53_175_14))
% 77.96/22.90
% 77.96/22.90 [4753] CLOSURE : ~left_apart_point(A52_175_14, L53_175_14)
% 77.96/22.90
% 77.96/22.90 [4672] BETA_OR : (distinct_lines(N40_28_8, N40_28_8) | distinct_lines(N40_28_8, N40_28_8))
% 77.96/22.90 -> [4754] distinct_lines(N40_28_8, N40_28_8)
% 77.96/22.90 -> [4755] distinct_lines(N40_28_8, N40_28_8)
% 77.96/22.90
% 77.96/22.90 [4754] CLOSURE : distinct_lines(N40_28_8, N40_28_8)
% 77.96/22.90
% 77.96/22.90 [4755] CLOSURE : distinct_lines(N40_28_8, N40_28_8)
% 77.96/22.90
% 77.96/22.90 [4494] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y18_11_4), Y18_11_4)
% 77.96/22.90
% 77.96/22.90 % SZS output end Proof for theBenchmark.p
% 77.96/22.90 [22.553367s][1][Res] 204497 goroutines created
% 77.96/22.90 ==== Result ====
% 77.96/22.90 [22.553407s][1][Res] VALID
% 77.96/22.90 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------