TSTP Solution File: GEO247+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO247+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n012.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 15:18:42 EDT 2022
% Result : Theorem 194.94s 34.91s
% Output : Proof 194.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO247+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 07:09:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000039s][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
% 194.94/34.88 % SZS output start Proof for theBenchmark.p
% 194.94/34.91 [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, L94_94, M95_95] : (((((((((left_apart_point(A90_90, L94_94) & left_apart_point(A90_90, M95_95)) & right_apart_point(B91_91, L94_94)) & right_apart_point(B91_91, M95_95)) & left_apart_point(C92_92, L94_94)) & right_apart_point(C92_92, M95_95)) & right_apart_point(D93_93, L94_94)) & left_apart_point(D93_93, M95_95)) => convergent_lines(L94_94, M95_95))))
% 194.94/34.91 -> [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, L94_94, M95_95] : (((((((((left_apart_point(A90_90, L94_94) & left_apart_point(A90_90, M95_95)) & right_apart_point(B91_91, L94_94)) & right_apart_point(B91_91, M95_95)) & left_apart_point(C92_92, L94_94)) & right_apart_point(C92_92, M95_95)) & right_apart_point(D93_93, L94_94)) & left_apart_point(D93_93, M95_95)) => convergent_lines(L94_94, M95_95)))
% 194.94/34.91
% 194.94/34.91 [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)))))
% 194.94/34.91 -> [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))))
% 194.94/34.91
% 194.94/34.91 [2] DELTA_NOT_FORALL : ~! [A90_90, B91_91, C92_92, D93_93, L94_94, M95_95] : (((((((((left_apart_point(A90_90, L94_94) & left_apart_point(A90_90, M95_95)) & right_apart_point(B91_91, L94_94)) & right_apart_point(B91_91, M95_95)) & left_apart_point(C92_92, L94_94)) & right_apart_point(C92_92, M95_95)) & right_apart_point(D93_93, L94_94)) & left_apart_point(D93_93, M95_95)) => convergent_lines(L94_94, M95_95)))
% 194.94/34.91 -> [3] ~((((((((left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)) & right_apart_point(skolem_B9191, skolem_L9494)) & right_apart_point(skolem_B9191, skolem_M9595)) & left_apart_point(skolem_C9292, skolem_L9494)) & right_apart_point(skolem_C9292, skolem_M9595)) & right_apart_point(skolem_D9393, skolem_L9494)) & left_apart_point(skolem_D9393, skolem_M9595)) => convergent_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [3] ALPHA_NOT_IMPLY : ~((((((((left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)) & right_apart_point(skolem_B9191, skolem_L9494)) & right_apart_point(skolem_B9191, skolem_M9595)) & left_apart_point(skolem_C9292, skolem_L9494)) & right_apart_point(skolem_C9292, skolem_M9595)) & right_apart_point(skolem_D9393, skolem_L9494)) & left_apart_point(skolem_D9393, skolem_M9595)) => convergent_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91 -> [4] (((((((left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)) & right_apart_point(skolem_B9191, skolem_L9494)) & right_apart_point(skolem_B9191, skolem_M9595)) & left_apart_point(skolem_C9292, skolem_L9494)) & right_apart_point(skolem_C9292, skolem_M9595)) & right_apart_point(skolem_D9393, skolem_L9494)) & left_apart_point(skolem_D9393, skolem_M9595)), ~convergent_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [4] Rewrite : ~convergent_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [5] ~(unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_opposite_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [5] ALPHA_AND : (((((((left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)) & right_apart_point(skolem_B9191, skolem_L9494)) & right_apart_point(skolem_B9191, skolem_M9595)) & left_apart_point(skolem_C9292, skolem_L9494)) & right_apart_point(skolem_C9292, skolem_M9595)) & right_apart_point(skolem_D9393, skolem_L9494)) & left_apart_point(skolem_D9393, skolem_M9595))
% 194.94/34.91 -> [6] ((((((left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)) & right_apart_point(skolem_B9191, skolem_L9494)) & right_apart_point(skolem_B9191, skolem_M9595)) & left_apart_point(skolem_C9292, skolem_L9494)) & right_apart_point(skolem_C9292, skolem_M9595)) & right_apart_point(skolem_D9393, skolem_L9494)), left_apart_point(skolem_D9393, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [6] ALPHA_AND : ((((((left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)) & right_apart_point(skolem_B9191, skolem_L9494)) & right_apart_point(skolem_B9191, skolem_M9595)) & left_apart_point(skolem_C9292, skolem_L9494)) & right_apart_point(skolem_C9292, skolem_M9595)) & right_apart_point(skolem_D9393, skolem_L9494))
% 194.94/34.91 -> [7] (((((left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)) & right_apart_point(skolem_B9191, skolem_L9494)) & right_apart_point(skolem_B9191, skolem_M9595)) & left_apart_point(skolem_C9292, skolem_L9494)) & right_apart_point(skolem_C9292, skolem_M9595)), right_apart_point(skolem_D9393, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [7] ALPHA_AND : (((((left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)) & right_apart_point(skolem_B9191, skolem_L9494)) & right_apart_point(skolem_B9191, skolem_M9595)) & left_apart_point(skolem_C9292, skolem_L9494)) & right_apart_point(skolem_C9292, skolem_M9595))
% 194.94/34.91 -> [8] ((((left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)) & right_apart_point(skolem_B9191, skolem_L9494)) & right_apart_point(skolem_B9191, skolem_M9595)) & left_apart_point(skolem_C9292, skolem_L9494)), right_apart_point(skolem_C9292, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [8] ALPHA_AND : ((((left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)) & right_apart_point(skolem_B9191, skolem_L9494)) & right_apart_point(skolem_B9191, skolem_M9595)) & left_apart_point(skolem_C9292, skolem_L9494))
% 194.94/34.91 -> [9] (((left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)) & right_apart_point(skolem_B9191, skolem_L9494)) & right_apart_point(skolem_B9191, skolem_M9595)), left_apart_point(skolem_C9292, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [9] ALPHA_AND : (((left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)) & right_apart_point(skolem_B9191, skolem_L9494)) & right_apart_point(skolem_B9191, skolem_M9595))
% 194.94/34.91 -> [10] ((left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)) & right_apart_point(skolem_B9191, skolem_L9494)), right_apart_point(skolem_B9191, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [10] ALPHA_AND : ((left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)) & right_apart_point(skolem_B9191, skolem_L9494))
% 194.94/34.91 -> [11] (left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595)), right_apart_point(skolem_B9191, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [11] ALPHA_AND : (left_apart_point(skolem_A9090, skolem_L9494) & left_apart_point(skolem_A9090, skolem_M9595))
% 194.94/34.91 -> [12] left_apart_point(skolem_A9090, skolem_L9494), left_apart_point(skolem_A9090, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [12] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_opposite_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91 -> [13] ~unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [14] ~unequally_directed_opposite_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [13] GAMMA_FORALL : ! [X9_9, Y10_10] : ((unequally_directed_opposite_lines(X9_9, Y10_10) <=> unequally_directed_lines(X9_9, reverse_line(Y10_10))))
% 194.94/34.91 -> [16] (unequally_directed_opposite_lines(skolem_L9494, skolem_L9494) <=> unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [16] BETA_EQUIV : (unequally_directed_opposite_lines(skolem_L9494, skolem_L9494) <=> unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [19] ~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494), ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91 -> [20] unequally_directed_opposite_lines(skolem_L9494, skolem_L9494), unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [20] GAMMA_FORALL : ! [X11_11, Y12_12] : ((right_apart_point(X11_11, Y12_12) <=> left_apart_point(X11_11, reverse_line(Y12_12))))
% 194.94/34.91 -> [25] (right_apart_point(skolem_C9292, skolem_M9595) <=> left_apart_point(skolem_C9292, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [25] BETA_EQUIV : (right_apart_point(skolem_C9292, skolem_M9595) <=> left_apart_point(skolem_C9292, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [28] ~right_apart_point(skolem_C9292, skolem_M9595), ~left_apart_point(skolem_C9292, reverse_line(skolem_M9595))
% 194.94/34.91 -> [29] right_apart_point(skolem_C9292, skolem_M9595), left_apart_point(skolem_C9292, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [28] CLOSURE : ~right_apart_point(skolem_C9292, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [34] BETA_EQUIV : (right_convergent_lines(skolem_L9494, skolem_M9595) <=> left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [2419] ~right_convergent_lines(skolem_L9494, skolem_M9595), ~left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91 -> [2420] right_convergent_lines(skolem_L9494, skolem_M9595), left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [2420] GAMMA_FORALL : ! [X15_15, Y16_16] : ((equally_directed_lines(X15_15, Y16_16) <=> ~unequally_directed_lines(X15_15, Y16_16)))
% 194.94/34.91 -> [2422] (equally_directed_lines(skolem_L9494, skolem_M9595) <=> ~unequally_directed_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [2422] BETA_EQUIV : (equally_directed_lines(skolem_L9494, skolem_M9595) <=> ~unequally_directed_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91 -> [2425] ~equally_directed_lines(skolem_L9494, skolem_M9595), ~~unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [2426] equally_directed_lines(skolem_L9494, skolem_M9595), ~unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [2425] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [2428] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [2428] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [2426] GAMMA_FORALL : ! [X17_17, Y18_18] : ((equally_directed_opposite_lines(X17_17, Y18_18) <=> ~unequally_directed_opposite_lines(X17_17, Y18_18)))
% 194.94/34.91 -> [2434] (equally_directed_opposite_lines(skolem_L9494, skolem_L9494) <=> ~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [2434] BETA_EQUIV : (equally_directed_opposite_lines(skolem_L9494, skolem_L9494) <=> ~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494))
% 194.94/34.91 -> [2439] ~equally_directed_opposite_lines(skolem_L9494, skolem_L9494), ~~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [2440] equally_directed_opposite_lines(skolem_L9494, skolem_L9494), ~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [2440] CLOSURE : ~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [2474] BETA_IMPLY : (distinct_points(C36_11_6, C36_11_6) => (distinct_points(C36_11_6, C36_11_6) | distinct_points(C36_11_6, C36_11_6)))
% 194.94/34.91 -> [3214] ~distinct_points(C36_11_6, C36_11_6)
% 194.94/34.91 -> [3215] (distinct_points(C36_11_6, C36_11_6) | distinct_points(C36_11_6, C36_11_6))
% 194.94/34.91
% 194.94/34.91 [3215] BETA_OR : (distinct_points(C36_11_6, C36_11_6) | distinct_points(C36_11_6, C36_11_6))
% 194.94/34.91 -> [3216] distinct_points(C36_11_6, C36_11_6)
% 194.94/34.91 -> [3217] distinct_points(C36_11_6, C36_11_6)
% 194.94/34.91
% 194.94/34.91 [3216] CLOSURE : distinct_points(C36_11_6, C36_11_6)
% 194.94/34.91
% 194.94/34.91 [3217] CLOSURE : distinct_points(C36_11_6, C36_11_6)
% 194.94/34.91
% 194.94/34.91 [3222] BETA_IMPLY : (distinct_lines(N40_19_8, N40_19_8) => (distinct_lines(N40_19_8, N40_19_8) | distinct_lines(N40_19_8, N40_19_8)))
% 194.94/34.91 -> [3656] ~distinct_lines(N40_19_8, N40_19_8)
% 194.94/34.91 -> [3657] (distinct_lines(N40_19_8, N40_19_8) | distinct_lines(N40_19_8, N40_19_8))
% 194.94/34.91
% 194.94/34.91 [3656] GAMMA_FORALL : ! [L41_41] : (equally_directed_lines(L41_41, L41_41))
% 194.94/34.91 -> [3660] equally_directed_lines(L41_37_9, L41_37_9)
% 194.94/34.91
% 194.94/34.91 [3660] 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))))
% 194.94/34.91 -> [3663] (unequally_directed_lines(skolem_L9494, skolem_L9494) => (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [3663] BETA_IMPLY : (unequally_directed_lines(skolem_L9494, skolem_L9494) => (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, skolem_M9595)))
% 194.94/34.91 -> [3666] ~unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [3667] (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [3667] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91 -> [3668] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [3669] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [3668] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [3669] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [3666] GAMMA_FORALL : ! [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))))))
% 194.94/34.91 -> [3693] ((unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))) => ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) | (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))))
% 194.94/34.91
% 194.94/34.91 [3693] BETA_IMPLY : ((unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))) => ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) | (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))))
% 194.94/34.91 -> [3694] ~(unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [3695] ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) | (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))))
% 194.94/34.91
% 194.94/34.91 [3695] BETA_OR : ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) | (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))))
% 194.94/34.91 -> [3698] (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [3699] (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [3698] ALPHA_AND : (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [3701] unequally_directed_lines(skolem_L9494, skolem_M9595), unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [3701] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [3700] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [3694] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [3738] ~unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [3739] ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [3739] CLOSURE : ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [3738] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 194.94/34.91 -> [3740] (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [3740] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [3741] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [3742] unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [3741] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [3743] BETA_IMPLY : ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) => (left_convergent_lines(skolem_L9494, skolem_M9595) | left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595))))
% 194.94/34.91 -> [3777] ~(unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [3778] (left_convergent_lines(skolem_L9494, skolem_M9595) | left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [3778] BETA_OR : (left_convergent_lines(skolem_L9494, skolem_M9595) | left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [3782] left_convergent_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [3783] left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [3783] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 194.94/34.91 -> [3790] ~(left_apart_point(A52_160_14, L53_160_14) | left_apart_point(A52_160_14, reverse_line(L53_160_14)))
% 194.94/34.91
% 194.94/34.91 [3790] ALPHA_NOT_OR : ~(left_apart_point(A52_160_14, L53_160_14) | left_apart_point(A52_160_14, reverse_line(L53_160_14)))
% 194.94/34.91 -> [3791] ~left_apart_point(A52_160_14, L53_160_14), ~left_apart_point(A52_160_14, reverse_line(L53_160_14))
% 194.94/34.91
% 194.94/34.91 [3791] CLOSURE : ~left_apart_point(A52_160_14, L53_160_14)
% 194.94/34.91
% 194.94/34.91 [3782] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 194.94/34.91 -> [3792] ~(left_apart_point(A52_161_14, L53_161_14) | left_apart_point(A52_161_14, reverse_line(L53_161_14)))
% 194.94/34.91
% 194.94/34.91 [3792] ALPHA_NOT_OR : ~(left_apart_point(A52_161_14, L53_161_14) | left_apart_point(A52_161_14, reverse_line(L53_161_14)))
% 194.94/34.91 -> [3793] ~left_apart_point(A52_161_14, L53_161_14), ~left_apart_point(A52_161_14, reverse_line(L53_161_14))
% 194.94/34.91
% 194.94/34.91 [3793] CLOSURE : ~left_apart_point(A52_161_14, L53_161_14)
% 194.94/34.91
% 194.94/34.91 [3777] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [3780] ~unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [3781] ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [3781] CLOSURE : ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [3780] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 194.94/34.91 -> [3794] ~(left_apart_point(A52_162_14, L53_162_14) | left_apart_point(A52_162_14, reverse_line(L53_162_14)))
% 194.94/34.91
% 194.94/34.91 [3794] ALPHA_NOT_OR : ~(left_apart_point(A52_162_14, L53_162_14) | left_apart_point(A52_162_14, reverse_line(L53_162_14)))
% 194.94/34.91 -> [3795] ~left_apart_point(A52_162_14, L53_162_14), ~left_apart_point(A52_162_14, reverse_line(L53_162_14))
% 194.94/34.91
% 194.94/34.91 [3795] CLOSURE : ~left_apart_point(A52_162_14, L53_162_14)
% 194.94/34.91
% 194.94/34.91 [3657] BETA_OR : (distinct_lines(N40_19_8, N40_19_8) | distinct_lines(N40_19_8, N40_19_8))
% 194.94/34.91 -> [3806] distinct_lines(N40_19_8, N40_19_8)
% 194.94/34.91 -> [3807] distinct_lines(N40_19_8, N40_19_8)
% 194.94/34.91
% 194.94/34.91 [3807] CLOSURE : distinct_lines(N40_19_8, N40_19_8)
% 194.94/34.91
% 194.94/34.91 [3806] CLOSURE : distinct_lines(N40_19_8, N40_19_8)
% 194.94/34.91
% 194.94/34.91 [2421] BETA_EQUIV : (equally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) <=> ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [3839] ~equally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)), ~~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91 -> [3840] equally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)), ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [3840] CLOSURE : ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [3841] GAMMA_FORALL : ! [X17_17, Y18_18] : ((equally_directed_opposite_lines(X17_17, Y18_18) <=> ~unequally_directed_opposite_lines(X17_17, Y18_18)))
% 194.94/34.91 -> [3848] (equally_directed_opposite_lines(skolem_L9494, skolem_L9494) <=> ~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [3848] BETA_EQUIV : (equally_directed_opposite_lines(skolem_L9494, skolem_L9494) <=> ~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494))
% 194.94/34.91 -> [3853] ~equally_directed_opposite_lines(skolem_L9494, skolem_L9494), ~~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [3854] equally_directed_opposite_lines(skolem_L9494, skolem_L9494), ~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [3854] CLOSURE : ~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [3871] BETA_IMPLY : (distinct_points(B35_14_6, B35_14_6) => (distinct_points(B35_14_6, B35_14_6) | distinct_points(B35_14_6, B35_14_6)))
% 194.94/34.91 -> [5753] ~distinct_points(B35_14_6, B35_14_6)
% 194.94/34.91 -> [5754] (distinct_points(B35_14_6, B35_14_6) | distinct_points(B35_14_6, B35_14_6))
% 194.94/34.91
% 194.94/34.91 [5754] BETA_OR : (distinct_points(B35_14_6, B35_14_6) | distinct_points(B35_14_6, B35_14_6))
% 194.94/34.91 -> [5755] distinct_points(B35_14_6, B35_14_6)
% 194.94/34.91 -> [5756] distinct_points(B35_14_6, B35_14_6)
% 194.94/34.91
% 194.94/34.91 [5755] CLOSURE : distinct_points(B35_14_6, B35_14_6)
% 194.94/34.91
% 194.94/34.91 [5756] CLOSURE : distinct_points(B35_14_6, B35_14_6)
% 194.94/34.91
% 194.94/34.91 [5762] BETA_IMPLY : (distinct_lines(N40_32_8, N40_32_8) => (distinct_lines(N40_32_8, N40_32_8) | distinct_lines(N40_32_8, N40_32_8)))
% 194.94/34.91 -> [6709] ~distinct_lines(N40_32_8, N40_32_8)
% 194.94/34.91 -> [6710] (distinct_lines(N40_32_8, N40_32_8) | distinct_lines(N40_32_8, N40_32_8))
% 194.94/34.91
% 194.94/34.91 [6709] GAMMA_FORALL : ! [L41_41] : (equally_directed_lines(L41_41, L41_41))
% 194.94/34.91 -> [6730] equally_directed_lines(L41_66_9, L41_66_9)
% 194.94/34.91
% 194.94/34.91 [6730] 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))))
% 194.94/34.91 -> [6741] (unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) => (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(reverse_line(skolem_L9494), skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [6741] BETA_IMPLY : (unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) => (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(reverse_line(skolem_L9494), skolem_M9595)))
% 194.94/34.91 -> [6742] ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91 -> [6743] (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(reverse_line(skolem_L9494), skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [6742] CLOSURE : ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [6743] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(reverse_line(skolem_L9494), skolem_M9595))
% 194.94/34.91 -> [6768] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [6769] unequally_directed_lines(reverse_line(skolem_L9494), skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [6769] GAMMA_FORALL : ! [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))))))
% 194.94/34.91 -> [6777] ((unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))) => ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) | (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))))
% 194.94/34.91
% 194.94/34.91 [6777] BETA_IMPLY : ((unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))) => ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) | (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))))
% 194.94/34.91 -> [6780] ~(unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [6781] ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) | (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))))
% 194.94/34.91
% 194.94/34.91 [6781] BETA_OR : ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) | (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))))
% 194.94/34.91 -> [6782] (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [6783] (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [6783] ALPHA_AND : (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [6786] unequally_directed_lines(skolem_L9494, skolem_M9595), unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [6786] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [6789] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [6780] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [6892] ~unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [6893] ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [6893] CLOSURE : ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [6892] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 194.94/34.91 -> [6894] (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [6894] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [6895] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [6896] unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [6895] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [6897] BETA_IMPLY : ((unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)) & unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_M9595)))) => (left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595)) | left_convergent_lines(skolem_L9494, reverse_line(reverse_line(skolem_M9595)))))
% 194.94/34.91 -> [6969] ~(unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)) & unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_M9595))))
% 194.94/34.91 -> [6970] (left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595)) | left_convergent_lines(skolem_L9494, reverse_line(reverse_line(skolem_M9595))))
% 194.94/34.91
% 194.94/34.91 [6970] BETA_OR : (left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595)) | left_convergent_lines(skolem_L9494, reverse_line(reverse_line(skolem_M9595))))
% 194.94/34.91 -> [6973] left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91 -> [6974] left_convergent_lines(skolem_L9494, reverse_line(reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [6973] CLOSURE : left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [6974] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 194.94/34.91 -> [6985] ~(left_apart_point(A52_315_14, L53_315_14) | left_apart_point(A52_315_14, reverse_line(L53_315_14)))
% 194.94/34.91
% 194.94/34.91 [6985] ALPHA_NOT_OR : ~(left_apart_point(A52_315_14, L53_315_14) | left_apart_point(A52_315_14, reverse_line(L53_315_14)))
% 194.94/34.91 -> [6986] ~left_apart_point(A52_315_14, L53_315_14), ~left_apart_point(A52_315_14, reverse_line(L53_315_14))
% 194.94/34.91
% 194.94/34.91 [6986] CLOSURE : ~left_apart_point(A52_315_14, L53_315_14)
% 194.94/34.91
% 194.94/34.91 [6969] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)) & unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_M9595))))
% 194.94/34.91 -> [6991] ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91 -> [6992] ~unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [6991] CLOSURE : ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [6992] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 194.94/34.91 -> [7021] ~(left_apart_point(A52_317_14, L53_317_14) | left_apart_point(A52_317_14, reverse_line(L53_317_14)))
% 194.94/34.91
% 194.94/34.91 [7021] ALPHA_NOT_OR : ~(left_apart_point(A52_317_14, L53_317_14) | left_apart_point(A52_317_14, reverse_line(L53_317_14)))
% 194.94/34.91 -> [7022] ~left_apart_point(A52_317_14, L53_317_14), ~left_apart_point(A52_317_14, reverse_line(L53_317_14))
% 194.94/34.91
% 194.94/34.91 [7022] CLOSURE : ~left_apart_point(A52_317_14, L53_317_14)
% 194.94/34.91
% 194.94/34.91 [6768] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [6710] BETA_OR : (distinct_lines(N40_32_8, N40_32_8) | distinct_lines(N40_32_8, N40_32_8))
% 194.94/34.91 -> [7058] distinct_lines(N40_32_8, N40_32_8)
% 194.94/34.91 -> [7059] distinct_lines(N40_32_8, N40_32_8)
% 194.94/34.91
% 194.94/34.91 [7058] CLOSURE : distinct_lines(N40_32_8, N40_32_8)
% 194.94/34.91
% 194.94/34.91 [7059] CLOSURE : distinct_lines(N40_32_8, N40_32_8)
% 194.94/34.91
% 194.94/34.91 [19] GAMMA_FORALL : ! [X11_11, Y12_12] : ((right_apart_point(X11_11, Y12_12) <=> left_apart_point(X11_11, reverse_line(Y12_12))))
% 194.94/34.91 -> [24] (right_apart_point(skolem_C9292, skolem_M9595) <=> left_apart_point(skolem_C9292, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [24] BETA_EQUIV : (right_apart_point(skolem_C9292, skolem_M9595) <=> left_apart_point(skolem_C9292, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [26] ~right_apart_point(skolem_C9292, skolem_M9595), ~left_apart_point(skolem_C9292, reverse_line(skolem_M9595))
% 194.94/34.91 -> [27] right_apart_point(skolem_C9292, skolem_M9595), left_apart_point(skolem_C9292, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [26] CLOSURE : ~right_apart_point(skolem_C9292, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [33] BETA_EQUIV : (right_convergent_lines(X13_1_2, Y14_1_2) <=> left_convergent_lines(X13_1_2, reverse_line(Y14_1_2)))
% 194.94/34.91 -> [4257] ~right_convergent_lines(X13_1_2, Y14_1_2), ~left_convergent_lines(X13_1_2, reverse_line(Y14_1_2))
% 194.94/34.91 -> [4258] right_convergent_lines(X13_1_2, Y14_1_2), left_convergent_lines(X13_1_2, reverse_line(Y14_1_2))
% 194.94/34.91
% 194.94/34.91 [4257] GAMMA_FORALL : ! [X15_15, Y16_16] : ((equally_directed_lines(X15_15, Y16_16) <=> ~unequally_directed_lines(X15_15, Y16_16)))
% 194.94/34.91 -> [4259] (equally_directed_lines(skolem_L9494, skolem_M9595) <=> ~unequally_directed_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [4259] BETA_EQUIV : (equally_directed_lines(skolem_L9494, skolem_M9595) <=> ~unequally_directed_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91 -> [4260] ~equally_directed_lines(skolem_L9494, skolem_M9595), ~~unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [4261] equally_directed_lines(skolem_L9494, skolem_M9595), ~unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [4260] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [4267] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [4267] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [4270] BETA_EQUIV : (equally_directed_opposite_lines(skolem_L9494, skolem_L9494) <=> ~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494))
% 194.94/34.91 -> [4993] ~equally_directed_opposite_lines(skolem_L9494, skolem_L9494), ~~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [4994] equally_directed_opposite_lines(skolem_L9494, skolem_L9494), ~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [4993] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [4996] unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [4996] CLOSURE : unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [5001] BETA_IMPLY : (distinct_points(C36_20_6, C36_20_6) => (distinct_points(C36_20_6, C36_20_6) | distinct_points(C36_20_6, C36_20_6)))
% 194.94/34.91 -> [6517] ~distinct_points(C36_20_6, C36_20_6)
% 194.94/34.91 -> [6518] (distinct_points(C36_20_6, C36_20_6) | distinct_points(C36_20_6, C36_20_6))
% 194.94/34.91
% 194.94/34.91 [6518] BETA_OR : (distinct_points(C36_20_6, C36_20_6) | distinct_points(C36_20_6, C36_20_6))
% 194.94/34.91 -> [6521] distinct_points(C36_20_6, C36_20_6)
% 194.94/34.91 -> [6522] distinct_points(C36_20_6, C36_20_6)
% 194.94/34.91
% 194.94/34.91 [6521] CLOSURE : distinct_points(C36_20_6, C36_20_6)
% 194.94/34.91
% 194.94/34.91 [6522] CLOSURE : distinct_points(C36_20_6, C36_20_6)
% 194.94/34.91
% 194.94/34.91 [6534] BETA_IMPLY : (distinct_lines(N40_36_8, N40_36_8) => (distinct_lines(N40_36_8, N40_36_8) | distinct_lines(N40_36_8, N40_36_8)))
% 194.94/34.91 -> [7189] ~distinct_lines(N40_36_8, N40_36_8)
% 194.94/34.91 -> [7190] (distinct_lines(N40_36_8, N40_36_8) | distinct_lines(N40_36_8, N40_36_8))
% 194.94/34.91
% 194.94/34.91 [7190] BETA_OR : (distinct_lines(N40_36_8, N40_36_8) | distinct_lines(N40_36_8, N40_36_8))
% 194.94/34.91 -> [7193] distinct_lines(N40_36_8, N40_36_8)
% 194.94/34.91 -> [7194] distinct_lines(N40_36_8, N40_36_8)
% 194.94/34.91
% 194.94/34.91 [7193] CLOSURE : distinct_lines(N40_36_8, N40_36_8)
% 194.94/34.91
% 194.94/34.91 [7194] CLOSURE : distinct_lines(N40_36_8, N40_36_8)
% 194.94/34.91
% 194.94/34.91 [7198] BETA_IMPLY : (unequally_directed_lines(skolem_L9494, skolem_L9494) => (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, skolem_M9595)))
% 194.94/34.91 -> [7460] ~unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [7461] (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [7461] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91 -> [7463] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [7464] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [7463] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [7464] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [7465] BETA_IMPLY : ((unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))) => ((unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))) | (unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))))
% 194.94/34.91 -> [7534] ~(unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [7535] ((unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))) | (unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))))
% 194.94/34.91
% 194.94/34.91 [7534] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [7537] ~unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [7538] ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [7538] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 194.94/34.91 -> [7548] (unequally_directed_lines(skolem_L9494, skolem_L9494) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [7548] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_L9494) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [7549] unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [7550] unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [7549] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [7550] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [7537] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 194.94/34.91 -> [7551] (unequally_directed_lines(skolem_L9494, skolem_L9494) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [7551] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_L9494) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [7552] unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [7553] unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [7552] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [7553] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [7535] BETA_OR : ((unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))) | (unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))))
% 194.94/34.91 -> [7585] (unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [7586] (unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [7585] ALPHA_AND : (unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [7587] unequally_directed_lines(skolem_L9494, skolem_L9494), unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [7587] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [7588] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [4262] BETA_EQUIV : (equally_directed_lines(skolem_L9494, skolem_M9595) <=> ~unequally_directed_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91 -> [7605] ~equally_directed_lines(skolem_L9494, skolem_M9595), ~~unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [7606] equally_directed_lines(skolem_L9494, skolem_M9595), ~unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [7605] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [7612] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [7612] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [7606] GAMMA_FORALL : ! [X17_17, Y18_18] : ((equally_directed_opposite_lines(X17_17, Y18_18) <=> ~unequally_directed_opposite_lines(X17_17, Y18_18)))
% 194.94/34.91 -> [7613] (equally_directed_opposite_lines(skolem_L9494, skolem_L9494) <=> ~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [7613] BETA_EQUIV : (equally_directed_opposite_lines(skolem_L9494, skolem_L9494) <=> ~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494))
% 194.94/34.91 -> [7614] ~equally_directed_opposite_lines(skolem_L9494, skolem_L9494), ~~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [7615] equally_directed_opposite_lines(skolem_L9494, skolem_L9494), ~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [7614] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [7623] unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [7623] CLOSURE : unequally_directed_opposite_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [7624] BETA_IMPLY : (distinct_points(C36_24_6, C36_24_6) => (distinct_points(C36_24_6, C36_24_6) | distinct_points(C36_24_6, C36_24_6)))
% 194.94/34.91 -> [7996] ~distinct_points(C36_24_6, C36_24_6)
% 194.94/34.91 -> [7997] (distinct_points(C36_24_6, C36_24_6) | distinct_points(C36_24_6, C36_24_6))
% 194.94/34.91
% 194.94/34.91 [7997] BETA_OR : (distinct_points(C36_24_6, C36_24_6) | distinct_points(C36_24_6, C36_24_6))
% 194.94/34.91 -> [7998] distinct_points(C36_24_6, C36_24_6)
% 194.94/34.91 -> [7999] distinct_points(C36_24_6, C36_24_6)
% 194.94/34.91
% 194.94/34.91 [7999] CLOSURE : distinct_points(C36_24_6, C36_24_6)
% 194.94/34.91
% 194.94/34.91 [7998] CLOSURE : distinct_points(C36_24_6, C36_24_6)
% 194.94/34.91
% 194.94/34.91 [8001] BETA_IMPLY : (distinct_lines(N40_40_8, N40_40_8) => (distinct_lines(N40_40_8, N40_40_8) | distinct_lines(N40_40_8, N40_40_8)))
% 194.94/34.91 -> [8149] ~distinct_lines(N40_40_8, N40_40_8)
% 194.94/34.91 -> [8150] (distinct_lines(N40_40_8, N40_40_8) | distinct_lines(N40_40_8, N40_40_8))
% 194.94/34.91
% 194.94/34.91 [8150] BETA_OR : (distinct_lines(N40_40_8, N40_40_8) | distinct_lines(N40_40_8, N40_40_8))
% 194.94/34.91 -> [8153] distinct_lines(N40_40_8, N40_40_8)
% 194.94/34.91 -> [8154] distinct_lines(N40_40_8, N40_40_8)
% 194.94/34.91
% 194.94/34.91 [8154] CLOSURE : distinct_lines(N40_40_8, N40_40_8)
% 194.94/34.91
% 194.94/34.91 [8153] CLOSURE : distinct_lines(N40_40_8, N40_40_8)
% 194.94/34.91
% 194.94/34.91 [8168] BETA_IMPLY : (unequally_directed_lines(skolem_L9494, skolem_L9494) => (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, skolem_M9595)))
% 194.94/34.91 -> [8260] ~unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [8261] (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [8261] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91 -> [8264] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [8265] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [8265] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [8264] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [8266] BETA_IMPLY : ((unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) & unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))) => ((unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))) | (unequally_directed_lines(reverse_line(skolem_L9494), skolem_L9494) & unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(skolem_L9494)))))
% 194.94/34.91 -> [8303] ~(unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) & unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494))))
% 194.94/34.91 -> [8304] ((unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))) | (unequally_directed_lines(reverse_line(skolem_L9494), skolem_L9494) & unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(skolem_L9494))))
% 194.94/34.91
% 194.94/34.91 [8303] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) & unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494))))
% 194.94/34.91 -> [8305] ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91 -> [8306] ~unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [8306] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 194.94/34.91 -> [8312] (unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) | unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494))))
% 194.94/34.91
% 194.94/34.91 [8312] BETA_OR : (unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) | unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494))))
% 194.94/34.91 -> [8315] unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91 -> [8316] unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [8315] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [8316] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [8311] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_L9494) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [8325] unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [8326] unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [8326] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [8325] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [8304] BETA_OR : ((unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))) | (unequally_directed_lines(reverse_line(skolem_L9494), skolem_L9494) & unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(skolem_L9494))))
% 194.94/34.91 -> [8341] (unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [8342] (unequally_directed_lines(reverse_line(skolem_L9494), skolem_L9494) & unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [8341] ALPHA_AND : (unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [8343] unequally_directed_lines(skolem_L9494, skolem_L9494), unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [8343] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [8342] ALPHA_AND : (unequally_directed_lines(reverse_line(skolem_L9494), skolem_L9494) & unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(skolem_L9494)))
% 194.94/34.91 -> [8344] unequally_directed_lines(reverse_line(skolem_L9494), skolem_L9494), unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [8344] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 194.94/34.91 -> [8345] (unequally_directed_lines(skolem_L9494, skolem_L9494) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [8345] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_L9494) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [8346] unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [8347] unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [8347] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [8346] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [14] GAMMA_FORALL : ! [X9_9, Y10_10] : ((unequally_directed_opposite_lines(X9_9, Y10_10) <=> unequally_directed_lines(X9_9, reverse_line(Y10_10))))
% 194.94/34.91 -> [15] (unequally_directed_opposite_lines(skolem_L9494, skolem_M9595) <=> unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [15] BETA_EQUIV : (unequally_directed_opposite_lines(skolem_L9494, skolem_M9595) <=> unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [17] ~unequally_directed_opposite_lines(skolem_L9494, skolem_M9595), ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91 -> [18] unequally_directed_opposite_lines(skolem_L9494, skolem_M9595), unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [18] CLOSURE : unequally_directed_opposite_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [21] BETA_EQUIV : (right_apart_point(skolem_D9393, skolem_L9494) <=> left_apart_point(skolem_D9393, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [8599] ~right_apart_point(skolem_D9393, skolem_L9494), ~left_apart_point(skolem_D9393, reverse_line(skolem_L9494))
% 194.94/34.91 -> [8600] right_apart_point(skolem_D9393, skolem_L9494), left_apart_point(skolem_D9393, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [8599] CLOSURE : ~right_apart_point(skolem_D9393, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [8600] GAMMA_FORALL : ! [X13_13, Y14_14] : ((right_convergent_lines(X13_13, Y14_14) <=> left_convergent_lines(X13_13, reverse_line(Y14_14))))
% 194.94/34.91 -> [8601] (right_convergent_lines(skolem_L9494, reverse_line(skolem_L9494)) <=> left_convergent_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494))))
% 194.94/34.91
% 194.94/34.91 [8601] BETA_EQUIV : (right_convergent_lines(skolem_L9494, reverse_line(skolem_L9494)) <=> left_convergent_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494))))
% 194.94/34.91 -> [8602] ~right_convergent_lines(skolem_L9494, reverse_line(skolem_L9494)), ~left_convergent_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))
% 194.94/34.91 -> [8603] right_convergent_lines(skolem_L9494, reverse_line(skolem_L9494)), left_convergent_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [8603] GAMMA_FORALL : ! [X15_15, Y16_16] : ((equally_directed_lines(X15_15, Y16_16) <=> ~unequally_directed_lines(X15_15, Y16_16)))
% 194.94/34.91 -> [8604] (equally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)) <=> ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [8604] BETA_EQUIV : (equally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)) <=> ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [8606] ~equally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)), ~~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91 -> [8607] equally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)), ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [8606] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91 -> [8612] unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [8612] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [8607] GAMMA_FORALL : ! [X17_17, Y18_18] : ((equally_directed_opposite_lines(X17_17, Y18_18) <=> ~unequally_directed_opposite_lines(X17_17, Y18_18)))
% 194.94/34.91 -> [8611] (equally_directed_opposite_lines(skolem_L9494, skolem_M9595) <=> ~unequally_directed_opposite_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [8611] BETA_EQUIV : (equally_directed_opposite_lines(skolem_L9494, skolem_M9595) <=> ~unequally_directed_opposite_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91 -> [8613] ~equally_directed_opposite_lines(skolem_L9494, skolem_M9595), ~~unequally_directed_opposite_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [8614] equally_directed_opposite_lines(skolem_L9494, skolem_M9595), ~unequally_directed_opposite_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [8613] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [8619] unequally_directed_opposite_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [8619] CLOSURE : unequally_directed_opposite_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [8625] BETA_IMPLY : (distinct_points(C36_28_6, C36_28_6) => (distinct_points(C36_28_6, C36_28_6) | distinct_points(C36_28_6, C36_28_6)))
% 194.94/34.91 -> [9063] ~distinct_points(C36_28_6, C36_28_6)
% 194.94/34.91 -> [9064] (distinct_points(C36_28_6, C36_28_6) | distinct_points(C36_28_6, C36_28_6))
% 194.94/34.91
% 194.94/34.91 [9064] BETA_OR : (distinct_points(C36_28_6, C36_28_6) | distinct_points(C36_28_6, C36_28_6))
% 194.94/34.91 -> [9065] distinct_points(C36_28_6, C36_28_6)
% 194.94/34.91 -> [9066] distinct_points(C36_28_6, C36_28_6)
% 194.94/34.91
% 194.94/34.91 [9065] CLOSURE : distinct_points(C36_28_6, C36_28_6)
% 194.94/34.91
% 194.94/34.91 [9066] CLOSURE : distinct_points(C36_28_6, C36_28_6)
% 194.94/34.91
% 194.94/34.91 [9068] BETA_IMPLY : (distinct_lines(N40_46_8, N40_46_8) => (distinct_lines(N40_46_8, N40_46_8) | distinct_lines(N40_46_8, N40_46_8)))
% 194.94/34.91 -> [9327] ~distinct_lines(N40_46_8, N40_46_8)
% 194.94/34.91 -> [9328] (distinct_lines(N40_46_8, N40_46_8) | distinct_lines(N40_46_8, N40_46_8))
% 194.94/34.91
% 194.94/34.91 [9328] BETA_OR : (distinct_lines(N40_46_8, N40_46_8) | distinct_lines(N40_46_8, N40_46_8))
% 194.94/34.91 -> [9329] distinct_lines(N40_46_8, N40_46_8)
% 194.94/34.91 -> [9330] distinct_lines(N40_46_8, N40_46_8)
% 194.94/34.91
% 194.94/34.91 [9329] CLOSURE : distinct_lines(N40_46_8, N40_46_8)
% 194.94/34.91
% 194.94/34.91 [9330] CLOSURE : distinct_lines(N40_46_8, N40_46_8)
% 194.94/34.91
% 194.94/34.91 [9332] BETA_IMPLY : (unequally_directed_lines(skolem_L9494, skolem_L9494) => (unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))))
% 194.94/34.91 -> [9417] ~unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [9418] (unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [9418] BETA_OR : (unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9419] unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91 -> [9420] unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9419] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9420] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9421] BETA_IMPLY : ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) => ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) | (unequally_directed_lines(skolem_M9595, skolem_M9595) & unequally_directed_lines(skolem_M9595, reverse_line(skolem_M9595)))))
% 194.94/34.91 -> [9492] ~(unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9493] ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) | (unequally_directed_lines(skolem_M9595, skolem_M9595) & unequally_directed_lines(skolem_M9595, reverse_line(skolem_M9595))))
% 194.94/34.91
% 194.94/34.91 [9492] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9494] ~unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [9495] ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9494] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 194.94/34.91 -> [9500] (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [9500] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9502] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [9503] unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9503] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9502] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [9495] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 194.94/34.91 -> [9501] (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [9501] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9504] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [9505] unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9505] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9504] 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)))))
% 194.94/34.91 -> [9508] ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) => (left_convergent_lines(skolem_L9494, skolem_M9595) | left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595))))
% 194.94/34.91
% 194.94/34.91 [9508] BETA_IMPLY : ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) => (left_convergent_lines(skolem_L9494, skolem_M9595) | left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595))))
% 194.94/34.91 -> [9509] ~(unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9510] (left_convergent_lines(skolem_L9494, skolem_M9595) | left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [9510] BETA_OR : (left_convergent_lines(skolem_L9494, skolem_M9595) | left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9513] left_convergent_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [9514] left_convergent_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9513] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 194.94/34.91 -> [9516] ~(left_apart_point(A52_430_14, L53_430_14) | left_apart_point(A52_430_14, reverse_line(L53_430_14)))
% 194.94/34.91
% 194.94/34.91 [9516] ALPHA_NOT_OR : ~(left_apart_point(A52_430_14, L53_430_14) | left_apart_point(A52_430_14, reverse_line(L53_430_14)))
% 194.94/34.91 -> [9518] ~left_apart_point(A52_430_14, L53_430_14), ~left_apart_point(A52_430_14, reverse_line(L53_430_14))
% 194.94/34.91
% 194.94/34.91 [9518] CLOSURE : ~left_apart_point(A52_430_14, L53_430_14)
% 194.94/34.91
% 194.94/34.91 [9514] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 194.94/34.91 -> [9515] ~(left_apart_point(A52_429_14, L53_429_14) | left_apart_point(A52_429_14, reverse_line(L53_429_14)))
% 194.94/34.91
% 194.94/34.91 [9515] ALPHA_NOT_OR : ~(left_apart_point(A52_429_14, L53_429_14) | left_apart_point(A52_429_14, reverse_line(L53_429_14)))
% 194.94/34.91 -> [9517] ~left_apart_point(A52_429_14, L53_429_14), ~left_apart_point(A52_429_14, reverse_line(L53_429_14))
% 194.94/34.91
% 194.94/34.91 [9517] CLOSURE : ~left_apart_point(A52_429_14, L53_429_14)
% 194.94/34.91
% 194.94/34.91 [9509] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9511] ~unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [9512] ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9511] CLOSURE : ~unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [9512] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 194.94/34.91 -> [9519] ~(left_apart_point(A52_431_14, L53_431_14) | left_apart_point(A52_431_14, reverse_line(L53_431_14)))
% 194.94/34.91
% 194.94/34.91 [9519] ALPHA_NOT_OR : ~(left_apart_point(A52_431_14, L53_431_14) | left_apart_point(A52_431_14, reverse_line(L53_431_14)))
% 194.94/34.91 -> [9520] ~left_apart_point(A52_431_14, L53_431_14), ~left_apart_point(A52_431_14, reverse_line(L53_431_14))
% 194.94/34.91
% 194.94/34.91 [9520] CLOSURE : ~left_apart_point(A52_431_14, L53_431_14)
% 194.94/34.91
% 194.94/34.91 [9493] BETA_OR : ((unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))) | (unequally_directed_lines(skolem_M9595, skolem_M9595) & unequally_directed_lines(skolem_M9595, reverse_line(skolem_M9595))))
% 194.94/34.91 -> [9528] (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9529] (unequally_directed_lines(skolem_M9595, skolem_M9595) & unequally_directed_lines(skolem_M9595, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [9528] ALPHA_AND : (unequally_directed_lines(skolem_L9494, skolem_M9595) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9531] unequally_directed_lines(skolem_L9494, skolem_M9595), unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9531] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9530] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 194.94/34.91 -> [9536] (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [9536] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_M9595) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9537] unequally_directed_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [9538] unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9538] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9537] 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)))))
% 194.94/34.91 -> [9541] ((unequally_directed_lines(skolem_M9595, skolem_M9595) & unequally_directed_lines(skolem_M9595, reverse_line(skolem_M9595))) => (left_convergent_lines(skolem_M9595, skolem_M9595) | left_convergent_lines(skolem_M9595, reverse_line(skolem_M9595))))
% 194.94/34.91
% 194.94/34.91 [9541] BETA_IMPLY : ((unequally_directed_lines(skolem_M9595, skolem_M9595) & unequally_directed_lines(skolem_M9595, reverse_line(skolem_M9595))) => (left_convergent_lines(skolem_M9595, skolem_M9595) | left_convergent_lines(skolem_M9595, reverse_line(skolem_M9595))))
% 194.94/34.91 -> [9542] ~(unequally_directed_lines(skolem_M9595, skolem_M9595) & unequally_directed_lines(skolem_M9595, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9543] (left_convergent_lines(skolem_M9595, skolem_M9595) | left_convergent_lines(skolem_M9595, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [9542] BETA_NOT_AND : ~(unequally_directed_lines(skolem_M9595, skolem_M9595) & unequally_directed_lines(skolem_M9595, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9544] ~unequally_directed_lines(skolem_M9595, skolem_M9595)
% 194.94/34.91 -> [9545] ~unequally_directed_lines(skolem_M9595, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9545] CLOSURE : ~unequally_directed_lines(skolem_M9595, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9544] CLOSURE : ~unequally_directed_lines(skolem_M9595, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [9543] BETA_OR : (left_convergent_lines(skolem_M9595, skolem_M9595) | left_convergent_lines(skolem_M9595, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9546] left_convergent_lines(skolem_M9595, skolem_M9595)
% 194.94/34.91 -> [9547] left_convergent_lines(skolem_M9595, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9546] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 194.94/34.91 -> [9548] ~(left_apart_point(A52_434_14, L53_434_14) | left_apart_point(A52_434_14, reverse_line(L53_434_14)))
% 194.94/34.91
% 194.94/34.91 [9548] ALPHA_NOT_OR : ~(left_apart_point(A52_434_14, L53_434_14) | left_apart_point(A52_434_14, reverse_line(L53_434_14)))
% 194.94/34.91 -> [9549] ~left_apart_point(A52_434_14, L53_434_14), ~left_apart_point(A52_434_14, reverse_line(L53_434_14))
% 194.94/34.91
% 194.94/34.91 [9549] CLOSURE : ~left_apart_point(A52_434_14, L53_434_14)
% 194.94/34.91
% 194.94/34.91 [9547] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 194.94/34.91 -> [9550] ~(left_apart_point(A52_435_14, L53_435_14) | left_apart_point(A52_435_14, reverse_line(L53_435_14)))
% 194.94/34.91
% 194.94/34.91 [9550] ALPHA_NOT_OR : ~(left_apart_point(A52_435_14, L53_435_14) | left_apart_point(A52_435_14, reverse_line(L53_435_14)))
% 194.94/34.91 -> [9551] ~left_apart_point(A52_435_14, L53_435_14), ~left_apart_point(A52_435_14, reverse_line(L53_435_14))
% 194.94/34.91
% 194.94/34.91 [9551] CLOSURE : ~left_apart_point(A52_435_14, L53_435_14)
% 194.94/34.91
% 194.94/34.91 [8602] GAMMA_FORALL : ! [X15_15, Y16_16] : ((equally_directed_lines(X15_15, Y16_16) <=> ~unequally_directed_lines(X15_15, Y16_16)))
% 194.94/34.91 -> [8605] (equally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)) <=> ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [8605] BETA_EQUIV : (equally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)) <=> ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [8608] ~equally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)), ~~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91 -> [8609] equally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)), ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [8608] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91 -> [8610] unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [8610] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [8615] BETA_EQUIV : (equally_directed_opposite_lines(skolem_L9494, skolem_M9595) <=> ~unequally_directed_opposite_lines(skolem_L9494, skolem_M9595))
% 194.94/34.91 -> [9433] ~equally_directed_opposite_lines(skolem_L9494, skolem_M9595), ~~unequally_directed_opposite_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91 -> [9434] equally_directed_opposite_lines(skolem_L9494, skolem_M9595), ~unequally_directed_opposite_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 [9434] GAMMA_FORALL : ! [A33_33] : (~distinct_points(A33_33, A33_33))
% 194.94/34.91 -> [9439] ~distinct_points(C36_29_6, C36_29_6)
% 194.94/34.91
% 194.94/34.91 [9439] 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))))
% 194.94/34.91 -> [9440] (distinct_points(C36_29_6, C36_29_6) => (distinct_points(C36_29_6, C36_29_6) | distinct_points(C36_29_6, C36_29_6)))
% 194.94/34.91
% 194.94/34.91 [9440] BETA_IMPLY : (distinct_points(C36_29_6, C36_29_6) => (distinct_points(C36_29_6, C36_29_6) | distinct_points(C36_29_6, C36_29_6)))
% 194.94/34.91 -> [9441] ~distinct_points(C36_29_6, C36_29_6)
% 194.94/34.91 -> [9442] (distinct_points(C36_29_6, C36_29_6) | distinct_points(C36_29_6, C36_29_6))
% 194.94/34.91
% 194.94/34.91 [9442] BETA_OR : (distinct_points(C36_29_6, C36_29_6) | distinct_points(C36_29_6, C36_29_6))
% 194.94/34.91 -> [9443] distinct_points(C36_29_6, C36_29_6)
% 194.94/34.91 -> [9444] distinct_points(C36_29_6, C36_29_6)
% 194.94/34.91
% 194.94/34.91 [9444] CLOSURE : distinct_points(C36_29_6, C36_29_6)
% 194.94/34.91
% 194.94/34.91 [9443] CLOSURE : distinct_points(C36_29_6, C36_29_6)
% 194.94/34.91
% 194.94/34.91 [9446] BETA_IMPLY : (distinct_lines(N40_48_8, N40_48_8) => (distinct_lines(N40_48_8, N40_48_8) | distinct_lines(N40_48_8, N40_48_8)))
% 194.94/34.91 -> [9734] ~distinct_lines(N40_48_8, N40_48_8)
% 194.94/34.91 -> [9735] (distinct_lines(N40_48_8, N40_48_8) | distinct_lines(N40_48_8, N40_48_8))
% 194.94/34.91
% 194.94/34.91 [9735] BETA_OR : (distinct_lines(N40_48_8, N40_48_8) | distinct_lines(N40_48_8, N40_48_8))
% 194.94/34.91 -> [9736] distinct_lines(N40_48_8, N40_48_8)
% 194.94/34.91 -> [9737] distinct_lines(N40_48_8, N40_48_8)
% 194.94/34.91
% 194.94/34.91 [9737] CLOSURE : distinct_lines(N40_48_8, N40_48_8)
% 194.94/34.91
% 194.94/34.91 [9736] CLOSURE : distinct_lines(N40_48_8, N40_48_8)
% 194.94/34.91
% 194.94/34.91 [9739] BETA_IMPLY : (unequally_directed_lines(skolem_L9494, skolem_L9494) => (unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))))
% 194.94/34.91 -> [9806] ~unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [9807] (unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91
% 194.94/34.91 [9807] BETA_OR : (unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595)))
% 194.94/34.91 -> [9808] unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91 -> [9809] unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9809] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9808] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_M9595))
% 194.94/34.91
% 194.94/34.91 [9810] BETA_IMPLY : ((unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) & unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))) => ((unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))) | (unequally_directed_lines(reverse_line(skolem_L9494), skolem_L9494) & unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(skolem_L9494)))))
% 194.94/34.91 -> [9829] ~(unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) & unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494))))
% 194.94/34.91 -> [9830] ((unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))) | (unequally_directed_lines(reverse_line(skolem_L9494), skolem_L9494) & unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(skolem_L9494))))
% 194.94/34.91
% 194.94/34.91 [9829] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) & unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494))))
% 194.94/34.91 -> [9833] ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91 -> [9834] ~unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [9833] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 194.94/34.91 -> [9837] (unequally_directed_lines(skolem_L9494, skolem_L9494) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [9837] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_L9494) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [9838] unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [9839] unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [9838] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [9839] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [9840] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_L9494) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [9858] unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [9859] unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [9858] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [9859] 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)))))
% 194.94/34.91 -> [9860] ((unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) & unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))) => (left_convergent_lines(skolem_L9494, reverse_line(skolem_L9494)) | left_convergent_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))))
% 194.94/34.91
% 194.94/34.91 [9860] BETA_IMPLY : ((unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) & unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))) => (left_convergent_lines(skolem_L9494, reverse_line(skolem_L9494)) | left_convergent_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))))
% 194.94/34.91 -> [9861] ~(unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) & unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494))))
% 194.94/34.91 -> [9862] (left_convergent_lines(skolem_L9494, reverse_line(skolem_L9494)) | left_convergent_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494))))
% 194.94/34.91
% 194.94/34.91 [9861] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)) & unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494))))
% 194.94/34.91 -> [9863] ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91 -> [9864] ~unequally_directed_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [9863] CLOSURE : ~unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [9864] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 194.94/34.91 -> [9867] ~(left_apart_point(A52_463_14, L53_463_14) | left_apart_point(A52_463_14, reverse_line(L53_463_14)))
% 194.94/34.91
% 194.94/34.91 [9867] ALPHA_NOT_OR : ~(left_apart_point(A52_463_14, L53_463_14) | left_apart_point(A52_463_14, reverse_line(L53_463_14)))
% 194.94/34.91 -> [9868] ~left_apart_point(A52_463_14, L53_463_14), ~left_apart_point(A52_463_14, reverse_line(L53_463_14))
% 194.94/34.91
% 194.94/34.91 [9868] CLOSURE : ~left_apart_point(A52_463_14, L53_463_14)
% 194.94/34.91
% 194.94/34.91 [9862] BETA_OR : (left_convergent_lines(skolem_L9494, reverse_line(skolem_L9494)) | left_convergent_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494))))
% 194.94/34.91 -> [9871] left_convergent_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91 -> [9872] left_convergent_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [9872] CLOSURE : left_convergent_lines(skolem_L9494, reverse_line(reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [9871] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 194.94/34.91 -> [9873] ~(left_apart_point(A52_465_14, L53_465_14) | left_apart_point(A52_465_14, reverse_line(L53_465_14)))
% 194.94/34.91
% 194.94/34.91 [9873] ALPHA_NOT_OR : ~(left_apart_point(A52_465_14, L53_465_14) | left_apart_point(A52_465_14, reverse_line(L53_465_14)))
% 194.94/34.91 -> [9874] ~left_apart_point(A52_465_14, L53_465_14), ~left_apart_point(A52_465_14, reverse_line(L53_465_14))
% 194.94/34.91
% 194.94/34.91 [9874] CLOSURE : ~left_apart_point(A52_465_14, L53_465_14)
% 194.94/34.91
% 194.94/34.91 [9830] BETA_OR : ((unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))) | (unequally_directed_lines(reverse_line(skolem_L9494), skolem_L9494) & unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(skolem_L9494))))
% 194.94/34.91 -> [9875] (unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [9876] (unequally_directed_lines(reverse_line(skolem_L9494), skolem_L9494) & unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [9875] ALPHA_AND : (unequally_directed_lines(skolem_L9494, skolem_L9494) & unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [9877] unequally_directed_lines(skolem_L9494, skolem_L9494), unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [9877] CLOSURE : unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [9876] ALPHA_AND : (unequally_directed_lines(reverse_line(skolem_L9494), skolem_L9494) & unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(skolem_L9494)))
% 194.94/34.91 -> [9878] unequally_directed_lines(reverse_line(skolem_L9494), skolem_L9494), unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [9878] GAMMA_FORALL : ! [L48_48, M49_49] : ((unequally_directed_lines(L48_48, M49_49) | unequally_directed_lines(L48_48, reverse_line(M49_49))))
% 194.94/34.91 -> [9879] (unequally_directed_lines(skolem_L9494, skolem_L9494) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91
% 194.94/34.91 [9879] BETA_OR : (unequally_directed_lines(skolem_L9494, skolem_L9494) | unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494)))
% 194.94/34.91 -> [9880] unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91 -> [9881] unequally_directed_lines(skolem_L9494, reverse_line(skolem_L9494))
% 194.94/34.91
% 194.94/34.91 [9880] CLOSURE : unequally_directed_lines(skolem_L9494, skolem_L9494)
% 194.94/34.91
% 194.94/34.91 [9881] 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)))))
% 194.94/34.91 -> [9882] ((unequally_directed_lines(reverse_line(skolem_L9494), M51_140_13) & unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(M51_140_13))) => (left_convergent_lines(reverse_line(skolem_L9494), M51_140_13) | left_convergent_lines(reverse_line(skolem_L9494), reverse_line(M51_140_13))))
% 194.94/34.91
% 194.94/34.91 [9882] BETA_IMPLY : ((unequally_directed_lines(reverse_line(skolem_L9494), M51_140_13) & unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(M51_140_13))) => (left_convergent_lines(reverse_line(skolem_L9494), M51_140_13) | left_convergent_lines(reverse_line(skolem_L9494), reverse_line(M51_140_13))))
% 194.94/34.91 -> [9883] ~(unequally_directed_lines(reverse_line(skolem_L9494), M51_140_13) & unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(M51_140_13)))
% 194.94/34.91 -> [9884] (left_convergent_lines(reverse_line(skolem_L9494), M51_140_13) | left_convergent_lines(reverse_line(skolem_L9494), reverse_line(M51_140_13)))
% 194.94/34.91
% 194.94/34.91 [9883] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(skolem_L9494), M51_140_13) & unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(M51_140_13)))
% 194.94/34.91 -> [9885] ~unequally_directed_lines(reverse_line(skolem_L9494), M51_140_13)
% 194.94/34.91 -> [9886] ~unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(M51_140_13))
% 194.94/34.91
% 194.94/34.91 [9885] CLOSURE : ~unequally_directed_lines(reverse_line(skolem_L9494), M51_140_13)
% 194.94/34.91
% 194.94/34.91 [9886] CLOSURE : ~unequally_directed_lines(reverse_line(skolem_L9494), reverse_line(M51_140_13))
% 194.94/34.91
% 194.94/34.91 [9884] BETA_OR : (left_convergent_lines(reverse_line(skolem_L9494), M51_140_13) | left_convergent_lines(reverse_line(skolem_L9494), reverse_line(M51_140_13)))
% 194.94/34.91 -> [9891] left_convergent_lines(reverse_line(skolem_L9494), M51_140_13)
% 194.94/34.91 -> [9892] left_convergent_lines(reverse_line(skolem_L9494), reverse_line(M51_140_13))
% 194.94/34.91
% 194.94/34.91 [9891] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 194.94/34.91 -> [9893] ~(left_apart_point(A52_467_14, L53_467_14) | left_apart_point(A52_467_14, reverse_line(L53_467_14)))
% 194.94/34.91
% 194.94/34.91 [9893] ALPHA_NOT_OR : ~(left_apart_point(A52_467_14, L53_467_14) | left_apart_point(A52_467_14, reverse_line(L53_467_14)))
% 194.94/34.91 -> [9895] ~left_apart_point(A52_467_14, L53_467_14), ~left_apart_point(A52_467_14, reverse_line(L53_467_14))
% 194.94/34.91
% 194.94/34.91 [9895] CLOSURE : ~left_apart_point(A52_467_14, L53_467_14)
% 194.94/34.91
% 194.94/34.91 [9892] GAMMA_FORALL : ! [A52_52, L53_53] : (~(left_apart_point(A52_52, L53_53) | left_apart_point(A52_52, reverse_line(L53_53))))
% 194.94/34.91 -> [9894] ~(left_apart_point(A52_468_14, L53_468_14) | left_apart_point(A52_468_14, reverse_line(L53_468_14)))
% 194.94/34.91
% 194.94/34.91 [9894] ALPHA_NOT_OR : ~(left_apart_point(A52_468_14, L53_468_14) | left_apart_point(A52_468_14, reverse_line(L53_468_14)))
% 194.94/34.91 -> [9896] ~left_apart_point(A52_468_14, L53_468_14), ~left_apart_point(A52_468_14, reverse_line(L53_468_14))
% 194.94/34.91
% 194.94/34.91 [9896] CLOSURE : ~left_apart_point(A52_468_14, L53_468_14)
% 194.94/34.91
% 194.94/34.91 [9438] CLOSURE : unequally_directed_opposite_lines(skolem_L9494, skolem_M9595)
% 194.94/34.91
% 194.94/34.91 % SZS output end Proof for theBenchmark.p
% 194.94/34.91 [34.565353s][1][Res] 458007 goroutines created
% 194.94/34.91 ==== Result ====
% 194.94/34.91 [34.565400s][1][Res] VALID
% 194.94/34.91 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------