TSTP Solution File: GEO253+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO253+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n029.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 15:18:45 EDT 2022
% Result : Theorem 113.15s 21.90s
% Output : Proof 113.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO253+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 07:21:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 [DMT] DMT loaded with preskolemization
% 0.13/0.34 [EQ] equality loaded.
% 0.13/0.34 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35 Conjecture not found
% 0.13/0.35 Start search
% 0.13/0.35 nb_step : 1 - limit : 37
% 0.13/0.35 Launch Gotab with destructive = true
% 113.15/21.88 % SZS output start Proof for theBenchmark.p
% 113.15/21.90 [0] ALPHA_AND : ((! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9)))) & ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11)))) & ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13)))) & ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15))) & ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17))) & ! [A32_32] : (~distinct_points(A32_32, A32_32)) & ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35)))) & ! [L36_36] : (~distinct_lines(L36_36, L36_36)) & ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39)))) & ! [L40_40] : (equally_directed_lines(L40_40, L40_40)) & ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43)))) & ! [L44_44, M45_45, N46_46] : (((unequally_directed_lines(L44_44, M45_45) & unequally_directed_lines(L44_44, reverse_line(M45_45))) => ((unequally_directed_lines(L44_44, N46_46) & unequally_directed_lines(L44_44, reverse_line(N46_46))) | (unequally_directed_lines(M45_45, N46_46) & unequally_directed_lines(M45_45, reverse_line(N46_46)))))) & ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48)))) & ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50))))) & ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52)))) & ! [L53_53, M54_54] : (~(left_convergent_lines(L53_53, M54_54) | left_convergent_lines(L53_53, reverse_line(M54_54)))) & ! [A55_55, B56_56] : ((((point(A55_55) & point(B56_56)) & distinct_points(A55_55, B56_56)) => line(line_connecting(A55_55, B56_56)))) & ! [L57_57, M58_58] : (((((line(L57_57) & line(M58_58)) & unequally_directed_lines(L57_57, M58_58)) & unequally_directed_lines(L57_57, reverse_line(M58_58))) => point(intersection_point(L57_57, M58_58)))) & ! [L59_59, A60_60] : (((point(A60_60) & line(L59_59)) => line(parallel_through_point(L59_59, A60_60)))) & ! [L61_61] : ((line(L61_61) => line(reverse_line(L61_61)))) & ! [A62_62, B63_63] : ((distinct_points(A62_62, B63_63) => (~apart_point_and_line(A62_62, line_connecting(A62_62, B63_63)) & ~apart_point_and_line(B63_63, line_connecting(A62_62, B63_63))))) & ! [L64_64, M65_65] : (((unequally_directed_lines(L64_64, M65_65) & unequally_directed_lines(L64_64, reverse_line(M65_65))) => (~apart_point_and_line(intersection_point(L64_64, M65_65), L64_64) & ~apart_point_and_line(intersection_point(L64_64, M65_65), M65_65)))) & ! [A66_66, L67_67] : (~apart_point_and_line(A66_66, parallel_through_point(L67_67, A66_66))) & ! [L68_68] : (~distinct_lines(L68_68, reverse_line(L68_68))) & ! [A69_69, B70_70] : ((distinct_points(A69_69, B70_70) => equally_directed_lines(line_connecting(A69_69, B70_70), reverse_line(line_connecting(B70_70, A69_69))))) & ! [A71_71, L72_72] : (equally_directed_lines(parallel_through_point(L72_72, A71_71), L72_72)) & ! [A73_73, B74_74, L75_75, M76_76] : (((distinct_points(A73_73, B74_74) & distinct_lines(L75_75, M76_76)) => (((((((left_apart_point(A73_73, L75_75) | left_apart_point(B74_74, L75_75)) | left_apart_point(A73_73, M76_76)) | left_apart_point(B74_74, M76_76)) | left_apart_point(A73_73, reverse_line(L75_75))) | left_apart_point(B74_74, reverse_line(L75_75))) | left_apart_point(A73_73, reverse_line(M76_76))) | left_apart_point(B74_74, reverse_line(M76_76))))) & ! [A77_77, B78_78, L79_79] : (((distinct_points(A77_77, B78_78) & left_apart_point(A77_77, L79_79)) => (left_apart_point(B78_78, L79_79) | left_convergent_lines(line_connecting(A77_77, B78_78), L79_79)))) & ! [A80_80, B81_81, L82_82] : ((left_apart_point(A80_80, L82_82) => (distinct_points(A80_80, B81_81) | left_apart_point(B81_81, L82_82)))) & ! [A83_83, L84_84, M85_85] : (((left_apart_point(A83_83, L84_84) & unequally_directed_lines(L84_84, M85_85)) => (distinct_lines(L84_84, M85_85) | left_apart_point(A83_83, reverse_line(M85_85))))) & ! [L86_86, M87_87, N88_88] : ((left_convergent_lines(L86_86, M87_87) => (unequally_directed_lines(M87_87, N88_88) | left_convergent_lines(L86_86, N88_88))))) & ~! [A89_89, B90_90, L91_91] : (((apart_point_and_line(A89_89, L91_91) & incident_point_and_line(B90_90, parallel_through_point(L91_91, A89_89))) => apart_point_and_line(B90_90, L91_91))))
% 113.15/21.90 -> [1] (! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9)))) & ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11)))) & ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13)))) & ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15))) & ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17))) & ! [A32_32] : (~distinct_points(A32_32, A32_32)) & ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35)))) & ! [L36_36] : (~distinct_lines(L36_36, L36_36)) & ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39)))) & ! [L40_40] : (equally_directed_lines(L40_40, L40_40)) & ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43)))) & ! [L44_44, M45_45, N46_46] : (((unequally_directed_lines(L44_44, M45_45) & unequally_directed_lines(L44_44, reverse_line(M45_45))) => ((unequally_directed_lines(L44_44, N46_46) & unequally_directed_lines(L44_44, reverse_line(N46_46))) | (unequally_directed_lines(M45_45, N46_46) & unequally_directed_lines(M45_45, reverse_line(N46_46)))))) & ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48)))) & ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50))))) & ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52)))) & ! [L53_53, M54_54] : (~(left_convergent_lines(L53_53, M54_54) | left_convergent_lines(L53_53, reverse_line(M54_54)))) & ! [A55_55, B56_56] : ((((point(A55_55) & point(B56_56)) & distinct_points(A55_55, B56_56)) => line(line_connecting(A55_55, B56_56)))) & ! [L57_57, M58_58] : (((((line(L57_57) & line(M58_58)) & unequally_directed_lines(L57_57, M58_58)) & unequally_directed_lines(L57_57, reverse_line(M58_58))) => point(intersection_point(L57_57, M58_58)))) & ! [L59_59, A60_60] : (((point(A60_60) & line(L59_59)) => line(parallel_through_point(L59_59, A60_60)))) & ! [L61_61] : ((line(L61_61) => line(reverse_line(L61_61)))) & ! [A62_62, B63_63] : ((distinct_points(A62_62, B63_63) => (~apart_point_and_line(A62_62, line_connecting(A62_62, B63_63)) & ~apart_point_and_line(B63_63, line_connecting(A62_62, B63_63))))) & ! [L64_64, M65_65] : (((unequally_directed_lines(L64_64, M65_65) & unequally_directed_lines(L64_64, reverse_line(M65_65))) => (~apart_point_and_line(intersection_point(L64_64, M65_65), L64_64) & ~apart_point_and_line(intersection_point(L64_64, M65_65), M65_65)))) & ! [A66_66, L67_67] : (~apart_point_and_line(A66_66, parallel_through_point(L67_67, A66_66))) & ! [L68_68] : (~distinct_lines(L68_68, reverse_line(L68_68))) & ! [A69_69, B70_70] : ((distinct_points(A69_69, B70_70) => equally_directed_lines(line_connecting(A69_69, B70_70), reverse_line(line_connecting(B70_70, A69_69))))) & ! [A71_71, L72_72] : (equally_directed_lines(parallel_through_point(L72_72, A71_71), L72_72)) & ! [A73_73, B74_74, L75_75, M76_76] : (((distinct_points(A73_73, B74_74) & distinct_lines(L75_75, M76_76)) => (((((((left_apart_point(A73_73, L75_75) | left_apart_point(B74_74, L75_75)) | left_apart_point(A73_73, M76_76)) | left_apart_point(B74_74, M76_76)) | left_apart_point(A73_73, reverse_line(L75_75))) | left_apart_point(B74_74, reverse_line(L75_75))) | left_apart_point(A73_73, reverse_line(M76_76))) | left_apart_point(B74_74, reverse_line(M76_76))))) & ! [A77_77, B78_78, L79_79] : (((distinct_points(A77_77, B78_78) & left_apart_point(A77_77, L79_79)) => (left_apart_point(B78_78, L79_79) | left_convergent_lines(line_connecting(A77_77, B78_78), L79_79)))) & ! [A80_80, B81_81, L82_82] : ((left_apart_point(A80_80, L82_82) => (distinct_points(A80_80, B81_81) | left_apart_point(B81_81, L82_82)))) & ! [A83_83, L84_84, M85_85] : (((left_apart_point(A83_83, L84_84) & unequally_directed_lines(L84_84, M85_85)) => (distinct_lines(L84_84, M85_85) | left_apart_point(A83_83, reverse_line(M85_85))))) & ! [L86_86, M87_87, N88_88] : ((left_convergent_lines(L86_86, M87_87) => (unequally_directed_lines(M87_87, N88_88) | left_convergent_lines(L86_86, N88_88))))), ~! [A89_89, B90_90, L91_91] : (((apart_point_and_line(A89_89, L91_91) & incident_point_and_line(B90_90, parallel_through_point(L91_91, A89_89))) => apart_point_and_line(B90_90, L91_91)))
% 113.15/21.90
% 113.15/21.90 [1] ALPHA_AND : (! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9)))) & ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11)))) & ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13)))) & ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15))) & ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17))) & ! [A32_32] : (~distinct_points(A32_32, A32_32)) & ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35)))) & ! [L36_36] : (~distinct_lines(L36_36, L36_36)) & ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39)))) & ! [L40_40] : (equally_directed_lines(L40_40, L40_40)) & ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43)))) & ! [L44_44, M45_45, N46_46] : (((unequally_directed_lines(L44_44, M45_45) & unequally_directed_lines(L44_44, reverse_line(M45_45))) => ((unequally_directed_lines(L44_44, N46_46) & unequally_directed_lines(L44_44, reverse_line(N46_46))) | (unequally_directed_lines(M45_45, N46_46) & unequally_directed_lines(M45_45, reverse_line(N46_46)))))) & ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48)))) & ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50))))) & ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52)))) & ! [L53_53, M54_54] : (~(left_convergent_lines(L53_53, M54_54) | left_convergent_lines(L53_53, reverse_line(M54_54)))) & ! [A55_55, B56_56] : ((((point(A55_55) & point(B56_56)) & distinct_points(A55_55, B56_56)) => line(line_connecting(A55_55, B56_56)))) & ! [L57_57, M58_58] : (((((line(L57_57) & line(M58_58)) & unequally_directed_lines(L57_57, M58_58)) & unequally_directed_lines(L57_57, reverse_line(M58_58))) => point(intersection_point(L57_57, M58_58)))) & ! [L59_59, A60_60] : (((point(A60_60) & line(L59_59)) => line(parallel_through_point(L59_59, A60_60)))) & ! [L61_61] : ((line(L61_61) => line(reverse_line(L61_61)))) & ! [A62_62, B63_63] : ((distinct_points(A62_62, B63_63) => (~apart_point_and_line(A62_62, line_connecting(A62_62, B63_63)) & ~apart_point_and_line(B63_63, line_connecting(A62_62, B63_63))))) & ! [L64_64, M65_65] : (((unequally_directed_lines(L64_64, M65_65) & unequally_directed_lines(L64_64, reverse_line(M65_65))) => (~apart_point_and_line(intersection_point(L64_64, M65_65), L64_64) & ~apart_point_and_line(intersection_point(L64_64, M65_65), M65_65)))) & ! [A66_66, L67_67] : (~apart_point_and_line(A66_66, parallel_through_point(L67_67, A66_66))) & ! [L68_68] : (~distinct_lines(L68_68, reverse_line(L68_68))) & ! [A69_69, B70_70] : ((distinct_points(A69_69, B70_70) => equally_directed_lines(line_connecting(A69_69, B70_70), reverse_line(line_connecting(B70_70, A69_69))))) & ! [A71_71, L72_72] : (equally_directed_lines(parallel_through_point(L72_72, A71_71), L72_72)) & ! [A73_73, B74_74, L75_75, M76_76] : (((distinct_points(A73_73, B74_74) & distinct_lines(L75_75, M76_76)) => (((((((left_apart_point(A73_73, L75_75) | left_apart_point(B74_74, L75_75)) | left_apart_point(A73_73, M76_76)) | left_apart_point(B74_74, M76_76)) | left_apart_point(A73_73, reverse_line(L75_75))) | left_apart_point(B74_74, reverse_line(L75_75))) | left_apart_point(A73_73, reverse_line(M76_76))) | left_apart_point(B74_74, reverse_line(M76_76))))) & ! [A77_77, B78_78, L79_79] : (((distinct_points(A77_77, B78_78) & left_apart_point(A77_77, L79_79)) => (left_apart_point(B78_78, L79_79) | left_convergent_lines(line_connecting(A77_77, B78_78), L79_79)))) & ! [A80_80, B81_81, L82_82] : ((left_apart_point(A80_80, L82_82) => (distinct_points(A80_80, B81_81) | left_apart_point(B81_81, L82_82)))) & ! [A83_83, L84_84, M85_85] : (((left_apart_point(A83_83, L84_84) & unequally_directed_lines(L84_84, M85_85)) => (distinct_lines(L84_84, M85_85) | left_apart_point(A83_83, reverse_line(M85_85))))) & ! [L86_86, M87_87, N88_88] : ((left_convergent_lines(L86_86, M87_87) => (unequally_directed_lines(M87_87, N88_88) | left_convergent_lines(L86_86, N88_88)))))
% 113.15/21.90 -> [2] ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9)))), ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11)))), ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13)))), ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15))), ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17))), ! [A32_32] : (~distinct_points(A32_32, A32_32)), ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35)))), ! [L36_36] : (~distinct_lines(L36_36, L36_36)), ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39)))), ! [L40_40] : (equally_directed_lines(L40_40, L40_40)), ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43)))), ! [L44_44, M45_45, N46_46] : (((unequally_directed_lines(L44_44, M45_45) & unequally_directed_lines(L44_44, reverse_line(M45_45))) => ((unequally_directed_lines(L44_44, N46_46) & unequally_directed_lines(L44_44, reverse_line(N46_46))) | (unequally_directed_lines(M45_45, N46_46) & unequally_directed_lines(M45_45, reverse_line(N46_46)))))), ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48)))), ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50))))), ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52)))), ! [L53_53, M54_54] : (~(left_convergent_lines(L53_53, M54_54) | left_convergent_lines(L53_53, reverse_line(M54_54)))), ! [A55_55, B56_56] : ((((point(A55_55) & point(B56_56)) & distinct_points(A55_55, B56_56)) => line(line_connecting(A55_55, B56_56)))), ! [L57_57, M58_58] : (((((line(L57_57) & line(M58_58)) & unequally_directed_lines(L57_57, M58_58)) & unequally_directed_lines(L57_57, reverse_line(M58_58))) => point(intersection_point(L57_57, M58_58)))), ! [L59_59, A60_60] : (((point(A60_60) & line(L59_59)) => line(parallel_through_point(L59_59, A60_60)))), ! [L61_61] : ((line(L61_61) => line(reverse_line(L61_61)))), ! [A62_62, B63_63] : ((distinct_points(A62_62, B63_63) => (~apart_point_and_line(A62_62, line_connecting(A62_62, B63_63)) & ~apart_point_and_line(B63_63, line_connecting(A62_62, B63_63))))), ! [L64_64, M65_65] : (((unequally_directed_lines(L64_64, M65_65) & unequally_directed_lines(L64_64, reverse_line(M65_65))) => (~apart_point_and_line(intersection_point(L64_64, M65_65), L64_64) & ~apart_point_and_line(intersection_point(L64_64, M65_65), M65_65)))), ! [A66_66, L67_67] : (~apart_point_and_line(A66_66, parallel_through_point(L67_67, A66_66))), ! [L68_68] : (~distinct_lines(L68_68, reverse_line(L68_68))), ! [A69_69, B70_70] : ((distinct_points(A69_69, B70_70) => equally_directed_lines(line_connecting(A69_69, B70_70), reverse_line(line_connecting(B70_70, A69_69))))), ! [A71_71, L72_72] : (equally_directed_lines(parallel_through_point(L72_72, A71_71), L72_72)), ! [A73_73, B74_74, L75_75, M76_76] : (((distinct_points(A73_73, B74_74) & distinct_lines(L75_75, M76_76)) => (((((((left_apart_point(A73_73, L75_75) | left_apart_point(B74_74, L75_75)) | left_apart_point(A73_73, M76_76)) | left_apart_point(B74_74, M76_76)) | left_apart_point(A73_73, reverse_line(L75_75))) | left_apart_point(B74_74, reverse_line(L75_75))) | left_apart_point(A73_73, reverse_line(M76_76))) | left_apart_point(B74_74, reverse_line(M76_76))))), ! [A77_77, B78_78, L79_79] : (((distinct_points(A77_77, B78_78) & left_apart_point(A77_77, L79_79)) => (left_apart_point(B78_78, L79_79) | left_convergent_lines(line_connecting(A77_77, B78_78), L79_79)))), ! [A80_80, B81_81, L82_82] : ((left_apart_point(A80_80, L82_82) => (distinct_points(A80_80, B81_81) | left_apart_point(B81_81, L82_82)))), ! [A83_83, L84_84, M85_85] : (((left_apart_point(A83_83, L84_84) & unequally_directed_lines(L84_84, M85_85)) => (distinct_lines(L84_84, M85_85) | left_apart_point(A83_83, reverse_line(M85_85))))), ! [L86_86, M87_87, N88_88] : ((left_convergent_lines(L86_86, M87_87) => (unequally_directed_lines(M87_87, N88_88) | left_convergent_lines(L86_86, N88_88))))
% 113.15/21.90
% 113.15/21.90 [2] DELTA_NOT_FORALL : ~! [A89_89, B90_90, L91_91] : (((apart_point_and_line(A89_89, L91_91) & incident_point_and_line(B90_90, parallel_through_point(L91_91, A89_89))) => apart_point_and_line(B90_90, L91_91)))
% 113.15/21.90 -> [3] ~((apart_point_and_line(skolem_A8989, skolem_L9191) & incident_point_and_line(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989))) => apart_point_and_line(skolem_B9090, skolem_L9191))
% 113.15/21.90
% 113.15/21.90 [3] ALPHA_NOT_IMPLY : ~((apart_point_and_line(skolem_A8989, skolem_L9191) & incident_point_and_line(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989))) => apart_point_and_line(skolem_B9090, skolem_L9191))
% 113.15/21.90 -> [4] (apart_point_and_line(skolem_A8989, skolem_L9191) & incident_point_and_line(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989))), ~apart_point_and_line(skolem_B9090, skolem_L9191)
% 113.15/21.90
% 113.15/21.90 [4] Rewrite : ~apart_point_and_line(skolem_B9090, skolem_L9191)
% 113.15/21.90 -> [5] ~(left_apart_point(skolem_B9090, skolem_L9191) | right_apart_point(skolem_B9090, skolem_L9191))
% 113.15/21.90
% 113.15/21.90 [5] ALPHA_AND : (apart_point_and_line(skolem_A8989, skolem_L9191) & incident_point_and_line(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989)))
% 113.15/21.90 -> [6] apart_point_and_line(skolem_A8989, skolem_L9191), incident_point_and_line(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989))
% 113.15/21.90
% 113.15/21.90 [6] Rewrite : apart_point_and_line(skolem_A8989, skolem_L9191)
% 113.15/21.90 -> [7] (left_apart_point(skolem_A8989, skolem_L9191) | right_apart_point(skolem_A8989, skolem_L9191))
% 113.15/21.90
% 113.15/21.90 [7] ALPHA_NOT_OR : ~(left_apart_point(skolem_B9090, skolem_L9191) | right_apart_point(skolem_B9090, skolem_L9191))
% 113.15/21.90 -> [8] ~left_apart_point(skolem_B9090, skolem_L9191), ~right_apart_point(skolem_B9090, skolem_L9191)
% 113.15/21.90
% 113.15/21.90 [8] BETA_OR : (left_apart_point(skolem_A8989, skolem_L9191) | right_apart_point(skolem_A8989, skolem_L9191))
% 113.15/21.90 -> [9] left_apart_point(skolem_A8989, skolem_L9191)
% 113.15/21.90 -> [10] right_apart_point(skolem_A8989, skolem_L9191)
% 113.15/21.90
% 113.15/21.90 [10] GAMMA_FORALL : ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9))))
% 113.15/21.90 -> [12] (unequally_directed_opposite_lines(reverse_line(Y9_1_0), Y9_1_0) <=> unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0)))
% 113.15/21.90
% 113.15/21.90 [12] BETA_EQUIV : (unequally_directed_opposite_lines(reverse_line(Y9_1_0), Y9_1_0) <=> unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0)))
% 113.15/21.90 -> [15] ~unequally_directed_opposite_lines(reverse_line(Y9_1_0), Y9_1_0), ~unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0))
% 113.15/21.90 -> [16] unequally_directed_opposite_lines(reverse_line(Y9_1_0), Y9_1_0), unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0))
% 113.15/21.90
% 113.15/21.90 [16] GAMMA_FORALL : ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11))))
% 113.15/21.90 -> [21] (right_apart_point(skolem_A8989, skolem_L9191) <=> left_apart_point(skolem_A8989, reverse_line(skolem_L9191)))
% 113.15/21.90
% 113.15/21.90 [21] BETA_EQUIV : (right_apart_point(skolem_A8989, skolem_L9191) <=> left_apart_point(skolem_A8989, reverse_line(skolem_L9191)))
% 113.15/21.90 -> [27] ~right_apart_point(skolem_A8989, skolem_L9191), ~left_apart_point(skolem_A8989, reverse_line(skolem_L9191))
% 113.15/21.90 -> [28] right_apart_point(skolem_A8989, skolem_L9191), left_apart_point(skolem_A8989, reverse_line(skolem_L9191))
% 113.15/21.90
% 113.15/21.90 [27] CLOSURE : ~right_apart_point(skolem_A8989, skolem_L9191)
% 113.15/21.90
% 113.15/21.90 [28] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 113.15/21.90 -> [45] (right_convergent_lines(X12_3_2, Y13_3_2) <=> left_convergent_lines(X12_3_2, reverse_line(Y13_3_2)))
% 113.15/21.90
% 113.15/21.90 [45] BETA_EQUIV : (right_convergent_lines(X12_3_2, Y13_3_2) <=> left_convergent_lines(X12_3_2, reverse_line(Y13_3_2)))
% 113.15/21.90 -> [49] ~right_convergent_lines(X12_3_2, Y13_3_2), ~left_convergent_lines(X12_3_2, reverse_line(Y13_3_2))
% 113.15/21.90 -> [50] right_convergent_lines(X12_3_2, Y13_3_2), left_convergent_lines(X12_3_2, reverse_line(Y13_3_2))
% 113.15/21.90
% 113.15/21.90 [49] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 113.15/21.90 -> [59] (equally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0)) <=> ~unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0)))
% 113.15/21.90
% 113.15/21.90 [59] BETA_EQUIV : (equally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0)) <=> ~unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0)))
% 113.15/21.90 -> [61] ~equally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0)), ~~unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0))
% 113.15/21.90 -> [62] equally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0)), ~unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0))
% 113.15/21.90
% 113.15/21.90 [61] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0))
% 113.15/21.90 -> [78] unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0))
% 113.15/21.90
% 113.15/21.90 [78] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 113.15/21.90 -> [97] (equally_directed_opposite_lines(X16_7_4, Y17_7_4) <=> ~unequally_directed_opposite_lines(X16_7_4, Y17_7_4))
% 113.15/21.90
% 113.15/21.90 [97] BETA_EQUIV : (equally_directed_opposite_lines(X16_7_4, Y17_7_4) <=> ~unequally_directed_opposite_lines(X16_7_4, Y17_7_4))
% 113.15/21.90 -> [107] ~equally_directed_opposite_lines(X16_7_4, Y17_7_4), ~~unequally_directed_opposite_lines(X16_7_4, Y17_7_4)
% 113.15/21.90 -> [108] equally_directed_opposite_lines(X16_7_4, Y17_7_4), ~unequally_directed_opposite_lines(X16_7_4, Y17_7_4)
% 113.15/21.90
% 113.15/21.90 [107] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(X16_7_4, Y17_7_4)
% 113.15/21.90 -> [120] unequally_directed_opposite_lines(X16_7_4, Y17_7_4)
% 113.15/21.90
% 113.15/21.90 [120] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 113.15/21.90 -> [136] ~distinct_points(C35_6_6, C35_6_6)
% 113.15/21.90
% 113.15/21.90 [136] GAMMA_FORALL : ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35))))
% 113.15/21.90 -> [156] (distinct_points(C35_6_6, C35_6_6) => (distinct_points(C35_6_6, C35_6_6) | distinct_points(C35_6_6, C35_6_6)))
% 113.15/21.90
% 113.15/21.90 [156] BETA_IMPLY : (distinct_points(C35_6_6, C35_6_6) => (distinct_points(C35_6_6, C35_6_6) | distinct_points(C35_6_6, C35_6_6)))
% 113.15/21.90 -> [157] ~distinct_points(C35_6_6, C35_6_6)
% 113.15/21.90 -> [158] (distinct_points(C35_6_6, C35_6_6) | distinct_points(C35_6_6, C35_6_6))
% 113.15/21.90
% 113.15/21.90 [158] BETA_OR : (distinct_points(C35_6_6, C35_6_6) | distinct_points(C35_6_6, C35_6_6))
% 113.15/21.90 -> [163] distinct_points(C35_6_6, C35_6_6)
% 113.15/21.90 -> [164] distinct_points(C35_6_6, C35_6_6)
% 113.15/21.90
% 113.15/21.90 [163] CLOSURE : distinct_points(C35_6_6, C35_6_6)
% 113.15/21.90
% 113.15/21.90 [164] CLOSURE : distinct_points(C35_6_6, C35_6_6)
% 113.15/21.90
% 113.15/21.90 [186] BETA_IMPLY : (distinct_lines(N39_5_8, N39_5_8) => (distinct_lines(N39_5_8, N39_5_8) | distinct_lines(N39_5_8, N39_5_8)))
% 113.15/21.90 -> [299] ~distinct_lines(N39_5_8, N39_5_8)
% 113.15/21.90 -> [300] (distinct_lines(N39_5_8, N39_5_8) | distinct_lines(N39_5_8, N39_5_8))
% 113.15/21.90
% 113.15/21.90 [300] BETA_OR : (distinct_lines(N39_5_8, N39_5_8) | distinct_lines(N39_5_8, N39_5_8))
% 113.15/21.90 -> [301] distinct_lines(N39_5_8, N39_5_8)
% 113.15/21.90 -> [302] distinct_lines(N39_5_8, N39_5_8)
% 113.15/21.90
% 113.15/21.90 [302] CLOSURE : distinct_lines(N39_5_8, N39_5_8)
% 113.15/21.90
% 113.15/21.90 [301] CLOSURE : distinct_lines(N39_5_8, N39_5_8)
% 113.15/21.90
% 113.15/21.90 [315] CLOSURE : equally_directed_lines(L40_9_9, L40_9_9)
% 113.15/21.90
% 113.15/21.90 [108] CLOSURE : ~unequally_directed_opposite_lines(X16_7_4, Y17_7_4)
% 113.15/21.90
% 113.15/21.90 [62] CLOSURE : ~unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0))
% 113.15/21.90
% 113.15/21.90 [50] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 113.15/21.90 -> [60] (equally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0)) <=> ~unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0)))
% 113.15/21.90
% 113.15/21.90 [60] BETA_EQUIV : (equally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0)) <=> ~unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0)))
% 113.15/21.90 -> [64] ~equally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0)), ~~unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0))
% 113.15/21.90 -> [65] equally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0)), ~unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0))
% 113.15/21.90
% 113.15/21.90 [64] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0))
% 113.15/21.90 -> [79] unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0))
% 113.15/21.90
% 113.15/21.90 [79] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 113.15/21.90 -> [96] (equally_directed_opposite_lines(X16_6_4, Y17_6_4) <=> ~unequally_directed_opposite_lines(X16_6_4, Y17_6_4))
% 113.15/21.90
% 113.15/21.90 [96] BETA_EQUIV : (equally_directed_opposite_lines(X16_6_4, Y17_6_4) <=> ~unequally_directed_opposite_lines(X16_6_4, Y17_6_4))
% 113.15/21.90 -> [101] ~equally_directed_opposite_lines(X16_6_4, Y17_6_4), ~~unequally_directed_opposite_lines(X16_6_4, Y17_6_4)
% 113.15/21.90 -> [102] equally_directed_opposite_lines(X16_6_4, Y17_6_4), ~unequally_directed_opposite_lines(X16_6_4, Y17_6_4)
% 113.15/21.90
% 113.15/21.90 [102] CLOSURE : ~unequally_directed_opposite_lines(X16_6_4, Y17_6_4)
% 113.15/21.90
% 113.15/21.90 [151] BETA_IMPLY : (distinct_points(C35_5_6, C35_5_6) => (distinct_points(C35_5_6, C35_5_6) | distinct_points(C35_5_6, C35_5_6)))
% 113.15/21.90 -> [342] ~distinct_points(C35_5_6, C35_5_6)
% 113.15/21.90 -> [343] (distinct_points(C35_5_6, C35_5_6) | distinct_points(C35_5_6, C35_5_6))
% 113.15/21.90
% 113.15/21.90 [342] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 113.15/21.90 -> [353] ~distinct_lines(L37_9_8, L37_9_8)
% 113.15/21.90
% 113.15/21.90 [353] GAMMA_FORALL : ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39))))
% 113.15/21.90 -> [369] (distinct_lines(L37_9_8, L37_9_8) => (distinct_lines(L37_9_8, L37_9_8) | distinct_lines(L37_9_8, L37_9_8)))
% 113.15/21.90
% 113.15/21.90 [369] BETA_IMPLY : (distinct_lines(L37_9_8, L37_9_8) => (distinct_lines(L37_9_8, L37_9_8) | distinct_lines(L37_9_8, L37_9_8)))
% 113.15/21.90 -> [372] ~distinct_lines(L37_9_8, L37_9_8)
% 113.15/21.90 -> [373] (distinct_lines(L37_9_8, L37_9_8) | distinct_lines(L37_9_8, L37_9_8))
% 113.15/21.90
% 113.15/21.90 [372] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 113.15/21.90 -> [386] equally_directed_lines(L40_13_9, L40_13_9)
% 113.15/21.90
% 113.15/21.90 [386] CLOSURE : equally_directed_lines(L40_13_9, L40_13_9)
% 113.15/21.90
% 113.15/21.90 [373] BETA_OR : (distinct_lines(L37_9_8, L37_9_8) | distinct_lines(L37_9_8, L37_9_8))
% 113.15/21.90 -> [391] distinct_lines(L37_9_8, L37_9_8)
% 113.15/21.90 -> [392] distinct_lines(L37_9_8, L37_9_8)
% 113.15/21.90
% 113.15/21.90 [392] CLOSURE : distinct_lines(L37_9_8, L37_9_8)
% 113.15/21.90
% 113.15/21.90 [391] CLOSURE : distinct_lines(L37_9_8, L37_9_8)
% 113.15/21.90
% 113.15/21.90 [343] BETA_OR : (distinct_points(C35_5_6, C35_5_6) | distinct_points(C35_5_6, C35_5_6))
% 113.15/21.90 -> [434] distinct_points(C35_5_6, C35_5_6)
% 113.15/21.90 -> [435] distinct_points(C35_5_6, C35_5_6)
% 113.15/21.90
% 113.15/21.90 [435] CLOSURE : distinct_points(C35_5_6, C35_5_6)
% 113.15/21.90
% 113.15/21.90 [434] CLOSURE : distinct_points(C35_5_6, C35_5_6)
% 113.15/21.90
% 113.15/21.90 [65] CLOSURE : ~unequally_directed_lines(reverse_line(Y9_1_0), reverse_line(Y9_1_0))
% 113.15/21.90
% 113.15/21.90 [18] BETA_EQUIV : (right_apart_point(skolem_A8989, skolem_L9191) <=> left_apart_point(skolem_A8989, reverse_line(skolem_L9191)))
% 113.15/21.90 -> [2584] ~right_apart_point(skolem_A8989, skolem_L9191), ~left_apart_point(skolem_A8989, reverse_line(skolem_L9191))
% 113.15/21.90 -> [2585] right_apart_point(skolem_A8989, skolem_L9191), left_apart_point(skolem_A8989, reverse_line(skolem_L9191))
% 113.15/21.90
% 113.15/21.90 [2584] CLOSURE : ~right_apart_point(skolem_A8989, skolem_L9191)
% 113.15/21.90
% 113.15/21.90 [2585] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 113.15/21.90 -> [2588] (right_convergent_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) <=> left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90
% 113.15/21.90 [2588] BETA_EQUIV : (right_convergent_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) <=> left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90 -> [2589] ~right_convergent_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)), ~left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90 -> [2590] right_convergent_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)), left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [2590] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 113.15/21.90 -> [2592] (equally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) <=> ~unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)))
% 113.15/21.90
% 113.15/21.90 [2592] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) <=> ~unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)))
% 113.15/21.90 -> [2595] ~equally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)), ~~unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 113.15/21.90 -> [2596] equally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)), ~unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 113.15/21.90
% 113.15/21.90 [2595] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 113.15/21.90 -> [2598] unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 113.15/21.90
% 113.15/21.90 [2598] CLOSURE : unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 113.15/21.90
% 113.15/21.90 [2600] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4))
% 113.15/21.90 -> [3392] ~equally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4)
% 113.15/21.90 -> [3393] equally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4), ~unequally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4)
% 113.15/21.90
% 113.15/21.90 [3392] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4)
% 113.15/21.90 -> [3394] unequally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4)
% 113.15/21.90
% 113.15/21.90 [3394] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4)
% 113.15/21.90
% 113.15/21.90 [3393] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 113.15/21.90 -> [3395] ~distinct_points(C35_20_6, C35_20_6)
% 113.15/21.90
% 113.15/21.90 [3395] GAMMA_FORALL : ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35))))
% 113.15/21.90 -> [3397] (distinct_points(C35_20_6, C35_20_6) => (distinct_points(C35_20_6, C35_20_6) | distinct_points(C35_20_6, C35_20_6)))
% 113.15/21.90
% 113.15/21.90 [3397] BETA_IMPLY : (distinct_points(C35_20_6, C35_20_6) => (distinct_points(C35_20_6, C35_20_6) | distinct_points(C35_20_6, C35_20_6)))
% 113.15/21.90 -> [3400] ~distinct_points(C35_20_6, C35_20_6)
% 113.15/21.90 -> [3401] (distinct_points(C35_20_6, C35_20_6) | distinct_points(C35_20_6, C35_20_6))
% 113.15/21.90
% 113.15/21.90 [3401] BETA_OR : (distinct_points(C35_20_6, C35_20_6) | distinct_points(C35_20_6, C35_20_6))
% 113.15/21.90 -> [3404] distinct_points(C35_20_6, C35_20_6)
% 113.15/21.90 -> [3405] distinct_points(C35_20_6, C35_20_6)
% 113.15/21.90
% 113.15/21.90 [3404] CLOSURE : distinct_points(C35_20_6, C35_20_6)
% 113.15/21.90
% 113.15/21.90 [3405] CLOSURE : distinct_points(C35_20_6, C35_20_6)
% 113.15/21.90
% 113.15/21.90 [3400] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 113.15/21.90 -> [3408] ~distinct_lines(N39_31_8, N39_31_8)
% 113.15/21.90
% 113.15/21.90 [3408] GAMMA_FORALL : ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39))))
% 113.15/21.90 -> [3409] (distinct_lines(N39_31_8, N39_31_8) => (distinct_lines(N39_31_8, N39_31_8) | distinct_lines(N39_31_8, N39_31_8)))
% 113.15/21.90
% 113.15/21.90 [3409] BETA_IMPLY : (distinct_lines(N39_31_8, N39_31_8) => (distinct_lines(N39_31_8, N39_31_8) | distinct_lines(N39_31_8, N39_31_8)))
% 113.15/21.90 -> [3410] ~distinct_lines(N39_31_8, N39_31_8)
% 113.15/21.90 -> [3411] (distinct_lines(N39_31_8, N39_31_8) | distinct_lines(N39_31_8, N39_31_8))
% 113.15/21.90
% 113.15/21.90 [3411] BETA_OR : (distinct_lines(N39_31_8, N39_31_8) | distinct_lines(N39_31_8, N39_31_8))
% 113.15/21.90 -> [3412] distinct_lines(N39_31_8, N39_31_8)
% 113.15/21.90 -> [3413] distinct_lines(N39_31_8, N39_31_8)
% 113.15/21.90
% 113.15/21.90 [3413] CLOSURE : distinct_lines(N39_31_8, N39_31_8)
% 113.15/21.90
% 113.15/21.90 [3412] CLOSURE : distinct_lines(N39_31_8, N39_31_8)
% 113.15/21.90
% 113.15/21.90 [3410] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 113.15/21.90 -> [3414] equally_directed_lines(L40_54_9, L40_54_9)
% 113.15/21.90
% 113.15/21.90 [3414] GAMMA_FORALL : ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43))))
% 113.15/21.90 -> [3415] (unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) => (unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) | unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11))))
% 113.15/21.90
% 113.15/21.90 [3415] BETA_IMPLY : (unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) => (unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) | unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11))))
% 113.15/21.90 -> [3417] ~unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11))
% 113.15/21.90 -> [3418] (unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) | unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)))
% 113.15/21.90
% 113.15/21.90 [3418] BETA_OR : (unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) | unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)))
% 113.15/21.90 -> [3420] unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11))
% 113.15/21.90 -> [3421] unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11))
% 113.15/21.90
% 113.15/21.90 [3420] CLOSURE : unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11))
% 113.15/21.90
% 113.15/21.90 [3421] CLOSURE : unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11))
% 113.15/21.90
% 113.15/21.90 [3422] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11))) & unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11))))) => ((unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) & unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11)))) | (unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(N46_54_11)) & unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(reverse_line(N46_54_11))))))
% 113.15/21.90 -> [3491] ~(unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11))) & unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11)))))
% 113.15/21.90 -> [3492] ((unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) & unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11)))) | (unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(N46_54_11)) & unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(reverse_line(N46_54_11)))))
% 113.15/21.90
% 113.15/21.90 [3491] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11))) & unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11)))))
% 113.15/21.90 -> [3496] ~unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11)))
% 113.15/21.90 -> [3497] ~unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11))))
% 113.15/21.90
% 113.15/21.90 [3496] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 113.15/21.90 -> [3503] (unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) | unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11))))
% 113.15/21.90
% 113.15/21.90 [3503] BETA_OR : (unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) | unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11))))
% 113.15/21.90 -> [3505] unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11))
% 113.15/21.90 -> [3506] unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11)))
% 113.15/21.90
% 113.15/21.90 [3505] CLOSURE : unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11))
% 113.15/21.90
% 113.15/21.90 [3506] CLOSURE : unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11)))
% 113.15/21.90
% 113.15/21.90 [3504] BETA_OR : (unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11)))) | unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(reverse_line(N46_54_11))))))
% 113.15/21.90 -> [3520] unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11))))
% 113.15/21.90 -> [3521] unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(reverse_line(N46_54_11)))))
% 113.15/21.90
% 113.15/21.90 [3520] CLOSURE : unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11))))
% 113.15/21.90
% 113.15/21.90 [3521] GAMMA_FORALL : ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50)))))
% 113.15/21.90 -> [3523] ((unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11)))) & unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(reverse_line(N46_54_11)))))) => (left_convergent_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11)))) | left_convergent_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(reverse_line(N46_54_11)))))))
% 113.15/21.90
% 113.15/21.90 [3523] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11)))) & unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(reverse_line(N46_54_11)))))) => (left_convergent_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11)))) | left_convergent_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(reverse_line(N46_54_11)))))))
% 113.15/21.90 -> [3524] ~(unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11)))) & unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(reverse_line(N46_54_11))))))
% 113.15/21.90 -> [3525] (left_convergent_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11)))) | left_convergent_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(reverse_line(N46_54_11))))))
% 113.15/21.90
% 113.15/21.90 [3525] BETA_OR : (left_convergent_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11)))) | left_convergent_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(reverse_line(N46_54_11))))))
% 113.15/21.90 -> [3528] left_convergent_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11))))
% 113.15/21.90 -> [3529] left_convergent_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(reverse_line(N46_54_11)))))
% 113.15/21.90
% 113.15/21.90 [3528] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 113.15/21.90 -> [3532] ~(left_apart_point(A51_74_14, L52_74_14) | left_apart_point(A51_74_14, reverse_line(L52_74_14)))
% 113.15/21.90
% 113.15/21.90 [3532] ALPHA_NOT_OR : ~(left_apart_point(A51_74_14, L52_74_14) | left_apart_point(A51_74_14, reverse_line(L52_74_14)))
% 113.15/21.90 -> [3534] ~left_apart_point(A51_74_14, L52_74_14), ~left_apart_point(A51_74_14, reverse_line(L52_74_14))
% 113.15/21.90
% 113.15/21.90 [3534] CLOSURE : ~left_apart_point(A51_74_14, L52_74_14)
% 113.15/21.90
% 113.15/21.90 [3529] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 113.15/21.90 -> [3533] ~(left_apart_point(A51_75_14, L52_75_14) | left_apart_point(A51_75_14, reverse_line(L52_75_14)))
% 113.15/21.90
% 113.15/21.90 [3533] ALPHA_NOT_OR : ~(left_apart_point(A51_75_14, L52_75_14) | left_apart_point(A51_75_14, reverse_line(L52_75_14)))
% 113.15/21.90 -> [3535] ~left_apart_point(A51_75_14, L52_75_14), ~left_apart_point(A51_75_14, reverse_line(L52_75_14))
% 113.15/21.90
% 113.15/21.90 [3535] CLOSURE : ~left_apart_point(A51_75_14, L52_75_14)
% 113.15/21.90
% 113.15/21.90 [3524] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11)))) & unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(reverse_line(N46_54_11))))))
% 113.15/21.90 -> [3526] ~unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(N46_54_11))))
% 113.15/21.90 -> [3527] ~unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(reverse_line(N46_54_11)))))
% 113.15/21.90
% 113.15/21.90 [3527] CLOSURE : ~unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(reverse_line(reverse_line(N46_54_11)))))
% 113.15/21.90
% 113.15/21.90 [3526] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 113.15/21.90 -> [3553] ~(left_apart_point(A51_76_14, L52_76_14) | left_apart_point(A51_76_14, reverse_line(L52_76_14)))
% 113.15/21.90
% 113.15/21.90 [3553] ALPHA_NOT_OR : ~(left_apart_point(A51_76_14, L52_76_14) | left_apart_point(A51_76_14, reverse_line(L52_76_14)))
% 113.15/21.90 -> [3554] ~left_apart_point(A51_76_14, L52_76_14), ~left_apart_point(A51_76_14, reverse_line(L52_76_14))
% 113.15/21.90
% 113.15/21.90 [3554] CLOSURE : ~left_apart_point(A51_76_14, L52_76_14)
% 113.15/21.90
% 113.15/21.90 [3492] BETA_OR : ((unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) & unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11)))) | (unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(N46_54_11)) & unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(reverse_line(N46_54_11)))))
% 113.15/21.90 -> [3565] (unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) & unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11))))
% 113.15/21.90 -> [3566] (unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(N46_54_11)) & unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(reverse_line(N46_54_11))))
% 113.15/21.90
% 113.15/21.90 [3565] ALPHA_AND : (unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) & unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11))))
% 113.15/21.90 -> [3567] unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)), unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11)))
% 113.15/21.90
% 113.15/21.90 [3567] CLOSURE : unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11)))
% 113.15/21.90
% 113.15/21.90 [3566] ALPHA_AND : (unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(N46_54_11)) & unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(reverse_line(N46_54_11))))
% 113.15/21.90 -> [3568] unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(N46_54_11)), unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(reverse_line(N46_54_11)))
% 113.15/21.90
% 113.15/21.90 [3568] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 113.15/21.90 -> [3570] (unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) | unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11))))
% 113.15/21.90
% 113.15/21.90 [3570] BETA_OR : (unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11)) | unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11))))
% 113.15/21.90 -> [3573] unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11))
% 113.15/21.90 -> [3574] unequally_directed_lines(reverse_line(N46_54_11), reverse_line(reverse_line(N46_54_11)))
% 113.15/21.90
% 113.15/21.90 [3573] CLOSURE : unequally_directed_lines(reverse_line(N46_54_11), reverse_line(N46_54_11))
% 113.15/21.90
% 113.15/21.90 [3574] GAMMA_FORALL : ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50)))))
% 113.15/21.90 -> [3585] ((unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), M50_29_13) & unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(M50_29_13))) => (left_convergent_lines(reverse_line(reverse_line(N46_54_11)), M50_29_13) | left_convergent_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(M50_29_13))))
% 113.15/21.90
% 113.15/21.90 [3585] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), M50_29_13) & unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(M50_29_13))) => (left_convergent_lines(reverse_line(reverse_line(N46_54_11)), M50_29_13) | left_convergent_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(M50_29_13))))
% 113.15/21.90 -> [3587] ~(unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), M50_29_13) & unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(M50_29_13)))
% 113.15/21.90 -> [3588] (left_convergent_lines(reverse_line(reverse_line(N46_54_11)), M50_29_13) | left_convergent_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(M50_29_13)))
% 113.15/21.90
% 113.15/21.90 [3587] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), M50_29_13) & unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(M50_29_13)))
% 113.15/21.90 -> [3592] ~unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), M50_29_13)
% 113.15/21.90 -> [3593] ~unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(M50_29_13))
% 113.15/21.90
% 113.15/21.90 [3592] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), M50_29_13)
% 113.15/21.90
% 113.15/21.90 [3593] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(M50_29_13))
% 113.15/21.90
% 113.15/21.90 [3588] BETA_OR : (left_convergent_lines(reverse_line(reverse_line(N46_54_11)), M50_29_13) | left_convergent_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(M50_29_13)))
% 113.15/21.90 -> [3594] left_convergent_lines(reverse_line(reverse_line(N46_54_11)), M50_29_13)
% 113.15/21.90 -> [3595] left_convergent_lines(reverse_line(reverse_line(N46_54_11)), reverse_line(M50_29_13))
% 113.15/21.90
% 113.15/21.90 [3594] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 113.15/21.90 -> [3596] ~(left_apart_point(A51_81_14, L52_81_14) | left_apart_point(A51_81_14, reverse_line(L52_81_14)))
% 113.15/21.90
% 113.15/21.90 [3596] ALPHA_NOT_OR : ~(left_apart_point(A51_81_14, L52_81_14) | left_apart_point(A51_81_14, reverse_line(L52_81_14)))
% 113.15/21.90 -> [3598] ~left_apart_point(A51_81_14, L52_81_14), ~left_apart_point(A51_81_14, reverse_line(L52_81_14))
% 113.15/21.90
% 113.15/21.90 [3598] CLOSURE : ~left_apart_point(A51_81_14, L52_81_14)
% 113.15/21.90
% 113.15/21.90 [3595] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 113.15/21.90 -> [3597] ~(left_apart_point(A51_82_14, L52_82_14) | left_apart_point(A51_82_14, reverse_line(L52_82_14)))
% 113.15/21.90
% 113.15/21.90 [3597] ALPHA_NOT_OR : ~(left_apart_point(A51_82_14, L52_82_14) | left_apart_point(A51_82_14, reverse_line(L52_82_14)))
% 113.15/21.90 -> [3599] ~left_apart_point(A51_82_14, L52_82_14), ~left_apart_point(A51_82_14, reverse_line(L52_82_14))
% 113.15/21.90
% 113.15/21.90 [3599] CLOSURE : ~left_apart_point(A51_82_14, L52_82_14)
% 113.15/21.90
% 113.15/21.90 [2589] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 113.15/21.90 -> [2591] (equally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) <=> ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [2591] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) <=> ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)))
% 113.15/21.90 -> [2593] ~equally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)), ~~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90 -> [2594] equally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)), ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90
% 113.15/21.90 [2593] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90 -> [2597] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90
% 113.15/21.90 [2597] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90
% 113.15/21.90 [2599] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4))
% 113.15/21.90 -> [3864] ~equally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 113.15/21.90 -> [3865] equally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4), ~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 113.15/21.90
% 113.15/21.90 [3865] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 113.15/21.90 -> [3867] ~distinct_points(C35_23_6, C35_23_6)
% 113.15/21.90
% 113.15/21.90 [3867] GAMMA_FORALL : ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35))))
% 113.15/21.90 -> [3868] (distinct_points(C35_23_6, C35_23_6) => (distinct_points(C35_23_6, C35_23_6) | distinct_points(C35_23_6, C35_23_6)))
% 113.15/21.90
% 113.15/21.90 [3868] BETA_IMPLY : (distinct_points(C35_23_6, C35_23_6) => (distinct_points(C35_23_6, C35_23_6) | distinct_points(C35_23_6, C35_23_6)))
% 113.15/21.90 -> [3869] ~distinct_points(C35_23_6, C35_23_6)
% 113.15/21.90 -> [3870] (distinct_points(C35_23_6, C35_23_6) | distinct_points(C35_23_6, C35_23_6))
% 113.15/21.90
% 113.15/21.90 [3870] BETA_OR : (distinct_points(C35_23_6, C35_23_6) | distinct_points(C35_23_6, C35_23_6))
% 113.15/21.90 -> [3871] distinct_points(C35_23_6, C35_23_6)
% 113.15/21.90 -> [3872] distinct_points(C35_23_6, C35_23_6)
% 113.15/21.90
% 113.15/21.90 [3872] CLOSURE : distinct_points(C35_23_6, C35_23_6)
% 113.15/21.90
% 113.15/21.90 [3871] CLOSURE : distinct_points(C35_23_6, C35_23_6)
% 113.15/21.90
% 113.15/21.90 [3876] BETA_IMPLY : (distinct_lines(N39_34_8, N39_34_8) => (distinct_lines(N39_34_8, N39_34_8) | distinct_lines(N39_34_8, N39_34_8)))
% 113.15/21.90 -> [4428] ~distinct_lines(N39_34_8, N39_34_8)
% 113.15/21.90 -> [4429] (distinct_lines(N39_34_8, N39_34_8) | distinct_lines(N39_34_8, N39_34_8))
% 113.15/21.90
% 113.15/21.90 [4428] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 113.15/21.90 -> [4432] equally_directed_lines(L40_62_9, L40_62_9)
% 113.15/21.90
% 113.15/21.90 [4432] GAMMA_FORALL : ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43))))
% 113.15/21.90 -> [4433] (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) => (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))))
% 113.15/21.90
% 113.15/21.90 [4433] BETA_IMPLY : (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) => (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))))
% 113.15/21.90 -> [4434] ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90 -> [4435] (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4435] BETA_OR : (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)))
% 113.15/21.90 -> [4436] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90 -> [4437] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90
% 113.15/21.90 [4437] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90
% 113.15/21.90 [4436] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90
% 113.15/21.90 [4438] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(reverse_line(Y17_14_4))))) => ((unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))) | (unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(reverse_line(Y17_14_4))))))
% 113.15/21.90 -> [4518] ~(unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(reverse_line(Y17_14_4)))))
% 113.15/21.90 -> [4519] ((unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))) | (unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(reverse_line(Y17_14_4)))))
% 113.15/21.90
% 113.15/21.90 [4518] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(reverse_line(Y17_14_4)))))
% 113.15/21.90 -> [4520] ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90 -> [4521] ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90
% 113.15/21.90 [4520] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 113.15/21.90 -> [4526] (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90
% 113.15/21.90 [4526] BETA_OR : (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90 -> [4528] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90 -> [4529] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4528] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90
% 113.15/21.90 [4529] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4527] BETA_OR : (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))) | unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(reverse_line(Y17_14_4)))))
% 113.15/21.90 -> [4548] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90 -> [4549] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90
% 113.15/21.90 [4549] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90
% 113.15/21.90 [4548] GAMMA_FORALL : ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50)))))
% 113.15/21.90 -> [4550] ((unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))) => (left_convergent_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))))
% 113.15/21.90
% 113.15/21.90 [4550] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))) => (left_convergent_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))))
% 113.15/21.90 -> [4551] ~(unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90 -> [4552] (left_convergent_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90
% 113.15/21.90 [4551] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90 -> [4555] ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90 -> [4556] ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4556] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4555] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 113.15/21.90 -> [4561] ~(left_apart_point(A51_115_14, L52_115_14) | left_apart_point(A51_115_14, reverse_line(L52_115_14)))
% 113.15/21.90
% 113.15/21.90 [4561] ALPHA_NOT_OR : ~(left_apart_point(A51_115_14, L52_115_14) | left_apart_point(A51_115_14, reverse_line(L52_115_14)))
% 113.15/21.90 -> [4562] ~left_apart_point(A51_115_14, L52_115_14), ~left_apart_point(A51_115_14, reverse_line(L52_115_14))
% 113.15/21.90
% 113.15/21.90 [4562] CLOSURE : ~left_apart_point(A51_115_14, L52_115_14)
% 113.15/21.90
% 113.15/21.90 [4552] BETA_OR : (left_convergent_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90 -> [4576] left_convergent_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90 -> [4577] left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4577] CLOSURE : left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4576] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 113.15/21.90 -> [4580] ~(left_apart_point(A51_120_14, L52_120_14) | left_apart_point(A51_120_14, reverse_line(L52_120_14)))
% 113.15/21.90
% 113.15/21.90 [4580] ALPHA_NOT_OR : ~(left_apart_point(A51_120_14, L52_120_14) | left_apart_point(A51_120_14, reverse_line(L52_120_14)))
% 113.15/21.90 -> [4581] ~left_apart_point(A51_120_14, L52_120_14), ~left_apart_point(A51_120_14, reverse_line(L52_120_14))
% 113.15/21.90
% 113.15/21.90 [4581] CLOSURE : ~left_apart_point(A51_120_14, L52_120_14)
% 113.15/21.90
% 113.15/21.90 [4519] BETA_OR : ((unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))) | (unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(reverse_line(Y17_14_4)))))
% 113.15/21.90 -> [4588] (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90 -> [4589] (unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90
% 113.15/21.90 [4588] ALPHA_AND : (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90 -> [4592] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)), unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4592] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4589] ALPHA_AND : (unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90 -> [4593] unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(Y17_14_4)), unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4593] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 113.15/21.90 -> [4600] (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90
% 113.15/21.90 [4600] BETA_OR : (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90 -> [4601] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90 -> [4602] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4601] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90
% 113.15/21.90 [4602] GAMMA_FORALL : ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50)))))
% 113.15/21.90 -> [4605] ((unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))) => (left_convergent_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))))
% 113.15/21.90
% 113.15/21.90 [4605] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))) => (left_convergent_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))))
% 113.15/21.90 -> [4606] ~(unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90 -> [4607] (left_convergent_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90
% 113.15/21.90 [4607] BETA_OR : (left_convergent_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90 -> [4610] left_convergent_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90 -> [4611] left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4611] CLOSURE : left_convergent_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4610] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 113.15/21.90 -> [4614] ~(left_apart_point(A51_121_14, L52_121_14) | left_apart_point(A51_121_14, reverse_line(L52_121_14)))
% 113.15/21.90
% 113.15/21.90 [4614] ALPHA_NOT_OR : ~(left_apart_point(A51_121_14, L52_121_14) | left_apart_point(A51_121_14, reverse_line(L52_121_14)))
% 113.15/21.90 -> [4617] ~left_apart_point(A51_121_14, L52_121_14), ~left_apart_point(A51_121_14, reverse_line(L52_121_14))
% 113.15/21.90
% 113.15/21.90 [4617] CLOSURE : ~left_apart_point(A51_121_14, L52_121_14)
% 113.15/21.90
% 113.15/21.90 [4606] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))
% 113.15/21.90 -> [4629] ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 113.15/21.90 -> [4630] ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4630] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 113.15/21.90
% 113.15/21.90 [4629] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 113.15/21.90 -> [4634] ~(left_apart_point(A51_122_14, L52_122_14) | left_apart_point(A51_122_14, reverse_line(L52_122_14)))
% 113.15/21.90
% 113.15/21.90 [4634] ALPHA_NOT_OR : ~(left_apart_point(A51_122_14, L52_122_14) | left_apart_point(A51_122_14, reverse_line(L52_122_14)))
% 113.15/21.90 -> [4637] ~left_apart_point(A51_122_14, L52_122_14), ~left_apart_point(A51_122_14, reverse_line(L52_122_14))
% 113.15/21.90
% 113.15/21.90 [4637] CLOSURE : ~left_apart_point(A51_122_14, L52_122_14)
% 113.15/21.90
% 113.15/21.90 [4429] BETA_OR : (distinct_lines(N39_34_8, N39_34_8) | distinct_lines(N39_34_8, N39_34_8))
% 113.15/21.90 -> [4672] distinct_lines(N39_34_8, N39_34_8)
% 113.15/21.90 -> [4673] distinct_lines(N39_34_8, N39_34_8)
% 113.15/21.90
% 113.15/21.90 [4673] CLOSURE : distinct_lines(N39_34_8, N39_34_8)
% 113.15/21.90
% 113.15/21.90 [4672] CLOSURE : distinct_lines(N39_34_8, N39_34_8)
% 113.15/21.90
% 113.15/21.90 [3866] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 113.15/21.90
% 113.15/21.90 [9] GAMMA_FORALL : ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9))))
% 113.15/21.90 -> [11] (unequally_directed_opposite_lines(reverse_line(Y9_0_0), Y9_0_0) <=> unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)))
% 113.15/21.90
% 113.15/21.90 [11] BETA_EQUIV : (unequally_directed_opposite_lines(reverse_line(Y9_0_0), Y9_0_0) <=> unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)))
% 113.15/21.90 -> [13] ~unequally_directed_opposite_lines(reverse_line(Y9_0_0), Y9_0_0), ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 113.15/21.90 -> [14] unequally_directed_opposite_lines(reverse_line(Y9_0_0), Y9_0_0), unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 113.15/21.90
% 113.15/21.90 [14] GAMMA_FORALL : ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11))))
% 113.15/21.90 -> [22] (right_apart_point(skolem_B9090, skolem_L9191) <=> left_apart_point(skolem_B9090, reverse_line(skolem_L9191)))
% 113.15/21.90
% 113.15/21.90 [22] BETA_EQUIV : (right_apart_point(skolem_B9090, skolem_L9191) <=> left_apart_point(skolem_B9090, reverse_line(skolem_L9191)))
% 113.15/21.90 -> [25] ~right_apart_point(skolem_B9090, skolem_L9191), ~left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 113.15/21.90 -> [26] right_apart_point(skolem_B9090, skolem_L9191), left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 113.15/21.90
% 113.15/21.90 [26] CLOSURE : right_apart_point(skolem_B9090, skolem_L9191)
% 113.15/21.90
% 113.15/21.90 [32] BETA_EQUIV : (right_convergent_lines(X12_1_2, Y13_1_2) <=> left_convergent_lines(X12_1_2, reverse_line(Y13_1_2)))
% 113.15/21.90 -> [921] ~right_convergent_lines(X12_1_2, Y13_1_2), ~left_convergent_lines(X12_1_2, reverse_line(Y13_1_2))
% 113.15/21.90 -> [922] right_convergent_lines(X12_1_2, Y13_1_2), left_convergent_lines(X12_1_2, reverse_line(Y13_1_2))
% 113.15/21.90
% 113.15/21.90 [921] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 113.15/21.90 -> [926] (equally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)) <=> ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)))
% 113.15/21.90
% 113.15/21.90 [926] BETA_EQUIV : (equally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)) <=> ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)))
% 113.15/21.90 -> [927] ~equally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)), ~~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 113.15/21.90 -> [928] equally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)), ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 113.15/21.90
% 113.15/21.90 [927] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 113.15/21.90 -> [929] unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 113.15/21.90
% 113.15/21.90 [929] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 113.15/21.90 -> [933] (equally_directed_opposite_lines(X16_9_4, Y17_9_4) <=> ~unequally_directed_opposite_lines(X16_9_4, Y17_9_4))
% 113.15/21.90
% 113.15/21.90 [933] BETA_EQUIV : (equally_directed_opposite_lines(X16_9_4, Y17_9_4) <=> ~unequally_directed_opposite_lines(X16_9_4, Y17_9_4))
% 113.15/21.90 -> [934] ~equally_directed_opposite_lines(X16_9_4, Y17_9_4), ~~unequally_directed_opposite_lines(X16_9_4, Y17_9_4)
% 113.15/21.90 -> [935] equally_directed_opposite_lines(X16_9_4, Y17_9_4), ~unequally_directed_opposite_lines(X16_9_4, Y17_9_4)
% 113.15/21.90
% 113.15/21.90 [934] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(X16_9_4, Y17_9_4)
% 113.15/21.90 -> [945] unequally_directed_opposite_lines(X16_9_4, Y17_9_4)
% 113.15/21.90
% 113.15/21.90 [945] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 113.15/21.90 -> [953] ~distinct_points(C35_10_6, C35_10_6)
% 113.15/21.90
% 113.15/21.90 [953] GAMMA_FORALL : ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35))))
% 113.15/21.90 -> [963] (distinct_points(C35_10_6, C35_10_6) => (distinct_points(C35_10_6, C35_10_6) | distinct_points(C35_10_6, C35_10_6)))
% 113.15/21.90
% 113.15/21.90 [963] BETA_IMPLY : (distinct_points(C35_10_6, C35_10_6) => (distinct_points(C35_10_6, C35_10_6) | distinct_points(C35_10_6, C35_10_6)))
% 113.15/21.90 -> [964] ~distinct_points(C35_10_6, C35_10_6)
% 113.15/21.90 -> [965] (distinct_points(C35_10_6, C35_10_6) | distinct_points(C35_10_6, C35_10_6))
% 113.15/21.90
% 113.15/21.90 [965] BETA_OR : (distinct_points(C35_10_6, C35_10_6) | distinct_points(C35_10_6, C35_10_6))
% 113.15/21.90 -> [966] distinct_points(C35_10_6, C35_10_6)
% 113.15/21.90 -> [967] distinct_points(C35_10_6, C35_10_6)
% 113.15/21.90
% 113.15/21.90 [966] CLOSURE : distinct_points(C35_10_6, C35_10_6)
% 113.15/21.90
% 113.15/21.90 [967] CLOSURE : distinct_points(C35_10_6, C35_10_6)
% 113.15/21.90
% 113.15/21.90 [975] BETA_IMPLY : (distinct_lines(L37_15_8, L37_15_8) => (distinct_lines(L37_15_8, L37_15_8) | distinct_lines(L37_15_8, L37_15_8)))
% 113.15/21.90 -> [1047] ~distinct_lines(L37_15_8, L37_15_8)
% 113.15/21.90 -> [1048] (distinct_lines(L37_15_8, L37_15_8) | distinct_lines(L37_15_8, L37_15_8))
% 113.15/21.90
% 113.15/21.90 [1048] BETA_OR : (distinct_lines(L37_15_8, L37_15_8) | distinct_lines(L37_15_8, L37_15_8))
% 113.15/21.90 -> [1049] distinct_lines(L37_15_8, L37_15_8)
% 113.15/21.90 -> [1050] distinct_lines(L37_15_8, L37_15_8)
% 113.15/21.90
% 113.15/21.90 [1050] CLOSURE : distinct_lines(L37_15_8, L37_15_8)
% 113.15/21.90
% 113.15/21.90 [1049] CLOSURE : distinct_lines(L37_15_8, L37_15_8)
% 113.15/21.90
% 113.15/21.90 [1051] CLOSURE : equally_directed_lines(L40_29_9, L40_29_9)
% 113.15/21.90
% 113.15/21.90 [935] CLOSURE : ~unequally_directed_opposite_lines(X16_9_4, Y17_9_4)
% 113.15/21.90
% 113.15/21.90 [928] CLOSURE : ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 113.15/21.90
% 113.15/21.90 [922] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 113.15/21.90 -> [923] (equally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)) <=> ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)))
% 113.15/21.90
% 113.15/21.90 [923] BETA_EQUIV : (equally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)) <=> ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)))
% 113.15/21.90 -> [924] ~equally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)), ~~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 113.15/21.90 -> [925] equally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)), ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 113.15/21.90
% 113.15/21.90 [924] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 113.15/21.90 -> [930] unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 113.15/21.90
% 113.15/21.90 [930] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 113.15/21.90 -> [936] (equally_directed_opposite_lines(X16_10_4, Y17_10_4) <=> ~unequally_directed_opposite_lines(X16_10_4, Y17_10_4))
% 113.15/21.90
% 113.15/21.90 [936] BETA_EQUIV : (equally_directed_opposite_lines(X16_10_4, Y17_10_4) <=> ~unequally_directed_opposite_lines(X16_10_4, Y17_10_4))
% 113.15/21.90 -> [940] ~equally_directed_opposite_lines(X16_10_4, Y17_10_4), ~~unequally_directed_opposite_lines(X16_10_4, Y17_10_4)
% 113.15/21.90 -> [941] equally_directed_opposite_lines(X16_10_4, Y17_10_4), ~unequally_directed_opposite_lines(X16_10_4, Y17_10_4)
% 113.15/21.90
% 113.15/21.90 [941] CLOSURE : ~unequally_directed_opposite_lines(X16_10_4, Y17_10_4)
% 113.15/21.90
% 113.15/21.90 [968] BETA_IMPLY : (distinct_points(C35_11_6, C35_11_6) => (distinct_points(C35_11_6, C35_11_6) | distinct_points(C35_11_6, C35_11_6)))
% 113.15/21.90 -> [1089] ~distinct_points(C35_11_6, C35_11_6)
% 113.15/21.90 -> [1090] (distinct_points(C35_11_6, C35_11_6) | distinct_points(C35_11_6, C35_11_6))
% 113.15/21.90
% 113.15/21.90 [1090] BETA_OR : (distinct_points(C35_11_6, C35_11_6) | distinct_points(C35_11_6, C35_11_6))
% 113.15/21.90 -> [1091] distinct_points(C35_11_6, C35_11_6)
% 113.15/21.90 -> [1092] distinct_points(C35_11_6, C35_11_6)
% 113.15/21.90
% 113.15/21.90 [1091] CLOSURE : distinct_points(C35_11_6, C35_11_6)
% 113.15/21.90
% 113.15/21.90 [1092] CLOSURE : distinct_points(C35_11_6, C35_11_6)
% 113.15/21.90
% 113.15/21.90 [1100] BETA_IMPLY : (distinct_lines(N39_17_8, N39_17_8) => (distinct_lines(N39_17_8, N39_17_8) | distinct_lines(N39_17_8, N39_17_8)))
% 113.15/21.90 -> [1160] ~distinct_lines(N39_17_8, N39_17_8)
% 113.15/21.90 -> [1161] (distinct_lines(N39_17_8, N39_17_8) | distinct_lines(N39_17_8, N39_17_8))
% 113.15/21.90
% 113.15/21.90 [1161] BETA_OR : (distinct_lines(N39_17_8, N39_17_8) | distinct_lines(N39_17_8, N39_17_8))
% 113.15/21.90 -> [1168] distinct_lines(N39_17_8, N39_17_8)
% 113.15/21.90 -> [1169] distinct_lines(N39_17_8, N39_17_8)
% 113.15/21.90
% 113.15/21.90 [1168] CLOSURE : distinct_lines(N39_17_8, N39_17_8)
% 113.15/21.90
% 113.15/21.90 [1169] CLOSURE : distinct_lines(N39_17_8, N39_17_8)
% 113.15/21.90
% 113.15/21.90 [1175] CLOSURE : equally_directed_lines(L40_32_9, L40_32_9)
% 113.15/21.90
% 113.15/21.90 [925] CLOSURE : ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 113.15/21.90
% 113.15/21.90 [17] BETA_EQUIV : (right_apart_point(skolem_B9090, skolem_L9191) <=> left_apart_point(skolem_B9090, reverse_line(skolem_L9191)))
% 113.15/21.90 -> [5315] ~right_apart_point(skolem_B9090, skolem_L9191), ~left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 113.15/21.90 -> [5316] right_apart_point(skolem_B9090, skolem_L9191), left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 113.15/21.90
% 113.15/21.90 [5316] CLOSURE : right_apart_point(skolem_B9090, skolem_L9191)
% 113.15/21.90
% 113.15/21.90 [5315] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 113.15/21.90 -> [5317] (right_convergent_lines(reverse_line(Y17_19_4), Y17_19_4) <=> left_convergent_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)))
% 113.15/21.90
% 113.15/21.90 [5317] BETA_EQUIV : (right_convergent_lines(reverse_line(Y17_19_4), Y17_19_4) <=> left_convergent_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)))
% 113.15/21.90 -> [5318] ~right_convergent_lines(reverse_line(Y17_19_4), Y17_19_4), ~left_convergent_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90 -> [5319] right_convergent_lines(reverse_line(Y17_19_4), Y17_19_4), left_convergent_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90
% 113.15/21.90 [5319] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 113.15/21.90 -> [5321] (equally_directed_lines(reverse_line(Y17_20_4), reverse_line(Y17_20_4)) <=> ~unequally_directed_lines(reverse_line(Y17_20_4), reverse_line(Y17_20_4)))
% 113.15/21.90
% 113.15/21.90 [5321] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_20_4), reverse_line(Y17_20_4)) <=> ~unequally_directed_lines(reverse_line(Y17_20_4), reverse_line(Y17_20_4)))
% 113.15/21.90 -> [5324] ~equally_directed_lines(reverse_line(Y17_20_4), reverse_line(Y17_20_4)), ~~unequally_directed_lines(reverse_line(Y17_20_4), reverse_line(Y17_20_4))
% 113.15/21.90 -> [5325] equally_directed_lines(reverse_line(Y17_20_4), reverse_line(Y17_20_4)), ~unequally_directed_lines(reverse_line(Y17_20_4), reverse_line(Y17_20_4))
% 113.15/21.90
% 113.15/21.90 [5324] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_20_4), reverse_line(Y17_20_4))
% 113.15/21.90 -> [5327] unequally_directed_lines(reverse_line(Y17_20_4), reverse_line(Y17_20_4))
% 113.15/21.90
% 113.15/21.90 [5327] CLOSURE : unequally_directed_lines(reverse_line(Y17_20_4), reverse_line(Y17_20_4))
% 113.15/21.90
% 113.15/21.90 [5329] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_20_4), Y17_20_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_20_4), Y17_20_4))
% 113.15/21.90 -> [6230] ~equally_directed_opposite_lines(reverse_line(Y17_20_4), Y17_20_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_20_4), Y17_20_4)
% 113.15/21.90 -> [6231] equally_directed_opposite_lines(reverse_line(Y17_20_4), Y17_20_4), ~unequally_directed_opposite_lines(reverse_line(Y17_20_4), Y17_20_4)
% 113.15/21.90
% 113.15/21.90 [6230] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_20_4), Y17_20_4)
% 113.15/21.90 -> [6233] unequally_directed_opposite_lines(reverse_line(Y17_20_4), Y17_20_4)
% 113.15/21.90
% 113.15/21.90 [6233] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_20_4), Y17_20_4)
% 113.15/21.90
% 113.15/21.90 [6231] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 113.15/21.90 -> [6234] ~distinct_points(C35_30_6, C35_30_6)
% 113.15/21.90
% 113.15/21.90 [6234] GAMMA_FORALL : ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35))))
% 113.15/21.90 -> [6235] (distinct_points(C35_30_6, C35_30_6) => (distinct_points(C35_30_6, C35_30_6) | distinct_points(C35_30_6, C35_30_6)))
% 113.15/21.90
% 113.15/21.90 [6235] BETA_IMPLY : (distinct_points(C35_30_6, C35_30_6) => (distinct_points(C35_30_6, C35_30_6) | distinct_points(C35_30_6, C35_30_6)))
% 113.15/21.90 -> [6236] ~distinct_points(C35_30_6, C35_30_6)
% 113.15/21.90 -> [6237] (distinct_points(C35_30_6, C35_30_6) | distinct_points(C35_30_6, C35_30_6))
% 113.15/21.90
% 113.15/21.90 [6237] BETA_OR : (distinct_points(C35_30_6, C35_30_6) | distinct_points(C35_30_6, C35_30_6))
% 113.15/21.90 -> [6238] distinct_points(C35_30_6, C35_30_6)
% 113.15/21.90 -> [6239] distinct_points(C35_30_6, C35_30_6)
% 113.15/21.90
% 113.15/21.90 [6239] CLOSURE : distinct_points(C35_30_6, C35_30_6)
% 113.15/21.90
% 113.15/21.90 [6238] CLOSURE : distinct_points(C35_30_6, C35_30_6)
% 113.15/21.90
% 113.15/21.90 [6236] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 113.15/21.90 -> [6242] ~distinct_lines(M38_44_8, M38_44_8)
% 113.15/21.90
% 113.15/21.90 [6242] GAMMA_FORALL : ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39))))
% 113.15/21.90 -> [6246] (distinct_lines(M38_44_8, M38_44_8) => (distinct_lines(M38_44_8, M38_44_8) | distinct_lines(M38_44_8, M38_44_8)))
% 113.15/21.90
% 113.15/21.90 [6246] BETA_IMPLY : (distinct_lines(M38_44_8, M38_44_8) => (distinct_lines(M38_44_8, M38_44_8) | distinct_lines(M38_44_8, M38_44_8)))
% 113.15/21.90 -> [6248] ~distinct_lines(M38_44_8, M38_44_8)
% 113.15/21.90 -> [6249] (distinct_lines(M38_44_8, M38_44_8) | distinct_lines(M38_44_8, M38_44_8))
% 113.15/21.90
% 113.15/21.90 [6249] BETA_OR : (distinct_lines(M38_44_8, M38_44_8) | distinct_lines(M38_44_8, M38_44_8))
% 113.15/21.90 -> [6250] distinct_lines(M38_44_8, M38_44_8)
% 113.15/21.90 -> [6251] distinct_lines(M38_44_8, M38_44_8)
% 113.15/21.90
% 113.15/21.90 [6250] CLOSURE : distinct_lines(M38_44_8, M38_44_8)
% 113.15/21.90
% 113.15/21.90 [6251] CLOSURE : distinct_lines(M38_44_8, M38_44_8)
% 113.15/21.90
% 113.15/21.90 [6248] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 113.15/21.90 -> [6252] equally_directed_lines(L40_77_9, L40_77_9)
% 113.15/21.90
% 113.15/21.90 [6252] GAMMA_FORALL : ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43))))
% 113.15/21.90 -> [6253] (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) => (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) | unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11))))
% 113.15/21.90
% 113.15/21.90 [6253] BETA_IMPLY : (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) => (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) | unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11))))
% 113.15/21.90 -> [6254] ~unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11))
% 113.15/21.90 -> [6255] (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) | unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)))
% 113.15/21.90
% 113.15/21.90 [6255] BETA_OR : (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) | unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)))
% 113.15/21.90 -> [6256] unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11))
% 113.15/21.90 -> [6257] unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11))
% 113.15/21.90
% 113.15/21.90 [6256] CLOSURE : unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11))
% 113.15/21.90
% 113.15/21.90 [6257] CLOSURE : unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11))
% 113.15/21.90
% 113.15/21.90 [6258] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))) => ((unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))) | (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))))))
% 113.15/21.90 -> [6337] ~(unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))))
% 113.15/21.90 -> [6338] ((unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))) | (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))))
% 113.15/21.90
% 113.15/21.90 [6337] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))))
% 113.15/21.90 -> [6339] ~unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11))
% 113.15/21.90 -> [6340] ~unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))
% 113.15/21.90
% 113.15/21.90 [6340] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 113.15/21.90 -> [6352] (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) | unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))))
% 113.15/21.90
% 113.15/21.90 [6352] BETA_OR : (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) | unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))))
% 113.15/21.90 -> [6353] unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11))
% 113.15/21.90 -> [6354] unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))
% 113.15/21.90
% 113.15/21.90 [6353] CLOSURE : unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11))
% 113.15/21.90
% 113.15/21.90 [6354] CLOSURE : unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))
% 113.15/21.90
% 113.15/21.90 [6349] BETA_OR : (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) | unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))))
% 113.15/21.90 -> [6357] unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11))
% 113.15/21.90 -> [6358] unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))
% 113.15/21.90
% 113.15/21.90 [6357] CLOSURE : unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11))
% 113.15/21.90
% 113.15/21.90 [6358] GAMMA_FORALL : ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50)))))
% 113.15/21.90 -> [6361] ((unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(reverse_line(N46_101_11))))) => (left_convergent_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))) | left_convergent_lines(reverse_line(N46_101_11), reverse_line(reverse_line(reverse_line(N46_101_11))))))
% 113.15/21.90
% 113.15/21.90 [6361] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(reverse_line(N46_101_11))))) => (left_convergent_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))) | left_convergent_lines(reverse_line(N46_101_11), reverse_line(reverse_line(reverse_line(N46_101_11))))))
% 113.15/21.90 -> [6362] ~(unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(reverse_line(N46_101_11)))))
% 113.15/21.90 -> [6363] (left_convergent_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))) | left_convergent_lines(reverse_line(N46_101_11), reverse_line(reverse_line(reverse_line(N46_101_11)))))
% 113.15/21.90
% 113.15/21.90 [6363] BETA_OR : (left_convergent_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))) | left_convergent_lines(reverse_line(N46_101_11), reverse_line(reverse_line(reverse_line(N46_101_11)))))
% 113.15/21.90 -> [6366] left_convergent_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))
% 113.15/21.90 -> [6367] left_convergent_lines(reverse_line(N46_101_11), reverse_line(reverse_line(reverse_line(N46_101_11))))
% 113.15/21.90
% 113.15/21.90 [6366] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 113.15/21.90 -> [6368] ~(left_apart_point(A51_198_14, L52_198_14) | left_apart_point(A51_198_14, reverse_line(L52_198_14)))
% 113.15/21.90
% 113.15/21.90 [6368] ALPHA_NOT_OR : ~(left_apart_point(A51_198_14, L52_198_14) | left_apart_point(A51_198_14, reverse_line(L52_198_14)))
% 113.15/21.90 -> [6370] ~left_apart_point(A51_198_14, L52_198_14), ~left_apart_point(A51_198_14, reverse_line(L52_198_14))
% 113.15/21.90
% 113.15/21.90 [6370] CLOSURE : ~left_apart_point(A51_198_14, L52_198_14)
% 113.15/21.90
% 113.15/21.90 [6367] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 113.15/21.90 -> [6369] ~(left_apart_point(A51_199_14, L52_199_14) | left_apart_point(A51_199_14, reverse_line(L52_199_14)))
% 113.15/21.90
% 113.15/21.90 [6369] ALPHA_NOT_OR : ~(left_apart_point(A51_199_14, L52_199_14) | left_apart_point(A51_199_14, reverse_line(L52_199_14)))
% 113.15/21.90 -> [6371] ~left_apart_point(A51_199_14, L52_199_14), ~left_apart_point(A51_199_14, reverse_line(L52_199_14))
% 113.15/21.90
% 113.15/21.90 [6371] CLOSURE : ~left_apart_point(A51_199_14, L52_199_14)
% 113.15/21.90
% 113.15/21.90 [6362] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(reverse_line(N46_101_11)))))
% 113.15/21.90 -> [6364] ~unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))
% 113.15/21.90 -> [6365] ~unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(reverse_line(N46_101_11))))
% 113.15/21.90
% 113.15/21.90 [6364] CLOSURE : ~unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))
% 113.15/21.90
% 113.15/21.90 [6365] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 113.15/21.90 -> [6372] ~(left_apart_point(A51_200_14, L52_200_14) | left_apart_point(A51_200_14, reverse_line(L52_200_14)))
% 113.15/21.90
% 113.15/21.90 [6372] ALPHA_NOT_OR : ~(left_apart_point(A51_200_14, L52_200_14) | left_apart_point(A51_200_14, reverse_line(L52_200_14)))
% 113.15/21.90 -> [6373] ~left_apart_point(A51_200_14, L52_200_14), ~left_apart_point(A51_200_14, reverse_line(L52_200_14))
% 113.15/21.90
% 113.15/21.90 [6373] CLOSURE : ~left_apart_point(A51_200_14, L52_200_14)
% 113.15/21.90
% 113.15/21.90 [6338] BETA_OR : ((unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))) | (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))))
% 113.15/21.90 -> [6374] (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))))
% 113.15/21.90 -> [6375] (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))))
% 113.15/21.90
% 113.15/21.90 [6374] ALPHA_AND : (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))))
% 113.15/21.90 -> [6376] unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)), unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))
% 113.15/21.90
% 113.15/21.90 [6376] CLOSURE : unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))
% 113.15/21.90
% 113.15/21.90 [6375] ALPHA_AND : (unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)) & unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11))))
% 113.15/21.90 -> [6377] unequally_directed_lines(reverse_line(N46_101_11), reverse_line(N46_101_11)), unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))
% 113.15/21.90
% 113.15/21.90 [6377] CLOSURE : unequally_directed_lines(reverse_line(N46_101_11), reverse_line(reverse_line(N46_101_11)))
% 113.15/21.90
% 113.15/21.90 [5318] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 113.15/21.90 -> [5320] (equally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) <=> ~unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)))
% 113.15/21.90
% 113.15/21.90 [5320] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) <=> ~unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)))
% 113.15/21.90 -> [5322] ~equally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)), ~~unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90 -> [5323] equally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)), ~unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90
% 113.15/21.90 [5322] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90 -> [5326] unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90
% 113.15/21.90 [5326] CLOSURE : unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90
% 113.15/21.90 [5328] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_19_4), Y17_19_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_19_4), Y17_19_4))
% 113.15/21.90 -> [5887] ~equally_directed_opposite_lines(reverse_line(Y17_19_4), Y17_19_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_19_4), Y17_19_4)
% 113.15/21.90 -> [5888] equally_directed_opposite_lines(reverse_line(Y17_19_4), Y17_19_4), ~unequally_directed_opposite_lines(reverse_line(Y17_19_4), Y17_19_4)
% 113.15/21.90
% 113.15/21.90 [5888] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 113.15/21.90 -> [5890] ~distinct_points(A33_29_6, A33_29_6)
% 113.15/21.90
% 113.15/21.90 [5890] GAMMA_FORALL : ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35))))
% 113.15/21.90 -> [5891] (distinct_points(A33_29_6, A33_29_6) => (distinct_points(A33_29_6, A33_29_6) | distinct_points(A33_29_6, A33_29_6)))
% 113.15/21.90
% 113.15/21.90 [5891] BETA_IMPLY : (distinct_points(A33_29_6, A33_29_6) => (distinct_points(A33_29_6, A33_29_6) | distinct_points(A33_29_6, A33_29_6)))
% 113.15/21.90 -> [5892] ~distinct_points(A33_29_6, A33_29_6)
% 113.15/21.90 -> [5893] (distinct_points(A33_29_6, A33_29_6) | distinct_points(A33_29_6, A33_29_6))
% 113.15/21.90
% 113.15/21.90 [5893] BETA_OR : (distinct_points(A33_29_6, A33_29_6) | distinct_points(A33_29_6, A33_29_6))
% 113.15/21.90 -> [5894] distinct_points(A33_29_6, A33_29_6)
% 113.15/21.90 -> [5895] distinct_points(A33_29_6, A33_29_6)
% 113.15/21.90
% 113.15/21.90 [5895] CLOSURE : distinct_points(A33_29_6, A33_29_6)
% 113.15/21.90
% 113.15/21.90 [5894] CLOSURE : distinct_points(A33_29_6, A33_29_6)
% 113.15/21.90
% 113.15/21.90 [5897] BETA_IMPLY : (distinct_lines(N39_43_8, N39_43_8) => (distinct_lines(N39_43_8, N39_43_8) | distinct_lines(N39_43_8, N39_43_8)))
% 113.15/21.90 -> [6378] ~distinct_lines(N39_43_8, N39_43_8)
% 113.15/21.90 -> [6379] (distinct_lines(N39_43_8, N39_43_8) | distinct_lines(N39_43_8, N39_43_8))
% 113.15/21.90
% 113.15/21.90 [6379] BETA_OR : (distinct_lines(N39_43_8, N39_43_8) | distinct_lines(N39_43_8, N39_43_8))
% 113.15/21.90 -> [6380] distinct_lines(N39_43_8, N39_43_8)
% 113.15/21.90 -> [6381] distinct_lines(N39_43_8, N39_43_8)
% 113.15/21.90
% 113.15/21.90 [6380] CLOSURE : distinct_lines(N39_43_8, N39_43_8)
% 113.15/21.90
% 113.15/21.90 [6381] CLOSURE : distinct_lines(N39_43_8, N39_43_8)
% 113.15/21.90
% 113.15/21.90 [6383] BETA_IMPLY : (unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) => (unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) | unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))))
% 113.15/21.90 -> [6465] ~unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90 -> [6466] (unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) | unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)))
% 113.15/21.90
% 113.15/21.90 [6466] BETA_OR : (unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) | unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)))
% 113.15/21.90 -> [6467] unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90 -> [6468] unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90
% 113.15/21.90 [6467] CLOSURE : unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90
% 113.15/21.90 [6468] CLOSURE : unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90
% 113.15/21.90 [6469] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))) => ((unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))) | (unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4))))))
% 113.15/21.90 -> [6492] ~(unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4))))
% 113.15/21.90 -> [6493] ((unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))) | (unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))))
% 113.15/21.90
% 113.15/21.90 [6493] BETA_OR : ((unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))) | (unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))))
% 113.15/21.90 -> [6494] (unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4))))
% 113.15/21.90 -> [6495] (unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4))))
% 113.15/21.90
% 113.15/21.90 [6494] ALPHA_AND : (unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4))))
% 113.15/21.90 -> [6499] unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)), unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))
% 113.15/21.90
% 113.15/21.90 [6499] CLOSURE : unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))
% 113.15/21.90
% 113.15/21.90 [6498] CLOSURE : unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90
% 113.15/21.90 [6492] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4))))
% 113.15/21.90 -> [6523] ~unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90 -> [6524] ~unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))
% 113.15/21.90
% 113.15/21.90 [6524] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 113.15/21.90 -> [6526] (unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) | unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4))))
% 113.15/21.90
% 113.15/21.90 [6526] BETA_OR : (unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) | unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4))))
% 113.15/21.90 -> [6529] unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90 -> [6530] unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))
% 113.15/21.90
% 113.15/21.90 [6529] CLOSURE : unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90
% 113.15/21.90 [6530] CLOSURE : unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))
% 113.15/21.90
% 113.15/21.90 [6523] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 113.15/21.90 -> [6525] (unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) | unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4))))
% 113.15/21.90
% 113.15/21.90 [6525] BETA_OR : (unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) | unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4))))
% 113.15/21.90 -> [6527] unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90 -> [6528] unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))
% 113.15/21.90
% 113.15/21.90 [6527] CLOSURE : unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90
% 113.15/21.90 [6528] GAMMA_FORALL : ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50)))))
% 113.15/21.90 -> [6531] ((unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))) => (left_convergent_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) | left_convergent_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))))
% 113.15/21.90
% 113.15/21.90 [6531] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))) => (left_convergent_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) | left_convergent_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))))
% 113.15/21.90 -> [6532] ~(unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4))))
% 113.15/21.90 -> [6533] (left_convergent_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) | left_convergent_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4))))
% 113.15/21.90
% 113.15/21.90 [6532] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) & unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4))))
% 113.15/21.90 -> [6534] ~unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90 -> [6535] ~unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))
% 113.15/21.90
% 113.15/21.90 [6535] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))
% 113.15/21.90
% 113.15/21.90 [6534] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 113.15/21.90 -> [6538] ~(left_apart_point(A51_210_14, L52_210_14) | left_apart_point(A51_210_14, reverse_line(L52_210_14)))
% 113.15/21.90
% 113.15/21.90 [6538] ALPHA_NOT_OR : ~(left_apart_point(A51_210_14, L52_210_14) | left_apart_point(A51_210_14, reverse_line(L52_210_14)))
% 113.15/21.90 -> [6539] ~left_apart_point(A51_210_14, L52_210_14), ~left_apart_point(A51_210_14, reverse_line(L52_210_14))
% 113.15/21.90
% 113.15/21.90 [6539] CLOSURE : ~left_apart_point(A51_210_14, L52_210_14)
% 113.15/21.90
% 113.15/21.90 [6533] BETA_OR : (left_convergent_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4)) | left_convergent_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4))))
% 113.15/21.90 -> [6542] left_convergent_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90 -> [6543] left_convergent_lines(reverse_line(Y17_19_4), reverse_line(reverse_line(Y17_19_4)))
% 113.15/21.90
% 113.15/21.90 [6542] CLOSURE : left_convergent_lines(reverse_line(Y17_19_4), reverse_line(Y17_19_4))
% 113.15/21.90
% 113.15/21.90 [6543] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 113.15/21.90 -> [6544] ~(left_apart_point(A51_212_14, L52_212_14) | left_apart_point(A51_212_14, reverse_line(L52_212_14)))
% 113.15/21.90
% 113.15/21.90 [6544] ALPHA_NOT_OR : ~(left_apart_point(A51_212_14, L52_212_14) | left_apart_point(A51_212_14, reverse_line(L52_212_14)))
% 113.15/21.90 -> [6545] ~left_apart_point(A51_212_14, L52_212_14), ~left_apart_point(A51_212_14, reverse_line(L52_212_14))
% 113.15/21.90
% 113.15/21.90 [6545] CLOSURE : ~left_apart_point(A51_212_14, L52_212_14)
% 113.15/21.90
% 113.15/21.90 [5889] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_19_4), Y17_19_4)
% 113.15/21.90
% 113.15/21.90 % SZS output end Proof for theBenchmark.p
% 113.15/21.90 [21.555785s][1][Res] 291674 goroutines created
% 113.15/21.90 ==== Result ====
% 113.15/21.90 [21.555825s][1][Res] VALID
% 113.15/21.90 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------