TSTP Solution File: GEO251+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO251+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n003.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 15:18:44 EDT 2022
% Result : Theorem 68.30s 20.28s
% Output : Proof 68.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO251+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : goeland -dmt -presko -proof %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 07:11:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.35 [DMT] DMT loaded with preskolemization
% 0.19/0.35 [EQ] equality loaded.
% 0.19/0.35 [0.000041s][1][MAIN] Problem : theBenchmark.p
% 0.19/0.36 Conjecture not found
% 0.19/0.36 Start search
% 0.19/0.36 nb_step : 1 - limit : 37
% 0.19/0.36 Launch Gotab with destructive = true
% 68.30/20.27 % SZS output start Proof for theBenchmark.p
% 68.30/20.28 [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] : ((right_apart_point(B90_90, parallel_through_point(L91_91, A89_89)) => left_apart_point(A89_89, parallel_through_point(L91_91, B90_90)))))
% 68.30/20.28 -> [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] : ((right_apart_point(B90_90, parallel_through_point(L91_91, A89_89)) => left_apart_point(A89_89, parallel_through_point(L91_91, B90_90))))
% 68.30/20.28
% 68.30/20.28 [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)))))
% 68.30/20.28 -> [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))))
% 68.30/20.28
% 68.30/20.28 [2] DELTA_NOT_FORALL : ~! [A89_89, B90_90, L91_91] : ((right_apart_point(B90_90, parallel_through_point(L91_91, A89_89)) => left_apart_point(A89_89, parallel_through_point(L91_91, B90_90))))
% 68.30/20.28 -> [3] ~(right_apart_point(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989)) => left_apart_point(skolem_A8989, parallel_through_point(skolem_L9191, skolem_B9090)))
% 68.30/20.28
% 68.30/20.28 [3] ALPHA_NOT_IMPLY : ~(right_apart_point(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989)) => left_apart_point(skolem_A8989, parallel_through_point(skolem_L9191, skolem_B9090)))
% 68.30/20.28 -> [4] right_apart_point(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989)), ~left_apart_point(skolem_A8989, parallel_through_point(skolem_L9191, skolem_B9090))
% 68.30/20.28
% 68.30/20.28 [4] GAMMA_FORALL : ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9))))
% 68.30/20.28 -> [5] (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)))
% 68.30/20.28
% 68.30/20.28 [5] 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)))
% 68.30/20.28 -> [6] ~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))
% 68.30/20.28 -> [7] 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))
% 68.30/20.28
% 68.30/20.28 [7] GAMMA_FORALL : ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11))))
% 68.30/20.28 -> [9] (right_apart_point(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989)) <=> left_apart_point(skolem_B9090, reverse_line(parallel_through_point(skolem_L9191, skolem_A8989))))
% 68.30/20.28
% 68.30/20.28 [9] BETA_EQUIV : (right_apart_point(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989)) <=> left_apart_point(skolem_B9090, reverse_line(parallel_through_point(skolem_L9191, skolem_A8989))))
% 68.30/20.28 -> [12] ~right_apart_point(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989)), ~left_apart_point(skolem_B9090, reverse_line(parallel_through_point(skolem_L9191, skolem_A8989)))
% 68.30/20.28 -> [13] right_apart_point(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989)), left_apart_point(skolem_B9090, reverse_line(parallel_through_point(skolem_L9191, skolem_A8989)))
% 68.30/20.28
% 68.30/20.28 [12] CLOSURE : ~right_apart_point(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989))
% 68.30/20.28
% 68.30/20.28 [15] BETA_EQUIV : (right_convergent_lines(X12_1_2, Y13_1_2) <=> left_convergent_lines(X12_1_2, reverse_line(Y13_1_2)))
% 68.30/20.28 -> [430] ~right_convergent_lines(X12_1_2, Y13_1_2), ~left_convergent_lines(X12_1_2, reverse_line(Y13_1_2))
% 68.30/20.28 -> [431] right_convergent_lines(X12_1_2, Y13_1_2), left_convergent_lines(X12_1_2, reverse_line(Y13_1_2))
% 68.30/20.28
% 68.30/20.28 [431] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 68.30/20.28 -> [433] (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)))
% 68.30/20.28
% 68.30/20.28 [433] 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)))
% 68.30/20.28 -> [436] ~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))
% 68.30/20.28 -> [437] 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))
% 68.30/20.28
% 68.30/20.28 [436] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 68.30/20.28 -> [439] unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 68.30/20.28
% 68.30/20.28 [439] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 68.30/20.28 -> [441] (equally_directed_opposite_lines(X16_6_4, Y17_6_4) <=> ~unequally_directed_opposite_lines(X16_6_4, Y17_6_4))
% 68.30/20.28
% 68.30/20.28 [441] BETA_EQUIV : (equally_directed_opposite_lines(X16_6_4, Y17_6_4) <=> ~unequally_directed_opposite_lines(X16_6_4, Y17_6_4))
% 68.30/20.28 -> [444] ~equally_directed_opposite_lines(X16_6_4, Y17_6_4), ~~unequally_directed_opposite_lines(X16_6_4, Y17_6_4)
% 68.30/20.28 -> [445] equally_directed_opposite_lines(X16_6_4, Y17_6_4), ~unequally_directed_opposite_lines(X16_6_4, Y17_6_4)
% 68.30/20.28
% 68.30/20.28 [444] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(X16_6_4, Y17_6_4)
% 68.30/20.28 -> [447] unequally_directed_opposite_lines(X16_6_4, Y17_6_4)
% 68.30/20.28
% 68.30/20.28 [447] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 68.30/20.28 -> [458] ~distinct_points(C35_7_6, C35_7_6)
% 68.30/20.28
% 68.30/20.28 [458] 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))))
% 68.30/20.28 -> [478] (distinct_points(C35_7_6, C35_7_6) => (distinct_points(C35_7_6, C35_7_6) | distinct_points(C35_7_6, C35_7_6)))
% 68.30/20.28
% 68.30/20.28 [478] BETA_IMPLY : (distinct_points(C35_7_6, C35_7_6) => (distinct_points(C35_7_6, C35_7_6) | distinct_points(C35_7_6, C35_7_6)))
% 68.30/20.28 -> [480] ~distinct_points(C35_7_6, C35_7_6)
% 68.30/20.28 -> [481] (distinct_points(C35_7_6, C35_7_6) | distinct_points(C35_7_6, C35_7_6))
% 68.30/20.28
% 68.30/20.28 [481] BETA_OR : (distinct_points(C35_7_6, C35_7_6) | distinct_points(C35_7_6, C35_7_6))
% 68.30/20.28 -> [489] distinct_points(C35_7_6, C35_7_6)
% 68.30/20.28 -> [490] distinct_points(C35_7_6, C35_7_6)
% 68.30/20.28
% 68.30/20.28 [490] CLOSURE : distinct_points(C35_7_6, C35_7_6)
% 68.30/20.28
% 68.30/20.28 [489] CLOSURE : distinct_points(C35_7_6, C35_7_6)
% 68.30/20.28
% 68.30/20.28 [508] BETA_IMPLY : (distinct_lines(N39_9_8, N39_9_8) => (distinct_lines(N39_9_8, N39_9_8) | distinct_lines(N39_9_8, N39_9_8)))
% 68.30/20.28 -> [532] ~distinct_lines(N39_9_8, N39_9_8)
% 68.30/20.28 -> [533] (distinct_lines(N39_9_8, N39_9_8) | distinct_lines(N39_9_8, N39_9_8))
% 68.30/20.28
% 68.30/20.28 [533] BETA_OR : (distinct_lines(N39_9_8, N39_9_8) | distinct_lines(N39_9_8, N39_9_8))
% 68.30/20.28 -> [534] distinct_lines(N39_9_8, N39_9_8)
% 68.30/20.28 -> [535] distinct_lines(N39_9_8, N39_9_8)
% 68.30/20.28
% 68.30/20.28 [534] CLOSURE : distinct_lines(N39_9_8, N39_9_8)
% 68.30/20.28
% 68.30/20.28 [535] CLOSURE : distinct_lines(N39_9_8, N39_9_8)
% 68.30/20.28
% 68.30/20.28 [537] CLOSURE : equally_directed_lines(L40_18_9, L40_18_9)
% 68.30/20.28
% 68.30/20.28 [445] CLOSURE : ~unequally_directed_opposite_lines(X16_6_4, Y17_6_4)
% 68.30/20.28
% 68.30/20.28 [437] CLOSURE : ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 68.30/20.28
% 68.30/20.28 [430] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 68.30/20.28 -> [432] (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)))
% 68.30/20.28
% 68.30/20.28 [432] 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)))
% 68.30/20.28 -> [434] ~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))
% 68.30/20.28 -> [435] 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))
% 68.30/20.28
% 68.30/20.28 [434] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 68.30/20.28 -> [438] unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 68.30/20.28
% 68.30/20.28 [438] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 68.30/20.28 -> [440] (equally_directed_opposite_lines(X16_5_4, Y17_5_4) <=> ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4))
% 68.30/20.28
% 68.30/20.28 [440] BETA_EQUIV : (equally_directed_opposite_lines(X16_5_4, Y17_5_4) <=> ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4))
% 68.30/20.28 -> [442] ~equally_directed_opposite_lines(X16_5_4, Y17_5_4), ~~unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 68.30/20.28 -> [443] equally_directed_opposite_lines(X16_5_4, Y17_5_4), ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 68.30/20.28
% 68.30/20.28 [443] CLOSURE : ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 68.30/20.28
% 68.30/20.28 [463] 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)))
% 68.30/20.28 -> [556] ~distinct_points(C35_6_6, C35_6_6)
% 68.30/20.28 -> [557] (distinct_points(C35_6_6, C35_6_6) | distinct_points(C35_6_6, C35_6_6))
% 68.30/20.28
% 68.30/20.28 [557] BETA_OR : (distinct_points(C35_6_6, C35_6_6) | distinct_points(C35_6_6, C35_6_6))
% 68.30/20.28 -> [558] distinct_points(C35_6_6, C35_6_6)
% 68.30/20.28 -> [559] distinct_points(C35_6_6, C35_6_6)
% 68.30/20.28
% 68.30/20.28 [558] CLOSURE : distinct_points(C35_6_6, C35_6_6)
% 68.30/20.28
% 68.30/20.28 [559] CLOSURE : distinct_points(C35_6_6, C35_6_6)
% 68.30/20.28
% 68.30/20.28 [561] BETA_IMPLY : (distinct_lines(N39_10_8, N39_10_8) => (distinct_lines(N39_10_8, N39_10_8) | distinct_lines(N39_10_8, N39_10_8)))
% 68.30/20.28 -> [585] ~distinct_lines(N39_10_8, N39_10_8)
% 68.30/20.28 -> [586] (distinct_lines(N39_10_8, N39_10_8) | distinct_lines(N39_10_8, N39_10_8))
% 68.30/20.28
% 68.30/20.28 [585] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 68.30/20.28 -> [593] equally_directed_lines(L40_20_9, L40_20_9)
% 68.30/20.28
% 68.30/20.28 [593] CLOSURE : equally_directed_lines(L40_20_9, L40_20_9)
% 68.30/20.28
% 68.30/20.28 [586] BETA_OR : (distinct_lines(N39_10_8, N39_10_8) | distinct_lines(N39_10_8, N39_10_8))
% 68.30/20.28 -> [609] distinct_lines(N39_10_8, N39_10_8)
% 68.30/20.28 -> [610] distinct_lines(N39_10_8, N39_10_8)
% 68.30/20.28
% 68.30/20.28 [609] CLOSURE : distinct_lines(N39_10_8, N39_10_8)
% 68.30/20.28
% 68.30/20.28 [610] CLOSURE : distinct_lines(N39_10_8, N39_10_8)
% 68.30/20.28
% 68.30/20.28 [435] CLOSURE : ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 68.30/20.28
% 68.30/20.28 [8] BETA_EQUIV : (right_apart_point(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989)) <=> left_apart_point(skolem_B9090, reverse_line(parallel_through_point(skolem_L9191, skolem_A8989))))
% 68.30/20.28 -> [3174] ~right_apart_point(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989)), ~left_apart_point(skolem_B9090, reverse_line(parallel_through_point(skolem_L9191, skolem_A8989)))
% 68.30/20.28 -> [3175] right_apart_point(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989)), left_apart_point(skolem_B9090, reverse_line(parallel_through_point(skolem_L9191, skolem_A8989)))
% 68.30/20.28
% 68.30/20.28 [3174] CLOSURE : ~right_apart_point(skolem_B9090, parallel_through_point(skolem_L9191, skolem_A8989))
% 68.30/20.28
% 68.30/20.28 [3175] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 68.30/20.28 -> [3176] (right_convergent_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(Y17_14_4)) <=> left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(reverse_line(Y17_14_4))))
% 68.30/20.28
% 68.30/20.28 [3176] BETA_EQUIV : (right_convergent_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(Y17_14_4)) <=> left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(reverse_line(Y17_14_4))))
% 68.30/20.28 -> [3177] ~right_convergent_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(Y17_14_4)), ~left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28 -> [3178] right_convergent_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(Y17_14_4)), left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28
% 68.30/20.28 [3178] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 68.30/20.28 -> [3180] (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)))
% 68.30/20.28
% 68.30/20.28 [3180] 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)))
% 68.30/20.28 -> [3183] ~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))
% 68.30/20.28 -> [3184] 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))
% 68.30/20.28
% 68.30/20.28 [3183] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28 -> [3186] unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28
% 68.30/20.28 [3186] CLOSURE : unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28
% 68.30/20.28 [3188] 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))
% 68.30/20.28 -> [3790] ~equally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4)
% 68.30/20.28 -> [3791] equally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4), ~unequally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4)
% 68.30/20.28
% 68.30/20.28 [3790] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4)
% 68.30/20.28 -> [3794] unequally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4)
% 68.30/20.28
% 68.30/20.28 [3794] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_15_4), Y17_15_4)
% 68.30/20.28
% 68.30/20.28 [3791] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 68.30/20.28 -> [3795] ~distinct_points(C35_19_6, C35_19_6)
% 68.30/20.28
% 68.30/20.28 [3795] 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))))
% 68.30/20.28 -> [3796] (distinct_points(C35_19_6, C35_19_6) => (distinct_points(C35_19_6, C35_19_6) | distinct_points(C35_19_6, C35_19_6)))
% 68.30/20.28
% 68.30/20.28 [3796] BETA_IMPLY : (distinct_points(C35_19_6, C35_19_6) => (distinct_points(C35_19_6, C35_19_6) | distinct_points(C35_19_6, C35_19_6)))
% 68.30/20.28 -> [3797] ~distinct_points(C35_19_6, C35_19_6)
% 68.30/20.28 -> [3798] (distinct_points(C35_19_6, C35_19_6) | distinct_points(C35_19_6, C35_19_6))
% 68.30/20.28
% 68.30/20.28 [3798] BETA_OR : (distinct_points(C35_19_6, C35_19_6) | distinct_points(C35_19_6, C35_19_6))
% 68.30/20.28 -> [3799] distinct_points(C35_19_6, C35_19_6)
% 68.30/20.28 -> [3800] distinct_points(C35_19_6, C35_19_6)
% 68.30/20.28
% 68.30/20.28 [3800] CLOSURE : distinct_points(C35_19_6, C35_19_6)
% 68.30/20.28
% 68.30/20.28 [3799] CLOSURE : distinct_points(C35_19_6, C35_19_6)
% 68.30/20.28
% 68.30/20.28 [3797] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 68.30/20.28 -> [3801] ~distinct_lines(N39_29_8, N39_29_8)
% 68.30/20.28
% 68.30/20.28 [3801] 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))))
% 68.30/20.28 -> [3804] (distinct_lines(N39_29_8, N39_29_8) => (distinct_lines(N39_29_8, N39_29_8) | distinct_lines(N39_29_8, N39_29_8)))
% 68.30/20.28
% 68.30/20.28 [3804] BETA_IMPLY : (distinct_lines(N39_29_8, N39_29_8) => (distinct_lines(N39_29_8, N39_29_8) | distinct_lines(N39_29_8, N39_29_8)))
% 68.30/20.28 -> [3806] ~distinct_lines(N39_29_8, N39_29_8)
% 68.30/20.28 -> [3807] (distinct_lines(N39_29_8, N39_29_8) | distinct_lines(N39_29_8, N39_29_8))
% 68.30/20.28
% 68.30/20.28 [3807] BETA_OR : (distinct_lines(N39_29_8, N39_29_8) | distinct_lines(N39_29_8, N39_29_8))
% 68.30/20.28 -> [3811] distinct_lines(N39_29_8, N39_29_8)
% 68.30/20.28 -> [3812] distinct_lines(N39_29_8, N39_29_8)
% 68.30/20.28
% 68.30/20.28 [3812] CLOSURE : distinct_lines(N39_29_8, N39_29_8)
% 68.30/20.28
% 68.30/20.28 [3811] CLOSURE : distinct_lines(N39_29_8, N39_29_8)
% 68.30/20.28
% 68.30/20.28 [3806] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 68.30/20.28 -> [3813] equally_directed_lines(L40_48_9, L40_48_9)
% 68.30/20.28
% 68.30/20.28 [3813] 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))))
% 68.30/20.28 -> [3814] (unequally_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)) | unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))))
% 68.30/20.28
% 68.30/20.28 [3814] BETA_IMPLY : (unequally_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)) | unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))))
% 68.30/20.28 -> [3815] ~unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28 -> [3816] (unequally_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)))
% 68.30/20.28
% 68.30/20.28 [3816] BETA_OR : (unequally_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)))
% 68.30/20.28 -> [3817] unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28 -> [3818] unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28
% 68.30/20.28 [3818] CLOSURE : unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28
% 68.30/20.28 [3817] CLOSURE : unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28
% 68.30/20.28 [3819] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))) => ((unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))) | (unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4))))))
% 68.30/20.28 -> [3846] ~(unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4))))
% 68.30/20.28 -> [3847] ((unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))) | (unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))))
% 68.30/20.28
% 68.30/20.28 [3847] BETA_OR : ((unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))) | (unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))))
% 68.30/20.28 -> [3851] (unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4))))
% 68.30/20.28 -> [3852] (unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4))))
% 68.30/20.28
% 68.30/20.28 [3852] ALPHA_AND : (unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4))))
% 68.30/20.28 -> [3856] unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)), unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))
% 68.30/20.28
% 68.30/20.28 [3856] CLOSURE : unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))
% 68.30/20.28
% 68.30/20.28 [3855] CLOSURE : unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28
% 68.30/20.28 [3846] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4))))
% 68.30/20.28 -> [3900] ~unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28 -> [3901] ~unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))
% 68.30/20.28
% 68.30/20.28 [3901] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 68.30/20.28 -> [3903] (unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) | unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4))))
% 68.30/20.28
% 68.30/20.28 [3903] BETA_OR : (unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) | unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4))))
% 68.30/20.28 -> [3906] unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28 -> [3907] unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))
% 68.30/20.28
% 68.30/20.28 [3906] CLOSURE : unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28
% 68.30/20.28 [3907] CLOSURE : unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))
% 68.30/20.28
% 68.30/20.28 [3900] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 68.30/20.28 -> [3902] (unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) | unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4))))
% 68.30/20.28
% 68.30/20.28 [3902] BETA_OR : (unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) | unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4))))
% 68.30/20.28 -> [3904] unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28 -> [3905] unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))
% 68.30/20.28
% 68.30/20.28 [3904] CLOSURE : unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28
% 68.30/20.28 [3905] 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)))))
% 68.30/20.28 -> [3908] ((unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))) => (left_convergent_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) | left_convergent_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))))
% 68.30/20.28
% 68.30/20.28 [3908] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))) => (left_convergent_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) | left_convergent_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))))
% 68.30/20.28 -> [3909] ~(unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4))))
% 68.30/20.28 -> [3910] (left_convergent_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) | left_convergent_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4))))
% 68.30/20.28
% 68.30/20.28 [3910] BETA_OR : (left_convergent_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) | left_convergent_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4))))
% 68.30/20.28 -> [3913] left_convergent_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28 -> [3914] left_convergent_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))
% 68.30/20.28
% 68.30/20.28 [3913] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 68.30/20.28 -> [3918] ~(left_apart_point(A51_141_14, L52_141_14) | left_apart_point(A51_141_14, reverse_line(L52_141_14)))
% 68.30/20.28
% 68.30/20.28 [3918] ALPHA_NOT_OR : ~(left_apart_point(A51_141_14, L52_141_14) | left_apart_point(A51_141_14, reverse_line(L52_141_14)))
% 68.30/20.28 -> [3920] ~left_apart_point(A51_141_14, L52_141_14), ~left_apart_point(A51_141_14, reverse_line(L52_141_14))
% 68.30/20.28
% 68.30/20.28 [3920] CLOSURE : ~left_apart_point(A51_141_14, L52_141_14)
% 68.30/20.28
% 68.30/20.28 [3914] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 68.30/20.28 -> [3917] ~(left_apart_point(A51_140_14, L52_140_14) | left_apart_point(A51_140_14, reverse_line(L52_140_14)))
% 68.30/20.28
% 68.30/20.28 [3917] ALPHA_NOT_OR : ~(left_apart_point(A51_140_14, L52_140_14) | left_apart_point(A51_140_14, reverse_line(L52_140_14)))
% 68.30/20.28 -> [3919] ~left_apart_point(A51_140_14, L52_140_14), ~left_apart_point(A51_140_14, reverse_line(L52_140_14))
% 68.30/20.28
% 68.30/20.28 [3919] CLOSURE : ~left_apart_point(A51_140_14, L52_140_14)
% 68.30/20.28
% 68.30/20.28 [3909] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4)) & unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4))))
% 68.30/20.28 -> [3911] ~unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(Y17_15_4))
% 68.30/20.28 -> [3912] ~unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))
% 68.30/20.28
% 68.30/20.28 [3912] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_15_4), reverse_line(reverse_line(Y17_15_4)))
% 68.30/20.28
% 68.30/20.28 [3911] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 68.30/20.28 -> [3921] ~(left_apart_point(A51_142_14, L52_142_14) | left_apart_point(A51_142_14, reverse_line(L52_142_14)))
% 68.30/20.28
% 68.30/20.28 [3921] ALPHA_NOT_OR : ~(left_apart_point(A51_142_14, L52_142_14) | left_apart_point(A51_142_14, reverse_line(L52_142_14)))
% 68.30/20.28 -> [3922] ~left_apart_point(A51_142_14, L52_142_14), ~left_apart_point(A51_142_14, reverse_line(L52_142_14))
% 68.30/20.28
% 68.30/20.28 [3922] CLOSURE : ~left_apart_point(A51_142_14, L52_142_14)
% 68.30/20.28
% 68.30/20.28 [3177] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 68.30/20.28 -> [3179] (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)))
% 68.30/20.28
% 68.30/20.28 [3179] 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)))
% 68.30/20.28 -> [3181] ~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))
% 68.30/20.28 -> [3182] 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))
% 68.30/20.28
% 68.30/20.28 [3181] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28 -> [3185] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28
% 68.30/20.28 [3185] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28
% 68.30/20.28 [3187] 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))
% 68.30/20.28 -> [3923] ~equally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 68.30/20.28 -> [3924] equally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4), ~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 68.30/20.28
% 68.30/20.28 [3924] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 68.30/20.28 -> [3926] ~distinct_points(A33_20_6, A33_20_6)
% 68.30/20.28
% 68.30/20.28 [3926] 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))))
% 68.30/20.28 -> [3927] (distinct_points(A33_20_6, A33_20_6) => (distinct_points(A33_20_6, A33_20_6) | distinct_points(A33_20_6, A33_20_6)))
% 68.30/20.28
% 68.30/20.28 [3927] BETA_IMPLY : (distinct_points(A33_20_6, A33_20_6) => (distinct_points(A33_20_6, A33_20_6) | distinct_points(A33_20_6, A33_20_6)))
% 68.30/20.28 -> [3928] ~distinct_points(A33_20_6, A33_20_6)
% 68.30/20.28 -> [3929] (distinct_points(A33_20_6, A33_20_6) | distinct_points(A33_20_6, A33_20_6))
% 68.30/20.28
% 68.30/20.28 [3929] BETA_OR : (distinct_points(A33_20_6, A33_20_6) | distinct_points(A33_20_6, A33_20_6))
% 68.30/20.28 -> [3930] distinct_points(A33_20_6, A33_20_6)
% 68.30/20.28 -> [3931] distinct_points(A33_20_6, A33_20_6)
% 68.30/20.28
% 68.30/20.28 [3931] CLOSURE : distinct_points(A33_20_6, A33_20_6)
% 68.30/20.28
% 68.30/20.28 [3930] CLOSURE : distinct_points(A33_20_6, A33_20_6)
% 68.30/20.28
% 68.30/20.28 [3933] BETA_IMPLY : (distinct_lines(N39_30_8, N39_30_8) => (distinct_lines(N39_30_8, N39_30_8) | distinct_lines(N39_30_8, N39_30_8)))
% 68.30/20.28 -> [4097] ~distinct_lines(N39_30_8, N39_30_8)
% 68.30/20.28 -> [4098] (distinct_lines(N39_30_8, N39_30_8) | distinct_lines(N39_30_8, N39_30_8))
% 68.30/20.28
% 68.30/20.28 [4098] BETA_OR : (distinct_lines(N39_30_8, N39_30_8) | distinct_lines(N39_30_8, N39_30_8))
% 68.30/20.28 -> [4099] distinct_lines(N39_30_8, N39_30_8)
% 68.30/20.28 -> [4100] distinct_lines(N39_30_8, N39_30_8)
% 68.30/20.28
% 68.30/20.28 [4100] CLOSURE : distinct_lines(N39_30_8, N39_30_8)
% 68.30/20.28
% 68.30/20.28 [4099] CLOSURE : distinct_lines(N39_30_8, N39_30_8)
% 68.30/20.28
% 68.30/20.28 [4102] 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(Y17_14_4)) | unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(Y17_14_4))))
% 68.30/20.28 -> [4182] ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28 -> [4183] (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(Y17_14_4)))
% 68.30/20.28
% 68.30/20.28 [4182] GAMMA_FORALL : ! [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))))))
% 68.30/20.28 -> [4186] ((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(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(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))))
% 68.30/20.28
% 68.30/20.28 [4186] 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)))) => ((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(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))))
% 68.30/20.28 -> [4187] ~(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))))
% 68.30/20.28 -> [4188] ((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(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))))
% 68.30/20.28
% 68.30/20.28 [4188] 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(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))))
% 68.30/20.28 -> [4191] (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))))
% 68.30/20.28 -> [4192] (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))))
% 68.30/20.28
% 68.30/20.28 [4191] 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))))
% 68.30/20.28 -> [4193] 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)))
% 68.30/20.28
% 68.30/20.28 [4193] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28
% 68.30/20.28 [4194] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28
% 68.30/20.28 [4187] 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))))
% 68.30/20.28 -> [4201] ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28 -> [4202] ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28
% 68.30/20.28 [4202] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 68.30/20.28 -> [4206] (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))))
% 68.30/20.28
% 68.30/20.28 [4206] 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))))
% 68.30/20.28 -> [4207] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28 -> [4208] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28
% 68.30/20.28 [4208] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28
% 68.30/20.28 [4207] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28
% 68.30/20.28 [4201] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 68.30/20.28 -> [4203] (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))))
% 68.30/20.28
% 68.30/20.28 [4203] 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))))
% 68.30/20.28 -> [4204] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28 -> [4205] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28
% 68.30/20.28 [4204] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28
% 68.30/20.28 [4205] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28
% 68.30/20.28 [4183] BETA_OR : (unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) | unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(Y17_14_4)))
% 68.30/20.28 -> [4209] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28 -> [4210] unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(Y17_14_4))
% 68.30/20.28
% 68.30/20.28 [4210] GAMMA_FORALL : ! [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))))))
% 68.30/20.28 -> [4211] ((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(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(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))))
% 68.30/20.28
% 68.30/20.28 [4211] 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)))) => ((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(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4))))))
% 68.30/20.28 -> [4212] ~(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))))
% 68.30/20.28 -> [4213] ((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(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))))
% 68.30/20.28
% 68.30/20.28 [4213] 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(Y17_14_4), reverse_line(Y17_14_4)) & unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))))
% 68.30/20.28 -> [4216] (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))))
% 68.30/20.28 -> [4217] (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))))
% 68.30/20.28
% 68.30/20.28 [4216] 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))))
% 68.30/20.28 -> [4218] 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)))
% 68.30/20.28
% 68.30/20.28 [4218] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28
% 68.30/20.28 [4219] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28
% 68.30/20.28 [4212] 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))))
% 68.30/20.28 -> [4238] ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28 -> [4239] ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28
% 68.30/20.28 [4239] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 68.30/20.28 -> [4241] (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))))
% 68.30/20.28
% 68.30/20.28 [4241] 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))))
% 68.30/20.28 -> [4244] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28 -> [4245] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28
% 68.30/20.28 [4244] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28
% 68.30/20.28 [4245] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28
% 68.30/20.28 [4238] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 68.30/20.28 -> [4240] (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))))
% 68.30/20.28
% 68.30/20.28 [4240] 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))))
% 68.30/20.28 -> [4242] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28 -> [4243] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(reverse_line(Y17_14_4)))
% 68.30/20.28
% 68.30/20.28 [4242] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28
% 68.30/20.28 [4243] 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)))))
% 68.30/20.28 -> [4246] ((unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), M50_56_13) & unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(M50_56_13))) => (left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), M50_56_13) | left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(M50_56_13))))
% 68.30/20.28
% 68.30/20.28 [4246] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), M50_56_13) & unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(M50_56_13))) => (left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), M50_56_13) | left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(M50_56_13))))
% 68.30/20.28 -> [4247] ~(unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), M50_56_13) & unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(M50_56_13)))
% 68.30/20.28 -> [4248] (left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), M50_56_13) | left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(M50_56_13)))
% 68.30/20.28
% 68.30/20.28 [4247] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), M50_56_13) & unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(M50_56_13)))
% 68.30/20.28 -> [4249] ~unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), M50_56_13)
% 68.30/20.28 -> [4250] ~unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(M50_56_13))
% 68.30/20.28
% 68.30/20.28 [4249] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(Y17_14_4)), M50_56_13)
% 68.30/20.28
% 68.30/20.28 [4250] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 68.30/20.28 -> [4253] ~(left_apart_point(A51_163_14, L52_163_14) | left_apart_point(A51_163_14, reverse_line(L52_163_14)))
% 68.30/20.28
% 68.30/20.28 [4253] ALPHA_NOT_OR : ~(left_apart_point(A51_163_14, L52_163_14) | left_apart_point(A51_163_14, reverse_line(L52_163_14)))
% 68.30/20.28 -> [4255] ~left_apart_point(A51_163_14, L52_163_14), ~left_apart_point(A51_163_14, reverse_line(L52_163_14))
% 68.30/20.28
% 68.30/20.28 [4255] CLOSURE : ~left_apart_point(A51_163_14, L52_163_14)
% 68.30/20.28
% 68.30/20.28 [4248] BETA_OR : (left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), M50_56_13) | left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(M50_56_13)))
% 68.30/20.28 -> [4257] left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), M50_56_13)
% 68.30/20.28 -> [4258] left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(M50_56_13))
% 68.30/20.28
% 68.30/20.28 [4258] CLOSURE : left_convergent_lines(reverse_line(reverse_line(Y17_14_4)), reverse_line(M50_56_13))
% 68.30/20.28
% 68.30/20.28 [4257] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 68.30/20.28 -> [4259] ~(left_apart_point(A51_165_14, L52_165_14) | left_apart_point(A51_165_14, reverse_line(L52_165_14)))
% 68.30/20.28
% 68.30/20.28 [4259] ALPHA_NOT_OR : ~(left_apart_point(A51_165_14, L52_165_14) | left_apart_point(A51_165_14, reverse_line(L52_165_14)))
% 68.30/20.28 -> [4260] ~left_apart_point(A51_165_14, L52_165_14), ~left_apart_point(A51_165_14, reverse_line(L52_165_14))
% 68.30/20.28
% 68.30/20.28 [4260] CLOSURE : ~left_apart_point(A51_165_14, L52_165_14)
% 68.30/20.28
% 68.30/20.28 [4209] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 68.30/20.28
% 68.30/20.28 [3925] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 68.30/20.28
% 68.30/20.28 % SZS output end Proof for theBenchmark.p
% 68.30/20.28 [19.933386s][1][Res] 166532 goroutines created
% 68.30/20.28 ==== Result ====
% 68.30/20.28 [19.933425s][1][Res] VALID
% 68.30/20.28 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------