TSTP Solution File: GEO236+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO236+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n011.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 15:18:37 EDT 2022
% Result : Theorem 101.76s 21.36s
% Output : Proof 101.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO236+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 07:05:26 EDT 2022
% 0.21/0.35 % CPUTime :
% 0.21/0.35 [DMT] DMT loaded with preskolemization
% 0.21/0.35 [EQ] equality loaded.
% 0.21/0.35 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.21/0.36 Conjecture not found
% 0.21/0.36 Start search
% 0.21/0.36 nb_step : 1 - limit : 37
% 0.21/0.36 Launch Gotab with destructive = true
% 101.63/21.35 % SZS output start Proof for theBenchmark.p
% 101.76/21.36 [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, L90_90, M91_91] : (((left_apart_point(A89_89, L90_90) & right_apart_point(A89_89, M91_91)) => (unequally_directed_lines(L90_90, M91_91) | distinct_lines(L90_90, M91_91)))))
% 101.76/21.36 -> [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, L90_90, M91_91] : (((left_apart_point(A89_89, L90_90) & right_apart_point(A89_89, M91_91)) => (unequally_directed_lines(L90_90, M91_91) | distinct_lines(L90_90, M91_91))))
% 101.76/21.36
% 101.76/21.36 [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)))))
% 101.76/21.36 -> [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))))
% 101.76/21.36
% 101.76/21.36 [2] DELTA_NOT_FORALL : ~! [A89_89, L90_90, M91_91] : (((left_apart_point(A89_89, L90_90) & right_apart_point(A89_89, M91_91)) => (unequally_directed_lines(L90_90, M91_91) | distinct_lines(L90_90, M91_91))))
% 101.76/21.36 -> [3] ~((left_apart_point(skolem_A8989, skolem_L9090) & right_apart_point(skolem_A8989, skolem_M9191)) => (unequally_directed_lines(skolem_L9090, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191)))
% 101.76/21.36
% 101.76/21.36 [3] ALPHA_NOT_IMPLY : ~((left_apart_point(skolem_A8989, skolem_L9090) & right_apart_point(skolem_A8989, skolem_M9191)) => (unequally_directed_lines(skolem_L9090, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191)))
% 101.76/21.36 -> [4] (left_apart_point(skolem_A8989, skolem_L9090) & right_apart_point(skolem_A8989, skolem_M9191)), ~(unequally_directed_lines(skolem_L9090, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [4] ALPHA_AND : (left_apart_point(skolem_A8989, skolem_L9090) & right_apart_point(skolem_A8989, skolem_M9191))
% 101.76/21.36 -> [5] left_apart_point(skolem_A8989, skolem_L9090), right_apart_point(skolem_A8989, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [5] ALPHA_NOT_OR : ~(unequally_directed_lines(skolem_L9090, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36 -> [6] ~unequally_directed_lines(skolem_L9090, skolem_M9191), ~distinct_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [6] GAMMA_FORALL : ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9))))
% 101.76/21.36 -> [7] (unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4) <=> unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [7] BETA_EQUIV : (unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4) <=> unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)))
% 101.76/21.36 -> [8] ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4), ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36 -> [9] unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4), unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [9] GAMMA_FORALL : ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11))))
% 101.76/21.36 -> [11] (right_apart_point(skolem_A8989, skolem_M9191) <=> left_apart_point(skolem_A8989, reverse_line(skolem_M9191)))
% 101.76/21.36
% 101.76/21.36 [11] BETA_EQUIV : (right_apart_point(skolem_A8989, skolem_M9191) <=> left_apart_point(skolem_A8989, reverse_line(skolem_M9191)))
% 101.76/21.36 -> [14] ~right_apart_point(skolem_A8989, skolem_M9191), ~left_apart_point(skolem_A8989, reverse_line(skolem_M9191))
% 101.76/21.36 -> [15] right_apart_point(skolem_A8989, skolem_M9191), left_apart_point(skolem_A8989, reverse_line(skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [14] CLOSURE : ~right_apart_point(skolem_A8989, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [17] BETA_EQUIV : (right_convergent_lines(reverse_line(Y17_8_4), Y17_8_4) <=> left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)))
% 101.76/21.36 -> [3037] ~right_convergent_lines(reverse_line(Y17_8_4), Y17_8_4), ~left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36 -> [3038] right_convergent_lines(reverse_line(Y17_8_4), Y17_8_4), left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [3038] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 101.76/21.36 -> [3039] (equally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) <=> ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [3039] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) <=> ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)))
% 101.76/21.36 -> [3041] ~equally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)), ~~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36 -> [3042] equally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)), ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [3042] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [3046] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 101.76/21.36 -> [3050] (equally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [3050] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4))
% 101.76/21.36 -> [3053] ~equally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 101.76/21.36 -> [3054] equally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4), ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 101.76/21.36
% 101.76/21.36 [3054] CLOSURE : ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 101.76/21.36
% 101.76/21.36 [3065] BETA_IMPLY : (distinct_points(C35_9_6, C35_9_6) => (distinct_points(C35_9_6, C35_9_6) | distinct_points(C35_9_6, C35_9_6)))
% 101.76/21.36 -> [3141] ~distinct_points(C35_9_6, C35_9_6)
% 101.76/21.36 -> [3142] (distinct_points(C35_9_6, C35_9_6) | distinct_points(C35_9_6, C35_9_6))
% 101.76/21.36
% 101.76/21.36 [3142] BETA_OR : (distinct_points(C35_9_6, C35_9_6) | distinct_points(C35_9_6, C35_9_6))
% 101.76/21.36 -> [3143] distinct_points(C35_9_6, C35_9_6)
% 101.76/21.36 -> [3144] distinct_points(C35_9_6, C35_9_6)
% 101.76/21.36
% 101.76/21.36 [3143] CLOSURE : distinct_points(C35_9_6, C35_9_6)
% 101.76/21.36
% 101.76/21.36 [3144] CLOSURE : distinct_points(C35_9_6, C35_9_6)
% 101.76/21.36
% 101.76/21.36 [3151] BETA_IMPLY : (distinct_lines(skolem_M9191, skolem_L9090) => (distinct_lines(skolem_M9191, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191)))
% 101.76/21.36 -> [3167] ~distinct_lines(skolem_M9191, skolem_L9090)
% 101.76/21.36 -> [3168] (distinct_lines(skolem_M9191, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [3168] BETA_OR : (distinct_lines(skolem_M9191, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36 -> [3169] distinct_lines(skolem_M9191, skolem_M9191)
% 101.76/21.36 -> [3170] distinct_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [3170] CLOSURE : distinct_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [3169] CLOSURE : distinct_lines(skolem_M9191, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [3174] CLOSURE : equally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [3040] BETA_EQUIV : (equally_directed_lines(skolem_L9090, skolem_M9191) <=> ~unequally_directed_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36 -> [3185] ~equally_directed_lines(skolem_L9090, skolem_M9191), ~~unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36 -> [3186] equally_directed_lines(skolem_L9090, skolem_M9191), ~unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [3185] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36 -> [3187] unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [3187] CLOSURE : unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [3186] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 101.76/21.36 -> [3202] (equally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [3202] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4))
% 101.76/21.36 -> [3203] ~equally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 101.76/21.36 -> [3204] equally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4), ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 101.76/21.36
% 101.76/21.36 [3203] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 101.76/21.36 -> [3205] unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 101.76/21.36
% 101.76/21.36 [3205] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 101.76/21.36 -> [3206] ~distinct_points(C35_11_6, C35_11_6)
% 101.76/21.36
% 101.76/21.36 [3206] 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))))
% 101.76/21.36 -> [3207] (distinct_points(C35_11_6, C35_11_6) => (distinct_points(C35_11_6, C35_11_6) | distinct_points(C35_11_6, C35_11_6)))
% 101.76/21.36
% 101.76/21.36 [3207] 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)))
% 101.76/21.36 -> [3208] ~distinct_points(C35_11_6, C35_11_6)
% 101.76/21.36 -> [3209] (distinct_points(C35_11_6, C35_11_6) | distinct_points(C35_11_6, C35_11_6))
% 101.76/21.36
% 101.76/21.36 [3209] BETA_OR : (distinct_points(C35_11_6, C35_11_6) | distinct_points(C35_11_6, C35_11_6))
% 101.76/21.36 -> [3210] distinct_points(C35_11_6, C35_11_6)
% 101.76/21.36 -> [3211] distinct_points(C35_11_6, C35_11_6)
% 101.76/21.36
% 101.76/21.36 [3211] CLOSURE : distinct_points(C35_11_6, C35_11_6)
% 101.76/21.36
% 101.76/21.36 [3210] CLOSURE : distinct_points(C35_11_6, C35_11_6)
% 101.76/21.36
% 101.76/21.36 [3213] BETA_IMPLY : (distinct_lines(skolem_L9090, skolem_M9191) => (distinct_lines(skolem_L9090, skolem_M9191) | distinct_lines(skolem_M9191, skolem_M9191)))
% 101.76/21.36 -> [3822] ~distinct_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36 -> [3823] (distinct_lines(skolem_L9090, skolem_M9191) | distinct_lines(skolem_M9191, skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [3823] BETA_OR : (distinct_lines(skolem_L9090, skolem_M9191) | distinct_lines(skolem_M9191, skolem_M9191))
% 101.76/21.36 -> [3824] distinct_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36 -> [3825] distinct_lines(skolem_M9191, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [3824] CLOSURE : distinct_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [3825] CLOSURE : distinct_lines(skolem_M9191, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [3827] BETA_IMPLY : (unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) => (unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))) | unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))))
% 101.76/21.36 -> [4141] ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36 -> [4142] (unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))) | unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36
% 101.76/21.36 [4141] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [4142] BETA_OR : (unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))) | unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4172] unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36 -> [4173] unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4173] 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))))))
% 101.76/21.36 -> [4181] ((unequally_directed_lines(skolem_L9090, skolem_L9090) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_L9090))) => ((unequally_directed_lines(skolem_L9090, skolem_M9191) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191))) | (unequally_directed_lines(skolem_L9090, skolem_M9191) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191)))))
% 101.76/21.36
% 101.76/21.36 [4181] BETA_IMPLY : ((unequally_directed_lines(skolem_L9090, skolem_L9090) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_L9090))) => ((unequally_directed_lines(skolem_L9090, skolem_M9191) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191))) | (unequally_directed_lines(skolem_L9090, skolem_M9191) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191)))))
% 101.76/21.36 -> [4184] ~(unequally_directed_lines(skolem_L9090, skolem_L9090) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_L9090)))
% 101.76/21.36 -> [4185] ((unequally_directed_lines(skolem_L9090, skolem_M9191) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191))) | (unequally_directed_lines(skolem_L9090, skolem_M9191) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191))))
% 101.76/21.36
% 101.76/21.36 [4185] BETA_OR : ((unequally_directed_lines(skolem_L9090, skolem_M9191) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191))) | (unequally_directed_lines(skolem_L9090, skolem_M9191) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191))))
% 101.76/21.36 -> [4190] (unequally_directed_lines(skolem_L9090, skolem_M9191) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191)))
% 101.76/21.36 -> [4191] (unequally_directed_lines(skolem_L9090, skolem_M9191) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191)))
% 101.76/21.36
% 101.76/21.36 [4190] ALPHA_AND : (unequally_directed_lines(skolem_L9090, skolem_M9191) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191)))
% 101.76/21.36 -> [4195] unequally_directed_lines(skolem_L9090, skolem_M9191), unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [4195] CLOSURE : unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [4197] CLOSURE : unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [4184] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L9090, skolem_L9090) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_L9090)))
% 101.76/21.36 -> [4200] ~unequally_directed_lines(skolem_L9090, skolem_L9090)
% 101.76/21.36 -> [4201] ~unequally_directed_lines(skolem_L9090, reverse_line(skolem_L9090))
% 101.76/21.36
% 101.76/21.36 [4201] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 101.76/21.36 -> [4210] (unequally_directed_lines(skolem_L9090, skolem_L9090) | unequally_directed_lines(skolem_L9090, reverse_line(skolem_L9090)))
% 101.76/21.36
% 101.76/21.36 [4210] BETA_OR : (unequally_directed_lines(skolem_L9090, skolem_L9090) | unequally_directed_lines(skolem_L9090, reverse_line(skolem_L9090)))
% 101.76/21.36 -> [4215] unequally_directed_lines(skolem_L9090, skolem_L9090)
% 101.76/21.36 -> [4216] unequally_directed_lines(skolem_L9090, reverse_line(skolem_L9090))
% 101.76/21.36
% 101.76/21.36 [4216] CLOSURE : unequally_directed_lines(skolem_L9090, reverse_line(skolem_L9090))
% 101.76/21.36
% 101.76/21.36 [4215] 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)))))
% 101.76/21.36 -> [4259] ((unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))) => (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))))
% 101.76/21.36
% 101.76/21.36 [4259] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))) => (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))))
% 101.76/21.36 -> [4260] ~(unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4261] (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36
% 101.76/21.36 [4260] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4264] ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36 -> [4265] ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4264] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [4265] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4261] BETA_OR : (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4292] left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36 -> [4293] left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4292] CLOSURE : left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [4293] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 101.76/21.36 -> [4307] ~(left_apart_point(A51_245_14, L52_245_14) | left_apart_point(A51_245_14, reverse_line(L52_245_14)))
% 101.76/21.36
% 101.76/21.36 [4307] ALPHA_NOT_OR : ~(left_apart_point(A51_245_14, L52_245_14) | left_apart_point(A51_245_14, reverse_line(L52_245_14)))
% 101.76/21.36 -> [4308] ~left_apart_point(A51_245_14, L52_245_14), ~left_apart_point(A51_245_14, reverse_line(L52_245_14))
% 101.76/21.36
% 101.76/21.36 [4308] CLOSURE : ~left_apart_point(A51_245_14, L52_245_14)
% 101.76/21.36
% 101.76/21.36 [4218] BETA_OR : (unequally_directed_lines(skolem_L9090, skolem_M9191) | unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191)))
% 101.76/21.36 -> [4387] unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36 -> [4388] unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [4387] CLOSURE : unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [4388] 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)))))
% 101.76/21.36 -> [4389] ((unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))) => (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))))
% 101.76/21.36
% 101.76/21.36 [4389] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))) => (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))))
% 101.76/21.36 -> [4390] ~(unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4391] (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36
% 101.76/21.36 [4390] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4392] ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36 -> [4393] ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4393] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4392] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [4391] BETA_OR : (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4394] left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36 -> [4395] left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4394] CLOSURE : left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [4395] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 101.76/21.36 -> [4400] ~(left_apart_point(A51_255_14, L52_255_14) | left_apart_point(A51_255_14, reverse_line(L52_255_14)))
% 101.76/21.36
% 101.76/21.36 [4400] ALPHA_NOT_OR : ~(left_apart_point(A51_255_14, L52_255_14) | left_apart_point(A51_255_14, reverse_line(L52_255_14)))
% 101.76/21.36 -> [4403] ~left_apart_point(A51_255_14, L52_255_14), ~left_apart_point(A51_255_14, reverse_line(L52_255_14))
% 101.76/21.36
% 101.76/21.36 [4403] CLOSURE : ~left_apart_point(A51_255_14, L52_255_14)
% 101.76/21.36
% 101.76/21.36 [4180] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))) => ((unequally_directed_lines(reverse_line(Y17_8_4), N46_69_11) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(N46_69_11))) | (unequally_directed_lines(reverse_line(Y17_8_4), N46_69_11) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(N46_69_11)))))
% 101.76/21.36 -> [4412] ~(unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4413] ((unequally_directed_lines(reverse_line(Y17_8_4), N46_69_11) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(N46_69_11))) | (unequally_directed_lines(reverse_line(Y17_8_4), N46_69_11) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(N46_69_11))))
% 101.76/21.36
% 101.76/21.36 [4412] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4418] ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36 -> [4419] ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4419] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4418] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [4413] BETA_OR : ((unequally_directed_lines(reverse_line(Y17_8_4), N46_69_11) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(N46_69_11))) | (unequally_directed_lines(reverse_line(Y17_8_4), N46_69_11) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(N46_69_11))))
% 101.76/21.36 -> [4450] (unequally_directed_lines(reverse_line(Y17_8_4), N46_69_11) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(N46_69_11)))
% 101.76/21.36 -> [4451] (unequally_directed_lines(reverse_line(Y17_8_4), N46_69_11) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(N46_69_11)))
% 101.76/21.36
% 101.76/21.36 [4450] ALPHA_AND : (unequally_directed_lines(reverse_line(Y17_8_4), N46_69_11) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(N46_69_11)))
% 101.76/21.36 -> [4452] unequally_directed_lines(reverse_line(Y17_8_4), N46_69_11), unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(N46_69_11))
% 101.76/21.36
% 101.76/21.36 [4452] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 101.76/21.36 -> [4462] (unequally_directed_lines(skolem_L9090, skolem_M9191) | unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191)))
% 101.76/21.36
% 101.76/21.36 [4462] BETA_OR : (unequally_directed_lines(skolem_L9090, skolem_M9191) | unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191)))
% 101.76/21.36 -> [4463] unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36 -> [4464] unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [4463] CLOSURE : unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [4464] 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)))))
% 101.76/21.36 -> [4468] ((unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))) => (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))))
% 101.76/21.36
% 101.76/21.36 [4468] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))) => (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))))
% 101.76/21.36 -> [4469] ~(unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4470] (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36
% 101.76/21.36 [4469] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4471] ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36 -> [4472] ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4472] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4471] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [4470] BETA_OR : (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4502] left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36 -> [4503] left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4502] CLOSURE : left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [4503] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 101.76/21.36 -> [4506] ~(left_apart_point(A51_264_14, L52_264_14) | left_apart_point(A51_264_14, reverse_line(L52_264_14)))
% 101.76/21.36
% 101.76/21.36 [4506] ALPHA_NOT_OR : ~(left_apart_point(A51_264_14, L52_264_14) | left_apart_point(A51_264_14, reverse_line(L52_264_14)))
% 101.76/21.36 -> [4507] ~left_apart_point(A51_264_14, L52_264_14), ~left_apart_point(A51_264_14, reverse_line(L52_264_14))
% 101.76/21.36
% 101.76/21.36 [4507] CLOSURE : ~left_apart_point(A51_264_14, L52_264_14)
% 101.76/21.36
% 101.76/21.36 [4451] ALPHA_AND : (unequally_directed_lines(reverse_line(Y17_8_4), N46_69_11) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(N46_69_11)))
% 101.76/21.36 -> [4453] unequally_directed_lines(reverse_line(Y17_8_4), N46_69_11), unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(N46_69_11))
% 101.76/21.36
% 101.76/21.36 [4453] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 101.76/21.36 -> [4465] (unequally_directed_lines(skolem_L9090, skolem_M9191) | unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191)))
% 101.76/21.36
% 101.76/21.36 [4465] BETA_OR : (unequally_directed_lines(skolem_L9090, skolem_M9191) | unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191)))
% 101.76/21.36 -> [4466] unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36 -> [4467] unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [4466] CLOSURE : unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [4467] 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)))))
% 101.76/21.36 -> [4475] ((unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))) => (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))))
% 101.76/21.36
% 101.76/21.36 [4475] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))) => (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))))
% 101.76/21.36 -> [4476] ~(unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4477] (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36
% 101.76/21.36 [4476] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) & unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4478] ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36 -> [4479] ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4478] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [4479] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4477] BETA_OR : (left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) | left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4))))
% 101.76/21.36 -> [4504] left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36 -> [4505] left_convergent_lines(reverse_line(Y17_8_4), reverse_line(reverse_line(Y17_8_4)))
% 101.76/21.36
% 101.76/21.36 [4504] CLOSURE : left_convergent_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 101.76/21.36
% 101.76/21.36 [4505] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 101.76/21.36 -> [4508] ~(left_apart_point(A51_265_14, L52_265_14) | left_apart_point(A51_265_14, reverse_line(L52_265_14)))
% 101.76/21.36
% 101.76/21.36 [4508] ALPHA_NOT_OR : ~(left_apart_point(A51_265_14, L52_265_14) | left_apart_point(A51_265_14, reverse_line(L52_265_14)))
% 101.76/21.36 -> [4509] ~left_apart_point(A51_265_14, L52_265_14), ~left_apart_point(A51_265_14, reverse_line(L52_265_14))
% 101.76/21.36
% 101.76/21.36 [4509] CLOSURE : ~left_apart_point(A51_265_14, L52_265_14)
% 101.76/21.36
% 101.76/21.36 [3204] CLOSURE : ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 101.76/21.36
% 101.76/21.36 [10] BETA_EQUIV : (right_apart_point(skolem_A8989, skolem_M9191) <=> left_apart_point(skolem_A8989, reverse_line(skolem_M9191)))
% 101.76/21.36 -> [5405] ~right_apart_point(skolem_A8989, skolem_M9191), ~left_apart_point(skolem_A8989, reverse_line(skolem_M9191))
% 101.76/21.36 -> [5406] right_apart_point(skolem_A8989, skolem_M9191), left_apart_point(skolem_A8989, reverse_line(skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [5405] CLOSURE : ~right_apart_point(skolem_A8989, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [5406] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 101.76/21.36 -> [5407] (right_convergent_lines(reverse_line(N46_119_11), N46_119_11) <=> left_convergent_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)))
% 101.76/21.36
% 101.76/21.36 [5407] BETA_EQUIV : (right_convergent_lines(reverse_line(N46_119_11), N46_119_11) <=> left_convergent_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)))
% 101.76/21.36 -> [5408] ~right_convergent_lines(reverse_line(N46_119_11), N46_119_11), ~left_convergent_lines(reverse_line(N46_119_11), reverse_line(N46_119_11))
% 101.76/21.36 -> [5409] right_convergent_lines(reverse_line(N46_119_11), N46_119_11), left_convergent_lines(reverse_line(N46_119_11), reverse_line(N46_119_11))
% 101.76/21.36
% 101.76/21.36 [5409] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 101.76/21.36 -> [5411] (equally_directed_lines(skolem_L9090, skolem_M9191) <=> ~unequally_directed_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [5411] BETA_EQUIV : (equally_directed_lines(skolem_L9090, skolem_M9191) <=> ~unequally_directed_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36 -> [5414] ~equally_directed_lines(skolem_L9090, skolem_M9191), ~~unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36 -> [5415] equally_directed_lines(skolem_L9090, skolem_M9191), ~unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [5414] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36 -> [5417] unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [5417] CLOSURE : unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [5418] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4))
% 101.76/21.36 -> [6000] ~equally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4)
% 101.76/21.36 -> [6001] equally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4), ~unequally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4)
% 101.76/21.36
% 101.76/21.36 [6000] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4)
% 101.76/21.36 -> [6005] unequally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4)
% 101.76/21.36
% 101.76/21.36 [6005] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4)
% 101.76/21.36
% 101.76/21.36 [6001] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 101.76/21.36 -> [6006] ~distinct_points(B34_20_6, B34_20_6)
% 101.76/21.36
% 101.76/21.36 [6006] 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))))
% 101.76/21.36 -> [6012] (distinct_points(B34_20_6, B34_20_6) => (distinct_points(B34_20_6, B34_20_6) | distinct_points(B34_20_6, B34_20_6)))
% 101.76/21.36
% 101.76/21.36 [6012] BETA_IMPLY : (distinct_points(B34_20_6, B34_20_6) => (distinct_points(B34_20_6, B34_20_6) | distinct_points(B34_20_6, B34_20_6)))
% 101.76/21.36 -> [6013] ~distinct_points(B34_20_6, B34_20_6)
% 101.76/21.36 -> [6014] (distinct_points(B34_20_6, B34_20_6) | distinct_points(B34_20_6, B34_20_6))
% 101.76/21.36
% 101.76/21.36 [6014] BETA_OR : (distinct_points(B34_20_6, B34_20_6) | distinct_points(B34_20_6, B34_20_6))
% 101.76/21.36 -> [6016] distinct_points(B34_20_6, B34_20_6)
% 101.76/21.36 -> [6017] distinct_points(B34_20_6, B34_20_6)
% 101.76/21.36
% 101.76/21.36 [6016] CLOSURE : distinct_points(B34_20_6, B34_20_6)
% 101.76/21.36
% 101.76/21.36 [6017] CLOSURE : distinct_points(B34_20_6, B34_20_6)
% 101.76/21.36
% 101.76/21.36 [6013] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 101.76/21.36 -> [6018] ~distinct_lines(skolem_M9191, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [6018] 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))))
% 101.76/21.36 -> [6025] (distinct_lines(skolem_M9191, skolem_L9090) => (distinct_lines(skolem_M9191, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191)))
% 101.76/21.36
% 101.76/21.36 [6025] BETA_IMPLY : (distinct_lines(skolem_M9191, skolem_L9090) => (distinct_lines(skolem_M9191, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191)))
% 101.76/21.36 -> [6026] ~distinct_lines(skolem_M9191, skolem_L9090)
% 101.76/21.36 -> [6027] (distinct_lines(skolem_M9191, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [6027] BETA_OR : (distinct_lines(skolem_M9191, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36 -> [6030] distinct_lines(skolem_M9191, skolem_M9191)
% 101.76/21.36 -> [6031] distinct_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [6031] CLOSURE : distinct_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [6030] CLOSURE : distinct_lines(skolem_M9191, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [6045] BETA_IMPLY : (unequally_directed_lines(skolem_L9090, skolem_L9090) => (unequally_directed_lines(skolem_L9090, skolem_M9191) | unequally_directed_lines(skolem_L9090, skolem_M9191)))
% 101.76/21.36 -> [6167] ~unequally_directed_lines(skolem_L9090, skolem_L9090)
% 101.76/21.36 -> [6168] (unequally_directed_lines(skolem_L9090, skolem_M9191) | unequally_directed_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [6168] BETA_OR : (unequally_directed_lines(skolem_L9090, skolem_M9191) | unequally_directed_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36 -> [6169] unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36 -> [6170] unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [6169] CLOSURE : unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [6170] CLOSURE : unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [6171] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11)) & unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11)))) => ((unequally_directed_lines(reverse_line(N46_112_11), N46_112_11) & unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11))) | (unequally_directed_lines(reverse_line(N46_112_11), N46_112_11) & unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11)))))
% 101.76/21.36 -> [6226] ~(unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11)) & unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11))))
% 101.76/21.36 -> [6227] ((unequally_directed_lines(reverse_line(N46_112_11), N46_112_11) & unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11))) | (unequally_directed_lines(reverse_line(N46_112_11), N46_112_11) & unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11))))
% 101.76/21.36
% 101.76/21.36 [6227] BETA_OR : ((unequally_directed_lines(skolem_L9090, skolem_M9191) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191))) | (unequally_directed_lines(reverse_line(skolem_M9191), skolem_M9191) & unequally_directed_lines(reverse_line(skolem_M9191), reverse_line(skolem_M9191))))
% 101.76/21.36 -> [6232] (unequally_directed_lines(skolem_L9090, skolem_M9191) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191)))
% 101.76/21.36 -> [6233] (unequally_directed_lines(reverse_line(skolem_M9191), skolem_M9191) & unequally_directed_lines(reverse_line(skolem_M9191), reverse_line(skolem_M9191)))
% 101.76/21.36
% 101.76/21.36 [6233] ALPHA_AND : (unequally_directed_lines(reverse_line(skolem_M9191), skolem_M9191) & unequally_directed_lines(reverse_line(skolem_M9191), reverse_line(skolem_M9191)))
% 101.76/21.36 -> [6235] unequally_directed_lines(reverse_line(skolem_M9191), skolem_M9191), unequally_directed_lines(reverse_line(skolem_M9191), reverse_line(skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [6235] CLOSURE : unequally_directed_lines(reverse_line(skolem_M9191), reverse_line(skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [6236] CLOSURE : unequally_directed_lines(skolem_L9090, reverse_line(skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [6226] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11)) & unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11))))
% 101.76/21.36 -> [6285] ~unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11))
% 101.76/21.36 -> [6286] ~unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11)))
% 101.76/21.36
% 101.76/21.36 [6286] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 101.76/21.36 -> [6288] (unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11)) | unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11))))
% 101.76/21.36
% 101.76/21.36 [6288] BETA_OR : (unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11)) | unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11))))
% 101.76/21.36 -> [6291] unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11))
% 101.76/21.36 -> [6292] unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11)))
% 101.76/21.36
% 101.76/21.36 [6292] CLOSURE : unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11)))
% 101.76/21.36
% 101.76/21.36 [6291] CLOSURE : unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11))
% 101.76/21.36
% 101.76/21.36 [6285] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 101.76/21.36 -> [6287] (unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11)) | unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11))))
% 101.76/21.36
% 101.76/21.36 [6287] BETA_OR : (unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11)) | unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11))))
% 101.76/21.36 -> [6289] unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11))
% 101.76/21.36 -> [6290] unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11)))
% 101.76/21.36
% 101.76/21.36 [6289] CLOSURE : unequally_directed_lines(reverse_line(N46_112_11), reverse_line(N46_112_11))
% 101.76/21.36
% 101.76/21.36 [6290] 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)))))
% 101.76/21.36 -> [6295] ((unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11))) & unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(reverse_line(N46_112_11))))) => (left_convergent_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11))) | left_convergent_lines(reverse_line(N46_112_11), reverse_line(reverse_line(reverse_line(N46_112_11))))))
% 101.76/21.36
% 101.76/21.36 [6295] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11))) & unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(reverse_line(N46_112_11))))) => (left_convergent_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11))) | left_convergent_lines(reverse_line(N46_112_11), reverse_line(reverse_line(reverse_line(N46_112_11))))))
% 101.76/21.36 -> [6296] ~(unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11))) & unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(reverse_line(N46_112_11)))))
% 101.76/21.36 -> [6297] (left_convergent_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11))) | left_convergent_lines(reverse_line(N46_112_11), reverse_line(reverse_line(reverse_line(N46_112_11)))))
% 101.76/21.36
% 101.76/21.36 [6297] BETA_OR : (left_convergent_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11))) | left_convergent_lines(reverse_line(N46_112_11), reverse_line(reverse_line(reverse_line(N46_112_11)))))
% 101.76/21.36 -> [6301] left_convergent_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11)))
% 101.76/21.36 -> [6302] left_convergent_lines(reverse_line(N46_112_11), reverse_line(reverse_line(reverse_line(N46_112_11))))
% 101.76/21.36
% 101.76/21.36 [6301] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 101.76/21.36 -> [6309] ~(left_apart_point(A51_298_14, L52_298_14) | left_apart_point(A51_298_14, reverse_line(L52_298_14)))
% 101.76/21.36
% 101.76/21.36 [6309] ALPHA_NOT_OR : ~(left_apart_point(A51_298_14, L52_298_14) | left_apart_point(A51_298_14, reverse_line(L52_298_14)))
% 101.76/21.36 -> [6310] ~left_apart_point(A51_298_14, L52_298_14), ~left_apart_point(A51_298_14, reverse_line(L52_298_14))
% 101.76/21.36
% 101.76/21.36 [6310] CLOSURE : ~left_apart_point(A51_298_14, L52_298_14)
% 101.76/21.36
% 101.76/21.36 [6302] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 101.76/21.36 -> [6311] ~(left_apart_point(A51_299_14, L52_299_14) | left_apart_point(A51_299_14, reverse_line(L52_299_14)))
% 101.76/21.36
% 101.76/21.36 [6311] ALPHA_NOT_OR : ~(left_apart_point(A51_299_14, L52_299_14) | left_apart_point(A51_299_14, reverse_line(L52_299_14)))
% 101.76/21.36 -> [6312] ~left_apart_point(A51_299_14, L52_299_14), ~left_apart_point(A51_299_14, reverse_line(L52_299_14))
% 101.76/21.36
% 101.76/21.36 [6312] CLOSURE : ~left_apart_point(A51_299_14, L52_299_14)
% 101.76/21.36
% 101.76/21.36 [6296] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11))) & unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(reverse_line(N46_112_11)))))
% 101.76/21.36 -> [6298] ~unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11)))
% 101.76/21.36 -> [6299] ~unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(reverse_line(N46_112_11))))
% 101.76/21.36
% 101.76/21.36 [6298] CLOSURE : ~unequally_directed_lines(reverse_line(N46_112_11), reverse_line(reverse_line(N46_112_11)))
% 101.76/21.36
% 101.76/21.36 [6299] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 101.76/21.36 -> [6313] ~(left_apart_point(A51_300_14, L52_300_14) | left_apart_point(A51_300_14, reverse_line(L52_300_14)))
% 101.76/21.36
% 101.76/21.36 [6313] ALPHA_NOT_OR : ~(left_apart_point(A51_300_14, L52_300_14) | left_apart_point(A51_300_14, reverse_line(L52_300_14)))
% 101.76/21.36 -> [6314] ~left_apart_point(A51_300_14, L52_300_14), ~left_apart_point(A51_300_14, reverse_line(L52_300_14))
% 101.76/21.36
% 101.76/21.36 [6314] CLOSURE : ~left_apart_point(A51_300_14, L52_300_14)
% 101.76/21.36
% 101.76/21.36 [5408] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 101.76/21.36 -> [5410] (equally_directed_lines(skolem_L9090, skolem_M9191) <=> ~unequally_directed_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [5410] BETA_EQUIV : (equally_directed_lines(skolem_L9090, skolem_M9191) <=> ~unequally_directed_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36 -> [5412] ~equally_directed_lines(skolem_L9090, skolem_M9191), ~~unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36 -> [5413] equally_directed_lines(skolem_L9090, skolem_M9191), ~unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [5412] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36 -> [5416] unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [5416] CLOSURE : unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [5419] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(N46_119_11), N46_119_11) <=> ~unequally_directed_opposite_lines(reverse_line(N46_119_11), N46_119_11))
% 101.76/21.36 -> [6190] ~equally_directed_opposite_lines(reverse_line(N46_119_11), N46_119_11), ~~unequally_directed_opposite_lines(reverse_line(N46_119_11), N46_119_11)
% 101.76/21.36 -> [6191] equally_directed_opposite_lines(reverse_line(N46_119_11), N46_119_11), ~unequally_directed_opposite_lines(reverse_line(N46_119_11), N46_119_11)
% 101.76/21.36
% 101.76/21.36 [6190] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(N46_119_11), N46_119_11)
% 101.76/21.36 -> [6194] unequally_directed_opposite_lines(reverse_line(N46_119_11), N46_119_11)
% 101.76/21.36
% 101.76/21.36 [6194] CLOSURE : unequally_directed_opposite_lines(reverse_line(N46_119_11), N46_119_11)
% 101.76/21.36
% 101.76/21.36 [6200] BETA_IMPLY : (distinct_points(C35_21_6, C35_21_6) => (distinct_points(C35_21_6, C35_21_6) | distinct_points(C35_21_6, C35_21_6)))
% 101.76/21.36 -> [6592] ~distinct_points(C35_21_6, C35_21_6)
% 101.76/21.36 -> [6593] (distinct_points(C35_21_6, C35_21_6) | distinct_points(C35_21_6, C35_21_6))
% 101.76/21.36
% 101.76/21.36 [6592] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 101.76/21.36 -> [6596] ~distinct_lines(L36_35_7, L36_35_7)
% 101.76/21.36
% 101.76/21.36 [6596] 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))))
% 101.76/21.36 -> [6597] (distinct_lines(skolem_L9090, skolem_L9090) => (distinct_lines(skolem_L9090, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191)))
% 101.76/21.36
% 101.76/21.36 [6597] BETA_IMPLY : (distinct_lines(skolem_L9090, skolem_L9090) => (distinct_lines(skolem_L9090, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191)))
% 101.76/21.36 -> [6598] ~distinct_lines(skolem_L9090, skolem_L9090)
% 101.76/21.36 -> [6599] (distinct_lines(skolem_L9090, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [6599] BETA_OR : (distinct_lines(skolem_L9090, skolem_M9191) | distinct_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36 -> [6600] distinct_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36 -> [6601] distinct_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [6600] CLOSURE : distinct_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [6601] CLOSURE : distinct_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [6603] BETA_IMPLY : (unequally_directed_lines(skolem_L9090, skolem_L9090) => (unequally_directed_lines(skolem_L9090, skolem_M9191) | unequally_directed_lines(skolem_L9090, skolem_M9191)))
% 101.76/21.36 -> [6685] ~unequally_directed_lines(skolem_L9090, skolem_L9090)
% 101.76/21.36 -> [6686] (unequally_directed_lines(skolem_L9090, skolem_M9191) | unequally_directed_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36
% 101.76/21.36 [6686] BETA_OR : (unequally_directed_lines(skolem_L9090, skolem_M9191) | unequally_directed_lines(skolem_L9090, skolem_M9191))
% 101.76/21.36 -> [6687] unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36 -> [6688] unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [6688] CLOSURE : unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [6687] CLOSURE : unequally_directed_lines(skolem_L9090, skolem_M9191)
% 101.76/21.36
% 101.76/21.36 [6689] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) & unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11)))) => ((unequally_directed_lines(reverse_line(N46_119_11), N46_119_11) & unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11))) | (unequally_directed_lines(reverse_line(N46_119_11), N46_119_11) & unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)))))
% 101.76/21.36 -> [6714] ~(unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) & unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11))))
% 101.76/21.36 -> [6715] ((unequally_directed_lines(reverse_line(N46_119_11), N46_119_11) & unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11))) | (unequally_directed_lines(reverse_line(N46_119_11), N46_119_11) & unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11))))
% 101.76/21.36
% 101.76/21.36 [6715] BETA_OR : ((unequally_directed_lines(reverse_line(skolem_L9090), skolem_L9090) & unequally_directed_lines(reverse_line(skolem_L9090), reverse_line(skolem_L9090))) | (unequally_directed_lines(skolem_L9090, skolem_L9090) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_L9090))))
% 101.76/21.36 -> [6718] (unequally_directed_lines(reverse_line(skolem_L9090), skolem_L9090) & unequally_directed_lines(reverse_line(skolem_L9090), reverse_line(skolem_L9090)))
% 101.76/21.36 -> [6719] (unequally_directed_lines(skolem_L9090, skolem_L9090) & unequally_directed_lines(skolem_L9090, reverse_line(skolem_L9090)))
% 101.76/21.36
% 101.76/21.36 [6718] ALPHA_AND : (unequally_directed_lines(reverse_line(skolem_L9090), skolem_L9090) & unequally_directed_lines(reverse_line(skolem_L9090), reverse_line(skolem_L9090)))
% 101.76/21.36 -> [6720] unequally_directed_lines(reverse_line(skolem_L9090), skolem_L9090), unequally_directed_lines(reverse_line(skolem_L9090), reverse_line(skolem_L9090))
% 101.76/21.36
% 101.76/21.36 [6720] CLOSURE : unequally_directed_lines(reverse_line(skolem_L9090), reverse_line(skolem_L9090))
% 101.76/21.36
% 101.76/21.36 [6721] CLOSURE : unequally_directed_lines(skolem_L9090, reverse_line(skolem_L9090))
% 101.76/21.36
% 101.76/21.36 [6714] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) & unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11))))
% 101.76/21.36 -> [6745] ~unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11))
% 101.76/21.36 -> [6746] ~unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11)))
% 101.76/21.36
% 101.76/21.36 [6746] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 101.76/21.36 -> [6748] (unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) | unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11))))
% 101.76/21.36
% 101.76/21.36 [6748] BETA_OR : (unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) | unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11))))
% 101.76/21.36 -> [6751] unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11))
% 101.76/21.36 -> [6752] unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11)))
% 101.76/21.36
% 101.76/21.36 [6752] CLOSURE : unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11)))
% 101.76/21.36
% 101.76/21.36 [6751] CLOSURE : unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11))
% 101.76/21.36
% 101.76/21.36 [6745] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 101.76/21.36 -> [6747] (unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) | unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11))))
% 101.76/21.36
% 101.76/21.36 [6747] BETA_OR : (unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) | unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11))))
% 101.76/21.36 -> [6749] unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11))
% 101.76/21.36 -> [6750] unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11)))
% 101.76/21.36
% 101.76/21.36 [6749] CLOSURE : unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11))
% 101.76/21.36
% 101.76/21.36 [6750] 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)))))
% 101.76/21.36 -> [6753] ((unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) & unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11)))) => (left_convergent_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) | left_convergent_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11)))))
% 101.76/21.36
% 101.76/21.36 [6753] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) & unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11)))) => (left_convergent_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) | left_convergent_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11)))))
% 101.76/21.36 -> [6754] ~(unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) & unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11))))
% 101.76/21.36 -> [6755] (left_convergent_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) | left_convergent_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11))))
% 101.76/21.36
% 101.76/21.36 [6754] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) & unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11))))
% 101.76/21.36 -> [6756] ~unequally_directed_lines(reverse_line(N46_119_11), reverse_line(N46_119_11))
% 101.76/21.36 -> [6757] ~unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11)))
% 101.76/21.36
% 101.76/21.36 [6757] CLOSURE : ~unequally_directed_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11)))
% 101.76/21.36
% 101.76/21.36 [6756] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 101.76/21.36 -> [6760] ~(left_apart_point(A51_334_14, L52_334_14) | left_apart_point(A51_334_14, reverse_line(L52_334_14)))
% 101.76/21.36
% 101.76/21.36 [6760] ALPHA_NOT_OR : ~(left_apart_point(A51_334_14, L52_334_14) | left_apart_point(A51_334_14, reverse_line(L52_334_14)))
% 101.76/21.36 -> [6761] ~left_apart_point(A51_334_14, L52_334_14), ~left_apart_point(A51_334_14, reverse_line(L52_334_14))
% 101.76/21.36
% 101.76/21.36 [6761] CLOSURE : ~left_apart_point(A51_334_14, L52_334_14)
% 101.76/21.36
% 101.76/21.36 [6755] BETA_OR : (left_convergent_lines(reverse_line(N46_119_11), reverse_line(N46_119_11)) | left_convergent_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11))))
% 101.76/21.36 -> [6764] left_convergent_lines(reverse_line(N46_119_11), reverse_line(N46_119_11))
% 101.76/21.36 -> [6765] left_convergent_lines(reverse_line(N46_119_11), reverse_line(reverse_line(N46_119_11)))
% 101.76/21.36
% 101.76/21.36 [6764] CLOSURE : left_convergent_lines(reverse_line(N46_119_11), reverse_line(N46_119_11))
% 101.76/21.36
% 101.76/21.36 [6765] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 101.76/21.36 -> [6766] ~(left_apart_point(A51_336_14, L52_336_14) | left_apart_point(A51_336_14, reverse_line(L52_336_14)))
% 101.76/21.36
% 101.76/21.36 [6766] ALPHA_NOT_OR : ~(left_apart_point(A51_336_14, L52_336_14) | left_apart_point(A51_336_14, reverse_line(L52_336_14)))
% 101.76/21.36 -> [6767] ~left_apart_point(A51_336_14, L52_336_14), ~left_apart_point(A51_336_14, reverse_line(L52_336_14))
% 101.76/21.36
% 101.76/21.36 [6767] CLOSURE : ~left_apart_point(A51_336_14, L52_336_14)
% 101.76/21.36
% 101.76/21.36 [6593] BETA_OR : (distinct_points(C35_21_6, C35_21_6) | distinct_points(C35_21_6, C35_21_6))
% 101.76/21.36 -> [6768] distinct_points(C35_21_6, C35_21_6)
% 101.76/21.36 -> [6769] distinct_points(C35_21_6, C35_21_6)
% 101.76/21.36
% 101.76/21.36 [6769] CLOSURE : distinct_points(C35_21_6, C35_21_6)
% 101.76/21.36
% 101.76/21.36 [6768] CLOSURE : distinct_points(C35_21_6, C35_21_6)
% 101.76/21.36
% 101.76/21.36 % SZS output end Proof for theBenchmark.p
% 101.76/21.36 [21.009507s][1][Res] 273477 goroutines created
% 101.76/21.36 ==== Result ====
% 101.76/21.36 [21.009577s][1][Res] VALID
% 101.76/21.36 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------