TSTP Solution File: GEO248+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO248+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 15:18:42 EDT 2022
% Result : Theorem 139.97s 26.90s
% Output : Proof 139.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO248+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : goeland -dmt -presko -proof %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 07:09:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 [DMT] DMT loaded with preskolemization
% 0.13/0.34 [EQ] equality loaded.
% 0.13/0.34 [0.000029s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.34 Conjecture not found
% 0.13/0.34 Start search
% 0.13/0.34 nb_step : 1 - limit : 37
% 0.13/0.34 Launch Gotab with destructive = true
% 139.97/26.87 % SZS output start Proof for theBenchmark.p
% 139.97/26.89 [0] ALPHA_AND : ((! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9)))) & ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11)))) & ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13)))) & ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15))) & ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17))) & ! [A32_32] : (~distinct_points(A32_32, A32_32)) & ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35)))) & ! [L36_36] : (~distinct_lines(L36_36, L36_36)) & ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39)))) & ! [L40_40] : (equally_directed_lines(L40_40, L40_40)) & ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43)))) & ! [L44_44, M45_45, N46_46] : (((unequally_directed_lines(L44_44, M45_45) & unequally_directed_lines(L44_44, reverse_line(M45_45))) => ((unequally_directed_lines(L44_44, N46_46) & unequally_directed_lines(L44_44, reverse_line(N46_46))) | (unequally_directed_lines(M45_45, N46_46) & unequally_directed_lines(M45_45, reverse_line(N46_46)))))) & ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48)))) & ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50))))) & ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52)))) & ! [L53_53, M54_54] : (~(left_convergent_lines(L53_53, M54_54) | left_convergent_lines(L53_53, reverse_line(M54_54)))) & ! [A55_55, B56_56] : ((((point(A55_55) & point(B56_56)) & distinct_points(A55_55, B56_56)) => line(line_connecting(A55_55, B56_56)))) & ! [L57_57, M58_58] : (((((line(L57_57) & line(M58_58)) & unequally_directed_lines(L57_57, M58_58)) & unequally_directed_lines(L57_57, reverse_line(M58_58))) => point(intersection_point(L57_57, M58_58)))) & ! [L59_59, A60_60] : (((point(A60_60) & line(L59_59)) => line(parallel_through_point(L59_59, A60_60)))) & ! [L61_61] : ((line(L61_61) => line(reverse_line(L61_61)))) & ! [A62_62, B63_63] : ((distinct_points(A62_62, B63_63) => (~apart_point_and_line(A62_62, line_connecting(A62_62, B63_63)) & ~apart_point_and_line(B63_63, line_connecting(A62_62, B63_63))))) & ! [L64_64, M65_65] : (((unequally_directed_lines(L64_64, M65_65) & unequally_directed_lines(L64_64, reverse_line(M65_65))) => (~apart_point_and_line(intersection_point(L64_64, M65_65), L64_64) & ~apart_point_and_line(intersection_point(L64_64, M65_65), M65_65)))) & ! [A66_66, L67_67] : (~apart_point_and_line(A66_66, parallel_through_point(L67_67, A66_66))) & ! [L68_68] : (~distinct_lines(L68_68, reverse_line(L68_68))) & ! [A69_69, B70_70] : ((distinct_points(A69_69, B70_70) => equally_directed_lines(line_connecting(A69_69, B70_70), reverse_line(line_connecting(B70_70, A69_69))))) & ! [A71_71, L72_72] : (equally_directed_lines(parallel_through_point(L72_72, A71_71), L72_72)) & ! [A73_73, B74_74, L75_75, M76_76] : (((distinct_points(A73_73, B74_74) & distinct_lines(L75_75, M76_76)) => (((((((left_apart_point(A73_73, L75_75) | left_apart_point(B74_74, L75_75)) | left_apart_point(A73_73, M76_76)) | left_apart_point(B74_74, M76_76)) | left_apart_point(A73_73, reverse_line(L75_75))) | left_apart_point(B74_74, reverse_line(L75_75))) | left_apart_point(A73_73, reverse_line(M76_76))) | left_apart_point(B74_74, reverse_line(M76_76))))) & ! [A77_77, B78_78, L79_79] : (((distinct_points(A77_77, B78_78) & left_apart_point(A77_77, L79_79)) => (left_apart_point(B78_78, L79_79) | left_convergent_lines(line_connecting(A77_77, B78_78), L79_79)))) & ! [A80_80, B81_81, L82_82] : ((left_apart_point(A80_80, L82_82) => (distinct_points(A80_80, B81_81) | left_apart_point(B81_81, L82_82)))) & ! [A83_83, L84_84, M85_85] : (((left_apart_point(A83_83, L84_84) & unequally_directed_lines(L84_84, M85_85)) => (distinct_lines(L84_84, M85_85) | left_apart_point(A83_83, reverse_line(M85_85))))) & ! [L86_86, M87_87, N88_88] : ((left_convergent_lines(L86_86, M87_87) => (unequally_directed_lines(M87_87, N88_88) | left_convergent_lines(L86_86, N88_88))))) & ~! [A89_89, B90_90, L91_91] : (((apart_point_and_line(A89_89, L91_91) & incident_point_and_line(B90_90, parallel_lines(L91_91, A89_89))) => apart_point_and_line(B90_90, L91_91))))
% 139.97/26.89 -> [1] (! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9)))) & ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11)))) & ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13)))) & ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15))) & ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17))) & ! [A32_32] : (~distinct_points(A32_32, A32_32)) & ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35)))) & ! [L36_36] : (~distinct_lines(L36_36, L36_36)) & ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39)))) & ! [L40_40] : (equally_directed_lines(L40_40, L40_40)) & ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43)))) & ! [L44_44, M45_45, N46_46] : (((unequally_directed_lines(L44_44, M45_45) & unequally_directed_lines(L44_44, reverse_line(M45_45))) => ((unequally_directed_lines(L44_44, N46_46) & unequally_directed_lines(L44_44, reverse_line(N46_46))) | (unequally_directed_lines(M45_45, N46_46) & unequally_directed_lines(M45_45, reverse_line(N46_46)))))) & ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48)))) & ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50))))) & ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52)))) & ! [L53_53, M54_54] : (~(left_convergent_lines(L53_53, M54_54) | left_convergent_lines(L53_53, reverse_line(M54_54)))) & ! [A55_55, B56_56] : ((((point(A55_55) & point(B56_56)) & distinct_points(A55_55, B56_56)) => line(line_connecting(A55_55, B56_56)))) & ! [L57_57, M58_58] : (((((line(L57_57) & line(M58_58)) & unequally_directed_lines(L57_57, M58_58)) & unequally_directed_lines(L57_57, reverse_line(M58_58))) => point(intersection_point(L57_57, M58_58)))) & ! [L59_59, A60_60] : (((point(A60_60) & line(L59_59)) => line(parallel_through_point(L59_59, A60_60)))) & ! [L61_61] : ((line(L61_61) => line(reverse_line(L61_61)))) & ! [A62_62, B63_63] : ((distinct_points(A62_62, B63_63) => (~apart_point_and_line(A62_62, line_connecting(A62_62, B63_63)) & ~apart_point_and_line(B63_63, line_connecting(A62_62, B63_63))))) & ! [L64_64, M65_65] : (((unequally_directed_lines(L64_64, M65_65) & unequally_directed_lines(L64_64, reverse_line(M65_65))) => (~apart_point_and_line(intersection_point(L64_64, M65_65), L64_64) & ~apart_point_and_line(intersection_point(L64_64, M65_65), M65_65)))) & ! [A66_66, L67_67] : (~apart_point_and_line(A66_66, parallel_through_point(L67_67, A66_66))) & ! [L68_68] : (~distinct_lines(L68_68, reverse_line(L68_68))) & ! [A69_69, B70_70] : ((distinct_points(A69_69, B70_70) => equally_directed_lines(line_connecting(A69_69, B70_70), reverse_line(line_connecting(B70_70, A69_69))))) & ! [A71_71, L72_72] : (equally_directed_lines(parallel_through_point(L72_72, A71_71), L72_72)) & ! [A73_73, B74_74, L75_75, M76_76] : (((distinct_points(A73_73, B74_74) & distinct_lines(L75_75, M76_76)) => (((((((left_apart_point(A73_73, L75_75) | left_apart_point(B74_74, L75_75)) | left_apart_point(A73_73, M76_76)) | left_apart_point(B74_74, M76_76)) | left_apart_point(A73_73, reverse_line(L75_75))) | left_apart_point(B74_74, reverse_line(L75_75))) | left_apart_point(A73_73, reverse_line(M76_76))) | left_apart_point(B74_74, reverse_line(M76_76))))) & ! [A77_77, B78_78, L79_79] : (((distinct_points(A77_77, B78_78) & left_apart_point(A77_77, L79_79)) => (left_apart_point(B78_78, L79_79) | left_convergent_lines(line_connecting(A77_77, B78_78), L79_79)))) & ! [A80_80, B81_81, L82_82] : ((left_apart_point(A80_80, L82_82) => (distinct_points(A80_80, B81_81) | left_apart_point(B81_81, L82_82)))) & ! [A83_83, L84_84, M85_85] : (((left_apart_point(A83_83, L84_84) & unequally_directed_lines(L84_84, M85_85)) => (distinct_lines(L84_84, M85_85) | left_apart_point(A83_83, reverse_line(M85_85))))) & ! [L86_86, M87_87, N88_88] : ((left_convergent_lines(L86_86, M87_87) => (unequally_directed_lines(M87_87, N88_88) | left_convergent_lines(L86_86, N88_88))))), ~! [A89_89, B90_90, L91_91] : (((apart_point_and_line(A89_89, L91_91) & incident_point_and_line(B90_90, parallel_lines(L91_91, A89_89))) => apart_point_and_line(B90_90, L91_91)))
% 139.97/26.89
% 139.97/26.89 [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)))))
% 139.97/26.89 -> [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))))
% 139.97/26.89
% 139.97/26.89 [2] DELTA_NOT_FORALL : ~! [A89_89, B90_90, L91_91] : (((apart_point_and_line(A89_89, L91_91) & incident_point_and_line(B90_90, parallel_lines(L91_91, A89_89))) => apart_point_and_line(B90_90, L91_91)))
% 139.97/26.89 -> [3] ~((apart_point_and_line(skolem_A8989, skolem_L9191) & incident_point_and_line(skolem_B9090, parallel_lines(skolem_L9191, skolem_A8989))) => apart_point_and_line(skolem_B9090, skolem_L9191))
% 139.97/26.89
% 139.97/26.89 [3] ALPHA_NOT_IMPLY : ~((apart_point_and_line(skolem_A8989, skolem_L9191) & incident_point_and_line(skolem_B9090, parallel_lines(skolem_L9191, skolem_A8989))) => apart_point_and_line(skolem_B9090, skolem_L9191))
% 139.97/26.89 -> [4] (apart_point_and_line(skolem_A8989, skolem_L9191) & incident_point_and_line(skolem_B9090, parallel_lines(skolem_L9191, skolem_A8989))), ~apart_point_and_line(skolem_B9090, skolem_L9191)
% 139.97/26.89
% 139.97/26.89 [4] Rewrite : ~apart_point_and_line(skolem_B9090, skolem_L9191)
% 139.97/26.89 -> [5] ~(left_apart_point(skolem_B9090, skolem_L9191) | right_apart_point(skolem_B9090, skolem_L9191))
% 139.97/26.89
% 139.97/26.89 [5] ALPHA_AND : (apart_point_and_line(skolem_A8989, skolem_L9191) & incident_point_and_line(skolem_B9090, parallel_lines(skolem_L9191, skolem_A8989)))
% 139.97/26.89 -> [6] apart_point_and_line(skolem_A8989, skolem_L9191), incident_point_and_line(skolem_B9090, parallel_lines(skolem_L9191, skolem_A8989))
% 139.97/26.89
% 139.97/26.89 [6] Rewrite : apart_point_and_line(skolem_A8989, skolem_L9191)
% 139.97/26.89 -> [7] (left_apart_point(skolem_A8989, skolem_L9191) | right_apart_point(skolem_A8989, skolem_L9191))
% 139.97/26.89
% 139.97/26.89 [7] ALPHA_NOT_OR : ~(left_apart_point(skolem_B9090, skolem_L9191) | right_apart_point(skolem_B9090, skolem_L9191))
% 139.97/26.89 -> [8] ~left_apart_point(skolem_B9090, skolem_L9191), ~right_apart_point(skolem_B9090, skolem_L9191)
% 139.97/26.89
% 139.97/26.89 [8] BETA_OR : (left_apart_point(skolem_A8989, skolem_L9191) | right_apart_point(skolem_A8989, skolem_L9191))
% 139.97/26.89 -> [9] left_apart_point(skolem_A8989, skolem_L9191)
% 139.97/26.89 -> [10] right_apart_point(skolem_A8989, skolem_L9191)
% 139.97/26.89
% 139.97/26.89 [10] GAMMA_FORALL : ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9))))
% 139.97/26.89 -> [12] (unequally_directed_opposite_lines(reverse_line(Y17_5_4), Y17_5_4) <=> unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4)))
% 139.97/26.89
% 139.97/26.89 [12] BETA_EQUIV : (unequally_directed_opposite_lines(reverse_line(Y17_5_4), Y17_5_4) <=> unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4)))
% 139.97/26.89 -> [15] ~unequally_directed_opposite_lines(reverse_line(Y17_5_4), Y17_5_4), ~unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4))
% 139.97/26.89 -> [16] unequally_directed_opposite_lines(reverse_line(Y17_5_4), Y17_5_4), unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4))
% 139.97/26.89
% 139.97/26.89 [16] GAMMA_FORALL : ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11))))
% 139.97/26.89 -> [26] (right_apart_point(skolem_B9090, skolem_L9191) <=> left_apart_point(skolem_B9090, reverse_line(skolem_L9191)))
% 139.97/26.89
% 139.97/26.89 [26] BETA_EQUIV : (right_apart_point(skolem_B9090, skolem_L9191) <=> left_apart_point(skolem_B9090, reverse_line(skolem_L9191)))
% 139.97/26.89 -> [27] ~right_apart_point(skolem_B9090, skolem_L9191), ~left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 139.97/26.89 -> [28] right_apart_point(skolem_B9090, skolem_L9191), left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 139.97/26.89
% 139.97/26.89 [28] CLOSURE : right_apart_point(skolem_B9090, skolem_L9191)
% 139.97/26.89
% 139.97/26.89 [27] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 139.97/26.89 -> [45] (right_convergent_lines(X12_3_2, Y13_3_2) <=> left_convergent_lines(X12_3_2, reverse_line(Y13_3_2)))
% 139.97/26.89
% 139.97/26.89 [45] BETA_EQUIV : (right_convergent_lines(X12_3_2, Y13_3_2) <=> left_convergent_lines(X12_3_2, reverse_line(Y13_3_2)))
% 139.97/26.89 -> [49] ~right_convergent_lines(X12_3_2, Y13_3_2), ~left_convergent_lines(X12_3_2, reverse_line(Y13_3_2))
% 139.97/26.89 -> [50] right_convergent_lines(X12_3_2, Y13_3_2), left_convergent_lines(X12_3_2, reverse_line(Y13_3_2))
% 139.97/26.89
% 139.97/26.89 [49] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 139.97/26.89 -> [59] (equally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4)) <=> ~unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4)))
% 139.97/26.89
% 139.97/26.89 [59] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4)) <=> ~unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4)))
% 139.97/26.89 -> [61] ~equally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4)), ~~unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4))
% 139.97/26.89 -> [62] equally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4)), ~unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4))
% 139.97/26.89
% 139.97/26.89 [62] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4))
% 139.97/26.89
% 139.97/26.89 [92] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_5_4), Y17_5_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_5_4), Y17_5_4))
% 139.97/26.89 -> [348] ~equally_directed_opposite_lines(reverse_line(Y17_5_4), Y17_5_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_5_4), Y17_5_4)
% 139.97/26.89 -> [349] equally_directed_opposite_lines(reverse_line(Y17_5_4), Y17_5_4), ~unequally_directed_opposite_lines(reverse_line(Y17_5_4), Y17_5_4)
% 139.97/26.89
% 139.97/26.89 [349] CLOSURE : ~unequally_directed_opposite_lines(reverse_line(Y17_5_4), Y17_5_4)
% 139.97/26.89
% 139.97/26.89 [369] BETA_IMPLY : (distinct_points(C35_8_6, C35_8_6) => (distinct_points(C35_8_6, C35_8_6) | distinct_points(C35_8_6, C35_8_6)))
% 139.97/26.89 -> [510] ~distinct_points(C35_8_6, C35_8_6)
% 139.97/26.89 -> [511] (distinct_points(C35_8_6, C35_8_6) | distinct_points(C35_8_6, C35_8_6))
% 139.97/26.89
% 139.97/26.89 [510] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 139.97/26.89 -> [520] ~distinct_lines(N39_12_8, N39_12_8)
% 139.97/26.89
% 139.97/26.89 [520] 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))))
% 139.97/26.89 -> [529] (distinct_lines(N39_12_8, N39_12_8) => (distinct_lines(N39_12_8, N39_12_8) | distinct_lines(N39_12_8, N39_12_8)))
% 139.97/26.89
% 139.97/26.89 [529] BETA_IMPLY : (distinct_lines(N39_12_8, N39_12_8) => (distinct_lines(N39_12_8, N39_12_8) | distinct_lines(N39_12_8, N39_12_8)))
% 139.97/26.89 -> [530] ~distinct_lines(N39_12_8, N39_12_8)
% 139.97/26.89 -> [531] (distinct_lines(N39_12_8, N39_12_8) | distinct_lines(N39_12_8, N39_12_8))
% 139.97/26.89
% 139.97/26.89 [530] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 139.97/26.89 -> [537] equally_directed_lines(L40_17_9, L40_17_9)
% 139.97/26.89
% 139.97/26.89 [537] CLOSURE : equally_directed_lines(L40_17_9, L40_17_9)
% 139.97/26.89
% 139.97/26.89 [531] BETA_OR : (distinct_lines(N39_12_8, N39_12_8) | distinct_lines(N39_12_8, N39_12_8))
% 139.97/26.89 -> [564] distinct_lines(N39_12_8, N39_12_8)
% 139.97/26.89 -> [565] distinct_lines(N39_12_8, N39_12_8)
% 139.97/26.89
% 139.97/26.89 [565] CLOSURE : distinct_lines(N39_12_8, N39_12_8)
% 139.97/26.89
% 139.97/26.89 [564] CLOSURE : distinct_lines(N39_12_8, N39_12_8)
% 139.97/26.89
% 139.97/26.89 [511] BETA_OR : (distinct_points(C35_8_6, C35_8_6) | distinct_points(C35_8_6, C35_8_6))
% 139.97/26.89 -> [577] distinct_points(C35_8_6, C35_8_6)
% 139.97/26.89 -> [578] distinct_points(C35_8_6, C35_8_6)
% 139.97/26.89
% 139.97/26.89 [578] CLOSURE : distinct_points(C35_8_6, C35_8_6)
% 139.97/26.89
% 139.97/26.89 [577] CLOSURE : distinct_points(C35_8_6, C35_8_6)
% 139.97/26.89
% 139.97/26.89 [76] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4)) <=> ~unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4)))
% 139.97/26.89 -> [681] ~equally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4)), ~~unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4))
% 139.97/26.89 -> [682] equally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4)), ~unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4))
% 139.97/26.89
% 139.97/26.89 [681] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4))
% 139.97/26.89 -> [692] unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4))
% 139.97/26.89
% 139.97/26.89 [692] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 139.97/26.89 -> [696] (equally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4))
% 139.97/26.89
% 139.97/26.89 [696] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4))
% 139.97/26.89 -> [697] ~equally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4)
% 139.97/26.89 -> [698] equally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4), ~unequally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4)
% 139.97/26.89
% 139.97/26.89 [698] CLOSURE : ~unequally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4)
% 139.97/26.89
% 139.97/26.89 [716] BETA_IMPLY : (distinct_points(C35_13_6, C35_13_6) => (distinct_points(C35_13_6, C35_13_6) | distinct_points(C35_13_6, C35_13_6)))
% 139.97/26.89 -> [877] ~distinct_points(C35_13_6, C35_13_6)
% 139.97/26.89 -> [878] (distinct_points(C35_13_6, C35_13_6) | distinct_points(C35_13_6, C35_13_6))
% 139.97/26.89
% 139.97/26.89 [878] BETA_OR : (distinct_points(C35_13_6, C35_13_6) | distinct_points(C35_13_6, C35_13_6))
% 139.97/26.89 -> [879] distinct_points(C35_13_6, C35_13_6)
% 139.97/26.89 -> [880] distinct_points(C35_13_6, C35_13_6)
% 139.97/26.89
% 139.97/26.89 [879] CLOSURE : distinct_points(C35_13_6, C35_13_6)
% 139.97/26.89
% 139.97/26.89 [880] CLOSURE : distinct_points(C35_13_6, C35_13_6)
% 139.97/26.89
% 139.97/26.89 [890] BETA_IMPLY : (distinct_lines(L37_20_8, L37_20_8) => (distinct_lines(L37_20_8, L37_20_8) | distinct_lines(L37_20_8, L37_20_8)))
% 139.97/26.89 -> [941] ~distinct_lines(L37_20_8, L37_20_8)
% 139.97/26.89 -> [942] (distinct_lines(L37_20_8, L37_20_8) | distinct_lines(L37_20_8, L37_20_8))
% 139.97/26.89
% 139.97/26.89 [941] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 139.97/26.89 -> [947] equally_directed_lines(L40_34_9, L40_34_9)
% 139.97/26.89
% 139.97/26.89 [947] CLOSURE : equally_directed_lines(L40_34_9, L40_34_9)
% 139.97/26.89
% 139.97/26.89 [942] BETA_OR : (distinct_lines(L37_20_8, L37_20_8) | distinct_lines(L37_20_8, L37_20_8))
% 139.97/26.89 -> [975] distinct_lines(L37_20_8, L37_20_8)
% 139.97/26.89 -> [976] distinct_lines(L37_20_8, L37_20_8)
% 139.97/26.89
% 139.97/26.89 [976] CLOSURE : distinct_lines(L37_20_8, L37_20_8)
% 139.97/26.89
% 139.97/26.89 [975] CLOSURE : distinct_lines(L37_20_8, L37_20_8)
% 139.97/26.89
% 139.97/26.89 [682] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_5_4), reverse_line(Y17_5_4))
% 139.97/26.89
% 139.97/26.89 [19] BETA_EQUIV : (right_apart_point(skolem_A8989, skolem_L9191) <=> left_apart_point(skolem_A8989, reverse_line(skolem_L9191)))
% 139.97/26.89 -> [3989] ~right_apart_point(skolem_A8989, skolem_L9191), ~left_apart_point(skolem_A8989, reverse_line(skolem_L9191))
% 139.97/26.89 -> [3990] right_apart_point(skolem_A8989, skolem_L9191), left_apart_point(skolem_A8989, reverse_line(skolem_L9191))
% 139.97/26.89
% 139.97/26.89 [3989] CLOSURE : ~right_apart_point(skolem_A8989, skolem_L9191)
% 139.97/26.89
% 139.97/26.89 [3990] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 139.97/26.89 -> [4000] (right_convergent_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) <=> left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))))
% 139.97/26.89
% 139.97/26.89 [4000] BETA_EQUIV : (right_convergent_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) <=> left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))))
% 139.97/26.89 -> [4001] ~right_convergent_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)), ~left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))
% 139.97/26.89 -> [4002] right_convergent_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)), left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))
% 139.97/26.89
% 139.97/26.89 [4002] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 139.97/26.89 -> [4006] (equally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) <=> ~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)))
% 139.97/26.89
% 139.97/26.89 [4006] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) <=> ~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)))
% 139.97/26.89 -> [4007] ~equally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)), ~~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 139.97/26.89 -> [4008] equally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)), ~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 139.97/26.89
% 139.97/26.89 [4007] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 139.97/26.89 -> [4013] unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 139.97/26.89
% 139.97/26.89 [4013] CLOSURE : unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 139.97/26.89
% 139.97/26.89 [4014] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4))
% 139.97/26.89 -> [5145] ~equally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4)
% 139.97/26.89 -> [5146] equally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4), ~unequally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4)
% 139.97/26.89
% 139.97/26.89 [5145] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4)
% 139.97/26.89 -> [5147] unequally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4)
% 139.97/26.89
% 139.97/26.89 [5147] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4)
% 139.97/26.89
% 139.97/26.89 [5146] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 139.97/26.89 -> [5148] ~distinct_points(B34_28_6, B34_28_6)
% 139.97/26.89
% 139.97/26.89 [5148] 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))))
% 139.97/26.89 -> [5158] (distinct_points(B34_28_6, B34_28_6) => (distinct_points(B34_28_6, B34_28_6) | distinct_points(B34_28_6, B34_28_6)))
% 139.97/26.89
% 139.97/26.89 [5158] BETA_IMPLY : (distinct_points(B34_28_6, B34_28_6) => (distinct_points(B34_28_6, B34_28_6) | distinct_points(B34_28_6, B34_28_6)))
% 139.97/26.89 -> [5161] ~distinct_points(B34_28_6, B34_28_6)
% 139.97/26.89 -> [5162] (distinct_points(B34_28_6, B34_28_6) | distinct_points(B34_28_6, B34_28_6))
% 139.97/26.89
% 139.97/26.89 [5162] BETA_OR : (distinct_points(B34_28_6, B34_28_6) | distinct_points(B34_28_6, B34_28_6))
% 139.97/26.89 -> [5164] distinct_points(B34_28_6, B34_28_6)
% 139.97/26.89 -> [5165] distinct_points(B34_28_6, B34_28_6)
% 139.97/26.89
% 139.97/26.89 [5164] CLOSURE : distinct_points(B34_28_6, B34_28_6)
% 139.97/26.89
% 139.97/26.89 [5165] CLOSURE : distinct_points(B34_28_6, B34_28_6)
% 139.97/26.89
% 139.97/26.89 [5161] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 139.97/26.89 -> [5175] ~distinct_lines(N39_41_8, N39_41_8)
% 139.97/26.89
% 139.97/26.89 [5175] 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))))
% 139.97/26.89 -> [5176] (distinct_lines(N39_41_8, N39_41_8) => (distinct_lines(N39_41_8, N39_41_8) | distinct_lines(N39_41_8, N39_41_8)))
% 139.97/26.89
% 139.97/26.89 [5176] BETA_IMPLY : (distinct_lines(N39_41_8, N39_41_8) => (distinct_lines(N39_41_8, N39_41_8) | distinct_lines(N39_41_8, N39_41_8)))
% 139.97/26.89 -> [5177] ~distinct_lines(N39_41_8, N39_41_8)
% 139.97/26.89 -> [5178] (distinct_lines(N39_41_8, N39_41_8) | distinct_lines(N39_41_8, N39_41_8))
% 139.97/26.89
% 139.97/26.89 [5178] BETA_OR : (distinct_lines(N39_41_8, N39_41_8) | distinct_lines(N39_41_8, N39_41_8))
% 139.97/26.89 -> [5179] distinct_lines(N39_41_8, N39_41_8)
% 139.97/26.89 -> [5180] distinct_lines(N39_41_8, N39_41_8)
% 139.97/26.89
% 139.97/26.89 [5180] CLOSURE : distinct_lines(N39_41_8, N39_41_8)
% 139.97/26.89
% 139.97/26.89 [5179] CLOSURE : distinct_lines(N39_41_8, N39_41_8)
% 139.97/26.89
% 139.97/26.89 [5177] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 139.97/26.89 -> [5183] equally_directed_lines(L40_71_9, L40_71_9)
% 139.97/26.89
% 139.97/26.89 [5183] 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))))
% 139.97/26.89 -> [5184] (unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) => (unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) | unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))))
% 139.97/26.89
% 139.97/26.89 [5184] BETA_IMPLY : (unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) => (unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) | unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))))
% 139.97/26.89 -> [5185] ~unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89 -> [5186] (unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) | unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)))
% 139.97/26.89
% 139.97/26.89 [5186] BETA_OR : (unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) | unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)))
% 139.97/26.89 -> [5187] unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89 -> [5188] unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89
% 139.97/26.89 [5188] CLOSURE : unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89
% 139.97/26.89 [5187] CLOSURE : unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89
% 139.97/26.89 [5189] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11)))) => ((unequally_directed_lines(reverse_line(N46_85_11), N46_85_11) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))) | (unequally_directed_lines(reverse_line(N46_85_11), N46_85_11) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)))))
% 139.97/26.89 -> [5299] ~(unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11))))
% 139.97/26.89 -> [5300] ((unequally_directed_lines(reverse_line(N46_85_11), N46_85_11) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))) | (unequally_directed_lines(reverse_line(N46_85_11), N46_85_11) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))))
% 139.97/26.89
% 139.97/26.89 [5300] BETA_OR : ((unequally_directed_lines(reverse_line(N46_85_11), N46_85_11) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))) | (unequally_directed_lines(reverse_line(N46_85_11), N46_85_11) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))))
% 139.97/26.89 -> [5302] (unequally_directed_lines(reverse_line(N46_85_11), N46_85_11) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)))
% 139.97/26.89 -> [5303] (unequally_directed_lines(reverse_line(N46_85_11), N46_85_11) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)))
% 139.97/26.89
% 139.97/26.89 [5302] ALPHA_AND : (unequally_directed_lines(reverse_line(N46_85_11), N46_85_11) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)))
% 139.97/26.89 -> [5308] unequally_directed_lines(reverse_line(N46_85_11), N46_85_11), unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89
% 139.97/26.89 [5308] CLOSURE : unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89
% 139.97/26.89 [5306] CLOSURE : unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89
% 139.97/26.89 [5299] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11))))
% 139.97/26.89 -> [5370] ~unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89 -> [5371] ~unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11)))
% 139.97/26.89
% 139.97/26.89 [5371] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 139.97/26.89 -> [5375] (unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) | unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11))))
% 139.97/26.89
% 139.97/26.89 [5375] BETA_OR : (unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) | unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11))))
% 139.97/26.89 -> [5376] unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89 -> [5377] unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11)))
% 139.97/26.89
% 139.97/26.89 [5376] CLOSURE : unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89
% 139.97/26.89 [5377] CLOSURE : unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11)))
% 139.97/26.89
% 139.97/26.89 [5370] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 139.97/26.89 -> [5372] (unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) | unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11))))
% 139.97/26.89
% 139.97/26.89 [5372] BETA_OR : (unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) | unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11))))
% 139.97/26.89 -> [5373] unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89 -> [5374] unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11)))
% 139.97/26.89
% 139.97/26.89 [5373] CLOSURE : unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89
% 139.97/26.89 [5374] 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)))))
% 139.97/26.89 -> [5378] ((unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11)))) => (left_convergent_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) | left_convergent_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11)))))
% 139.97/26.89
% 139.97/26.89 [5378] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11)))) => (left_convergent_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) | left_convergent_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11)))))
% 139.97/26.89 -> [5379] ~(unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11))))
% 139.97/26.89 -> [5380] (left_convergent_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) | left_convergent_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11))))
% 139.97/26.89
% 139.97/26.89 [5380] BETA_OR : (left_convergent_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) | left_convergent_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11))))
% 139.97/26.89 -> [5385] left_convergent_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89 -> [5386] left_convergent_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11)))
% 139.97/26.89
% 139.97/26.89 [5386] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 139.97/26.89 -> [5389] ~(left_apart_point(A51_214_14, L52_214_14) | left_apart_point(A51_214_14, reverse_line(L52_214_14)))
% 139.97/26.89
% 139.97/26.89 [5389] ALPHA_NOT_OR : ~(left_apart_point(A51_214_14, L52_214_14) | left_apart_point(A51_214_14, reverse_line(L52_214_14)))
% 139.97/26.89 -> [5390] ~left_apart_point(A51_214_14, L52_214_14), ~left_apart_point(A51_214_14, reverse_line(L52_214_14))
% 139.97/26.89
% 139.97/26.89 [5390] CLOSURE : ~left_apart_point(A51_214_14, L52_214_14)
% 139.97/26.89
% 139.97/26.89 [5385] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 139.97/26.89 -> [5392] ~(left_apart_point(A51_215_14, L52_215_14) | left_apart_point(A51_215_14, reverse_line(L52_215_14)))
% 139.97/26.89
% 139.97/26.89 [5392] ALPHA_NOT_OR : ~(left_apart_point(A51_215_14, L52_215_14) | left_apart_point(A51_215_14, reverse_line(L52_215_14)))
% 139.97/26.89 -> [5395] ~left_apart_point(A51_215_14, L52_215_14), ~left_apart_point(A51_215_14, reverse_line(L52_215_14))
% 139.97/26.89
% 139.97/26.89 [5395] CLOSURE : ~left_apart_point(A51_215_14, L52_215_14)
% 139.97/26.89
% 139.97/26.89 [5379] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11)) & unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11))))
% 139.97/26.89 -> [5381] ~unequally_directed_lines(reverse_line(N46_85_11), reverse_line(N46_85_11))
% 139.97/26.89 -> [5382] ~unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11)))
% 139.97/26.89
% 139.97/26.89 [5382] CLOSURE : ~unequally_directed_lines(reverse_line(N46_85_11), reverse_line(reverse_line(N46_85_11)))
% 139.97/26.89
% 139.97/26.89 [5381] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 139.97/26.89 -> [5419] ~(left_apart_point(A51_216_14, L52_216_14) | left_apart_point(A51_216_14, reverse_line(L52_216_14)))
% 139.97/26.89
% 139.97/26.89 [5419] ALPHA_NOT_OR : ~(left_apart_point(A51_216_14, L52_216_14) | left_apart_point(A51_216_14, reverse_line(L52_216_14)))
% 139.97/26.89 -> [5422] ~left_apart_point(A51_216_14, L52_216_14), ~left_apart_point(A51_216_14, reverse_line(L52_216_14))
% 139.97/26.89
% 139.97/26.89 [5422] CLOSURE : ~left_apart_point(A51_216_14, L52_216_14)
% 139.97/26.89
% 139.97/26.89 [4001] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 139.97/26.89 -> [4003] (equally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) <=> ~unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)))
% 139.97/26.89
% 139.97/26.89 [4003] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) <=> ~unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)))
% 139.97/26.89 -> [4004] ~equally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)), ~~unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.89 -> [4005] equally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)), ~unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.89
% 139.97/26.89 [4004] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.89 -> [4009] unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.89
% 139.97/26.89 [4009] CLOSURE : unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.89
% 139.97/26.89 [4010] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_16_4), Y17_16_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_16_4), Y17_16_4))
% 139.97/26.89 -> [4526] ~equally_directed_opposite_lines(reverse_line(Y17_16_4), Y17_16_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_16_4), Y17_16_4)
% 139.97/26.89 -> [4527] equally_directed_opposite_lines(reverse_line(Y17_16_4), Y17_16_4), ~unequally_directed_opposite_lines(reverse_line(Y17_16_4), Y17_16_4)
% 139.97/26.89
% 139.97/26.89 [4527] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 139.97/26.89 -> [4531] ~distinct_points(C35_25_6, C35_25_6)
% 139.97/26.89
% 139.97/26.89 [4531] 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))))
% 139.97/26.89 -> [4532] (distinct_points(C35_25_6, C35_25_6) => (distinct_points(C35_25_6, C35_25_6) | distinct_points(C35_25_6, C35_25_6)))
% 139.97/26.89
% 139.97/26.89 [4532] BETA_IMPLY : (distinct_points(C35_25_6, C35_25_6) => (distinct_points(C35_25_6, C35_25_6) | distinct_points(C35_25_6, C35_25_6)))
% 139.97/26.89 -> [4533] ~distinct_points(C35_25_6, C35_25_6)
% 139.97/26.89 -> [4534] (distinct_points(C35_25_6, C35_25_6) | distinct_points(C35_25_6, C35_25_6))
% 139.97/26.89
% 139.97/26.89 [4534] BETA_OR : (distinct_points(C35_25_6, C35_25_6) | distinct_points(C35_25_6, C35_25_6))
% 139.97/26.89 -> [4535] distinct_points(C35_25_6, C35_25_6)
% 139.97/26.89 -> [4536] distinct_points(C35_25_6, C35_25_6)
% 139.97/26.89
% 139.97/26.89 [4535] CLOSURE : distinct_points(C35_25_6, C35_25_6)
% 139.97/26.89
% 139.97/26.89 [4536] CLOSURE : distinct_points(C35_25_6, C35_25_6)
% 139.97/26.89
% 139.97/26.89 [4538] BETA_IMPLY : (distinct_lines(N39_38_8, N39_38_8) => (distinct_lines(N39_38_8, N39_38_8) | distinct_lines(N39_38_8, N39_38_8)))
% 139.97/26.89 -> [5116] ~distinct_lines(N39_38_8, N39_38_8)
% 139.97/26.89 -> [5117] (distinct_lines(N39_38_8, N39_38_8) | distinct_lines(N39_38_8, N39_38_8))
% 139.97/26.89
% 139.97/26.89 [5117] BETA_OR : (distinct_lines(N39_38_8, N39_38_8) | distinct_lines(N39_38_8, N39_38_8))
% 139.97/26.89 -> [5118] distinct_lines(N39_38_8, N39_38_8)
% 139.97/26.89 -> [5119] distinct_lines(N39_38_8, N39_38_8)
% 139.97/26.89
% 139.97/26.89 [5119] CLOSURE : distinct_lines(N39_38_8, N39_38_8)
% 139.97/26.89
% 139.97/26.89 [5118] CLOSURE : distinct_lines(N39_38_8, N39_38_8)
% 139.97/26.89
% 139.97/26.89 [5121] BETA_IMPLY : (unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) => (unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) | unequally_directed_lines(Y17_16_4, reverse_line(Y17_16_4))))
% 139.97/26.89 -> [5393] ~unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4)
% 139.97/26.89 -> [5394] (unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) | unequally_directed_lines(Y17_16_4, reverse_line(Y17_16_4)))
% 139.97/26.89
% 139.97/26.89 [5393] 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))))))
% 139.97/26.89 -> [5398] ((unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))) => ((unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))) | (unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)))))
% 139.97/26.89
% 139.97/26.89 [5398] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))) => ((unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))) | (unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)))))
% 139.97/26.89 -> [5399] ~(unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))))
% 139.97/26.89 -> [5400] ((unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))) | (unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))))
% 139.97/26.89
% 139.97/26.89 [5400] BETA_OR : ((unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))) | (unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))))
% 139.97/26.89 -> [5403] (unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)))
% 139.97/26.89 -> [5404] (unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)))
% 139.97/26.89
% 139.97/26.89 [5404] ALPHA_AND : (unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)))
% 139.97/26.89 -> [5405] unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4), unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.89
% 139.97/26.89 [5405] CLOSURE : unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.89
% 139.97/26.89 [5409] CLOSURE : unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.89
% 139.97/26.89 [5399] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))))
% 139.97/26.89 -> [5466] ~unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.89 -> [5467] ~unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))
% 139.97/26.89
% 139.97/26.89 [5466] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 139.97/26.90 -> [5473] (unequally_directed_lines(L47_431_12, M48_431_12) | unequally_directed_lines(L47_431_12, reverse_line(M48_431_12)))
% 139.97/26.90
% 139.97/26.90 [5473] BETA_OR : (unequally_directed_lines(L47_431_12, M48_431_12) | unequally_directed_lines(L47_431_12, reverse_line(M48_431_12)))
% 139.97/26.90 -> [5476] unequally_directed_lines(L47_431_12, M48_431_12)
% 139.97/26.90 -> [5477] unequally_directed_lines(L47_431_12, reverse_line(M48_431_12))
% 139.97/26.90
% 139.97/26.90 [5476] CLOSURE : unequally_directed_lines(L47_431_12, M48_431_12)
% 139.97/26.90
% 139.97/26.90 [5477] CLOSURE : unequally_directed_lines(L47_431_12, reverse_line(M48_431_12))
% 139.97/26.90
% 139.97/26.90 [5467] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 139.97/26.90 -> [5472] (unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) | unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))))
% 139.97/26.90
% 139.97/26.90 [5472] BETA_OR : (unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) | unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))))
% 139.97/26.90 -> [5474] unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.90 -> [5475] unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))
% 139.97/26.90
% 139.97/26.90 [5474] CLOSURE : unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.90
% 139.97/26.90 [5475] CLOSURE : unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))
% 139.97/26.90
% 139.97/26.90 [5394] BETA_OR : (unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) | unequally_directed_lines(Y17_16_4, reverse_line(Y17_16_4)))
% 139.97/26.90 -> [5486] unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.90 -> [5487] unequally_directed_lines(Y17_16_4, reverse_line(Y17_16_4))
% 139.97/26.90
% 139.97/26.90 [5486] CLOSURE : unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.90
% 139.97/26.90 [5488] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))) => ((unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))) | (unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)))))
% 139.97/26.90 -> [5623] ~(unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))))
% 139.97/26.90 -> [5624] ((unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))) | (unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))))
% 139.97/26.90
% 139.97/26.90 [5624] BETA_OR : ((unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))) | (unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))))
% 139.97/26.90 -> [5628] (unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)))
% 139.97/26.90 -> [5629] (unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)))
% 139.97/26.90
% 139.97/26.90 [5628] ALPHA_AND : (unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)))
% 139.97/26.90 -> [5630] unequally_directed_lines(reverse_line(Y17_16_4), Y17_16_4), unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.90
% 139.97/26.90 [5630] CLOSURE : unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.90
% 139.97/26.90 [5631] CLOSURE : unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.90
% 139.97/26.90 [5623] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))))
% 139.97/26.90 -> [5708] ~unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.90 -> [5709] ~unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))
% 139.97/26.90
% 139.97/26.90 [5709] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 139.97/26.90 -> [5714] (unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) | unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))))
% 139.97/26.90
% 139.97/26.90 [5714] BETA_OR : (unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) | unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))))
% 139.97/26.90 -> [5717] unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.90 -> [5718] unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))
% 139.97/26.90
% 139.97/26.90 [5717] CLOSURE : unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.90
% 139.97/26.90 [5718] CLOSURE : unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))
% 139.97/26.90
% 139.97/26.90 [5708] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 139.97/26.90 -> [5711] (unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) | unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))))
% 139.97/26.90
% 139.97/26.90 [5711] BETA_OR : (unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4)) | unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))))
% 139.97/26.90 -> [5715] unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.90 -> [5716] unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))
% 139.97/26.90
% 139.97/26.90 [5715] CLOSURE : unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 139.97/26.90
% 139.97/26.90 [5716] 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)))))
% 139.97/26.90 -> [5723] ((unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(reverse_line(Y17_16_4))))) => (left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))) | left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(reverse_line(Y17_16_4))))))
% 139.97/26.90
% 139.97/26.90 [5723] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(reverse_line(Y17_16_4))))) => (left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))) | left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(reverse_line(Y17_16_4))))))
% 139.97/26.90 -> [5724] ~(unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(reverse_line(Y17_16_4)))))
% 139.97/26.90 -> [5725] (left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))) | left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(reverse_line(Y17_16_4)))))
% 139.97/26.90
% 139.97/26.90 [5724] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))) & unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(reverse_line(Y17_16_4)))))
% 139.97/26.90 -> [5729] ~unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))
% 139.97/26.90 -> [5730] ~unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(reverse_line(Y17_16_4))))
% 139.97/26.90
% 139.97/26.90 [5729] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))
% 139.97/26.90
% 139.97/26.90 [5730] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 139.97/26.90 -> [5743] ~(left_apart_point(A51_236_14, L52_236_14) | left_apart_point(A51_236_14, reverse_line(L52_236_14)))
% 139.97/26.90
% 139.97/26.90 [5743] ALPHA_NOT_OR : ~(left_apart_point(A51_236_14, L52_236_14) | left_apart_point(A51_236_14, reverse_line(L52_236_14)))
% 139.97/26.90 -> [5744] ~left_apart_point(A51_236_14, L52_236_14), ~left_apart_point(A51_236_14, reverse_line(L52_236_14))
% 139.97/26.90
% 139.97/26.90 [5744] CLOSURE : ~left_apart_point(A51_236_14, L52_236_14)
% 139.97/26.90
% 139.97/26.90 [5725] BETA_OR : (left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4))) | left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(reverse_line(Y17_16_4)))))
% 139.97/26.90 -> [5758] left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))
% 139.97/26.90 -> [5759] left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(reverse_line(Y17_16_4))))
% 139.97/26.90
% 139.97/26.90 [5758] CLOSURE : left_convergent_lines(reverse_line(Y17_16_4), reverse_line(reverse_line(Y17_16_4)))
% 139.97/26.90
% 139.97/26.90 [5759] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 139.97/26.90 -> [5771] ~(left_apart_point(A51_239_14, L52_239_14) | left_apart_point(A51_239_14, reverse_line(L52_239_14)))
% 139.97/26.90
% 139.97/26.90 [5771] ALPHA_NOT_OR : ~(left_apart_point(A51_239_14, L52_239_14) | left_apart_point(A51_239_14, reverse_line(L52_239_14)))
% 139.97/26.90 -> [5772] ~left_apart_point(A51_239_14, L52_239_14), ~left_apart_point(A51_239_14, reverse_line(L52_239_14))
% 139.97/26.90
% 139.97/26.90 [5772] CLOSURE : ~left_apart_point(A51_239_14, L52_239_14)
% 139.97/26.90
% 139.97/26.90 [4530] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_16_4), Y17_16_4)
% 139.97/26.90
% 139.97/26.90 [9] GAMMA_FORALL : ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9))))
% 139.97/26.90 -> [11] (unequally_directed_opposite_lines(reverse_line(Y9_0_0), Y9_0_0) <=> unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)))
% 139.97/26.90
% 139.97/26.90 [11] BETA_EQUIV : (unequally_directed_opposite_lines(reverse_line(Y9_0_0), Y9_0_0) <=> unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)))
% 139.97/26.90 -> [13] ~unequally_directed_opposite_lines(reverse_line(Y9_0_0), Y9_0_0), ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 139.97/26.90 -> [14] unequally_directed_opposite_lines(reverse_line(Y9_0_0), Y9_0_0), unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 139.97/26.90
% 139.97/26.90 [14] GAMMA_FORALL : ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11))))
% 139.97/26.90 -> [17] (right_apart_point(skolem_B9090, skolem_L9191) <=> left_apart_point(skolem_B9090, reverse_line(skolem_L9191)))
% 139.97/26.90
% 139.97/26.90 [17] BETA_EQUIV : (right_apart_point(skolem_B9090, skolem_L9191) <=> left_apart_point(skolem_B9090, reverse_line(skolem_L9191)))
% 139.97/26.90 -> [20] ~right_apart_point(skolem_B9090, skolem_L9191), ~left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 139.97/26.90 -> [21] right_apart_point(skolem_B9090, skolem_L9191), left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 139.97/26.90
% 139.97/26.90 [21] CLOSURE : right_apart_point(skolem_B9090, skolem_L9191)
% 139.97/26.90
% 139.97/26.90 [29] BETA_EQUIV : (right_convergent_lines(X12_0_2, Y13_0_2) <=> left_convergent_lines(X12_0_2, reverse_line(Y13_0_2)))
% 139.97/26.90 -> [457] ~right_convergent_lines(X12_0_2, Y13_0_2), ~left_convergent_lines(X12_0_2, reverse_line(Y13_0_2))
% 139.97/26.90 -> [458] right_convergent_lines(X12_0_2, Y13_0_2), left_convergent_lines(X12_0_2, reverse_line(Y13_0_2))
% 139.97/26.90
% 139.97/26.90 [458] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 139.97/26.90 -> [470] (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)))
% 139.97/26.90
% 139.97/26.90 [470] 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)))
% 139.97/26.90 -> [475] ~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))
% 139.97/26.90 -> [476] 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))
% 139.97/26.90
% 139.97/26.90 [475] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 139.97/26.90 -> [485] unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 139.97/26.90
% 139.97/26.90 [485] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 139.97/26.90 -> [490] (equally_directed_opposite_lines(X16_9_4, Y17_9_4) <=> ~unequally_directed_opposite_lines(X16_9_4, Y17_9_4))
% 139.97/26.90
% 139.97/26.90 [490] BETA_EQUIV : (equally_directed_opposite_lines(X16_9_4, Y17_9_4) <=> ~unequally_directed_opposite_lines(X16_9_4, Y17_9_4))
% 139.97/26.90 -> [491] ~equally_directed_opposite_lines(X16_9_4, Y17_9_4), ~~unequally_directed_opposite_lines(X16_9_4, Y17_9_4)
% 139.97/26.90 -> [492] equally_directed_opposite_lines(X16_9_4, Y17_9_4), ~unequally_directed_opposite_lines(X16_9_4, Y17_9_4)
% 139.97/26.90
% 139.97/26.90 [492] CLOSURE : ~unequally_directed_opposite_lines(X16_9_4, Y17_9_4)
% 139.97/26.90
% 139.97/26.90 [521] 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)))
% 139.97/26.90 -> [661] ~distinct_points(C35_11_6, C35_11_6)
% 139.97/26.90 -> [662] (distinct_points(C35_11_6, C35_11_6) | distinct_points(C35_11_6, C35_11_6))
% 139.97/26.90
% 139.97/26.90 [662] BETA_OR : (distinct_points(C35_11_6, C35_11_6) | distinct_points(C35_11_6, C35_11_6))
% 139.97/26.90 -> [663] distinct_points(C35_11_6, C35_11_6)
% 139.97/26.90 -> [664] distinct_points(C35_11_6, C35_11_6)
% 139.97/26.90
% 139.97/26.90 [663] CLOSURE : distinct_points(C35_11_6, C35_11_6)
% 139.97/26.90
% 139.97/26.90 [664] CLOSURE : distinct_points(C35_11_6, C35_11_6)
% 139.97/26.90
% 139.97/26.90 [672] BETA_IMPLY : (distinct_lines(N39_16_8, N39_16_8) => (distinct_lines(N39_16_8, N39_16_8) | distinct_lines(N39_16_8, N39_16_8)))
% 139.97/26.90 -> [742] ~distinct_lines(N39_16_8, N39_16_8)
% 139.97/26.90 -> [743] (distinct_lines(N39_16_8, N39_16_8) | distinct_lines(N39_16_8, N39_16_8))
% 139.97/26.90
% 139.97/26.90 [743] BETA_OR : (distinct_lines(N39_16_8, N39_16_8) | distinct_lines(N39_16_8, N39_16_8))
% 139.97/26.90 -> [744] distinct_lines(N39_16_8, N39_16_8)
% 139.97/26.90 -> [745] distinct_lines(N39_16_8, N39_16_8)
% 139.97/26.90
% 139.97/26.90 [744] CLOSURE : distinct_lines(N39_16_8, N39_16_8)
% 139.97/26.90
% 139.97/26.90 [745] CLOSURE : distinct_lines(N39_16_8, N39_16_8)
% 139.97/26.90
% 139.97/26.90 [766] CLOSURE : equally_directed_lines(L40_26_9, L40_26_9)
% 139.97/26.90
% 139.97/26.90 [476] CLOSURE : ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 139.97/26.90
% 139.97/26.90 [471] 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)))
% 139.97/26.90 -> [829] ~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))
% 139.97/26.90 -> [830] 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))
% 139.97/26.90
% 139.97/26.90 [829] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 139.97/26.90 -> [840] unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 139.97/26.90
% 139.97/26.90 [840] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 139.97/26.90 -> [845] (equally_directed_opposite_lines(reverse_line(Y17_11_4), Y17_11_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_11_4), Y17_11_4))
% 139.97/26.90
% 139.97/26.90 [845] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_11_4), Y17_11_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_11_4), Y17_11_4))
% 139.97/26.90 -> [846] ~equally_directed_opposite_lines(reverse_line(Y17_11_4), Y17_11_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_11_4), Y17_11_4)
% 139.97/26.90 -> [847] equally_directed_opposite_lines(reverse_line(Y17_11_4), Y17_11_4), ~unequally_directed_opposite_lines(reverse_line(Y17_11_4), Y17_11_4)
% 139.97/26.90
% 139.97/26.90 [847] CLOSURE : ~unequally_directed_opposite_lines(reverse_line(Y17_11_4), Y17_11_4)
% 139.97/26.90
% 139.97/26.90 [868] BETA_IMPLY : (distinct_points(C35_14_6, C35_14_6) => (distinct_points(C35_14_6, C35_14_6) | distinct_points(C35_14_6, C35_14_6)))
% 139.97/26.90 -> [1017] ~distinct_points(C35_14_6, C35_14_6)
% 139.97/26.90 -> [1018] (distinct_points(C35_14_6, C35_14_6) | distinct_points(C35_14_6, C35_14_6))
% 139.97/26.90
% 139.97/26.90 [1018] BETA_OR : (distinct_points(C35_14_6, C35_14_6) | distinct_points(C35_14_6, C35_14_6))
% 139.97/26.90 -> [1019] distinct_points(C35_14_6, C35_14_6)
% 139.97/26.90 -> [1020] distinct_points(C35_14_6, C35_14_6)
% 139.97/26.90
% 139.97/26.90 [1019] CLOSURE : distinct_points(C35_14_6, C35_14_6)
% 139.97/26.90
% 139.97/26.90 [1020] CLOSURE : distinct_points(C35_14_6, C35_14_6)
% 139.97/26.90
% 139.97/26.90 [1046] BETA_IMPLY : (distinct_lines(N39_21_8, N39_21_8) => (distinct_lines(N39_21_8, N39_21_8) | distinct_lines(N39_21_8, N39_21_8)))
% 139.97/26.90 -> [1073] ~distinct_lines(N39_21_8, N39_21_8)
% 139.97/26.90 -> [1074] (distinct_lines(N39_21_8, N39_21_8) | distinct_lines(N39_21_8, N39_21_8))
% 139.97/26.90
% 139.97/26.90 [1073] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 139.97/26.90 -> [1077] equally_directed_lines(L40_39_9, L40_39_9)
% 139.97/26.90
% 139.97/26.90 [1077] CLOSURE : equally_directed_lines(L40_39_9, L40_39_9)
% 139.97/26.90
% 139.97/26.90 [1074] BETA_OR : (distinct_lines(N39_21_8, N39_21_8) | distinct_lines(N39_21_8, N39_21_8))
% 139.97/26.90 -> [1090] distinct_lines(N39_21_8, N39_21_8)
% 139.97/26.90 -> [1091] distinct_lines(N39_21_8, N39_21_8)
% 139.97/26.90
% 139.97/26.90 [1090] CLOSURE : distinct_lines(N39_21_8, N39_21_8)
% 139.97/26.90
% 139.97/26.90 [1091] CLOSURE : distinct_lines(N39_21_8, N39_21_8)
% 139.97/26.90
% 139.97/26.90 [830] CLOSURE : ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 139.97/26.90
% 139.97/26.90 [18] BETA_EQUIV : (right_apart_point(skolem_B9090, skolem_L9191) <=> left_apart_point(skolem_B9090, reverse_line(skolem_L9191)))
% 139.97/26.90 -> [6577] ~right_apart_point(skolem_B9090, skolem_L9191), ~left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 139.97/26.90 -> [6578] right_apart_point(skolem_B9090, skolem_L9191), left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 139.97/26.90
% 139.97/26.90 [6578] CLOSURE : right_apart_point(skolem_B9090, skolem_L9191)
% 139.97/26.90
% 139.97/26.90 [6577] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 139.97/26.90 -> [6579] (right_convergent_lines(reverse_line(Y17_23_4), Y17_23_4) <=> left_convergent_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)))
% 139.97/26.90
% 139.97/26.90 [6579] BETA_EQUIV : (right_convergent_lines(reverse_line(Y17_23_4), Y17_23_4) <=> left_convergent_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)))
% 139.97/26.90 -> [6580] ~right_convergent_lines(reverse_line(Y17_23_4), Y17_23_4), ~left_convergent_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90 -> [6581] right_convergent_lines(reverse_line(Y17_23_4), Y17_23_4), left_convergent_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90
% 139.97/26.90 [6581] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 139.97/26.90 -> [6583] (equally_directed_lines(reverse_line(Y17_22_4), reverse_line(Y17_22_4)) <=> ~unequally_directed_lines(reverse_line(Y17_22_4), reverse_line(Y17_22_4)))
% 139.97/26.90
% 139.97/26.90 [6583] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_22_4), reverse_line(Y17_22_4)) <=> ~unequally_directed_lines(reverse_line(Y17_22_4), reverse_line(Y17_22_4)))
% 139.97/26.90 -> [6586] ~equally_directed_lines(reverse_line(Y17_22_4), reverse_line(Y17_22_4)), ~~unequally_directed_lines(reverse_line(Y17_22_4), reverse_line(Y17_22_4))
% 139.97/26.90 -> [6587] equally_directed_lines(reverse_line(Y17_22_4), reverse_line(Y17_22_4)), ~unequally_directed_lines(reverse_line(Y17_22_4), reverse_line(Y17_22_4))
% 139.97/26.90
% 139.97/26.90 [6586] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_22_4), reverse_line(Y17_22_4))
% 139.97/26.90 -> [6589] unequally_directed_lines(reverse_line(Y17_22_4), reverse_line(Y17_22_4))
% 139.97/26.90
% 139.97/26.90 [6589] CLOSURE : unequally_directed_lines(reverse_line(Y17_22_4), reverse_line(Y17_22_4))
% 139.97/26.90
% 139.97/26.90 [6590] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_22_4), Y17_22_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_22_4), Y17_22_4))
% 139.97/26.90 -> [7081] ~equally_directed_opposite_lines(reverse_line(Y17_22_4), Y17_22_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_22_4), Y17_22_4)
% 139.97/26.90 -> [7082] equally_directed_opposite_lines(reverse_line(Y17_22_4), Y17_22_4), ~unequally_directed_opposite_lines(reverse_line(Y17_22_4), Y17_22_4)
% 139.97/26.90
% 139.97/26.90 [7081] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_22_4), Y17_22_4)
% 139.97/26.90 -> [7083] unequally_directed_opposite_lines(reverse_line(Y17_22_4), Y17_22_4)
% 139.97/26.90
% 139.97/26.90 [7083] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_22_4), Y17_22_4)
% 139.97/26.90
% 139.97/26.90 [7082] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 139.97/26.90 -> [7084] ~distinct_points(C35_35_6, C35_35_6)
% 139.97/26.90
% 139.97/26.90 [7084] 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))))
% 139.97/26.90 -> [7085] (distinct_points(C35_35_6, C35_35_6) => (distinct_points(C35_35_6, C35_35_6) | distinct_points(C35_35_6, C35_35_6)))
% 139.97/26.90
% 139.97/26.90 [7085] BETA_IMPLY : (distinct_points(C35_35_6, C35_35_6) => (distinct_points(C35_35_6, C35_35_6) | distinct_points(C35_35_6, C35_35_6)))
% 139.97/26.90 -> [7086] ~distinct_points(C35_35_6, C35_35_6)
% 139.97/26.90 -> [7087] (distinct_points(C35_35_6, C35_35_6) | distinct_points(C35_35_6, C35_35_6))
% 139.97/26.90
% 139.97/26.90 [7087] BETA_OR : (distinct_points(C35_35_6, C35_35_6) | distinct_points(C35_35_6, C35_35_6))
% 139.97/26.90 -> [7088] distinct_points(C35_35_6, C35_35_6)
% 139.97/26.90 -> [7089] distinct_points(C35_35_6, C35_35_6)
% 139.97/26.90
% 139.97/26.90 [7089] CLOSURE : distinct_points(C35_35_6, C35_35_6)
% 139.97/26.90
% 139.97/26.90 [7088] CLOSURE : distinct_points(C35_35_6, C35_35_6)
% 139.97/26.90
% 139.97/26.90 [7086] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 139.97/26.90 -> [7090] ~distinct_lines(N39_50_8, N39_50_8)
% 139.97/26.90
% 139.97/26.90 [7090] 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))))
% 139.97/26.90 -> [7091] (distinct_lines(N39_50_8, N39_50_8) => (distinct_lines(N39_50_8, N39_50_8) | distinct_lines(N39_50_8, N39_50_8)))
% 139.97/26.90
% 139.97/26.90 [7091] BETA_IMPLY : (distinct_lines(N39_50_8, N39_50_8) => (distinct_lines(N39_50_8, N39_50_8) | distinct_lines(N39_50_8, N39_50_8)))
% 139.97/26.90 -> [7092] ~distinct_lines(N39_50_8, N39_50_8)
% 139.97/26.90 -> [7093] (distinct_lines(N39_50_8, N39_50_8) | distinct_lines(N39_50_8, N39_50_8))
% 139.97/26.90
% 139.97/26.90 [7093] BETA_OR : (distinct_lines(N39_50_8, N39_50_8) | distinct_lines(N39_50_8, N39_50_8))
% 139.97/26.90 -> [7094] distinct_lines(N39_50_8, N39_50_8)
% 139.97/26.90 -> [7095] distinct_lines(N39_50_8, N39_50_8)
% 139.97/26.90
% 139.97/26.90 [7095] CLOSURE : distinct_lines(N39_50_8, N39_50_8)
% 139.97/26.90
% 139.97/26.90 [7094] CLOSURE : distinct_lines(N39_50_8, N39_50_8)
% 139.97/26.90
% 139.97/26.90 [7099] BETA_IMPLY : (unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) => (unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) | unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))))
% 139.97/26.90 -> [7258] ~unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90 -> [7259] (unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) | unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)))
% 139.97/26.90
% 139.97/26.90 [7259] BETA_OR : (unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) | unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)))
% 139.97/26.90 -> [7260] unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90 -> [7261] unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90
% 139.97/26.90 [7260] CLOSURE : unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90
% 139.97/26.90 [7261] CLOSURE : unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90
% 139.97/26.90 [7268] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11)))) => ((unequally_directed_lines(reverse_line(N46_124_11), N46_124_11) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))) | (unequally_directed_lines(reverse_line(N46_124_11), N46_124_11) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)))))
% 139.97/26.90 -> [7314] ~(unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11))))
% 139.97/26.90 -> [7315] ((unequally_directed_lines(reverse_line(N46_124_11), N46_124_11) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))) | (unequally_directed_lines(reverse_line(N46_124_11), N46_124_11) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))))
% 139.97/26.90
% 139.97/26.90 [7315] BETA_OR : ((unequally_directed_lines(reverse_line(N46_124_11), N46_124_11) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))) | (unequally_directed_lines(reverse_line(N46_124_11), N46_124_11) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))))
% 139.97/26.90 -> [7316] (unequally_directed_lines(reverse_line(N46_124_11), N46_124_11) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)))
% 139.97/26.90 -> [7317] (unequally_directed_lines(reverse_line(N46_124_11), N46_124_11) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)))
% 139.97/26.90
% 139.97/26.90 [7317] ALPHA_AND : (unequally_directed_lines(reverse_line(N46_124_11), N46_124_11) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)))
% 139.97/26.90 -> [7321] unequally_directed_lines(reverse_line(N46_124_11), N46_124_11), unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90
% 139.97/26.90 [7321] CLOSURE : unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90
% 139.97/26.90 [7320] CLOSURE : unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90
% 139.97/26.90 [7314] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11))))
% 139.97/26.90 -> [7376] ~unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90 -> [7377] ~unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11)))
% 139.97/26.90
% 139.97/26.90 [7377] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 139.97/26.90 -> [7379] (unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) | unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11))))
% 139.97/26.90
% 139.97/26.90 [7379] BETA_OR : (unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) | unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11))))
% 139.97/26.90 -> [7382] unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90 -> [7383] unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11)))
% 139.97/26.90
% 139.97/26.90 [7382] CLOSURE : unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90
% 139.97/26.90 [7383] CLOSURE : unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11)))
% 139.97/26.90
% 139.97/26.90 [7376] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 139.97/26.90 -> [7378] (unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) | unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11))))
% 139.97/26.90
% 139.97/26.90 [7378] BETA_OR : (unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) | unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11))))
% 139.97/26.90 -> [7380] unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90 -> [7381] unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11)))
% 139.97/26.90
% 139.97/26.90 [7380] CLOSURE : unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90
% 139.97/26.90 [7381] 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)))))
% 139.97/26.90 -> [7392] ((unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11)))) => (left_convergent_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) | left_convergent_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11)))))
% 139.97/26.90
% 139.97/26.90 [7392] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11)))) => (left_convergent_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) | left_convergent_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11)))))
% 139.97/26.90 -> [7393] ~(unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11))))
% 139.97/26.90 -> [7394] (left_convergent_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) | left_convergent_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11))))
% 139.97/26.90
% 139.97/26.90 [7394] BETA_OR : (left_convergent_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) | left_convergent_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11))))
% 139.97/26.90 -> [7397] left_convergent_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90 -> [7398] left_convergent_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11)))
% 139.97/26.90
% 139.97/26.90 [7397] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 139.97/26.90 -> [7399] ~(left_apart_point(A51_303_14, L52_303_14) | left_apart_point(A51_303_14, reverse_line(L52_303_14)))
% 139.97/26.90
% 139.97/26.90 [7399] ALPHA_NOT_OR : ~(left_apart_point(A51_303_14, L52_303_14) | left_apart_point(A51_303_14, reverse_line(L52_303_14)))
% 139.97/26.90 -> [7401] ~left_apart_point(A51_303_14, L52_303_14), ~left_apart_point(A51_303_14, reverse_line(L52_303_14))
% 139.97/26.90
% 139.97/26.90 [7401] CLOSURE : ~left_apart_point(A51_303_14, L52_303_14)
% 139.97/26.90
% 139.97/26.90 [7398] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 139.97/26.90 -> [7400] ~(left_apart_point(A51_304_14, L52_304_14) | left_apart_point(A51_304_14, reverse_line(L52_304_14)))
% 139.97/26.90
% 139.97/26.90 [7400] ALPHA_NOT_OR : ~(left_apart_point(A51_304_14, L52_304_14) | left_apart_point(A51_304_14, reverse_line(L52_304_14)))
% 139.97/26.90 -> [7402] ~left_apart_point(A51_304_14, L52_304_14), ~left_apart_point(A51_304_14, reverse_line(L52_304_14))
% 139.97/26.90
% 139.97/26.90 [7402] CLOSURE : ~left_apart_point(A51_304_14, L52_304_14)
% 139.97/26.90
% 139.97/26.90 [7393] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11)) & unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11))))
% 139.97/26.90 -> [7395] ~unequally_directed_lines(reverse_line(N46_124_11), reverse_line(N46_124_11))
% 139.97/26.90 -> [7396] ~unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11)))
% 139.97/26.90
% 139.97/26.90 [7396] CLOSURE : ~unequally_directed_lines(reverse_line(N46_124_11), reverse_line(reverse_line(N46_124_11)))
% 139.97/26.90
% 139.97/26.90 [7395] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 139.97/26.90 -> [7403] ~(left_apart_point(A51_305_14, L52_305_14) | left_apart_point(A51_305_14, reverse_line(L52_305_14)))
% 139.97/26.90
% 139.97/26.90 [7403] ALPHA_NOT_OR : ~(left_apart_point(A51_305_14, L52_305_14) | left_apart_point(A51_305_14, reverse_line(L52_305_14)))
% 139.97/26.90 -> [7404] ~left_apart_point(A51_305_14, L52_305_14), ~left_apart_point(A51_305_14, reverse_line(L52_305_14))
% 139.97/26.90
% 139.97/26.90 [7404] CLOSURE : ~left_apart_point(A51_305_14, L52_305_14)
% 139.97/26.90
% 139.97/26.90 [6580] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 139.97/26.90 -> [6582] (equally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) <=> ~unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)))
% 139.97/26.90
% 139.97/26.90 [6582] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) <=> ~unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)))
% 139.97/26.90 -> [6584] ~equally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)), ~~unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90 -> [6585] equally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)), ~unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90
% 139.97/26.90 [6584] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90 -> [6588] unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90
% 139.97/26.90 [6588] CLOSURE : unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90
% 139.97/26.90 [6591] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_23_4), Y17_23_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_23_4), Y17_23_4))
% 139.97/26.90 -> [7476] ~equally_directed_opposite_lines(reverse_line(Y17_23_4), Y17_23_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_23_4), Y17_23_4)
% 139.97/26.90 -> [7477] equally_directed_opposite_lines(reverse_line(Y17_23_4), Y17_23_4), ~unequally_directed_opposite_lines(reverse_line(Y17_23_4), Y17_23_4)
% 139.97/26.90
% 139.97/26.90 [7476] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_23_4), Y17_23_4)
% 139.97/26.90 -> [7478] unequally_directed_opposite_lines(reverse_line(Y17_23_4), Y17_23_4)
% 139.97/26.90
% 139.97/26.90 [7478] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_23_4), Y17_23_4)
% 139.97/26.90
% 139.97/26.90 [7480] BETA_IMPLY : (distinct_points(C35_36_6, C35_36_6) => (distinct_points(C35_36_6, C35_36_6) | distinct_points(C35_36_6, C35_36_6)))
% 139.97/26.90 -> [7783] ~distinct_points(C35_36_6, C35_36_6)
% 139.97/26.90 -> [7784] (distinct_points(C35_36_6, C35_36_6) | distinct_points(C35_36_6, C35_36_6))
% 139.97/26.90
% 139.97/26.90 [7783] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 139.97/26.90 -> [7787] ~distinct_lines(N39_53_8, N39_53_8)
% 139.97/26.90
% 139.97/26.90 [7787] 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))))
% 139.97/26.90 -> [7788] (distinct_lines(N39_53_8, N39_53_8) => (distinct_lines(N39_53_8, N39_53_8) | distinct_lines(N39_53_8, N39_53_8)))
% 139.97/26.90
% 139.97/26.90 [7788] BETA_IMPLY : (distinct_lines(N39_53_8, N39_53_8) => (distinct_lines(N39_53_8, N39_53_8) | distinct_lines(N39_53_8, N39_53_8)))
% 139.97/26.90 -> [7789] ~distinct_lines(N39_53_8, N39_53_8)
% 139.97/26.90 -> [7790] (distinct_lines(N39_53_8, N39_53_8) | distinct_lines(N39_53_8, N39_53_8))
% 139.97/26.90
% 139.97/26.90 [7790] BETA_OR : (distinct_lines(N39_53_8, N39_53_8) | distinct_lines(N39_53_8, N39_53_8))
% 139.97/26.90 -> [7791] distinct_lines(N39_53_8, N39_53_8)
% 139.97/26.90 -> [7792] distinct_lines(N39_53_8, N39_53_8)
% 139.97/26.90
% 139.97/26.90 [7792] CLOSURE : distinct_lines(N39_53_8, N39_53_8)
% 139.97/26.90
% 139.97/26.90 [7791] CLOSURE : distinct_lines(N39_53_8, N39_53_8)
% 139.97/26.90
% 139.97/26.90 [7794] BETA_IMPLY : (unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) => (unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) | unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))))
% 139.97/26.90 -> [7878] ~unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90 -> [7879] (unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) | unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)))
% 139.97/26.90
% 139.97/26.90 [7879] BETA_OR : (unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) | unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)))
% 139.97/26.90 -> [7880] unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90 -> [7881] unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90
% 139.97/26.90 [7880] CLOSURE : unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90
% 139.97/26.90 [7881] CLOSURE : unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90
% 139.97/26.90 [7882] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))) => ((unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))) | (unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4))))))
% 139.97/26.90 -> [7905] ~(unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4))))
% 139.97/26.90 -> [7906] ((unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))) | (unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))))
% 139.97/26.90
% 139.97/26.90 [7906] BETA_OR : ((unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))) | (unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))))
% 139.97/26.90 -> [7909] (unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4))))
% 139.97/26.90 -> [7910] (unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4))))
% 139.97/26.90
% 139.97/26.90 [7909] ALPHA_AND : (unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4))))
% 139.97/26.90 -> [7911] unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)), unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))
% 139.97/26.90
% 139.97/26.90 [7911] CLOSURE : unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))
% 139.97/26.90
% 139.97/26.90 [7912] CLOSURE : unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90
% 139.97/26.90 [7905] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4))))
% 139.97/26.90 -> [7936] ~unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90 -> [7937] ~unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))
% 139.97/26.90
% 139.97/26.90 [7937] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 139.97/26.90 -> [7941] (unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) | unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4))))
% 139.97/26.90
% 139.97/26.90 [7941] BETA_OR : (unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) | unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4))))
% 139.97/26.90 -> [7942] unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90 -> [7943] unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))
% 139.97/26.90
% 139.97/26.90 [7942] CLOSURE : unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90
% 139.97/26.90 [7943] CLOSURE : unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))
% 139.97/26.90
% 139.97/26.90 [7936] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 139.97/26.90 -> [7938] (unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) | unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4))))
% 139.97/26.90
% 139.97/26.90 [7938] BETA_OR : (unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) | unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4))))
% 139.97/26.90 -> [7939] unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90 -> [7940] unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))
% 139.97/26.90
% 139.97/26.90 [7939] CLOSURE : unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90
% 139.97/26.90 [7940] 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)))))
% 139.97/26.90 -> [7944] ((unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))) => (left_convergent_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) | left_convergent_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))))
% 139.97/26.90
% 139.97/26.90 [7944] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))) => (left_convergent_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) | left_convergent_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))))
% 139.97/26.90 -> [7945] ~(unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4))))
% 139.97/26.90 -> [7946] (left_convergent_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) | left_convergent_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4))))
% 139.97/26.90
% 139.97/26.90 [7945] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) & unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4))))
% 139.97/26.90 -> [7947] ~unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90 -> [7948] ~unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))
% 139.97/26.90
% 139.97/26.90 [7948] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))
% 139.97/26.90
% 139.97/26.90 [7947] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 139.97/26.90 -> [7951] ~(left_apart_point(A51_336_14, L52_336_14) | left_apart_point(A51_336_14, reverse_line(L52_336_14)))
% 139.97/26.90
% 139.97/26.90 [7951] ALPHA_NOT_OR : ~(left_apart_point(A51_336_14, L52_336_14) | left_apart_point(A51_336_14, reverse_line(L52_336_14)))
% 139.97/26.90 -> [7953] ~left_apart_point(A51_336_14, L52_336_14), ~left_apart_point(A51_336_14, reverse_line(L52_336_14))
% 139.97/26.90
% 139.97/26.90 [7953] CLOSURE : ~left_apart_point(A51_336_14, L52_336_14)
% 139.97/26.90
% 139.97/26.90 [7946] BETA_OR : (left_convergent_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4)) | left_convergent_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4))))
% 139.97/26.90 -> [7955] left_convergent_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90 -> [7956] left_convergent_lines(reverse_line(Y17_23_4), reverse_line(reverse_line(Y17_23_4)))
% 139.97/26.90
% 139.97/26.90 [7955] CLOSURE : left_convergent_lines(reverse_line(Y17_23_4), reverse_line(Y17_23_4))
% 139.97/26.90
% 139.97/26.90 [7956] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 139.97/26.90 -> [7957] ~(left_apart_point(A51_338_14, L52_338_14) | left_apart_point(A51_338_14, reverse_line(L52_338_14)))
% 139.97/26.90
% 139.97/26.90 [7957] ALPHA_NOT_OR : ~(left_apart_point(A51_338_14, L52_338_14) | left_apart_point(A51_338_14, reverse_line(L52_338_14)))
% 139.97/26.90 -> [7958] ~left_apart_point(A51_338_14, L52_338_14), ~left_apart_point(A51_338_14, reverse_line(L52_338_14))
% 139.97/26.90
% 139.97/26.90 [7958] CLOSURE : ~left_apart_point(A51_338_14, L52_338_14)
% 139.97/26.90
% 139.97/26.90 [7784] BETA_OR : (distinct_points(C35_36_6, C35_36_6) | distinct_points(C35_36_6, C35_36_6))
% 139.97/26.90 -> [7959] distinct_points(C35_36_6, C35_36_6)
% 139.97/26.90 -> [7960] distinct_points(C35_36_6, C35_36_6)
% 139.97/26.90
% 139.97/26.90 [7959] CLOSURE : distinct_points(C35_36_6, C35_36_6)
% 139.97/26.90
% 139.97/26.90 [7960] CLOSURE : distinct_points(C35_36_6, C35_36_6)
% 139.97/26.90
% 139.97/26.90 % SZS output end Proof for theBenchmark.p
% 139.97/26.90 [26.555145s][1][Res] 360635 goroutines created
% 139.97/26.90 ==== Result ====
% 139.97/26.90 [26.555182s][1][Res] VALID
% 139.97/26.90 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------