TSTP Solution File: GEO243+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO243+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 15:18:40 EDT 2022
% Result : Theorem 45.27s 12.86s
% Output : Proof 45.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO243+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 07:10:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 [DMT] DMT loaded with preskolemization
% 0.13/0.35 [EQ] equality loaded.
% 0.13/0.35 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.20/0.36 Conjecture not found
% 0.20/0.36 Start search
% 0.20/0.36 nb_step : 1 - limit : 37
% 0.20/0.36 Launch Gotab with destructive = true
% 45.25/12.85 % SZS output start Proof for theBenchmark.p
% 45.27/12.86 [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, C91_91] : ((distinct_points(A89_89, B90_90) => (left_apart_point(C91_91, line_connecting(A89_89, B90_90)) => right_apart_point(C91_91, line_connecting(B90_90, A89_89))))))
% 45.27/12.86 -> [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, C91_91] : ((distinct_points(A89_89, B90_90) => (left_apart_point(C91_91, line_connecting(A89_89, B90_90)) => right_apart_point(C91_91, line_connecting(B90_90, A89_89)))))
% 45.27/12.86
% 45.27/12.86 [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)))))
% 45.27/12.86 -> [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))))
% 45.27/12.86
% 45.27/12.86 [2] DELTA_NOT_FORALL : ~! [A89_89, B90_90, C91_91] : ((distinct_points(A89_89, B90_90) => (left_apart_point(C91_91, line_connecting(A89_89, B90_90)) => right_apart_point(C91_91, line_connecting(B90_90, A89_89)))))
% 45.27/12.86 -> [3] ~(distinct_points(skolem_A8989, skolem_B9090) => (left_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) => right_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989))))
% 45.27/12.86
% 45.27/12.86 [3] ALPHA_NOT_IMPLY : ~(distinct_points(skolem_A8989, skolem_B9090) => (left_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) => right_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989))))
% 45.27/12.86 -> [4] distinct_points(skolem_A8989, skolem_B9090), ~(left_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) => right_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989)))
% 45.27/12.86
% 45.27/12.86 [4] ALPHA_NOT_IMPLY : ~(left_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) => right_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989)))
% 45.27/12.86 -> [5] left_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)), ~right_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989))
% 45.27/12.86
% 45.27/12.86 [5] GAMMA_FORALL : ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9))))
% 45.27/12.86 -> [6] (unequally_directed_opposite_lines(reverse_line(Y17_6_4), Y17_6_4) <=> unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4)))
% 45.27/12.86
% 45.27/12.86 [6] BETA_EQUIV : (unequally_directed_opposite_lines(reverse_line(Y17_6_4), Y17_6_4) <=> unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4)))
% 45.27/12.86 -> [7] ~unequally_directed_opposite_lines(reverse_line(Y17_6_4), Y17_6_4), ~unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4))
% 45.27/12.86 -> [8] unequally_directed_opposite_lines(reverse_line(Y17_6_4), Y17_6_4), unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4))
% 45.27/12.86
% 45.27/12.86 [8] GAMMA_FORALL : ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11))))
% 45.27/12.86 -> [10] (right_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989)) <=> left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_B9090, skolem_A8989))))
% 45.27/12.86
% 45.27/12.86 [10] BETA_EQUIV : (right_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989)) <=> left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_B9090, skolem_A8989))))
% 45.27/12.86 -> [13] ~right_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989)), ~left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_B9090, skolem_A8989)))
% 45.27/12.86 -> [14] right_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989)), left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_B9090, skolem_A8989)))
% 45.27/12.86
% 45.27/12.86 [14] CLOSURE : right_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989))
% 45.27/12.86
% 45.27/12.86 [16] BETA_EQUIV : (right_convergent_lines(X12_1_2, Y13_1_2) <=> left_convergent_lines(X12_1_2, reverse_line(Y13_1_2)))
% 45.27/12.86 -> [341] ~right_convergent_lines(X12_1_2, Y13_1_2), ~left_convergent_lines(X12_1_2, reverse_line(Y13_1_2))
% 45.27/12.86 -> [342] right_convergent_lines(X12_1_2, Y13_1_2), left_convergent_lines(X12_1_2, reverse_line(Y13_1_2))
% 45.27/12.86
% 45.27/12.86 [342] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 45.27/12.86 -> [346] (equally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4)) <=> ~unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4)))
% 45.27/12.86
% 45.27/12.86 [346] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4)) <=> ~unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4)))
% 45.27/12.86 -> [347] ~equally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4)), ~~unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4))
% 45.27/12.86 -> [348] equally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4)), ~unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4))
% 45.27/12.86
% 45.27/12.86 [348] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4))
% 45.27/12.86
% 45.27/12.86 [355] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_6_4), Y17_6_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_6_4), Y17_6_4))
% 45.27/12.86 -> [488] ~equally_directed_opposite_lines(reverse_line(Y17_6_4), Y17_6_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_6_4), Y17_6_4)
% 45.27/12.86 -> [489] equally_directed_opposite_lines(reverse_line(Y17_6_4), Y17_6_4), ~unequally_directed_opposite_lines(reverse_line(Y17_6_4), Y17_6_4)
% 45.27/12.86
% 45.27/12.86 [488] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_6_4), Y17_6_4)
% 45.27/12.86 -> [498] unequally_directed_opposite_lines(reverse_line(Y17_6_4), Y17_6_4)
% 45.27/12.86
% 45.27/12.86 [498] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 45.27/12.86 -> [501] ~distinct_points(skolem_A8989, skolem_A8989)
% 45.27/12.86
% 45.27/12.86 [501] 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))))
% 45.27/12.86 -> [502] (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989)))
% 45.27/12.86
% 45.27/12.86 [502] BETA_IMPLY : (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989)))
% 45.27/12.86 -> [503] ~distinct_points(skolem_A8989, skolem_B9090)
% 45.27/12.86 -> [504] (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989))
% 45.27/12.86
% 45.27/12.86 [503] CLOSURE : ~distinct_points(skolem_A8989, skolem_B9090)
% 45.27/12.86
% 45.27/12.86 [504] BETA_OR : (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989))
% 45.27/12.86 -> [519] distinct_points(skolem_A8989, skolem_A8989)
% 45.27/12.86 -> [520] distinct_points(skolem_B9090, skolem_A8989)
% 45.27/12.86
% 45.27/12.86 [519] CLOSURE : distinct_points(skolem_A8989, skolem_A8989)
% 45.27/12.86
% 45.27/12.86 [520] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 45.27/12.86 -> [531] ~distinct_lines(N39_15_8, N39_15_8)
% 45.27/12.86
% 45.27/12.86 [531] 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))))
% 45.27/12.86 -> [532] (distinct_lines(N39_15_8, N39_15_8) => (distinct_lines(N39_15_8, N39_15_8) | distinct_lines(N39_15_8, N39_15_8)))
% 45.27/12.86
% 45.27/12.86 [532] BETA_IMPLY : (distinct_lines(N39_15_8, N39_15_8) => (distinct_lines(N39_15_8, N39_15_8) | distinct_lines(N39_15_8, N39_15_8)))
% 45.27/12.86 -> [533] ~distinct_lines(N39_15_8, N39_15_8)
% 45.27/12.86 -> [534] (distinct_lines(N39_15_8, N39_15_8) | distinct_lines(N39_15_8, N39_15_8))
% 45.27/12.86
% 45.27/12.86 [534] BETA_OR : (distinct_lines(N39_15_8, N39_15_8) | distinct_lines(N39_15_8, N39_15_8))
% 45.27/12.86 -> [535] distinct_lines(N39_15_8, N39_15_8)
% 45.27/12.86 -> [536] distinct_lines(N39_15_8, N39_15_8)
% 45.27/12.86
% 45.27/12.86 [535] CLOSURE : distinct_lines(N39_15_8, N39_15_8)
% 45.27/12.86
% 45.27/12.86 [536] CLOSURE : distinct_lines(N39_15_8, N39_15_8)
% 45.27/12.86
% 45.27/12.86 [539] CLOSURE : equally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4))
% 45.27/12.86
% 45.27/12.86 [489] CLOSURE : ~unequally_directed_opposite_lines(reverse_line(Y17_6_4), Y17_6_4)
% 45.27/12.86
% 45.27/12.86 [343] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4)) <=> ~unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4)))
% 45.27/12.86 -> [578] ~equally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4)), ~~unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4))
% 45.27/12.86 -> [579] equally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4)), ~unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4))
% 45.27/12.86
% 45.27/12.86 [578] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4))
% 45.27/12.86 -> [580] unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4))
% 45.27/12.86
% 45.27/12.86 [580] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 45.27/12.86 -> [581] (equally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4))
% 45.27/12.86
% 45.27/12.86 [581] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4))
% 45.27/12.86 -> [582] ~equally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 45.27/12.86 -> [583] equally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4), ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 45.27/12.86
% 45.27/12.86 [582] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 45.27/12.86 -> [586] unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 45.27/12.86
% 45.27/12.86 [586] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 45.27/12.86 -> [593] ~distinct_points(skolem_A8989, skolem_A8989)
% 45.27/12.86
% 45.27/12.86 [593] 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))))
% 45.27/12.86 -> [594] (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989)))
% 45.27/12.86
% 45.27/12.86 [594] BETA_IMPLY : (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989)))
% 45.27/12.86 -> [595] ~distinct_points(skolem_A8989, skolem_B9090)
% 45.27/12.86 -> [596] (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989))
% 45.27/12.86
% 45.27/12.86 [595] CLOSURE : ~distinct_points(skolem_A8989, skolem_B9090)
% 45.27/12.86
% 45.27/12.86 [596] BETA_OR : (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989))
% 45.27/12.86 -> [601] distinct_points(skolem_A8989, skolem_A8989)
% 45.27/12.86 -> [602] distinct_points(skolem_B9090, skolem_A8989)
% 45.27/12.86
% 45.27/12.86 [601] CLOSURE : distinct_points(skolem_A8989, skolem_A8989)
% 45.27/12.86
% 45.27/12.86 [602] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 45.27/12.86 -> [603] ~distinct_lines(N39_17_8, N39_17_8)
% 45.27/12.86
% 45.27/12.86 [603] 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))))
% 45.27/12.86 -> [604] (distinct_lines(N39_17_8, N39_17_8) => (distinct_lines(N39_17_8, N39_17_8) | distinct_lines(N39_17_8, N39_17_8)))
% 45.27/12.86
% 45.27/12.86 [604] BETA_IMPLY : (distinct_lines(N39_17_8, N39_17_8) => (distinct_lines(N39_17_8, N39_17_8) | distinct_lines(N39_17_8, N39_17_8)))
% 45.27/12.86 -> [605] ~distinct_lines(N39_17_8, N39_17_8)
% 45.27/12.86 -> [606] (distinct_lines(N39_17_8, N39_17_8) | distinct_lines(N39_17_8, N39_17_8))
% 45.27/12.86
% 45.27/12.86 [605] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 45.27/12.86 -> [609] equally_directed_lines(L40_17_9, L40_17_9)
% 45.27/12.86
% 45.27/12.86 [609] CLOSURE : equally_directed_lines(L40_17_9, L40_17_9)
% 45.27/12.86
% 45.27/12.86 [606] BETA_OR : (distinct_lines(N39_17_8, N39_17_8) | distinct_lines(N39_17_8, N39_17_8))
% 45.27/12.86 -> [610] distinct_lines(N39_17_8, N39_17_8)
% 45.27/12.86 -> [611] distinct_lines(N39_17_8, N39_17_8)
% 45.27/12.86
% 45.27/12.86 [610] CLOSURE : distinct_lines(N39_17_8, N39_17_8)
% 45.27/12.86
% 45.27/12.86 [611] CLOSURE : distinct_lines(N39_17_8, N39_17_8)
% 45.27/12.86
% 45.27/12.86 [583] CLOSURE : ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 45.27/12.86
% 45.27/12.86 [579] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_6_4), reverse_line(Y17_6_4))
% 45.27/12.86
% 45.27/12.86 [9] BETA_EQUIV : (right_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989)) <=> left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_B9090, skolem_A8989))))
% 45.27/12.86 -> [1859] ~right_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989)), ~left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_B9090, skolem_A8989)))
% 45.27/12.86 -> [1860] right_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989)), left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_B9090, skolem_A8989)))
% 45.27/12.86
% 45.27/12.86 [1860] CLOSURE : right_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989))
% 45.27/12.86
% 45.27/12.86 [1859] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 45.27/12.86 -> [1861] (right_convergent_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) <=> left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))))
% 45.27/12.86
% 45.27/12.86 [1861] BETA_EQUIV : (right_convergent_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) <=> left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))))
% 45.27/12.86 -> [1862] ~right_convergent_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)), ~left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11)))
% 45.27/12.86 -> [1863] right_convergent_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)), left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11)))
% 45.27/12.86
% 45.27/12.86 [1863] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 45.27/12.86 -> [1865] (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)))
% 45.27/12.86
% 45.27/12.86 [1865] 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)))
% 45.27/12.86 -> [1868] ~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))
% 45.27/12.86 -> [1869] 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))
% 45.27/12.86
% 45.27/12.86 [1868] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 45.27/12.86 -> [1871] unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 45.27/12.86
% 45.27/12.86 [1871] CLOSURE : unequally_directed_lines(reverse_line(Y17_16_4), reverse_line(Y17_16_4))
% 45.27/12.86
% 45.27/12.86 [1875] 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))
% 45.27/12.86 -> [2142] ~equally_directed_opposite_lines(reverse_line(Y17_16_4), Y17_16_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_16_4), Y17_16_4)
% 45.27/12.86 -> [2143] equally_directed_opposite_lines(reverse_line(Y17_16_4), Y17_16_4), ~unequally_directed_opposite_lines(reverse_line(Y17_16_4), Y17_16_4)
% 45.27/12.86
% 45.27/12.86 [2142] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_16_4), Y17_16_4)
% 45.27/12.86 -> [2144] unequally_directed_opposite_lines(reverse_line(Y17_16_4), Y17_16_4)
% 45.27/12.86
% 45.27/12.86 [2144] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_16_4), Y17_16_4)
% 45.27/12.86
% 45.27/12.86 [2143] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 45.27/12.86 -> [2145] ~distinct_points(skolem_B9090, skolem_B9090)
% 45.27/12.86
% 45.27/12.86 [2145] 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))))
% 45.27/12.86 -> [2146] (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090)))
% 45.27/12.86
% 45.27/12.86 [2146] BETA_IMPLY : (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090)))
% 45.27/12.86 -> [2147] ~distinct_points(skolem_A8989, skolem_B9090)
% 45.27/12.86 -> [2148] (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090))
% 45.27/12.86
% 45.27/12.86 [2147] CLOSURE : ~distinct_points(skolem_A8989, skolem_B9090)
% 45.27/12.86
% 45.27/12.86 [2148] BETA_OR : (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090))
% 45.27/12.86 -> [2165] distinct_points(skolem_A8989, skolem_B9090)
% 45.27/12.86 -> [2166] distinct_points(skolem_B9090, skolem_B9090)
% 45.27/12.86
% 45.27/12.86 [2166] CLOSURE : distinct_points(skolem_B9090, skolem_B9090)
% 45.27/12.86
% 45.27/12.86 [2165] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 45.27/12.86 -> [2169] ~distinct_lines(N39_32_8, N39_32_8)
% 45.27/12.86
% 45.27/12.86 [2169] 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))))
% 45.27/12.86 -> [2172] (distinct_lines(N39_32_8, N39_32_8) => (distinct_lines(N39_32_8, N39_32_8) | distinct_lines(N39_32_8, N39_32_8)))
% 45.27/12.86
% 45.27/12.86 [2172] BETA_IMPLY : (distinct_lines(N39_32_8, N39_32_8) => (distinct_lines(N39_32_8, N39_32_8) | distinct_lines(N39_32_8, N39_32_8)))
% 45.27/12.86 -> [2173] ~distinct_lines(N39_32_8, N39_32_8)
% 45.27/12.86 -> [2174] (distinct_lines(N39_32_8, N39_32_8) | distinct_lines(N39_32_8, N39_32_8))
% 45.27/12.86
% 45.27/12.86 [2174] BETA_OR : (distinct_lines(N39_32_8, N39_32_8) | distinct_lines(N39_32_8, N39_32_8))
% 45.27/12.86 -> [2175] distinct_lines(N39_32_8, N39_32_8)
% 45.27/12.86 -> [2176] distinct_lines(N39_32_8, N39_32_8)
% 45.27/12.86
% 45.27/12.86 [2175] CLOSURE : distinct_lines(N39_32_8, N39_32_8)
% 45.27/12.86
% 45.27/12.86 [2176] CLOSURE : distinct_lines(N39_32_8, N39_32_8)
% 45.27/12.86
% 45.27/12.86 [2178] BETA_IMPLY : (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))) => (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | unequally_directed_lines(reverse_line(reverse_line(N46_36_11)), reverse_line(N46_36_11))))
% 45.27/12.86 -> [2353] ~unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 45.27/12.86 -> [2354] (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | unequally_directed_lines(reverse_line(reverse_line(N46_36_11)), reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2353] 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))))))
% 45.27/12.86 -> [2359] ((unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))) => ((unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))) | (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)))))
% 45.27/12.86
% 45.27/12.86 [2359] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))) => ((unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))) | (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)))))
% 45.27/12.86 -> [2360] ~(unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86 -> [2361] ((unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))) | (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))))
% 45.27/12.86
% 45.27/12.86 [2360] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86 -> [2362] ~unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86 -> [2363] ~unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2362] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 45.27/12.86 -> [2368] (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86
% 45.27/12.86 [2368] BETA_OR : (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86 -> [2369] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86 -> [2370] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2369] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86
% 45.27/12.86 [2370] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2363] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 45.27/12.86 -> [2371] (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86
% 45.27/12.86 [2371] BETA_OR : (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86 -> [2372] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86 -> [2373] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2372] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86
% 45.27/12.86 [2373] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2361] BETA_OR : ((unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))) | (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))))
% 45.27/12.86 -> [2385] (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)))
% 45.27/12.86 -> [2386] (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2386] ALPHA_AND : (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)))
% 45.27/12.86 -> [2388] unequally_directed_lines(reverse_line(N46_36_11), N46_36_11), unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86
% 45.27/12.86 [2388] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86
% 45.27/12.86 [2387] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86
% 45.27/12.86 [2354] BETA_OR : (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | unequally_directed_lines(reverse_line(reverse_line(N46_36_11)), reverse_line(N46_36_11)))
% 45.27/12.86 -> [2393] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86 -> [2394] unequally_directed_lines(reverse_line(reverse_line(N46_36_11)), reverse_line(N46_36_11))
% 45.27/12.86
% 45.27/12.86 [2393] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86
% 45.27/12.86 [2395] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))) => ((unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))) | (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)))))
% 45.27/12.86 -> [2483] ~(unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86 -> [2484] ((unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))) | (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))))
% 45.27/12.86
% 45.27/12.86 [2484] BETA_OR : ((unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))) | (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))))
% 45.27/12.86 -> [2487] (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)))
% 45.27/12.86 -> [2488] (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2487] ALPHA_AND : (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)))
% 45.27/12.86 -> [2489] unequally_directed_lines(reverse_line(N46_36_11), N46_36_11), unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86
% 45.27/12.86 [2489] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86
% 45.27/12.86 [2490] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86
% 45.27/12.86 [2483] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86 -> [2529] ~unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86 -> [2530] ~unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2530] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 45.27/12.86 -> [2534] (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86
% 45.27/12.86 [2534] BETA_OR : (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86 -> [2535] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86 -> [2536] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2535] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86
% 45.27/12.86 [2536] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2529] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 45.27/12.86 -> [2531] (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86
% 45.27/12.86 [2531] BETA_OR : (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86 -> [2532] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86 -> [2533] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2532] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86
% 45.27/12.86 [2533] 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)))))
% 45.27/12.86 -> [2539] ((unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))) => (left_convergent_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | left_convergent_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))))
% 45.27/12.86
% 45.27/12.86 [2539] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))) => (left_convergent_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | left_convergent_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))))
% 45.27/12.86 -> [2540] ~(unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86 -> [2541] (left_convergent_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | left_convergent_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86
% 45.27/12.86 [2541] BETA_OR : (left_convergent_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | left_convergent_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86 -> [2544] left_convergent_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86 -> [2545] left_convergent_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2544] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 45.27/12.86 -> [2546] ~(left_apart_point(A51_78_14, L52_78_14) | left_apart_point(A51_78_14, reverse_line(L52_78_14)))
% 45.27/12.86
% 45.27/12.86 [2546] ALPHA_NOT_OR : ~(left_apart_point(A51_78_14, L52_78_14) | left_apart_point(A51_78_14, reverse_line(L52_78_14)))
% 45.27/12.86 -> [2548] ~left_apart_point(A51_78_14, L52_78_14), ~left_apart_point(A51_78_14, reverse_line(L52_78_14))
% 45.27/12.86
% 45.27/12.86 [2548] CLOSURE : ~left_apart_point(A51_78_14, L52_78_14)
% 45.27/12.86
% 45.27/12.86 [2545] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 45.27/12.86 -> [2547] ~(left_apart_point(A51_79_14, L52_79_14) | left_apart_point(A51_79_14, reverse_line(L52_79_14)))
% 45.27/12.86
% 45.27/12.86 [2547] ALPHA_NOT_OR : ~(left_apart_point(A51_79_14, L52_79_14) | left_apart_point(A51_79_14, reverse_line(L52_79_14)))
% 45.27/12.86 -> [2549] ~left_apart_point(A51_79_14, L52_79_14), ~left_apart_point(A51_79_14, reverse_line(L52_79_14))
% 45.27/12.86
% 45.27/12.86 [2549] CLOSURE : ~left_apart_point(A51_79_14, L52_79_14)
% 45.27/12.86
% 45.27/12.86 [2540] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11))))
% 45.27/12.86 -> [2542] ~unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 45.27/12.86 -> [2543] ~unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2543] CLOSURE : ~unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 45.27/12.86
% 45.27/12.86 [2542] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 45.27/12.86 -> [2557] ~(left_apart_point(A51_80_14, L52_80_14) | left_apart_point(A51_80_14, reverse_line(L52_80_14)))
% 45.27/12.86
% 45.27/12.86 [2557] ALPHA_NOT_OR : ~(left_apart_point(A51_80_14, L52_80_14) | left_apart_point(A51_80_14, reverse_line(L52_80_14)))
% 45.27/12.86 -> [2558] ~left_apart_point(A51_80_14, L52_80_14), ~left_apart_point(A51_80_14, reverse_line(L52_80_14))
% 45.27/12.86
% 45.27/12.86 [2558] CLOSURE : ~left_apart_point(A51_80_14, L52_80_14)
% 45.27/12.86
% 45.27/12.86 [1862] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 45.27/12.86 -> [1864] (equally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) <=> ~unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)))
% 45.27/12.86
% 45.27/12.86 [1864] BETA_EQUIV : (equally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) <=> ~unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)))
% 45.27/12.86 -> [1866] ~equally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)), ~~unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86 -> [1867] equally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)), ~unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86
% 45.27/12.86 [1866] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86 -> [1870] unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86
% 45.27/12.86 [1870] CLOSURE : unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86
% 45.27/12.86 [1872] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(N46_39_11), N46_39_11) <=> ~unequally_directed_opposite_lines(reverse_line(N46_39_11), N46_39_11))
% 45.27/12.86 -> [2260] ~equally_directed_opposite_lines(reverse_line(N46_39_11), N46_39_11), ~~unequally_directed_opposite_lines(reverse_line(N46_39_11), N46_39_11)
% 45.27/12.86 -> [2261] equally_directed_opposite_lines(reverse_line(N46_39_11), N46_39_11), ~unequally_directed_opposite_lines(reverse_line(N46_39_11), N46_39_11)
% 45.27/12.86
% 45.27/12.86 [2260] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(N46_39_11), N46_39_11)
% 45.27/12.86 -> [2262] unequally_directed_opposite_lines(reverse_line(N46_39_11), N46_39_11)
% 45.27/12.86
% 45.27/12.86 [2262] CLOSURE : unequally_directed_opposite_lines(reverse_line(N46_39_11), N46_39_11)
% 45.27/12.86
% 45.27/12.86 [2264] BETA_IMPLY : (distinct_points(C35_23_6, C35_23_6) => (distinct_points(C35_23_6, C35_23_6) | distinct_points(C35_23_6, C35_23_6)))
% 45.27/12.86 -> [2590] ~distinct_points(C35_23_6, C35_23_6)
% 45.27/12.86 -> [2591] (distinct_points(C35_23_6, C35_23_6) | distinct_points(C35_23_6, C35_23_6))
% 45.27/12.86
% 45.27/12.86 [2591] BETA_OR : (distinct_points(C35_23_6, C35_23_6) | distinct_points(C35_23_6, C35_23_6))
% 45.27/12.86 -> [2592] distinct_points(C35_23_6, C35_23_6)
% 45.27/12.86 -> [2593] distinct_points(C35_23_6, C35_23_6)
% 45.27/12.86
% 45.27/12.86 [2593] CLOSURE : distinct_points(C35_23_6, C35_23_6)
% 45.27/12.86
% 45.27/12.86 [2592] CLOSURE : distinct_points(C35_23_6, C35_23_6)
% 45.27/12.86
% 45.27/12.86 [2590] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 45.27/12.86 -> [2594] ~distinct_lines(N39_34_8, N39_34_8)
% 45.27/12.86
% 45.27/12.86 [2594] 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))))
% 45.27/12.86 -> [2595] (distinct_lines(N39_34_8, N39_34_8) => (distinct_lines(N39_34_8, N39_34_8) | distinct_lines(N39_34_8, N39_34_8)))
% 45.27/12.86
% 45.27/12.86 [2595] BETA_IMPLY : (distinct_lines(N39_34_8, N39_34_8) => (distinct_lines(N39_34_8, N39_34_8) | distinct_lines(N39_34_8, N39_34_8)))
% 45.27/12.86 -> [2596] ~distinct_lines(N39_34_8, N39_34_8)
% 45.27/12.86 -> [2597] (distinct_lines(N39_34_8, N39_34_8) | distinct_lines(N39_34_8, N39_34_8))
% 45.27/12.86
% 45.27/12.86 [2597] BETA_OR : (distinct_lines(N39_34_8, N39_34_8) | distinct_lines(N39_34_8, N39_34_8))
% 45.27/12.86 -> [2598] distinct_lines(N39_34_8, N39_34_8)
% 45.27/12.86 -> [2599] distinct_lines(N39_34_8, N39_34_8)
% 45.27/12.86
% 45.27/12.86 [2599] CLOSURE : distinct_lines(N39_34_8, N39_34_8)
% 45.27/12.86
% 45.27/12.86 [2598] CLOSURE : distinct_lines(N39_34_8, N39_34_8)
% 45.27/12.86
% 45.27/12.86 [2601] BETA_IMPLY : (unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) => (unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) | unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))))
% 45.27/12.86 -> [2681] ~unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86 -> [2682] (unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) | unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)))
% 45.27/12.86
% 45.27/12.86 [2682] BETA_OR : (unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) | unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)))
% 45.27/12.86 -> [2683] unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86 -> [2684] unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86
% 45.27/12.86 [2684] CLOSURE : unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86
% 45.27/12.86 [2683] CLOSURE : unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86
% 45.27/12.86 [2685] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11)))) => ((unequally_directed_lines(reverse_line(N46_39_11), N46_39_11) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))) | (unequally_directed_lines(reverse_line(N46_39_11), N46_39_11) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)))))
% 45.27/12.86 -> [2708] ~(unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))))
% 45.27/12.86 -> [2709] ((unequally_directed_lines(reverse_line(N46_39_11), N46_39_11) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))) | (unequally_directed_lines(reverse_line(N46_39_11), N46_39_11) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))))
% 45.27/12.86
% 45.27/12.86 [2709] BETA_OR : ((unequally_directed_lines(reverse_line(N46_39_11), N46_39_11) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))) | (unequally_directed_lines(reverse_line(N46_39_11), N46_39_11) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))))
% 45.27/12.86 -> [2712] (unequally_directed_lines(reverse_line(N46_39_11), N46_39_11) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)))
% 45.27/12.86 -> [2713] (unequally_directed_lines(reverse_line(N46_39_11), N46_39_11) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)))
% 45.27/12.86
% 45.27/12.86 [2712] ALPHA_AND : (unequally_directed_lines(reverse_line(N46_39_11), N46_39_11) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)))
% 45.27/12.86 -> [2714] unequally_directed_lines(reverse_line(N46_39_11), N46_39_11), unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86
% 45.27/12.86 [2714] CLOSURE : unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86
% 45.27/12.86 [2715] CLOSURE : unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86
% 45.27/12.86 [2708] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))))
% 45.27/12.86 -> [2739] ~unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86 -> [2740] ~unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11)))
% 45.27/12.86
% 45.27/12.86 [2740] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 45.27/12.86 -> [2742] (unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) | unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))))
% 45.27/12.86
% 45.27/12.86 [2742] BETA_OR : (unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) | unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))))
% 45.27/12.86 -> [2745] unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86 -> [2746] unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11)))
% 45.27/12.86
% 45.27/12.86 [2745] CLOSURE : unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86
% 45.27/12.86 [2746] CLOSURE : unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11)))
% 45.27/12.86
% 45.27/12.86 [2739] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 45.27/12.86 -> [2741] (unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) | unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))))
% 45.27/12.86
% 45.27/12.86 [2741] BETA_OR : (unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11)) | unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))))
% 45.27/12.86 -> [2743] unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86 -> [2744] unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11)))
% 45.27/12.86
% 45.27/12.86 [2743] CLOSURE : unequally_directed_lines(reverse_line(N46_39_11), reverse_line(N46_39_11))
% 45.27/12.86
% 45.27/12.86 [2744] 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)))))
% 45.27/12.86 -> [2747] ((unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(reverse_line(N46_39_11))))) => (left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))) | left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(reverse_line(N46_39_11))))))
% 45.27/12.86
% 45.27/12.86 [2747] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(reverse_line(N46_39_11))))) => (left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))) | left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(reverse_line(N46_39_11))))))
% 45.27/12.86 -> [2748] ~(unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(reverse_line(N46_39_11)))))
% 45.27/12.86 -> [2749] (left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))) | left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(reverse_line(N46_39_11)))))
% 45.27/12.86
% 45.27/12.86 [2748] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))) & unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(reverse_line(N46_39_11)))))
% 45.27/12.86 -> [2750] ~unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11)))
% 45.27/12.86 -> [2751] ~unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(reverse_line(N46_39_11))))
% 45.27/12.86
% 45.27/12.86 [2750] CLOSURE : ~unequally_directed_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11)))
% 45.27/12.86
% 45.27/12.86 [2751] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 45.27/12.86 -> [2754] ~(left_apart_point(A51_96_14, L52_96_14) | left_apart_point(A51_96_14, reverse_line(L52_96_14)))
% 45.27/12.86
% 45.27/12.86 [2754] ALPHA_NOT_OR : ~(left_apart_point(A51_96_14, L52_96_14) | left_apart_point(A51_96_14, reverse_line(L52_96_14)))
% 45.27/12.86 -> [2756] ~left_apart_point(A51_96_14, L52_96_14), ~left_apart_point(A51_96_14, reverse_line(L52_96_14))
% 45.27/12.86
% 45.27/12.86 [2756] CLOSURE : ~left_apart_point(A51_96_14, L52_96_14)
% 45.27/12.86
% 45.27/12.86 [2749] BETA_OR : (left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11))) | left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(reverse_line(N46_39_11)))))
% 45.27/12.86 -> [2758] left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11)))
% 45.27/12.86 -> [2759] left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(reverse_line(N46_39_11))))
% 45.27/12.86
% 45.27/12.86 [2758] CLOSURE : left_convergent_lines(reverse_line(N46_39_11), reverse_line(reverse_line(N46_39_11)))
% 45.27/12.86
% 45.27/12.86 [2759] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 45.27/12.86 -> [2760] ~(left_apart_point(A51_98_14, L52_98_14) | left_apart_point(A51_98_14, reverse_line(L52_98_14)))
% 45.27/12.86
% 45.27/12.86 [2760] ALPHA_NOT_OR : ~(left_apart_point(A51_98_14, L52_98_14) | left_apart_point(A51_98_14, reverse_line(L52_98_14)))
% 45.27/12.86 -> [2761] ~left_apart_point(A51_98_14, L52_98_14), ~left_apart_point(A51_98_14, reverse_line(L52_98_14))
% 45.27/12.86
% 45.27/12.86 [2761] CLOSURE : ~left_apart_point(A51_98_14, L52_98_14)
% 45.27/12.86
% 45.27/12.86 % SZS output end Proof for theBenchmark.p
% 45.27/12.86 [12.508863s][1][Res] 115467 goroutines created
% 45.27/12.86 ==== Result ====
% 45.27/12.86 [12.508900s][1][Res] VALID
% 45.27/12.86 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------