TSTP Solution File: GEO244+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO244+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n005.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 38.90s 11.12s
% Output : Proof 38.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO244+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n005.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 07:09:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.35 [DMT] DMT loaded with preskolemization
% 0.20/0.35 [EQ] equality loaded.
% 0.20/0.35 [0.000036s][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
% 38.90/11.11 % SZS output start Proof for theBenchmark.p
% 38.90/11.12 [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) => (right_apart_point(C91_91, line_connecting(A89_89, B90_90)) => left_apart_point(C91_91, line_connecting(B90_90, A89_89))))))
% 38.90/11.12 -> [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) => (right_apart_point(C91_91, line_connecting(A89_89, B90_90)) => left_apart_point(C91_91, line_connecting(B90_90, A89_89)))))
% 38.90/11.12
% 38.90/11.12 [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)))))
% 38.90/11.12 -> [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))))
% 38.90/11.12
% 38.90/11.12 [2] DELTA_NOT_FORALL : ~! [A89_89, B90_90, C91_91] : ((distinct_points(A89_89, B90_90) => (right_apart_point(C91_91, line_connecting(A89_89, B90_90)) => left_apart_point(C91_91, line_connecting(B90_90, A89_89)))))
% 38.90/11.12 -> [3] ~(distinct_points(skolem_A8989, skolem_B9090) => (right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) => left_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989))))
% 38.90/11.12
% 38.90/11.12 [3] ALPHA_NOT_IMPLY : ~(distinct_points(skolem_A8989, skolem_B9090) => (right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) => left_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989))))
% 38.90/11.12 -> [4] distinct_points(skolem_A8989, skolem_B9090), ~(right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) => left_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989)))
% 38.90/11.12
% 38.90/11.12 [4] ALPHA_NOT_IMPLY : ~(right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) => left_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989)))
% 38.90/11.12 -> [5] right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)), ~left_apart_point(skolem_C9191, line_connecting(skolem_B9090, skolem_A8989))
% 38.90/11.12
% 38.90/11.12 [5] GAMMA_FORALL : ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9))))
% 38.90/11.12 -> [6] (unequally_directed_opposite_lines(reverse_line(Y9_0_0), Y9_0_0) <=> unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0)))
% 38.90/11.12
% 38.90/11.12 [6] 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)))
% 38.90/11.12 -> [7] ~unequally_directed_opposite_lines(reverse_line(Y9_0_0), Y9_0_0), ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 38.90/11.12 -> [8] 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))
% 38.90/11.12
% 38.90/11.12 [8] GAMMA_FORALL : ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11))))
% 38.90/11.12 -> [10] (right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) <=> left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090))))
% 38.90/11.12
% 38.90/11.12 [10] BETA_EQUIV : (right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) <=> left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090))))
% 38.90/11.12 -> [13] ~right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)), ~left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090)))
% 38.90/11.12 -> [14] right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)), left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090)))
% 38.90/11.12
% 38.90/11.12 [13] CLOSURE : ~right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090))
% 38.90/11.12
% 38.90/11.12 [16] BETA_EQUIV : (right_convergent_lines(X12_1_2, Y13_1_2) <=> left_convergent_lines(X12_1_2, reverse_line(Y13_1_2)))
% 38.90/11.12 -> [210] ~right_convergent_lines(X12_1_2, Y13_1_2), ~left_convergent_lines(X12_1_2, reverse_line(Y13_1_2))
% 38.90/11.12 -> [211] right_convergent_lines(X12_1_2, Y13_1_2), left_convergent_lines(X12_1_2, reverse_line(Y13_1_2))
% 38.90/11.12
% 38.90/11.12 [211] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 38.90/11.12 -> [218] (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)))
% 38.90/11.12
% 38.90/11.12 [218] 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)))
% 38.90/11.12 -> [219] ~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))
% 38.90/11.12 -> [220] 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))
% 38.90/11.12
% 38.90/11.12 [219] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 38.90/11.12 -> [224] unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 38.90/11.12
% 38.90/11.12 [224] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 38.90/11.12 -> [226] (equally_directed_opposite_lines(X16_4_4, Y17_4_4) <=> ~unequally_directed_opposite_lines(X16_4_4, Y17_4_4))
% 38.90/11.12
% 38.90/11.12 [226] BETA_EQUIV : (equally_directed_opposite_lines(X16_4_4, Y17_4_4) <=> ~unequally_directed_opposite_lines(X16_4_4, Y17_4_4))
% 38.90/11.12 -> [227] ~equally_directed_opposite_lines(X16_4_4, Y17_4_4), ~~unequally_directed_opposite_lines(X16_4_4, Y17_4_4)
% 38.90/11.12 -> [228] equally_directed_opposite_lines(X16_4_4, Y17_4_4), ~unequally_directed_opposite_lines(X16_4_4, Y17_4_4)
% 38.90/11.12
% 38.90/11.12 [228] CLOSURE : ~unequally_directed_opposite_lines(X16_4_4, Y17_4_4)
% 38.90/11.12
% 38.90/11.12 [243] BETA_IMPLY : (distinct_points(A33_5_6, A33_5_6) => (distinct_points(A33_5_6, A33_5_6) | distinct_points(A33_5_6, A33_5_6)))
% 38.90/11.12 -> [307] ~distinct_points(A33_5_6, A33_5_6)
% 38.90/11.12 -> [308] (distinct_points(A33_5_6, A33_5_6) | distinct_points(A33_5_6, A33_5_6))
% 38.90/11.12
% 38.90/11.12 [308] BETA_OR : (distinct_points(A33_5_6, A33_5_6) | distinct_points(A33_5_6, A33_5_6))
% 38.90/11.12 -> [309] distinct_points(A33_5_6, A33_5_6)
% 38.90/11.12 -> [310] distinct_points(A33_5_6, A33_5_6)
% 38.90/11.12
% 38.90/11.12 [310] CLOSURE : distinct_points(A33_5_6, A33_5_6)
% 38.90/11.12
% 38.90/11.12 [309] CLOSURE : distinct_points(A33_5_6, A33_5_6)
% 38.90/11.12
% 38.90/11.12 [307] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 38.90/11.12 -> [315] ~distinct_lines(N39_7_8, N39_7_8)
% 38.90/11.12
% 38.90/11.12 [315] 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))))
% 38.90/11.12 -> [319] (distinct_lines(N39_7_8, N39_7_8) => (distinct_lines(N39_7_8, N39_7_8) | distinct_lines(N39_7_8, N39_7_8)))
% 38.90/11.12
% 38.90/11.12 [319] BETA_IMPLY : (distinct_lines(N39_7_8, N39_7_8) => (distinct_lines(N39_7_8, N39_7_8) | distinct_lines(N39_7_8, N39_7_8)))
% 38.90/11.12 -> [321] ~distinct_lines(N39_7_8, N39_7_8)
% 38.90/11.12 -> [322] (distinct_lines(N39_7_8, N39_7_8) | distinct_lines(N39_7_8, N39_7_8))
% 38.90/11.12
% 38.90/11.12 [322] BETA_OR : (distinct_lines(N39_7_8, N39_7_8) | distinct_lines(N39_7_8, N39_7_8))
% 38.90/11.12 -> [325] distinct_lines(N39_7_8, N39_7_8)
% 38.90/11.12 -> [326] distinct_lines(N39_7_8, N39_7_8)
% 38.90/11.12
% 38.90/11.12 [325] CLOSURE : distinct_lines(N39_7_8, N39_7_8)
% 38.90/11.12
% 38.90/11.12 [326] CLOSURE : distinct_lines(N39_7_8, N39_7_8)
% 38.90/11.12
% 38.90/11.12 [329] CLOSURE : equally_directed_lines(L40_7_9, L40_7_9)
% 38.90/11.12
% 38.90/11.12 [220] CLOSURE : ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 38.90/11.12
% 38.90/11.12 [210] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 38.90/11.12 -> [221] (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)))
% 38.90/11.12
% 38.90/11.12 [221] 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)))
% 38.90/11.12 -> [222] ~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))
% 38.90/11.12 -> [223] 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))
% 38.90/11.12
% 38.90/11.12 [222] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 38.90/11.12 -> [225] unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 38.90/11.12
% 38.90/11.12 [225] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 38.90/11.12 -> [229] (equally_directed_opposite_lines(X16_5_4, Y17_5_4) <=> ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4))
% 38.90/11.12
% 38.90/11.12 [229] BETA_EQUIV : (equally_directed_opposite_lines(X16_5_4, Y17_5_4) <=> ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4))
% 38.90/11.12 -> [230] ~equally_directed_opposite_lines(X16_5_4, Y17_5_4), ~~unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 38.90/11.12 -> [231] equally_directed_opposite_lines(X16_5_4, Y17_5_4), ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 38.90/11.12
% 38.90/11.12 [231] CLOSURE : ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 38.90/11.12
% 38.90/11.12 [238] BETA_IMPLY : (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989)))
% 38.90/11.12 -> [299] ~distinct_points(skolem_A8989, skolem_B9090)
% 38.90/11.12 -> [300] (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989))
% 38.90/11.12
% 38.90/11.12 [299] CLOSURE : ~distinct_points(skolem_A8989, skolem_B9090)
% 38.90/11.12
% 38.90/11.12 [300] BETA_OR : (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989))
% 38.90/11.12 -> [313] distinct_points(skolem_A8989, skolem_A8989)
% 38.90/11.12 -> [314] distinct_points(skolem_B9090, skolem_A8989)
% 38.90/11.12
% 38.90/11.12 [313] CLOSURE : distinct_points(skolem_A8989, skolem_A8989)
% 38.90/11.12
% 38.90/11.12 [314] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 38.90/11.12 -> [316] ~distinct_lines(N39_8_8, N39_8_8)
% 38.90/11.12
% 38.90/11.12 [316] 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))))
% 38.90/11.12 -> [320] (distinct_lines(N39_8_8, N39_8_8) => (distinct_lines(N39_8_8, N39_8_8) | distinct_lines(N39_8_8, N39_8_8)))
% 38.90/11.12
% 38.90/11.12 [320] BETA_IMPLY : (distinct_lines(N39_8_8, N39_8_8) => (distinct_lines(N39_8_8, N39_8_8) | distinct_lines(N39_8_8, N39_8_8)))
% 38.90/11.12 -> [323] ~distinct_lines(N39_8_8, N39_8_8)
% 38.90/11.12 -> [324] (distinct_lines(N39_8_8, N39_8_8) | distinct_lines(N39_8_8, N39_8_8))
% 38.90/11.12
% 38.90/11.12 [324] BETA_OR : (distinct_lines(N39_8_8, N39_8_8) | distinct_lines(N39_8_8, N39_8_8))
% 38.90/11.12 -> [327] distinct_lines(N39_8_8, N39_8_8)
% 38.90/11.12 -> [328] distinct_lines(N39_8_8, N39_8_8)
% 38.90/11.12
% 38.90/11.12 [328] CLOSURE : distinct_lines(N39_8_8, N39_8_8)
% 38.90/11.12
% 38.90/11.12 [327] CLOSURE : distinct_lines(N39_8_8, N39_8_8)
% 38.90/11.12
% 38.90/11.12 [330] CLOSURE : equally_directed_lines(L40_8_9, L40_8_9)
% 38.90/11.12
% 38.90/11.12 [223] CLOSURE : ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 38.90/11.12
% 38.90/11.12 [9] BETA_EQUIV : (right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) <=> left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090))))
% 38.90/11.12 -> [1669] ~right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)), ~left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090)))
% 38.90/11.12 -> [1670] right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)), left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090)))
% 38.90/11.12
% 38.90/11.12 [1669] CLOSURE : ~right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090))
% 38.90/11.12
% 38.90/11.12 [1670] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 38.90/11.12 -> [1671] (right_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))) <=> left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11)))))
% 38.90/11.12
% 38.90/11.12 [1671] BETA_EQUIV : (right_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))) <=> left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11)))))
% 38.90/11.12 -> [1672] ~right_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))), ~left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11))))
% 38.90/11.12 -> [1673] right_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))), left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11))))
% 38.90/11.12
% 38.90/11.12 [1673] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 38.90/11.12 -> [1675] (equally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) <=> ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)))
% 38.90/11.12
% 38.90/11.12 [1675] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)) <=> ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)))
% 38.90/11.12 -> [1678] ~equally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)), ~~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 38.90/11.12 -> [1679] equally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4)), ~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 38.90/11.12
% 38.90/11.12 [1678] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 38.90/11.12 -> [1681] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 38.90/11.12
% 38.90/11.12 [1681] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 38.90/11.12
% 38.90/11.12 [1683] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4))
% 38.90/11.12 -> [1972] ~equally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 38.90/11.12 -> [1973] equally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4), ~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 38.90/11.12
% 38.90/11.12 [1972] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 38.90/11.12 -> [1977] unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 38.90/11.12
% 38.90/11.12 [1977] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 38.90/11.12
% 38.90/11.12 [1973] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 38.90/11.12 -> [1982] ~distinct_points(skolem_A8989, skolem_A8989)
% 38.90/11.12
% 38.90/11.12 [1982] 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))))
% 38.90/11.12 -> [1983] (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989)))
% 38.90/11.12
% 38.90/11.12 [1983] BETA_IMPLY : (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989)))
% 38.90/11.12 -> [1984] ~distinct_points(skolem_A8989, skolem_B9090)
% 38.90/11.12 -> [1985] (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989))
% 38.90/11.12
% 38.90/11.12 [1984] CLOSURE : ~distinct_points(skolem_A8989, skolem_B9090)
% 38.90/11.12
% 38.90/11.12 [1985] BETA_OR : (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989))
% 38.90/11.12 -> [1992] distinct_points(skolem_A8989, skolem_A8989)
% 38.90/11.12 -> [1993] distinct_points(skolem_B9090, skolem_A8989)
% 38.90/11.12
% 38.90/11.12 [1992] CLOSURE : distinct_points(skolem_A8989, skolem_A8989)
% 38.90/11.12
% 38.90/11.12 [1993] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 38.90/11.12 -> [1996] ~distinct_lines(N39_26_8, N39_26_8)
% 38.90/11.12
% 38.90/11.12 [1996] 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))))
% 38.90/11.12 -> [1997] (distinct_lines(N39_26_8, N39_26_8) => (distinct_lines(N39_26_8, N39_26_8) | distinct_lines(N39_26_8, N39_26_8)))
% 38.90/11.12
% 38.90/11.12 [1997] BETA_IMPLY : (distinct_lines(N39_26_8, N39_26_8) => (distinct_lines(N39_26_8, N39_26_8) | distinct_lines(N39_26_8, N39_26_8)))
% 38.90/11.12 -> [1999] ~distinct_lines(N39_26_8, N39_26_8)
% 38.90/11.12 -> [2000] (distinct_lines(N39_26_8, N39_26_8) | distinct_lines(N39_26_8, N39_26_8))
% 38.90/11.12
% 38.90/11.12 [2000] BETA_OR : (distinct_lines(N39_26_8, N39_26_8) | distinct_lines(N39_26_8, N39_26_8))
% 38.90/11.12 -> [2002] distinct_lines(N39_26_8, N39_26_8)
% 38.90/11.12 -> [2003] distinct_lines(N39_26_8, N39_26_8)
% 38.90/11.12
% 38.90/11.12 [2002] CLOSURE : distinct_lines(N39_26_8, N39_26_8)
% 38.90/11.12
% 38.90/11.12 [2003] CLOSURE : distinct_lines(N39_26_8, N39_26_8)
% 38.90/11.12
% 38.90/11.12 [1999] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 38.90/11.12 -> [2004] equally_directed_lines(L40_26_9, L40_26_9)
% 38.90/11.12
% 38.90/11.12 [2004] 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))))
% 38.90/11.12 -> [2005] (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) => (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))))
% 38.90/11.12
% 38.90/11.12 [2005] 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(N46_36_11)) | unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))))
% 38.90/11.12 -> [2006] ~unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12 -> [2007] (unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)) | unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)))
% 38.90/11.12
% 38.90/11.12 [2007] 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(N46_36_11)))
% 38.90/11.12 -> [2008] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12 -> [2009] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12
% 38.90/11.12 [2009] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12
% 38.90/11.12 [2008] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12
% 38.90/11.12 [2010] 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)))))
% 38.90/11.12 -> [2048] ~(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))))
% 38.90/11.12 -> [2049] ((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))))
% 38.90/11.12
% 38.90/11.12 [2049] 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))))
% 38.90/11.12 -> [2056] (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)))
% 38.90/11.12 -> [2057] (unequally_directed_lines(reverse_line(N46_36_11), N46_36_11) & unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11)))
% 38.90/11.12
% 38.90/11.12 [2057] 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)))
% 38.90/11.12 -> [2061] unequally_directed_lines(reverse_line(N46_36_11), N46_36_11), unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12
% 38.90/11.12 [2061] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12
% 38.90/11.12 [2060] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12
% 38.90/11.12 [2048] 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))))
% 38.90/11.12 -> [2095] ~unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12 -> [2096] ~unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 38.90/11.12
% 38.90/11.12 [2096] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 38.90/11.12 -> [2098] (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))))
% 38.90/11.12
% 38.90/11.12 [2098] 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))))
% 38.90/11.12 -> [2101] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12 -> [2102] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 38.90/11.12
% 38.90/11.12 [2101] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12
% 38.90/11.12 [2102] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 38.90/11.12
% 38.90/11.12 [2095] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 38.90/11.12 -> [2097] (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))))
% 38.90/11.12
% 38.90/11.12 [2097] 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))))
% 38.90/11.12 -> [2099] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12 -> [2100] unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 38.90/11.12
% 38.90/11.12 [2099] CLOSURE : unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12
% 38.90/11.12 [2100] 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)))))
% 38.90/11.12 -> [2107] ((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)))))
% 38.90/11.12
% 38.90/11.12 [2107] 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)))))
% 38.90/11.12 -> [2109] ~(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))))
% 38.90/11.12 -> [2110] (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))))
% 38.90/11.12
% 38.90/11.12 [2110] 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))))
% 38.90/11.12 -> [2115] left_convergent_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12 -> [2116] left_convergent_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 38.90/11.12
% 38.90/11.12 [2115] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 38.90/11.12 -> [2127] ~(left_apart_point(A51_41_14, L52_41_14) | left_apart_point(A51_41_14, reverse_line(L52_41_14)))
% 38.90/11.12
% 38.90/11.12 [2127] ALPHA_NOT_OR : ~(left_apart_point(A51_41_14, L52_41_14) | left_apart_point(A51_41_14, reverse_line(L52_41_14)))
% 38.90/11.12 -> [2130] ~left_apart_point(A51_41_14, L52_41_14), ~left_apart_point(A51_41_14, reverse_line(L52_41_14))
% 38.90/11.12
% 38.90/11.12 [2130] CLOSURE : ~left_apart_point(A51_41_14, L52_41_14)
% 38.90/11.12
% 38.90/11.12 [2116] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 38.90/11.12 -> [2131] ~(left_apart_point(A51_42_14, L52_42_14) | left_apart_point(A51_42_14, reverse_line(L52_42_14)))
% 38.90/11.12
% 38.90/11.12 [2131] ALPHA_NOT_OR : ~(left_apart_point(A51_42_14, L52_42_14) | left_apart_point(A51_42_14, reverse_line(L52_42_14)))
% 38.90/11.12 -> [2132] ~left_apart_point(A51_42_14, L52_42_14), ~left_apart_point(A51_42_14, reverse_line(L52_42_14))
% 38.90/11.12
% 38.90/11.12 [2132] CLOSURE : ~left_apart_point(A51_42_14, L52_42_14)
% 38.90/11.12
% 38.90/11.12 [2109] 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))))
% 38.90/11.12 -> [2113] ~unequally_directed_lines(reverse_line(N46_36_11), reverse_line(N46_36_11))
% 38.90/11.12 -> [2114] ~unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 38.90/11.12
% 38.90/11.12 [2114] CLOSURE : ~unequally_directed_lines(reverse_line(N46_36_11), reverse_line(reverse_line(N46_36_11)))
% 38.90/11.12
% 38.90/11.12 [2113] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 38.90/11.12 -> [2133] ~(left_apart_point(A51_43_14, L52_43_14) | left_apart_point(A51_43_14, reverse_line(L52_43_14)))
% 38.90/11.12
% 38.90/11.12 [2133] ALPHA_NOT_OR : ~(left_apart_point(A51_43_14, L52_43_14) | left_apart_point(A51_43_14, reverse_line(L52_43_14)))
% 38.90/11.12 -> [2134] ~left_apart_point(A51_43_14, L52_43_14), ~left_apart_point(A51_43_14, reverse_line(L52_43_14))
% 38.90/11.12
% 38.90/11.12 [2134] CLOSURE : ~left_apart_point(A51_43_14, L52_43_14)
% 38.90/11.12
% 38.90/11.12 [1672] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 38.90/11.12 -> [1674] (equally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)) <=> ~unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)))
% 38.90/11.12
% 38.90/11.12 [1674] BETA_EQUIV : (equally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)) <=> ~unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)))
% 38.90/11.12 -> [1676] ~equally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)), ~~unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12 -> [1677] equally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)), ~unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12
% 38.90/11.12 [1676] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12 -> [1680] unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12
% 38.90/11.12 [1680] CLOSURE : unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12
% 38.90/11.12 [1682] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(N46_40_11), N46_40_11) <=> ~unequally_directed_opposite_lines(reverse_line(N46_40_11), N46_40_11))
% 38.90/11.12 -> [1888] ~equally_directed_opposite_lines(reverse_line(N46_40_11), N46_40_11), ~~unequally_directed_opposite_lines(reverse_line(N46_40_11), N46_40_11)
% 38.90/11.12 -> [1889] equally_directed_opposite_lines(reverse_line(N46_40_11), N46_40_11), ~unequally_directed_opposite_lines(reverse_line(N46_40_11), N46_40_11)
% 38.90/11.12
% 38.90/11.12 [1888] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(N46_40_11), N46_40_11)
% 38.90/11.12 -> [1892] unequally_directed_opposite_lines(reverse_line(N46_40_11), N46_40_11)
% 38.90/11.12
% 38.90/11.12 [1892] CLOSURE : unequally_directed_opposite_lines(reverse_line(N46_40_11), N46_40_11)
% 38.90/11.12
% 38.90/11.12 [1894] BETA_IMPLY : (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989)))
% 38.90/11.12 -> [2196] ~distinct_points(skolem_A8989, skolem_B9090)
% 38.90/11.12 -> [2197] (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989))
% 38.90/11.12
% 38.90/11.12 [2196] CLOSURE : ~distinct_points(skolem_A8989, skolem_B9090)
% 38.90/11.12
% 38.90/11.12 [2197] BETA_OR : (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989))
% 38.90/11.12 -> [2200] distinct_points(skolem_A8989, skolem_A8989)
% 38.90/11.12 -> [2201] distinct_points(skolem_B9090, skolem_A8989)
% 38.90/11.12
% 38.90/11.12 [2200] CLOSURE : distinct_points(skolem_A8989, skolem_A8989)
% 38.90/11.12
% 38.90/11.12 [2201] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 38.90/11.12 -> [2202] ~distinct_lines(N39_27_8, N39_27_8)
% 38.90/11.12
% 38.90/11.12 [2202] 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))))
% 38.90/11.12 -> [2203] (distinct_lines(N39_27_8, N39_27_8) => (distinct_lines(N39_27_8, N39_27_8) | distinct_lines(N39_27_8, N39_27_8)))
% 38.90/11.12
% 38.90/11.12 [2203] BETA_IMPLY : (distinct_lines(N39_27_8, N39_27_8) => (distinct_lines(N39_27_8, N39_27_8) | distinct_lines(N39_27_8, N39_27_8)))
% 38.90/11.12 -> [2204] ~distinct_lines(N39_27_8, N39_27_8)
% 38.90/11.12 -> [2205] (distinct_lines(N39_27_8, N39_27_8) | distinct_lines(N39_27_8, N39_27_8))
% 38.90/11.12
% 38.90/11.12 [2205] BETA_OR : (distinct_lines(N39_27_8, N39_27_8) | distinct_lines(N39_27_8, N39_27_8))
% 38.90/11.12 -> [2206] distinct_lines(N39_27_8, N39_27_8)
% 38.90/11.12 -> [2207] distinct_lines(N39_27_8, N39_27_8)
% 38.90/11.12
% 38.90/11.12 [2206] CLOSURE : distinct_lines(N39_27_8, N39_27_8)
% 38.90/11.12
% 38.90/11.12 [2207] CLOSURE : distinct_lines(N39_27_8, N39_27_8)
% 38.90/11.12
% 38.90/11.12 [2209] BETA_IMPLY : (unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)) => (unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)) | unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))))
% 38.90/11.12 -> [2307] ~unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12 -> [2308] (unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)) | unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)))
% 38.90/11.12
% 38.90/11.12 [2308] BETA_OR : (unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)) | unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)))
% 38.90/11.12 -> [2309] unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12 -> [2310] unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12
% 38.90/11.12 [2310] CLOSURE : unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12
% 38.90/11.12 [2309] CLOSURE : unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12
% 38.90/11.12 [2311] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11)))) => ((unequally_directed_lines(reverse_line(N46_40_11), N46_40_11) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))) | (unequally_directed_lines(reverse_line(N46_40_11), N46_40_11) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)))))
% 38.90/11.12 -> [2334] ~(unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))))
% 38.90/11.12 -> [2335] ((unequally_directed_lines(reverse_line(N46_40_11), N46_40_11) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))) | (unequally_directed_lines(reverse_line(N46_40_11), N46_40_11) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))))
% 38.90/11.12
% 38.90/11.12 [2335] BETA_OR : ((unequally_directed_lines(reverse_line(N46_40_11), N46_40_11) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))) | (unequally_directed_lines(reverse_line(N46_40_11), N46_40_11) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))))
% 38.90/11.12 -> [2338] (unequally_directed_lines(reverse_line(N46_40_11), N46_40_11) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)))
% 38.90/11.12 -> [2339] (unequally_directed_lines(reverse_line(N46_40_11), N46_40_11) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)))
% 38.90/11.12
% 38.90/11.12 [2338] ALPHA_AND : (unequally_directed_lines(reverse_line(N46_40_11), N46_40_11) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)))
% 38.90/11.12 -> [2340] unequally_directed_lines(reverse_line(N46_40_11), N46_40_11), unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12
% 38.90/11.12 [2340] CLOSURE : unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12
% 38.90/11.12 [2341] CLOSURE : unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12
% 38.90/11.12 [2334] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))))
% 38.90/11.12 -> [2365] ~unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12 -> [2366] ~unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11)))
% 38.90/11.12
% 38.90/11.12 [2366] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 38.90/11.12 -> [2368] (unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)) | unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))))
% 38.90/11.12
% 38.90/11.12 [2368] BETA_OR : (unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)) | unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))))
% 38.90/11.12 -> [2371] unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12 -> [2372] unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11)))
% 38.90/11.12
% 38.90/11.12 [2371] CLOSURE : unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12
% 38.90/11.12 [2372] CLOSURE : unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11)))
% 38.90/11.12
% 38.90/11.12 [2365] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 38.90/11.12 -> [2367] (unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)) | unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))))
% 38.90/11.12
% 38.90/11.12 [2367] BETA_OR : (unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11)) | unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))))
% 38.90/11.12 -> [2369] unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12 -> [2370] unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11)))
% 38.90/11.12
% 38.90/11.12 [2369] CLOSURE : unequally_directed_lines(reverse_line(N46_40_11), reverse_line(N46_40_11))
% 38.90/11.12
% 38.90/11.12 [2370] 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)))))
% 38.90/11.12 -> [2373] ((unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11))))) => (left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))) | left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11))))))
% 38.90/11.12
% 38.90/11.12 [2373] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11))))) => (left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))) | left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11))))))
% 38.90/11.12 -> [2374] ~(unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11)))))
% 38.90/11.12 -> [2375] (left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))) | left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11)))))
% 38.90/11.12
% 38.90/11.12 [2374] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))) & unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11)))))
% 38.90/11.12 -> [2376] ~unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11)))
% 38.90/11.12 -> [2377] ~unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11))))
% 38.90/11.12
% 38.90/11.12 [2376] CLOSURE : ~unequally_directed_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11)))
% 38.90/11.12
% 38.90/11.12 [2377] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 38.90/11.12 -> [2380] ~(left_apart_point(A51_62_14, L52_62_14) | left_apart_point(A51_62_14, reverse_line(L52_62_14)))
% 38.90/11.12
% 38.90/11.12 [2380] ALPHA_NOT_OR : ~(left_apart_point(A51_62_14, L52_62_14) | left_apart_point(A51_62_14, reverse_line(L52_62_14)))
% 38.90/11.12 -> [2382] ~left_apart_point(A51_62_14, L52_62_14), ~left_apart_point(A51_62_14, reverse_line(L52_62_14))
% 38.90/11.12
% 38.90/11.12 [2382] CLOSURE : ~left_apart_point(A51_62_14, L52_62_14)
% 38.90/11.12
% 38.90/11.12 [2375] BETA_OR : (left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11))) | left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11)))))
% 38.90/11.12 -> [2384] left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(N46_40_11)))
% 38.90/11.12 -> [2385] left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11))))
% 38.90/11.12
% 38.90/11.12 [2385] CLOSURE : left_convergent_lines(reverse_line(N46_40_11), reverse_line(reverse_line(reverse_line(N46_40_11))))
% 38.90/11.12
% 38.90/11.12 [2384] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 38.90/11.12 -> [2386] ~(left_apart_point(A51_64_14, L52_64_14) | left_apart_point(A51_64_14, reverse_line(L52_64_14)))
% 38.90/11.12
% 38.90/11.12 [2386] ALPHA_NOT_OR : ~(left_apart_point(A51_64_14, L52_64_14) | left_apart_point(A51_64_14, reverse_line(L52_64_14)))
% 38.90/11.12 -> [2387] ~left_apart_point(A51_64_14, L52_64_14), ~left_apart_point(A51_64_14, reverse_line(L52_64_14))
% 38.90/11.12
% 38.90/11.12 [2387] CLOSURE : ~left_apart_point(A51_64_14, L52_64_14)
% 38.90/11.12
% 38.90/11.12 % SZS output end Proof for theBenchmark.p
% 38.90/11.12 [10.768608s][1][Res] 102853 goroutines created
% 38.90/11.12 ==== Result ====
% 38.90/11.12 [10.768645s][1][Res] VALID
% 38.90/11.12 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------