TSTP Solution File: GEO245+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO245+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n022.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 15:18:41 EDT 2022
% Result : Theorem 56.23s 16.97s
% Output : Proof 56.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO245+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : goeland -dmt -presko -proof %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 07:11:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000035s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.35 Conjecture not found
% 0.12/0.35 Start search
% 0.12/0.35 nb_step : 1 - limit : 37
% 0.12/0.35 Launch Gotab with destructive = true
% 56.23/16.95 % SZS output start Proof for theBenchmark.p
% 56.23/16.96 [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(B90_90, line_connecting(A89_89, C91_91))))))
% 56.23/16.96 -> [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(B90_90, line_connecting(A89_89, C91_91)))))
% 56.23/16.96
% 56.23/16.96 [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)))))
% 56.23/16.96 -> [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))))
% 56.23/16.96
% 56.23/16.96 [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(B90_90, line_connecting(A89_89, C91_91)))))
% 56.23/16.96 -> [3] ~(distinct_points(skolem_A8989, skolem_B9090) => (left_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) => right_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191))))
% 56.23/16.96
% 56.23/16.96 [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_B9090, line_connecting(skolem_A8989, skolem_C9191))))
% 56.23/16.96 -> [4] distinct_points(skolem_A8989, skolem_B9090), ~(left_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) => right_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191)))
% 56.23/16.96
% 56.23/16.96 [4] ALPHA_NOT_IMPLY : ~(left_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) => right_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191)))
% 56.23/16.96 -> [5] left_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)), ~right_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191))
% 56.23/16.96
% 56.23/16.96 [5] GAMMA_FORALL : ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9))))
% 56.23/16.96 -> [6] (unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4) <=> unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)))
% 56.23/16.96
% 56.23/16.96 [6] BETA_EQUIV : (unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4) <=> unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)))
% 56.23/16.96 -> [7] ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4), ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 56.23/16.96 -> [8] unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4), unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 56.23/16.96
% 56.23/16.96 [8] GAMMA_FORALL : ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11))))
% 56.23/16.96 -> [10] (right_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191)) <=> left_apart_point(skolem_B9090, reverse_line(line_connecting(skolem_A8989, skolem_C9191))))
% 56.23/16.96
% 56.23/16.96 [10] BETA_EQUIV : (right_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191)) <=> left_apart_point(skolem_B9090, reverse_line(line_connecting(skolem_A8989, skolem_C9191))))
% 56.23/16.96 -> [13] ~right_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191)), ~left_apart_point(skolem_B9090, reverse_line(line_connecting(skolem_A8989, skolem_C9191)))
% 56.23/16.96 -> [14] right_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191)), left_apart_point(skolem_B9090, reverse_line(line_connecting(skolem_A8989, skolem_C9191)))
% 56.23/16.96
% 56.23/16.96 [14] CLOSURE : right_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191))
% 56.23/16.96
% 56.23/16.96 [16] BETA_EQUIV : (right_convergent_lines(X12_1_2, Y13_1_2) <=> left_convergent_lines(X12_1_2, reverse_line(Y13_1_2)))
% 56.23/16.96 -> [338] ~right_convergent_lines(X12_1_2, Y13_1_2), ~left_convergent_lines(X12_1_2, reverse_line(Y13_1_2))
% 56.23/16.96 -> [339] right_convergent_lines(X12_1_2, Y13_1_2), left_convergent_lines(X12_1_2, reverse_line(Y13_1_2))
% 56.23/16.96
% 56.23/16.96 [338] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 56.23/16.96 -> [340] (equally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) <=> ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)))
% 56.23/16.96
% 56.23/16.96 [340] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) <=> ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)))
% 56.23/16.96 -> [343] ~equally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)), ~~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 56.23/16.96 -> [344] equally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)), ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 56.23/16.96
% 56.23/16.96 [343] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 56.23/16.96 -> [353] unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 56.23/16.96
% 56.23/16.96 [353] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 56.23/16.96 -> [355] (equally_directed_opposite_lines(X16_5_4, Y17_5_4) <=> ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4))
% 56.23/16.96
% 56.23/16.96 [355] BETA_EQUIV : (equally_directed_opposite_lines(X16_5_4, Y17_5_4) <=> ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4))
% 56.23/16.96 -> [357] ~equally_directed_opposite_lines(X16_5_4, Y17_5_4), ~~unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 56.23/16.96 -> [358] equally_directed_opposite_lines(X16_5_4, Y17_5_4), ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 56.23/16.96
% 56.23/16.96 [357] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 56.23/16.96 -> [361] unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 56.23/16.96
% 56.23/16.96 [361] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 56.23/16.96 -> [367] ~distinct_points(skolem_A8989, skolem_A8989)
% 56.23/16.96
% 56.23/16.96 [367] 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))))
% 56.23/16.96 -> [369] (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989)))
% 56.23/16.96
% 56.23/16.96 [369] BETA_IMPLY : (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989)))
% 56.23/16.96 -> [371] ~distinct_points(skolem_A8989, skolem_B9090)
% 56.23/16.96 -> [372] (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989))
% 56.23/16.96
% 56.23/16.96 [371] CLOSURE : ~distinct_points(skolem_A8989, skolem_B9090)
% 56.23/16.96
% 56.23/16.96 [372] BETA_OR : (distinct_points(skolem_A8989, skolem_A8989) | distinct_points(skolem_B9090, skolem_A8989))
% 56.23/16.96 -> [383] distinct_points(skolem_A8989, skolem_A8989)
% 56.23/16.96 -> [384] distinct_points(skolem_B9090, skolem_A8989)
% 56.23/16.96
% 56.23/16.96 [383] CLOSURE : distinct_points(skolem_A8989, skolem_A8989)
% 56.23/16.96
% 56.23/16.96 [384] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 56.23/16.96 -> [387] ~distinct_lines(N39_8_8, N39_8_8)
% 56.23/16.96
% 56.23/16.96 [387] 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))))
% 56.23/16.96 -> [389] (distinct_lines(N39_8_8, N39_8_8) => (distinct_lines(N39_8_8, N39_8_8) | distinct_lines(N39_8_8, N39_8_8)))
% 56.23/16.96
% 56.23/16.96 [389] 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)))
% 56.23/16.96 -> [390] ~distinct_lines(N39_8_8, N39_8_8)
% 56.23/16.96 -> [391] (distinct_lines(N39_8_8, N39_8_8) | distinct_lines(N39_8_8, N39_8_8))
% 56.23/16.96
% 56.23/16.96 [391] BETA_OR : (distinct_lines(N39_8_8, N39_8_8) | distinct_lines(N39_8_8, N39_8_8))
% 56.23/16.96 -> [392] distinct_lines(N39_8_8, N39_8_8)
% 56.23/16.96 -> [393] distinct_lines(N39_8_8, N39_8_8)
% 56.23/16.96
% 56.23/16.96 [393] CLOSURE : distinct_lines(N39_8_8, N39_8_8)
% 56.23/16.96
% 56.23/16.96 [392] CLOSURE : distinct_lines(N39_8_8, N39_8_8)
% 56.23/16.96
% 56.23/16.96 [397] CLOSURE : equally_directed_lines(L40_8_9, L40_8_9)
% 56.23/16.96
% 56.23/16.96 [358] CLOSURE : ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 56.23/16.96
% 56.23/16.96 [344] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 56.23/16.96
% 56.23/16.96 [342] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)) <=> ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)))
% 56.23/16.96 -> [511] ~equally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)), ~~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 56.23/16.96 -> [512] equally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4)), ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 56.23/16.96
% 56.23/16.96 [512] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_8_4), reverse_line(Y17_8_4))
% 56.23/16.96
% 56.23/16.96 [514] 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))
% 56.23/16.96 -> [579] ~equally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 56.23/16.96 -> [580] equally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4), ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 56.23/16.96
% 56.23/16.96 [580] CLOSURE : ~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 56.23/16.96
% 56.23/16.96 [579] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 56.23/16.96 -> [582] unequally_directed_opposite_lines(reverse_line(Y17_8_4), Y17_8_4)
% 56.23/16.96
% 56.23/16.96 [582] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 56.23/16.97 -> [589] ~distinct_points(skolem_B9090, skolem_B9090)
% 56.23/16.97
% 56.23/16.97 [589] 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))))
% 56.23/16.97 -> [594] (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090)))
% 56.23/16.97
% 56.23/16.97 [594] BETA_IMPLY : (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090)))
% 56.23/16.97 -> [597] ~distinct_points(skolem_A8989, skolem_B9090)
% 56.23/16.97 -> [598] (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090))
% 56.23/16.97
% 56.23/16.97 [597] CLOSURE : ~distinct_points(skolem_A8989, skolem_B9090)
% 56.23/16.97
% 56.23/16.97 [598] BETA_OR : (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090))
% 56.23/16.97 -> [629] distinct_points(skolem_A8989, skolem_B9090)
% 56.23/16.97 -> [630] distinct_points(skolem_B9090, skolem_B9090)
% 56.23/16.97
% 56.23/16.97 [630] CLOSURE : distinct_points(skolem_B9090, skolem_B9090)
% 56.23/16.97
% 56.23/16.97 [629] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 56.23/16.97 -> [631] ~distinct_lines(M38_15_8, M38_15_8)
% 56.23/16.97
% 56.23/16.97 [631] 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))))
% 56.23/16.97 -> [636] (distinct_lines(M38_15_8, M38_15_8) => (distinct_lines(M38_15_8, M38_15_8) | distinct_lines(M38_15_8, M38_15_8)))
% 56.23/16.97
% 56.23/16.97 [636] BETA_IMPLY : (distinct_lines(M38_15_8, M38_15_8) => (distinct_lines(M38_15_8, M38_15_8) | distinct_lines(M38_15_8, M38_15_8)))
% 56.23/16.97 -> [637] ~distinct_lines(M38_15_8, M38_15_8)
% 56.23/16.97 -> [638] (distinct_lines(M38_15_8, M38_15_8) | distinct_lines(M38_15_8, M38_15_8))
% 56.23/16.97
% 56.23/16.97 [637] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 56.23/16.97 -> [641] equally_directed_lines(L40_15_9, L40_15_9)
% 56.23/16.97
% 56.23/16.97 [641] CLOSURE : equally_directed_lines(L40_15_9, L40_15_9)
% 56.23/16.97
% 56.23/16.97 [638] BETA_OR : (distinct_lines(M38_15_8, M38_15_8) | distinct_lines(M38_15_8, M38_15_8))
% 56.23/16.97 -> [639] distinct_lines(M38_15_8, M38_15_8)
% 56.23/16.97 -> [640] distinct_lines(M38_15_8, M38_15_8)
% 56.23/16.97
% 56.23/16.97 [639] CLOSURE : distinct_lines(M38_15_8, M38_15_8)
% 56.23/16.97
% 56.23/16.97 [640] CLOSURE : distinct_lines(M38_15_8, M38_15_8)
% 56.23/16.97
% 56.23/16.97 [9] BETA_EQUIV : (right_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191)) <=> left_apart_point(skolem_B9090, reverse_line(line_connecting(skolem_A8989, skolem_C9191))))
% 56.23/16.97 -> [2513] ~right_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191)), ~left_apart_point(skolem_B9090, reverse_line(line_connecting(skolem_A8989, skolem_C9191)))
% 56.23/16.97 -> [2514] right_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191)), left_apart_point(skolem_B9090, reverse_line(line_connecting(skolem_A8989, skolem_C9191)))
% 56.23/16.97
% 56.23/16.97 [2514] CLOSURE : right_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191))
% 56.23/16.97
% 56.23/16.97 [2513] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 56.23/16.97 -> [2515] (right_convergent_lines(reverse_line(Y13_2_2), Y13_2_2) <=> left_convergent_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)))
% 56.23/16.97
% 56.23/16.97 [2515] BETA_EQUIV : (right_convergent_lines(reverse_line(Y13_2_2), Y13_2_2) <=> left_convergent_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)))
% 56.23/16.97 -> [2516] ~right_convergent_lines(reverse_line(Y13_2_2), Y13_2_2), ~left_convergent_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97 -> [2517] right_convergent_lines(reverse_line(Y13_2_2), Y13_2_2), left_convergent_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97
% 56.23/16.97 [2517] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 56.23/16.97 -> [2519] (equally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) <=> ~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)))
% 56.23/16.97
% 56.23/16.97 [2519] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) <=> ~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)))
% 56.23/16.97 -> [2522] ~equally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)), ~~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97 -> [2523] equally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)), ~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97
% 56.23/16.97 [2522] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97 -> [2525] unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97
% 56.23/16.97 [2525] CLOSURE : unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97
% 56.23/16.97 [2529] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4))
% 56.23/16.97 -> [2897] ~equally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4)
% 56.23/16.97 -> [2898] equally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4), ~unequally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4)
% 56.23/16.97
% 56.23/16.97 [2897] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4)
% 56.23/16.97 -> [2899] unequally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4)
% 56.23/16.97
% 56.23/16.97 [2899] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_17_4), Y17_17_4)
% 56.23/16.97
% 56.23/16.97 [2898] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 56.23/16.97 -> [2900] ~distinct_points(skolem_B9090, skolem_B9090)
% 56.23/16.97
% 56.23/16.97 [2900] 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))))
% 56.23/16.97 -> [2901] (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090)))
% 56.23/16.97
% 56.23/16.97 [2901] BETA_IMPLY : (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090)))
% 56.23/16.97 -> [2902] ~distinct_points(skolem_A8989, skolem_B9090)
% 56.23/16.97 -> [2903] (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090))
% 56.23/16.97
% 56.23/16.97 [2902] CLOSURE : ~distinct_points(skolem_A8989, skolem_B9090)
% 56.23/16.97
% 56.23/16.97 [2903] BETA_OR : (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090))
% 56.23/16.97 -> [2906] distinct_points(skolem_A8989, skolem_B9090)
% 56.23/16.97 -> [2907] distinct_points(skolem_B9090, skolem_B9090)
% 56.23/16.97
% 56.23/16.97 [2907] CLOSURE : distinct_points(skolem_B9090, skolem_B9090)
% 56.23/16.97
% 56.23/16.97 [2906] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 56.23/16.97 -> [2908] ~distinct_lines(L37_33_8, L37_33_8)
% 56.23/16.97
% 56.23/16.97 [2908] 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))))
% 56.23/16.97 -> [2909] (distinct_lines(L37_33_8, L37_33_8) => (distinct_lines(L37_33_8, L37_33_8) | distinct_lines(L37_33_8, L37_33_8)))
% 56.23/16.97
% 56.23/16.97 [2909] BETA_IMPLY : (distinct_lines(L37_33_8, L37_33_8) => (distinct_lines(L37_33_8, L37_33_8) | distinct_lines(L37_33_8, L37_33_8)))
% 56.23/16.97 -> [2910] ~distinct_lines(L37_33_8, L37_33_8)
% 56.23/16.97 -> [2911] (distinct_lines(L37_33_8, L37_33_8) | distinct_lines(L37_33_8, L37_33_8))
% 56.23/16.97
% 56.23/16.97 [2911] BETA_OR : (distinct_lines(L37_33_8, L37_33_8) | distinct_lines(L37_33_8, L37_33_8))
% 56.23/16.97 -> [2912] distinct_lines(L37_33_8, L37_33_8)
% 56.23/16.97 -> [2913] distinct_lines(L37_33_8, L37_33_8)
% 56.23/16.97
% 56.23/16.97 [2913] CLOSURE : distinct_lines(L37_33_8, L37_33_8)
% 56.23/16.97
% 56.23/16.97 [2912] CLOSURE : distinct_lines(L37_33_8, L37_33_8)
% 56.23/16.97
% 56.23/16.97 [2910] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 56.23/16.97 -> [2914] equally_directed_lines(L40_33_9, L40_33_9)
% 56.23/16.97
% 56.23/16.97 [2914] 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))))
% 56.23/16.97 -> [2915] (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) => (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) | unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))))
% 56.23/16.97
% 56.23/16.97 [2915] BETA_IMPLY : (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) => (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) | unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))))
% 56.23/16.97 -> [2916] ~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97 -> [2917] (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) | unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)))
% 56.23/16.97
% 56.23/16.97 [2917] BETA_OR : (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) | unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)))
% 56.23/16.97 -> [2918] unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97 -> [2919] unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97
% 56.23/16.97 [2919] CLOSURE : unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97
% 56.23/16.97 [2918] CLOSURE : unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97
% 56.23/16.97 [2920] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))) => ((unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))) | (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4))))))
% 56.23/16.97 -> [2993] ~(unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4))))
% 56.23/16.97 -> [2994] ((unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))) | (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))))
% 56.23/16.97
% 56.23/16.97 [2994] BETA_OR : ((unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))) | (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))))
% 56.23/16.97 -> [2997] (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4))))
% 56.23/16.97 -> [2998] (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4))))
% 56.23/16.97
% 56.23/16.97 [2997] ALPHA_AND : (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4))))
% 56.23/16.97 -> [2999] unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)), unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))
% 56.23/16.97
% 56.23/16.97 [2999] CLOSURE : unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))
% 56.23/16.97
% 56.23/16.97 [3000] CLOSURE : unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97
% 56.23/16.97 [2993] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4))))
% 56.23/16.97 -> [3042] ~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97 -> [3043] ~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))
% 56.23/16.97
% 56.23/16.97 [3043] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 56.23/16.97 -> [3045] (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) | unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4))))
% 56.23/16.97
% 56.23/16.97 [3045] BETA_OR : (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) | unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4))))
% 56.23/16.97 -> [3049] unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97 -> [3050] unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))
% 56.23/16.97
% 56.23/16.97 [3049] CLOSURE : unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97
% 56.23/16.97 [3050] CLOSURE : unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))
% 56.23/16.97
% 56.23/16.97 [3042] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 56.23/16.97 -> [3044] (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) | unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4))))
% 56.23/16.97
% 56.23/16.97 [3044] BETA_OR : (unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) | unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4))))
% 56.23/16.97 -> [3047] unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97 -> [3048] unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))
% 56.23/16.97
% 56.23/16.97 [3047] CLOSURE : unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97
% 56.23/16.97 [3048] 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)))))
% 56.23/16.97 -> [3057] ((unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))) => (left_convergent_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) | left_convergent_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))))
% 56.23/16.97
% 56.23/16.97 [3057] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))) => (left_convergent_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) | left_convergent_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))))
% 56.23/16.97 -> [3058] ~(unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4))))
% 56.23/16.97 -> [3059] (left_convergent_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) | left_convergent_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4))))
% 56.23/16.97
% 56.23/16.97 [3059] BETA_OR : (left_convergent_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) | left_convergent_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4))))
% 56.23/16.97 -> [3062] left_convergent_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97 -> [3063] left_convergent_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))
% 56.23/16.97
% 56.23/16.97 [3063] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 56.23/16.97 -> [3069] ~(left_apart_point(A51_122_14, L52_122_14) | left_apart_point(A51_122_14, reverse_line(L52_122_14)))
% 56.23/16.97
% 56.23/16.97 [3069] ALPHA_NOT_OR : ~(left_apart_point(A51_122_14, L52_122_14) | left_apart_point(A51_122_14, reverse_line(L52_122_14)))
% 56.23/16.97 -> [3071] ~left_apart_point(A51_122_14, L52_122_14), ~left_apart_point(A51_122_14, reverse_line(L52_122_14))
% 56.23/16.97
% 56.23/16.97 [3071] CLOSURE : ~left_apart_point(A51_122_14, L52_122_14)
% 56.23/16.97
% 56.23/16.97 [3062] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 56.23/16.97 -> [3068] ~(left_apart_point(A51_121_14, L52_121_14) | left_apart_point(A51_121_14, reverse_line(L52_121_14)))
% 56.23/16.97
% 56.23/16.97 [3068] ALPHA_NOT_OR : ~(left_apart_point(A51_121_14, L52_121_14) | left_apart_point(A51_121_14, reverse_line(L52_121_14)))
% 56.23/16.97 -> [3070] ~left_apart_point(A51_121_14, L52_121_14), ~left_apart_point(A51_121_14, reverse_line(L52_121_14))
% 56.23/16.97
% 56.23/16.97 [3070] CLOSURE : ~left_apart_point(A51_121_14, L52_121_14)
% 56.23/16.97
% 56.23/16.97 [3058] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4)) & unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4))))
% 56.23/16.97 -> [3060] ~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(Y17_17_4))
% 56.23/16.97 -> [3061] ~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))
% 56.23/16.97
% 56.23/16.97 [3061] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_17_4), reverse_line(reverse_line(Y17_17_4)))
% 56.23/16.97
% 56.23/16.97 [3060] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 56.23/16.97 -> [3072] ~(left_apart_point(A51_123_14, L52_123_14) | left_apart_point(A51_123_14, reverse_line(L52_123_14)))
% 56.23/16.97
% 56.23/16.97 [3072] ALPHA_NOT_OR : ~(left_apart_point(A51_123_14, L52_123_14) | left_apart_point(A51_123_14, reverse_line(L52_123_14)))
% 56.23/16.97 -> [3075] ~left_apart_point(A51_123_14, L52_123_14), ~left_apart_point(A51_123_14, reverse_line(L52_123_14))
% 56.23/16.97
% 56.23/16.97 [3075] CLOSURE : ~left_apart_point(A51_123_14, L52_123_14)
% 56.23/16.97
% 56.23/16.97 [2516] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 56.23/16.97 -> [2518] (equally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) <=> ~unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)))
% 56.23/16.97
% 56.23/16.97 [2518] BETA_EQUIV : (equally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) <=> ~unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)))
% 56.23/16.97 -> [2520] ~equally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)), ~~unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97 -> [2521] equally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)), ~unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97
% 56.23/16.97 [2520] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97 -> [2524] unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97
% 56.23/16.97 [2524] CLOSURE : unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97
% 56.23/16.97 [2526] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y13_2_2), Y13_2_2) <=> ~unequally_directed_opposite_lines(reverse_line(Y13_2_2), Y13_2_2))
% 56.23/16.97 -> [2937] ~equally_directed_opposite_lines(reverse_line(Y13_2_2), Y13_2_2), ~~unequally_directed_opposite_lines(reverse_line(Y13_2_2), Y13_2_2)
% 56.23/16.97 -> [2938] equally_directed_opposite_lines(reverse_line(Y13_2_2), Y13_2_2), ~unequally_directed_opposite_lines(reverse_line(Y13_2_2), Y13_2_2)
% 56.23/16.97
% 56.23/16.97 [2937] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y13_2_2), Y13_2_2)
% 56.23/16.97 -> [2939] unequally_directed_opposite_lines(reverse_line(Y13_2_2), Y13_2_2)
% 56.23/16.97
% 56.23/16.97 [2939] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y13_2_2), Y13_2_2)
% 56.23/16.97
% 56.23/16.97 [2941] BETA_IMPLY : (distinct_points(C35_25_6, C35_25_6) => (distinct_points(C35_25_6, C35_25_6) | distinct_points(C35_25_6, C35_25_6)))
% 56.23/16.97 -> [3164] ~distinct_points(C35_25_6, C35_25_6)
% 56.23/16.97 -> [3165] (distinct_points(C35_25_6, C35_25_6) | distinct_points(C35_25_6, C35_25_6))
% 56.23/16.97
% 56.23/16.97 [3165] BETA_OR : (distinct_points(C35_25_6, C35_25_6) | distinct_points(C35_25_6, C35_25_6))
% 56.23/16.97 -> [3166] distinct_points(C35_25_6, C35_25_6)
% 56.23/16.97 -> [3167] distinct_points(C35_25_6, C35_25_6)
% 56.23/16.97
% 56.23/16.97 [3166] CLOSURE : distinct_points(C35_25_6, C35_25_6)
% 56.23/16.97
% 56.23/16.97 [3167] CLOSURE : distinct_points(C35_25_6, C35_25_6)
% 56.23/16.97
% 56.23/16.97 [3164] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 56.23/16.97 -> [3168] ~distinct_lines(N39_35_8, N39_35_8)
% 56.23/16.97
% 56.23/16.97 [3168] 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))))
% 56.23/16.97 -> [3169] (distinct_lines(N39_35_8, N39_35_8) => (distinct_lines(N39_35_8, N39_35_8) | distinct_lines(N39_35_8, N39_35_8)))
% 56.23/16.97
% 56.23/16.97 [3169] BETA_IMPLY : (distinct_lines(N39_35_8, N39_35_8) => (distinct_lines(N39_35_8, N39_35_8) | distinct_lines(N39_35_8, N39_35_8)))
% 56.23/16.97 -> [3170] ~distinct_lines(N39_35_8, N39_35_8)
% 56.23/16.97 -> [3171] (distinct_lines(N39_35_8, N39_35_8) | distinct_lines(N39_35_8, N39_35_8))
% 56.23/16.97
% 56.23/16.97 [3171] BETA_OR : (distinct_lines(N39_35_8, N39_35_8) | distinct_lines(N39_35_8, N39_35_8))
% 56.23/16.97 -> [3172] distinct_lines(N39_35_8, N39_35_8)
% 56.23/16.97 -> [3173] distinct_lines(N39_35_8, N39_35_8)
% 56.23/16.97
% 56.23/16.97 [3173] CLOSURE : distinct_lines(N39_35_8, N39_35_8)
% 56.23/16.97
% 56.23/16.97 [3172] CLOSURE : distinct_lines(N39_35_8, N39_35_8)
% 56.23/16.97
% 56.23/16.97 [3175] BETA_IMPLY : (unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) => (unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) | unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))))
% 56.23/16.97 -> [3257] ~unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97 -> [3258] (unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) | unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)))
% 56.23/16.97
% 56.23/16.97 [3258] BETA_OR : (unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) | unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)))
% 56.23/16.97 -> [3259] unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97 -> [3260] unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97
% 56.23/16.97 [3259] CLOSURE : unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97
% 56.23/16.97 [3260] CLOSURE : unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97
% 56.23/16.97 [3261] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))) => ((unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))) | (unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2))))))
% 56.23/16.97 -> [3284] ~(unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2))))
% 56.23/16.97 -> [3285] ((unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))) | (unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))))
% 56.23/16.97
% 56.23/16.97 [3285] BETA_OR : ((unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))) | (unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))))
% 56.23/16.97 -> [3288] (unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2))))
% 56.23/16.97 -> [3289] (unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2))))
% 56.23/16.97
% 56.23/16.97 [3288] ALPHA_AND : (unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2))))
% 56.23/16.97 -> [3291] unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)), unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))
% 56.23/16.97
% 56.23/16.97 [3291] CLOSURE : unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))
% 56.23/16.97
% 56.23/16.97 [3290] CLOSURE : unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97
% 56.23/16.97 [3284] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2))))
% 56.23/16.97 -> [3315] ~unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97 -> [3316] ~unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))
% 56.23/16.97
% 56.23/16.97 [3316] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 56.23/16.97 -> [3320] (unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) | unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2))))
% 56.23/16.97
% 56.23/16.97 [3320] BETA_OR : (unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) | unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2))))
% 56.23/16.97 -> [3321] unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97 -> [3322] unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))
% 56.23/16.97
% 56.23/16.97 [3321] CLOSURE : unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97
% 56.23/16.97 [3322] CLOSURE : unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))
% 56.23/16.97
% 56.23/16.97 [3315] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 56.23/16.97 -> [3317] (unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) | unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2))))
% 56.23/16.97
% 56.23/16.97 [3317] BETA_OR : (unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) | unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2))))
% 56.23/16.97 -> [3318] unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97 -> [3319] unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))
% 56.23/16.97
% 56.23/16.97 [3318] CLOSURE : unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97
% 56.23/16.97 [3319] 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)))))
% 56.23/16.97 -> [3323] ((unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))) => (left_convergent_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) | left_convergent_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))))
% 56.23/16.97
% 56.23/16.97 [3323] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))) => (left_convergent_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) | left_convergent_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))))
% 56.23/16.97 -> [3324] ~(unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2))))
% 56.23/16.97 -> [3325] (left_convergent_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) | left_convergent_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2))))
% 56.23/16.97
% 56.23/16.97 [3325] BETA_OR : (left_convergent_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) | left_convergent_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2))))
% 56.23/16.97 -> [3328] left_convergent_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97 -> [3329] left_convergent_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))
% 56.23/16.97
% 56.23/16.97 [3328] CLOSURE : left_convergent_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97
% 56.23/16.97 [3329] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 56.23/16.97 -> [3330] ~(left_apart_point(A51_140_14, L52_140_14) | left_apart_point(A51_140_14, reverse_line(L52_140_14)))
% 56.23/16.97
% 56.23/16.97 [3330] ALPHA_NOT_OR : ~(left_apart_point(A51_140_14, L52_140_14) | left_apart_point(A51_140_14, reverse_line(L52_140_14)))
% 56.23/16.97 -> [3331] ~left_apart_point(A51_140_14, L52_140_14), ~left_apart_point(A51_140_14, reverse_line(L52_140_14))
% 56.23/16.97
% 56.23/16.97 [3331] CLOSURE : ~left_apart_point(A51_140_14, L52_140_14)
% 56.23/16.97
% 56.23/16.97 [3324] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2))))
% 56.23/16.97 -> [3334] ~unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(Y13_2_2))
% 56.23/16.97 -> [3335] ~unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))
% 56.23/16.97
% 56.23/16.97 [3335] CLOSURE : ~unequally_directed_lines(reverse_line(Y13_2_2), reverse_line(reverse_line(Y13_2_2)))
% 56.23/16.97
% 56.23/16.97 [3334] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 56.23/16.97 -> [3336] ~(left_apart_point(A51_142_14, L52_142_14) | left_apart_point(A51_142_14, reverse_line(L52_142_14)))
% 56.23/16.97
% 56.23/16.97 [3336] ALPHA_NOT_OR : ~(left_apart_point(A51_142_14, L52_142_14) | left_apart_point(A51_142_14, reverse_line(L52_142_14)))
% 56.23/16.97 -> [3337] ~left_apart_point(A51_142_14, L52_142_14), ~left_apart_point(A51_142_14, reverse_line(L52_142_14))
% 56.23/16.97
% 56.23/16.97 [3337] CLOSURE : ~left_apart_point(A51_142_14, L52_142_14)
% 56.23/16.97
% 56.23/16.97 % SZS output end Proof for theBenchmark.p
% 56.23/16.97 [16.619798s][1][Res] 144936 goroutines created
% 56.23/16.97 ==== Result ====
% 56.23/16.97 [16.619836s][1][Res] VALID
% 56.23/16.97 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------