TSTP Solution File: GEO246+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO246+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 15:18:41 EDT 2022
% Result : Theorem 51.37s 14.36s
% Output : Proof 51.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO246+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 07:10:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.35 [DMT] DMT loaded with preskolemization
% 0.19/0.35 [EQ] equality loaded.
% 0.19/0.35 [0.000042s][1][MAIN] Problem : theBenchmark.p
% 0.19/0.36 Conjecture not found
% 0.19/0.36 Start search
% 0.19/0.36 nb_step : 1 - limit : 37
% 0.19/0.36 Launch Gotab with destructive = true
% 51.37/14.34 % SZS output start Proof for theBenchmark.p
% 51.37/14.35 [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(B90_90, line_connecting(A89_89, C91_91))))))
% 51.37/14.35 -> [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(B90_90, line_connecting(A89_89, C91_91)))))
% 51.37/14.35
% 51.37/14.35 [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)))))
% 51.37/14.35 -> [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))))
% 51.37/14.35
% 51.37/14.35 [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(B90_90, line_connecting(A89_89, C91_91)))))
% 51.37/14.35 -> [3] ~(distinct_points(skolem_A8989, skolem_B9090) => (right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) => left_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191))))
% 51.37/14.35
% 51.37/14.35 [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_B9090, line_connecting(skolem_A8989, skolem_C9191))))
% 51.37/14.35 -> [4] distinct_points(skolem_A8989, skolem_B9090), ~(right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) => left_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191)))
% 51.37/14.35
% 51.37/14.35 [4] ALPHA_NOT_IMPLY : ~(right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)) => left_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191)))
% 51.37/14.35 -> [5] right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)), ~left_apart_point(skolem_B9090, line_connecting(skolem_A8989, skolem_C9191))
% 51.37/14.35
% 51.37/14.35 [5] GAMMA_FORALL : ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9))))
% 51.37/14.35 -> [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)))
% 51.37/14.35
% 51.37/14.35 [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)))
% 51.37/14.35 -> [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))
% 51.37/14.35 -> [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))
% 51.37/14.35
% 51.37/14.35 [8] GAMMA_FORALL : ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11))))
% 51.37/14.35 -> [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))))
% 51.37/14.35
% 51.37/14.35 [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))))
% 51.37/14.35 -> [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)))
% 51.37/14.35 -> [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)))
% 51.37/14.35
% 51.37/14.35 [13] CLOSURE : ~right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090))
% 51.37/14.35
% 51.37/14.35 [16] BETA_EQUIV : (right_convergent_lines(X12_1_2, Y13_1_2) <=> left_convergent_lines(X12_1_2, reverse_line(Y13_1_2)))
% 51.37/14.35 -> [394] ~right_convergent_lines(X12_1_2, Y13_1_2), ~left_convergent_lines(X12_1_2, reverse_line(Y13_1_2))
% 51.37/14.35 -> [395] right_convergent_lines(X12_1_2, Y13_1_2), left_convergent_lines(X12_1_2, reverse_line(Y13_1_2))
% 51.37/14.35
% 51.37/14.35 [394] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 51.37/14.35 -> [400] (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)))
% 51.37/14.35
% 51.37/14.35 [400] 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)))
% 51.37/14.35 -> [403] ~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))
% 51.37/14.35 -> [404] 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))
% 51.37/14.35
% 51.37/14.35 [403] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 51.37/14.35 -> [405] unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 51.37/14.35
% 51.37/14.35 [405] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 51.37/14.35 -> [407] (equally_directed_opposite_lines(X16_5_4, Y17_5_4) <=> ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4))
% 51.37/14.35
% 51.37/14.35 [407] BETA_EQUIV : (equally_directed_opposite_lines(X16_5_4, Y17_5_4) <=> ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4))
% 51.37/14.35 -> [408] ~equally_directed_opposite_lines(X16_5_4, Y17_5_4), ~~unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 51.37/14.35 -> [409] equally_directed_opposite_lines(X16_5_4, Y17_5_4), ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 51.37/14.35
% 51.37/14.35 [408] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 51.37/14.35 -> [413] unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 51.37/14.35
% 51.37/14.35 [413] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 51.37/14.35 -> [415] ~distinct_points(skolem_B9090, skolem_B9090)
% 51.37/14.35
% 51.37/14.35 [415] 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))))
% 51.37/14.35 -> [425] (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090)))
% 51.37/14.35
% 51.37/14.35 [425] BETA_IMPLY : (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090)))
% 51.37/14.35 -> [426] ~distinct_points(skolem_A8989, skolem_B9090)
% 51.37/14.35 -> [427] (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090))
% 51.37/14.35
% 51.37/14.35 [426] CLOSURE : ~distinct_points(skolem_A8989, skolem_B9090)
% 51.37/14.35
% 51.37/14.35 [427] BETA_OR : (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090))
% 51.37/14.35 -> [443] distinct_points(skolem_A8989, skolem_B9090)
% 51.37/14.35 -> [444] distinct_points(skolem_B9090, skolem_B9090)
% 51.37/14.35
% 51.37/14.35 [444] CLOSURE : distinct_points(skolem_B9090, skolem_B9090)
% 51.37/14.35
% 51.37/14.35 [443] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 51.37/14.35 -> [460] ~distinct_lines(M38_10_8, M38_10_8)
% 51.37/14.35
% 51.37/14.35 [460] 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))))
% 51.37/14.35 -> [462] (distinct_lines(M38_10_8, M38_10_8) => (distinct_lines(M38_10_8, M38_10_8) | distinct_lines(M38_10_8, M38_10_8)))
% 51.37/14.35
% 51.37/14.35 [462] BETA_IMPLY : (distinct_lines(M38_10_8, M38_10_8) => (distinct_lines(M38_10_8, M38_10_8) | distinct_lines(M38_10_8, M38_10_8)))
% 51.37/14.35 -> [463] ~distinct_lines(M38_10_8, M38_10_8)
% 51.37/14.35 -> [464] (distinct_lines(M38_10_8, M38_10_8) | distinct_lines(M38_10_8, M38_10_8))
% 51.37/14.35
% 51.37/14.35 [464] BETA_OR : (distinct_lines(M38_10_8, M38_10_8) | distinct_lines(M38_10_8, M38_10_8))
% 51.37/14.35 -> [465] distinct_lines(M38_10_8, M38_10_8)
% 51.37/14.35 -> [466] distinct_lines(M38_10_8, M38_10_8)
% 51.37/14.35
% 51.37/14.35 [465] CLOSURE : distinct_lines(M38_10_8, M38_10_8)
% 51.37/14.35
% 51.37/14.35 [466] CLOSURE : distinct_lines(M38_10_8, M38_10_8)
% 51.37/14.35
% 51.37/14.35 [467] CLOSURE : equally_directed_lines(L40_10_9, L40_10_9)
% 51.37/14.35
% 51.37/14.35 [409] CLOSURE : ~unequally_directed_opposite_lines(X16_5_4, Y17_5_4)
% 51.37/14.35
% 51.37/14.35 [404] CLOSURE : ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 51.37/14.35
% 51.37/14.35 [399] 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)))
% 51.37/14.35 -> [547] ~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))
% 51.37/14.35 -> [548] 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))
% 51.37/14.35
% 51.37/14.35 [547] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 51.37/14.35 -> [551] unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 51.37/14.35
% 51.37/14.35 [551] GAMMA_FORALL : ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17)))
% 51.37/14.35 -> [552] (equally_directed_opposite_lines(reverse_line(Y17_7_4), Y17_7_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_7_4), Y17_7_4))
% 51.37/14.35
% 51.37/14.35 [552] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_7_4), Y17_7_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_7_4), Y17_7_4))
% 51.37/14.35 -> [553] ~equally_directed_opposite_lines(reverse_line(Y17_7_4), Y17_7_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_7_4), Y17_7_4)
% 51.37/14.35 -> [554] equally_directed_opposite_lines(reverse_line(Y17_7_4), Y17_7_4), ~unequally_directed_opposite_lines(reverse_line(Y17_7_4), Y17_7_4)
% 51.37/14.35
% 51.37/14.35 [554] CLOSURE : ~unequally_directed_opposite_lines(reverse_line(Y17_7_4), Y17_7_4)
% 51.37/14.35
% 51.37/14.35 [559] BETA_IMPLY : (distinct_points(C35_10_6, C35_10_6) => (distinct_points(C35_10_6, C35_10_6) | distinct_points(C35_10_6, C35_10_6)))
% 51.37/14.35 -> [641] ~distinct_points(C35_10_6, C35_10_6)
% 51.37/14.35 -> [642] (distinct_points(C35_10_6, C35_10_6) | distinct_points(C35_10_6, C35_10_6))
% 51.37/14.35
% 51.37/14.35 [642] BETA_OR : (distinct_points(C35_10_6, C35_10_6) | distinct_points(C35_10_6, C35_10_6))
% 51.37/14.35 -> [643] distinct_points(C35_10_6, C35_10_6)
% 51.37/14.35 -> [644] distinct_points(C35_10_6, C35_10_6)
% 51.37/14.35
% 51.37/14.35 [643] CLOSURE : distinct_points(C35_10_6, C35_10_6)
% 51.37/14.35
% 51.37/14.35 [644] CLOSURE : distinct_points(C35_10_6, C35_10_6)
% 51.37/14.35
% 51.37/14.35 [641] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 51.37/14.35 -> [647] ~distinct_lines(N39_15_8, N39_15_8)
% 51.37/14.35
% 51.37/14.35 [647] 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))))
% 51.37/14.35 -> [650] (distinct_lines(N39_15_8, N39_15_8) => (distinct_lines(N39_15_8, N39_15_8) | distinct_lines(N39_15_8, N39_15_8)))
% 51.37/14.35
% 51.37/14.35 [650] BETA_IMPLY : (distinct_lines(N39_15_8, N39_15_8) => (distinct_lines(N39_15_8, N39_15_8) | distinct_lines(N39_15_8, N39_15_8)))
% 51.37/14.35 -> [651] ~distinct_lines(N39_15_8, N39_15_8)
% 51.37/14.35 -> [652] (distinct_lines(N39_15_8, N39_15_8) | distinct_lines(N39_15_8, N39_15_8))
% 51.37/14.35
% 51.37/14.35 [652] BETA_OR : (distinct_lines(N39_15_8, N39_15_8) | distinct_lines(N39_15_8, N39_15_8))
% 51.37/14.35 -> [653] distinct_lines(N39_15_8, N39_15_8)
% 51.37/14.35 -> [654] distinct_lines(N39_15_8, N39_15_8)
% 51.37/14.35
% 51.37/14.35 [653] CLOSURE : distinct_lines(N39_15_8, N39_15_8)
% 51.37/14.35
% 51.37/14.35 [654] CLOSURE : distinct_lines(N39_15_8, N39_15_8)
% 51.37/14.35
% 51.37/14.35 [655] CLOSURE : equally_directed_lines(L40_15_9, L40_15_9)
% 51.37/14.35
% 51.37/14.35 [548] CLOSURE : ~unequally_directed_lines(reverse_line(Y9_0_0), reverse_line(Y9_0_0))
% 51.37/14.35
% 51.37/14.35 [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))))
% 51.37/14.35 -> [2677] ~right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)), ~left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090)))
% 51.37/14.35 -> [2678] right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090)), left_apart_point(skolem_C9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090)))
% 51.37/14.35
% 51.37/14.35 [2677] CLOSURE : ~right_apart_point(skolem_C9191, line_connecting(skolem_A8989, skolem_B9090))
% 51.37/14.35
% 51.37/14.35 [2678] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 51.37/14.35 -> [2679] (right_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))) <=> left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4)))))
% 51.37/14.35
% 51.37/14.35 [2679] BETA_EQUIV : (right_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))) <=> left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4)))))
% 51.37/14.35 -> [2680] ~right_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))), ~left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.35 -> [2681] right_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))), left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.35
% 51.37/14.35 [2681] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 51.37/14.35 -> [2683] (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)))
% 51.37/14.35
% 51.37/14.35 [2683] 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)))
% 51.37/14.35 -> [2686] ~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))
% 51.37/14.35 -> [2687] 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))
% 51.37/14.35
% 51.37/14.35 [2686] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 51.37/14.35 -> [2689] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 51.37/14.35
% 51.37/14.35 [2689] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 51.37/14.35
% 51.37/14.35 [2693] 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))
% 51.37/14.35 -> [2887] ~equally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 51.37/14.35 -> [2888] equally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4), ~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 51.37/14.35
% 51.37/14.35 [2887] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 51.37/14.35 -> [2889] unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 51.37/14.35
% 51.37/14.35 [2889] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 51.37/14.35
% 51.37/14.35 [2888] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 51.37/14.35 -> [2890] ~distinct_points(skolem_B9090, skolem_B9090)
% 51.37/14.35
% 51.37/14.35 [2890] 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))))
% 51.37/14.35 -> [2891] (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090)))
% 51.37/14.35
% 51.37/14.35 [2891] BETA_IMPLY : (distinct_points(skolem_A8989, skolem_B9090) => (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090)))
% 51.37/14.35 -> [2892] ~distinct_points(skolem_A8989, skolem_B9090)
% 51.37/14.35 -> [2893] (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090))
% 51.37/14.35
% 51.37/14.35 [2892] CLOSURE : ~distinct_points(skolem_A8989, skolem_B9090)
% 51.37/14.35
% 51.37/14.35 [2893] BETA_OR : (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_B9090, skolem_B9090))
% 51.37/14.35 -> [2896] distinct_points(skolem_A8989, skolem_B9090)
% 51.37/14.35 -> [2897] distinct_points(skolem_B9090, skolem_B9090)
% 51.37/14.35
% 51.37/14.35 [2897] CLOSURE : distinct_points(skolem_B9090, skolem_B9090)
% 51.37/14.35
% 51.37/14.35 [2896] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 51.37/14.35 -> [2898] ~distinct_lines(N39_31_8, N39_31_8)
% 51.37/14.35
% 51.37/14.35 [2898] 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))))
% 51.37/14.35 -> [2899] (distinct_lines(N39_31_8, N39_31_8) => (distinct_lines(N39_31_8, N39_31_8) | distinct_lines(N39_31_8, N39_31_8)))
% 51.37/14.35
% 51.37/14.35 [2899] BETA_IMPLY : (distinct_lines(N39_31_8, N39_31_8) => (distinct_lines(N39_31_8, N39_31_8) | distinct_lines(N39_31_8, N39_31_8)))
% 51.37/14.35 -> [2900] ~distinct_lines(N39_31_8, N39_31_8)
% 51.37/14.35 -> [2901] (distinct_lines(N39_31_8, N39_31_8) | distinct_lines(N39_31_8, N39_31_8))
% 51.37/14.35
% 51.37/14.35 [2901] BETA_OR : (distinct_lines(N39_31_8, N39_31_8) | distinct_lines(N39_31_8, N39_31_8))
% 51.37/14.35 -> [2902] distinct_lines(N39_31_8, N39_31_8)
% 51.37/14.35 -> [2903] distinct_lines(N39_31_8, N39_31_8)
% 51.37/14.35
% 51.37/14.35 [2902] CLOSURE : distinct_lines(N39_31_8, N39_31_8)
% 51.37/14.35
% 51.37/14.35 [2903] CLOSURE : distinct_lines(N39_31_8, N39_31_8)
% 51.37/14.35
% 51.37/14.35 [2900] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 51.37/14.35 -> [2904] equally_directed_lines(L40_31_9, L40_31_9)
% 51.37/14.35
% 51.37/14.35 [2904] 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))))
% 51.37/14.35 -> [2905] (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) => (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) | unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11))))
% 51.37/14.35
% 51.37/14.35 [2905] BETA_IMPLY : (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) => (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) | unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11))))
% 51.37/14.35 -> [2906] ~unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11))
% 51.37/14.35 -> [2907] (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) | unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)))
% 51.37/14.35
% 51.37/14.35 [2907] BETA_OR : (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) | unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)))
% 51.37/14.35 -> [2908] unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11))
% 51.37/14.35 -> [2909] unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11))
% 51.37/14.35
% 51.37/14.35 [2909] CLOSURE : unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11))
% 51.37/14.35
% 51.37/14.35 [2908] CLOSURE : unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11))
% 51.37/14.35
% 51.37/14.35 [2910] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))) => ((unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))) | (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11))))))
% 51.37/14.35 -> [2959] ~(unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11))))
% 51.37/14.35 -> [2960] ((unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))) | (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))))
% 51.37/14.35
% 51.37/14.35 [2959] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11))))
% 51.37/14.35 -> [2965] ~unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11))
% 51.37/14.35 -> [2966] ~unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))
% 51.37/14.35
% 51.37/14.35 [2966] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 51.37/14.35 -> [2982] (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) | unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11))))
% 51.37/14.35
% 51.37/14.35 [2982] BETA_OR : (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) | unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11))))
% 51.37/14.35 -> [2983] unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11))
% 51.37/14.35 -> [2984] unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))
% 51.37/14.35
% 51.37/14.35 [2983] CLOSURE : unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11))
% 51.37/14.35
% 51.37/14.35 [2984] CLOSURE : unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))
% 51.37/14.35
% 51.37/14.35 [2979] BETA_OR : (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) | unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11))))
% 51.37/14.35 -> [2987] unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11))
% 51.37/14.35 -> [2988] unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))
% 51.37/14.35
% 51.37/14.35 [2987] CLOSURE : unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11))
% 51.37/14.35
% 51.37/14.35 [2988] 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)))))
% 51.37/14.35 -> [2989] ((unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))) => (left_convergent_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) | left_convergent_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))))
% 51.37/14.35
% 51.37/14.35 [2989] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))) => (left_convergent_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) | left_convergent_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))))
% 51.37/14.35 -> [2990] ~(unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11))))
% 51.37/14.35 -> [2991] (left_convergent_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) | left_convergent_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11))))
% 51.37/14.35
% 51.37/14.35 [2991] BETA_OR : (left_convergent_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) | left_convergent_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11))))
% 51.37/14.35 -> [2994] left_convergent_lines(reverse_line(N46_46_11), reverse_line(N46_46_11))
% 51.37/14.35 -> [2995] left_convergent_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))
% 51.37/14.36
% 51.37/14.36 [2995] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 51.37/14.36 -> [2996] ~(left_apart_point(A51_100_14, L52_100_14) | left_apart_point(A51_100_14, reverse_line(L52_100_14)))
% 51.37/14.36
% 51.37/14.36 [2996] ALPHA_NOT_OR : ~(left_apart_point(A51_100_14, L52_100_14) | left_apart_point(A51_100_14, reverse_line(L52_100_14)))
% 51.37/14.36 -> [2998] ~left_apart_point(A51_100_14, L52_100_14), ~left_apart_point(A51_100_14, reverse_line(L52_100_14))
% 51.37/14.36
% 51.37/14.36 [2998] CLOSURE : ~left_apart_point(A51_100_14, L52_100_14)
% 51.37/14.36
% 51.37/14.36 [2994] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 51.37/14.36 -> [2997] ~(left_apart_point(A51_101_14, L52_101_14) | left_apart_point(A51_101_14, reverse_line(L52_101_14)))
% 51.37/14.36
% 51.37/14.36 [2997] ALPHA_NOT_OR : ~(left_apart_point(A51_101_14, L52_101_14) | left_apart_point(A51_101_14, reverse_line(L52_101_14)))
% 51.37/14.36 -> [2999] ~left_apart_point(A51_101_14, L52_101_14), ~left_apart_point(A51_101_14, reverse_line(L52_101_14))
% 51.37/14.36
% 51.37/14.36 [2999] CLOSURE : ~left_apart_point(A51_101_14, L52_101_14)
% 51.37/14.36
% 51.37/14.36 [2990] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11))))
% 51.37/14.36 -> [2992] ~unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11))
% 51.37/14.36 -> [2993] ~unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))
% 51.37/14.36
% 51.37/14.36 [2993] CLOSURE : ~unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))
% 51.37/14.36
% 51.37/14.36 [2992] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 51.37/14.36 -> [3004] ~(left_apart_point(A51_102_14, L52_102_14) | left_apart_point(A51_102_14, reverse_line(L52_102_14)))
% 51.37/14.36
% 51.37/14.36 [3004] ALPHA_NOT_OR : ~(left_apart_point(A51_102_14, L52_102_14) | left_apart_point(A51_102_14, reverse_line(L52_102_14)))
% 51.37/14.36 -> [3005] ~left_apart_point(A51_102_14, L52_102_14), ~left_apart_point(A51_102_14, reverse_line(L52_102_14))
% 51.37/14.36
% 51.37/14.36 [3005] CLOSURE : ~left_apart_point(A51_102_14, L52_102_14)
% 51.37/14.36
% 51.37/14.36 [2960] BETA_OR : ((unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))) | (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))))
% 51.37/14.36 -> [3009] (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11))))
% 51.37/14.36 -> [3010] (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11))))
% 51.37/14.36
% 51.37/14.36 [3009] ALPHA_AND : (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11))))
% 51.37/14.36 -> [3011] unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)), unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))
% 51.37/14.36
% 51.37/14.36 [3011] CLOSURE : unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))
% 51.37/14.36
% 51.37/14.36 [3010] ALPHA_AND : (unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)) & unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11))))
% 51.37/14.36 -> [3012] unequally_directed_lines(reverse_line(N46_46_11), reverse_line(N46_46_11)), unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))
% 51.37/14.36
% 51.37/14.36 [3012] CLOSURE : unequally_directed_lines(reverse_line(N46_46_11), reverse_line(reverse_line(N46_46_11)))
% 51.37/14.36
% 51.37/14.36 [2680] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 51.37/14.36 -> [2682] (equally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) <=> ~unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)))
% 51.37/14.36
% 51.37/14.36 [2682] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) <=> ~unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)))
% 51.37/14.36 -> [2684] ~equally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)), ~~unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))
% 51.37/14.36 -> [2685] equally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)), ~unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))
% 51.37/14.36
% 51.37/14.36 [2684] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))
% 51.37/14.36 -> [2688] unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))
% 51.37/14.36
% 51.37/14.36 [2688] CLOSURE : unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))
% 51.37/14.36
% 51.37/14.36 [2690] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4))
% 51.37/14.36 -> [2925] ~equally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4)
% 51.37/14.36 -> [2926] equally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4), ~unequally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4)
% 51.37/14.36
% 51.37/14.36 [2925] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4)
% 51.37/14.36 -> [2927] unequally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4)
% 51.37/14.36
% 51.37/14.36 [2927] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_13_4), Y17_13_4)
% 51.37/14.36
% 51.37/14.36 [2929] BETA_IMPLY : (distinct_points(C35_20_6, C35_20_6) => (distinct_points(C35_20_6, C35_20_6) | distinct_points(C35_20_6, C35_20_6)))
% 51.37/14.36 -> [3129] ~distinct_points(C35_20_6, C35_20_6)
% 51.37/14.36 -> [3130] (distinct_points(C35_20_6, C35_20_6) | distinct_points(C35_20_6, C35_20_6))
% 51.37/14.36
% 51.37/14.36 [3130] BETA_OR : (distinct_points(C35_20_6, C35_20_6) | distinct_points(C35_20_6, C35_20_6))
% 51.37/14.36 -> [3131] distinct_points(C35_20_6, C35_20_6)
% 51.37/14.36 -> [3132] distinct_points(C35_20_6, C35_20_6)
% 51.37/14.36
% 51.37/14.36 [3131] CLOSURE : distinct_points(C35_20_6, C35_20_6)
% 51.37/14.36
% 51.37/14.36 [3132] CLOSURE : distinct_points(C35_20_6, C35_20_6)
% 51.37/14.36
% 51.37/14.36 [3129] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 51.37/14.36 -> [3133] ~distinct_lines(N39_33_8, N39_33_8)
% 51.37/14.36
% 51.37/14.36 [3133] 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))))
% 51.37/14.36 -> [3134] (distinct_lines(N39_33_8, N39_33_8) => (distinct_lines(N39_33_8, N39_33_8) | distinct_lines(N39_33_8, N39_33_8)))
% 51.37/14.36
% 51.37/14.36 [3134] BETA_IMPLY : (distinct_lines(N39_33_8, N39_33_8) => (distinct_lines(N39_33_8, N39_33_8) | distinct_lines(N39_33_8, N39_33_8)))
% 51.37/14.36 -> [3135] ~distinct_lines(N39_33_8, N39_33_8)
% 51.37/14.36 -> [3136] (distinct_lines(N39_33_8, N39_33_8) | distinct_lines(N39_33_8, N39_33_8))
% 51.37/14.36
% 51.37/14.36 [3136] BETA_OR : (distinct_lines(N39_33_8, N39_33_8) | distinct_lines(N39_33_8, N39_33_8))
% 51.37/14.36 -> [3137] distinct_lines(N39_33_8, N39_33_8)
% 51.37/14.36 -> [3138] distinct_lines(N39_33_8, N39_33_8)
% 51.37/14.36
% 51.37/14.36 [3138] CLOSURE : distinct_lines(N39_33_8, N39_33_8)
% 51.37/14.36
% 51.37/14.36 [3137] CLOSURE : distinct_lines(N39_33_8, N39_33_8)
% 51.37/14.36
% 51.37/14.36 [3140] BETA_IMPLY : (unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) => (unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) | unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))))
% 51.37/14.36 -> [3221] ~unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))
% 51.37/14.36 -> [3222] (unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) | unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)))
% 51.37/14.36
% 51.37/14.36 [3222] BETA_OR : (unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) | unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)))
% 51.37/14.36 -> [3223] unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))
% 51.37/14.36 -> [3224] unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))
% 51.37/14.36
% 51.37/14.36 [3223] CLOSURE : unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))
% 51.37/14.36
% 51.37/14.36 [3224] CLOSURE : unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))
% 51.37/14.36
% 51.37/14.36 [3225] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))) & unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4))))) => ((unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) & unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4)))) | (unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(Y17_13_4)) & unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(reverse_line(Y17_13_4))))))
% 51.37/14.36 -> [3248] ~(unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))) & unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4)))))
% 51.37/14.36 -> [3249] ((unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) & unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4)))) | (unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(Y17_13_4)) & unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(reverse_line(Y17_13_4)))))
% 51.37/14.36
% 51.37/14.36 [3248] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))) & unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4)))))
% 51.37/14.36 -> [3250] ~unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4)))
% 51.37/14.36 -> [3251] ~unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.36
% 51.37/14.36 [3250] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 51.37/14.36 -> [3256] (unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) | unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.36
% 51.37/14.36 [3256] BETA_OR : (unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) | unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.36 -> [3258] unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))
% 51.37/14.36 -> [3259] unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4)))
% 51.37/14.36
% 51.37/14.36 [3258] CLOSURE : unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))
% 51.37/14.36
% 51.37/14.36 [3259] CLOSURE : unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4)))
% 51.37/14.36
% 51.37/14.36 [3257] BETA_OR : (unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))) | unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4)))))
% 51.37/14.36 -> [3262] unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4)))
% 51.37/14.36 -> [3263] unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.36
% 51.37/14.36 [3263] CLOSURE : unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.36
% 51.37/14.36 [3262] 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)))))
% 51.37/14.36 -> [3264] ((unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))) & unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4))))) => (left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))) | left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4))))))
% 51.37/14.36
% 51.37/14.36 [3264] BETA_IMPLY : ((unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))) & unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4))))) => (left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))) | left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4))))))
% 51.37/14.36 -> [3265] ~(unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))) & unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4)))))
% 51.37/14.36 -> [3266] (left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))) | left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4)))))
% 51.37/14.36
% 51.37/14.36 [3265] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))) & unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4)))))
% 51.37/14.36 -> [3267] ~unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4)))
% 51.37/14.36 -> [3268] ~unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.36
% 51.37/14.36 [3267] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4)))
% 51.37/14.36
% 51.37/14.36 [3268] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 51.37/14.36 -> [3271] ~(left_apart_point(A51_118_14, L52_118_14) | left_apart_point(A51_118_14, reverse_line(L52_118_14)))
% 51.37/14.36
% 51.37/14.36 [3271] ALPHA_NOT_OR : ~(left_apart_point(A51_118_14, L52_118_14) | left_apart_point(A51_118_14, reverse_line(L52_118_14)))
% 51.37/14.36 -> [3272] ~left_apart_point(A51_118_14, L52_118_14), ~left_apart_point(A51_118_14, reverse_line(L52_118_14))
% 51.37/14.36
% 51.37/14.36 [3272] CLOSURE : ~left_apart_point(A51_118_14, L52_118_14)
% 51.37/14.36
% 51.37/14.36 [3266] BETA_OR : (left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))) | left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4)))))
% 51.37/14.36 -> [3275] left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4)))
% 51.37/14.36 -> [3276] left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.36
% 51.37/14.36 [3276] CLOSURE : left_convergent_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.36
% 51.37/14.36 [3275] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 51.37/14.36 -> [3277] ~(left_apart_point(A51_120_14, L52_120_14) | left_apart_point(A51_120_14, reverse_line(L52_120_14)))
% 51.37/14.36
% 51.37/14.36 [3277] ALPHA_NOT_OR : ~(left_apart_point(A51_120_14, L52_120_14) | left_apart_point(A51_120_14, reverse_line(L52_120_14)))
% 51.37/14.36 -> [3278] ~left_apart_point(A51_120_14, L52_120_14), ~left_apart_point(A51_120_14, reverse_line(L52_120_14))
% 51.37/14.36
% 51.37/14.36 [3278] CLOSURE : ~left_apart_point(A51_120_14, L52_120_14)
% 51.37/14.36
% 51.37/14.36 [3249] BETA_OR : ((unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) & unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4)))) | (unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(Y17_13_4)) & unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(reverse_line(Y17_13_4)))))
% 51.37/14.36 -> [3279] (unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) & unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.36 -> [3280] (unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(Y17_13_4)) & unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.36
% 51.37/14.36 [3279] ALPHA_AND : (unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) & unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.36 -> [3281] unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)), unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4)))
% 51.37/14.36
% 51.37/14.36 [3281] CLOSURE : unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4)))
% 51.37/14.36
% 51.37/14.36 [3280] ALPHA_AND : (unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(Y17_13_4)) & unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.36 -> [3282] unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(Y17_13_4)), unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(reverse_line(Y17_13_4)))
% 51.37/14.36
% 51.37/14.36 [3282] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 51.37/14.36 -> [3283] (unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) | unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.36
% 51.37/14.36 [3283] BETA_OR : (unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4)) | unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4))))
% 51.37/14.36 -> [3284] unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))
% 51.37/14.36 -> [3285] unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(reverse_line(Y17_13_4)))
% 51.37/14.36
% 51.37/14.36 [3284] CLOSURE : unequally_directed_lines(reverse_line(Y17_13_4), reverse_line(Y17_13_4))
% 51.37/14.36
% 51.37/14.36 [3285] 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)))))
% 51.37/14.36 -> [3286] ((unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), M50_42_13) & unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(M50_42_13))) => (left_convergent_lines(reverse_line(reverse_line(Y17_13_4)), M50_42_13) | left_convergent_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(M50_42_13))))
% 51.37/14.36
% 51.37/14.36 [3286] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), M50_42_13) & unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(M50_42_13))) => (left_convergent_lines(reverse_line(reverse_line(Y17_13_4)), M50_42_13) | left_convergent_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(M50_42_13))))
% 51.37/14.36 -> [3287] ~(unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), M50_42_13) & unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(M50_42_13)))
% 51.37/14.36 -> [3288] (left_convergent_lines(reverse_line(reverse_line(Y17_13_4)), M50_42_13) | left_convergent_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(M50_42_13)))
% 51.37/14.36
% 51.37/14.36 [3287] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), M50_42_13) & unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(M50_42_13)))
% 51.37/14.36 -> [3289] ~unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), M50_42_13)
% 51.37/14.36 -> [3290] ~unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(M50_42_13))
% 51.37/14.36
% 51.37/14.36 [3289] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), M50_42_13)
% 51.37/14.36
% 51.37/14.36 [3290] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(M50_42_13))
% 51.37/14.36
% 51.37/14.36 [3288] BETA_OR : (left_convergent_lines(reverse_line(reverse_line(Y17_13_4)), M50_42_13) | left_convergent_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(M50_42_13)))
% 51.37/14.36 -> [3295] left_convergent_lines(reverse_line(reverse_line(Y17_13_4)), M50_42_13)
% 51.37/14.36 -> [3296] left_convergent_lines(reverse_line(reverse_line(Y17_13_4)), reverse_line(M50_42_13))
% 51.37/14.36
% 51.37/14.36 [3296] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 51.37/14.36 -> [3297] ~(left_apart_point(A51_122_14, L52_122_14) | left_apart_point(A51_122_14, reverse_line(L52_122_14)))
% 51.37/14.36
% 51.37/14.36 [3297] ALPHA_NOT_OR : ~(left_apart_point(A51_122_14, L52_122_14) | left_apart_point(A51_122_14, reverse_line(L52_122_14)))
% 51.37/14.36 -> [3299] ~left_apart_point(A51_122_14, L52_122_14), ~left_apart_point(A51_122_14, reverse_line(L52_122_14))
% 51.37/14.36
% 51.37/14.36 [3299] CLOSURE : ~left_apart_point(A51_122_14, L52_122_14)
% 51.37/14.36
% 51.37/14.36 [3295] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 51.37/14.36 -> [3298] ~(left_apart_point(A51_123_14, L52_123_14) | left_apart_point(A51_123_14, reverse_line(L52_123_14)))
% 51.37/14.36
% 51.37/14.36 [3298] ALPHA_NOT_OR : ~(left_apart_point(A51_123_14, L52_123_14) | left_apart_point(A51_123_14, reverse_line(L52_123_14)))
% 51.37/14.36 -> [3300] ~left_apart_point(A51_123_14, L52_123_14), ~left_apart_point(A51_123_14, reverse_line(L52_123_14))
% 51.37/14.36
% 51.37/14.36 [3300] CLOSURE : ~left_apart_point(A51_123_14, L52_123_14)
% 51.37/14.36
% 51.37/14.36 % SZS output end Proof for theBenchmark.p
% 51.37/14.36 [14.004829s][1][Res] 141701 goroutines created
% 51.37/14.36 ==== Result ====
% 51.37/14.36 [14.004867s][1][Res] VALID
% 51.37/14.36 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------