TSTP Solution File: GEO235+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO235+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n024.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 15:18:36 EDT 2022
% Result : Theorem 61.26s 17.44s
% Output : Proof 61.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO235+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 07:09:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.18/0.35 Conjecture not found
% 0.18/0.35 Start search
% 0.18/0.35 nb_step : 1 - limit : 37
% 0.18/0.35 Launch Gotab with destructive = true
% 61.20/17.43 % SZS output start Proof for theBenchmark.p
% 61.26/17.44 [0] ALPHA_AND : ((! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9)))) & ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11)))) & ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13)))) & ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15))) & ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17))) & ! [A32_32] : (~distinct_points(A32_32, A32_32)) & ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35)))) & ! [L36_36] : (~distinct_lines(L36_36, L36_36)) & ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39)))) & ! [L40_40] : (equally_directed_lines(L40_40, L40_40)) & ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43)))) & ! [L44_44, M45_45, N46_46] : (((unequally_directed_lines(L44_44, M45_45) & unequally_directed_lines(L44_44, reverse_line(M45_45))) => ((unequally_directed_lines(L44_44, N46_46) & unequally_directed_lines(L44_44, reverse_line(N46_46))) | (unequally_directed_lines(M45_45, N46_46) & unequally_directed_lines(M45_45, reverse_line(N46_46)))))) & ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48)))) & ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50))))) & ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52)))) & ! [L53_53, M54_54] : (~(left_convergent_lines(L53_53, M54_54) | left_convergent_lines(L53_53, reverse_line(M54_54)))) & ! [A55_55, B56_56] : ((((point(A55_55) & point(B56_56)) & distinct_points(A55_55, B56_56)) => line(line_connecting(A55_55, B56_56)))) & ! [L57_57, M58_58] : (((((line(L57_57) & line(M58_58)) & unequally_directed_lines(L57_57, M58_58)) & unequally_directed_lines(L57_57, reverse_line(M58_58))) => point(intersection_point(L57_57, M58_58)))) & ! [L59_59, A60_60] : (((point(A60_60) & line(L59_59)) => line(parallel_through_point(L59_59, A60_60)))) & ! [L61_61] : ((line(L61_61) => line(reverse_line(L61_61)))) & ! [A62_62, B63_63] : ((distinct_points(A62_62, B63_63) => (~apart_point_and_line(A62_62, line_connecting(A62_62, B63_63)) & ~apart_point_and_line(B63_63, line_connecting(A62_62, B63_63))))) & ! [L64_64, M65_65] : (((unequally_directed_lines(L64_64, M65_65) & unequally_directed_lines(L64_64, reverse_line(M65_65))) => (~apart_point_and_line(intersection_point(L64_64, M65_65), L64_64) & ~apart_point_and_line(intersection_point(L64_64, M65_65), M65_65)))) & ! [A66_66, L67_67] : (~apart_point_and_line(A66_66, parallel_through_point(L67_67, A66_66))) & ! [L68_68] : (~distinct_lines(L68_68, reverse_line(L68_68))) & ! [A69_69, B70_70] : ((distinct_points(A69_69, B70_70) => equally_directed_lines(line_connecting(A69_69, B70_70), reverse_line(line_connecting(B70_70, A69_69))))) & ! [A71_71, L72_72] : (equally_directed_lines(parallel_through_point(L72_72, A71_71), L72_72)) & ! [A73_73, B74_74, L75_75, M76_76] : (((distinct_points(A73_73, B74_74) & distinct_lines(L75_75, M76_76)) => (((((((left_apart_point(A73_73, L75_75) | left_apart_point(B74_74, L75_75)) | left_apart_point(A73_73, M76_76)) | left_apart_point(B74_74, M76_76)) | left_apart_point(A73_73, reverse_line(L75_75))) | left_apart_point(B74_74, reverse_line(L75_75))) | left_apart_point(A73_73, reverse_line(M76_76))) | left_apart_point(B74_74, reverse_line(M76_76))))) & ! [A77_77, B78_78, L79_79] : (((distinct_points(A77_77, B78_78) & left_apart_point(A77_77, L79_79)) => (left_apart_point(B78_78, L79_79) | left_convergent_lines(line_connecting(A77_77, B78_78), L79_79)))) & ! [A80_80, B81_81, L82_82] : ((left_apart_point(A80_80, L82_82) => (distinct_points(A80_80, B81_81) | left_apart_point(B81_81, L82_82)))) & ! [A83_83, L84_84, M85_85] : (((left_apart_point(A83_83, L84_84) & unequally_directed_lines(L84_84, M85_85)) => (distinct_lines(L84_84, M85_85) | left_apart_point(A83_83, reverse_line(M85_85))))) & ! [L86_86, M87_87, N88_88] : ((left_convergent_lines(L86_86, M87_87) => (unequally_directed_lines(M87_87, N88_88) | left_convergent_lines(L86_86, N88_88))))) & ~! [A89_89, B90_90, L91_91] : (((left_apart_point(A89_89, L91_91) & right_apart_point(B90_90, L91_91)) => distinct_points(A89_89, B90_90))))
% 61.26/17.44 -> [1] (! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9)))) & ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11)))) & ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13)))) & ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15))) & ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17))) & ! [A32_32] : (~distinct_points(A32_32, A32_32)) & ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35)))) & ! [L36_36] : (~distinct_lines(L36_36, L36_36)) & ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39)))) & ! [L40_40] : (equally_directed_lines(L40_40, L40_40)) & ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43)))) & ! [L44_44, M45_45, N46_46] : (((unequally_directed_lines(L44_44, M45_45) & unequally_directed_lines(L44_44, reverse_line(M45_45))) => ((unequally_directed_lines(L44_44, N46_46) & unequally_directed_lines(L44_44, reverse_line(N46_46))) | (unequally_directed_lines(M45_45, N46_46) & unequally_directed_lines(M45_45, reverse_line(N46_46)))))) & ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48)))) & ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50))))) & ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52)))) & ! [L53_53, M54_54] : (~(left_convergent_lines(L53_53, M54_54) | left_convergent_lines(L53_53, reverse_line(M54_54)))) & ! [A55_55, B56_56] : ((((point(A55_55) & point(B56_56)) & distinct_points(A55_55, B56_56)) => line(line_connecting(A55_55, B56_56)))) & ! [L57_57, M58_58] : (((((line(L57_57) & line(M58_58)) & unequally_directed_lines(L57_57, M58_58)) & unequally_directed_lines(L57_57, reverse_line(M58_58))) => point(intersection_point(L57_57, M58_58)))) & ! [L59_59, A60_60] : (((point(A60_60) & line(L59_59)) => line(parallel_through_point(L59_59, A60_60)))) & ! [L61_61] : ((line(L61_61) => line(reverse_line(L61_61)))) & ! [A62_62, B63_63] : ((distinct_points(A62_62, B63_63) => (~apart_point_and_line(A62_62, line_connecting(A62_62, B63_63)) & ~apart_point_and_line(B63_63, line_connecting(A62_62, B63_63))))) & ! [L64_64, M65_65] : (((unequally_directed_lines(L64_64, M65_65) & unequally_directed_lines(L64_64, reverse_line(M65_65))) => (~apart_point_and_line(intersection_point(L64_64, M65_65), L64_64) & ~apart_point_and_line(intersection_point(L64_64, M65_65), M65_65)))) & ! [A66_66, L67_67] : (~apart_point_and_line(A66_66, parallel_through_point(L67_67, A66_66))) & ! [L68_68] : (~distinct_lines(L68_68, reverse_line(L68_68))) & ! [A69_69, B70_70] : ((distinct_points(A69_69, B70_70) => equally_directed_lines(line_connecting(A69_69, B70_70), reverse_line(line_connecting(B70_70, A69_69))))) & ! [A71_71, L72_72] : (equally_directed_lines(parallel_through_point(L72_72, A71_71), L72_72)) & ! [A73_73, B74_74, L75_75, M76_76] : (((distinct_points(A73_73, B74_74) & distinct_lines(L75_75, M76_76)) => (((((((left_apart_point(A73_73, L75_75) | left_apart_point(B74_74, L75_75)) | left_apart_point(A73_73, M76_76)) | left_apart_point(B74_74, M76_76)) | left_apart_point(A73_73, reverse_line(L75_75))) | left_apart_point(B74_74, reverse_line(L75_75))) | left_apart_point(A73_73, reverse_line(M76_76))) | left_apart_point(B74_74, reverse_line(M76_76))))) & ! [A77_77, B78_78, L79_79] : (((distinct_points(A77_77, B78_78) & left_apart_point(A77_77, L79_79)) => (left_apart_point(B78_78, L79_79) | left_convergent_lines(line_connecting(A77_77, B78_78), L79_79)))) & ! [A80_80, B81_81, L82_82] : ((left_apart_point(A80_80, L82_82) => (distinct_points(A80_80, B81_81) | left_apart_point(B81_81, L82_82)))) & ! [A83_83, L84_84, M85_85] : (((left_apart_point(A83_83, L84_84) & unequally_directed_lines(L84_84, M85_85)) => (distinct_lines(L84_84, M85_85) | left_apart_point(A83_83, reverse_line(M85_85))))) & ! [L86_86, M87_87, N88_88] : ((left_convergent_lines(L86_86, M87_87) => (unequally_directed_lines(M87_87, N88_88) | left_convergent_lines(L86_86, N88_88))))), ~! [A89_89, B90_90, L91_91] : (((left_apart_point(A89_89, L91_91) & right_apart_point(B90_90, L91_91)) => distinct_points(A89_89, B90_90)))
% 61.26/17.44
% 61.26/17.44 [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)))))
% 61.26/17.44 -> [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))))
% 61.26/17.44
% 61.26/17.44 [2] DELTA_NOT_FORALL : ~! [A89_89, B90_90, L91_91] : (((left_apart_point(A89_89, L91_91) & right_apart_point(B90_90, L91_91)) => distinct_points(A89_89, B90_90)))
% 61.26/17.44 -> [3] ~((left_apart_point(skolem_A8989, skolem_L9191) & right_apart_point(skolem_B9090, skolem_L9191)) => distinct_points(skolem_A8989, skolem_B9090))
% 61.26/17.44
% 61.26/17.44 [3] ALPHA_NOT_IMPLY : ~((left_apart_point(skolem_A8989, skolem_L9191) & right_apart_point(skolem_B9090, skolem_L9191)) => distinct_points(skolem_A8989, skolem_B9090))
% 61.26/17.44 -> [4] (left_apart_point(skolem_A8989, skolem_L9191) & right_apart_point(skolem_B9090, skolem_L9191)), ~distinct_points(skolem_A8989, skolem_B9090)
% 61.26/17.44
% 61.26/17.44 [4] ALPHA_AND : (left_apart_point(skolem_A8989, skolem_L9191) & right_apart_point(skolem_B9090, skolem_L9191))
% 61.26/17.44 -> [5] left_apart_point(skolem_A8989, skolem_L9191), right_apart_point(skolem_B9090, skolem_L9191)
% 61.26/17.44
% 61.26/17.44 [5] GAMMA_FORALL : ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9))))
% 61.26/17.44 -> [6] (unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))) <=> unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44
% 61.26/17.44 [6] BETA_EQUIV : (unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))) <=> unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44 -> [7] ~unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))), ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [8] unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))), unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [8] GAMMA_FORALL : ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11))))
% 61.26/17.44 -> [10] (right_apart_point(skolem_B9090, skolem_L9191) <=> left_apart_point(skolem_B9090, reverse_line(skolem_L9191)))
% 61.26/17.44
% 61.26/17.44 [10] BETA_EQUIV : (right_apart_point(skolem_B9090, skolem_L9191) <=> left_apart_point(skolem_B9090, reverse_line(skolem_L9191)))
% 61.26/17.44 -> [11] ~right_apart_point(skolem_B9090, skolem_L9191), ~left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 61.26/17.44 -> [12] right_apart_point(skolem_B9090, skolem_L9191), left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 61.26/17.44
% 61.26/17.44 [11] CLOSURE : ~right_apart_point(skolem_B9090, skolem_L9191)
% 61.26/17.44
% 61.26/17.44 [15] BETA_EQUIV : (right_convergent_lines(X12_0_2, Y13_0_2) <=> left_convergent_lines(X12_0_2, reverse_line(Y13_0_2)))
% 61.26/17.44 -> [422] ~right_convergent_lines(X12_0_2, Y13_0_2), ~left_convergent_lines(X12_0_2, reverse_line(Y13_0_2))
% 61.26/17.44 -> [423] right_convergent_lines(X12_0_2, Y13_0_2), left_convergent_lines(X12_0_2, reverse_line(Y13_0_2))
% 61.26/17.44
% 61.26/17.44 [422] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 61.26/17.44 -> [425] (equally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) <=> ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44
% 61.26/17.44 [425] BETA_EQUIV : (equally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) <=> ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44 -> [428] ~equally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))), ~~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [429] equally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))), ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [429] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [435] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))) <=> ~unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [511] ~equally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))), ~~unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44 -> [512] equally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))), ~unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44
% 61.26/17.44 [512] CLOSURE : ~unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44
% 61.26/17.44 [519] BETA_IMPLY : (distinct_points(C35_8_6, C35_8_6) => (distinct_points(C35_8_6, C35_8_6) | distinct_points(C35_8_6, C35_8_6)))
% 61.26/17.44 -> [602] ~distinct_points(C35_8_6, C35_8_6)
% 61.26/17.44 -> [603] (distinct_points(C35_8_6, C35_8_6) | distinct_points(C35_8_6, C35_8_6))
% 61.26/17.44
% 61.26/17.44 [603] BETA_OR : (distinct_points(C35_8_6, C35_8_6) | distinct_points(C35_8_6, C35_8_6))
% 61.26/17.44 -> [604] distinct_points(C35_8_6, C35_8_6)
% 61.26/17.44 -> [605] distinct_points(C35_8_6, C35_8_6)
% 61.26/17.44
% 61.26/17.44 [604] CLOSURE : distinct_points(C35_8_6, C35_8_6)
% 61.26/17.44
% 61.26/17.44 [605] CLOSURE : distinct_points(C35_8_6, C35_8_6)
% 61.26/17.44
% 61.26/17.44 [607] BETA_IMPLY : (distinct_lines(N39_12_8, N39_12_8) => (distinct_lines(N39_12_8, N39_12_8) | distinct_lines(N39_12_8, N39_12_8)))
% 61.26/17.44 -> [637] ~distinct_lines(N39_12_8, N39_12_8)
% 61.26/17.44 -> [638] (distinct_lines(N39_12_8, N39_12_8) | distinct_lines(N39_12_8, N39_12_8))
% 61.26/17.44
% 61.26/17.44 [637] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 61.26/17.44 -> [643] equally_directed_lines(L40_24_9, L40_24_9)
% 61.26/17.44
% 61.26/17.44 [643] CLOSURE : equally_directed_lines(L40_24_9, L40_24_9)
% 61.26/17.44
% 61.26/17.44 [638] BETA_OR : (distinct_lines(N39_12_8, N39_12_8) | distinct_lines(N39_12_8, N39_12_8))
% 61.26/17.44 -> [646] distinct_lines(N39_12_8, N39_12_8)
% 61.26/17.44 -> [647] distinct_lines(N39_12_8, N39_12_8)
% 61.26/17.44
% 61.26/17.44 [647] CLOSURE : distinct_lines(N39_12_8, N39_12_8)
% 61.26/17.44
% 61.26/17.44 [646] CLOSURE : distinct_lines(N39_12_8, N39_12_8)
% 61.26/17.44
% 61.26/17.44 [424] BETA_EQUIV : (equally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) <=> ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44 -> [656] ~equally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))), ~~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [657] equally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))), ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [657] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [659] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))) <=> ~unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [775] ~equally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))), ~~unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44 -> [776] equally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))), ~unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44
% 61.26/17.44 [776] CLOSURE : ~unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44
% 61.26/17.44 [775] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44 -> [783] unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44
% 61.26/17.44 [783] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 61.26/17.44 -> [790] ~distinct_points(skolem_B9090, skolem_B9090)
% 61.26/17.44
% 61.26/17.44 [790] 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))))
% 61.26/17.44 -> [799] (distinct_points(skolem_B9090, skolem_A8989) => (distinct_points(skolem_B9090, skolem_B9090) | distinct_points(skolem_A8989, skolem_B9090)))
% 61.26/17.44
% 61.26/17.44 [799] BETA_IMPLY : (distinct_points(skolem_B9090, skolem_A8989) => (distinct_points(skolem_B9090, skolem_B9090) | distinct_points(skolem_A8989, skolem_B9090)))
% 61.26/17.44 -> [800] ~distinct_points(skolem_B9090, skolem_A8989)
% 61.26/17.44 -> [801] (distinct_points(skolem_B9090, skolem_B9090) | distinct_points(skolem_A8989, skolem_B9090))
% 61.26/17.44
% 61.26/17.44 [801] BETA_OR : (distinct_points(skolem_B9090, skolem_B9090) | distinct_points(skolem_A8989, skolem_B9090))
% 61.26/17.44 -> [802] distinct_points(skolem_B9090, skolem_B9090)
% 61.26/17.44 -> [803] distinct_points(skolem_A8989, skolem_B9090)
% 61.26/17.44
% 61.26/17.44 [802] CLOSURE : distinct_points(skolem_B9090, skolem_B9090)
% 61.26/17.44
% 61.26/17.44 [803] CLOSURE : distinct_points(skolem_A8989, skolem_B9090)
% 61.26/17.44
% 61.26/17.44 [800] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 61.26/17.44 -> [804] ~distinct_lines(M38_15_8, M38_15_8)
% 61.26/17.44
% 61.26/17.44 [804] 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))))
% 61.26/17.44 -> [805] (distinct_lines(M38_15_8, M38_15_8) => (distinct_lines(M38_15_8, M38_15_8) | distinct_lines(M38_15_8, M38_15_8)))
% 61.26/17.44
% 61.26/17.44 [805] 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)))
% 61.26/17.44 -> [806] ~distinct_lines(M38_15_8, M38_15_8)
% 61.26/17.44 -> [807] (distinct_lines(M38_15_8, M38_15_8) | distinct_lines(M38_15_8, M38_15_8))
% 61.26/17.44
% 61.26/17.44 [806] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 61.26/17.44 -> [817] equally_directed_lines(L40_29_9, L40_29_9)
% 61.26/17.44
% 61.26/17.44 [817] CLOSURE : equally_directed_lines(L40_29_9, L40_29_9)
% 61.26/17.44
% 61.26/17.44 [807] BETA_OR : (distinct_lines(M38_15_8, M38_15_8) | distinct_lines(M38_15_8, M38_15_8))
% 61.26/17.44 -> [808] distinct_lines(M38_15_8, M38_15_8)
% 61.26/17.44 -> [809] distinct_lines(M38_15_8, M38_15_8)
% 61.26/17.44
% 61.26/17.44 [808] CLOSURE : distinct_lines(M38_15_8, M38_15_8)
% 61.26/17.44
% 61.26/17.44 [809] CLOSURE : distinct_lines(M38_15_8, M38_15_8)
% 61.26/17.44
% 61.26/17.44 [9] BETA_EQUIV : (right_apart_point(skolem_B9090, skolem_L9191) <=> left_apart_point(skolem_B9090, reverse_line(skolem_L9191)))
% 61.26/17.44 -> [2471] ~right_apart_point(skolem_B9090, skolem_L9191), ~left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 61.26/17.44 -> [2472] right_apart_point(skolem_B9090, skolem_L9191), left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 61.26/17.44
% 61.26/17.44 [2472] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 61.26/17.44 -> [2473] (right_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), Y13_2_2) <=> left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2)))
% 61.26/17.44
% 61.26/17.44 [2473] BETA_EQUIV : (right_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), Y13_2_2) <=> left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2)))
% 61.26/17.44 -> [2474] ~right_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), Y13_2_2), ~left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2))
% 61.26/17.44 -> [2475] right_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), Y13_2_2), left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2))
% 61.26/17.44
% 61.26/17.44 [2475] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 61.26/17.44 -> [2477] (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)))
% 61.26/17.44
% 61.26/17.44 [2477] 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)))
% 61.26/17.44 -> [2480] ~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))
% 61.26/17.44 -> [2481] 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))
% 61.26/17.44
% 61.26/17.44 [2480] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 61.26/17.44 -> [2483] unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 61.26/17.44
% 61.26/17.44 [2483] CLOSURE : unequally_directed_lines(reverse_line(Y17_14_4), reverse_line(Y17_14_4))
% 61.26/17.44
% 61.26/17.44 [2487] 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))
% 61.26/17.44 -> [3182] ~equally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 61.26/17.44 -> [3183] equally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4), ~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 61.26/17.44
% 61.26/17.44 [3182] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 61.26/17.44 -> [3184] unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 61.26/17.44
% 61.26/17.44 [3184] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_14_4), Y17_14_4)
% 61.26/17.44
% 61.26/17.44 [3183] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 61.26/17.44 -> [3185] ~distinct_points(A32_21_5, A32_21_5)
% 61.26/17.44
% 61.26/17.44 [3185] 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))))
% 61.26/17.44 -> [3186] (distinct_points(skolem_A8989, skolem_A8989) => (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_A8989, skolem_B9090)))
% 61.26/17.44
% 61.26/17.44 [3186] BETA_IMPLY : (distinct_points(skolem_A8989, skolem_A8989) => (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_A8989, skolem_B9090)))
% 61.26/17.44 -> [3187] ~distinct_points(skolem_A8989, skolem_A8989)
% 61.26/17.44 -> [3188] (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_A8989, skolem_B9090))
% 61.26/17.44
% 61.26/17.44 [3188] BETA_OR : (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_A8989, skolem_B9090))
% 61.26/17.44 -> [3189] distinct_points(skolem_A8989, skolem_B9090)
% 61.26/17.44 -> [3190] distinct_points(skolem_A8989, skolem_B9090)
% 61.26/17.44
% 61.26/17.44 [3190] CLOSURE : distinct_points(skolem_A8989, skolem_B9090)
% 61.26/17.44
% 61.26/17.44 [3189] CLOSURE : distinct_points(skolem_A8989, skolem_B9090)
% 61.26/17.44
% 61.26/17.44 [3187] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 61.26/17.44 -> [3191] ~distinct_lines(N39_29_8, N39_29_8)
% 61.26/17.44
% 61.26/17.44 [3191] 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))))
% 61.26/17.44 -> [3194] (distinct_lines(N39_29_8, N39_29_8) => (distinct_lines(N39_29_8, N39_29_8) | distinct_lines(N39_29_8, N39_29_8)))
% 61.26/17.44
% 61.26/17.44 [3194] BETA_IMPLY : (distinct_lines(N39_29_8, N39_29_8) => (distinct_lines(N39_29_8, N39_29_8) | distinct_lines(N39_29_8, N39_29_8)))
% 61.26/17.44 -> [3195] ~distinct_lines(N39_29_8, N39_29_8)
% 61.26/17.44 -> [3196] (distinct_lines(N39_29_8, N39_29_8) | distinct_lines(N39_29_8, N39_29_8))
% 61.26/17.44
% 61.26/17.44 [3196] BETA_OR : (distinct_lines(N39_29_8, N39_29_8) | distinct_lines(N39_29_8, N39_29_8))
% 61.26/17.44 -> [3197] distinct_lines(N39_29_8, N39_29_8)
% 61.26/17.44 -> [3198] distinct_lines(N39_29_8, N39_29_8)
% 61.26/17.44
% 61.26/17.44 [3197] CLOSURE : distinct_lines(N39_29_8, N39_29_8)
% 61.26/17.44
% 61.26/17.44 [3198] CLOSURE : distinct_lines(N39_29_8, N39_29_8)
% 61.26/17.44
% 61.26/17.44 [3195] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 61.26/17.44 -> [3203] equally_directed_lines(L40_53_9, L40_53_9)
% 61.26/17.44
% 61.26/17.44 [3203] 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))))
% 61.26/17.44 -> [3206] (unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)) => (unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)) | unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))))
% 61.26/17.44
% 61.26/17.44 [3206] BETA_IMPLY : (unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)) => (unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)) | unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))))
% 61.26/17.44 -> [3207] ~unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))
% 61.26/17.44 -> [3208] (unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)) | unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)))
% 61.26/17.44
% 61.26/17.44 [3208] BETA_OR : (unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)) | unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)))
% 61.26/17.44 -> [3209] unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))
% 61.26/17.44 -> [3210] unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))
% 61.26/17.44
% 61.26/17.44 [3209] CLOSURE : unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))
% 61.26/17.44
% 61.26/17.44 [3210] CLOSURE : unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))
% 61.26/17.44
% 61.26/17.44 [3211] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11)))) => ((unequally_directed_lines(reverse_line(N46_52_11), N46_52_11) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))) | (unequally_directed_lines(reverse_line(N46_52_11), N46_52_11) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)))))
% 61.26/17.44 -> [3273] ~(unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11))))
% 61.26/17.44 -> [3274] ((unequally_directed_lines(reverse_line(N46_52_11), N46_52_11) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))) | (unequally_directed_lines(reverse_line(N46_52_11), N46_52_11) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))))
% 61.26/17.44
% 61.26/17.44 [3274] BETA_OR : ((unequally_directed_lines(reverse_line(N46_52_11), N46_52_11) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))) | (unequally_directed_lines(reverse_line(N46_52_11), N46_52_11) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))))
% 61.26/17.44 -> [3277] (unequally_directed_lines(reverse_line(N46_52_11), N46_52_11) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)))
% 61.26/17.44 -> [3278] (unequally_directed_lines(reverse_line(N46_52_11), N46_52_11) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)))
% 61.26/17.44
% 61.26/17.44 [3277] ALPHA_AND : (unequally_directed_lines(reverse_line(N46_52_11), N46_52_11) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)))
% 61.26/17.44 -> [3279] unequally_directed_lines(reverse_line(N46_52_11), N46_52_11), unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))
% 61.26/17.44
% 61.26/17.44 [3279] CLOSURE : unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))
% 61.26/17.44
% 61.26/17.44 [3280] CLOSURE : unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))
% 61.26/17.44
% 61.26/17.44 [3273] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11))))
% 61.26/17.44 -> [3317] ~unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))
% 61.26/17.44 -> [3318] ~unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11)))
% 61.26/17.44
% 61.26/17.44 [3318] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 61.26/17.44 -> [3326] (unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)) | unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11))))
% 61.26/17.44
% 61.26/17.44 [3326] BETA_OR : (unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)) | unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11))))
% 61.26/17.44 -> [3327] unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))
% 61.26/17.44 -> [3328] unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11)))
% 61.26/17.44
% 61.26/17.44 [3327] CLOSURE : unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))
% 61.26/17.44
% 61.26/17.44 [3328] CLOSURE : unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11)))
% 61.26/17.44
% 61.26/17.44 [3317] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 61.26/17.44 -> [3322] (unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)) | unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11))))
% 61.26/17.44
% 61.26/17.44 [3322] BETA_OR : (unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11)) | unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11))))
% 61.26/17.44 -> [3324] unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))
% 61.26/17.44 -> [3325] unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11)))
% 61.26/17.44
% 61.26/17.44 [3324] CLOSURE : unequally_directed_lines(reverse_line(N46_52_11), reverse_line(N46_52_11))
% 61.26/17.44
% 61.26/17.44 [3325] 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)))))
% 61.26/17.44 -> [3332] ((unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11))) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(reverse_line(N46_52_11))))) => (left_convergent_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11))) | left_convergent_lines(reverse_line(N46_52_11), reverse_line(reverse_line(reverse_line(N46_52_11))))))
% 61.26/17.44
% 61.26/17.44 [3332] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11))) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(reverse_line(N46_52_11))))) => (left_convergent_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11))) | left_convergent_lines(reverse_line(N46_52_11), reverse_line(reverse_line(reverse_line(N46_52_11))))))
% 61.26/17.44 -> [3333] ~(unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11))) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(reverse_line(N46_52_11)))))
% 61.26/17.44 -> [3334] (left_convergent_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11))) | left_convergent_lines(reverse_line(N46_52_11), reverse_line(reverse_line(reverse_line(N46_52_11)))))
% 61.26/17.44
% 61.26/17.44 [3334] BETA_OR : (left_convergent_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11))) | left_convergent_lines(reverse_line(N46_52_11), reverse_line(reverse_line(reverse_line(N46_52_11)))))
% 61.26/17.44 -> [3337] left_convergent_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11)))
% 61.26/17.44 -> [3338] left_convergent_lines(reverse_line(N46_52_11), reverse_line(reverse_line(reverse_line(N46_52_11))))
% 61.26/17.44
% 61.26/17.44 [3338] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 61.26/17.44 -> [3342] ~(left_apart_point(A51_78_14, L52_78_14) | left_apart_point(A51_78_14, reverse_line(L52_78_14)))
% 61.26/17.44
% 61.26/17.44 [3342] ALPHA_NOT_OR : ~(left_apart_point(A51_78_14, L52_78_14) | left_apart_point(A51_78_14, reverse_line(L52_78_14)))
% 61.26/17.44 -> [3346] ~left_apart_point(A51_78_14, L52_78_14), ~left_apart_point(A51_78_14, reverse_line(L52_78_14))
% 61.26/17.44
% 61.26/17.44 [3346] CLOSURE : ~left_apart_point(A51_78_14, L52_78_14)
% 61.26/17.44
% 61.26/17.44 [3337] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 61.26/17.44 -> [3343] ~(left_apart_point(A51_79_14, L52_79_14) | left_apart_point(A51_79_14, reverse_line(L52_79_14)))
% 61.26/17.44
% 61.26/17.44 [3343] ALPHA_NOT_OR : ~(left_apart_point(A51_79_14, L52_79_14) | left_apart_point(A51_79_14, reverse_line(L52_79_14)))
% 61.26/17.44 -> [3349] ~left_apart_point(A51_79_14, L52_79_14), ~left_apart_point(A51_79_14, reverse_line(L52_79_14))
% 61.26/17.44
% 61.26/17.44 [3349] CLOSURE : ~left_apart_point(A51_79_14, L52_79_14)
% 61.26/17.44
% 61.26/17.44 [3333] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11))) & unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(reverse_line(N46_52_11)))))
% 61.26/17.44 -> [3335] ~unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11)))
% 61.26/17.44 -> [3336] ~unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(reverse_line(N46_52_11))))
% 61.26/17.44
% 61.26/17.44 [3335] CLOSURE : ~unequally_directed_lines(reverse_line(N46_52_11), reverse_line(reverse_line(N46_52_11)))
% 61.26/17.44
% 61.26/17.44 [3336] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 61.26/17.44 -> [3350] ~(left_apart_point(A51_80_14, L52_80_14) | left_apart_point(A51_80_14, reverse_line(L52_80_14)))
% 61.26/17.44
% 61.26/17.44 [3350] ALPHA_NOT_OR : ~(left_apart_point(A51_80_14, L52_80_14) | left_apart_point(A51_80_14, reverse_line(L52_80_14)))
% 61.26/17.44 -> [3351] ~left_apart_point(A51_80_14, L52_80_14), ~left_apart_point(A51_80_14, reverse_line(L52_80_14))
% 61.26/17.44
% 61.26/17.44 [3351] CLOSURE : ~left_apart_point(A51_80_14, L52_80_14)
% 61.26/17.44
% 61.26/17.44 [2474] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 61.26/17.44 -> [2476] (equally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) <=> ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44
% 61.26/17.44 [2476] BETA_EQUIV : (equally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) <=> ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44 -> [2478] ~equally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))), ~~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [2479] equally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))), ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [2478] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [2482] unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [2482] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [2484] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))) <=> ~unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [2887] ~equally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))), ~~unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44 -> [2888] equally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))), ~unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44
% 61.26/17.44 [2887] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44 -> [2889] unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44
% 61.26/17.44 [2889] CLOSURE : unequally_directed_opposite_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44
% 61.26/17.44 [2891] BETA_IMPLY : (distinct_points(skolem_A8989, skolem_A8989) => (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_A8989, skolem_B9090)))
% 61.26/17.44 -> [3609] ~distinct_points(skolem_A8989, skolem_A8989)
% 61.26/17.44 -> [3610] (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_A8989, skolem_B9090))
% 61.26/17.44
% 61.26/17.44 [3610] BETA_OR : (distinct_points(skolem_A8989, skolem_B9090) | distinct_points(skolem_A8989, skolem_B9090))
% 61.26/17.44 -> [3611] distinct_points(skolem_A8989, skolem_B9090)
% 61.26/17.44 -> [3612] distinct_points(skolem_A8989, skolem_B9090)
% 61.26/17.44
% 61.26/17.44 [3611] CLOSURE : distinct_points(skolem_A8989, skolem_B9090)
% 61.26/17.44
% 61.26/17.44 [3612] CLOSURE : distinct_points(skolem_A8989, skolem_B9090)
% 61.26/17.44
% 61.26/17.44 [3614] BETA_IMPLY : (distinct_lines(N39_30_8, N39_30_8) => (distinct_lines(N39_30_8, N39_30_8) | distinct_lines(N39_30_8, N39_30_8)))
% 61.26/17.44 -> [3829] ~distinct_lines(N39_30_8, N39_30_8)
% 61.26/17.44 -> [3830] (distinct_lines(N39_30_8, N39_30_8) | distinct_lines(N39_30_8, N39_30_8))
% 61.26/17.44
% 61.26/17.44 [3829] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 61.26/17.44 -> [3833] equally_directed_lines(L40_56_9, L40_56_9)
% 61.26/17.44
% 61.26/17.44 [3833] 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))))
% 61.26/17.44 -> [3834] (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) => (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))))
% 61.26/17.44
% 61.26/17.44 [3834] BETA_IMPLY : (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) => (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))))
% 61.26/17.44 -> [3835] ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [3836] (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44
% 61.26/17.44 [3836] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44 -> [3837] unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [3838] unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [3838] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [3837] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [3839] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2)))))) => ((unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2)))))) | (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2))))))))
% 61.26/17.44 -> [3862] ~(unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2))))))
% 61.26/17.44 -> [3863] ((unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2)))))) | (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2)))))))
% 61.26/17.44
% 61.26/17.44 [3862] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2))))))
% 61.26/17.44 -> [3864] ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [3865] ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44
% 61.26/17.44 [3865] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 61.26/17.44 -> [3871] (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2))))))
% 61.26/17.44
% 61.26/17.44 [3871] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2))))))
% 61.26/17.44 -> [3874] unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [3875] unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44
% 61.26/17.44 [3874] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [3875] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44
% 61.26/17.44 [3870] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))) | unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44 -> [3876] unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44 -> [3877] unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [3877] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [3876] 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)))))
% 61.26/17.44 -> [3878] ((unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))) => (left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44
% 61.26/17.44 [3878] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))) => (left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44 -> [3879] ~(unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [3880] (left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44
% 61.26/17.44 [3879] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2)) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [3881] ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2))
% 61.26/17.44 -> [3882] ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44
% 61.26/17.44 [3882] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44
% 61.26/17.44 [3881] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 61.26/17.44 -> [3886] ~(left_apart_point(A51_127_14, L52_127_14) | left_apart_point(A51_127_14, reverse_line(L52_127_14)))
% 61.26/17.44
% 61.26/17.44 [3886] ALPHA_NOT_OR : ~(left_apart_point(A51_127_14, L52_127_14) | left_apart_point(A51_127_14, reverse_line(L52_127_14)))
% 61.26/17.44 -> [3888] ~left_apart_point(A51_127_14, L52_127_14), ~left_apart_point(A51_127_14, reverse_line(L52_127_14))
% 61.26/17.44
% 61.26/17.44 [3888] CLOSURE : ~left_apart_point(A51_127_14, L52_127_14)
% 61.26/17.44
% 61.26/17.44 [3880] BETA_OR : (left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2)) | left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2))))
% 61.26/17.44 -> [3889] left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2))
% 61.26/17.44 -> [3890] left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(Y13_2_2)))
% 61.26/17.44
% 61.26/17.44 [3889] CLOSURE : left_convergent_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(Y13_2_2))
% 61.26/17.44
% 61.26/17.44 [3890] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 61.26/17.44 -> [3891] ~(left_apart_point(A51_128_14, L52_128_14) | left_apart_point(A51_128_14, reverse_line(L52_128_14)))
% 61.26/17.44
% 61.26/17.44 [3891] ALPHA_NOT_OR : ~(left_apart_point(A51_128_14, L52_128_14) | left_apart_point(A51_128_14, reverse_line(L52_128_14)))
% 61.26/17.44 -> [3892] ~left_apart_point(A51_128_14, L52_128_14), ~left_apart_point(A51_128_14, reverse_line(L52_128_14))
% 61.26/17.44
% 61.26/17.44 [3892] CLOSURE : ~left_apart_point(A51_128_14, L52_128_14)
% 61.26/17.44
% 61.26/17.44 [3863] BETA_OR : ((unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2)))))) | (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2)))))))
% 61.26/17.44 -> [3893] (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2))))))
% 61.26/17.44 -> [3894] (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2))))))
% 61.26/17.44
% 61.26/17.44 [3894] ALPHA_AND : (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2))))))
% 61.26/17.44 -> [3895] unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))), unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44
% 61.26/17.44 [3895] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44
% 61.26/17.44 [3893] ALPHA_AND : (unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))) & unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2))))))
% 61.26/17.44 -> [3896] unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(Y13_2_2)))), unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44
% 61.26/17.44 [3896] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(reverse_line(Y13_2_2))), reverse_line(reverse_line(reverse_line(reverse_line(Y13_2_2)))))
% 61.26/17.44
% 61.26/17.44 [3830] BETA_OR : (distinct_lines(N39_30_8, N39_30_8) | distinct_lines(N39_30_8, N39_30_8))
% 61.26/17.44 -> [3897] distinct_lines(N39_30_8, N39_30_8)
% 61.26/17.44 -> [3898] distinct_lines(N39_30_8, N39_30_8)
% 61.26/17.44
% 61.26/17.44 [3897] CLOSURE : distinct_lines(N39_30_8, N39_30_8)
% 61.26/17.44
% 61.26/17.44 [3898] CLOSURE : distinct_lines(N39_30_8, N39_30_8)
% 61.26/17.44
% 61.26/17.44 [2471] CLOSURE : ~right_apart_point(skolem_B9090, skolem_L9191)
% 61.26/17.44
% 61.26/17.44 % SZS output end Proof for theBenchmark.p
% 61.26/17.44 [17.100922s][1][Res] 147448 goroutines created
% 61.26/17.44 ==== Result ====
% 61.26/17.44 [17.100959s][1][Res] VALID
% 61.26/17.44 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------