TSTP Solution File: GEO258+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO258+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n021.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 15:18:47 EDT 2022
% Result : Theorem 1.11s 0.61s
% Output : Proof 1.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO258+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n021.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 07:09:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 [DMT] DMT loaded with preskolemization
% 0.12/0.33 [EQ] equality loaded.
% 0.12/0.33 [0.000036s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.34 Conjecture not found
% 0.12/0.34 Start search
% 0.12/0.34 nb_step : 1 - limit : 37
% 0.12/0.34 Launch Gotab with destructive = true
% 1.11/0.59 % SZS output start Proof for theBenchmark.p
% 1.11/0.60 [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))))) & ~! [L89_89, A90_90, B91_91, C92_92] : ((between_on_line(L89_89, A90_90, B91_91, C92_92) => between_on_line(L89_89, C92_92, B91_91, A90_90))))
% 1.11/0.60 -> [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))))), ~! [L89_89, A90_90, B91_91, C92_92] : ((between_on_line(L89_89, A90_90, B91_91, C92_92) => between_on_line(L89_89, C92_92, B91_91, A90_90)))
% 1.11/0.60
% 1.11/0.60 [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)))))
% 1.11/0.60 -> [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))))
% 1.11/0.60
% 1.11/0.60 [2] DELTA_NOT_FORALL : ~! [L89_89, A90_90, B91_91, C92_92] : ((between_on_line(L89_89, A90_90, B91_91, C92_92) => between_on_line(L89_89, C92_92, B91_91, A90_90)))
% 1.11/0.60 -> [3] ~(between_on_line(skolem_L8989, skolem_A9090, skolem_B9191, skolem_C9292) => between_on_line(skolem_L8989, skolem_C9292, skolem_B9191, skolem_A9090))
% 1.11/0.60
% 1.11/0.60 [3] ALPHA_NOT_IMPLY : ~(between_on_line(skolem_L8989, skolem_A9090, skolem_B9191, skolem_C9292) => between_on_line(skolem_L8989, skolem_C9292, skolem_B9191, skolem_A9090))
% 1.11/0.60 -> [4] between_on_line(skolem_L8989, skolem_A9090, skolem_B9191, skolem_C9292), ~between_on_line(skolem_L8989, skolem_C9292, skolem_B9191, skolem_A9090)
% 1.11/0.60
% 1.11/0.60 [4] Rewrite : between_on_line(skolem_L8989, skolem_A9090, skolem_B9191, skolem_C9292)
% 1.11/0.60 -> [5] ((before_on_line(skolem_L8989, skolem_A9090, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_C9292)) | (before_on_line(skolem_L8989, skolem_C9292, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_A9090)))
% 1.11/0.60
% 1.11/0.60 [5] Rewrite : ~between_on_line(skolem_L8989, skolem_C9292, skolem_B9191, skolem_A9090)
% 1.11/0.60 -> [6] ~((before_on_line(skolem_L8989, skolem_C9292, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_A9090)) | (before_on_line(skolem_L8989, skolem_A9090, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_C9292)))
% 1.11/0.60
% 1.11/0.60 [6] ALPHA_NOT_OR : ~((before_on_line(skolem_L8989, skolem_C9292, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_A9090)) | (before_on_line(skolem_L8989, skolem_A9090, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_C9292)))
% 1.11/0.60 -> [7] ~(before_on_line(skolem_L8989, skolem_C9292, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_A9090)), ~(before_on_line(skolem_L8989, skolem_A9090, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_C9292))
% 1.11/0.60
% 1.11/0.60 [7] BETA_OR : ((before_on_line(skolem_L8989, skolem_A9090, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_C9292)) | (before_on_line(skolem_L8989, skolem_C9292, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_A9090)))
% 1.11/0.60 -> [8] (before_on_line(skolem_L8989, skolem_A9090, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_C9292))
% 1.11/0.60 -> [9] (before_on_line(skolem_L8989, skolem_C9292, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_A9090))
% 1.11/0.60
% 1.11/0.60 [9] ALPHA_AND : (before_on_line(skolem_L8989, skolem_C9292, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_A9090))
% 1.11/0.60 -> [11] before_on_line(skolem_L8989, skolem_C9292, skolem_B9191), before_on_line(skolem_L8989, skolem_B9191, skolem_A9090)
% 1.11/0.60
% 1.11/0.60 [11] Rewrite : before_on_line(skolem_L8989, skolem_C9292, skolem_B9191)
% 1.11/0.60 -> [13] (((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191)))
% 1.11/0.60
% 1.11/0.60 [13] Rewrite : before_on_line(skolem_L8989, skolem_B9191, skolem_A9090)
% 1.11/0.60 -> [15] (((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090)))
% 1.11/0.60
% 1.11/0.60 [15] ALPHA_AND : (((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191)))
% 1.11/0.60 -> [17] ((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)), equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [17] ALPHA_AND : (((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090)))
% 1.11/0.60 -> [19] ((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989)), equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090))
% 1.11/0.60
% 1.11/0.60 [19] ALPHA_AND : ((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [21] (distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)), incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [21] ALPHA_AND : ((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [23] (distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)), incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [23] ALPHA_AND : (distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [25] distinct_points(skolem_C9292, skolem_B9191), incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [25] ALPHA_AND : (distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [27] distinct_points(skolem_B9191, skolem_A9090), incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [27] BETA_NOT_AND : ~(before_on_line(skolem_L8989, skolem_C9292, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_A9090))
% 1.11/0.60 -> [30] ~before_on_line(skolem_L8989, skolem_C9292, skolem_B9191)
% 1.11/0.60 -> [31] ~before_on_line(skolem_L8989, skolem_B9191, skolem_A9090)
% 1.11/0.60
% 1.11/0.60 [30] Rewrite : ~before_on_line(skolem_L8989, skolem_C9292, skolem_B9191)
% 1.11/0.60 -> [36] ~(((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191)))
% 1.11/0.60
% 1.11/0.60 [36] BETA_NOT_AND : ~(before_on_line(skolem_L8989, skolem_A9090, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_C9292))
% 1.11/0.60 -> [40] ~before_on_line(skolem_L8989, skolem_A9090, skolem_B9191)
% 1.11/0.60 -> [41] ~before_on_line(skolem_L8989, skolem_B9191, skolem_C9292)
% 1.11/0.60
% 1.11/0.60 [40] Rewrite : ~before_on_line(skolem_L8989, skolem_A9090, skolem_B9191)
% 1.11/0.60 -> [56] ~(((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191)))
% 1.11/0.60
% 1.11/0.60 [56] BETA_NOT_AND : ~(((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191)))
% 1.11/0.60 -> [62] ~((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [63] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [63] CLOSURE : ~equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [62] BETA_NOT_AND : ~(((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191)))
% 1.11/0.60 -> [74] ~((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [75] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [74] BETA_NOT_AND : ~((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [82] ~(distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [83] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [83] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [82] BETA_NOT_AND : ~((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [148] ~(distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [149] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [149] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [148] BETA_NOT_AND : ~(distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [150] ~distinct_points(skolem_C9292, skolem_B9191)
% 1.11/0.60 -> [151] ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [150] CLOSURE : ~distinct_points(skolem_C9292, skolem_B9191)
% 1.11/0.60
% 1.11/0.60 [151] CLOSURE : ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [75] BETA_NOT_AND : ~((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [114] ~(distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [115] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [115] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [114] BETA_NOT_AND : ~(distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [160] ~distinct_points(skolem_C9292, skolem_B9191)
% 1.11/0.60 -> [161] ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [161] CLOSURE : ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [160] CLOSURE : ~distinct_points(skolem_C9292, skolem_B9191)
% 1.11/0.60
% 1.11/0.60 [41] Rewrite : ~before_on_line(skolem_L8989, skolem_B9191, skolem_C9292)
% 1.11/0.60 -> [59] ~(((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292)))
% 1.11/0.60
% 1.11/0.60 [59] BETA_NOT_AND : ~(((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191)))
% 1.11/0.60 -> [66] ~((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [67] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [67] CLOSURE : ~equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [66] BETA_NOT_AND : ~(((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292)))
% 1.11/0.60 -> [90] ~((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [91] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292))
% 1.11/0.60
% 1.11/0.60 [91] BETA_NOT_AND : ~((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [136] ~(distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [137] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [137] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [136] BETA_NOT_AND : ~(distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [166] ~distinct_points(skolem_C9292, skolem_B9191)
% 1.11/0.60 -> [167] ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [167] CLOSURE : ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [166] CLOSURE : ~distinct_points(skolem_C9292, skolem_B9191)
% 1.11/0.60
% 1.11/0.60 [90] BETA_NOT_AND : ~((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [106] ~(distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [107] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [107] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [106] BETA_NOT_AND : ~((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [120] ~(distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [121] ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [121] CLOSURE : ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [120] BETA_NOT_AND : ~(distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [128] ~distinct_points(skolem_C9292, skolem_B9191)
% 1.11/0.60 -> [129] ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [129] CLOSURE : ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [128] CLOSURE : ~distinct_points(skolem_C9292, skolem_B9191)
% 1.11/0.60
% 1.11/0.60 [31] Rewrite : ~before_on_line(skolem_L8989, skolem_B9191, skolem_A9090)
% 1.11/0.60 -> [39] ~(((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090)))
% 1.11/0.60
% 1.11/0.60 [39] BETA_NOT_AND : ~(before_on_line(skolem_L8989, skolem_A9090, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_C9292))
% 1.11/0.60 -> [43] ~before_on_line(skolem_L8989, skolem_A9090, skolem_B9191)
% 1.11/0.60 -> [44] ~before_on_line(skolem_L8989, skolem_B9191, skolem_C9292)
% 1.11/0.60
% 1.11/0.60 [44] Rewrite : ~before_on_line(skolem_L8989, skolem_B9191, skolem_C9292)
% 1.11/0.60 -> [54] ~(((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292)))
% 1.11/0.60
% 1.11/0.60 [54] BETA_NOT_AND : ~(((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090)))
% 1.11/0.60 -> [64] ~((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [65] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090))
% 1.11/0.60
% 1.11/0.60 [65] CLOSURE : ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090))
% 1.11/0.60
% 1.11/0.60 [64] BETA_NOT_AND : ~(((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292)))
% 1.11/0.60 -> [104] ~((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [105] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292))
% 1.11/0.60
% 1.11/0.60 [104] BETA_NOT_AND : ~((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [112] ~(distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [113] ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [113] CLOSURE : ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [112] BETA_NOT_AND : ~((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [126] ~(distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [127] ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [127] CLOSURE : ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [126] BETA_NOT_AND : ~(distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [134] ~distinct_points(skolem_B9191, skolem_A9090)
% 1.11/0.60 -> [135] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [135] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [134] CLOSURE : ~distinct_points(skolem_B9191, skolem_A9090)
% 1.11/0.60
% 1.11/0.60 [105] BETA_NOT_AND : ~((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [118] ~(distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [119] ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [119] CLOSURE : ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [118] BETA_NOT_AND : ~(distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [170] ~distinct_points(skolem_B9191, skolem_A9090)
% 1.11/0.60 -> [171] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [171] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [170] CLOSURE : ~distinct_points(skolem_B9191, skolem_A9090)
% 1.11/0.60
% 1.11/0.60 [43] Rewrite : ~before_on_line(skolem_L8989, skolem_A9090, skolem_B9191)
% 1.11/0.60 -> [55] ~(((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191)))
% 1.11/0.60
% 1.11/0.60 [55] BETA_NOT_AND : ~(((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090)))
% 1.11/0.60 -> [88] ~((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [89] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090))
% 1.11/0.60
% 1.11/0.60 [89] CLOSURE : ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090))
% 1.11/0.60
% 1.11/0.60 [88] BETA_NOT_AND : ~(((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191)))
% 1.11/0.60 -> [96] ~((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [97] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [96] BETA_NOT_AND : ~((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [154] ~(distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [155] ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [155] CLOSURE : ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [154] BETA_NOT_AND : ~((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [164] ~(distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [165] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [165] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [164] BETA_NOT_AND : ~(distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [168] ~distinct_points(skolem_B9191, skolem_A9090)
% 1.11/0.60 -> [169] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [168] CLOSURE : ~distinct_points(skolem_B9191, skolem_A9090)
% 1.11/0.60
% 1.11/0.60 [169] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [97] BETA_NOT_AND : ~((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [144] ~(distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [145] ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [145] CLOSURE : ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [144] BETA_NOT_AND : ~(distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [172] ~distinct_points(skolem_B9191, skolem_A9090)
% 1.11/0.60 -> [173] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [173] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [172] CLOSURE : ~distinct_points(skolem_B9191, skolem_A9090)
% 1.11/0.60
% 1.11/0.60 [8] ALPHA_AND : (before_on_line(skolem_L8989, skolem_A9090, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_C9292))
% 1.11/0.60 -> [10] before_on_line(skolem_L8989, skolem_A9090, skolem_B9191), before_on_line(skolem_L8989, skolem_B9191, skolem_C9292)
% 1.11/0.60
% 1.11/0.60 [10] Rewrite : before_on_line(skolem_L8989, skolem_A9090, skolem_B9191)
% 1.11/0.60 -> [12] (((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191)))
% 1.11/0.60
% 1.11/0.60 [12] Rewrite : before_on_line(skolem_L8989, skolem_B9191, skolem_C9292)
% 1.11/0.60 -> [14] (((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292)))
% 1.11/0.60
% 1.11/0.60 [14] ALPHA_AND : (((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191)))
% 1.11/0.60 -> [16] ((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)), equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [16] ALPHA_AND : (((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292)))
% 1.11/0.60 -> [18] ((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989)), equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292))
% 1.11/0.60
% 1.11/0.60 [18] ALPHA_AND : ((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [20] (distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)), incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [20] ALPHA_AND : ((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [22] (distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)), incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [22] ALPHA_AND : (distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [24] distinct_points(skolem_A9090, skolem_B9191), incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [24] ALPHA_AND : (distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [26] distinct_points(skolem_B9191, skolem_C9292), incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [26] BETA_NOT_AND : ~(before_on_line(skolem_L8989, skolem_C9292, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_A9090))
% 1.11/0.60 -> [28] ~before_on_line(skolem_L8989, skolem_C9292, skolem_B9191)
% 1.11/0.60 -> [29] ~before_on_line(skolem_L8989, skolem_B9191, skolem_A9090)
% 1.11/0.60
% 1.11/0.60 [28] Rewrite : ~before_on_line(skolem_L8989, skolem_C9292, skolem_B9191)
% 1.11/0.60 -> [32] ~(((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191)))
% 1.11/0.60
% 1.11/0.60 [32] BETA_NOT_AND : ~(before_on_line(skolem_L8989, skolem_A9090, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_C9292))
% 1.11/0.60 -> [34] ~before_on_line(skolem_L8989, skolem_A9090, skolem_B9191)
% 1.11/0.60 -> [35] ~before_on_line(skolem_L8989, skolem_B9191, skolem_C9292)
% 1.11/0.60
% 1.11/0.60 [34] Rewrite : ~before_on_line(skolem_L8989, skolem_A9090, skolem_B9191)
% 1.11/0.60 -> [42] ~(((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191)))
% 1.11/0.60
% 1.11/0.60 [42] BETA_NOT_AND : ~(((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191)))
% 1.11/0.60 -> [48] ~((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [49] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [49] BETA_NOT_AND : ~(((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191)))
% 1.11/0.60 -> [80] ~((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [81] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [81] CLOSURE : ~equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [80] BETA_NOT_AND : ~((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [152] ~(distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [153] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [153] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [152] BETA_NOT_AND : ~(distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [156] ~distinct_points(skolem_A9090, skolem_B9191)
% 1.11/0.60 -> [157] ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [157] CLOSURE : ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [156] CLOSURE : ~distinct_points(skolem_A9090, skolem_B9191)
% 1.11/0.60
% 1.11/0.60 [48] BETA_NOT_AND : ~(((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191)))
% 1.11/0.60 -> [60] ~((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [61] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [61] CLOSURE : ~equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [60] BETA_NOT_AND : ~((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [70] ~(distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [71] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [71] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [70] BETA_NOT_AND : ~((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [78] ~(distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [79] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [79] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [78] BETA_NOT_AND : ~(distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [98] ~distinct_points(skolem_C9292, skolem_B9191)
% 1.11/0.60 -> [99] ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [99] CLOSURE : ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [98] BETA_NOT_AND : ~(distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [142] ~distinct_points(skolem_A9090, skolem_B9191)
% 1.11/0.60 -> [143] ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [143] CLOSURE : ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [142] CLOSURE : ~distinct_points(skolem_A9090, skolem_B9191)
% 1.11/0.60
% 1.11/0.60 [35] Rewrite : ~before_on_line(skolem_L8989, skolem_B9191, skolem_C9292)
% 1.11/0.60 -> [45] ~(((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292)))
% 1.11/0.60
% 1.11/0.60 [45] BETA_NOT_AND : ~(((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191)))
% 1.11/0.60 -> [50] ~((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [51] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_C9292, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [50] BETA_NOT_AND : ~(((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292)))
% 1.11/0.60 -> [72] ~((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [73] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292))
% 1.11/0.60
% 1.11/0.60 [73] CLOSURE : ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292))
% 1.11/0.60
% 1.11/0.60 [72] BETA_NOT_AND : ~((distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [84] ~(distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [85] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [85] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [84] BETA_NOT_AND : ~((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [102] ~(distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [103] ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [103] CLOSURE : ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [102] BETA_NOT_AND : ~(distinct_points(skolem_C9292, skolem_B9191) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [110] ~distinct_points(skolem_C9292, skolem_B9191)
% 1.11/0.60 -> [111] ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [111] CLOSURE : ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [110] BETA_NOT_AND : ~(distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [158] ~distinct_points(skolem_B9191, skolem_C9292)
% 1.11/0.60 -> [159] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [159] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [158] CLOSURE : ~distinct_points(skolem_B9191, skolem_C9292)
% 1.11/0.60
% 1.11/0.60 [51] BETA_NOT_AND : ~(((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292)))
% 1.11/0.60 -> [100] ~((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [101] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292))
% 1.11/0.60
% 1.11/0.60 [101] CLOSURE : ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292))
% 1.11/0.60
% 1.11/0.60 [100] BETA_NOT_AND : ~((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.60 -> [138] ~(distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [139] ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [139] CLOSURE : ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [138] BETA_NOT_AND : ~(distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [174] ~distinct_points(skolem_B9191, skolem_C9292)
% 1.11/0.60 -> [175] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [174] CLOSURE : ~distinct_points(skolem_B9191, skolem_C9292)
% 1.11/0.60
% 1.11/0.60 [175] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [29] Rewrite : ~before_on_line(skolem_L8989, skolem_B9191, skolem_A9090)
% 1.11/0.60 -> [33] ~(((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090)))
% 1.11/0.60
% 1.11/0.60 [33] BETA_NOT_AND : ~(before_on_line(skolem_L8989, skolem_A9090, skolem_B9191) & before_on_line(skolem_L8989, skolem_B9191, skolem_C9292))
% 1.11/0.60 -> [37] ~before_on_line(skolem_L8989, skolem_A9090, skolem_B9191)
% 1.11/0.60 -> [38] ~before_on_line(skolem_L8989, skolem_B9191, skolem_C9292)
% 1.11/0.60
% 1.11/0.60 [37] Rewrite : ~before_on_line(skolem_L8989, skolem_A9090, skolem_B9191)
% 1.11/0.60 -> [46] ~(((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191)))
% 1.11/0.60
% 1.11/0.60 [46] BETA_NOT_AND : ~(((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090)))
% 1.11/0.60 -> [52] ~((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [53] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090))
% 1.11/0.60
% 1.11/0.60 [53] BETA_NOT_AND : ~(((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191)))
% 1.11/0.60 -> [76] ~((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [77] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [77] CLOSURE : ~equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191))
% 1.11/0.60
% 1.11/0.60 [76] BETA_NOT_AND : ~((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.60 -> [122] ~(distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [123] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [123] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.60
% 1.11/0.60 [122] BETA_NOT_AND : ~(distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.60 -> [130] ~distinct_points(skolem_A9090, skolem_B9191)
% 1.11/0.60 -> [131] ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [130] CLOSURE : ~distinct_points(skolem_A9090, skolem_B9191)
% 1.11/0.61
% 1.11/0.61 [131] CLOSURE : ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [52] BETA_NOT_AND : ~(((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191)))
% 1.11/0.61 -> [68] ~((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.61 -> [69] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191))
% 1.11/0.61
% 1.11/0.61 [69] CLOSURE : ~equally_directed_lines(skolem_L8989, line_connecting(skolem_A9090, skolem_B9191))
% 1.11/0.61
% 1.11/0.61 [68] BETA_NOT_AND : ~((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.61 -> [86] ~(distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.61 -> [87] ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [87] CLOSURE : ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [86] BETA_NOT_AND : ~((distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989)) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.61 -> [94] ~(distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.61 -> [95] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [95] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [94] BETA_NOT_AND : ~(distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.61 -> [116] ~distinct_points(skolem_B9191, skolem_A9090)
% 1.11/0.61 -> [117] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [117] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [116] BETA_NOT_AND : ~(distinct_points(skolem_A9090, skolem_B9191) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.61 -> [162] ~distinct_points(skolem_A9090, skolem_B9191)
% 1.11/0.61 -> [163] ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [162] CLOSURE : ~distinct_points(skolem_A9090, skolem_B9191)
% 1.11/0.61
% 1.11/0.61 [163] CLOSURE : ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [38] Rewrite : ~before_on_line(skolem_L8989, skolem_B9191, skolem_C9292)
% 1.11/0.61 -> [47] ~(((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292)))
% 1.11/0.61
% 1.11/0.61 [47] BETA_NOT_AND : ~(((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090)))
% 1.11/0.61 -> [57] ~((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.61 -> [58] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_A9090))
% 1.11/0.61
% 1.11/0.61 [58] BETA_NOT_AND : ~(((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292)))
% 1.11/0.61 -> [108] ~((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.61 -> [109] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292))
% 1.11/0.61
% 1.11/0.61 [109] CLOSURE : ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292))
% 1.11/0.61
% 1.11/0.61 [108] BETA_NOT_AND : ~((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.61 -> [146] ~(distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.61 -> [147] ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [147] CLOSURE : ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [146] BETA_NOT_AND : ~(distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.61 -> [176] ~distinct_points(skolem_B9191, skolem_C9292)
% 1.11/0.61 -> [177] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [176] CLOSURE : ~distinct_points(skolem_B9191, skolem_C9292)
% 1.11/0.61
% 1.11/0.61 [177] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [57] BETA_NOT_AND : ~(((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989)) & equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292)))
% 1.11/0.61 -> [92] ~((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.61 -> [93] ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292))
% 1.11/0.61
% 1.11/0.61 [93] CLOSURE : ~equally_directed_lines(skolem_L8989, line_connecting(skolem_B9191, skolem_C9292))
% 1.11/0.61
% 1.11/0.61 [92] BETA_NOT_AND : ~((distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_A9090, skolem_L8989))
% 1.11/0.61 -> [124] ~(distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.61 -> [125] ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [125] CLOSURE : ~incident_point_and_line(skolem_A9090, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [124] BETA_NOT_AND : ~((distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989)) & incident_point_and_line(skolem_C9292, skolem_L8989))
% 1.11/0.61 -> [132] ~(distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.61 -> [133] ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [133] CLOSURE : ~incident_point_and_line(skolem_C9292, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [132] BETA_NOT_AND : ~(distinct_points(skolem_B9191, skolem_A9090) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.61 -> [140] ~distinct_points(skolem_B9191, skolem_A9090)
% 1.11/0.61 -> [141] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [141] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [140] BETA_NOT_AND : ~(distinct_points(skolem_B9191, skolem_C9292) & incident_point_and_line(skolem_B9191, skolem_L8989))
% 1.11/0.61 -> [178] ~distinct_points(skolem_B9191, skolem_C9292)
% 1.11/0.61 -> [179] ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 [178] CLOSURE : ~distinct_points(skolem_B9191, skolem_C9292)
% 1.11/0.61
% 1.11/0.61 [179] CLOSURE : ~incident_point_and_line(skolem_B9191, skolem_L8989)
% 1.11/0.61
% 1.11/0.61 % SZS output end Proof for theBenchmark.p
% 1.11/0.61 [0.268657s][1][Res] 1029 goroutines created
% 1.11/0.61 ==== Result ====
% 1.11/0.61 [0.268700s][1][Res] VALID
% 1.11/0.61 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------