TSTP Solution File: GEO240+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO240+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n009.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 15:18:39 EDT 2022
% Result : Theorem 75.59s 27.69s
% Output : Proof 75.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO240+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : goeland -dmt -presko -proof %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 07:06:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.35 Conjecture not found
% 0.12/0.35 Start search
% 0.12/0.35 nb_step : 1 - limit : 37
% 0.12/0.35 Launch Gotab with destructive = true
% 75.59/27.68 % SZS output start Proof for theBenchmark.p
% 75.59/27.69 [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] : (((incident_point_and_line(A89_89, L91_91) & right_apart_point(B90_90, L91_91)) => right_convergent_lines(L91_91, line_connecting(A89_89, B90_90)))))
% 75.59/27.69 -> [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] : (((incident_point_and_line(A89_89, L91_91) & right_apart_point(B90_90, L91_91)) => right_convergent_lines(L91_91, line_connecting(A89_89, B90_90))))
% 75.59/27.69
% 75.59/27.69 [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)))))
% 75.59/27.69 -> [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))))
% 75.59/27.69
% 75.59/27.69 [2] DELTA_NOT_FORALL : ~! [A89_89, B90_90, L91_91] : (((incident_point_and_line(A89_89, L91_91) & right_apart_point(B90_90, L91_91)) => right_convergent_lines(L91_91, line_connecting(A89_89, B90_90))))
% 75.59/27.69 -> [3] ~((incident_point_and_line(skolem_A8989, skolem_L9191) & right_apart_point(skolem_B9090, skolem_L9191)) => right_convergent_lines(skolem_L9191, line_connecting(skolem_A8989, skolem_B9090)))
% 75.59/27.69
% 75.59/27.69 [3] ALPHA_NOT_IMPLY : ~((incident_point_and_line(skolem_A8989, skolem_L9191) & right_apart_point(skolem_B9090, skolem_L9191)) => right_convergent_lines(skolem_L9191, line_connecting(skolem_A8989, skolem_B9090)))
% 75.59/27.69 -> [4] (incident_point_and_line(skolem_A8989, skolem_L9191) & right_apart_point(skolem_B9090, skolem_L9191)), ~right_convergent_lines(skolem_L9191, line_connecting(skolem_A8989, skolem_B9090))
% 75.59/27.69
% 75.59/27.69 [4] ALPHA_AND : (incident_point_and_line(skolem_A8989, skolem_L9191) & right_apart_point(skolem_B9090, skolem_L9191))
% 75.59/27.69 -> [5] incident_point_and_line(skolem_A8989, skolem_L9191), right_apart_point(skolem_B9090, skolem_L9191)
% 75.59/27.69
% 75.59/27.69 [5] GAMMA_FORALL : ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9))))
% 75.59/27.69 -> [6] (unequally_directed_opposite_lines(reverse_line(Y17_4_4), Y17_4_4) <=> unequally_directed_lines(reverse_line(Y17_4_4), reverse_line(Y17_4_4)))
% 75.59/27.69
% 75.59/27.69 [6] BETA_EQUIV : (unequally_directed_opposite_lines(reverse_line(Y17_4_4), Y17_4_4) <=> unequally_directed_lines(reverse_line(Y17_4_4), reverse_line(Y17_4_4)))
% 75.59/27.69 -> [7] ~unequally_directed_opposite_lines(reverse_line(Y17_4_4), Y17_4_4), ~unequally_directed_lines(reverse_line(Y17_4_4), reverse_line(Y17_4_4))
% 75.59/27.69 -> [8] unequally_directed_opposite_lines(reverse_line(Y17_4_4), Y17_4_4), unequally_directed_lines(reverse_line(Y17_4_4), reverse_line(Y17_4_4))
% 75.59/27.69
% 75.59/27.69 [8] GAMMA_FORALL : ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11))))
% 75.59/27.69 -> [10] (right_apart_point(skolem_B9090, skolem_L9191) <=> left_apart_point(skolem_B9090, reverse_line(skolem_L9191)))
% 75.59/27.69
% 75.59/27.69 [10] BETA_EQUIV : (right_apart_point(skolem_B9090, skolem_L9191) <=> left_apart_point(skolem_B9090, reverse_line(skolem_L9191)))
% 75.59/27.69 -> [13] ~right_apart_point(skolem_B9090, skolem_L9191), ~left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 75.59/27.69 -> [14] right_apart_point(skolem_B9090, skolem_L9191), left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 75.59/27.69
% 75.59/27.69 [13] CLOSURE : ~right_apart_point(skolem_B9090, skolem_L9191)
% 75.59/27.69
% 75.59/27.69 [16] BETA_EQUIV : (right_convergent_lines(skolem_L9191, line_connecting(skolem_A8989, skolem_B9090)) <=> left_convergent_lines(skolem_L9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090))))
% 75.59/27.69 -> [227] ~right_convergent_lines(skolem_L9191, line_connecting(skolem_A8989, skolem_B9090)), ~left_convergent_lines(skolem_L9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090)))
% 75.59/27.69 -> [228] right_convergent_lines(skolem_L9191, line_connecting(skolem_A8989, skolem_B9090)), left_convergent_lines(skolem_L9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090)))
% 75.59/27.69
% 75.59/27.69 [228] CLOSURE : right_convergent_lines(skolem_L9191, line_connecting(skolem_A8989, skolem_B9090))
% 75.59/27.69
% 75.59/27.69 [229] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_4_4), reverse_line(Y17_4_4)) <=> ~unequally_directed_lines(reverse_line(Y17_4_4), reverse_line(Y17_4_4)))
% 75.59/27.69 -> [351] ~equally_directed_lines(reverse_line(Y17_4_4), reverse_line(Y17_4_4)), ~~unequally_directed_lines(reverse_line(Y17_4_4), reverse_line(Y17_4_4))
% 75.59/27.69 -> [352] equally_directed_lines(reverse_line(Y17_4_4), reverse_line(Y17_4_4)), ~unequally_directed_lines(reverse_line(Y17_4_4), reverse_line(Y17_4_4))
% 75.59/27.69
% 75.59/27.69 [352] CLOSURE : ~unequally_directed_lines(reverse_line(Y17_4_4), reverse_line(Y17_4_4))
% 75.59/27.69
% 75.59/27.69 [354] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_4_4), Y17_4_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_4_4), Y17_4_4))
% 75.59/27.69 -> [388] ~equally_directed_opposite_lines(reverse_line(Y17_4_4), Y17_4_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_4_4), Y17_4_4)
% 75.59/27.69 -> [389] equally_directed_opposite_lines(reverse_line(Y17_4_4), Y17_4_4), ~unequally_directed_opposite_lines(reverse_line(Y17_4_4), Y17_4_4)
% 75.59/27.69
% 75.59/27.69 [389] CLOSURE : ~unequally_directed_opposite_lines(reverse_line(Y17_4_4), Y17_4_4)
% 75.59/27.69
% 75.59/27.69 [392] BETA_IMPLY : (distinct_points(C35_7_6, C35_7_6) => (distinct_points(C35_7_6, C35_7_6) | distinct_points(C35_7_6, C35_7_6)))
% 75.59/27.69 -> [429] ~distinct_points(C35_7_6, C35_7_6)
% 75.59/27.69 -> [430] (distinct_points(C35_7_6, C35_7_6) | distinct_points(C35_7_6, C35_7_6))
% 75.59/27.69
% 75.59/27.69 [430] BETA_OR : (distinct_points(C35_7_6, C35_7_6) | distinct_points(C35_7_6, C35_7_6))
% 75.59/27.69 -> [437] distinct_points(C35_7_6, C35_7_6)
% 75.59/27.69 -> [438] distinct_points(C35_7_6, C35_7_6)
% 75.59/27.69
% 75.59/27.69 [437] CLOSURE : distinct_points(C35_7_6, C35_7_6)
% 75.59/27.69
% 75.59/27.69 [438] CLOSURE : distinct_points(C35_7_6, C35_7_6)
% 75.59/27.69
% 75.59/27.69 [440] BETA_IMPLY : (distinct_lines(N39_10_8, N39_10_8) => (distinct_lines(N39_10_8, N39_10_8) | distinct_lines(N39_10_8, N39_10_8)))
% 75.59/27.69 -> [450] ~distinct_lines(N39_10_8, N39_10_8)
% 75.59/27.69 -> [451] (distinct_lines(N39_10_8, N39_10_8) | distinct_lines(N39_10_8, N39_10_8))
% 75.59/27.69
% 75.59/27.69 [450] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 75.59/27.69 -> [454] equally_directed_lines(L40_20_9, L40_20_9)
% 75.59/27.69
% 75.59/27.69 [454] CLOSURE : equally_directed_lines(L40_20_9, L40_20_9)
% 75.59/27.69
% 75.59/27.69 [451] BETA_OR : (distinct_lines(N39_10_8, N39_10_8) | distinct_lines(N39_10_8, N39_10_8))
% 75.59/27.69 -> [457] distinct_lines(N39_10_8, N39_10_8)
% 75.59/27.69 -> [458] distinct_lines(N39_10_8, N39_10_8)
% 75.59/27.69
% 75.59/27.69 [458] CLOSURE : distinct_lines(N39_10_8, N39_10_8)
% 75.59/27.69
% 75.59/27.69 [457] CLOSURE : distinct_lines(N39_10_8, N39_10_8)
% 75.59/27.69
% 75.59/27.69 [9] BETA_EQUIV : (right_apart_point(skolem_B9090, skolem_L9191) <=> left_apart_point(skolem_B9090, reverse_line(skolem_L9191)))
% 75.59/27.69 -> [2741] ~right_apart_point(skolem_B9090, skolem_L9191), ~left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 75.59/27.69 -> [2742] right_apart_point(skolem_B9090, skolem_L9191), left_apart_point(skolem_B9090, reverse_line(skolem_L9191))
% 75.59/27.69
% 75.59/27.69 [2741] CLOSURE : ~right_apart_point(skolem_B9090, skolem_L9191)
% 75.59/27.69
% 75.59/27.69 [2742] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 75.59/27.69 -> [2743] (right_convergent_lines(skolem_L9191, line_connecting(skolem_A8989, skolem_B9090)) <=> left_convergent_lines(skolem_L9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090))))
% 75.59/27.69
% 75.59/27.69 [2743] BETA_EQUIV : (right_convergent_lines(skolem_L9191, line_connecting(skolem_A8989, skolem_B9090)) <=> left_convergent_lines(skolem_L9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090))))
% 75.59/27.69 -> [2744] ~right_convergent_lines(skolem_L9191, line_connecting(skolem_A8989, skolem_B9090)), ~left_convergent_lines(skolem_L9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090)))
% 75.59/27.69 -> [2745] right_convergent_lines(skolem_L9191, line_connecting(skolem_A8989, skolem_B9090)), left_convergent_lines(skolem_L9191, reverse_line(line_connecting(skolem_A8989, skolem_B9090)))
% 75.59/27.69
% 75.59/27.69 [2745] CLOSURE : right_convergent_lines(skolem_L9191, line_connecting(skolem_A8989, skolem_B9090))
% 75.59/27.69
% 75.59/27.69 [2746] BETA_EQUIV : (equally_directed_lines(reverse_line(Y17_10_4), reverse_line(Y17_10_4)) <=> ~unequally_directed_lines(reverse_line(Y17_10_4), reverse_line(Y17_10_4)))
% 75.59/27.69 -> [3689] ~equally_directed_lines(reverse_line(Y17_10_4), reverse_line(Y17_10_4)), ~~unequally_directed_lines(reverse_line(Y17_10_4), reverse_line(Y17_10_4))
% 75.59/27.69 -> [3690] equally_directed_lines(reverse_line(Y17_10_4), reverse_line(Y17_10_4)), ~unequally_directed_lines(reverse_line(Y17_10_4), reverse_line(Y17_10_4))
% 75.59/27.69
% 75.59/27.69 [3689] ALPHA_NOT_NOT : ~~unequally_directed_lines(reverse_line(Y17_10_4), reverse_line(Y17_10_4))
% 75.59/27.69 -> [3691] unequally_directed_lines(reverse_line(Y17_10_4), reverse_line(Y17_10_4))
% 75.59/27.69
% 75.59/27.69 [3691] CLOSURE : unequally_directed_lines(reverse_line(Y17_10_4), reverse_line(Y17_10_4))
% 75.59/27.69
% 75.59/27.69 [3692] BETA_EQUIV : (equally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4) <=> ~unequally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4))
% 75.59/27.69 -> [4027] ~equally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4), ~~unequally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4)
% 75.59/27.69 -> [4028] equally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4), ~unequally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4)
% 75.59/27.69
% 75.59/27.69 [4027] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4)
% 75.59/27.69 -> [4029] unequally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4)
% 75.59/27.69
% 75.59/27.69 [4029] CLOSURE : unequally_directed_opposite_lines(reverse_line(Y17_10_4), Y17_10_4)
% 75.59/27.69
% 75.59/27.69 [4028] GAMMA_FORALL : ! [A32_32] : (~distinct_points(A32_32, A32_32))
% 75.59/27.69 -> [4030] ~distinct_points(C35_17_6, C35_17_6)
% 75.59/27.69
% 75.59/27.69 [4030] 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))))
% 75.59/27.69 -> [4031] (distinct_points(C35_17_6, C35_17_6) => (distinct_points(C35_17_6, C35_17_6) | distinct_points(C35_17_6, C35_17_6)))
% 75.59/27.69
% 75.59/27.69 [4031] BETA_IMPLY : (distinct_points(C35_17_6, C35_17_6) => (distinct_points(C35_17_6, C35_17_6) | distinct_points(C35_17_6, C35_17_6)))
% 75.59/27.69 -> [4032] ~distinct_points(C35_17_6, C35_17_6)
% 75.59/27.69 -> [4033] (distinct_points(C35_17_6, C35_17_6) | distinct_points(C35_17_6, C35_17_6))
% 75.59/27.69
% 75.59/27.69 [4033] BETA_OR : (distinct_points(C35_17_6, C35_17_6) | distinct_points(C35_17_6, C35_17_6))
% 75.59/27.69 -> [4034] distinct_points(C35_17_6, C35_17_6)
% 75.59/27.69 -> [4035] distinct_points(C35_17_6, C35_17_6)
% 75.59/27.69
% 75.59/27.69 [4034] CLOSURE : distinct_points(C35_17_6, C35_17_6)
% 75.59/27.69
% 75.59/27.69 [4035] CLOSURE : distinct_points(C35_17_6, C35_17_6)
% 75.59/27.69
% 75.59/27.69 [4032] GAMMA_FORALL : ! [L36_36] : (~distinct_lines(L36_36, L36_36))
% 75.59/27.69 -> [4036] ~distinct_lines(N39_27_8, N39_27_8)
% 75.59/27.69
% 75.59/27.69 [4036] 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))))
% 75.59/27.69 -> [4037] (distinct_lines(N39_27_8, N39_27_8) => (distinct_lines(N39_27_8, N39_27_8) | distinct_lines(N39_27_8, N39_27_8)))
% 75.59/27.69
% 75.59/27.69 [4037] BETA_IMPLY : (distinct_lines(N39_27_8, N39_27_8) => (distinct_lines(N39_27_8, N39_27_8) | distinct_lines(N39_27_8, N39_27_8)))
% 75.59/27.69 -> [4038] ~distinct_lines(N39_27_8, N39_27_8)
% 75.59/27.69 -> [4039] (distinct_lines(N39_27_8, N39_27_8) | distinct_lines(N39_27_8, N39_27_8))
% 75.59/27.69
% 75.59/27.69 [4039] BETA_OR : (distinct_lines(N39_27_8, N39_27_8) | distinct_lines(N39_27_8, N39_27_8))
% 75.59/27.69 -> [4040] distinct_lines(N39_27_8, N39_27_8)
% 75.59/27.69 -> [4041] distinct_lines(N39_27_8, N39_27_8)
% 75.59/27.69
% 75.59/27.69 [4040] CLOSURE : distinct_lines(N39_27_8, N39_27_8)
% 75.59/27.69
% 75.59/27.69 [4041] CLOSURE : distinct_lines(N39_27_8, N39_27_8)
% 75.59/27.69
% 75.59/27.69 [4038] GAMMA_FORALL : ! [L40_40] : (equally_directed_lines(L40_40, L40_40))
% 75.59/27.69 -> [4042] equally_directed_lines(L40_48_9, L40_48_9)
% 75.59/27.69
% 75.59/27.69 [4042] 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))))
% 75.59/27.69 -> [4043] (unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) => (unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) | unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))))
% 75.59/27.69
% 75.59/27.69 [4043] BETA_IMPLY : (unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) => (unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) | unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))))
% 75.59/27.69 -> [4044] ~unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69 -> [4045] (unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) | unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)))
% 75.59/27.69
% 75.59/27.69 [4045] BETA_OR : (unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) | unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)))
% 75.59/27.69 -> [4046] unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69 -> [4047] unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69
% 75.59/27.69 [4047] CLOSURE : unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69
% 75.59/27.69 [4046] CLOSURE : unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69
% 75.59/27.69 [4048] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11)))) => ((unequally_directed_lines(reverse_line(N46_64_11), N46_64_11) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))) | (unequally_directed_lines(reverse_line(N46_64_11), N46_64_11) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)))))
% 75.59/27.69 -> [4071] ~(unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11))))
% 75.59/27.69 -> [4072] ((unequally_directed_lines(reverse_line(N46_64_11), N46_64_11) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))) | (unequally_directed_lines(reverse_line(N46_64_11), N46_64_11) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))))
% 75.59/27.69
% 75.59/27.69 [4072] BETA_OR : ((unequally_directed_lines(reverse_line(N46_64_11), N46_64_11) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))) | (unequally_directed_lines(reverse_line(N46_64_11), N46_64_11) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))))
% 75.59/27.69 -> [4075] (unequally_directed_lines(reverse_line(N46_64_11), N46_64_11) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)))
% 75.59/27.69 -> [4076] (unequally_directed_lines(reverse_line(N46_64_11), N46_64_11) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)))
% 75.59/27.69
% 75.59/27.69 [4075] ALPHA_AND : (unequally_directed_lines(reverse_line(N46_64_11), N46_64_11) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)))
% 75.59/27.69 -> [4077] unequally_directed_lines(reverse_line(N46_64_11), N46_64_11), unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69
% 75.59/27.69 [4077] CLOSURE : unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69
% 75.59/27.69 [4078] CLOSURE : unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69
% 75.59/27.69 [4071] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11))))
% 75.59/27.69 -> [4104] ~unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69 -> [4105] ~unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11)))
% 75.59/27.69
% 75.59/27.69 [4105] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 75.59/27.69 -> [4107] (unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) | unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11))))
% 75.59/27.69
% 75.59/27.69 [4107] BETA_OR : (unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) | unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11))))
% 75.59/27.69 -> [4110] unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69 -> [4111] unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11)))
% 75.59/27.69
% 75.59/27.69 [4110] CLOSURE : unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69
% 75.59/27.69 [4111] CLOSURE : unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11)))
% 75.59/27.69
% 75.59/27.69 [4104] GAMMA_FORALL : ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48))))
% 75.59/27.69 -> [4106] (unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) | unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11))))
% 75.59/27.69
% 75.59/27.69 [4106] BETA_OR : (unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) | unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11))))
% 75.59/27.69 -> [4108] unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69 -> [4109] unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11)))
% 75.59/27.69
% 75.59/27.69 [4108] CLOSURE : unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69
% 75.59/27.69 [4109] 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)))))
% 75.59/27.69 -> [4112] ((unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11)))) => (left_convergent_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) | left_convergent_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11)))))
% 75.59/27.69
% 75.59/27.69 [4112] BETA_IMPLY : ((unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11)))) => (left_convergent_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) | left_convergent_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11)))))
% 75.59/27.69 -> [4113] ~(unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11))))
% 75.59/27.69 -> [4114] (left_convergent_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) | left_convergent_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11))))
% 75.59/27.69
% 75.59/27.69 [4113] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) & unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11))))
% 75.59/27.69 -> [4115] ~unequally_directed_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69 -> [4116] ~unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11)))
% 75.59/27.69
% 75.59/27.69 [4116] CLOSURE : ~unequally_directed_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11)))
% 75.59/27.69
% 75.59/27.69 [4115] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 75.59/27.69 -> [4119] ~(left_apart_point(A51_182_14, L52_182_14) | left_apart_point(A51_182_14, reverse_line(L52_182_14)))
% 75.59/27.69
% 75.59/27.69 [4119] ALPHA_NOT_OR : ~(left_apart_point(A51_182_14, L52_182_14) | left_apart_point(A51_182_14, reverse_line(L52_182_14)))
% 75.59/27.69 -> [4121] ~left_apart_point(A51_182_14, L52_182_14), ~left_apart_point(A51_182_14, reverse_line(L52_182_14))
% 75.59/27.69
% 75.59/27.69 [4121] CLOSURE : ~left_apart_point(A51_182_14, L52_182_14)
% 75.59/27.69
% 75.59/27.69 [4114] BETA_OR : (left_convergent_lines(reverse_line(N46_64_11), reverse_line(N46_64_11)) | left_convergent_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11))))
% 75.59/27.69 -> [4123] left_convergent_lines(reverse_line(N46_64_11), reverse_line(N46_64_11))
% 75.59/27.69 -> [4124] left_convergent_lines(reverse_line(N46_64_11), reverse_line(reverse_line(N46_64_11)))
% 75.59/27.69
% 75.59/27.69 [4123] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 75.59/27.69 -> [4125] ~(left_apart_point(A51_184_14, L52_184_14) | left_apart_point(A51_184_14, reverse_line(L52_184_14)))
% 75.59/27.69
% 75.59/27.69 [4125] ALPHA_NOT_OR : ~(left_apart_point(A51_184_14, L52_184_14) | left_apart_point(A51_184_14, reverse_line(L52_184_14)))
% 75.59/27.69 -> [4127] ~left_apart_point(A51_184_14, L52_184_14), ~left_apart_point(A51_184_14, reverse_line(L52_184_14))
% 75.59/27.69
% 75.59/27.69 [4127] CLOSURE : ~left_apart_point(A51_184_14, L52_184_14)
% 75.59/27.69
% 75.59/27.69 [4124] GAMMA_FORALL : ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52))))
% 75.59/27.69 -> [4126] ~(left_apart_point(A51_185_14, L52_185_14) | left_apart_point(A51_185_14, reverse_line(L52_185_14)))
% 75.59/27.69
% 75.59/27.69 [4126] ALPHA_NOT_OR : ~(left_apart_point(A51_185_14, L52_185_14) | left_apart_point(A51_185_14, reverse_line(L52_185_14)))
% 75.59/27.69 -> [4128] ~left_apart_point(A51_185_14, L52_185_14), ~left_apart_point(A51_185_14, reverse_line(L52_185_14))
% 75.59/27.69
% 75.59/27.69 [4128] CLOSURE : ~left_apart_point(A51_185_14, L52_185_14)
% 75.59/27.69
% 75.59/27.69 % SZS output end Proof for theBenchmark.p
% 75.59/27.69 [27.340700s][1][Res] 171187 goroutines created
% 75.59/27.69 ==== Result ====
% 75.59/27.69 [27.340740s][1][Res] VALID
% 75.59/27.69 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------